Sabah Sabah Shawkat Sabah Shawkat Sabah Shawkat Shawkat
Sabah Shawkat
STRUCTURES STRUCTURES STRUCTURES STRUCTURES
LIGHTWEIGHT STEEL STRUCTURES
STEEL STEEL STEEL STEEL LIGHTWEIGHT LIGHTWEIGHT LIGHTWEIGHT LIGHTWEIGHT
LIGHTWEIGHT LIGHTWEIGHT LIGHTWEIGHT LIGHTWEIGHT LIGHTWEIGHT STEEL STEEL STEEL STEEL STEEL STRUCTURES STRUCTURES STRUCTURES STRUCTURES STRUCTURES
Sabah Shawkat © Sabah Sabah Sabah Sabah Sabah Shawkat Shawkat Shawkat Shawkat Shawkat
Reviewer: Cover Design: Editor: Software Support: Publisher:
Prof. Dipl. Ing. Ján Hudák, PhD. Ing. Peter Novysedlák, PhD, M.Eng. Mgr. art. Peter Nosáľ prof. Ing. arch. Zuzana Pešková, PhD, Mgr.art. Ing. Richard Schlesinger, PhD. asc. Applied Software Consultants, s.r.o., Bratislava, Slovakia Tribun EU, s.r.o., Brno, Czech Republic
Sabah Shawkat © All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, including photocopying, without permission in writing from the author.
Lightweight Steel Structures ©
Assoc. Prof. Dipl. Ing. Sabah Shawkat, MSc, PhD. 1. Edition, Tribun EU, s.r.o. Brno, Czech republic 2019 ISBN 978-80-263-1458-5
Definitions
Connections in steel structures Bolt connections Welded connections Splices Slip resistance Calculate the tension resistance of the joint Bearing resistance of splice plates Shear resistance of bolts Resistant the welds Calculate the resistance of the shear joint Shear resistance of bolts Resistance of welds Calculate the bending resistance of the flange plate joint Calculate the bending resistance of the splice with end-plates Rotation capacity of the splice Design the joint Column Bracket Detail of attachment - Steel Beam to Steel Column Beam-to-column joint Resistance of the joint
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Sabah Shawkat ©
132 132
Connections in steel structures Connections in steel structures
condition at steel beam supports. contrast element may fixed in its plane to transmit be be fixed in its plane to transmit condition at steel beam supports. ByBy contrast thethe element may bending allow rotation about axis. Note if pinned fixed joints made between bending butbut allow rotation about its its axis. Note thatthat if pinned or or fixed joints areare made between
Joints between structural elements, in one plane, may classified simple connections, Joints between structural lineline elements, in one plane, may be be classified as as simple connections,
element immovable support then of the element may move translationally an an element andand an an immovable support then thatthat endend of the element may notnot move translationally
sliding connections, pinned connections fixed connections, also known rigid as as sliding connections, as as pinpin or or pinned connections as as fixed connections, also known as as rigid
rotate in space, distinct from a movement which is merely relative to the member or or rotate in space, as as distinct from a movement which is merely relative to the member on on thethe
connections. simple connection allows rotation movement direction except connections. AA simple connection allows rotation andand movement in in anyany direction except
other side joint. Fixed joints, nearly fixed joints, between members said other side of of thethe joint. Fixed joints, or or nearly fixed joints, between twotwo members areare said to to
downwards only transmits shear force downwards a support. sliding downwards andand only transmits shear force thatthat actsacts downwards at at a support. AA sliding
provide continuity there is little or no rotation between members at the joint provide continuity so so thatthat there is little or no rotation between thethe members at the joint andand thethe
connection allows movement along of the element rotation only transmits shear connection allows movement along thethe lineline of the element andand rotation andand only transmits shear
members behave as no if no joint existed. However, joint is not necessarily fixed in space members behave as if joint existed. However, thethe joint is not necessarily fixed in space andand
force. A pinned connection allows rotation translational movement, it transmits shear force. A pinned connection allows rotation butbut no no translational movement, it transmits shear
may rotate about a support example. A way of characterising degree of fixity or stiffness may rotate about a support forfor example. A way of characterising thethe degree of fixity or stiffness
axial forces bending moment. fixed connection does allow translational andand axial forces butbut notnot bending moment. AA fixed connection does notnot allow translational
provided a semi-rigid connection either a support another member is to measure provided by by a semi-rigid connection either to to a support or or another member is to measure thethe
movement or rotation transmits shear, axial forces, bending torsional moment. movement or rotation andand transmits shear, axial forces, bending andand torsional moment.
rotation at the joint as the bending moment joint is varied. rotation at the joint as the bending moment on on thethe joint is varied. Figure bellow defines strength, stiffness deformation capacity a beam-to-column Figure bellow defines thethe strength, stiffness andand deformation capacity of of a beam-to-column connection designed to transfer a moment from beam column. M-φ curves in general M-φ curves in general connection designed to transfer a moment from thethe beam intointo thethe column. non-linear, practical application, it necessary is necessary idealise M-φcurves. curves. rotation non-linear, forfor practical application, it is to to idealise thethe M-φ TheThe rotation capacity a measure deformation obtained before failure somewhere in the capacity is aismeasure of of thethe deformation thatthat cancan be be obtained before failure somewhere in the
Sabah Shawkat © connection causes a drop in the moment resistance. connection causes a drop in the moment resistance.
strength, following classes distinguished: ForFor strength, thethe following classes cancan be be distinguished:
M≤Rd0,25 ≤ 0,25 Mpl.Rd MRd Mpl.Rd
nominally pinned nominally pinned partial-strength partial-strength
0,25 Mpl.Rd < Rd M< < pl.Rd Mpl.Rd 0,25 Mpl.Rd <M RdM
full-strength full-strength
M≥RdM ≥ pl.Rd Mpl.Rd MRd
full-strength if rotation capacity full-strength if rotation capacity is is
≥ 1,2 Mpl.Rd M≥Rd1,2 Mpl.Rd MRd
checked notnot checked where where MRd MRd
is the design moment resistance of the connection is the design moment resistance of the connection
Mpl.Rd Mpl.Rd
is the design strength of the beam (full plastic moment). is the design strength of the beam (full plastic moment).
Column web in shear, compression tension Column web in shear, compression andand tension practice is often difficult to fabricate fixed connections some rotation may take place In In practice it isit often difficult to fabricate fixed connections andand some rotation may take place between element side joint other. Such a joint is known between thethe element on on oneone side of of thethe joint andand thatthat on on thethe other. Such a joint is known as as a a semi-rigid connection and, strictly speaking is the condition of most joints which described semi-rigid connection and, strictly speaking is the condition of most joints which areare described being fixed rigid. A moment connection could described which although only as as being fixed or or rigid. A moment connection could be be described as as oneone which although only semi-rigid approaches behaviour a fixed connection transfers a substantial bending semi-rigid approaches thethe behaviour of of a fixed connection andand transfers a substantial bending moment. Note connections may fabricated particular requirements that, moment. Note thatthat connections may be be fabricated forfor particular requirements so so that, forfor example, they may allow rotation plane elements prevent twisting about example, they may allow rotation in in thethe plane of of thethe elements butbut prevent twisting about thethe axis element thus allowing torsional moments transmitted. This a common axis of of thethe element thus allowing torsional moments to to be be transmitted. This is ais common
Moment-rotation characteristic a semi-rigid joint with enough plastic rotation capacity Moment-rotation characteristic of aofsemi-rigid joint with enough plastic rotation capacity stiffness, classification is follows: as follows: ForFor stiffness, thethe classification is as
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
133
Sj ≤ 0,5 EIb/Lb
nominally pinned semi-rigid
be a design requirement in certain instances, e.g. when plastic design is employed with plastic
0,5 EIb/Lb < Sj < 8 EIb/Lb (braced frames) or 25 EIb/Lb
(unbraced frames) rigid
Sj ≥ 8 EIb/Lb (braced frames)
or
Sj ≥ 25 EIb/Lb (unbraced frames)
EIb Lb
The Moment is equal to the stiffness of the member times the modulus of elasticity times the curvature. where curvature is given by,
where Sj
hinges forming in the connections.
is the (secant) rotational stiffness of the connection is the bending stiffness of the beam
1
M
EI
Now, the moment is also equal to the load applied times the deflection at the centre of the
is the span of the beam
column due to buckling, which is the acting moment, For the determination of the forces on the connection, a static analysis must be carried out. Such
2
d y
analysis includes the determination of the design loads and the modelling of the structure. In
1
the schematization of the structure, the stiffness of the connections is an important element.
1
M
Connections can be assumed rigid, as hinges or as having a stiffness between these two. The
EI
deformation capacity of the members (beams and columns) and of the connections plays an
2
dx
1
3
2 dy dx 2
important role in the ultimate distribution of forces in the structure. All parts of the structure
Thus when you equate the acting and the reacting, that is the work done by the load and the
must be designed so that they can resist the calculated forces and have a deformation capacity
strain energy stored in the member and solve it you will get the Euler's formula which can be
that is consistent with the assumptions made in the global analysis.
written as below.
Sabah Shawkat ©
The stiffness of the connection affects the level of loading for which it should be designed. A
M
F a
2
F
connection of low rotational stiffness does not attract major bending moments and therefore
non-braced frames the stiffness of the connections may have a major effect on the deflections
2
L
may be assumed as a pinned connection in the schematization of the structure.
Of course, the stiffness of the connections affects the deflections of the beams. Especially in
2
n EI
Here n defines the mode shape of the column. Mode shape is the shape of the deformed structure. You will also find that the minimum value of F is when n =1.
of the structure as a whole and on its stability. If the connections are assumed rigid in the modelling for the static analysis of the structure, then consequently the form of the connections should be such that their deformations have a negligible influence on the load distribution and the deformations of the structure.
Connections may be bolted, riveted or welded. The principal design considerations are shear, tension and compression, and the calculations are relatively straightforward for the types of design covered.
On the other hand, if pinned connections are assumed, they should have sufficient flexibility to accommodate rotations without causing significant bending moments that may lead to premature failure of (parts of) the connection or connected members. The requirements for strength and stiffness are clear. They result from the static calculation. The requirement for deformation capacity is more qualitative. In practice it is sometimes difficult to check this requirement. Ductile connections that have a great deformation capacity contribute to the overall safety of the structure in the event that the connection becomes overloaded. Such connections may also
Connections in steel structures Connections in steel structures
134 132
Connections in steel structures
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints between structural line elements, in one plane, may be classified as simple connections,
an element and an immovable support then that end of the element may not move translationally
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid
or rotate in space, as distinct from a movement which is merely relative to the member on the
connections. A simple connection allows rotation and movement in any direction except
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
downwards and only transmits shear force that acts downwards at a support. A sliding
provide continuity so that there is little or no rotation between the members at the joint and the
connection allows movement along the line of the element and rotation and only transmits shear
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A pinned connection allows rotation but no translational movement, it transmits shear
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
and axial forces but not bending moment. A fixed connection does not allow translational
provided by a semi-rigid connection either to a support or another member is to measure the
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied. Distinction between joint and connection Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column
Joints in portal frames
distinction between a joint from and athe connection shown in figure above ainconnection M-φ curves general connectionThe designed to transfer a moment beam intoisthe column.
Diagonal bracing is used to make framed walls and structures stiff. Long braces should
means a location at which two members are interconnected furthermore, therotation means of non-linear, for practical application, it is necessary to idealise and, the M-φ curves. The
preferably transfer the load with a tensile stress to avoid buckling.
interconnection (bolted connection). joint failure is as ansomewhere assembly in of the basic capacity is a measure of theconnection, deformationwelded that can be obtainedAbefore
Sabah Shawkat ©
components (e.g.a drop bolt, in end-plate, stiffeners) that enables members to be connected together in connection causes the moment resistance. a waythe thatfollowing the relevant internal forces and moments can be transferred between them. Forsuch strength, classes can be distinguished: nominally pinned MRd ≤ 0,25 Mpl.Rd Bolt connections partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd Connections should be designed to transferM moments and/or shear forces and/or normal forces. full-strength Rd ≥ Mpl.Rd The next step in the capacity analysis is is to determine the distribution of forces within the connection, full-strength if rotation see figure below. It is not necessary andMoften not feasible to determine the real internal not checked Rd ≥ 1,2 Mpl.Rd distribution of forces. It is sufficient to assume a realistic distribution, provided that: where forcesmoment are in equilibrium with applied loading MRd 1. the internal is the design resistance of thethe connection
capableofofthe resisting the forces Mpl.Rd 2. each iscomponent the designisstrength beam (full plastic moment). 3. the deformations implied by the assumed distribution are within the deformation Column web in shear, compression and tension
capacity of the fasteners (bolts, welds) and of the connected parts.
In practice it is often difficult to fabricate fixed connections and some rotation may take place
Design forces can be assumed distributed according to the theory of elasticity, or according to
between the element on one side of the joint and that on the other. Such a joint is known as a
the theory of plasticity. The elastic distribution may always be used. Then the distribution of
semi-rigid connection and, strictly speaking is the condition of most joints which are described
the forces is proportional to the distance from the centre of rotation. The elastic distribution has
as being fixed or rigid. A moment connection could be described as one which although only
to be used, Slip-resistant connection at ultimate limit state, and in the case of those shear
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending Joints in portal frames moment. Note that connections may be fabricated for particular requirements so that, for Braces are usually supplied in pairs, i.e. on both diagonals, so that one will always be in tension example, they may rotation in the plane of the elements but prevent twisting about the independently of allow the wind direction. axis of the element thus allowing torsional moments to be transmitted. This is a common
connections where the design shear resistance of the bolts is less than the bearing resistance (i.e. FvRd < FbRd). In other cases, the plastic distribution of internal forces may be used. Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
135
If the distance between the outermost bolts of a connection in the direction of the force is more than 15d (d being the nominal diameter), the shear resistance of the bolts shall be reduced by multiplying it by the following factor.
1
Lf
Lj 15d 200d
0.75 Lf 1.0
but
The bearing resistance shall be calculated as follows: 2.5
FbRd
fu
dt
Mb
e1
min
3 do
t
is the thickness of the relevant part
fu
is the ultimate tensile strength of the relevant part.
1 fub 1.0 4 fu
Distribution of forces between bolts
Sabah Shawkat ©
Shear resistant of the bolt shall be calculated as follows:
Bearing resistance FbRd (kN) per bolt for t = 10mm
FvRd
FvRd
fub
0.6
0.5
fub
Mb fub
Mb
As
for 8.8 grade
As
Distance
for 10.9 grade
Mb
is the partial safety factor 1,25
If the shear plane passes through the unthreaded shank of the bolt, the shear resistant of the bolt shall be calculated as follows:
fub
M20
M24
18
22
26
M30 33
minim.
rec.
minim.
rec.
minim.
rec.
minim.
rec.
minim.
rec.
e1 mm
16
30
22
40
27
50
32
60
40
75
P1 mm
29
40
40
55
49
70
58
80
73
100
S235
35,4
66,5
46,9
85,3
58,9
109,1
70,9
132,9
87,3
163,6
S275
42,3
79,4
56,1
101,9
70,4
130,3
84,7
158,8
104,2
195,5
S335
50,2
94,2
66,5
120,9
83,5
154,5
100,4
188,3
123,6
231,8
S275N
38,4
72,0
50,8
92,4
63,8
118,2
76,8
144,0
94,5
177,3
S355N
48,2
90,5
63,9
116,1
80,2
148,5
96,5
180,9
118,8
222,7
S420N
51,2
96,0
67,8
123,3
85,1
157,6
102,4
192,0
126,1
236,4
S355M
46,3
86,8
61,3
111,4
76,9
142,4
92,6
173,5
113,9
213,6
S420M
49,2
92,3
65,2
118,5
81,8
151,5
98,5
184,6
121,2
227,3
S460M
52,2
97,8
69,1
125,6
86,7
160,6
104,4
195,7
128,5
240,9
spacing’s
is the tensile stress area of the bolt
0.6
M16
13
and
is the ultimate tensile strength of the bolt
As
FvRd
M12
do mm
A
Mb Where A is the gross cross-section area of the bolt. The values have been calculated using value in EC2, Mb=1.25.
Connections in steel structures Connections in steel structures
136 132
The valuesininsteel this table have been calculated using the basic value in EC3, gMb = 1,25. For other Connections structures
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
thicknesses (but t<40mm) the values in the table shall be multiplied by a correction factor of
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints between structural plane, may classified 1/10. The values in theline tableelements, are validinforone bolt grades 8.8beand 10.9. as simple connections,
an element and an immovable support then that end of the element may not move translationally
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid Shear rupture resistance connections. A simple connection allows rotation and movement in any direction except A bolt group break down near theforce end ofthat profile. is called aatblock shear failure, which downwards andcan only transmits shear actsThis downwards a support. A sliding
or rotate in space, as distinct from a movement which is merely relative to the member on the
is causedallows by tensile rupture along holes on tension the holeshear group, connection movement along thethe linefastener of the element andthe rotation andface onlyoftransmits accompanied the grossallows sectionrotation yielding shear at the rowmovement, of the fastener holes along force. A pinned by connection butinno translational it transmits shearthe
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
of the Themoment. block rupture mayconnection determine the the connection andshear axialface forces buthole notgroup. bending A fixed doesresistance not allowof translational where high-grade steels and bolts with small edge distances are used. movement or rotation and transmits shear, axial forces, bending and torsional moment.
provided by a semi-rigid connection either to a support or another member is to measure the
The shear rupture resistance of the profile end shall be calculated using the following formula:
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column
VeffRd
fy 3
Aveff M0
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to provide continuity so that there is little or no rotation between the members at the joint and the
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
rotation at the joint as the bending moment on the joint is varied.
connection designed to transfer a moment from the beam into the column. M-φ curves in general
Aveff
t Lveff
Lveff
Lv L1 L2
non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation Block shear-effective shear area capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © connection causes a drop in the moment resistance.
but
fu a2 k d0t f y
L1 5 d
L2
but
fu L3 Lv a1 a3 n d0v fy
L3
Lv a1 a3
is the effective shear area
t
is the thickness of the web or the plate
classified according to its rigidity as a nominally full-strength MRd ≥pinned, Mpl.Rd rigid or semi-rigid joint. According to its strength, it may be classified as a nominally pinned, full-strength or partial-strength joint. full-strength if rotation capacity is 1,2 they Mpl.Rdcannot develop significant moments notNominally checked pinned joints shall be so designed MRd ≥that where which might adversely affect members of the structure. The joint shall be capable of MRd thecalculated design moment of the connection transmitting isthe designresistance forces, and it shall be capable of accepting the resulting
Where AeffRd
For strength, the following classes can be distinguished: Welded connections nominally pinned MRd ≤ 0,25 Mpl.Rd Joints may be classified by0,25 either their rigidity of strength characteristics. A joint may be partial-strength Mpl.Rd <M Rd < Mpl.Rd
Mpl.Rd rotations.
d0t
is the design strength of the beam (full plastic moment).
is the hole size for the tension face (for horizontally slotted holes the slot length Column web in shear, compression and tension should be used) In practice it is often difficult to fabricate fixed connections and some rotation may take place
The design of semi-rigid joints for moment-resisting steel framed is based on the interaction
between the element onnumber one sideofoffastener the joint andon that the other. n is the holes theonshear face Such a joint is known as a
for nominally pinned joints of rigid joints are treated as semi-rigid joints.
semi-rigid connection and, strictly speaking is the condition of most joints which are described k = 0,5 for a single row of bolts as being fixed or rigid. A moment connection could be described as one which although only k =2,5 for rows ofofbolts. semi-rigid approaches the two behaviour a fixed connection and transfers a substantial bending
between members, i.e. on the moment-rotation characteristics. Joints not meeting the criteria
The design resistance of a full-strength joint shall not be less than that of the member connected. The rigidity of the full-strength joint shall be such that the rotation in any necessary plastic hinge does not exceed its rotation capacity at the ultimate limit state.
moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
A partial-strengthcharacteristic joint shall be of capable of resisting all internal and moments applied to Moment-rotation a semi-rigid joint with enoughforces plastic rotation capacity but its resistance may be less that of the member. Forit,stiffness, the classification is asthan follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
137
Connections made by welding on site should be avoided as far as possible, because welding is more awkward on site than in a workshop. Furthermore, the quality assurance of welding is
Nominal ultimate tensile strengths and correlation factors Steel grade
Nominal ultimate tensile strengths fu (MPa) for
more successful in a workshop. The resistance of a fillet weld per unit length shall be calculated from the following formula: fu
FwRd
fvwd a
Correlation factor w
t<4mm
3
fvwd
w
EN 10025 S235
360
0,8
S275
430
0,85
510
0,9
S355
Mw
EN10113
Where fvwd
is the design shear strength of the weld
a
is the throat thickness of the weld
fu
is the nominal ultimate tensile strength of the weaker part joined
bw
is the appropriate correlation factor
Mw
is the partial safety factor
S275N
390
0,8
S355N
490
0,9
S420N
520
1,0
S355N
470
0,9
S420N
500
1,0
S460N
530
1,0
Sabah Shawkat © t<100mm
Welds with effective lengths shorter than 40mm or six times the throat thickness, whichever is
larger, should be ignored for transmission of forces. The throat thickness of a fillet weld should not be less than 3mm.
The design resistance of a fillet weld in a long lap connection shall be reduced by multiplying it by the following factor.:
for lap connections longer than 150a in the direction of the force transfer: Lw
1.2
0.2 Lj 150 a
Lw
1.0
And for fillet welds longer than 1.7 metres connecting transfer stiffeners in plated members: Lw
1.1
Lw 17
0.6 Lw 1.0
Where Lj
is the overall length of the lap connection in the direction of the force transfer
Lw
is the length of the weld (in metres) Weld length (mm) vs Force in (Tone)- resistance of a weld seam
Connections in steel structures Connections in steel structures
138 132
Connections structures Resistanceinofsteel the weld FwRd (kN) for weld length 100 mm
condition Splices at steel beam supports. By contrast the element may be fixed in its plane to transmit
Throat thickness of the 3 4 5 6 7 8 9 10 Joints between structural line elements, in one plane, may be classified as simple connections, weld (mm) as sliding connections, as pin or pinned connections as fixed connections, also known as rigid S235 62,4 83,1 103,9 124,7 145,5 166,3 187,1 207,8 connections. A simple connection allows rotation and movement in any direction except S275 70,1 93,5 116,8 140,2 163,6 186,9 210,3 233,7 downwards and only transmits shear force that acts downwards at a support. A sliding S335 78,5 104,7 130,9 157,0 183,2 209,4 235,5 261,7 connection allows movement along the line of the element and rotation and only transmits shear S275N 67,5 90,1 112,6 135,1 157,6 180,1 202,6 225,2 force. A pinned connection allows rotation but no translational movement, it transmits shear S355N 75,4 100,6 125,7 150,9 176,0 201,2 226,3 251,5 and axial forces but not bending moment. A fixed connection does not allow translational S420N 72,1 96,1 120,1 144,1 168,1 192,1 216,2 240,2 movement or rotation and transmits shear, axial forces, bending and torsional moment. S355M 72,4 96,5 120,6 144,7 168,8 193,0 217,1 241,2
a
S420M
69,3
92,4
115,5
138,6
161,7
184,8
207,8
230,9
S460M
73,4
97,9
122,4
146,9
171,4
195,8
220,3
244,8
therotate places of the possiblefornominally already at the thedegree structural modelling stage. It may about a support example.pinned A way splices of characterising of fixity or stiffness is worth locating a moment-resistant splice in design at the least loaded place if assembly of the provided by a semi-rigid connection either to a support or another member is to measure the spliceatisthe notjoint unduly awkward and if the lengths short enough. If the bending moment is rotation as the bending moment on the remain joint is varied. accompanied by shear and axial forceand at the place, the latter forces have to be taken Figure bellow defines theforce strength, stiffness deformation capacity of aalso beam-to-column into account. connection designed to transfer a moment from the beam into the column. M-φ curves in general the M-φ The rotation non-linear, forofpractical is necessary to idealise The design a splice application, in a member itsubject to compressive forces has tocurves. take the second-order capacity is ainto measure of the deformation can beisobtained before failure in thethe moments account if the strength ofthat the splice not at least equal to thatsomewhere of the member,
Sabah Shawkat ©
connection a drop in the moment additionalcauses moments have their origin resistance. in the eccentricity of the compressive force and in the Forinitial strength, the following classes can be distinguished: curvature of the profile. The additional second-order moment can be calculated as
e1 e2 2
2
e1 e2
tg
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between Beam splices are necessary, for example, in long rafters because it is often more economical to an element and an immovable support then that end of the element may not move translationally transport a beam in short parts and make splices with bolted connections than to transport it as or rotate in space, as distinct from a movement which is merely relative to the member on the an oversized load. Although a bolted connection is normally preferable to a welded connection other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to of bridge girders and crane runway girders. provide continuity so that there is little or no rotation between the members at the joint and the It is possible make either asHowever, pinned orthe as moment resistant. The designer to decide members behavetoas if nosplices joint existed. joint is not necessarily fixed in has space and
0 5
1 2
e2
e2 e1
e1
2
V
0.75 2 a h w
MRd ≤ 0,25 Mpl.Rd
not checked
MRd ≥ 1,2 Mpl.Rd
0,25 Mpl.Rd < MRd < Mpl.Rd Weff M 1 x ≥ Mpl.Rd full-strength M sd Nsd 1 sin Rd Aeff l is full-strength if rotation capacity
e1 e2
nominally follows:pinned partial-strength
where Where
e
MRd Mpl.Rd
V-is shear force hw is the web depth
is the design moment resistance of the connection is the reduction factor in plane buckling is the design strength of the beam (full plastic moment).
Aeff
is the effective area of the cross-section
Weff
is the effective section modulus of the cross-section
x
is the distance between the nearest inflection point in the buckled state and splice
Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a
or end fastening
semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only
l
is the buckling length of the member.
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the Usefultorsional thicknessmoments of asymmetrical cords axis of the element thus allowing to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
139
Riveted and bolted assemblies working in shear
Bolts working at double shear
Thin-element assemblies, in the case of mild steel, the graphs below give the admissible value
Unsheared threaded part
of shearing force for each bolts according to its diameter ϕ and the thickness e of the assembled part, in the zone of these graphs located at left of interrupted line, it is necessary to check the longitudinal clamp condition. The longitudinal clamp condition we determine as follow: V l 0.8 e
e
Bolts working with simple shear Unsheared threaded portion
Sheared threaded part
Sabah Shawkat ©
In the zone of the graph located at left of solid line, it is necessary to check the longitudinal clamp condition. Bolts assembling with double shear thicknesses less than 13mm without shearing of the threaded part or 8mm with shearing of the threaded part.
Connections in steel structures Connections in steel structures
140 132
Connections in steel structures
Bolts working at double shear
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Rivets
Sheared threaded part Joints between structural line elements, in one plane, may be classified as simple connections,
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between Simple shear an element and an immovable support then that end of the element may not move translationally
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid
or rotate in space, as distinct from a movement which is merely relative to the member on the
connections. A simple connection allows rotation and movement in any direction except
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
downwards and only transmits shear force that acts downwards at a support. A sliding
provide continuity so that there is little or no rotation between the members at the joint and the
connection allows movement along the line of the element and rotation and only transmits shear
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A pinned connection allows rotation but no translational movement, it transmits shear
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
and axial forces but not bending moment. A fixed connection does not allow translational
provided by a semi-rigid connection either to a support or another member is to measure the
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © connection causes a drop in the moment resistance.
For strength, the following classes can be distinguished:
MRd ≤ 0,25 Mpl.Rd
nominally pinned partial-strength
0,25 Mpl.Rd < MRd < Mpl.Rd
MRd ≥ Mpl.Rd
full-strength
full-strength if rotation capacity is
MRd ≥ 1,2 Mpl.Rd
not checked where MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
Column web in shear, compression and tension
In practice it is often difficult to fabricate fixed connections and some rotation may take place
In the the zone of the on graph of and solidthat line, is other. necessary longitudinal between element onelocated side of at theleft joint onitthe Suchtoacheck joint isthe known as a
Rivets simple shear it is necessary to check and not check the longitudinal clamp condition
clamp condition. semi-rigid connection and, strictly speaking is the condition of most joints which are described
In the zone of the graph located at left of solid line, it is necessary to check the longitudinal
as being fixed or rigid. A moment connection could be described as one which although only
clamp condition. Rivets assembling at simple shear thicknesses less than 4mm and at double
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending
shear splicer less than 14mm
moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
141
Rivets
Slip resistance In slip resistance connections, the preloaded bolts clamp the contact surfaces together and the
Double shear
contact surfaces cannot slip with respect to each other. The resistance of the connection depends on the preloading force in the bolt as well as the slip factor of the contact surfaces in addition to the material properties of the connected parts. The design value of the slip resistance is obtained from the following formula:
FsRd
ks n
FpCd
Ms
Where =1,0
ks
is standard hole clearances are used
n
is the number of slip planes
is the slip factor
Sabah Shawkat © FpCd
= 0,7 fub As
is the preloading force
Ms,ult and gMs,ser are partial safety factors.
The contact surfaces are classified according to their slip factors into four classes. The
slip factors corresponding to the classes and slip resistance are obtained from table below. Contact surfaces in slip-resistant connections Class
Slip factor
A
0,50
Treatment of contact surfaces Surfaces blasted with shot or grit, with any loose rust removed, no pitting Surfaces blasted with shot or grit, and spray-metallized with aluminium Surfaces blasted with shot or grit, and spray-metallized with zincbased coating certified to provide a slip factor not less than 0.5
B
0,4
Rivets double shear it is necessary to check and not check the longitudinal clamp condition In the zone of the graph located at left of solid line, it is necessary to check the longitudinal
Surfaces blasted with shot or grit, and painted with an alkali-zinc silicate paint to produce a coating thickness of 50-80 m
C
0,3
clamp condition.
Surfaces blasted with wire brushing or flame cleaning, with any loose rust removed
D
0,2
Surfaces not treated
Connections in steel structures Connections in steel structures
142 132
Connections in steel Slip resistance FsRdstructures (kN) in Class D per slip plane
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
Bolt M12 M16 M20 M24 M30 Joints between structural line elements, in one plane, may be classified as simple connections, Slip resistance at the serviceability limit state as sliding connections, as pin or pinned connections as fixed connections, also known as rigid Grade 8,8 8,6 16 24,9 25,9 57,1 connections. A simple connection allows rotation and movement in any direction except 10,9 10,7 20 31,2 44,9 71,4 downwards and only transmits shear force that acts downwards at a support. A sliding Slip resistance at the ultimate limit state connection allows movement along the line of the element and rotation and only transmits shear Grade 8,8 7,6 14,1 22 31,6 50,3 force. A pinned connection allows rotation but no translational movement, it transmits shear 10,9 9,4 17,6 27,4 39,5 62,8 and axial forces but not bending moment. A fixed connection does not allow translational If a slip-resistance connection is subject to an applied tensile force in addition to the shear force, movement or rotation and transmits shear, axial forces, bending and torsional moment. the slip resistance shall be calculated as follows: in Category B
F sRdser
k s n
F pCd
0.8 F tSdser
Msser
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between an element and an immovable support then that end of the element may not move translationally or rotate in space, as distinct from a movement which is merely relative to the member on the other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to provide continuity so that there is little or no rotation between the members at the joint and the members behave as if no joint existed. However, the joint is not necessarily fixed in space and may rotate about a support for example. A way of characterising the degree of fixity or stiffness provided by a semi-rigid connection either to a support or another member is to measure the rotation at the joint as the bending moment on the joint is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat ©
in Category C
FsRd
ks n
FpCd 0.8 FtSd
Msult
connection causes a drop in the moment resistance.
For strength, the following classes can be distinguished:
MRd ≤ 0,25 Mpl.Rd
The stiffness of the splice in a compression member has to be at least equal to that of the
nominally pinned
member with respect to both principal axes even if the member is axially loaded only and
partial-strength
abutting ends are provided at the splice. Furthermore, the parts of the splice must be able to
full-strength
carry 2,5% of the compressive force in any direction perpendicular to the axis of the member.
full-strength if rotation capacity is
0,25 Mpl.Rd < MRd < Mpl.Rd
MRd ≥ Mpl.Rd
MRd ≥ 1,2 Mpl.Rd
not checked where MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only Some types of splices - continuity semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending It is worth the splice of a column as nearfor to aparticular support asrequirements possible, where the lateral moment. Notelocating that connections may be fabricated so that, for
deflection small. Thenrotation the inner andof of the second-order moments as small effect example, theyismay allow in forces the plane elements but preventhave twisting about the on the resistance of the joint as possible. axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic a semi-rigid jointhollow with enough rotation capacity from square sectionplastic profiles Plane truss of beam, For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
143
Calculate the tension resistance of the adjacent joint. The dimensions of the hollow section are
Mb
is the partial safety factor of the bolt joints
200x200x8, and the steel designing used is S355J2H. The steel grade used in splices is S355J2. The strength grade of the M30 bolts is 8.8. The parameters of the joint geometry are:
Resistance of the splice plate net cross-section The splice plates can be taken as tension cross-section. Thus, the resistance of a cross-section containing holes can be obtained from:
Data t1 22mm
t2 12 mm
dM30 30 mm
d0 0.0324 m
hp 240 mm
a1 50 mm
p1 Lv
p2 Lv
a2 Lv
e2 50 mm
M2
1.25
n1 2
n 6
M0
1.1
d0 1.08 dM30 Lv 140 mm e1 50 mm Mb
The tension resistance of the cross-section is the smallest of the following: Anet t1 hp n1 d0
Anet 3854.4 mm
A v t1 hp
Av 5280 mm
2
1.25
k 2.5
fub 800 MPa fu 490 MPa fy 355 MPa The resistance of the joint is determined separately for the bolts and splices. The bolts transfer
2
F tRd Av
fy
FtRd 1704 kN
M0
FtRdnet 0.9 Anet
fu M2
FtRdnet 1359.83 kN
Sabah Shawkat ©
the force affecting on the joint by their shear resistance. The bolts shear resistance per shear plane is determined from the following formula, assuming the shear plane does not pass through
Anet
is the net area (the area of the holes subtracted from the gross area)
fu
is the ultimate strength of the material
NtRd
is the design value of tension resistance
the threaded portion of the bolts.
Bearing resistance of splice plates
The tension resistance of the splice plates is calculated by taking into account both the net crosssection and the bearing resistance. The resistance of the net cross-section can be calculated by the same principle as that of a hollow section in tension. The bearing resistance of a splice plate depends on the positioning of the holes and the strength of the bolts. This relationship is
FvRd
0.6 fub A
illustrated by the parameter α, obtained as the minimum value from the following equation:
Mb
fub
is the ultimate strength of the bolt
A
is the cross-section of the bolt
fub fu
p1 1 fub 3d 3d 4 fu 0 0
e1
min
1.63265
Connections in steel structures Connections in steel structures
e1 3d0
0.5144
p1 3d0
1 4
1.19033
144 132
Connections e1in steel structures 0.5144 3 d 0
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Shear resistance of bolts
Joints structural elements, in one may betoclassified is the distanceline of the bolt from the plane, edge parallel force as simple connections, e1 between as sliding connections, as pin or pinned connections as fixed connections, also known as rigid is the diameter of the bolt hole d0 connections. A simple connection allows rotation and movement in any direction except is the distance between bolts parallel to force p1 downwards and only transmits shear force that acts downwards at a support. A sliding is the ultimate strength fub connection allows movement along of thethe linebolt of the element and rotation and only transmits shear force. allowsofrotation but no translational movement, it transmits shear is theconnection ultimate strength the splice fu A pinned andWhen axial the forces butarenotsituated bending A fixedthe connection does not allow translational holes as moment. in the example, bearing resistance of splice plates is as follows: or rotation and transmits shear, axial forces, bending and torsional moment. movement FbRd
2.5 fu dM30t1 Mb
FbRd 332.71605 kN
dM30
is the diameter of the bolt
t1
is the thickness of the splice
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between The shear resistance of bolts is determined by assuming that the shear plane does not pass an element and an immovable support then that end of the element may not move translationally through the threaded portion of the bolts: or rotate in space, as distinct from a movement which is merely relative to the member on the 2 other side of the two members are said to djoint. M30 Fixed joints, or nearly fixed joints, between 2 AM30 AM30 706.86 mm provide continuity4 so that there is little or no rotation between the members at the joint and the
members behave as if no joint existed. However, the joint is not necessarily fixed in space and 0.6 fub AM30 271.43361 kN the degree of fixity or stiffness mayFrotate characterising vRd of vRd about a support for example. AFway Mb
provided by 6a bolts semi-rigid connection either to aplanes, supportsoortheanother member is: is to measure the shear bolt resistance There are and the joint has two rotation at the joint as the bending moment on the joint is varied. 12 FvRd FvRdtot 3257.20326 kN FvRdtot Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column connection designed to transfer a moment from the beam into the column. M-φ curves in general Resistant the welds non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation Designisthe fillet welds with a throat thickness of obtained 10 mm, the axial forcesomewhere introduced in into capacity a measure of the deformation that can be before failure thethe
weld is assumed equalintothethe hollowresistance. section plastic tension resistance. The plastic tension connection causes a drop moment resistance of a hollow section with dimensions 200x200x8 is: For strength, the following classes can be distinguished:
Sabah Shawkat ©
Mb
is the partial safety factor of the bolt joints
Now there are 6 bolts per plate, so the bearing resistance is: FbRdtot n FbRd
FbRdtot 1996.2963 kN
nominally pinned MRd ≤ 0,25 Mpl.Rd 2 2 A200.200.8 52.84 10 mm w 0.9 a 10 mm partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd
fy full-strength NplRd A200.200.8 M0 full-strength if rotation capacity is
Block shear failure resistance of splice plates
First, calculate the effective shear area from the formula:
fu Lveff 2 Lv a1 a2 k d0 fy fu 2 Lv 5 d0 a2 k d0 685.43662 mm fy
not checked where Lw MRd
Mw
1.25
MRd ≥ Mpl.Rd NplRd 1705.29 kN
3 w Mw NplRd
MRd ≥ 1,2 Mpl.Rd
Lw 169.53 mm 4 fu a is the design moment resistance of the connection
Mpl.Rd is the design strength of the beam (full plastic moment). Resistance of joints
fu Column web in shear, compression and tension Lveff 2 Lv 5 d a2 k d0 Lveff 461.44 mm In practice it is often difficult to fabricate fixed connections and some rotation fymay take place 2 between the that on the other. Such a joint is known as a Aveff element t1 Lveff on one side of the joint Aveff and 10151.61 mm
semi-rigid connection and, strictly speaking is the condition of most joints which are described
resistance for block shear failure of the splice in be checked. as Additionally, being fixed orthe rigid. A moment connection could be described asthe onemiddle which must although only The design value forthe block shear failure is determined from formula: semi-rigid approaches behaviour of a fixed connection andthe transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for fy Aveff VeffRdthey may allow rotation in theVplane 1891.51 kN but prevent twisting about the example, the elements effRd of 3 M0 axis of the element thus allowing torsional moments to be transmitted. This is a common
The entire resistance of the joint is then determined by the resistance of the net cross-section: FtRdnet 1359.83232 kN
where fu
is the ultimate strength of the hollow section
fy
is the yield strength of the hollow section
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
145
Calculate the resistance of the adjacent shear joint. The dimensions of the hollow sections are 250x250x8, and the steel grade used S355J2H. At the end of the hollow section, the joint is subjected to a force Fsd. The thickness of the splice plate is 20mm, and the strength grade of the
Bearing resistance of the splice plates The bearing resistance of the splices is calculated as:
M22 bolts is 8.8. Data
Fsd 250 kN
Nsd 450 kN
fyk 355 MPa
fu 490 MPa
M1
The axial force of the column is Nsd
1.1
Mj
1.1
M0
dM22 22 mm d0 26 mm
Lv 160 mm a1 50 mm Msd Fsd a2
p1 Lv
1.1
Mw
1.25
k 0.5
a3 50 mm
fu Mb
p1 1 fub 3d 3d 0 0 4 fu
1.63265
1.25
FbRd
tp 20 mm
a2 50 mm
fub
fub 800 MPa
e1
e1
min
3d0
e1 3 d0
2.5 fu dM22tp
0.64103
p1 3d0
1 1.80128 4
0.64103
FbRd 276.41026 kN
Mb
Now there are 2 bolts per plate, so the bearing resistance is: e1 50 mm
FbRdtot n FbRd
n 2
FbRdtot 552.82051 kN
FbRdtot Fsd
Sabah Shawkat © Msd 12.5 m kN
Block shear failure resistance of splice plates
First, calculate the effective shear area from the formula:
fu fyk
Lveff Lv a1 a2 k d0
2
Aveff 5221.41 mm
tp Lveff Aveff f
Lv a1 a3 n d0 f u
yk
a1 5 dm22
Lveff 261 mm
0.2871 m
Lveff Lv a1 a3 n d0
5 dM22 110 mm
a1 50 mm
Obtain the block shear failure resistance by substituting in formula: Joint of steel hollow section
VeffRd
fyk Aveff 3 M0
VeffRd Fsd
VeffRd 972.89 kN Fsd 250 kN
Connections in steel structures Connections in steel structures
fu fyk
146 132
Connections in steelofstructures Shear resistance bolts
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Resistance of welds
The shear resistance of bolts is determined by assuming that the shear plane passes through the Joints between structural line elements, in one plane, may be classified as simple connections, threaded portion of the bolt: as sliding connections, as pin or pinned connections as fixed connections, also known as rigid
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between The weld between the column and the splice must transfer the force Fsd vertically and the tensile an element and an immovable support then that end of the element may not move translationally force due to moment Msd horizontally. Therefore, determine the stress components of the weld: or rotate in space, as distinct from a movement which is merely relative to the member on the 4 of L 260 mmor nearly fixed joints, between two members are said to a side mm other the joint. Fixed joints,
2 connections. A dsimple M22 connection allows rotation and 2movement in any direction except AM22 AM22 380.13 mm downwards and 4only transmits shear force that acts downwards at a support. A sliding
connection allows movement along the line of the element and rotation and only transmits shear 0.6 fub AM22 FvRd but 145.97096 kN FvRd force. A pinned connection allows rotation no translational movement, it transmits shear Mb
and axial forces but not bending moment. A fixed connection does not allow translational movement or rotation and transmits shear, axial forces, bending and torsional moment. There are 2 bolts and the joint has two shear planes, so the bolt resistance is:
2 FvRd FvRdtot
FvRdtot 291.94192 kN
FvRdtot Fsd
Fsd 250 kN
provide continuity so that there is little or no rotation between the members at the joint and the Fsd II 240.38462 MPa the joint is not necessarily fixed in space and members behave as if no II joint existed. However, a L The weldabout strength is checked with formulae in characterising Ec3 may rotate a support for example. A way of the degree of fixity or stiffness provided by a semi-rigid connection either to a support or another member is to measure the fu fu par at the joint as the bending 392 MPa rotation moment on the joint is varied. Mw
Mw
Figure theofstrength, stiffness and capacity of a(fillet beam-to-column Try abellow throat defines thickness 4 mm, which gives thedeformation following weld stresses welds on both connection designed faces of the plate):to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation Fsd capacity that can be obtained before failure somewhere in the II is a measure of the deformation II 120.19231 MPa 2 a L connection causes a drop in the moment resistance. The same throat thickness can be used in the weld between the hollow section and plate and the For strength, the following classes can be distinguished: splice. nominally pinned MRd ≤ 0,25 Mpl.Rd Resistance of the joint partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd
Sabah Shawkat ©
Resistance of the column wall
The resistance of the column wall is calculated as: 250x250x8
hc 250 mm 2
2
Ac250.250.8 75.24 10 mm
n
M0 Mj
1.1
bc 250 mm 3
tc 8 mm
3
Wel 578.3 10 mm
Nsd Msd A f W c250.250.8 yk el fyk
n 0.2523
full-strength Mpl.Rd Rd ≥ Compare the calculated resistance values toMthe force quantities: full-strength if rotation capacity is FvRdtot 291.94192 kN not checked
Fsd 250 kN MRd ≥ 1,2 Mpl.Rd
where M1Rd 14.47376 m kN
Msd 12.5 m kN
ok
MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
compression and tension km 1.3 ( 1 n ) Column web km in shear, 0.97201 In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a 2 fyk tc hc 2 hc tp 1 of most joints which are described semi-rigid connection M1Rd 0.5 km and, strictly speaking 4 is1 the condition M1Rd 14.47376 m kN tp bc bc Mj M0 as being fixed or rigid.1A moment connection could be described as one which although only bc semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. that connections may M1Rd Note Msd Msdbefabricated 12.5 m kNfor particular OK requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity Incorrect production and installation of a steel column that was carried out on site For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
147
Calculate the bending resistance of the flange plate joint. The column dimensions are 250x250x10 and those of the hollow section are 350x250x10. The steel grade used is S355J2H.
Usually the joint also includes shear force, which must be taken into account in the joint design.
The flange thickness is 22mm. The steel grade used in the flanges is S355J2. The strength grade
Resistance of hollow sections subjected to shear force
of the M24 bolts is 8.8. fu 490 MPa M1
1.1
m 50 mm w
0.9
The design criterion for hollow section subject to shear force is:
fyk 355 MPa Mj
1.1
M0
e 50 mm
1.1
tp 22 mm
Mw
Vsd VRd
1.25
p 300 mm
Vsd
is the design value for the shear force
VRd
is the design value for the shear resistance
hr 350 mm
Lw 300 mm d24 24 mm The method for calculating the shear resistance depends on slenderness of the web of the
The bending and shear resistance values of the joint components are:
hb 400 mm bb 200 mm
tb 10 mm
Beam
cross-section as follows: 400x200x10
h t
69
235 MPa fyk
3
calculate the plastic shear resistance
Sabah Shawkat © 2
2
Ab400.200.10 112.6 10 mm
Vb.plzRd 1398 kN
Vb.plyRd 699.1 kN
Mb.cyRd 462.7kN m
Mb.czRd 236.2 kN m
h t
69
69
235 MPa fyk
235 MPa fyk
3
calculate the resistance to shear buckling
hb
3 59.13954
tc
40
Shear buckling need not be considered for square and rectangular hollow sections for which h/t < 59,1 and the yield strength of the material fy < 355 MPa. In practice, shear buckling governs only for a very few hollow section.
Shear resistance of the column web plastic shear resistance of the column web is:
Column
hc 200 mm
200x200x10 2
bc 200 mm tc 10 mm
fyk Av 3 M0
Av
A
h bh
2
Ac200.200.10 72.57 10 mm McRd 164.0 kN m
Vpl.Rd
Vc.plRd 676.1 kN
NcRd 2342 kN
h
in this case is the dimension parallel to shear force
Connections in steel structures Connections in steel structures
148 132
2 Connections in steel structures column Ac200.200.10 7257 mm hc 0.2 m bc 0.2 m hc 2 Avc 3628.5 mm A Ac200.200.10 Jointsvc between structuralbcline in one plane, may be classified as simple connections, helements, c
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit By multiplying the shear resistance by the height of the hollow section, the moment resistance bending but allow rotation about its axis. Note that if pinned or fixed joints are made between for the column web is obtained: an element and an immovable support then that end of the element may not move translationally
as sliding connections, fyk Avc as pin or pinned connections as fixed connections, also known as rigid VplRd VplRd 676.08635 kN connections. A 3simple M0 connection allows rotation and movement in any direction except
or rotate to themmember on the MRd in space, VplRd as hdistinct MRd relative 263.67368 kN b tb from a movement which is merely other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
downwards and only transmits shear force that acts downwards at a support. A sliding
provide continuity so that there is little or no rotation between the members at the joint and the Resistance of flanges and bolts members behave as if no joint existed. However, the joint is not necessarily fixed in space and The resistance of flanges and bolts can be estimated by calculating the resistance of the joint may rotate about a support for example. A way of characterising the degree of fixity or stiffness between the flange and hollow section using equivalent T models. Equivalent T models consist provided by a semi-rigid connection either to a support or another member is to measure the of a column and flange, and hollow section and flange. There are three potential failure modes rotation at the joint as the bending moment on the joint is varied. for a T model. According to these modes, the tension resistance values of the bolt row are as Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column follows. connection designed to transfer a moment from the beam into the column. M-φ curves in general
connection allows movement along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear and axial forces but not bending moment. A fixed connection does not allow translational movement or rotation and transmits shear, axial forces, bending and torsional moment.
Shear buckling resistance of square and rectangular hollow sections
the M-φ curves. The rotation non-linear, for practical application, it the is necessary to idealise 1. flange yield at the location of bolt row and at the hollow section webs
The shear buckling resistance of hollow sections is calculated using the following formula:
capacity is a measure of the deformation that can be obtained before failure somewhere in the 4 MplRd connection FrRdcauses a drop in the moment resistance. m For strength, following be at distinguished: 2. boltthe failure as theclasses flangescan yield the hollow section webs nominally pinned MRd ≤ 0,25 Mpl.Rd
Sabah Shawkat ©
VbaRd
2 hc 3tc tc
ba
M1
The web shear buckling stress τba depends on the slenderness of the web λw as follows: hc 3 tc
w
ba
tc
w
235 MPa 86.4 fyk
1 0.625 w 0.8
0.24183
fyk
0.8 w 1.2
for
3 ba
as being fixed or rigid. A moment connection could be described as one which although only Bending resistance of the column web semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending The resistance of the column web determined from: moment. Note that connections mayis be fabricated for particular requirements so that, for example, they may allow rotation in the 1.1 plane of the elements but prevent twisting about the 2 M 326.76136 m kN Mip1Rd 0.5 fyk tc hb 5 tc axis of the element thus allowing torsional moments to beip1Rd transmitted. This is a common Mj M0
2
full-strength if rotation capacity is not checked 3. bolt or flange failure
VbaRd 854.51372 kN 276.46032 MPa VbaRd 2 hc 3tc tc M1tension Column web in shear, compression and The resistance to shear buckling is calculated according to the instructions in reference: In practice it is often difficult to fabricate fixed connections and some rotation may take place on one side of the joint and that on the other. Such a joint is known as a between If the element w 1.2 semi-rigid connection and, strictly speaking is the condition of most joints which are described ba
0.25 Leff fyk tp partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd 2 MplRd e 2 BtRd MplRd FtRd M0 me full-strength MRd ≥ Mpl.Rd
where FtRd MRd
Mpl.Rd where
MRd ≥ 1,2 Mpl.Rd
2 BtRd is the design moment resistance of the connection is the design strength of the beam (full plastic moment).
FtRd
is the tension resistance of the bolt row
Leff
is the effective length of the bolt row
tp
is the thickness of the flange
m
is the bolts distance from the outer edge of the hollow section
e is the bolts distance from the edge of the flange, e < 1,25m Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity is the tension resistance of the bolt or the punching resistance of the flange BtRd For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
149
we see that the failure mode to be used in the design is therefore bolt failure with flange yielding FtRd. It is normally recommended to design the flange joint so that the flanges yield before the bolts fail. The failure mode is then ductile. For flanges and bolts, the joint bending resistance is: MRd FtRd hr
MRd 204.8238 m kN
Design of welds The effective length of the bolt row depends on the shape of the flanges yield line pattern. From
The welds must transfer the tensile force due to bending moment into the hollow sections upper
the following equations, select the one giving the smallest result:
flange
Leff1 2 m
Leff1 314.15927 mm
Leff2 4 m 1.25 e Leff2 262.5 mm
Nsd
MRd
Nsd 512.0595 kN
hb
since the letter formula gave the smallest value, it is used as the effective length of the bolt row The fillet weld is provided across the width of the entire column 200mm, which gives a required
Leff2 0.2625 m
Sabah Shawkat © throat thickness of:
Then substitute the effective length of the bolt row in the failure mode equations for the T stub:
MplRd
0.25 Leff2fyk tp
a
2
3 w Mw Nsd 6.7876 mm fu Lw
fu Lw
MplRd 10.251 m kN
M0
Flange yield at the location of the bolt row and at the hollow section web FrRd
3 w Mw Nsd
The bending resistance of the joint is obtained by multiplying the tension resistance values of
the horizontal bolt rows by the distance of the bolt rows from the centre of compression. Only
4 MplRd
FrRd 820.05 kN
m
the bolt rows in the tension zone are considered. The tension zone of the joint is located above the neutral axis of the hollow section. The following value for bending resistance is therefore
bolt failure as the flanges yield at the hollow section webs: BtRd 0.6 0.75 d24tp
fu M2
BtRd 292.605 kN
obtained: MRd
R h tRd
i
r
i
i
where
FtRd
2 MplRd e 2 BtRd me
FtRd 497.61793 kN
bolt or flange failure FtRd 2 BtRd
FtRd
is the design value for the bolt rows tension resistance
hr
is the distance of the bolt row distance from the compression centre
MRd 204.8238 m kN
FtRd 585.21085 kN
Connections in steel structures Connections in steel structures
150 132
Connections in steel structures Calculate the bending resistance of the splice with end-plates shown in the adjacent picture. It
condition at widths steel beam supports. yield-line By contrast the element may be fixed in its plane to transmit Effective (non-circular patterns):
is assumed that the requirement of rotation capacity as a provision for a plastic global analysis
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between Leffnc 4 mx 1.25 ex Leffnc 278.79613 mm an element and an immovable support then that end of the element may not move translationally Leffncinspace, e 2as mxdistinct 0.625from ex a movement Leffncwhich 204.39807 mm or rotate is merely relative to the member on the
Joints between structural line elements, in one plane,the may be classified simple connections, is not set. The beam profile is WI600-8-20x300. thickness of theasend-plate is 25mm. The as steel sliding connections, as pin or bolts pinned grade is S355J2G3. The areconnections 6xM24 8.8.as fixed connections, also known as rigid connections. A simple connection allows rotation and movement in any direction except
connection allows movement along the line of the element and rotation and only transmits shear
otherL side of 0.5 the w joint. joints,eor nearly joints, between 2 Fixed mx 0.625 Leffncfixed 199.39807 mm two members are said to effnc x provide continuity so that there is little or no rotation between the members at the joint and the Leffnc 0.5 bp Leffnc 150 mm members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A pinned connection allows rotation but no translational movement, it transmits shear
mayleff1 rotate a support for example. A way the degree of fixity or stiffness about 2 Leffnc leff1of characterising 0.3 m
and axial forces but not bending moment. A fixed connection does not allow translational
provided by a semi-rigid connection either to a support or another member is to measure the
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied. The tension resistance of the T-stub: Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column Use boltsdesigned M24 8.8to transfer a moment from the beam into the column. M-φ curves in general connection
downwards and only transmits shear force that acts downwards at a support. A sliding
non-linear, for practical application, it is 2necessary to idealise the M-φ curves. The rotation from the table 3.3 fu 800 MPa As 353 mm capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat ©
connection causes a drop in the moment resistance. The resistance BtRd is determined by the tensile resistance of the bolt, the punching shear For strength, the following classes can be distinguished: resistance is not decisive. nominally pinned MRd ≤ 0,25 Mpl.Rd
The dimensions of the splice
Msd 350 kN m fyw 355 MPa
tf 20 mm h 600 mm
e 65 mm
e min 60 mm w 120 mm
mmax 1.25 mx
M0
1.1
bp 300 mm tp 25 mm af 8 mm ex 60 mm
m x s e x 0.8 a f n emin
fyp 355 MPa
2
tw 6 mm s 120 mm
mx 50.949 mm
mmax 63.686 mm
z h tf
z 0.58 m
< MRd < Mpl.Rd partial-strength 0,25 fMpl.Rd BtRd1 203.3 kN ub fyp Mb 1.25 full-strength MRd ≥ Mpl.Rd BtRd 4 BtRd1 B 813.2 kN full-strength if rotation capacity is tRd
M2
1.25
not checked MRd ≥ 1,2 Mpl.Rd 2 fyp M Mpl1Rd 15.12784 m kN pl1Rd 0.25 leff1 tp where M0 is the design moment resistance of the connection MRd 2 fyp Mpl.Rd thedesign (full plastic moment). M 0.25 leff1 tp strength Mpl2Rd 15.12784 m kN of the beam pl2Rd is
M0
Column web in shear, compression and tension In The practice it is often to fabricate fixedaccording connections rotation may take place resistance of difficult the splice is calculated to and EC3.some A simplified method is used
Failure mode 1 (yield of the end-plate):
between thethe element on one side the joint and thatare onasthe Suchabove. a joint is known as a whereby bolt forces and theofequivalent T-stub inother. the figure semi-rigid connection strictly is the condition of mostregion, joints which are described This method is validand, when there speaking are two bolt rows on the tension the resistance FRd does as not being fixed3,8 or rigid. A momentlater connection could be force described one which on) and the axial in theassplice is lessalthough than 10%only of the exceed BtRd (presented semi-rigid approaches theofbehaviour plastic axial resistance the beam.of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Ft1Rd 4
Mpl1Rd mx
Ft1Rd 1187.68424 kN
Failure mode 2 (combined bolt failure and yield of the end-plate): Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity 2 Mpl2Rd n BtRd Ft2Rd the classification is as follows:Ft2Rd 712.46841 kN For stiffness, m n x
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
151
Rotation capacity of the splice:
Failure mode 3 (bolt failure): Ft3Rd BtRd
The following criteria have to be valid in order that the forces in the splice may be distributed
Ft3Rd 813.2 kN
according to the theory of plasticity: Tension resistance of the equivalent T-stub is Ft2Rd
Bending in the end-plate sets the bending resistance of the splice.
In addition to the resistance of the T-stub, the resistance of the compression flange and web as
tp 0.36 d
well as that of the tension region of the web have to be checked.
fub fyp
Resistance of the compression flange and the web of the beam:
In this example, neither of these criteria is valid. However, the plastic resistance may be taken
McRd 729.5 kN m
FcfRd
McRd
as the resistance of the splice, because the splice in this example is not subject to further rotation capacity requirements due to additional plastic hinges appearing later on.
FcfRd 1257.75862 kN
h tf
The plastic bending moment:
In the formula above, McRd is the resistance of the beam. In this case the cross-section is
Sabah Shawkat ©
Class2, and its plastic bending resistance is 729.5kNm.
M jRd FRd z
MjRd 336.92727 m kN
Resistance of the tension region of the beam web: befftw leff1 fyw 355 MPa
befftw 0.3 m
FtwRd befftw tw
fyw
M0
tw 0.006 m
In sufficient rotation capacity is required in the splice and the criteria mentioned above are not
valid, it is possible to take the value of 2/3 of the plastic bending resistance as the elastic bending resistance. The bending resistance of the splice would then be
FtwRd 580.90909 kN
2
MjRd 3
224.61818m kN
The resistance of the splice is the least of the resistances calculated above: FRd Ft1Rd
FRd 1187.68424 kN
FRd Ft2Rd
FRd 712.46841 kN
FRd Ft3Rd
FRd 813.2 kN
FRd FcfRd
FRd 1257.75862 kN
FRd FtwRd
FRd 580.90909 kN
The criterion for the calculation method to valid:
FRd 3.8 BtRd1
0.75195
FRd 3.8 BtRd1
1.0
Ok
Failure to respect the bearings of the supporting elements during the realization
Connections in steel structures Connections in steel structures
152 132
Connections in steel structures Using the beam profile WI500-8-15x250, design the joint shown in the adjacent figure.
condition at steel beam supports. By contrast Resistance on the basis of material strength:the element may be fixed in its plane to transmit
The steel grade is S355J2G3. The joint is subject to shear force Vsd at the ultimate limit state. Joints between structural line elements, in one plane, may be classified as simple connections,
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between Vsd tp and an immovable tp support 7.437 then mm that end of the element may not move translationally an element fy or rotate inbpspace, as distinct from a movement which is merely relative to the member on the
Vsd connections, 600 kN fy or 355 MPa M0 as1.1 k 0.43also tknown mm as sliding as pin pinned connections fixed connections, rigid f 15as
M0
connections. A simple connection allows rotation and movement in any direction except fu 510 MPa bp 250 mm Mw 1.25 a 5 mm H 600 mm downwards and only transmits shear force that acts downwards at a support. A sliding 235the MPa connection along line of the and rotation and only transmits hw Hallows 2 tfmovement hwelement 0.57 m 0.66197 b 360 shear mm fy force. A pinned connection allows rotation but no translational movement, it transmits shear
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
and axial forces but not bending moment. A fixed connection does not allow translational
provided a semi-rigid connection either to a support or another member is to measure the becomebycritical.
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied.
provide continuity so that there is little or no rotation between the members at the joint and the Resistance against local buckling: members behave as if no joint existed. However, the joint is not necessarily fixed in space and may rotate about aofsupport for example. A way of characterising degree of fixity or stiffness The thickness the end-plate is chosen so that the resistance the against local buckling does not
b
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column tp b tp p 0.673 connection28.4 designed the beam) into the column. M-φ curves in general ( 28.4 0.673 k kto transfer a moment from
non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the b is the width of an outstand plate element. connection causes a drop in the moment resistance. b For strength, the following classes can be tdistinguished: tp p 0.04339m ( 28.4 0.673 ) k nominally pinned MRd ≤ 0,25 Mpl.Rd
Sabah Shawkat © 0,25 Mpl.Rd < MRd < Mpl.Rd
partial-strength
full-strength MRd ≥ M pl.Rd when the end-plate is in the middle of an I-profile (subpanels of equal size), the following full-strength if obtained rotation capacity is condition is for the thickness of the end-plate: not checked tp where
MRd a
Is the throat thickness of the weld
The nominal ultimate tensile strength of the weaker part joint Column web in shear, compression and tension fu 510 In practice it isMPa often difficult to fabricate fixed connections and some rotation may take place
between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid strictly of most joints which are described Is the and, design shearspeaking strength is ofthe thecondition weld fvwd connection as being fixed or rigid. A moment connection could be described as one which although only Is the appropriate correlation factor w 0.9 w semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for Is the partial safety factor Mw example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
bp
MRd ≥ 1,2 Mpl.Rd
tp 0.01506 m
tp 16 mm ( 38.23) k is the design moment resistance of the connection
Mpl.Rd is the design strength of the beam (full plastic moment). Connection weld of the end-plate The twin fillet weld between the end-plate and the web is assumed to be effective. The following condition is obtained for the throat thickness of the weld: fu
fvwd
3 w Mw
fvwd 261.732 MPa
Vsd aw 2.01089 mm aw Moment-rotation 2 hw fvwdcharacteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
153
On the basis of the cooling rate of the weld, the result is aw
tp mm
0.5
aw 3.5
aw 4 mm
then aw will be
Column Bracket: The thickness of the bracket is normally 30-50mm. Its width is taken as equal to that of the endplate of the beam. Its depth is determined by the connection welds. Vertical welds and the lower horizontal weld are taken to be load-bearing. the upper surface has to be flat so that the endplate of the beam is able to rest on it. The following condition is obtained for the bracket depth: hk
Vsd 2 a fvwd
bp 2
hk 104.242 mm
hk 200 mm
Sabah Shawkat © Some beam - to – column joints
1. The pinned joints in Fig. a) and b) are normally used when an I-beam is to be joined to a column. 2. The joint in Fig. a) is faster and more economical to make than the joint in Fig. b). 3. The rotation at the beam end is, however, larger in the case of the joint in Fig. a). 4. A typical pinned joint between a rafter and column is shown in Fig. c) 5. A rigid joint shown in Fig. d)
Connections in steel structures Connections in steel structures
154 132
Connections in steelwe structures In This example try to explain the geometrical and mechanical properties of ordinary bolts
condition at attachment steel beam -supports. By contrast the element may be fixed in its plane to transmit Detail of Steel Beam to Steel Column. bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
and describes their behaviour in shear, tension or combined shear and tension. Joints between connections, structural linebolts elements, in one plane, loads may be classified as to simple connections, In structural are used to transfer from one plate another. We explain
an Data: element and an immovable support then that end of the element may not move translationally
as here sliding connections, pin loaded or pinned where bolts areas used, by:connections as fixed connections, also known as rigid
or rotate in space, as distinct from a movement which is merely relative to the member on the Steel "s 235" fy 235 MPa fu 360 MPa m0 1.1 m1 1.1 m2 1.3 other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
connections. A simple connection allows rotation and movement in any direction except downwards and force only transmits shear force that acts downwards at a support. A sliding 1. Shear
5 or no rotation between the members at the joint and the provide continuity so that little E there 2.1 is 10 MPa
connection movement the of line the element and on rotation and only plates. transmits The loadallows is transmitted intoalong and out theofbolts by bearing the connected Theshear forces
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A bolts pinned rotation shear. but no translational movement, it transmits shear in the areconnection transmittedallows by transverse and axial forces but not(only bending 2. Tension force M) moment. A fixed connection does not allow translational
may rotate about a support for example. A way of characterising the degree of fixity or stiffness Steel =orS235 provided by a semi-rigid connection either to a support another member is to measure the
movement or rotation and transmits shear, axial moment. by axial In the case of moment loading (M) only, theforces, tensionbending part ofand the torsional load is transmitted
rotation at the joint as the bending moment on the joint is varied. t=40mm
8.8 and 10.9.
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column E=210000MPa connection designed to transfer a moment from the beam into the column. M-φ curves in general 2 M10 58 mmthe non-linear, for practical application, it is necessary to =idealise M-φ curves. The rotation M12 = 84 mm2 2 capacity is a measure of the deformation that can be obtained M16 = 157 before mm failure somewhere in the 2 connection causes a drop in the moment resistance.M20 = 245 mm2 M24 = 353 mm For strength, the following classes can be distinguished: M30 = 561 mm2 mm2 nominally pinned MRd ≤M37 0,25=M459 pl.Rd
According to Euro-code 3, the design yield stress fyb and the design ultimate stress fub of the
full-strength
usual bolts are as given in Table below.
full-strength if rotation capacity is Except for fitted bolts or where low-clearance or oversize holes are specified, the nominal not checked MRd ≥ 1,2 Mpl.Rd clearance in standard holes shall be: where
tension in the bolt. 3. Combined tension and shear force (M and V) In the case of combined moment (M) and transverse loading (V), the bolts may be required to transmit a combination of transverse shear and axial tension.
Sabah Shawkat ©
Bolts and nuts are available in steels of minimum tensile strengths up to about 1370 MPa. The grade of the bolts is indicated by two numbers. The most common grades are 4.6, 5.6, 6.5, 6.8,
partial-strength 0,25connection Mpl.Rd < MRd < Mpl.Rd Bolted beam-to column
Mechanical properties of bolts Grade fyb (MPa) fub (MPa)
4.6 240 400
5.6 300 500
6.5 300 600
6.8 480 600
8.8 640 800
10.9 900 1000
Column web in shear, compression and tension design fyb can be derivedfixed fromconnections the grade byand multiplying the first by the In The practice it isyield oftenstress difficult to fabricate some rotation maynumber take place secondthe number times 10. The ultimate is the first number times 100 (stresses between element on one side design of the joint and stress that onfubthe other. Such a joint is known as a in MPa).connection and, strictly speaking is the condition of most joints which are described semi-rigid grade areAused most connection frequently. could be described as one which although only as Bolts being of fixed or 8.8 rigid. moment semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
MRd ≥ Mpl.Rd
is the design moment resistance of the connection MRd 1mm for M12 and M14 bolts Mpl.Rd is the design strength of the beam (full plastic moment). 2mm for M16 to M24 bolts 3mm for M27 and larger bolts. Holes will be formed by drilling or punching. Punching holes in steelwork is much faster than drilling but some cracking may appear in the material and therefore, in some cases, holes will not be punched full size but must be punched 2mm diameter less than full size and then reamed. A = πd2/4 The area of the threaded part that is used in design formulae is called the stress area As: Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity As = πds2 /4 For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
155
The diameter ds are somewhat larger than the diameter of the core, because of the fact that a
The coefficient 0,5 is the result of a statistical evaluation based on a very large number of
rupture plane always includes at least one thread.
test results. It appears that bolts of these grades are less ductile and that the rupture occurs
ds is the mean value between the core diameter (dc) and the flank diameter (df) of the thread;
suddenly. 2. For the shear plane passing through the unthreaded portion of the bolt:
the flank diameter is the mean value between the core diameter and the nominal diameter (d):
Fv,Rd = 0,6 fub A /γ Mb df
dc d
ds
2
df dc
Vsd 300kN
Design shearing force:
2
fub 800MPa
Strength grade of Bolt 8.8:
fvb 640MPa
Resistance to shear for one shear plane: 2
Bolt core area:
As 157mm
Partial safety factor:
Diameters of bolts 0.6 fub As
Mb 1.45
Sabah Shawkat © Fv.Rd
The value of As for common bolt diameters is given in table below: Nominal diameter db (mm)
Nominal area A (mm2)
Stress area As (mm2)
8 10 12 14 16 18 20 22 24 27 30
50,3 78,5 113 154 201 254 314 380 452 573 707
36,6 58,0 84,3 115 157 192 245 303 353 459 561
The design shear resistance of a bolt (FvRd) in normal conditions, per shear plane, is:
FvRd = 0,5 fub As /γMb
for strength grades 4.8, 5.8, 6.8 and 10.9
d 16mm
d0 18mm
Bore diameter:
The thickness of the front plate:
t =12mm
Distances from the ends and edges :
e1 2 d0
e1 36 mm
Force direction: Perpendicular to the direction of force:
e2 1.5 d0
e2 27 mm
Hole spacing: p1 3.5 d0
Force direction
Perpendicular to the direction of force
for strength grades 4.6, 5.6 and 8.8
Fv.Rd 51.972kN
Mb
Bolt diameter:
1. For the shear plane passing through the threaded portion of the bolt: FvRd = 0,6 fub As / γMb
p1 1 fub 1.0 3d0 3 d0 4 fu
e1
min
Fb.Rd
2.5 fu d t
Mb
Connections in steel structures Connections in steel structures
p1 63 mm
p1=3.5 d0
p1 63 mm
0.667
Fb.Rd 79.448 kN
156 132
Connections in Bolts: steel structures Number of Vsd n Joints between structural line elements, inn one plane, may be Iclassified as M16 simple suggest 6x connections, 5.772 min Fv.Rd Fb.Rd as sliding connections, as pin or pinned connections as fixed connections, also known as rigid connections. simple connection allows rotation and movement in any direction except DetermineAthe desired height of face plate: downwards and only transmits shear force that acts downwards at a support. A sliding Aw fy connection element Awof thetw.p dc and rotation and only transmits shear Vpl.Rdallows movement along the line 3 m1 force. A pinned connection allows rotation but no translational movement, it transmits shear
and axial forces but not bending moment. A fixed connection does not allow translational tw.p 12.5mm Wall thickness of steel beam movement or rotation and transmits shear, axial forces, bending and torsional moment. Vsd 3 m1 hc.d hc.d 194.579 mm tw.pfy
Specify the depth of the face plate 220 mm
hcd 210mm
Carrying capacity fillet welds:
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Av.net fy but allow rotation about bending its axis. Note that if pinned or fixed joints are made between 0.653 0.914 A f an element and an immovable support then that end of the element may not move translationally v u or rotate in space, as distinct from a movement which is merely relative to the member on the fy Av.net If side of the joint. Fixednot considering weakening of the effective area of the shear, other joints, or nearly fixed joints, between two members are said to fu Av provide continuity so that there is little or no rotation between the members at the joint and the otherwise members behave as if no joint existed. However, the joint is not necessarily fixed in space and Deal = Not considering weakening the effective area of the shear may rotate about a support for example. A way of characterising the degree of fixity or stiffness
Av fy connection either to a support or another member is to measure the provided by a semi-rigid Vpl.Rd 310.824 kN Vpl.Rd rotation at the joint 3 bending moment on the joint is varied. m1as the Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column Condition "front plate suits" if Vfrom V connection designed to transfer a moment beam pl.Rdthe sd into the column. M-φ curves in general non-linear, for practical it "isotherwise necessary to idealise the M-φ curves. The rotation "Face application, plate does not capacity is a measure of the deformation that can be obtained before failure somewhere in the Condition = front plate satisfies connection causes a drop in the moment resistance.
Sabah Shawkat ©
(connecting the steel beam to the front panel) We suppose the depth of weld
aw 4mm
weld length:
Lw 2 220mm
Factor for adequate strength steel grade:
w
Partial safety factor of welded joints:
Fw.Rd
fu awLw
w
w 3
0.8
w 1.5
Fw.Rd 304.841 kN
For strength, the following classes can be distinguished:
MRd ≤ 0,25 Mpl.Rd
nominally pinned
0,25 Mpl.Rd < MRd < Mpl.Rd
partial-strength
MRd ≥ Mpl.Rd
full-strength
full-strength if rotation capacity is
MRd ≥ 1,2 Mpl.Rd
not checked where MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
Condition
"Weld Pass" if Fw.Rd Vsd Column web in shear, compression and tension "The weld was " otherwise In practice it is often difficult to fabricate fixed connections and some rotation may take place
between the element one side of the joint and that on the other. Such a joint is known as a Condition = Weldon Pass semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed orofrigid. A moment Assessment the face plate onconnection the shear: could be described as one which although only semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending 3 2 Av.net t hcd d0 Av.net 2.304 10 mm moment. Note that connections may be fabricated for particular requirements so that, for
Two layers’ steel shelter structure using circular hollow sections
example, they may allow rotation in the plane of the elements but prevent twisting about the 2 A t hcd Av 2520 mm v axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
157
Single sided beam-to-column joint configuration, bolted end-plate connection
e
2 e 0.05 m
To be evaluated: Design moment resistance, initial stiffness Data 3
2
IPE270
A270 4.59 10 mm
HEB180
Ac 6.53 10 mm
3
2
Material S335
6
4
Iy270 57.9 10 mm 6
4
Iyc 38.3 10 mm M0
bc w
tfc fyc mplfc 0.25 M0
iy270 112 mm
mplfc 16.415 kN
iyc 76.6 mm
1
M1
2
1
4M20 8.8
p 60
u 10 mm
w 80 mm
Sabah Shawkat © Beam:
hc 180 mm
tfc 14 mm
tfc 14 mm
hwc hc 2 tfc 2 rc hwc 0.122 m Avc Ac 2 bc tfc twc 2 rc tfc 2
Avc 2029 mm
0.8 rc 2 m 23.75 mm m
3
Wplyb 484 10 mm
1
twb 6.6 mm
Level arm
twc 8.5 mm
rc 15 mm
z hb u
tfb
w twc
3
bc 180 mm fyc 335 MPa
M0
p 70 mm
tfb 10.2 mm
u 10 mm
fyb 335 MPa
Equivalent T-stub tension Column:
hb 270 mm
McRd
2
p
Wplyb fyb M0
z 0.2049 m
McRd 162.14 m kN
End plate: bp 180 mm
a w 3 mm
af 5 mm
w 80 mm
fyp 335 MPa
mp
w twb 2
0.8 2 aw
Connections in steel structures Connections in steel structures
tp 18 mm
158 132
condition steel beam supports. By contrast the element may be fixed in its plane to transmit Tensionatresistance:
Connections in steel mmstructures mp 33.31
mp2 p u tfb 0.8 2 af Joints between structural line elements, in one plane, may be classified as simple connections, as sliding mp2 connections, 44.14 mm as pin or pinned connections as fixed connections, also known as rigid connections. A simple connection allows rotation and movement in any direction except bp w ep and only transmits shear force that acts downwards at a support. A sliding downwards 2 connection allows movement along the line of the element and rotation and only transmits shear 0.05 m connection allows rotation but no translational movement, it transmits ep A pinned force. shear and axial forces but2 not bending moment. A fixed connection does not allow translational tp fyp mplp or0.25 movement rotation and transmits shear, axial forces, bending and torsional moment. M0
mplp 27.135 kN
or rotate in space, asA distinct from a movement which is merely relative to the member on the 0.6 fub s20 FvRd 94.08 kN FvRd other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to Mb Lb tfc tp so0.5 hthere hnut 4mm Lb 52.4 mm or2 no bolt is provide continuity that little rotation between the members at the joint and the
members behave as if no joint existed. However, the joint is not necessarily fixed in space and Column web ina shear: may rotate about support for example. A way of characterising the degree of fixity or stiffness provided by a semi-rigid connection either to a support or another member is to measure the
rotation at the joint as the bending moment on the joint is varied. 0.9 Avc fycw Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column VwcRd 3 M0 connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for353.19027 practical kN application, it is necessary to idealise the M-φ curves. The rotation VwcRd
Alpha factor for effective lengths mp
bending but allow 0.9 fubrotation As20 about its axis. Note that if pinned or fixed joints are made between F 141.12 kN FtRd an element and an immovable supporttRd then that end of the element may not move translationally Mb
capacity is a measure of the deformation that can be obtained before failure somewhere in the Assumption 1 connection causes a drop in the moment resistance. VwcRd FRd1 the following classes can be distinguished: For strength,
Sabah Shawkat ©
1
1
0.3998
mp ep
nominally FRd1 pinned 353.19027 kN partial-strength Stiffness coefficient
mp2
2
2
0.52989
MRd ≤ 0,25 Mpl.Rd
0,25 Mpl.Rd < MRd < Mpl.Rd
full-strength z 204.9 mm h z full-strength if rotation capacity is
mp ep
MRd ≥ Mpl.Rd
h 204.9 mm not checked MRd ≥ 1,2 Mpl.Rd 0.38 Avc where k1 k1 3.76 mm h is the design moment resistance of the connection MRd
Mpl.Rd Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place
Bolts:the element on one side of the joint and that on the other. Such a joint is known as a between 2
fub connection 800 MPa and, Astrictly 245 mm is the condition Mb of1.25 tfc are 14 described mm semi-rigid most joints which s20 speaking as being fixed or rigid. A moment connection could be described as one which although only tp 18 mm h hnut 14.8 mm bolt 10 mm semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending
moment. Note that connections may be fabricated for particular requirements so that, for
example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
is the design strength of the beam (full plastic moment).
Component N2-Column web in compression Resistance: tfb 0.0102 m
af 0.005 m
tp 0.018 m
tfc 0.014 m
s 12 mm
u 0.01 m
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity
For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
159
beffcwc
mintfb 2 af 2 2 tp 5 tfc s
tfb 2 af 2 2 tp 5 tfc s 0.19034 m
1
tfb af 2 tp u 5 tfc s 0.17527 m
beffcwc tfb af 2 tp u 5 tfc s
beffcwc 0.17527 m
1 twc 1 1.3 befftwc A vc
FRd3 befftwc twc
Reduction factors to account for compression stresses and instability fywc 335 MPa
dc 92 mm 2
Avc 2029 mm
twc 0.0085 m
E 210 GPa
kwc
p 0.932
beffcwc 0.17527 m
kwc 1
M1
1
1
0.7 befftwc twc
twc 1 1.3 beffcwc A vc
2
0.55611
0.76677
p
1
0.673
1
1
0.7 beffcwc twc
in this example only bolt row 1 is considered for tension forces lefftfc befftwc n
fywc
lefftfc 0.1575 m
see column web in tension
bp w
bp w
2
2
mine 1.25 m
FRd2 382.68231 kN
M1
n
e 0.05 m
0.05 m
bp w 2
1.25 m 0.02969 m
n 0.05 m
Component N4-Column flange in bending Model1 Complete yielding of the flange k2 8.55 mm
Fi
k1 E i
lefftfc 0.1575 m
FfcRdt1
Component N3 - column web in tension m 0.02375 m
e 0.05 m
fywc 335 MPa
twc 0.0085 m
m
Resistance: min( 2 m 4 m 1.25 e)
4 lefftfc mplfc
FfcRdt1 435.43 kN
befftwc
Component N5-End plate in bending
Bolt rows considered
0.76677
Stiffness coefficient
3.14159
k3 7.68 mm
hwc
Sabah Shawkat © Etwc
p
Column web in compression:
FRd3 343.88 kN
M0
Component N4-Column flange in bending
1
hwc
fywc
2
FRd2 kwc beffcwc twc
k2
0.79912
1
2
Stiffness coefficient k3
beffcwc dc fywc
befftwc 0.1575 m
comRd min 1.0 1.7 fzwc
befftwc 4 m 1.25 e
4 m 1.25 e 0.1575 m
2 m 0.14923 m
Connections in steel structures Connections in steel structures
160 132
Connections steel structures Mode2 boltinfailure with yielding of the flange
BtRd 141.1 kN Joints between structural line elements, in one plane, may be classified as simple connections, 2 lefftfc m 2 pinned BtRd n connections as fixed connections, also known as rigid as sliding connections, asplfc pin or FfcRdt2 FfcRdt2 261.43356 kN m n connections. A simple connection allows rotation and movement in any direction except
downwards andfailure only transmits shear force that acts downwards at a support. A sliding Mode 3 bolt
connection allows movement along the line of the element and rotation and only transmits shear FfcRdt3 2 BtRd FfcRdt3 282.2 kN force. A pinned connection allows rotation but no translational movement, it transmits shear
N4but column flange inmoment. bending A fixed connection does not allow translational andComponent axial forces not bending
movement or rotation and transmits shear, axial forces, bending and torsional moment. Resistance:
min FfcRd1 FfcRd2 FfcRd3
FRd4
FRd4 FfcRdt2
FRd4 261.43356 kN
Stiffness coefficient
or rotate in space, as distinct from a movement which is merely relative to the member on the McRd k1 are said to FRd7 otherFRd7 sideof the joint. Fixed joints, or 624.1 nearlykN fixedStiffness joints, coefficient between two members hb tfb provide continuity so that there is little or no rotation between the members at the joint and the Component N8as -Beam tensionHowever, the joint is not necessarily fixed in space and members behave if noweb jointinexisted.
mayResistance rotate about a support for example. A way of characterising the degree of fixity or stiffness lefftwbby alefftp mmor another member is to measure the provided semi-rigid connectionlefftwb either to 203.17 a support rotation at the joint as the bending moment on the joint is varied. fyb Stiffness coefficient kN k8 FRd8 lefftwb twb the strength, Fstiffness Rd8 449.2 Figure bellow defines and deformation capacity of a beam-to-column M0
connection designed to transfer a moment from the beam into the column. M-φ curves in general Component tension it is necessary to idealise the M-φ curves. The rotation 10-Bolts in non-linear, for Npractical application,
0.9 lefftfc tfc
k4 29.03 mm
Sabah Shawkat ©
lefftp
m
3
min 2 mp mp
mp lefftp
Model1
2 mp 0.20927 m
lefftp 0.20317 m
1.25 mp 0.04163 m
an Resistance element and an immovable support then that end of the element may not move translationally
capacity is a measure of the deformation that can be obtained before failure somewhere in the Resistance: connection causes a drop in the moment resistance. FRd10 2 BtRd FRd10 282.2 kN Lb 47.4 mm For strength, the following classes can be distinguished:
3
k4
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Component N7-Beam flange and web in compression bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
e 0.05 m
FepRd1
FepRd2
np
mp
0.20317 m
min ep 1.25 mp e
np 1.25 mp
ep 0.05 m
np 0.04163 m
Stiffness coefficient partial-strength
not checked Relevant component
4 lefftp mplp
FepRd1 662.09 kN
mp 2 lefftp mplp 2 BtRd np
FepRd2 303.91 kN mp np Column web in shear, compression and tension FRd5 itmin FepRd1 FepRd2 FepRd3 fixed connections FepRd1 662.09 kN may take place In practice is often difficult to fabricate andsome rotation Model2
MRd ≤ 0,25 Mpl.Rd As20 k0,25 10 M1.6 pl.Rd < MRd < Mpl.Rd k10 8.27 mm Lb full-strength MRd ≥ Mpl.Rd Design moment resistance: full-strength if rotation capacity is
nominally pinned
between theelement thejoint and that onFthe other. Such a joint is known as a 303.91 on kN one side of FRd5 FepRd2 FepRd2 Rd5 303.91 kN semi-rigid connection and, strictly speaking is the condition of most joints which are described N5-rigid. End plate in bending as Component being fixed or A moment connection could be described as one which although only
Design plastic moment resistance M jRd FRd z MjRd 53.57 m kN Design plastic moment resistance
MjelRd
semi-rigid Stiffnessapproaches coefficient the behaviour of a fixed connection and transfers a substantial bending
FRd FRd4
moment. Note that connections may be fabricated for particular requirements so that, for 3 0.9 lefftp tp example, the plane k5 they may allow rotation k5 in 28.86 mm of the elements but prevent twisting about the 3 m axis of the element thus allowing torsional moments to be transmitted. This is a common p
MRd ≥ 1,2 Mpl.Rd
where FRd4 261.43 kN FRd4 FfcRdt2 FfcRdt2 261.43 kN is the design moment resistance of the connection MRd Column flange in bending kNdesign strength FRd 261.43 Mpl.Rd is the of the beam (full plastic moment).
2 3
MjRd
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity MjelRd 35.71 m kN For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
161
Stiffnes
E 210 GPa
Initial stiffness
k1 3.76 mm
k2 8.55 mm
k4 29.03 mm k5 28.86 mm
Calculate the resistance of the joint shown in the adjacent figure. The joint is subject to a shear
h 0.2049 m
force Vsd. The primary beam is of WI800-15-20x300 and the secondary beam of WI700-1015x250, both of S355J2G3 grade. Angle sections L100x10 of S355J0 grade and bolts of M20
k3 7.68 mm
8.8 are to be used in the joint. Vsd 700 kN
k10 8.27 mm
e1 60 mm e2 50 mm
d0 22 mm
p1 70 mm P2 70 mm
E h
Sjini
1 k1
1 k2
1 k3
2
1 k4
1 k5
1
hprimary 800 mm
Sjini 12542.72 m kN
Sj
Sjini
tfprimary 20 mm
Twprimary 10 mm
tp 8 mm
t 15 mm
d 20 mm
a1 50 mm
a2 50 mm
a3 105 mm
hp 600 mm
fub 800 MPa fu 510 MPa
fy 355 MPa
M0
1.1
2
Sj 6271.36 m kN
k 0.5
n 6
Sabah Shawkat ©
Secant stiffness
bprimary 300 mm
hsecondary 700 mm bsecondary 250 mm tfsecondary 15 mm twsecondary 10 mm
k10
e 65 mm
because the bolts are in one row.
fu
Is the ultimate tensile strength of the relevant part.
t
Is the thickness of the relevant part
Connections in steel structures Connections in steel structures
Mb
1.25
162 132
Connections in steel structures Primary beam - angle section:
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
Shear resistance of the bolts
maxor ( 12tfixed 150mm ) bending but allow rotation about its axis. Note thateif pinned joints are made between 1max
Joints between structural line elements, in one plane, may be classified Vsdas simple connections, 2 FvRd 120.6 kN FvRd As 245 mm as sliding connections, as pin or pinned connections as fixed connections, 10 also known as rigid
1.2 d 0 an element and an immovable support then that end eof1min the element may not move translationally
connections. A simple connection allows rotation and movement in any direction except (kN) force that acts downwards at a support. A sliding Shear resistance of atransmits bolt FvRd shear downwards and only Bolt M16 and M20 M24 M30 connection allows movement along the line of the elementM12 and rotation only transmits shear
other side of the joint. Fixed joints, or nearly fixedp joints,3.0between two members are said to d0 1min
2
stress area (mm allows ) 84,3 movement, 157 245 it transmits 353 561 force.Tensile A pinned connection rotation but no translational shear Shear resistance F per shear plane if the grade vRd and axial forces but not bending moment. A fixed connection does not allow translational shear or plan passes theshear, threaded 8.8 bending 32,4 and 60,3torsional 94,1 moment. 135,6 215,4 movement rotation andthrough transmits axial forces, portion of the bolt 10.9 33,7 62,8 98,0 141,2 224,4 Cross-section area of the unthreaded shank (mm)
113
201
314
452
707
shear plane passes through the unthreaded 8.8
43,4
77,2
120,6 173,7
271,4
shank of the bolt
45,2
90,4
125,7 181,0
282,8
Shear resistant FvRd per shear plane if the grade 10.9
e
1.5 d
e2max
max( 12t 150mm)
0 2min or rotate in space, as distinct from a movement which is merely relative to the member on the
p 1max min(the 14t 200mm ) provide continuity so that there is little or no rotation between members at the joint and the e3min 1.5 d 0 members behave as if no joint existed. However, the joint is not necessarily fixed in space and p 2max
min( 14t 200mm)
may rotate about a support for example. A way of characterising the degree of fixity or stiffness e4
1.5 d 0
provided bythe a semi-rigid either to a support or another member is to measure the Key to symbols ofconnection the bolt distances is varied. the diameter of the bolt hole d 0 is rotation at the joint as the bending moment on the joint and spacing F shows the direction of the force Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column t is lesser of the thicknesses of the connection designed to transfer a moment from the beam into the column. M-φ curves in general connected parts non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the Minimum and recommended bolt distances and spacing: connection causes a drop in the moment resistance. e2 p1 p2 e1 Bolt Hole do For strength, the following classes can be distinguished: (mm) (mm) (mm) (mm) (mm) nominally pinned MRd ≤ 0,25 Mpl.Rd d minim. rec. minim. rec. minim. rec. minim. rec. o (mm) <M <M partial-strength 0,25 M
Sabah Shawkat ©
Normally, high-strength bolts of 8.8 and 10.9 grades are used. Those of 8.8 grades can be
considered as basic grade bolts. There are still other grades, but they are not normally in use. The ultimate tensile strength and the yield strength are obtained as follows: 2
2
Ultimate tensile strength: fub = 10 * 100 N/mm = 1000 N/ mm
fyb = 1000 * 0.9 N/mm2 = 900 N/mm2
Yield strength:
pl.Rd
Rd
pl.Rd
M12 13 16 30 full-strength M16 if rotation 18 22 full-strength capacity is 40
20MRd ≥ M 25pl.Rd 27 30
M20 not checked whereM24
80
78
80
33the design 40moment 75resistance 50 of the 60 73 is connection
100
99
100
M30
22
27
50
26
32
60
29
40
39
40
40
55
54
55
33 40Mpl.Rd 49 MRd ≥ 1,2 39 50 58
70
66
70
The recommended bolt sizes are M12, M16, M20, and M30. Intermediate sizes (M14, M22
MRd
and M27) exist according to strands, but they may not be available. These are bolts of a size
Mpl.Rd is the design strength of the beam (full plastic moment). Angle section:
larger than M30 (e.g. M36), but they are to be avoided, because smaller bolts cab be handled Column web in shear, compression and tension more easily and faster on site. In practice it is often difficult to fabricate fixed connections and some rotation may take place The grades of nuts must correspond with the grades of the bolts. The nut grades between the element on one side of the joint and that on the other. Such a joint is known as a corresponding to high-strength bolts are 8 and 10. semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only Positioning bolts semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending Bearing resistance shall be calculated as follows: moment. Note that connections may be fabricated for particular requirements so that, for 2.5 fu d t FbRd they may allow rotation example, in the plane of the elements but prevent twisting about the
Mb
axis of the element thus allowing torsional moments to be transmitted. This is a common
e1
min
p1
3 d0 3 d0
fub fu p1 3 d0
1 4
1 fub 1.0 4 fu
1.56863
0.81061
e1
d0
2.72727
1
Moment-rotation of a semi-rigid joint with enough plastic rotation fu d tp Vsd capacity 2.5 characteristic FbRd FbRd 132.29091 kN FbRd OK is as follows: For stiffness, the classification 10 Mb
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
163
Web of the beam:
p1
min
3 d0
p1
3 d0
FbRd
1 fub 1.0 4 fu
1
4
Connection in double shear
fub
fu
1
2.5 fu d t 2 Mb
FbRd
0.81061
2.5 fu d t
Mb
Secondary Beam - angle section:
2
2
Ip
2
x1 120 mm
z 200 mm
Ip 2 x x1 z
2
112000mm
0.81061
fub
e1
3 d0
fu
1
0.90909
FvRd 2 FvRd
2
Avnet hp n d0 t
fy 2 Av 6264.70588 mm fu
FbSd 142.17128 kN
FvRd 241.2 kN
FbRd 278.18182 kN
Av 9000 mm
Av hp t
2 Vsd z Msd Ip 6
FbRd
Vsd 10
OK
2
Avnet 7020 mm
fy Av fu
Avnet
The holes do not reduce the shear resistance:
FvRd FbSd
Bearing resistance: Distance e1 is calculated in the direction of the force resultant FbSd. It is, however, possible to use the smallest of the edge distances:
fy 1 3 M0
VplRd Av
VplRd 1676.9401 kN
VplRd Vsd
The tension resistance of a bolt-plate assembly, BtRd, shall be taken as the smaller of the tension resistance of the bolt and the punching shear resistance of the bolt head and the nut. The tension
Angle section:
resistance of a bolt shall be calculated as follows:
p1 1 fub 1.0 3 d0 3 d0 4 fu
e1
min
1.56863
4
Shear resistance of the angle sections:
Shear resistance of the bolts - connection in double shear:
1
Sabah Shawkat © Msd 45.5 m kN
2
p1 3 d0
2.5 fu d t Mb
Shear force resultant: FbSd
e1 p1 1 fub 1.0 3 d0 3 d0 4 fu
min
FbRd
Moment due to eccentricity Msd Vsd e
OK
Web of the beam:
FbRd 248.04545 kN
x 40 mm
Vsd 2 10
FbRd
FbRd 556.36364 kN
Vsd 2 140kN 10
OK
10
0.81061
Vsd
FbRd
p1 3 d0
1 4
1.56863
fub
0.90909
fu
FtRd
0.9
fub
Mb
As
Connections in steel structures Connections in steel structures
164 132
Connections in steel structures Tension resistance of a bolt FtRd:
fixed its plane transmit condition at steel beam supports. By calculated contrast theusing element may be The values in this table have been the basic value in in EC3, Mb = to 1,25,
Bolt M12 M16 M20 M24 M30 Joints between structural line elements, in one plane, may be classified as simple connections, Grade 8.8 48,6 90,4 141,1 203,3 323,1 as sliding connections, as pin or pinned connections as fixed connections, also known as rigid Grade 10.9 60,7 113,0 176,4 254,2 403,9 connections. A simple connection allows rotation and movement in any direction except The values in this table have been calculated using the basic value in EC3, Mb = 1,25. downwards and only transmits shear force that acts downwards at a support. A sliding
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between M2 = 1,25 an element and an immovable support then that end of the element may not move translationally
The punching resistance ofthe theline boltofhead and the nut be calculated as follows: connection allowsshear movement along the element andshall rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear fu 0.6 but dmnot tp bending moment. A fixed connection does not allow translational and Baxial pRd forces Mb movement or rotation and transmits shear, axial forces, bending and torsional moment.
the bolt is subject to bothfrom sheara and tensionwhich force the following provision holdon true: or If rotate in space, as distinct movement is merely relative to theshall member the other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to Fvsd Ftsd 1there is little or no rotation between the members at the joint and the provide continuity so that FvRd 1.4 FtRd members behave as if no joint existed. However, the joint is not necessarily fixed in space and may rotate about a support for example. A way of characterising the degree of fixity or stiffness
Resistance the end ofconnection the secondary beam: provided by aof semi-rigid either to a support or another member is to measure the rotation at the joint as the bending moment on the joint is varied.
Bending moment in section I-I: stiffness and deformation capacity of a beam-to-column Figure bellow defines the strength,
Where tp
is the thickness of the plate under the bolt head or the nut
dm
is the smaller of the following values:
connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation bprimary M 10 mm MIsd 112 m kN Isd Vsd 2 capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © the mean of the across points dimension and across flats dimension of the bolt head. The mean of the across points dimension and across flats dimension of the nut.
8,8
10,9
8,8
10,9
M20 8,8
M24
full-strength if rotation capacity is fy MelRd 210.031 m kN MelRd WTel Mpl.Rd MelRd MIsd not checked MRd ≥ 1,2
10,9
8,8
10,9
M30 8,8
M0
where
10,9
6 7 in shear, 9 9 10and tension 11 13 13 16 Column web compression S275 4 5 6 8 8 9 9 11 11 13 In practice it is often difficult to fabricate fixed connections and some rotation may take place S235
3
partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd Bending resistance in section I-I full-strength MRd ≥ Mpl.Rd
Limit thickness (mm) for the punching shear resistance of the bolt head or the nut M16
3
WTel 650.8 10 mm
MRd ≤ 0,25 Mpl.Rd
nominally pinned
The punching shear resistance of the bolt head determines the tension resistance, if the 1.5 fub As M2 following condition holds true: tp dm fu Mb
M12
connection causes a drop in the moment resistance. 2 4 4 AT 8070 mm IT 25963.1 10 mm For strength, the following classes can be distinguished:
5
S335the element 4 6 and 6that on the 8 other.8Such a 9joint is known 9 between on5one side5of the joint as11a S275N 5 6 7 8 8 10 10 12 12 15 semi-rigid connection and, strictly speaking is the condition of most joints which are described S355N 4 rigid. A 5 moment 5 connection 7 7 be described 8 8 one which 10 although 10 12 as being fixed or could as only
OK
is theindesign resistance of the connection MRd Shear resistance sectionmoment I-I: Mpl.Rd is the design strength of the beam (full plastic moment). AIv hsecondary 2tfsecondary 30 mm twsecondary
fy 1 3 M0
VplRd AIv
2
AIv 6400 mm
VplRd 1192.49074 kN
VplRd Vsd
Combined bending and shear resistance in section I-I:
S420N approaches 4 5 behaviour 5 of a6fixed connection 6 7 and transfers 7 9 9 bending 11 semi-rigid the a substantial S355MNote 4that connections 5 6 may be7 fabricated 7 for particular 8 8 requirements 10 10 that, for 12 moment. so S420Mthey may 4 allow 5 rotation 5 in the 7plane of7the elements 8 12 example, but8 prevent10twisting9 about the
4 5 allowing 5 torsional 6 moments 6 7 9This is a9 common 11 axisS460M of the element thus to7be transmitted.
Vsd 0.5 VplRd 0.5 VplRd 596.24537 kN Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity
For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
165
The shear force reduces the bending resistance The simplified method is used (reduced strength is used for the whole profile)
2
Vsd
VplRd
Lveff hp 2 a1 L1 L2
2
1
fu hp 2 a1 a1 a3 n d0 0.75135 m fy
0.03028
fy 1 3 M0
VeffRd twsecondary Lveff
MIsd 112 m kN
MelVRd MelRd ( 1 )
MelVRd 203.67104 m kN
Lveff 606.02817 mm VeffRd 1129.19215 kN
Lveff L3 VeffRd Vsd
Some typical connections are illustrated in figure below. Bolts and welds in connections should
MelVRd MIsd
be able to resist the beam reaction and any relevant moment due to the eccentricity of the force to the centre line of the connecting components.
Shear resistance in the force crossing the holes: AIvnet hsecondary 2tfsecondary 30 mm n d0 twsecondary 2
Sabah Shawkat ©
A 5080 mm Ivnet
fy AIv fu
AIvnet
fy 2 AIv 4454.90196 mm fu
The holes do not reduce the shear resistance. The shear resistance has already been calculated in section I-I.
Shear rupture resistance of the beam end: d0 0.022 m
d 0.02m L1 a1
L1 50 mm
fu fy
L2 a2 k d0
L2 56.03 mm
L3 hp 2 a1 a1 a3
L3 655 mm
L1 5 d
5 d 0.1 m
Some typical connections beam – to - beam joints
fu L3 hp 2 a1 a1 a3 n d0 f y
Connections in steel structures Connections in steel structures
166 132
Connections in steel structures
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints between structural line elements, in one plane, may be classified as simple connections,
an element and an immovable support then that end of the element may not move translationally
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid
or rotate in space, as distinct from a movement which is merely relative to the member on the
connections. A simple connection allows rotation and movement in any direction except
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
downwards and only transmits shear force that acts downwards at a support. A sliding
provide continuity so that there is little or no rotation between the members at the joint and the
connection allows movement along the line of the element and rotation and only transmits shear
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A pinned connection allows rotation but no translational movement, it transmits shear
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
and axial forces but not bending moment. A fixed connection does not allow translational
provided by a semi-rigid connection either to a support or another member is to measure the
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © connection causes a drop in the moment resistance.
For strength, the following classes can be distinguished:
MRd ≤ 0,25 Mpl.Rd
nominally pinned partial-strength
0,25 Mpl.Rd < MRd < Mpl.Rd
MRd ≥ Mpl.Rd
full-strength
full-strength if rotation capacity is
MRd ≥ 1,2 Mpl.Rd
not checked where MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the bolt distances spacings This is a common axis of the element thus Incorrect allowing production torsional moments to beand transmitted.
Realizationsofbalcony familyjoint home using I steel profiles Moment-rotation characteristic a semi-rigid with enough plastic rotation capacity For stiffness, the classification is as follows:
Connections Connectionsininsteel steelstructures structures Connections Connectionsininsteel steelstructures structures
167
on the basis of tension resistance, shear resistance and the combined tension and shear
Joint to the foundation The foundation of a building shall be designed to carry the working load with adequate factor of safety. Dead load, imposed load and wind load should be assessed in accordance with the Building (Construction) Regulations and the relevant codes of practice.
resistance. In some cases, the situation under the erection period may be the critical load case. in this case, the holding-down bolts are chosen on the basis of buckling resistance. A column base connection always consists of a plate welded to the foot of the column and
The allowable capacity of the soil/rock under working loads where any foundation is founded
bolted down to the foundations. A second, usually rather thicker, steel plate is normally
shall be the lesser of:
incorporated into the top of the foundation, as illustrated in figure below. It helps both to locate
(a) the ultimate capacity for bearing, bond or friction with an adequate factor of safety against
the foot of the column accurately and in spreading the load into the weaker (concrete or
failure; or
masonry) foundation material.
(b) the value in relation to bearing, bond or friction such that the maximum deformation or movement induced to the foundation under working loads can be tolerated by the building, any other building, structure, land, street and services A welded column is normally joined to the foundation by using holding-down bolts. It may be necessary to strengthen the base of the column. The thickness of the base plate may be reduced by using stiffeners. However, it is often more economical to make the base plate thicker and
Sabah Shawkat ©
abandon the stiffeners. A dowel profile welded on the under-side of the base plate is designed
to carry the shear force either in one or both directions with reference to the principal axes. in
this case, the holding-down bolts can be designed for tension or compression (buckling
Some column joints to the foundation
resistance) applied under the erection period only. in order to get the bearing pressure more
evenly distributed on the foundation, it is possible to use stiffening. This method of strengthening is used in heavily loaded hollow section columns.
Joint of an axially loaded column to the foundation
In the case of an axially loaded column, the resistance of the foundation against bearing pressure due to axial force must be checked. The bearing pressure gives rise to a bending moment in the
base plate, the value of which determines the size of the base plate as follows: tp
A welded column- joined to the foundation or to the RC slab by using holding-down bolts.
6 Msd M0 beff fy
Where
Msd
is the bending moment applied to the base plate
beff
is the effective width of the base plate
fy
is the yield strength of the base plate
The design of the holding-down bolts and foundation must comprise different load cases to be checked. In order to determine the resistance of the foundation, the load case causing the highest bearing pressure on the foundation has to be ascertained. The holding-down bolts are chosen
Connections in steel structures Connections in steel structures
168 132
Connections in steel structures
be fixed in strength its plane of to the transmit condition By contrast element maycompressive is =beam fck / supports. γc is the design value the of the cylinder fcd at steel
Joints between structural line elements, in one plane, may be classified as simple connections,
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between concrete an element and an immovable support then that end of the element may not move translationally is the characteristic cylinder compressive strength of the concrete fck or rotate in space, as distinct from a movement which is merely relative to the member on the
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid connections. A simple connection allows rotation and movement in any direction except downwards and only transmits shear force that acts downwards at a support. A sliding connection allows movement along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear and axial forces but not bending moment. A fixed connection does not allow translational movement or rotation and transmits shear, axial forces, bending and torsional moment.
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to The bearing area under the base plate. The width of the effective area is obtained as provide continuity so that there is little or no rotation between the members at the joint and the follows: members behave as if no joint existed. However, the joint is not necessarily fixed in space and may rotate about a support for example. A way of characterising the degree of fixity or stiffness fy c tpby a semi-rigid connection either to a support or another member is to measure the provided 3 fj M0 rotation at the joint as the bending moment on the joint is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © b b c c 1 3 1 1 c1 b b c 1 1 1
connection causes a drop in the moment resistance.
For strength, the following classes can be distinguished:
MRd ≤ 0,25 Mpl.Rd
nominally pinned
The design bearing strength of the foundation is obtained as follows:
fj
partial-strength
0,25 Mpl.Rd < MRd < Mpl.Rd
MRd ≥ Mpl.Rd
full-strength
full-strength if rotation capacity is
Bjkj fcd
MRd ≥ 1,2 Mpl.Rd
not checked where
where
c
MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
is the partial safety factor for concrete Column web in shear, compression and tension
In practice it is often difficult to fabricate fixed connections and some rotation may take place is 2/3 provided that the characteristic strength of the grout is not less than 0,2 Bj between the element on one side of the joint and that on the other. Such a joint is known as a times the characteristic strength of the concrete foundation and the thickness of semi-rigid connection and, strictly speaking is the condition of most joints which are described the grout is not greater than 0,2 times the smallest width of the steel base plate as being fixed or rigid. A moment connection could be described as one which although only semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending is a concentration factor, kj = 1 as a conservative default value (for more exact kj moment. Note that connections may be fabricated for particular requirements so that, for calculation refer to in EC3) example, they may allow rotation the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Area in compression under base plate
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
169
Incorrectly anchoring the baseplate to the foundation
Sabah Shawkat © Anchoring the steel plate into the reinforced concrete foundation-hinged connection
Incorrectly anchoring the baseplate to the foundation where the bolts is missing
Baseplate connections in simple construction are generally modelled as pins, and designed to transfer either concentric force (compression or tension) or a combination of axial and shear force (usually when the column is part of the bracing system). In some instances, they may, however, be designed to transmit also bending moments due to moderate load eccentricity, or for erection stability. The plate is always attached to the column by means of fillet welds. However, if the column carries only compression loads, direct bearing may be assumed, provided that the contact
Baseplate connection is generally modelled as pin
surfaces are machined or can be considered to be flat. No verification of the welds is then required. Machining may be omitted if loads are relatively small. Where there are moderate tension forces or no net tension the holding down bolts are usually cast into the foundation.
When tensile forces are significant, it is necessary to provide appropriate anchorage to the bolts. For example, threaded bolts may be used in conjunction with channel sections embedded in the concrete.
Connections in steel structures Connections in steel structures
170 132
In tensioninconnections the baseplate thickness is often dictated by the bending moments Connections steel structures
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
produced by the holding down bolts. The bending moments may require the use of stiffeners.
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints between structural line elements, in one plane, may be classified as simple connections,
an element and an immovable support then that end of the element may not move translationally
as Joint sliding as pintoor pinned connections as fixed connections, also known as rigid ofconnections, a beam - column foundation
or rotate in space, as distinct from a movement which is merely relative to the member on the
connections. connection allows rotation movement direction except In the joint A of asimple beam-column to the foundation the and tension resistanceinofany the holding-down bolts downwards and onlyin transmits force thatofacts downwards at and a support. A sliding has to be checked addition toshear the resistance the steel base plate the foundation if the
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
connection allowsbolts movement alongtothe line offorce. the element and rotation andofonly transmits shear holding-down are subject tensile in addition, the effect the shear force has to force. A pinned connection allows rotation but no translational movement, it transmits be taken account of. the thickness of the base plate has to be determined with respectshear to both
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
andcompression axial forcesand buttension not bending sides. moment. A fixed connection does not allow translational movement or rotation and transmits shear, axial forces, bending torsionalfigure moment. the following equilibrium equations are obtained according to and the adjacent for the doubly
provided by a semi-rigid connection either to a support or another member is to measure the
Nc Ns
rotation at the joint as the bending moment on the joint is varied.
connection designed to transfer a moment from the beam into the column. M-φ curves in general
beff yfj As fyb
Msd Nsd 0.5 ap ap d
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column
symmetric I-profile located centrally with respect to the steel base plate: Nsd
provide continuity so that there is little or no rotation between the members at the joint and the
non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation
Nc ( d 0.5 y)
capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat ©
From the later equation, it is possible to calculate the depth of the concrete section in compression:
P
beff yfj ( d 0.5 y)
partial-strength
fBB full-strength
0.5 beff fj y beff fj dy Msd Nsd d 0.5 ap 2
beff fj d
beff fj d 2 2 beff fj Msd Nsd d 0.5 ap
tw
V S
V
VBB
P b a1
2 b e
2
1 VBB MRd 2
W BB
≤ 0,25 Mpl.Rd
0,25 Mpl.Rd 2 < MRd < Mpl.Rd
2
P a1 b 6
M BB
fAA
P a b 1 3 a e
2
ecpl.Rd MeRdR ≥ M
b ep
2
6
fBB
0.5 b 1
36 EI
3
36 EI K b c L0
p p full-strength if rotation capacity is K represent the modulus of elasticity of the soil not checked MRd ≥ 1,2 Mpl.Rd
tf
6 Mbb b ea
10
2
24 e
where
beff fj where beff is the effective width of the steel base on the compression side. e1 e2
N
nominallyaxb pinned
Msd Nsd d 0.5 ap
y
connection causes a drop in the moment resistance. we calculate the pressure on the foundation For strength, the following classes can be distinguished: a
MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
F
e 1 mm e Column web in0.75 shear, 0.75and 2 atension h w 0.75 lweld a 2 2 a compression I 2 2 e1 e2 In practice it is often difficult to fabricate fixed connections and some rotation may take place
a
a
verification of welded jointcolumn between the element on one sidefoundation of the jointvsand that on the other. Such a joint is known as a N M h is the condition semi-rigid connection and, strictly speaking most joints which are described of e 1.18 e I a 2 l1 a1 1connection 2 h I 2 t fcould a 2 l2 be as being fixed or rigid. hAI moment described as one which although only 2 2 semi-rigid approaches the jointbehaviour of aweb fixed connection and transfers a substantial bending verification of welded column
moment. Note that connections may be fabricated for particular requirements so that, for 2 2 N T 1 1.4 1.8 prevent 0.8 1 twisting allow e plane of the elements but example, they may rotation in the about the I a a 2 I3 a3 3 axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows: Joint of column to foundation
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
171
Calculates the efforts in the plates fixed at the foundation
Definitions
Where
Allowable load. The maximum load that may be applied safely to a foundation after taking into
F is normal force
account its ultimate bearing capacity, negative skin friction, pile spacing, overall bearing capacity of the ground below the foundation and allowable settlement.
M is bending moment b is width of the plates
Allowable bearing pressure. The maximum allowable bearing pressure that may be applied at
h dimension to the massive subjected to M and F
the base of the foundation, taking into account the ultimate bearing capacity of the soil or rock,
Ar is total resistance section
h´3 3( L h ) h´2 6m A L h´ 6m A L h r b r b Calculate the compression stress of the concrete
the amount and kind of settlement expected and the ability of the structure to accommodate 0
such settlement. The allowable bearing pressure is a combined function of the site conditions, including all construction in the vicinity, and the characteristics of the proposed foundation/structure.
2 F L
c
b h´ h
F L
h´
h´ h´ b h 3 2 c 1
3
Sabah Shawkat ©
Calculate the tension stress h´ b h N 3 a Ar h´ h 3
Verification of the plates of the column 1. next case A's position with ya = b/2
ep
4 F
a 2 a b a YA b 2. Case position B
ep
4 F
a 2 a b a YB b YB
The ground plan of the foundation made of steel profiles
Connections in steel structures Connections in steel structures
172 132
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit Column-to –Foundation connections
Connections in steel structures
Joints between structural line elements, in one plane, may be classified as simple connections, as sliding connections, as pin or pinned connections as fixed connections, also known as rigid connections. A simple connection allows rotation and movement in any direction except downwards and only transmits shear force that acts downwards at a support. A sliding connection allows movement along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear and axial forces but not bending moment. A fixed connection does not allow translational movement or rotation and transmits shear, axial forces, bending and torsional moment.
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between if a rigid column-to-foundation is assumed in the structural model the moments transferred into an element and an immovable support then that end of the element may not move translationally the foundation by the column must be accounted for when designing the holding down bolts or rotate in space, as distinct from a movement which is merely relative to the member on the and the base plate. If a pinned joint is assumed in the model, moments need not be taken into other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to account. provide continuity so that there is little or no rotation between the members at the joint and the The holding down mustexisted. be designed such the thatjoint theyisarenot able to carry the construction loads members behave as ifbolts no joint However, necessarily fixed in space and therotate column is subjected thickness of the stage concrete layer takenorinto account may about a supportto. forThe example. A way of second characterising the degree ofisfixity stiffness when calculating the buckling length for the design of the holding down bolts. provided by a semi-rigid connection either to a support or another member is to measure the rotation at the jointinasthe themodel bending moment on the joint is varied. Column design building Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column Design the columns in a primary frames. The column-to-foundation is in this case assumed connection designed to transfer a moment from the beam into the column. M-φ curves in general rigid. The moment transferred from the column to the foundation must thus be taken into non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation account when designing the connection. The horizontal loads on the building are carried by the capacity is a measure of the deformation that can be obtained before failure somewhere in the bracing lattices, so the column are supported by the hinges at the upper end. The buckling length connection causes a drop in the moment resistance. of the columns can thus be obtained directly, given Lcy = 0,7 Lc. For strength, the following classes can be distinguished:
Sabah Shawkat © MRd ≤ 0,25 Mpl.Rd
nominally pinned
partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd Calculate the resistance of the foundation joint shown in the adjacent figure. The profile of the full-strength MRd ≥ Mpl.Rd column is WI700-15-20x400. Both the column and base plate material is S355J2G3 grade full-strength if rotation capacity is steel. not checked MRd ≥ 1,2 Mpl.Rd af 6 mm tw 15 mm aw 4 mm Mw 1.25 h 700 mm where MRd is the design the connection fck 30 MPa tf moment 20 mm resistance M0 of 1.1 fu 510 MPa Mpl.Rd is the design strength of the beam (full plastic moment). Loading
Column web in shear, compression and tension
N sd 950 kN
Msd 610 kN m
Vsd 250 kN
w
c
0.9
1.5
In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only
Cross-section parameters: 6
4
Iy 2209.0 10 mm
3
3
2
Wely 6312.9 10 mm A 25900 mm
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may fabricated particular requirements so that, for Realization of the be shelter of steelfor profiles for parking cars example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
173
perpendicular 2 3 perpendicular 2 134.84314 MPa fu
fu 453.33 MPa
w Mw
408 MPa
Mw
parpendicular 2 3 parpendicular 2
fu
OK
w Mw
parpendicular
fu Mw
If the weld to be checked is part of a statically indeterminate structure, the size of the weld is determined on the basis of the deformability as follows (a twin fillet weld): 0.7 w
af
Sizing of welds
2
tf
af 8.90955 mm
af 9 mm
Sabah Shawkat © Stress at the connection line between web and flange:
It is possible to transfer compressive stresses through bearing pressure, whereby the welds need not be designed for other than tensile and shear forces. Then there must be a tight
x
Msd h Nsd tf Iy 2 A
x
54.45 MPa
contact between the base plate and the abutting end of the column. This must be mentioned in
Throat thickness of the weld:
the assembly drawing of the column.
perpendicular
Stress on the centre-line of the flange: II
Msd h tf Nsd x 2 Iy A
x
57.2091 MPa
x
2 2 aw
tw
perpendicular
Vsd
II
2 aw h 2 tf
72.19 MPa
47.35 MPa
Compression of stresses: Throat thickness of the weld: perpendicular
Stress in the twin fillet weld: x
tf
perpendicular
perpendicular
perpendicular
2 2 af
perpendicular
67.42157 MPa
perpendicular
67.42157 MPa
perpendicular
perpendicular
2
2
2
2
2
3 perpendicular II 159.92 MPa
3 perpendicular II fu Mw
OK
Connections in steel structures Connections in steel structures
2
fu w Mw
perpendicular
fu 453.33 MPa
w Mw
OK
72.19 MPa
fu 408 MPa
Mw
174 132
Chooseatribbed steel bolts 4xM36 the table of be thefixed manufacture. Thetocombined in its plane transmit condition steel beam supports. Byconforming contrast thetoelement may
Connections in of steel structures On the basis deformability:
0.7 w awbetween tw aw 6.68216 mm may be classified aw 7 as mmsimple connections, Joints structural line elements, in one plane, 2 as sliding connections, as pin or pinned connections as fixed connections, also known as rigid connections. A simple connection allows rotation and movement in any direction except Sizing of the base plate and holding - down bolts: downwards and only transmits shear force that acts downwards at a support. A sliding connection allows movement Dimensions of the plate: along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear ap 940 mm s 120 mm b 460 mm e 60 mm d 820 mm and axial forces but not bending moment. A fixed connection does not allow translational e1 50 tp forces, 60 mmbending fand 335 MPamoment. w transmits 300 mmshear, axial y torsional movement ormm rotation and
an of element and an immovable support then that end of the element may not move translationally the manufacturer. or rotate in space, as distinct from a movement which is merely relative to the member on the Thickness of the base plate on the compression side: other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to j provide continuity so there is little or no rotation between the members at the joint and the 2 fthat McSd beff s McSd 44.16 m kN tp 60 mm 2 members behave as if no joint existed. However, the joint is not necessarily fixed in space and may rotate about a support 6 McSd M0 for example. A way of characterising the degree of fixity or stiffness tpc either 43.49 to mm t pc tp member is to measure the pc provided by a semi-rigid connection a support or tanother beff fy rotation at the joint as the bending moment on the joint is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column Thickness of the base plate on the tension side: connection designed to transfer a moment from the beam into the column. M-φ curves in general ( s e) application, it is necessary to idealise the M-φ curves. The rotation non-linear, for practical MtSd 11.21 m kN M tSd N s 2 of the deformation that can be obtained before failure somewhere in the capacity is a measure
Strength of concrete C25/30:
2 fck fj 1 3 c
tensionbut and shear resistance should alsoNote be checked to see that if conforms to made the instructions bending allow rotation about its axis. that if pinned or fixed joints are between
fj 13.333 MPa
Sabah Shawkat © connection drop m ( scauses e) a0.8 af in the 2 moment resistance. m 49.82 mm For strength, the following classes can be distinguished:
Width of the bearing region: c tp
fy
3 fj M0
nominally Rd ≤ 0,25 Mpl.Rd leff pinned 2 m 0.625 e e1 lM eff 187.14 mm partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd
c 165.557 mm
beff b
b 0.46 m
beff 0.46 m
Depth of the bearing region:
not checked
MpRd where
d 0.82 m y1
beff fj d
full-strength 11.21 m kN MtSd full-strength if rotation capacity is
beff fj d 2 2 beff fj Msd Nsd d 0.5 ap
MRd
2
leff tp fy
MRd ≥ Mpl.Rd
MRd ≥ 1,2 Mpl.Rd
MpRd 51.29 m kN
4 M0 is the design moment resistance of the connection
MpRd MtSd
y1 1424.2 mm
Mpl.Rd is the design strength of the beam (full plastic moment). When tensile forces are significant, it is necessary to provide appropriate anchorage to the bolts.
Column web in shear, compression and tension d difficult fj connections Msd Nsd and 0.5 arotation beff tofj dfabricate 2 2 beff d some p In practicebiteffisfjoften fixed may take place y2 y2 215.8 mm f b eff j between the element on one side of the joint and that on the other. Such a joint is known as a
For example, threaded bolts may be used in conjunction with channel sections embedded in the
semi-rigid strictlymspeaking is the condition of most joints which are described 0.2158 y y2connectionyand, as being fixed or rigid. A moment connection could be described as one which although only
produced by the holding down bolts. The bending moments may require the use of stiffeners.
beff fj
concrete. In tension connections the baseplate thickness is often dictated by the bending moments
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending Forces on the compression and tension region: moment. Note that connections may be fabricated for particular requirements so that, for N c beff yfj N c 1323.546 kN example, they may allow rotation in the plane of the elements but prevent twisting about the Nofs theNelement N s 373.546 kNmoments to be transmitted. This is a common axis torsional c N sd thus allowing
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
175
Calculate the joint resistance of a hollow section with dimensions 200x200x8. the steel grade used is S355J2H, and the design value for the compression resistance of concrete is 14 N/mm2. The base plate dimensions are a x b = 400x400. The steel grade used in the holding down bolts is S355. The column is subjected to the following loads: N sd 1600kN beff 400 mm a1 100 mm
Msd 45 kN m
Vsd 120 kN
fy 345 MPa
fcd 14 MPa
d 350 mm
a 400 mm
M0
y2
beff fcd d
beff fcd d 2 2 beff fcd Msd Nsd (d 0.5 a ) beff fcd
y2 0.20608 m N c beff y2 fcd
N c 1154.02 kN
N s N c N sd
N s 445.98 kN
Holding down bolts are not subjected to tension
1.1
Resistance of the holding down bolts Since the holding down bolts are not subjected to tension, the holding down bolts need be designed for shear only: As
Vsd 3 1.1
As 0.00066m
2
Sabah Shawkat © fy
4bolts24
n 4
24 mm
As
2
0.78
4
4
As 0.001411 m
2
Base plate resistance
The value of the bending moment in the base plate at the column edge is as follows: 2
Msd
beff a1 fcd
Msd 28 m kN
2
The thickness of the base plate is obtained by substituting the bending moment Msd into the First determine whether the holding down bolts are subjected to tension at the ultimate limit state:
y1
beff fcd d
y1 0.49392 m
beff fcd d 2 2 beff fcd Msd Nsd (d 0.5 a ) beff fcd
formula
tp select
6 M sd M0 b eff fy
6 M sd M0
tp 36 mm
Connections in steel structures Connections in steel structures
b eff fy
0.03659 m
176 132
Trusses and structures Connections in reticulated steel structures
condition at steel beam supports. By contrast the element may be fixed in its plane to transmit bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Stable assemblages of line individual tie and strut elements areclassified known asasreticulated structures. A Joints between structural elements, in one plane, may be simple connections,
an element and an immovable support then that end of the element may not move translationally
assemblage oforties and struts in twoasdimensions is knownalso as known a planeastruss as triangulated sliding connections, as pin pinned connections fixed connections, rigidand
of material and movement are more economical forof long or and heavy loads,and in spite of the extra costs connection allows along the line the spans element rotation only transmits shear
or rotate in space, as distinct from a movement which is merely relative to the member on the Removal of member from a determinate truss structure causes bending in members and other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to collapse. provide continuity so that there is little or no rotation between the members at the joint and the A simple check for statically determinacy in a planar truss with pinned joints is given by: members behave as if no joint existed. However, the joint is not necessarily fixed in space and
of their fabrication. An essential point is but thatno thetranslational elements are always arranged in triangular force. A pinned connection allows rotation movement, it transmits shear
may rotate about a support for example. A way of characterising the degree of fixity or stiffness
which inherently stable,Aassuming none of thedoes angles the triangle is small. andconfigurations axial forces but notare bending moment. fixed connection notinallow translational
provided by a semi-rigid connection either to a support or another member is to measure the Where rotation at the joint as the bending moment on the joint is varied. n is the degree of indeterminacy which is zero for determinate structure and one or any Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column number above one for an indeterminate structure. connection designed to transfer a moment from the beam into the column. M-φ curves in general b is the number of bars in the truss structure, non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation r is the total number of reactive forces, being two for a pinned joint with a horizontal and capacity is a measure of the deformation that can be obtained before failure somewhere in the vertical reaction, three for a fixed support, which also has a moment reaction, and one connection causes a drop in the moment resistance. for a sliding support. For strength, the following classes can be distinguished: j is the number of joints including the joints at supports. nominally pinned MRd ≤ 0,25 Mpl.Rd If n is one or greater than one, then the truss is indeterminate and the forces in it cannot be found partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd out by consideration of equilibrium alone. If the degree of indeterminacy is less than zero, then full-strength MRd ≥ Mpl.Rd the arrangement of bars is inherently unstable and known as a mechanism. As already noted for full-strength if rotation capacity is the truss, a mechanism can be created by removal of a bar or a support restraint. not checked MRd ≥ 1,2 Mpl.Rd
consists, inAprinciple, of elementsallows connected by pin joints workingininany tension or compression connections. simple connection rotation and movement direction except see pictureand below. are shear often used place of rolled steel beams, they make downwards onlyTrusses transmits forceinthat acts downwards at a support. A better slidinguse
Comparing a beam to truss,axial bothforces, simplybending supported, horizontal top and bottom movement or rotation anda rectangular transmits shear, andthe torsional moment. beam members of the truss carry compression and tension respectively while diagonal and vertical elements serve to carry the shear force which is a maximum near supports. An important aspect of the design of plane trusses is that the top boom be stabilised to prevent buckling in the plane at right angles to the truss see picture below.
n
b r 2 j
Sabah Shawkat © Top boom of truss restrained at ends and mid-span showing likely buckling mode and associated length between lateral supports,a.
where
Plane truss, top, and pinned-jointed model, bottom, which is determinate and used for preliminary analysis
Column web in shear, compression and tension In In practice it isthe often difficult to fabricate connections and some rotation may take place practice elements of the truss arefixed not usually connected by pure pin connections so that between the element one side ofinto thethe joint and thatalthough on the other. Suchisanot joint is known as a secondary bendingon is introduced members, the effect usually significant. semi-rigid connection is local the condition joints Individual elementsand, willstrictly also bespeaking subject to bending of if most any load is which appliedare at described right angles as anywhere being fixeddown or rigid. momentrather connection be described as oneThe which although onlyone theirAlength, than atcould the joints of the truss. removal of any semi-rigid behaviourtruss, of a fixed connection and transfers a substantialand bending member approaches of staticallythe determinate however, turns the truss into a mechanism loads to moment. that connections may be fabricated for particular requirements so that, for collapseNote see figure below. example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
MRd is the design moment resistance of the connection The truss to be designed is to support a roof which is only accessible for normal maintenance Mpl.Rd is the design strength of the beam (full plastic moment). and repair. The truss is 16 m span with 20° pitch. The dimensions of the truss are shown in the figure below. The imposed roof load due to snow is 1.05 kN/m2. The truss uses hollow sections for its tension chord, rafters, and internal members. The truss is fully welded. Truss analysis is carried out by placing concentrated loads at the joints of the truss. All of the joints are assumed to be pinned in the analysis and therefore only axial forces are carried by members. 1 20 deg
2 90 deg
3 2 1
4 35 deg
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
177
g L1 Gd cos 1
1
Gd 18.93 kN m
Design value of combined actions on truss, for a purlin span of Lp 5.5 m
Fd Gd Lp
Fd 104.116kN
Truss analysis due to forces Reaction force at support a
Ra 2 Fd
Ra 208.231kN
At joint a Characteristic actions:
V
Permanent actions:
0
2
Self-weight of roof construction
g oroof 2 kN m
Fd Fab sin 1 RA 2
Fd 2 Fab sin 1 Ra
Sabah Shawkat © 2
self-weight of services
g oservice 0.3 kN m
Total permanent actions
go
2.3 kN m
H
2
Variable actions:
Fab 456.621 kN
0
Fab cos ( ) Fac
0
Fac Fab cos 1
Fac 429.083kN
2
imposed roof load
q roof 1.05 kN m
Total imposed load
q roof 1.05 kN m
At point b
2
V
Ultimate limit state (ULS): Partial factor for permanent actions
0
Partial factors actions:
Fbc Fd cos 1
0
Fbc Fd cos 1
Fbc 97.837 kN
G 1.35
Partial factor for variable actions
Q 1.5
Reduction factor
0.925
H
2
g 4.447 kN m
Fbd 421.011 kN
Fbd Fab Fd sin 1
At point c
Design value of obtained actions on purlins supported by truss For the distance of 4.0 m between purlins to centre
0
Fbd Fab Fd sin 1
Design value of combined actions: g G g o Q q roof
0
V
0
Fbc sin 3 Fcd sin 1
0
L1 4 m
Connections in steel structures Connections in steel structures
Fcd
Fbc sin 4 sin 1
Fcd 164.075kN
0
178 132
Compression of the cross-section: condition at steelresistance beam supports. By contrast the element may be fixed in its plane to transmit
Connections H 0 in steel structures
3 linecdelements, 4 in one plane, 3 as 4 connections, ac structural bc ce ac bc classified cd simple Jointscebetween may be F
F
F cos
F
cos
0
F
F
F cos
F
cos
as sliding connections, as pin or pinned connections as fixed connections, also known as rigid
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between Fab 456.621 Fbd support 421.011 kN that end Fof element 421.011 kNmay Fgf translationally 456.621 kN an element and an kN immovable then not move fd the
or rotate in space, member on the A ab fy as distinct from a movement which Fab is merely relative to Fthe bd N
N
0.466
979.155kN
0.43
downwards and only transmits shear force that acts downwards at a support. A sliding
0Rd N0Rd N0Rd other 0Rd side of the joints, between two members are said to M0 joint. Fixed joints, or nearly fixed provide is little or no rotation between the members at the joint and the F F continuity so that there
Partial safety connection allowsfactor: movement along the line of1.1 the element and rotation transmits M1 1 and only M2 1.25 shear M0
members N0Rdexisted. However, the joint is not necessarily fixed in space and N0Rd behave as if no joint
force. A pinned allows rotation Design of topconnection chords (members a-b, b-d,but d-f,no f-g)translational movement, it transmits shear and Maximum axial forces but not bending moment. design force (member a-b, f-g)A fixed connection does not allow translational
may rotate about support for example. A way ofischaracterising the degree of fixity or stiffness Therefore, the acompression design resistance adequate provided by a semi-rigid connection either to a support or another member is to measure the
movement or rotation and transmits shear, axial forces, bending and torsional moment.
rotation at the joint asresistance the bending moment on the joint is varied. Flexural buckling Figure bellow defines the strength,slenderness stiffness and capacity of a beam-to-column Determine the non-dimensional for deformation flexural buckling:
Fce 261.219kN connections. A simple connection allows rotation and movement in any direction except
Fab 456.621 kN Fbd 421.011 kN
Try
Fgf Fab Ffd Fbd
Fgf 456.621 kN
0.466
non-linear,Afor practical application, it is necessary to idealise the M-φ curves. The Erotation fy lab Lcr 1 s L 1.0 Labcr before 4.257m failuresomewhere z abcr ab1 capacity isNa measure cos can be obtained f in the i of the deformation that cr
z
1
1
Sabah Shawkat © fy
nominally pinned abcr
fy 355 MPa
Nabcr 1.373 10 kN
2 2
MRd ≥ Mpl.Rd
MRd ≥ 1,2 Mpl.Rd L abcr
not checked A f ab y ab where N
ab 0.886
abcr
b ab 160 mm
h ab 160 mm
tab 5 mm
2 In practice it is often difficult to fabricate fixed connections and some rotation may take place Area A 3034 mm
ab
between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described Classification of the cross-section: as being fixed or rigid. A moment connection could be described as one which although only cab 0.145m
MRd
iab
1
ab1
0.886
is the design moment resistance of the connection
Mpl.Rd is the design strength of the beam (full plastic moment). Determine the reduction factor due to buckling, use buckling curve a
Radius of gyration Column web in shear, 62.9 mm and tension iabcompression
cab h ab 3 tab
MRd ≤ 0,25 Mpl.Rd
0,25 Mpl.Rd < MRd < M3pl.Rd
full-strength if rotation capacity is
Section properties
Thickness
2
Labcr 1
full-strength
0.814
Depth and width of section
2
A ab fy iab ab1 partial-strength N
t 16 mm
Yield strength 235 MPa
ab1 76.409
Es 210 GPa
Steel grade S355 and thickness
y
connection causes a drop in the moment resistance.
For strength, the following classes can be distinguished:
Metal properties
e 0.81
Fbd 421.011 kN
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending c
ab Note that connections may be fabricated forc particular requirements so that, for moment. 29 42 e 34.02 42 e Class 3 limit tab
gf
0.43
connection designed to transfer a moment from the beam into the column. M-φ curves in general
Ffd 421.011 kN
square hollow section in S355 steel
160x160x
fd
t
example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
0.21
ab 0.5 1 ab 0.2 ab
ab
2
1 ab
2
ab ab
2
ab 0.964
ab 0.743
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
179
NbRd Fab NbRd
ab A ab fy
1
Following the same design process as above, the following resistances can be calculated:
NbRd 800.58kN
M1 Ok
Fab NbRd
Flexural buckling resistance:
0.57
Determine the non-dimensional slenderness for flexural buckling: L bccr 1200 mm
Therefore, the design flexural buckling resistance of the selected 160x160x5 is satisfactory
bc
A bc fy
Lbccr
Nbccr
ibc
Design the bottom chords members (a-c, c-e, e-g) bc1
Maximum design force (member a-c and e-g) Fac 429.083kN
Fce 261.219kN
Feg Fac
Feg 429.083kN
1
Lbccr 1.2m
Lbccr 1.0 lbc
bc1
2
Es
bc1 76.409
fy
A bc fy
bc
bc 0.695
Nbccr
Nbccr Lbccr ibc
A bc fy ibc bc1
2
2 2
Lbccr 1 1
bc1
Nbccr 628.55kN
0.695
Determine the reduction factor due to buckling, use buckling curve a The bottom chord will also be 160x160x5mm, S355. By inspection the design tension resistance
Sabah Shawkat © 0.21
is equal to the design plastic resistance of the cross-section.
bc 0.5 1 bc 0.2 bc
A ac A ab
iac iab
A ac fy
NplRd M0
NplRd 979.155kN
NplRd Fac
bc
Maximum design compression force
Fbc 97.837 kN
Ffe Fbc
Ffe 97.837 kN
Maximum design compression force
Fcd 164.075kN
Fed Fcd
Fed 164.075kN
2
1
bc
NbcRd
Design the internal members (b-c, c-d, e-d, f-e):
2
bc bc
bc A bc fy M1
A bc fy NplRd M0
bc 0.793 bc 0.85
2
NbcRd 258.032kN
NplRd 275.932kN
Fbc
NbcRd
Fbc
0.379
NplRd Fbc
NbcbRd
1
Ok
Ok
Serviceability limit state (SLS) Maximum length in compression is b-c and f-e
lfe lbc
lbc 1200 mm
lfe 1.2m
EC provides suggested limits for vertical and horizontal deflections. The deflection should be checked under variable loads and that permanent loads should not be included.
Try b bc 60 mm
60x60x4 h bc 60 mm
Partial safety factor for actions:
in steel S355 2
2
tbc 4 mm A bc 8.55 10 mm ibc 2.26 10 mm
Partial safety factor for variable actions
G 1.0
Design value of combined actions
f0 q roof G
Design value of combined actions on truss
Connections in steel structures Connections in steel structures
Lp 5.5m
2
f0 1.05 kN m
180 132
L1 structures Connections in steel f0d Lp f0 cos 1
Design at ofsteel trusses condition beam supports. By contrast the element may be fixed in its plane to transmit
f0d 24.583kN
Steps but in trusses bending allow design rotation about its axis. Note that if pinned or fixed joints are made between
connections. A simple connection allows rotation andspan/300 movement in any direction except The maximum allowable deflection is assumed to be
Task support then that end of the element may Illustration an element and an immovable not move translationally 1. Determination the loads in the or rotate in space, as distinct from a movement which is merely relative to the member on the structure. other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
downwards and only transmits Ltrussshear force that acts downwards at a support. A sliding
provide continuity so that there is little or no rotation between the members at the joint and the
300 the line of the element and rotation and only transmits shear connection allows movement along
members behave as if no joint existed. However, the joint is not necessarily fixed in space and
force. A pinned connection allows rotation but no translational movement, it transmits shear andConnections axial forces but not bending moment. A fixed connection does not allow translational
may rotate about a support for example. A way of characterising the degree of fixity or stiffness 2. Determine the height of the lattice. provided by a semi-rigid connection either to a support or another member is to measure the
The jointorresistances depend on the type axial of joint, the geometry of the joint and the forces in the movement rotation and transmits shear, forces, bending and torsional moment.
rotation at the joint as the bending moment on the joint is varied.
Joints between structural line elements, in one plane, may be classified as simple connections, as Deflection sliding connections, as pin or pinned connections as fixed connections, also known as rigid
16 m Ltruss
d
d 53.333 mm
members. It is unlikely that the joints in hollow section fabrications can carry as much as load as the members themselves, without expensive strengthening, which should be avoided.
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column 3. Preliminary selection of the members. connection designed to transfer a moment from the beam into the column. M-φ curves in general
Joint resistance should be checked at the design stage, so that appropriate members can be
non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation
chosen to ensure that in addition to the members resisting the design load, the joints can also
capacity is a measure of the deformation that can be obtained before failure somewhere in the
transfer the member forces without strengthening.
connection causes a drop in the moment resistance.
Sabah Shawkat © For strength, the following classes can be distinguished:
nominally pinned MRd ≤ 0,25 Mpl.Rd 4. Determine the actual member forces. partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd MRd ≥ Mpl.Rd
full-strength
full-strength if rotation capacity is 5. Calculate the local resistance of not checkedjoints. MRd ≥ 1,2 Mpl.Rd where MRd
is the design moment resistance of the connection
Mpl.Rd
is the design strength of the beam (full plastic moment).
Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place
6. Calculate the deflection.
between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending
7. Design the transverse support of the lattice and the purlin –to-lattice joints.
moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the Realization of the ceiling of the hall from truss steel structures axis of the element thus allowing torsional moments to the be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
181
N1Rd N1sd
Y joint
Resistance of the joint:
A Y joint with a tension brace member
The resistance of the joint is thus N1Rd, which is > than the brace member axial force N1sd.
The joint geometry and loading are as follows: fy 355MPa M0 1.1 Mj 1.1
Thus the brace member or the chord face have a sufficient resistance of the joint.
Brace member:
48 deg
Chord member: 2
120x120x6
A1 3364 mm
200x200x10
b1 120 mm
h1 120 mm
b0 200 mm
t1 8 mm
N1sd 610 kN
tension
h0 200 mm
t0 10 mm
N0sd 1250kN
b0 h1
h0
0.6
h1
0.6
h0
The chord axial force N0sd influences the resistance of the joint in the form of the term kn: n
M0 Mj
compression
b1
b0
2
35 deg
b1
A0 7257 mm
1.1
N 0sd
n 0.53372
A0 fy
N Rdchord A1
Ok
fy
kn 1.3
0.4 n
kn 0.94418
NRdchord 1085.655kN
M0
Sabah Shawkat © 0.6
Chord face yield:
0.6
since β =0.6 less than 0.85 the chord face resistance must be checked: 2
N 1Rd
fy t0
2 4 1 k 1.1 n ( 1 ) sin( ) sin( ) Mj M0
N1Rd 424.85kN
The chord axial force N0sd influences the resistance of the joint in the form of the term kn:
n
M0 Mj
1.1
N 0sd
kn 1.3 n 0.53372
A0 fy
N Rdchord A1
fy
N1Rd NRdchord
0.4 n
Ok
kn 0.94418
NRdchord 1085.65455kN
N1Rd N1sd
Does not
NRdchord 1085.655kN
M0
In the case when we increase the angle between the brace member and the chord face then Chord face yield:
the resistance of the joint is thus N1Rd, which is remarkably less than the brace member
since β =0.6 less than 0.85 the chord face resistance must be checked:
axial force N1sd. A larger hollow section must be selected as the brace member or the chord face must be reinforced to obtain a sufficient resistance of the joint.
2
N 1Rd
fy t0
2 4 1 k 1.1 n ( 1 ) sin( ) sin( ) Mj M0
N1Rd NRdchord
Ok
NRdchord 1085.65455kN
N1Rd 613.86kN N1sd 610kN
Connections in steel structures Connections in steel structures
182 132
Now we can calculate the chord resistance: condition at steel beam supports. Byweb contrast the element may be fixed in its plane to transmit
T joint in steel structures Connections A T joint with a compression brace member
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints structural line elements, in one plane, may classified Thebetween joint geometry and loading are the following: fy be355 MPa as simple connections, as sliding as pin or pinned connections as fixed connections, also known as rigid Brace connections, member: Cord member:
an element and an immovable then that fb t0 2support h1 end 1.1of the element may not move translationally N1Rdchord 654.4kN N 1Rdchord 10 t0 or rotate in space, sin as (distinct from ) sin ( ) a movement M0 is merely relative to the member on the Mjwhich
connections. A simple connection allows rotation and movement in any direction except 2 2 A1 3364 mm A0 3364 mm 120x120x8 120x120x8 downwards and only transmits shear force that acts downwards at a support. A sliding compression b1 120 mmmovement h1along 120 N0sd and 480 kN and connection allows themm line of the element rotation only transmits shear
other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to
compression 8 mm connection M0 1.1 1.1but no N t1 A pinned force. allows Mj rotation translational movement, it transmits shear 1sd 380 kN
may rotate about a support for example. A way of characterising the degree of fixity or stiffness 2 10 b1 t0 beff 0.08m 0.12m beff member b1 beff by a semi-rigid connection provided either to ba 1support or another is to measure the b0 t1 rotation at the joint as the bending moment on the joint is varied. 1.1 Figure bellow definesthe capacity of a beam-to-column N1Rdbracebuckling fy strength, t1 2 h1 stiffness 4 t1 2 and beff deformation M0 Mj connection designed to transfer a moment from the beam into the column. M-φ curves in general N1Rdbracebuckling 950.11kN non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation
and forces does allow Eaxial 210 GPabut not bending moment. A fixed 120 mm h0 not120 mm translational t0 8 mm b0 connection movement or rotation and transmits shear, axial forces, bending and torsional moment. A1 fy 90deg N Rdbrace 1.1 b1 1 NRdbrace 1085.655kN b0 n
M0 Mj
1.1
N 0sd A0 fy
n 0.44213
provide continuity so that there is little or no rotation between the members at the joint and the Brace web buckling: members behave as joint existed. themember: joint is not necessarily fixed in space and Next, determine ifthenoeffective widthHowever, of the brace
capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat ©
kn 1.3
kn 1
0.4 n
connection causes a drop Resistance of the joint:in the moment resistance. For The strength, the following classes can be the distinguished: chord web resistance determines resistance of the entire joint, which then is:
kn 1.12315
MRd ≤ 0,25 Mpl.Rd
nominally pinned
kn 1
governing failure mode (β = 0.85).
partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd N1Rdbracebuckling 950.10909kN N1sd 380kN NRdbrace 1085.655kN full-strength MRd ≥ Mpl.Rd N 1Rdbracebuckling full-strength capacity is N1sd Ok NRdbraceifrotation N1Rdbracebuckling 2.50029 N 1sd not checked MRd ≥ 1,2 Mpl.Rd N1Rdchord 654.4kN N1Rdchord N0sd N0sd 480 kN OK where
Chord web buckling:
Mpl.Rd N0sd
Note that the term kn is not relevant in this example, since the chord face yield is not the
MRd N 1Rdchord is the design moment resistance of the connection 1.36333 is the design strength of the beam (full plastic moment).
The chord web buckling may be a relevant failure mode for the design, since β is 1.0. in using shear,buckling compression First, determine the Column bucklingweb stress curveand C: tension In practice it is often difficult to fabricate fixed connections and some rotation may take place fy h0 1 C as a the 3.46element on 2 one side of the joint and that 0.58867 0.49 between on the other. Such a jointCurve is known t0 E( sin( ) ) semi-rigid connection and, strictly speaking is the condition of most joints which are described 2 fixed 0.5 1orrigid. ( A moment 0.2) connection be 0.76849 as being could described as one which although only
1 semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending 0.79208 2 2 moment. Note may be fabricated for particular requirements so that, for that connections
example, may allow rotation the plane of the elements but prevent twisting about the fb they fb in281.19 MPa fy axis of the element thus allowing torsional moments to be transmitted. This is a common
When we changing the angle Θ from 90deg to 75deg,
90deg 1.2 then we obtain the 75deg
results as follow:
75deg
kn 1.3
0.4 n
b1 b0
1
kn 1.12315
n
kn 1
M0 Mj
1.1
N 0sd A0 fy
n 0.44213
kn 1
in this example, theplastic chord rotation face yield is not the Note that the term kn is not relevant Moment-rotation characteristic of a semi-rigid joint withsince enough capacity governing failure mode (β = 0.85). For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
183
Chord web buckling:
X joint
The chord web buckling may be a relevant failure mode for the design, since β is 1.0.
An X joint with compression brace members
First, determine the buckling stress using buckling curve C:
The joint geometry and loading are as follows: fy 355MPa
fy h0 1 3.46 2 t0 E( sin( ) )
2 0.5 1 ( 0.2)
1
2
2
0.786
0.59897
0.49
Mj
Curve C
Brace member:
Chord member:
180x180x8
200x200x10
0.77713
fb fy
fb 279.03MPa
b1 180 mm h1 180 mm
Now we can calculate the chord web resistance: fb t0 2 h1 1.1 10 t0 sin( ) sin( ) Mj M0
N1Rdchord 690.07kN
A1 5284 mm
t0 10 mm
A0 7257 mm
fy
e 0 mm
1.1
N0sdchord 730kN
beff 0.08 m
b1 0.12m
N1Rdbracebuckling fy t1 2 h1 4 t1 2 beff
beff b1
1.1 M0 Mj
30deg
0.9
b1
N1sdbrace 1320kN
b0
0.5
0.9
b0
t0
h1 h0
10
Chord face punching shear:
Resistance of the joint:
The chord face punching shear must be checked, since:
1
The chord web resistance determines the resistance of the entire joint, which then is:
N1Rdbracebuckling 950.10909kN
N1sd 380kN
NRdbrace N1Rdbracebuckling N1sd Ok N1Rdchord 690.07kN
N0sd
Tension
kn 1
N1Rdbracebuckling 950.11kN
N 1Rdchord
2
Compression
Sabah Shawkat ©
2
b0 t1
h0 200 mm
NRdbrace 1705.29kN
Next, determine the effective width of the brace member: 10 b1 t0
b0 200 mm 2
NRdbrace A1
Brace web buckling:
beff
1.1
1.1 E 210 GPa
t1 8 mm
N 1Rdchord
M0
1.43765
N1Rdchord N0sd
0.85 1
NRdbrace 1085.655kN
N 1Rdbracebuckling N 1sd
bep
2.50029
N 0sd 480 kN
OK
10 t0 b1 b0
N 1Rdchordpunching
1 0.9
1
bep 0.09m
b1 0.18m
bep b1
1.1 2 h1 b1 bep M0 Mj 3 sin( ) sin( ) fy t0
N1Rdchordpunching 3689.26822kN
Connections in steel structures Connections in steel structures
184 132
Next check thebeam chord shear resistance: condition at steel supports. By contrast the element may be fixed in its plane to transmit
Chord face and chord web buckling: Connections in yield steel structures Joints structural line elements, in one mayface be classified simple Thebetween resistance of the joint is calculated for plane, the chord when β =as0.85 and connections, for the chord
bending but allow rotationfyabout Av its axis. 1.1 Note that if pinned or fixed joints are made between N1Rdchordshear 1513.65435kN N 1Rdchordshear an element and an immovable then that end of the element may not move translationally Mj ) M0 3 sin(support
as sliding connections, as the pin resistance or pinned connections fixed connections, also known as rigid web when β =1. Then is determinedasby linear interpolation when β =0.9.
or rotate in space, as distinct from a movement which is merely relative to the member on the
connections. 0.85A simple connection allows rotation and movement in any direction except downwards and only transmits shear force that acts downwards at a support. A sliding 2 fy t0 1.1 2 N 1Rdjoint movement along the lineof4the 1element knand connection allows rotation and only transmits shear ( 1 ) sin( ) sin( ) M0 Mj force. A pinned connection allows rotation but no translational movement, it transmits shear N1Rdjoint 2215.7135kN NRdbrace 1705.29kN N1Rdjoint NRdbrace and axial forces but not bending moment. A fixed connection does not allow translational
other side member of the joint. Fixed joints, or nearly fixed joints, between two members are said to Brace failure: provide so that there is little no rotation the members at the joint and the Alsocontinuity the effective width of the braceormember mustbetween be checked:
The chord resistance must be determined for both chord face and web, since 0.85 1
1 or rotation and transmits shear, axial forces, bending and torsional moment. movement
h0
3.46
t0
2
fy 1 E( sin( ) )
2 0.5 1 ( 0.2)
1
1.15271
1.39778
0.49
Curve C
members behave as 2if no joint existed. However, the joint is not necessarily fixed in space and 10 b1 t0 beff 112.5mm b1ofcharacterising 180mm beff b1 of fixity or stiffness maybrotate for example. A way the degree eff about a support b0 t1 provided by a semi-rigid connection either to a support or another member is to measure the 1.1 rotation at the joint N1Rdbrace fy as t1the 2 beff on the joint isNvaried. 2 hbending 1Rdbrace 1427.74545kN 1 4 t1 moment M0 Mj Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column N1sdbrace 1320kN connection designed to transfer a moment from the beam into the column. M-φ curves in general non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation
Resistance of joint:of the deformation that can be obtained before failure somewhere in the capacity is a measure
Sabah Shawkat ©
2
2
0.45696
The resistance the joint the smallest of the above values, that is: connection causes aofdrop in theismoment resistance.
fb 0.8 sin( ) fy
fb 64.89MPa
N 1Rdbrace For strength, the following classes can be distinguished: N1Rdbrace N1sdbrace 1.08163 N1Rdchordpunching 3689.26822kN N nominally pinned MRd ≤ 0,25 Mpl.Rd 1sdbrace
partial-strength NRdbrace 1705.29kN
Now we can calculate the chord web resistance: N 1Rdchordweb
fb t0 2 h1 1.1 10 t0 sin( ) sin( ) Mj M0
N1Rdchordweb 967.42kN
Now determine the chord resistance by interpolation using the values calculated above:
N1Rdchord N1Rdchordweb NRdbrace N1Rdchordweb
( 1 0.9) 0.15
Column web in shear, compression and tension N0sdchord N1Rdchord 1459.34kN N0sdchord 730kN N1Rdchord In practice it is often difficult to fabricate fixed connections and some rotation may take place Chord shear: between the element on one side of the joint and that on the other. Such a joint is known as a h0 sin( ) h1 h0 1 of most joints which are g econnection and, strictly is the condition 0.03091 semi-rigid described 2 2 sin( ) 2 sin(speaking ) 2 sin( ) 4 g as being fixed or rigid. A moment connection could be described 1as one which although only 2 3 t semi-rigid approaches the behaviour of a fixed connection and transfers 0a substantial bending 2 moment. be fabricated Av Note connections b0 t0 Avmay 4061.82939 mmfor particular requirements so that, for 2 h0that
example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
0,25 Mpl.Rd< 2215.7135kN MRd < Mpl.Rd N1Rdjoint
N1sdbrace 1320kN
MRd ≥ Mpl.Rd N1Rdchordweb 967.42kN
full-strength N1Rdchordshear 1513.65435kN full-strength if rotation capacity is N1Rdbrace 1427.74545kN not checked
N1Rdchord 1459.34kN MRd ≥ 1,2 Mpl.Rd 45deg where 1.5 it means that we increase the Now we propose that the joint angle is 45deg 30deg MRd is the design moment resistance of the connection thenstrength the results willbeam be as(full follows. M angle aboutis1.5time the design of the plastic moment). pl.Rd
45deg
b1 b0
0.9
h1 h0
0.9
0.5
b0
t0
10
Chord face punching shear:
1
The chord face punching shear must be checked, since 0.85 1
1 1 0.9 characteristic of a semi-rigid joint with enough plastic rotation capacity Moment-rotation
For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
185
bep
10 t0 b1
bep 0.09m
b0
b1 0.18m
Chord shear:
bep b1
1.1 2 h1 b1 bep ( ) sin M0 Mj 3 sin( ) fy t0
N 1Rdchordpunching
g e
h0 sin( ) h1 h0 2 sin( ) 2 sin( ) 2 sin( )
1
2
1
N1Rdchordpunching 2053.01751kN
4 g
0.05127
2
3 t0
This increase of the angle joint cause the decrease of the value of N1Rdchordpunching about 0.55
Av 2 h0 b0 t0
2
Av 4102.5351mm
time or percent.
Chord face yield and chord web buckling:
Next check the chord shear resistance:
The chord resistance must be determined for both chord face and web, since
N 1Rdchordshear
0.85 1
The resistance of the joint is calculated for the chord face when β = 0.85 and for the chord
fy Av 1.1 3 sin( ) M0 Mj
N1Rdchordshear 1081.04144kN
Also the value N1Rchordshear will decrease about 0.71 percent
web when β=1. Then the resistance is determined by linear interpolation when β =0.9.
0.85
Sabah Shawkat © Brace member failure:
2
N 1Rdjoint
fy t0
2 4 1 k 1.1 n ( 1 ) sin( ) sin( ) M0 Mj
N1Rdjoint 1245.91881kN
NRdbrace 1705.29kN
Also the effective width of the brace member must be checked:
N1Rdjoint NRdbrace
the value of NRdbrace decrease about 0.73 time.
1
fy h0 1 3.46 2 t0 E( sin( ) )
2
0.5 1 ( 0.2)
1
2
10 b1 t0 b0 t1
beff 112.5mm
N1Rdbrace fy t1 2 h1 4 t1 2 beff
0.96931
1.15826
2
fb 0.8 sin( ) fy
2
beff
0.49
Curve C
1.1
M0 Mj
beff b1
N1Rdbrace 1427.74545kN
N1sdbrace 1320kN
Resistance of joint:
0.55794
The resistance of the joint is the smallest of the above values, that is:
fb 112.05MPa
N1Rdchordshear N1sdbrace
N 1Rdchordshear
Now we can calculate the chord web resistance: fb t0 2 h1 1.1 N 1Rdchordweb 10 t0 sin( ) sin( ) Mj M0
b1 180mm
N 1sdbrace
0.81897
We see that the value N1Rdchordshear is < than the value N1sdbrace about 0.82, this it means
N1Rdchordweb 877.44kN
that the joint is not sufficient.
The value of N1Rdchord web will decrease about 0.90 time
Connections in steel structures Connections in steel structures
186 132
K joint in steel structures Connections
fixed in 0.25h its plane transmit condition atM0 steel supports. Byecontrast may0 bewhere Mjbeam N 0sdchord e 0.25h 0.055m 0.015the m element 0 to n bending but allow A0 fyabout its axis. Note that if pinned or fixed joints are made between 1.1 rotation
An K joint with compression and tension brace members A gapped Joint Joints betweenKstructural line elements, in one plane, may be classified as simple connections,
an element and an immovable supporteccentricity then that end of the element may not move translationally n 0.6461 is within the limits allowed
The joint geometry as andpin loading are as follows: as fixed connections, also known as rigid as sliding connections, or pinned connections
or rotate in space, as distinct from a movement which is merely relative to the member on the 0.4 n k 1.3 other nside of the joint. Fixed joints, or nearly fixed joints, between two members are said to
connections. simple connection in any direction except fy 355A MPa Mjrotation 1.1 and movement E 210 GPa M0 1.1 allows downwards and only transmits shear force that Chord acts downwards Brace member: member: at a support. A sliding connection allows movement along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no 220x220x translational 160x160x8 10 movement, it transmits shear and axial forces but not bending moment. A fixed connection does not allow translational b1 160 mm h1 160 mm b0 220 mm h0 220 mm movement or rotation and transmits shear, axial forces, bending and torsional moment. 2 2 t1 8 mm t0 10 mm A1 4644 mm A0 8057 mm
b2 160 mm h2 160 mm
e 15 mm
N0sdchord 1680kN Compression
t2 8 mm NRdbrace A1
fy
N1sdbrace 750kN
Compression
1.1
N2sdbrace 750kN
Tension
rotation at the joint as the bending moment on the joint is varied. Chord face yield: Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column First calculate the resistance by chord face yield: connection designed to transfer a moment from the beam into the column. M-φ curves in general i 1 2 non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation b 1 b1 h 1 h1 b 2 b1 h h1 m 1 capacity is a measure of the deformation that2 can be obtained before failure somewhere in the m m moment connection causes a drop in the resistance. bi hi For strength, the following2classes can be distinguished: fy t0 i 1 1.1 i1 N1Rdchord kn M pl.Rd nominally pinned 8.9 MRd ≤ 0,25 2 m b0 M0 Mj sin( ) partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd 2 fy t0 b1 hM 1 Rd ≥ Mpl.Rd 1.1 full-strength N 1Rdchordfaceyield 8.9 k n ( ) M0 Mj sin 2 m b 0 full-strength if rotation capacity is
Sabah Shawkat ©
NRdbrace 1498.75kN 1
provide continuity so that there is little or no rotation between the members at the joint and the kn 0.94464 members behave as if no joint existed. However, the joint is not necessarily fixed in space and Determine the resistance of the joint by brace member 1 only, since the brace members are may rotate about a support for example. A way of characterising the degree of fixity or stiffness of equal size and carrying equal loads. provided by a semi-rigid connection either to a support or another member is to measure the
45deg 2 45deg
45deg
b1 b0
h1 h0
0.72727
0.72727
not checked N1Rdchordfaceyield 925.55612kN
MRd ≥ 1,2 Mpl.Rd
where
The joint gap presented by the joint geometry is:
b0
Column web in shear, compression and tension 11 0.5 In practice it ist0often difficult to fabricate fixed connections and some rotation may take place h0 thatsin h1 is knownhas 2 Such a joint and 2 a between the element on one joint on the1 other. 1 side of the 0.75 1 1 g e 2 sin sin 2 sin 2 sin 2 speaking is the condition 1 of most2 joints which1are described semi-rigid connection and, strictly
1 or rigid. A moment connection could be described as one which although only as beingfixed 1 0.90909 semi-rigid approaches the behaviourgof a23.72583 fixed connection and transfers a substantial bending mm So theNote chordthat punching shear may be fabricated for particular requirements so that, for moment. connections must be checked. example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
MRdChord shear: is the design moment resistance of the connection Mpl.Rd is the design strength the beam (full plastic moment). Obtain the following value for theofshear resistance of the entire chord:
1
1
2
4 g
0.34289
2
3 t0
Av 2 h0 b0 t0 N 1Rdshear
fy Av
1.1 3 sin( ) Mj M0
2
Av 5154.34828mm
N1Rdshear 1358.2kN
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
187
Brace member failure:
Eccentricity is within the limits
The effective width of the brace member is:
Determine the resistance of the joint by brace member 1 only, since the brace members are of equal size and carrying equal loads.
2
beff
10 b1 t0
beff 0.09091m
b0 t1
b1 0.16m
N1Rdbrace fy t1 2 h1 4 t1 b1 beff
1.1 Mj M0
beff b1 N1Rdbrace 1391.36529kN
Chord face yield: First calculate the resistance by chord face yield: i 1 2
Chord punching shear:
b 1 b1
h 1 h1
In this case the chord punching shear resistance must also be taken into account bep 10 t0
b1
bep 0.07273m
b0
b1 0.16m
bep b1
h 2 h1
m m bi hi 2 fy t0 i 1 i1 8.9 kn sin( ) 2 m b0
N1Rdchord
1.1 2 h1 b1 bep ( ) sin M0 Mj 3 sin( ) fy t0
N 1Rdchordpunching
b 2 b1
m 1
1.1 M0 Mj
2
N1Rdchordpunching 1805.7404kN
b1 h1 1.1 k n M0 Mj sin( ) 2 m b0 fy t0
Sabah Shawkat © N 1Rdchordfaceyield 8.9
N1Rdchordfaceyield 755.71341kN
Resistance of the joint:
The chord face yield determines the resistance of the joint, which then is:
The value N1Rdchordfaceyield decrease about (1-0.816 = 0.184 times)
N1Rdchordfaceyield 925.55612kN
Chord shear:
N1sdbrace 750kN
N1Rdchordfaceyield N1sdbrace
Obtain the following value for the shear resistance of the entire chord:
Ok
Now we changing the angles from 45deg. to 60deg, then we watching the changing of value of the forces. 1
60deg
2
60deg
1
60deg
The joint gap presented by the joint geometry is:
h0 sin 1 2 h1 h2 g e 2 sin 1 sin 2 2 sin 1 2 sin 2
e 0.015 m
e 0.25h0
where
0.25h0 0.055m
1
0.20953
2
3 t0
Av 2 h0 b0 t0 g 40.41452 mm
2
4 g
N 1Rdshear
2
Av 4860.964mm
fy Av 1.1 3 sin( ) Mj M0
N1Rdshear 1045.84kN
The value N1Rdshear decrease about (1-0.769 = 0.231 times)
Connections in steel structures Connections in steel structures
188 132
Brace member Connections in steelfailure: structures
A gapped K joint condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
The effective width of the brace member is:
bending but allow rotation its are axis. that iffy pinned fixedjoints The joint geometry andabout loading as Note follows: 355or MPa 1.1made Mj between 1.1 M0 are
2 Joints between structural line elements, in one plane, may be classified as simple connections, 10 b1 t0 beffor pinned 0.09091m b1 as 0.16m beff b1also known as rigid b eff connections, as pin as sliding connections fixed connections, b0 t1 connections. A simple connection allows rotation and movement in any direction except 1.1 N1Rdbraceat a1391.36529kN N1Rdbraceand only fy t1transmits 2 h1 4 t1shear b1 force beff that acts downwards downwards support. A sliding Mj M0 connection allows movement along the line of the element and rotation and only transmits shear The value N1Rdbrace remained without changing because no place for angles in the force. A pinned connection allows rotation but no translational movement, it transmits shear above. and formulae axial forces but not bending moment. A fixed connection does not allow translational
an element and an immovable support then that end Chord of the element not move8translationally Brace member: member:may200x200x 150x150x8 or rotate in space, as distinct from a movement which is merely relative to the member on the b1 110 mm h1 110 mm b0 200 mm h0 200 mm other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to 2 2 t1 continuity t0 between 6 mm so that 8 mmthe members A1 is4324 A0 at the 5924 mm provide there littlemm or no rotation joint and the members as if no joint is not fixed in space and b2 behave 110 mm h2 existed. 110 mmHowever, theNjoint necessarily 1230kN Tension 0sdchord
movement or rotation and transmits shear, axial forces, bending and torsional moment. Chord punching shear:
may rotate about a support for example. A way degree ofCompression fixity or stiffness 2 of characterising N1sdbrace the 430kN t2 6 mm A2 2403 mm provided by a semi-rigid connection either to a support or another member is to measure the Tension N2sdbrace 430kN fy rotation at the joint NRdbrace A1 as the bending moment on the joint is varied. 1.1the strength, stiffness and deformation 1 50deg 2 50deg 50deg Figure bellow defines capacity of a beam-to-column
In this case the chord punching shear resistance must also be taken into account
NRdbrace 1395.47kN connection designed to transfer a moment from the beam into the column. M-φ curves in general
bep 10 t0
b1 b0
bep 0.07273m
b1 0.16m
bep b1
non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation The joint overlap expressed by the joint is as follows: capacity is a measure of the deformation thatgeometry can be obtained before failure somewhere in the
fy t0 1.1 2 h1 b1 bep M0 Mj 3 sin( ) sin( )
connection causes in the moment resistance. e 0.55 h0 0.55h0 0.11 m e 60 mm a drop
Sabah Shawkat ©
N 1Rdchordpunching
N1Rdchordpunching 1295.71008kN
The value N1Rdchordpunching decrease about (1-0.717 = 0.283 times) Resistance of the joint:
The chord face yield determines the resistance of the joint, which then is:
N1Rdchordfaceyield 755.71341kN
N1sdbrace 750kN
N1Rdchordfaceyield N1sdbrace
Ok
Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place between the element on one side of the joint and that on the other. Such a joint is known as a
For (joint strength, the following classes beallowed) distinguished: eccentricity is within the can limits
nominally pinnedh MhRd ≤ 0,25 Mpl.Rd h2 0 sin 1 2 1 q e q 76.46683 mm partial-strength 0,25 M pl.Rd < MRd < Mpl.Rd 2 sin 1 sin 2 2 sin 1 2 sin 2 full-strength MRd ≥ Mpl.Rd q sin 1 The relative value of the overlap λ is: ov 0.53252 ov full-strength if rotation capacity is ov h1 not checked MRd ≥ 1,2 Mpl.Rd Brace member failure: Now 0.5 ov 0.8 so the following value is obtained for the where MRdeffective width: is the design moment resistance of the connection 2 Mpl.Rd 10 isb1the t0 design strength of the beam (full plastic moment). beff b0 t1
beff 0.05867m beff b1 b1 0.11m 2
semi-rigid connection and, strictly speaking is the condition of most joints which are described as being fixed or rigid. A moment connection could be described as one which although only semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
beov
10 b1 t2
beov b1
b2 t1
beov 0.06m
N1Rdbrace fy t1 2 h1 4 t1 beff beov
1.1 M0 Mj
N1Rdbrace 609.3kN
Resistance of the joint: The resistance of the joint is Resistance of thecharacteristic joint: Moment-rotation of a semi-rigid joint with enough plastic rotation capacity sufficient, since N1Rdbrace is > than N1sd. For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
189
A lower corner joint in a lattice structure
A T or a Y joint
The resistance of the lattice´s lower corner can be determined using the formulae for
The joint geometry and loading are as follows:
fy 355MPa
overlapped joints which consider the lower chord as continuous Figure below.
M0
1.1
Mj
1.1
E 210 GPa
The resistance of the joint can be determined for the lower corner with the following joint
Brace member:
Chord member:
members:
168.3x8
219.1x12
fy 355MPa
1.1
M0
1.1
Mj
E 210 GPa
Brace member:
Chord member:
110x110x6
160x160x10
b1 110 mm
h1 110 mm 2
t1 6 mm
A1 2403 mm
N Rd A1 1
fy
NRd 775.51kN
1.1
90deg
2
2
b0 160 mm
h0 160 mm
t0 10 mm
A0 5657 mm
N Rd A1 2
N0sdchord 1420kN
Tension
N1sdbrace 670kN
Compression
np
47deg
pEd
Npsd
b2 b0
The following overlap value is obtained:
q e
q sin 1 h1
ov
i
pEd
M0 Mj
fz0
1.1
90deg
N1sdbrace 560kN
Compression
Npsdchord 1320kN
Compression
N psd
A 0 fz0
M 0sd W el fz0
is the chord compression stress due to force Npsd and bending moment M0sd
N0sd N iSd cos i
is the angle between the brace
M0sd is the bending moment of the chord
Now ov 0.8 so the following value is obtained
fy0
is the yield resistance of
d0
is the diameter of the chord
d1
is the diameter of the brace
for the effective width is obtained: 2
beov b1
1.1
member and the chord
0.81623
Brace member failure:
beff b1
M0 Mj
member
The relative value of the overlap λov is:
NRd 1300.27kN
Nisd is the axial force of the brace
q 89.78499 mm
ov
fy 1.1
N0sd is the axial force of the chord
h1 h2 sin 1 2 2 sin 1 sin 2 2 sin 1 2 sin 2
h0
t0 12 mm
Sabah Shawkat ©
h2 h0 t2 t0
e 0 mm
d0 219.1mm A0 7807mm
t1 8 mm
The joint must be design in such a manner that eccentricity:
2
d1 168.3mm A1 4029 mm
beov
10 b1 t2 b2 t1
beov 0.11458m
the chord 1.1 N1Rdbrace fy t1 2 h1 4 t1 beff beov M0 Mj
N1Rdbrace 814.4kN NRd N1Rdbrace
NRd 775.51364kN N1Rdbrace 814.4kN
member
Connections in steel structures Connections in steel structures
190 132
Connections M0 in steel Mj structures N psdchord np fy A0 1.1
A X joint condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
np 0.52391
bending but allow rotation about its axis. Note that if pinned or fixed joints are made between
Joints between structural line2elements, in one plane, may be classified as simple connections, kp 1.0 0.3 np np kp 0.76048 as sliding connections, as pin or pinned connections as fixed connections, also known as rigid d1 d0 connections. A simple connection allows rotation and movement any direction except 0.76814 in9.12917 d0 2 t0 downwards and only transmits shear force that acts downwards at a support. A sliding connection allows movement along the line of the element and rotation and only transmits shear force. A pinned connection allows rotation but no translational movement, it transmits shear Chord face yield: and The axialresistance forces but not joint bending moment. of the determined byAthefixed chordconnection face yield does is: not allow translational movement or rotation and transmits shear, axial forces, bending and torsional moment. 2
N 1Rdchordface
fy t0
sin( )
2 0.2 2.8 14.2 kp
1.1 M0 Mj
N1Rdchordface 614.84kN
The joint geometry and loading arethen as follows: an element and an immovable support that end of the element may not move translationally or rotate space, from a movement to the member on the fy in355 MPaas distinct M0 1.1 Mj which 1.1 is merely E relative 210 GPa other side of the joint. Fixed joints, or nearly fixed joints, between two members are said to provide continuity between the members at the joint and the Chord member: Brace member:so that there is little or no rotation members behave as if no joint existed. However, the joint 193.7x12 is not necessarily fixed in space and 168.3x8 may rotate about a support for example. A way of characterising the degree of fixity or stiffness 2 2 d1 168.3mm d0 193.7mm A1 4029 mm A 6850mm provided by a semi-rigid connection either to a 0support or another member is to measure the t1 at8the mmjoint as the bending moment on tthe 12 mm 90deg 0 joint rotation is varied. Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column Compression fy N1sdbrace 490kN N Rd A1 connection designed the beam into the column. curves in general 1.1 to transfer a moment from N Compression 1620 kN M-φ psdchord
non-linear, practical application, it is necessary to idealise the M-φ curves. The rotation NRd for 1300.27kN capacity is a measure of the deformation that can be obtained before failure somewhere in the
Sabah Shawkat © connection causes a drop in the moment resistance. M0 Mj pEd M0 Mj N psd M0sd For strength, the following classes can be np distinguished: fz0 1.1 1.1 z0 Rd ≤W el fz0Mpl.Rd A0 fM nominally pinned 0,25
Chord punching shear:
partial-strength
The chord punching shear resistance is given by:
N1Rdchorpunching
fy t0 d1 1 sin( ) 2 3 2 sin( )
1.1 N 1182.2kN M0 Mj 1Rdchorpunching
Resistance of the joint: The resistance of the joint is the smallest of the above values: Column web in shear, compression and tension
N1Rdchordface 614.8404kN N1sdbrace N1sdbrace 560kN In practice it is often difficult to fabricateNfixed connections and some rotation maytake place 1Rdchordface
MRd ≥ Mpl.Rd
full-strength if rotation capacity is M0 Mj N psdchord np not checked fy A0 1.1
MRd ≥ 1,2 Mpl.Rd
where np 0.73281 MRd is the design moment resistance of the connection
as being fixed or rigid. A moment connection could be described as one which although only
Mpl.Rd is the design strength of the beam (full plastic moment). 2 kp 1.0 0.3 np np
kp 0.61906
between the element on one side of the joint and that on the other. Such a joint is known as a semi-rigid connection and, strictly speaking is the condition of most joints which are described
0,25 Mpl.Rd < MRd < Mpl.Rd
Npsd N0sd N iSd cos i full-strength
d1 d0
0.86887
semi-rigid approaches the behaviour of a fixed connection and transfers a substantial bending moment. Note that connections may be fabricated for particular requirements so that, for example, they may allow rotation in the plane of the elements but prevent twisting about the axis of the element thus allowing torsional moments to be transmitted. This is a common
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
191
Chord face yield:
An overlapped K joint
The resistance of the joint determined by the chord face yield is:
The joint geometry and loading are as follows:
fy 355MPa 2
N 1Rdchordface
fy t0 1.1 5.2 k p M0 Mj sin( ) 1 0.81
N1Rdchordface 505.04kN
M0
1.1
Mj
Chord member:
193.7x12 5
Compression member 2
2
t1 6.3mm 1 45 deg
fy t0 d1 1 sin( ) 1.1 N1Rdchorpunching 2 3 2 sin( ) M0 Mj
152x6 3
d1 152 mm A1 2884mm
t0 12.5 mm
The chord punching shear resistance is given by:
E 210 GPa
Brace member:
d0 193.7mm A0 7116 mm
Chord punching shear:
1.1
N1Rdchorpunching 1182.2kN
2 55 deg
N 1Sd 720 kN
Compression
N 2Sd 610 kN
Tension
N pSd 750 kN
Compression
N 1Rd A1
fy 1.1
N1Rd 930.75kN
Tension member
Sabah Shawkat © 127x6 3
2
A2 2389mm
Resistance of the joint:
np
The resistance of the joint is the smallest of the above values
N1Rdchordface 505.03794kN
N1Rdchordface N1sdbrace
N1sdbrace 490kN
1.1 N pSd 1 fy A0
np 0.32658
t2 6.3 mm N 2Rd A2
kp 1.0 0.3 np np
d2 127 mm
fy
1.1
N2Rd 771kN
2
kp 0.87003
d1 d2
0.72019
2 d 0
e1 35 mm
20 mm
9.685
e1 0.25d0
0.25d0 0.04842m
q e1
d0
Ok
sin 1 2 d1 d2 2 sin 1 sin 2 2 sin 1 2 sin 2
d0
Connections in steel structures Connections in steel structures
q 39.17295 mm
192 132
Chord face Connections in yield: steel structures
An overlapped K joint condition at steel beam supports. By contrast the element may be fixed in its plane to transmit
The chord face yield resistance for the compression is given by:
The joint geometry andabout loading as Note follows: bending but allow rotation its are axis. that if pinned or fixed joints are made between
Joints between structural line elements, in one plane, may be classified as simple connections,
an element andMPa an immovable end1.1 of the element fy 355 M0support 1.1 thenthat E may 210 not GPamove translationally Mj
as sliding connections, as pin or1.2 pinned connections as fixed connections, also known as rigid 0.024 0.2 kg 1.82901 kg 1 connections. A simple connection allows rotation and movement in any direction except q
or rotate space, as distinct from a movement which is merely relative to the member on the Braceinmember: Chord member:
1.33
2 t 0 shear downwards and only1 transmits force that acts downwards at a support. A sliding e
connection allows movement along the line of the element and rotation and only transmits shear 2 fy t0 1.1 force. A pinned connection allows movement, it transmits shear N 1Rdchordface ( 1.8 rotation 10.2 )but kgno kp translational M0 Mj sin 1 and axial forces but not bending moment. A fixed connection does not allow translational N1Rdchordface 1037.88kN movement or rotation and transmits shear, axial forces, bending and torsional moment. For the tension member, the corresponding resistance is:
sin 1 sin 2
N2Rd 895.92kN
N 2Rd N 1Rdchordface
other133x6 side of joints, between two members are said to 3 the joint. Fixed joints, or nearly fixed193.7x12 provide continuity so that there is little or no rotation between the members at the joint and the 2 2 d 133 mm d0 193.7mm A1 2508 mm A 6850mm members behave as if no joint1 existed. However, the 0joint is not necessarily fixed in space and 6.3 mma support for example. A way of characterising t0 12 mm the degree of fixity or stiffness t1rotate may about provided by a semi-rigid connection either to a support todeg measure the fy 1 or33another deg member 2 is46 N1Rd 809.4kN N 1Rd A1 rotation at the joint is varied. 1.1as the bending moment on the joint Compression N 720 kN 1Sd
Figure bellow defines the strength, stiffness and deformation capacity of a beam-to-column N2Sd 600.5kN Tension connection designed to transfer a moment from the beam into the column. M-φ curves in general Compression 800kN NpSd non-linear, for practical application, it is necessary to idealise the M-φ curves. The rotation
Chord punching shear:
N pSd of the deformation that can be obtained before failure somewhere in the capacity is1.1 a measure np 1 fy Aa0drop in the moment resistance. connection causes
The chord punching shear resistance for the compression is given by:
For strength, the following classes can be distinguished: np 0.36188
N 1Rdchorpunching
nominally pinned MRd ≤ 0,25 Mpl.Rd 2 kp 1.0 0.3 np np partial-strength 0,25 Mpl.Rd < MRd < Mpl.Rd kp 0.85215 full-strength MRd ≥ Mpl.Rd
Sabah Shawkat © fy t0 d1 1 sin 1 1.1 2 sin 1 2 M0 Mj 3
N1Rdchorpunching 1898.63kN
For the tension member, the corresponding resistance is:
fy t0 d2 1 sin 2 1.1 N 2Rdchorpunching 2 sin 2 2 M0 Mj 3
N2Rdchorpunching 1259.65kN Column web in shear, compression and tension In practice it is often difficult to fabricate fixed connections and some rotation may take place Resistance of the on joint: between the element one side of the joint and that on the other. Such a joint is known as a The resistance of the joint is thespeaking smallestisofthe thecondition above values: semi-rigid connection and, strictly of most joints which are described Compression as being fixed or member: rigid. A moment connection could be described as one which although only
N1Rdchordface 1037.88247kN N1Sd N1Sd asubstantial 720kN bending 1Rdchordface semi-rigid approaches the behaviour of aNfixed connection and transfers moment. Note that connections may be fabricated for particular requirements so that, for Tension member: example, may allow rotation in the N plane of Nthe 895.91882kN N2Sd twisting 610kNabout the N2Rd they 2Rd 2Sdelements but prevent axis of the element thus allowing torsional moments to be transmitted. This is a common
full-strength d1if rotation capacity is 0.68663 not checkedd0 where
MRd ≥ 1,2 Mpl.Rd
d0 9.685 is the design moment resistance of the connection 20 mm M is the design strength the beam (full plastic moment). pl.Rd e1 40.0mm e1 0.55dof 0
MRd
0.55d0 0.10654m
q e1
Ok
sin 1 2 d1 d0 2 sin 1 sin 2 2 sin 1 2 sin 2
d0
q 114.29583 mm
Moment-rotation characteristic of a semi-rigid joint with enough plastic rotation capacity For stiffness, the classification is as follows:
Connectionsininsteel steelstructures structures Connections Connections Connectionsininsteel steelstructures structures
193
Chord face yield: The chord face yield resistance for the compression is given by:
kg
0.2
0.024
1
1.2
kg 2.14992
q 1.33 2 t 0
1 e
2
N 1Rdchordface
fy t0
sin 1
( 1.8 10.2 ) kg kp
1.1 M0 Mj
N1Rdchordface 1376.22kN For the tension member, the corresponding resistance is:
sin 1 sin 2
N2Rd 1041.99kN
N 2Rd N 1Rdchordface
Sabah Shawkat ©
Chord punching shear:
The chord punching shear resistance for the compression is given by: N 1Rdchorpunching
fy t0 d1 1 sin 1 1.1 2 sin 1 2 M0 Mj 3
N1Rdchorpunching 2432.41kN
For the tension member, the corresponding resistance is: N 2Rdchorpunching
fy t0 d0 1 sin 2 2 sin 2 2 3
1.1 M0 Mj
N2Rdchorpunching 2260.47kN Resistance of the joint: The resistance of the joint expressed by the brace member is: Compression member:
N1Rdchordface 1376.21874kN N1Rdchordface N1Sd
N1Sd 720kN
Tension member:
N2Rd 1041.98662kN
N2Rd N2Sd
N2Sd 600.5kN
Connections in steel structures Connections in steel structures
Sabah Shawkat © Fire design / protection Unprotected steel structure Steelwork insulated by fire protection material Calculate the resistance of column in a fire situation Hollow section exposed to fire on three sides Hollow section exposed to fire on two opposite sides Hollow section exposed to fire on two adjacent sides
Sabah Shawkat ©
196 196
Fire design / protection Fire design / protection
strength modulus of elasticity decrease at elevated temperatures. Moreover, whole TheThe strength andand modulus of elasticity decrease at elevated temperatures. Moreover, thethe whole steel cross-section heats during fire. Normally steel structures have protected steel cross-section heats up up during fire. Normally thethe steel structures have to to be be protected
structural engineer is not specifically involved in the design active protection, or in TheThe structural engineer is not specifically involved in the design forfor active firefire protection, or in layouts compartment sizes escape routes. These aspects under guidance thethe layouts forfor firefire compartment sizes andand escape routes. These aspects fallfall under thethe guidance of the architect integral of building design. A structural engineer must aware of the architect andand areare an an integral partpart of building design. A structural engineer must be be aware
against fire, demonstrated calculations structures capable against fire, or or hashas to to be be demonstrated by by calculations thatthat thethe structures areare capable of of withstanding in an unprotected state required time. withstanding firefire in an unprotected state forfor thethe required time. stress-strain relationship elevated temperature presented figure above. Three TheThe stress-strain relationship at at elevated temperature is is presented in in figure above. Three
of what is intended in this respect however, as fire safety design requires integrated approach of what is intended in this respect however, as fire safety design requires an an integrated approach
reduction factors relative to the yield strength have been defined steel. factor . The The reduction factors relative to the yield strength have been defined forfor steel. TheThe factor kp,k.p,
members of the design team. by by all all members of the design team.
effective yield strength corresponds strain modified reduction factor effective yield strength corresponds to to thethe strain y,The modified reduction factor y,The
required level of fire performance structures is typically given in terms a reaction TheThe required level of fire performance forfor structures is typically given in terms of aofreaction to to
used in calculations where deformation of the appropriate structure to be taken k,kis used in calculations where thethe deformation of the appropriate structure hashas to be taken ,is
classification a fire resistance rating, as given in the Building Regulations. firefire classification andand a fire resistance rating, as given in the Building Regulations.
account. modulus of elasticity in fire condition is obtained using factor intointo account. TheThe modulus of elasticity in fire condition is obtained using factor kE,kE,
Fire resistance is typically presented a duration time. resistance element Fire resistance is typically presented as as a duration of of time. TheThe firefire resistance of of an an element (wall, floor roof) a measure ability withstand effects more (wall, floor or or roof) is aismeasure of of its its ability to to withstand thethe effects of of firefire in in oneone or or more
situations, temperature steel increases together with temperature In In firefire situations, thethe temperature of of thethe steel increases together with thethe temperature of of thethe
ways as follows: ways as follows:
gases in fire component. temperature of the steel increases, strength deformation gases in fire component. AsAs thethe temperature of the steel increases, its its strength andand deformation properties transformed. According their structures have different resistance properties areare transformed. According to to their use,use, structures have different firefire resistance
Structural ‘loadbearing capacity’ to maintain design loads under 1. 1.Structural ‘loadbearing capacity’ to maintain thethe design loads under firefire (R)(R)
requirement (e.g. requirements bearing capacity compartment). requirement (e.g. requirements forfor bearing capacity andand compartment).
Sabah Shawkat ©
Integrity’ of the element which is the resistance to fire penetration 2. 2.Integrity’ of the element which is the resistance to fire penetration (E)(E)
In the situations, temperature of the steel members increases slower than of the In the firefire situations, thethe temperature of the steel members increases slower than thatthat of the firefire
Insulation’ which is the resistance transfer heat face element 3. 3.Insulation’ which is the resistance to to thethe transfer of of heat to to thethe face of of thethe element
compartment. development distribution steel temperature depends shape compartment. TheThe development andand distribution of of steel temperature depends on on thethe shape of of
remote metal components such as nails, screws bolts remote forfor thethe firefire (I) (I) metal components such as nails, screws andand bolts
steel member thermal properties. It is always necessary calculate steel thethe steel member andand its its thermal properties. It is always necessary to to calculate thethe steel
temperature increases, strength modulus of elasticity of the steel changes. AsAs thethe temperature increases, thethe strength andand thethe modulus of elasticity of the steel changes.
temperature required resistance period, since a steel member may reach temperature up up to to thethe required firefire resistance period, since a steel member may reach its its
o o However, room temperature values yield strength used to 400 yield C. C. TheThe yield However, thethe room temperature values forfor yield strength cancan be be used up up to 400
maximum temperature during a point where compartment temperature starts maximum temperature during firefire at at a point where thethe firefire compartment temperature starts
strength corresponds a total elongation modulus elasticity is constant strength corresponds to to a total elongation of of 2%.2%. TheThe modulus of of elasticity is constant up up to to
decreasing according parametric model. using a fire retardant material, decreasing according to to thethe parametric firefire model. ByBy using a fire retardant material, thethe
o o 100100 C. C.
evolution of steel temperature slowed down, which lengthens resistance period. evolution of steel temperature cancan be be slowed down, which lengthens thethe firefire resistance period. Often it is necessary protect steel components order slow down increase Often it is necessary to to protect steel components in in order to to slow down thethe increase in in temperature during fire. temperature during fire. Several retardant methods applicable with allow sections Structural steelwork Several firefire retardant methods areare applicable forfor useuse with allow sections Structural steelwork must either protected or designed in such a way as avoid to avoid premature failure of the structure must either be be protected or designed in such a way as to premature failure of the structure when exposed to fire. when exposed to fire. Fire protection may given to structural steelwork members Fire protection may be be given to structural steelwork members by by thethe useuse of:of: a) Intumescent paints a) Intumescent paints b) Mineral boards b) Mineral boards c) Concrete encasement. c) Concrete encasement.
Stress-strain relationship at elevated temperatures Stress-strain relationship at elevated temperatures
Firedesign design Fire Fire Firedesign design
197
For the engineers, there is a responsibility to specify materials, and to provide details that: a.
reduce the potential for fire ignition
b. limit the spread of fire c.
stop the passage of hot gases and smoke
An appropriately designed building will allow people remote from the seat of a fire to escape
Fire design can be based on either the standard time – temperature curve common to all fire situation or on parametric temperature-time curve. An alternative method for calculating the evolution of temperature in fire compartment is the parametric model presented in Euro-code 1, section 2.2. This model also accounts for openings in the fire compartment, the thermal properties of the wall materials and the magnitude of the
and provide a building from which the fire service can deal with the fire safely and effectively.
fire load in determining the development of the temperature. The parametric model can be used
Structural fire safety is achieved either by what is called ‘passive protection’ e.g. fire resistant
if the fire compartment area is less than 100 m2, there are no openings in the fire compartment
lining boards and/or ‘active protection’ e.g. smoke ventilation, alarm systems and sprinklers.
ceiling, and the height of the fire compartment does not exceed 4m. The temperature of the fire
For the structural engineer, the material choice within the structural solution will influence the
compartment increases as long as there is flammable material. Finally, the temperature reaches
passive and active fire protection strategy.
a maximum value of max after which the fire compartment temperature starts decreasing.
Steel structures can be protected against fire by insulating them or increasing their heat retention capacity. Structural solutions can also be used to increase the fire resistance period. In addition to the cost of materials, installation and maintenance costs should be considered when selecting the fire retardant method
Sabah Shawkat ©
Fire retardation by (mineral wool boards, vermiculite boards, calcium silicate boards, plaster
board and profiled elements, wood fibre plaster boards, cement cellulose boards, sprayed
boards, sprayed vermiculite, fire retardant paints, concrete infill of hollow section, water infill of hollow sections, placing columns outside the fire compartment, placing columns outside the wall).
There are two broad standards for the design methods of fire resistance of buildings: prescriptive and performance-based.
Temperature-time curve in standard and parametric fire models
A prescriptive method defines a structural fire design fairly precisely in terms of the materials used, shape and size of structural elements, thickness of fire protection materials and construction details etc.
The heat retention capacity of hollow sections can be improved for instance with concrete infill.
Traditionally, the design recommendations are mainly based on the experience with identical
Hollow sections are efficient in fire design, since their section factor (the ratio of fire-exposed
or similar standard fire tests. This concept works very well in a static situation but inhibits
area to unit mass) is smaller than that of open sections. In addition, hollow sections with their
innovation and development of construction industry. It can become very restrictive in
rounded corners are well-suited for fire –retardant painting.
situations where designs need to evolve to meet architectural or aesthetic requirements. For
Unfortunately, a fire heated structural element in a building does not behave in an isolation
these reasons, the prescriptive designs have been evolving for many years towards the
manner. The continuity and interaction of the heated elements to the rest of the building
performance-based designs.
inevitably cause additional thermal stresses. Their softening due to elevated temperatures will
Factors affecting the development of a real fire include the mode of combustion, the shape of
reduce their stiffness and lead to load redistribution.
fire compartment, the magnitude and type of fire load, the supply of air needed for combustion and the fire extinguishing system. However, the models used in practical design are simpler.
Fire design Fire design
198 196
Fire design / protection Unprotected steel structure The increase of temperature in an unprotected steel structure is calculated as follows: Am The structural engineer is not specifically involved in the design for active fire protection, or in V compartment sizes and escape routes. These aspects fall under the guidance the layouts for fire
al hneta t c a of the architectaand are an integral part of building design. A structural engineer must be aware
of what is intended in this respect however, as fire safety design requires an integrated approach A by all m members of the design team. is the section factor for unprotected steel members (m-1), but not less than 10 m-1 V The required level of fire performance for structures is typically given in terms of a reaction to fire classification and a fire resistance rating, as member given in per the unit Building Regulations. is the exposed surface area of the length m2/ m Am Fire resistance is typically presented as a duration of time. The fire resistance of an element 3/m) the volume of the of member per unit length (mthe V floor or isroof) (wall, is a measure its ability to withstand effects of fire in one or more wayscdas follows: is the specific heat of steel (J/kg K) is the design value of the net flux per unit area (W/under m2) fire (R) hnetdStructural 1. ‘loadbearing capacity’ to heat maintain the design loads
The strength and modulus of elasticity decrease at elevated temperatures. Moreover, the whole is theheats ambient gas temperature of the steel member (oC) have to be protected g steel cross-section up during fire. Normally the steel structures against fire, or has to be demonstrated by calculations that the structures are capable of is the surface temperature of the steel member (oC) m withstanding fire in an unprotected state for the required time. The stress-strain relationship at elevated temperature is presented in figure above. Three The radiative net heat flux reduction factors relative to the yield strength have been defined for steel. The factor kp,. The 8 hnetr yield 273the res 5.67 10 4 strain m y,273 4 r to effective strength corresponds The modified reduction factor k,is used in calculations where the deformation of the appropriate structure has to be taken is the configuration factor, 1 into account. The modulus of elasticity in fire conditionisobtained using factor kE, is the resultant emissivity, res 0.50 res In fire situations, the temperature of the steel increases together with the temperature of the temperature of the environment of the and member (oC), rin fire component.is gases Asthe theradiation temperature of the steel increases, its strength deformation whichAccording may be represented by the gas temperature θ g fire resistance properties are transformed. to their use, structures have different requirement (e.g. requirements for bearing capacity and compartment). the surfaceof temperature of the member (oC) mfire situations, the is In the temperature the steel members increases slower than that of the fire
Sabah Shawkat ©
2. Integrity’ of the element which is the resistance to fire penetration (E) t is the time interval (s), but not more than 5 s 3. Insulation’ which is the resistance to the transfer of heat to the face of the element
kgas nails, screws and bolts remoteisforthe theunit firemass (I) metal components such , a of steel a 7850 3 As the temperature increases, the strength and the modulus of elasticity of the steel changes. m
compartment. The development and distribution of steel temperature depends on the shape of 8 2 K4) Stefanproperties. Boltzmann Itconstant (W/m 67 member 10 the 5steel and is itsthe thermal is always necessary to calculate the steel
The design value oftothe met heat flux of 2%. The modulus of elasticity is constant up to strength corresponds a total elongation
temperature to theJ/kg required resistance a steel The value up Ca=600 K mayfire be taken as theperiod, specificsince heat value of member steel, or itmay mayreach be its maximum temperature during fire at a point where the fire compartment temperature starts calculated more accurately as follows: decreasing according to the parametric fire model. By using a fire retardant material, the
100ohC. netd
3 2 down, which 6 3 o resistance period. o evolution temperature can10 be slowed the for 20 Ca of 425steel 0.773 a 1.69 a 2.22 10 alengthens Cfire a 600 C
However, the room temperature values for yield strength can be used up to 400oC. The yield nc hnetc
nr hnetr
nc
is the factor to account for different national types of test
hnetc
is the net heat flux due to convection (W/m2)
nr
is a factor to account for different national types of test,
Often it is necessary to protect steel components in order to slow down the increase in 13002 o o for 600 C a 735 C Ca 666 fire. temperature during 738 a Several fire retardant methods are applicable for use with allow sections Structural steelwork 17820or designed in such a wayoas to avoid premature o mustCeither545 be protected failure of the structure for 735 C a 900 C a a 731 when exposed to fire.
knetr
is the net heat flux due to radiation (W/m3)
for Ca 650 900 C a 1200 C Fire protection may be given to structural steelwork members by the use of:
o
a) Intumescent paints Where θ a is the steel temperature b) Mineral boards
The convective net heat flux hnetc c
c g
m
c) Concrete encasement.
W
is the coefficient of heat transfer by convection c 25 2 Stress-strain relationship at elevated temperatures m K fire
in standard
Firedesign design Fire Fire Firedesign design
o
199
Steelwork insulated by fire protection material The temperature increase in an insulated steel member is calculated as follows. p
Ap gt at 10 at t e 1 gt Ca a V 1 3 Ap cp p dp ca a V dp
Ap V
but
at
0
is the section factor for steel members insulated by fire protection material (m-1)
is the inner surface area of the fire protection material per unit length of the member Ap (m2/m)
Sabah Shawkat ©
V
is the volume of the member per unit length (m3/m)
ca
is the specific heat of steel (J/kg K), 600J/kg K
cp
is the specific heat of the fire protection material (J/kg K) 1000J/kg K
dp
is the thickness of the fire protection material (m)
t
is the time interval (s), but not more than 30 s
at
is the steel temperature (oC)
gt
is the ambient gas temperature (oC)
gt
is the increase of the ambient gas temperature (oC) during the time interval Δ t
p
is the thermal conductivity of the fire protection material (W/m K) 0,25W/m K
a
is the unit mass of steel (kg/m3) 7850 kg/m3
p
is the unit mass of the fire protection material (kg/m3) 140kg/m3
State of construction after fire
Fire design Fire design
200 196
The moisture in fire protection material delays the rise of the steel temperature until the moisture Fire design / protection
development of theoftemperature for bothatthe unprotected and the fire-protected TheThe strength and modulus elasticity decrease elevated temperatures. Moreover, theprofile whole as
evaporates. During the time delay, it can be assumed that the steel temperature stays at 100oC,
well as for the fire compartment one hour in fire is presented following steel cross-section heats up duringduring fire. Normally thestandard steel structures have to in bethe protected
the engineer moistureisinnot thespecifically fire protection material getsdesign out through the fire surface oppositeortointhe Thebecause structural involved in the for active protection,
figure.fire, Theortemperature thecalculations unprotected that profile calculatedare from the formula against has to be development demonstratedofby theisstructures capable of
The for delay can be calculated the routes. following formula: thefire. layouts firetime compartment sizes andfrom escape These aspects fall under the guidance
withstanding fire in state for the required time. Δ θ at. of an theunprotected fire-protected profile from the formula Δ θ at and that
of the architect and2are an integral part of building design. A structural engineer must be aware pp p dp of what tv is intended in this respect however, as fire safety design requires an integrated approach 5 p by all members of the design team.
effective yield strength corresponds to the strain y,The modified reduction factor
The stress-strain relationship at elevated temperature is presented in figure above. Three reduction factors relative to the yield strength have been defined for steel. The factor kp,. The
The required level of fire performance for structures is typically given in terms of a reaction to pp is theand moisture of rating, the fireasprotection material as a Regulations. percentage by weight. firewhere classification a fire content resistance given in the Building
k,is used in calculations where the deformation of the appropriate structure has to be taken
After the delay time, the presented steel temperature is assumed to develop theanformula Fire resistance is typically as a duration of time. The fireaccording resistancetoof element
In The fire following situations, values the temperature steel increases together with the temperature of the are used inofthethe calculation:
(wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more p
ways as follows: dp
Ap gt at 10 at t e 1 gt Ca a V 1 3 1. Structural ‘loadbearing capacity’ to maintain the design loads under fire (R)
into account. The modulus of elasticity in fire condition is obtained using factor kE,
gases in fire component. As the temperature of the steel increases, its strength and deformation kN kN fy have 355 different MPa Gk 45 Q 40 to their L use, 6 mstructures properties are transformed. fire resistance k1According m m requirement (e.g. requirements for bearing capacity and compartment). GA 1 the 1.35 ofQthe steel 1.5 members Mfi 1 M1 1.1 than that of the fire G In the firesituations, temperature increases slower
Sabah Shawkat ©
2. Integrity’ of the element which is the resistance to fire penetration (E)
3. Insulation’ which is the resistance to the transfer of heat to the face of the element remote for the fire (I) metal components such as nails, screws and bolts
compartment. The development and distribution of steel temperature depends on the shape of tf 20 mm bf 250 mm tw 10 mm the steel member and its thermal properties. It is always necessary to calculate the steel
As the temperature increases, the strength and the modulus of elasticity of the steel changes.
tf hsince m member may reach its h 800up mm H required 800 mm temperature to the fire hresistance a steel w h 2period, w 0.76
However, the room temperature values for yield strength can be used up to 400oC. The yield
maximum temperature during fire at a point where the fire compartment temperature starts Am 2.33 m Am 3 bf 4 tf 2 hw 2 tw decreasing according to the parametric fire model. By using a fire retardant material, the
strength corresponds to a total elongation of 2%. The modulus of elasticity is constant up to 100oC.
2 evolution temperature can be slowedVdown, which V 2ofbsteel 0.0176 m lengthens the fire resistance period. f tf hw tw Often it is necessary to protect steel components in order to slow down the increase in
Schematic picture of the influence of the moisture content in the fire protection material on the steel temperature development.
temperature during fire. Several fire retardant methods are applicable for use with allow sections Structural steelwork must either be protected or designed in such a way as to avoid premature failure of the structure when exposed to fire.
Calculate the bending and shear resistances of the WI800-10-20x250 profile for the fire situation, when the required resistance to fire is 60 minutes. Lateral-torsional buckling of the
Fire protection may be given to structural steelwork members by the use of:
profile is prevented. The cross-section is loaded by the permanent load gk and by the variable
a) Intumescent paints
load qk .and the span length is L. The cross-section is protected with mineral fibre batts and it
b) Mineral boards c) Concrete encasement.
is exposed to fire on three sides according to the figure shown below. The steel grade is S355J2G3.
Stress-strain relationship at elevated temperatures
The temperature – time curve according to the ISO 834 standard
Firedesign design Fire Fire Firedesign design
201
Am V
132.38636m
1
ca 700
J
c 25
kg K
W 2
m K
a 7850
kg m
3
700 oC according to the figure shown below. The following values for the reduction factors are obtained: ky 0.230
1.0
res
p 0.25
W
0.50
t
p 140
m K
cp 1000 5 s
kg m
3
nc
1
nr
J kg K
kx 0.167
kE 0.130
dp 0.020 m
1
Next the cross-section classification is verified:
235 MPa kE fy kx
0.71785
hw tw
76
hw tw
124
section class 3
Sabah Shawkat ©
124 89.0133
Reduction factors for steel strength and modulus of elasticity at elevated temperature
The values of the adaptation factors for the resistance calculation are taken as k1 0.7
and
a 4 mm
fyd
fyf
bw
After one hour of fire, the temperature of the unprotected profile is 939 oC and that of the fire-
tw
5.71716
74.86863
protected one is 600. The reduction factors of the strength and the modulus of elasticity in the fire-protected cross-section are obtained using the value corresponding to the temperatures of
Fire design Fire design
1.1
fyf 355 MPa
fyd 322.72727 MPa
c
throat thickness of the neck weld
bw H 2 tf Flange
tf Web
k2 1.0
2 a
bw 0.74869 m
Compression
Bending
c
bf
tw 2
hw H 2 tf
c 7.3 t f bw tw
67.5
2 a
c 0.11434m hw 0.76 m
Class 1
Class 2
202 196
0.00005 at Moreover, the whole The strength and modulus of elasticitydecrease 0.005 166666.66666667 elevated temperatures.
The entire/ protection flange is effective. Calculate the effective width of the web Fire design
235 k 23.9 0.81362 The structural engineer is not355 specifically involved in the design for active fire protection, or in the layouts for fire compartment sizes and escape routes. These aspects fall under the guidance bw
of the architect and design. A structural engineer must be aware tw are an integral part of building p 0.22 p of what is intended in this respect however, as fire safety design requires an integrated approach 2 28.4 k p by all members of the design team. p 0.663 The required level of fire performance for1.00798 structures is typically given in terms of a reaction to fire classification and a fire resistance rating, as given in the Building Regulations.
0.6 beff‘loadbearing be2 0.22982 m to maintain the design loads under fire (R) be2 Structural 1. capacity’ The depth of the ineffective region: 2. Integrity’ of the element which is the resistance to fire penetration (E)
withstanding fire in an for the required time. 166666.66666667 0.005 unprotected state 0.00395 The stress-strain relationship at elevated temperature is presented in figure above. Three The depth of the tension side: reduction factors relative to the yield strength have been defined for steel. The factor kp,. The
effective yield corresponds to the strain y,The modified reduction factor Rstrength i
where the deformation of the appropriate structure has to be taken k,is used iin calculations et 0.40039 m et A into account. Theimodulus of elasticity in fire condition is obtained using factor kE,
Fire resistance is typically presented as a duration fire resistance of cross-section: an element The compression region and the tension region ofofthetime. webThe are equal in the gross (wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more hw waysbeff as follows: beff 0.38303 m be1 0.4 beff be1 0.15321 m 2
steel cross-section fire. Normally structures have to be protected 0.0061 heats m 2 up during 0.00198 m 3the steel 188983208.01320994 mm4 Ai Ri Ii of 0.00153 0.00108 2997140.04875064 against fire, or has to be demonstrated by calculations that the structures are capable
i
The depth of the compression side: In fire situations, the temperature of the steel increases together with the temperature of the gases component. As the temperature ecin fire H et ec 0.39961ofmthe steel increases, its strength and deformation The centroid axis shifts down by properties are transformed. According to their use, structures have different fire resistance requirement (e.g. requirements for bearing capacity and compartment). H eM 0.00039 m eM et In the fire situations, the temperature of the steel members increases slower than that of the fire 2 The effective second moment and of area about theofnew centroid axis: depends on the shape of compartment. The development distribution steel temperature
Sabah Shawkat ©
3. Insulation’ hw which is the resistance to the transfer of heat to the face of the element2 bneg be1 be2 bneg 0.00303 m Aw tw H 2 tf Aw 0.0076m remote2 for the fire (I) metal components such as nails, screws and bolts As the temperature increases, the strength and the modulus of elasticity of the steel changes. 2 2 A A 2 Af Aw Af 0.005 m A 0.0176 m f tf bf However, the room temperature values for yield strength can be used up to 400oC. The yield strength to a total elongation of 2%. The modulus of elasticity is constant up to i 1corresponds 4 100oC. b 1 250 mm h 2
H 2
tf 2
z1 0.01 m
Ai
10 mm
b 3 10 mm
be2 h 1 h 2 609.82 mm
h 4 tf
z1
b2
b i h i
h 1 tf
b 4 250 mm
h 3 be1 h 3 153.213 mm
h2 2
z3 H tf
z2 0.32491 m
R i A i zi
h3
z4 H
2
z3 0.70339 m
Ii
1 12
b i h i
its thermal properties. It is always necessary to calculate the steel 4 Ai zi 2 et2 Ai Ieffy 0.00188872m required fire resistance period, since a steel member may reach its
i
i
i
maximum temperature during fire at a point where the fire compartment temperature starts decreasing according to the parametric fire model. By using a fire retardant material, the If the yield strength of the web were 355 MPa, the moment resistance would be evolution of steel temperature can be slowed down, which lengthens the fire resistance period. Often it is necessary Ieffy to protect steel components in order to slow down the increase in MRD 1525.35521 m kN M RD fyd temperature duringecfire.
The value of MRd ismethods obtainedare forapplicable the bending to theStructural theory of steelwork elasticity at Several fire retardant forresistance use with according allow sections theeither normal must be temperature. protected or designed in such a way as to avoid premature failure of the structure
h 4 0.02 m
z2 tf
the steel member and Ieffy Ii temperature up to the
tf
Theexposed reduction when to factor fire. of the design load, when the combination factor of the variable load
z4 0.79 m
11 0.7 Fire protection may be given to structural steelwork members by the use of: GAGk 11Q k1 fi fi 0.60455 a) Intumescent paints GGk Q Q k1 b) Mineral boards
3
c) Concrete encasement. The reduction factor above has been calculated using the partial safety factors. The values for
2
each country have to be checked in the relevant National Application Document NAD
Stress-strain relationship at elevated temperatures
Firedesign design Fire Fire Firedesign design
203
The bending moment at the ultimate limit state:
The shear force at ultimate limit state:
GGk QQk1 L2
Msd 543.375 m kN 8 The bending moment in the fire situation:
Msd
fiMsd Mfi Ed
GGk QQk1 L 2
Vsd
Vsd 362.25 kN
MfiEd 328.5 m kN
The shear force in fire situation: Vfi Ed
fiVsd
VfiEd 219 kN
The shear resistance in the fire situation: M1
VfiRd kx VRd
Mfi
k1 k2
VfiRd 325.149 kN
VfiRd VfiEd
OK
Sabah Shawkat ©
Because the shear resistance in the fire situation is more than twice the design shear force in the fire situation, it is not necessary to study the interaction between the moment and the shear force to the resistance. Moreover, the maximum values of the moment and the shear force appear in different cross-sections.
The reduction factor for the design load level in the fire situation as a function of the ratio between the principal variable load and the permanent loading.
for the fire situation at time t=0 regarding both the bending moment and the shear force.
The bending resistance in the fire situation:
kx 0.167
MRD 1525.35521 m kN
Calculate the critical temperature of the cross-section. The degrees of utilization are calculated
M fi0Rd MRD k1 0.7
k2 1
0M
M1
MfiRd kx MRD
Mfi
k1 k2
MfiRd 400.29679 m kN
MfiRd MfiEd OK
The value of VRd is obtained for the shear resistance at the normal temperature.
Mfi
MfiEd
VfiEd Vfi0Rd
VRd 1239 kN
Fire design Fire design
Mfi0Rd 1677.89073 m kN
0M
Mfi0Rd
V fi0Rd VRd
0V
M1
M1 Mfi
0.19578
Vfi0Rd 1362.9 kN
0V
0.16069
204 196
Fire design The value/ protection of the critical temperature of the cross-section is obtained according to the bending
temperatures. Moreover, TheCalculate strength the andresistance modulus of of elasticity column 190x190x7 decrease attoelevated axial loads in the building shownthe in whole the steel cross-section heats during fire. Normally the steel have to adjacent figure. In a fireupsituation, the compressive load on astructures hollow section is be protected
resistance as: The structural engineer involved in the design for active fire protection, or in is not 1specifically acr 757.90289 acr 39.19 ln 1 482 3.833and escape routes. These aspects fall under the guidance the layouts for fire compartment sizes 0.9674 0V of the architect and are an integral part of building design. A structural engineer must be aware
against fire, or has to be demonstrated by calculations that the structures are capable of Efld 670 kN N flED Efld N flED 670 kN withstanding fire in an unprotected state for the required time. The stress-strain relationship at elevated temperature is presented in figure above. Three
of what is intended in this respect however, as fire safety design requires an integrated approach
reduction factors relative to the yield strength have been defined for steel. The factor kp,. The
by all members of the design team.
effective yield strength corresponds to the strain y,The modified reduction factor
The required level of fire performance for structures is typically given in terms of a reaction to
k,is used in calculations where the deformation of the appropriate structure has to be taken
fire classification and a fire resistance rating, as given in the Building Regulations.
into account. The modulus of elasticity in fire condition is obtained using factor kE,
Fire resistance is typically presented as a duration of time. The fire resistance of an element (wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more
In fire situations, the temperature of the steel increases together with the temperature of the
ways as follows:
gases in fire component. As the temperature of the steel increases, its strength and deformation properties are transformed. According to their use, structures have different fire resistance
1. Structural ‘loadbearing capacity’ to maintain the design loads under fire (R)
Sabah Shawkat ©
2. Integrity’ of the element which is the resistance to fire penetration (E)
3. Insulation’ which is the resistance to the transfer of heat to the face of the element remote for the fire (I) metal components such as nails, screws and bolts
As the temperature increases, the strength and the modulus of elasticity of the steel changes.
o cross-section
Critical steel temperature a function of the degreecan of utilization However, the room temperature as values for yield strength be used upoftothe 400 C. The yield strength corresponds to a total elongation of 2%. The modulus of elasticity is constant up to 100oC.
requirement (e.g. requirements for bearing capacity andsection compartment). Column hollow
In the fire situations, the temperature of the steel members increases slower than that of the fire The fire resistance period required for the building is 15 min. The steel grade used is S355J2H compartment. The development and distribution of steel temperature depends on the shape of and the buckling length of the column is Lfl. The temperature evolution in the fire compartment the steel member and its thermal properties. It is always necessary to calculate the steel is determined with standardfire time-temperature curve. temperature up to thetherequired resistance period, since a steel member may reach its maximum temperature during L t 15fire at a point where the fire compartment temperature starts ft 5 m decreasing according to the parametric fire model. By using a fire retardant material, the evolution of steel temperature can be slowed down, which lengthens the fire resistance period. The temperature of the fire compartment varies with time. In ISO - 834, this is expressed with Often it is necessary to protect steel components in order to slow down the increase in the following formula: temperature during fire. g fire 20retardant 345 log ( 8 t 1are ) applicable g for 738.56095 Several methods use with allow sections Structural steelwork
must either be protected or designed in such a way as to avoid premature failure of the structure when exposed toof fire. Development temperature in unprotected hollow section The temperature increase of unprotected steel is obtained as follow": Fire protection may be given to structural steelwork members by the use of: m a) IntumescentApaints
V
b) Mineral al boards hneta t ca a c) Concrete encasement. Stress-strain relationship at elevated temperatures Industrial hall using I and rectangular steel hollow sections
Fire Firedesign design Fire Firedesign design
205
hnetr
8
res 5.67 10
4 4 g 273 m 273 Am
hnetc
c g
m
hnetd
nc hnetc
nr hnetr
V
at
ca a
hnetd t
Cross-section factors in design, hollow section exposed to fire on all sides
The temperature- time curve according to the ISO 834 standard Development of temperature in unprotected hollow section
Sabah Shawkat ©
The temperature increase of unprotected steel is obtained as follow: Am al
V
ca a
hneta t
b 190 mm h 190 mm
t 7 mm
fy 355 MPa
r1 5mm
M0
1.1
A m 2 b h 4 r0 r0
Am V
146.81576m
c 25 t
5 s
r0 10mm 2
V 2 t ( b h 2 t ) ( 4 ) r0 r1
2
Hollow section
1
W
2
1.0
res
m K nc
1
nr
1
0.50
cp 1000
ca 600 J kg K
p 0.25
J kg K
Square rectangular
or
Am
Ap
V
V
2 b h 4 r0 r0
Circular
d d t t
Fire design Fire design
2 (b h ) 2
W m K
2t ( b h 2 t ) 4 ( 4 ) r0 ri
2
2
2t(b h 2t) 4(4 )r0 ri 2
2
206 196
Fire designbelow / protection Figure presents the evolution of unprotected 190x190x7 hollow section in a standard
of what is intended in this respect however, as fire safety design requires an integrated approach
The strength and modulus of elasticity decrease at elevated temperatures. Moreover, the whole Ap 2 steelVcross-section have to be 1protected 150.20893m 0.00506 mheats up during fire. Normally the steel structures V against fire, or has to be demonstrated by calculations that the structures are capable of J W dp 200 mm ca 600fire in an unprotected p 0.25 t 5 withstanding state for the required time. kg K m K The stress-strain kgrelationship at elevatedkgtemperature is presented J in figure above. Three cp 1000 p 150 a 7850 3 3 reduction factors forK steel. The factor kp,. The m relative to the yield strength m have been defined kg
by all members of the design team.
effective yield strength corresponds to the strain y,The modified reduction factor
The required level of fire performance for structures is typically given in terms of a reaction to
isparameter used in calculations wherewith the deformation the appropriate structure has to be taken k,The ϕ is determined the followingofformula
fire classification and a fire resistance rating, as given in the Building Regulations.
into account. The modulus of elasticity in fire condition is obtained using factor kE, Ap cp p 0.95674 dp ca a V In fire situations, the temperature of the steel increases together with the temperature of the
fire. The curve is calculated using the formula above with time steps of 5 seconds. The conforming to the required resistance periodfire (15 protection, min) is Themaximum structuraltemperature engineer is not specifically involved in fire the design for active or in the layouts fire compartment sizes and escape routes. These aspects fall under the guidance amax for673C of the architect and are an integral part of building design. A structural engineer must be aware
Fire resistance is typically presented as a duration of time. The fire resistance of an element (wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more ways as follows: 1. Structural ‘loadbearing capacity’ to maintain the design loads under fire (R)
gases in fire component. As the temperature of the steel increases, its strength and deformation By replacing the values of material properties and the parameter ϕ in the formula above, the properties are transformed. According to their use, structures have different fire resistance following expression is obtained: requirement (e.g. requirements for bearing capacity and compartment).
Sabah Shawkat ©
2. Integrity’ of the element which is the resistance to fire penetration (E)
In the fire situations, the temperature of the steel members increases slower than that of the fire p
3. Insulation’ which is the resistance to the transfer of heat to the face of the element remote for the fire (I) metal components such as nails, screws and bolts
As the temperature increases, the strength and the modulus of elasticity of the steel changes. Increase in temperature of unprotected hollow sections protected with mineral wool boards However, the room temperature values for yield strength can be used up to 400oC. The yield (t = 15corresponds min) of dimensions strength to a total190x190x7 elongation of 2%. The modulus of elasticity is constant up to o 100Development C. of temperature in a protected hollow section
A column of 190x190x7 is protected with 200 mm mineral wool boards. The temperature increase of the fire protected steel structure conforms with the following formula p
at
Ap gt at 10 t e 1 gt Ca a V 1 3 dp
A p 2 ( b h )
Ap 0.76 m
2
2 t ( b h 2 t ) ( 4 ) r0 r1
temperature during fire. Figurefire above showsmethods the increase in temperature of awith 190x190x7 hollowStructural section protected with Several retardant are applicable for use allow sections steelwork 200mm woolor boards during a standard fire. is calculated formula must eithermineral be protected designed in such a way as to The avoidcurve premature failure using of the the structure above with time steps of 5 seconds. The maximum temperature conforming to the required fire when exposed to fire. resistance period (15 min) is: Fire protection may be given to structural steelwork members by the use of: amax 301oC a) Intumescent paints
Stress-strain relationship at elevated temperatures 2 2 V 2 t ( b h 2 t ) ( 4 ) r0 r1
Ap decreasing according material, the dp 1 to the parametric fire 1 model. By using a10fire retardant t 0.00015 time e 1 0.1004 ca aof V evolution steel temperature can be slowed down, which lengthens the fire resistance period. 1 Often it is necessary3 to protect steel components in order to slow down the increase in
c) Concrete encasement.
maximum p temperature during fire at a point where the fire compartment temperature starts
b) Mineral boards
2
Ap gt and dp development 10 of steel temperature depends on the shape of compartment. The at distribution at t e 1 gt Ca aandV its thermal the steel member properties. It is always necessary to calculate the steel 1 3 temperature up to the required fire resistance period, since a steel member may reach its
Fire Firedesign design Fire Firedesign design
207
Calculate the compression resistance of the box column, where the length of the column is
Calculating structural strength When calculating the compression resistance, the changes in the steel strength and modulus of elasticity caused by temperature during fire resistance period. The adaptation factors for strength and the modulus of elasticity kEθ and kyθ.
5m. Steel S355J2G3 is the material used. Classification of the cross-section, when the effect of the welds is not taken into account:
h 190 mm
tf 7 mm
tw 7 mm
hw h
b 190 mm
bf b 2 tf
fy 355 MPa
M1
hw 0.19 m
1.1
M0
1.1
The strength of hollow section in tension is given by the following formula: Mft
1
Lft 5 m
ft
y
ft
0.67706
Buckling length L cy 5 m
A
1
0.34
L cz 5 m
E 210000 MPa
The column can resist at 15 (min) fire if a 150mm layer of mineral wool is used, because the Flange
compression resistance at 301oC is
bf ky protected 1.0 ft
y
kEprotected 0.7990 0.87525
fy ft A kyprotected 1.2 Mft
Efld 670 kN
b
25.143
tf
Class 1
26.8
Sabah Shawkat © ft
NftRd
kEprotected 0.7990
tf
Web
N ftRd 1026.31871 kN
N ftRd Efld
hw tw
hw
Class 3
34.2
tw
27.143
The cross-sectional parameters:
Lft iy
ky protected fy
kEprotected E
0.97917
An unprotected column does not meet the fire resistance requirements, because the compression
2
A w tw hw
Aw 1330 mm
A f tf bf
Af 1232 mm
area of the web
2
area of the flange
2
A 2 Aw 2 Af
A 5124 mm
resistance at 673 oC ky unprotected 0.2948
kEunprotected 0.17860
fy ft A kyunprotected 1.2 Mft
NftRd
Efld 670 kN
ft
y
ft
0.87525
Iy
N ftRd 302.55876 kN N ftRd Efld
Iz
2 tw hw 12 2 tf bf 12
Fire design Fire design
3
3
2 bf tf
3
12 3
2 hw tw 12
h tf 2 2
2
4
2 Af
b tw 2 2
2 Aw
Iy 28641452mm
2
4
Iz 32179252 mm
208 196
Fire design /Iyprotection iy A
iy 74.76407 mm
The structural engineer is not specifically involved in the design for active fire protection, or in Iz iz for fire compartment iz sizes 79.24711 mm routes. These aspects fall under the guidance the layouts and escape A of the architect and are an integral part of building design. A structural engineer must be aware Resistance based on the strength of the cross-section: of what is intended in this respect however, as fire safety design requires an integrated approach
The strength and modulus of elasticity decrease at elevated temperatures. Moreover, the whole 1 y 0.67706 y 1 y 2 up2 during fire. Normally the steel structures have to be protected steel cross-section heats y y y against fire, or has to be demonstrated by calculations that the structures are capable of withstanding fire in anfunprotected state for the required time. y N ybRd 1119.62in kNfigure above. Three ybRd y A The N stress-strain relationship at elevated temperature is presented M1
reduction factors relative to the yield strength have been defined for steel. The factor kp,. The effective yield strength Buckling about z-axis:corresponds to the strain y,The modified reduction factor
by all members of fthe y design team. N plRd 1653.655 kN N plRd A The required level of fire performance for structures is typically given in terms of a reaction to M0
k,is used in calculations where the deformation of the appropriate structure has to be taken
fire classification and a fire resistance rating, as given in the Building Regulations.
into account. The modulus of elasticity in fire condition is obtained using factor kE,
Fire resistanceofisthe typically presented as flexural a duration of time. The fire resistance of an element Resistance cross-section to the buckling: (wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more b h ways fas follows: Buckling curve b regarding both axes 27.143 25.14286 tw tf
Lcz fy z 0.82574 z A E temperature of the steel increases together with the temperature of the iz the In fire situations,
1. Structural ‘loadbearing capacity’ to maintain the design loads under fire (R)
gases in fire component. As the temperature of the steel increases, its strength and deformation properties aretransformed. According structures z 0.5 z 0.9473 have different fire resistance z2 to their use, 1 z 0.2 requirement (e.g. requirements for bearing capacity and compartment).
Sabah Shawkat ©
Buckling aboutofy-axis: 2. Integrity’ the element which is the resistance to fire penetration (E)
3. Insulation’ which is the resistance to the transfer of heat to the face of the element
remote for the fire (I) metal components such as nails, screws and bolts Lcy increases, fy As the temperature the strength and the modulus of elasticity of the steel changes. y 0.87525 y A i Etemperature However, the yroom values for yield strength can be used up to 400oC. The yield strength corresponds to a total elongation of 2%. The modulus of elasticity is constant up to o 100 C.y 0.5 1 y 0.2 y
2
y
In the fire situations, 1 the temperature of the steel members increases slower than that of the fire z 0.70844 z 1 z compartment. The development and distribution of steel temperature depends on the shape of 2 2 z z z the steel member and its thermal properties. It is always necessary to calculate the steel temperature up to the required fire resistance period, since a steel member may reach its fy N zbRd 1171.521 kN N z A during fire at a point where maximum the fire compartment temperature starts zbRd temperature M1
decreasing according to the parametric fire model. By using a fire retardant material, the evolution of steel temperature can be slowed down, which lengthens the fire resistance period.
0.99782
Often it is necessary to protect steel components in order to slow down the increase in y
1
y
y
N ybRd y A
2
y
fy M1
2
y
0.67706
y
1
temperature during fire. Several fire retardant methods are applicable for use with allow sections Structural steelwork must either be protected or designed in such a way as to avoid premature failure of the structure when exposed to fire.
N ybRd 1119.62 kN
Fire protection may be given to structural steelwork members by the use of:
Buckling about y-axis:
a) Intumescent paints b) Mineral boards
fy y A iy E Lcy
y
0.87525
c) Concrete encasement.
Stress-strain relationship at elevated temperatures y 0.5 1 y 0.99782 y 0.2 y2
Fire Firedesign design Fire Firedesign design
209
Sabah Shawkat ©
Fire design Fire design
210 196
Fire designsection / protection Hollow exposed to fire on three sides
temperatures. Moreover, the whole TheHollow strength and modulus decrease at elevated section exposedof toelasticity fire on two opposite sides steel cross-section heats up during fire. Normally the steel structures have to be protected against fire, or has to be demonstrated by calculations that the structures are capable of
The structural engineer is not specifically involved in the design for active fire protection, or in
withstanding fire in an unprotected state for the required time.
the layouts for fire compartment sizes and escape routes. These aspects fall under the guidance
The stress-strain relationship at elevated temperature is presented in figure above. Three
of the architect and are an integral part of building design. A structural engineer must be aware of what is intended in this respect however, as fire safety design requires an integrated approach
reduction factors relative to the yield strength have been defined for steel. The factor kp,. The
by all members of the design team.
effective yield strength corresponds to the strain y,The modified reduction factor
The required level of fire performance for structures is typically given in terms of a reaction to
k,is used in calculations where the deformation of the appropriate structure has to be taken
fire classification and a fire resistance rating, as given in the Building Regulations.
into account. The modulus of elasticity in fire condition is obtained using factor kE,
Fire resistance is typically presented as a duration of time. The fire resistance of an element (wall, floor or roof) is a measure of its ability to withstand the effects of fire in one or more
In fire situations, the temperature of the steel increases together with the temperature of the
ways as follows:
gases in fire component. As the temperature of the steel increases, its strength and deformation properties are transformed. According to their use, structures have different fire resistance
1. Structural ‘loadbearing capacity’ to maintain the design loads under fire (R)
requirement (e.g. requirements for bearing capacity and compartment).
Sabah Shawkat ©
2. Integrity’ of the element which is the resistance to fire penetration (E)
In the fire situations, the temperature of the steel members increases slower than that of the fire
3. Insulation’ which is the resistance to the transfer of heat to the face of the element
compartment. The development and distribution of steel temperature depends on the shape of
remote for the fire (I) metal components such as nails, screws and bolts
the steel member and its thermal properties. It is always necessary to calculate the steel
As the temperature increases, the strength and the modulus of elasticity of the steel changes.
temperature up to the required fire resistance period, since a steel member may reach its
However, the room temperature values for yield strength can be used up to 400oC. The yield
maximum temperature during fire at a point where the fire compartment temperature starts
strength corresponds to a total elongation of 2%. The modulus of elasticity is constant up to
decreasing according to the parametric fire model. By using a fire retardant material, the
100oC.
evolution of steel temperature can be slowed down, which lengthens the fire resistance period.
Hollow Section
Am
Ap
V
V
Often it is necessary to protect steel components in order to slow down the increase in Am Ap Hollow Section temperature during fire. V
V
Rectangular with
b 2 h 6 r0 2 r0
non-exposed short
2 2 2 t ( b h 2 t) ( 4 ) r0 ri
Several fire retardant methods are applicable for use with allow sections Structural steelwork
b 2 h 2 t ( b h 2 t ) ( 4 ) r0 ri 2
2
side Rectangular with
2 b h 6 r0 2 r0
non-exposed long
2 2 2 t ( b h 2 t) ( 4 ) r0 ri
2 b h 2 t ( b h 2 t ) ( 4 ) r0 ri 2
2
side Square
b 2 h 6 r0 2 r0 2 t ( b h 2 t) ( 4 ) r0 ri 2
b 2 h 2
2 t ( b h 2 t) ( 4 ) r0 ri
Stress-strain relationship at elevated temperatures
2
2
must Rectangular either be protected 4 r a way 2 r as with or designed 2 hinsuch to avoid premature failure2 hof the structure whennon-exposed exposed to fire. short
0
0
2 t ( b h 2 t ) ( 4 ) r0 ri 2
2
2 t ( b h 2 t) ( 4 ) r0 ri
2
2
2 t ( b h 2 t ) ( 4 ) r0 ri
2
2
side Fire protection may be given to structural members by the use of: 2 b Rectangular with 2 b 4 rsteelwork 0 2 r0 2 2 a) Intumescent paints 2 2 2 t ( b h 2 t) ( 4 ) r0 ri non-exposed long 2 t ( b h 2 t ) ( 4 ) r0 ri b) Mineral boards side c) Concrete encasement. 2 h Square 2 h 4 r 2 r
Fire Firedesign design Fire Firedesign design
0
0
2 t ( b h 2 t ) ( 4 ) r0 ri 2
2
211
Hollow section exposed to fire on two adjacent sides
Sabah Shawkat ©
Hollow Section
Square or rectangular
Am
Ap
V
V
b h 4 r0 1.5 r0
2t ( b h 2 t ) ( 4 ) r0 ri 2
(b h )
2
2 t ( b h 2 t ) ( 4 ) r0 ri
2
2
Fire design Fire design
Sabah Shawkat ©
Sabah Shawkat © Composite slab Composite Steel Concrete Ceilings
Sabah Shawkat ©
226 224
Composite slab Determination M plech with the maximum stresses in the extreme chord of the sheet:
The roof structure is designed as a roof system "Hoesch" (supporting plates). Material Characteristics:
Introduction
fy
M m.max M sheet M md.max fy This example the composite the second storey that is W y.a demonstrates the design of M sheet floor slab on M W y.a W y.a M W y.a supported by the composite. Verification is needed for both the construction stage (non-
composite stage) and constructed stage (composite stage). Although generally checks at the
M sheet 20.50 kN m
non-composite on two M continuous spans, for simplicity only a single span case Determination ofstage M slabare at 1based m linear: slab M p.max M sheet will be considered here. M slab
53.80 kN m
Design and evaluate the composite steel-concrete slab on a span is L, the distance of the ceiling
is L1, the thickness of the concrete slab is h, the imposed load on the ceiling is v. The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment Floorbeslab and material should recalculated to aproperties-design width of 0.75m. of composite slab: M slab.0.75
(-) DesignCeramic of reinforcement ribs slab: paving to concrete1,35 CementMglue 1,35 Input data: doska.0.75 40.351 kNm
gd
(kN / m2)
(kN / m2)
0,2
0,27
0,08 M slab.0.75
0,108
yd
fyd 356.522 MPa
1.15
fctm 1.2MPa
The floor slab should be designed for both construction stage and composite stage fcyl f cd 17 MPa fcd 0.85 1.5 metal decking acts as formwork and has to support its own During the construction stage, the
fycd 356.522MPa
weight, wet concrete, and construction loads. The resistance of the metal decking during the construction stage needs to concrete be verified at the ultimate andthe serviceability limit state Distance from the edge of the cross-section along axis of the reinforcement: g
2
g
g 2.892 kN m
g
2
g o.d
g ms.d 3.904 kN m
ms.n height o.n of the concrete ms.n cross section: d 220mm ms.d Effective in of service stage – live part loadof+ the floor layers TheLoad depth the compression concrete
2 2 0.0774 d g x 0.017m x u g ps.d 0.8 g xs.d v d xu 0.0147.274 m kN m g s.n xv gps.d g ps.n n ps.n 5.24 kN m
Design of roofing sheets and reinforced concrete slab: M dim Ipropose plate 2 b d d fcd
Hoesch: Depth mm b d1.5 0.825m
d 0.22m
0.059
0.01737
Sabah Shawkat ©
Cement fry CSFE
M dim
40.351
kN m
Thermal insulation
h py 280mm l 7m
gn
40.35 kN m
410MPa Load - reinforced concrete slab + sheet metal f
f cyl 30 MPa
b py 75mm
Nobasil l st ceiling 750 mm false
M dim
1,35
0,9
1,215
0,06
0,081
0,15
0,2025
1,24
1,674
1,35
2,7
3,645
1,35
0,192
0,2592
2,892
3,9042
1,35
l 7000mm
h d 75mm
1,35
lst 0.75m
Reinforced concrete slab
Hoesch plate Imposing load
1,4
4
5,6
2
Effective sheet width "bd": 2
m 1g s.d 6 1.674 2 kN 0.13
b d3 0.5 lst
2
A st
b d xu fcd
2
2R20
A st 5.359 cm
fyd
Sheet metal:
2
A str
2
6.28 cm
d
20 mm
g plechu 0.192 kN m
Cross-sectional characteristics of the current 1m: Check the degree of reinforcement of the concrete cross section: 3
W y.a 68348 mm b avrge 122.5mm M 1.1
4
4
Iy.a 1030 f10 mm 1 ctm st.min
Ea 210000 MPa fy 235 MPa
3 fyd
slab + sheet
The load takes over the sheet, we consider the construction supports
2
2
kN 0.45m m v d b 5.6 kN b d1 g o.d 1 h3.9042 bd1 2 m l d d2
b d3 0.375m
The required reinforcement area will be:
The actual depth of the compression part of the concrete: b 1.0 m Effective load width:
2
g o.n 2.892 kN m v 4.0 kN m b dI min b d1 b d2 b d3 n
A req 5.35 cm
A str Assessment of the construction stage - reinforced concrete st st 0.018 st.max 0.02 h py b avrage
Load - floor layers, reinforced concrete slab, live load g s.n 1.24 kN m
2
A req b d d fcd
b d 2 b d3 b py
b d2 0.91m
A str fyd xu q ms.n g ms.n bxu b d fcd
b d 0.825m
Compositeslab slab Composite Composite Compositeslab slab
420 1 d MPa 104.81 mm 3.904 kN m 1 15.94 mm 2.892xu.lim q ms.n kN m q gxu.lim q ms.d ms.d b 525 MPa ms.d fyd
225
Verification at ULS
Assessment of the service stage - floor layer +live load
The maximum bending moment from the calculation design load above the support: M md.max 5.9 kN m
Reaction in the supports:
Rmd.k 5.10 kN
Rmd.s 17.0 kN
A part of the load takes over the sheet and a part of it reinforced concrete slab: Load width: b 1.0 m
q ps.n g ps.n b
1
q ps.n 5.24 kN m
q ps.d g ps.d b
1
q ps.d 7.274 kN m
L 7.0 m Sheet profile length:
Assessment for the ULS: reinforced concrete slab + sheet + live loads + floor layers
Sabah Shawkat ©
Stress in the extreme cross-section of the sheet metal: sheet
Mmdmax W ya
sheet
86.323 MPa
Reactions from the calculation load: floor layers + live load + sheet metal + reinforced concrete slab
Verification at SLS – sheet metal + reinforced concrete slab Maximum deflection from characteristic load:
fmax 3.8 mm
Reaction in supports: sheet metal + reinforced concrete slab R mn.s 12.6 kN
Rmn.k 3.8 kN
flim
0.5 L 250
1
Rmd.s 17 kN
q ps.d 7.274 kN m
Rpd.k
q ps.d L 2
Rmd.s 2
Rpd.k 33.959 kN
Reactions from characteristic load: f lim 14 mm
floor layers + live load + sheet metal + reinforced concrete slab: R mn.s 12.6 kN
2
q ps.n 5.24m kN m
Rpn.k
q ps.n L 2
Rmn.s 2
Rpn.k 24.64 kN
Maximum bending moment: (part of the bending transmits the sheet and the rest of the reinforced concrete slab) M p.max
1 8
2
q ps.d L
Composite slab Composite slab
R md.s L 4
M p.max 74.303 kN m
226 226
Determination with maximum stresses in the extreme chord of the sheet: Determination with thethe maximum stresses in the extreme chord of the sheet: M plech M plech M sheet M m.max M m.maxM sheet W y.a M M W y.a W y.a W y.a fy fy
M md.max fy fy Mmd.max M sheet W y.a M sheet Wy.a M M W y.a W y.a
Material Characteristics: Material Characteristics: 410MPa 410MPa fyd fyd 1.151.15
30MPa MPa f 30 cyl cylf
fcylfcyl MPa fycdfycd MPa 356.522 fcd 0.85 356.522 fcd 0.85 1.5 1.5
M sheet 20.50 M sheet 20.50 kNkN m m
fyd fyd 356.522 MPa 356.522 MPa
1.2MPa fctmfctm 1.2MPa
17 MPa f cdf cd 17 MPa
Determination of M m linear: M slab Determination of M at 1atm1 linear: slabslab M slabM p.max M p.max M sheet Msheet Distance from edge of the concrete cross-section along axis of the reinforcement: Distance from thethe edge of the concrete cross-section along thethe axis of the reinforcement:
M slab53.80 53.80 M slab kNkN m m
reinforcement designed in one spaced apart 750mm, moment TheThe reinforcement willwill be be designed in one rib,rib, thethe ribsribs areare spaced apart by by 750mm, thethe moment should recalculated a width of 0.75m. should be be recalculated to atowidth of 0.75m.
220mm Effective height of the concrete cross section: d d 220mm Effective height of the concrete cross section:
depth of the compression of the concrete TheThe depth of the compression partpart of the concrete 0.0774 0.0774
M slab.0.75 kNkN M slab.0.7540.35 40.35 m m
x x d d
M dim M dim 2 2 b d b dd d fcd fcd
Design of reinforcement to concrete slab: Design of reinforcement to concrete ribsribs slab: Input data: M doska.0.75 Input data: M dimM slab.0.75 M slab.0.75 M doska.0.75 40.351 40.351 kNm M dim kNm
0.017m x x0.017m
x u x u 0.80.8 x x
0.22m b d bd 0.825m 0.825m d d0.22m
0.014 xu xu 0.014 m m
0.059 0.059
0.01737 0.01737
Sabah Shawkat © A req fcd A req b d b dd dfcd
40.351kNkN m m MM dimdim 40.351
7000mm 280mm b pyb py 75mm h d hd 75mm 75mm l l 7000mm h pyh py 280mm 75mm
2 2
A req A req 5.35 5.35 cm cm
required reinforcement area TheThe required reinforcement area willwill be:be:
l l7m7 ml st l st 750750 mmmm
fcd b d b dxu xufcd 2 2 2R20 A stA cm cm 2R20 5.359 A st f f stA st5.359 yd yd
0.75m lst lst0.75m
2 2
A strA str 6.286.28 cm cm
20 mm d d 20 mm
Check degree of reinforcement of the concrete cross section: Check thethe degree of reinforcement of the concrete cross section: b avrge 122.5mm 122.5mm b avrge
st st
Effective sheet width Effective sheet width "bd"b ":d":
b d3 0.5 b d3 0.5 lst lst
0.018 st.max st st0.018 st.max 0.02 0.02
actual depth of the compression of the concrete: TheThe actual depth of the compression partpart of the concrete:
bd2 b d3 b dIb dIminmin b d1bd1 b d2 b d3
1 0.130.13 b d1 0.45m b d1 1 1h d h d b d1b d1 0.45m 2 1 6 6 2
A strA str b avrage h pyhpy b avrage
1 fctm 1 fctm st.min st.min 3 f3yd fyd
b d2b d2 2 2l l
0.91m b d2b d2 0.91m
A strAstr fyd fyd xu xu b d bfcd d fcd
0.375m b d bd 2 2b d3 b d3 0.825m b d3b d3 0.375m bpyb py b d bd 0.825m
Compositeslab slab Composite Composite Compositeslab slab
15.94 mm xu xu15.94 mm
d MPa 420420 d MPa xu.lim104.81 104.81 mm xu.lim mm xu.lim xu.lim MPa fyd 525525 MPa fyd
227
Calculation of load bearing moment "Mu"
sv
lst 750 mm
35 mm
h s 211.5 mm
Determination Iy.i (moment of inertia of the ideal cross-section where the reinforcement is Mu
Mu
A st.r fyd d e.r
xu.r 2 u
A str fyd d
2
replaced by concrete using the working coefficient "n"):
M dim 40.351 kNm
working coefficient:
xu
M u 47.47 kN m
Mu
47.47 kN m
xb
Note: A 75 mm thick concrete slab needs to be reinforced with a mesh across the entire surface and must be verify due to bending moment between the two ribs as bearing slab reinforced on
Lv L 2 32.5mm 0.5 b p
In the middle of the span: Construction stage:
L 7m
Lv 6.635m
fm 0mm
Bf
q pn Lv Bf
4
2
Rmn.s Lv
A b h s A s.i s v A b A s.i
z1 149.4 mm
z2 62.1 mm
Ea Iy.a Ei Iy.i
Iy.i.0.75
1 l x 3 l x z 2 0.5 A z 2 A z s 2 st b st b 2 s.i 1 s.i 1 v 12 4
Iy.i.0.75 3.449 10 mm
1
8
4
Iy.i 4.598 10 mm
0.75
4 Overall bending stiffness of the cross section: Bf Ea Iy.a Ei Iy.i Bf 9.635 MPa m
48 Bf
- is the total flexural stiffness of the cross-section, expressed as the sum of the bending
E a 210000 MPa
7
Service stage:
fp
Total deflection:
4
Iy.a 1.030 10 mm
5 384
Ei 16250 MPa
q ps.n Lv
4
Bf
f
Limit deflection: Ei 0.5 Ec
z1
A s.i 8116 mm
Moment of inertia at 1m normal: Iy.i Iy.i.0.75
3
rigidity of the sheet and the concrete slab with ribs Bf
A b 14966 mm
8
Service stage - floor layers + utility loads + reaction from reinforced concrete and sheet metal:
0.8
Sabah Shawkat ©
More precise determination of the ceiling Length according to the manufacturer HEB 360:
5
xu.r
2
A b lst xb
z2 hs z1
Assessment for the SLS:
384
n 12.923
0.5 Ec
20.0 mm
A s.i n A st.skut
one-way with a span 0,75m
fp
Es
Determining the depth of the compression concrete area: xb
Assessment of concrete cross-section due to bending moment:
b p 300mm
n
R mn.s Lv
3
48 B f
f 21.7 mm
fm fp
Lv flim 250
flim 26.5 mm
Design of composite beam:
Note: Only the compression area of concrete is considered in the calculation of the moment of inertia, because cracks are created in the tensile part and this reduces the bending stiffness of the cross-section. In fact, however, the tension concrete area contributes to the overall flexural
The width of the sheet metal: The length of the beam:
lp
Preliminary design of the beam:
stiffness of the cross section, then this calculation is on the safety side.
Composite slab Composite slab
b pl.d
8.4
h pr
1 20
7.0 m
m lp
h pr 0.42m
fp 21.7 mm
228 226
d 315 mm c b p t w 0.5 Material Characteristics:
I suggest a beam HEB 360 Determination with the maximum stresses in the extreme chord of the sheet: M plech fI. y
Stage - the load is transferred only by a steel beam in the centre of the span M m.max M sheet M md.max fy supported M sheet W y.a M W y.a W y.a y.aload Mslab, W Load: floor layers, sheet metal + reinforced concrete live M sheet 20.50 kNmm 2 g s.n 1.24 kN
2
2
g s.d 1.674 kN m
g o.n 2.892 kN m
Determination of M slab at 1 m linear: 2
g o.d 3.904 kN m
M slab
53.80 kN m
kN
kN
kN q n 20.244 m
kN
6 4 fctm 1.2MPa Iy 432 10 mm
y
d f cd 17 MPa bended section:
25.2
tw
determined thatcross-section we use a plastic layers + sheet metal Distance from by theClass edge 1of. It thefollows concrete alongcalculation. the axis ofFloor the reinforcement: + reinforced concrete slab Effective height of the concrete cross section: d 220mm 1 the concrete 2 of 2 The M depth of1 the compression part d 8 g s.d b pl.d lp 8 g o.d b pl.d lp x d
fy M W pl.Rd M dim pl mo 2 b d d fcd
x u 0.8 x
x 0.017m
M pl.Rd
572.545
b d 0.825m
M d 344.386 kN m
kNm
xu 0.014 m
M max.I 61.5 kNm
d 0.22m
0.059
0.01737
Sabah Shawkat © M dim
40.351 kNm
M slab.0.75
Assessment of the serviceability limit state 2(SLS):
Maximum bending moment of the beam in stage I: Mdmax 37.3 kN m
M dim 40.351 kN m M max.I 61.5 kNm
h py 280mm l 7m
MPa
fyd 356.522 MPa f
fcyl fycd 356.522MPa limited fcd of 0.85 The slenderness the web 1.5
0.0774
Total design loads per 1m of beam: sheet + reinforced concrete slab: q d g o.d b pl.d Design of reinforcement to concrete ribs slab: q d 27.328 Input data: Mmdoska.0.75
235
410MPa f MPa 103mm3fyd m 2680 cylW pl30 1.15
The cross sectional web is determined by Class 1 and the cross-sectional area is also
M slab M p.max M sheet 2 2 v n 4.0 kN m v d 5.6 kN m
Beam- self weight HEB 360: q pr.n 1.42 q pr.d 1.917 q pr.d q pr.n f m m The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment Total characteristic loads per 1m of beam: sheet + reinforced concrete slab: should be recalculated to a width of 0.75m. q n g o.n b pl.d M slab.0.75 40.35 kN m
c 143.75 mm
b py 75mm
A req b d d fcd
kN q d 27.328 m
l 7000mm
h d 75mm
A req 5.35 cm
f lim
lp
400 The required reinforcement area will be:
l st 750 mm
fmax 0.184mm
b d xu fcd 2 2R20 AII. cm A st 5.359 Stage f- beam as composite structure st yd
lst 0.75m
A str
f lim 21 mm
2
6.28 cm
d
20 mm
Layers + Reduced long-term live load + Sheet and reinforced concrete slab
kN kN Check degree reinforcement concrete A -the dead load of - floor layers: of the q nII.et 1.24 cross section: q dII.et 1.674 2
Live load: uniform b avrge 122.5mm
1 fctm
2
m
m
st.min live load of the roofs and floors is permitted to change: at beams, frame 3 fyd
2 2 and beam A slabs, without the ceiling with a load area A in m greater than 36 m , reduces by
str
st
the hcoefficients: py b avrage
Effective sheet width "bd": Design of the beam HEB 360: 1 6
2 0.13
b dI
b d1 1 h d
min b d1 b d2 b d3 b d1 0.45m
1 0.5327
The actual depth of the compression part of the concrete: Reduced value of the live load (but not less than 50% of the value):
b d2 2 l
b d2 0.91m
Classification of cross-section HEB 360 subjected to bending: b d3h 0.5360mm lst p
st 0.018 2 st.max 0.02 3m A 8398.784 m 1 0.5 A
0.375m t b 2 b b py t bd 22.5mm 0.825m b p bd3300mm w d12.5mm d3 f
xu
A str fyd
xu b d fcd v n.red 1 v n
d hp 2 tf
Compositeslab slab Composite Composite Compositeslab slab
420 d MPa xu.lim xu.lim kN525 MPa fyd kN v v n.red 2.131 2 n 4 2 m m
15.94 mm
104.81 mm
229
v d.red 2.983
v d.red 1 v d
kN
v d 5.6
2
m
Long-term imposed load: v dl.d 0.5 v d.red v dl.n 1.065
2
+ Reduced imposed load:
m
v dl.d 1.492
kN
v dl.n 0.5 v n.red
2
m
kN
M max.III
1 8
2 1 2 q dl.III.et.a lp q pr.d lp 8
kN 2
m
v kr.n 0.5 v n.red
E
a
c
2
Ecm 32500MPa
m
Long-term component of imposed load II. stage: q dl.II.et v dl.d q dII.et kN
q dl.II.et.a 22.16
q dl.II.et.a q dl.II.et b pl.d
2
m
c 1.5
c
a
Ec
Ec
1
Ea
Ea
n
Ea
fck 25MPa
210000
MPa
Moment of inertia for the long-term component: b eff bstr if b eff b str b eff if b eff b str
m
4
Ec 0.5 Ecm
n II
Ec 1.625 10 MPa
q nl.II.et
2.305
kN m
b eff 2
2
Lo
b eff 2.1m
8
3
2
Maximum bending moment in the mid-span of the beam in II. stage:
A HEB 18.1 10 mm
Layers + reduced long-term imposed loads + reaction from sheet metal and reinforced
h p 360 mm
Ea
n II 12.923
Ec
b str 4200mm
6
4
Iy.HEB 432 10 mm
Lo lp
h p1
kN m
M max.II 439.207
1
M max.II
2
kNm
8
205 mm
1 Ra g o.d b pl.d lp 2
R a 114.778
h
short-term component of the imposed load III. stage: q kr.III.et 1.492 kN 2
m
2
m
q dl.III.et.a q kr.III.et b pl.d
zcgi.II
p The ideal moment of inertia: zcgi.II 87.521 mm 2
2
2
1 h b eff h h n II p 2
A HEB b eff h
1 n II
h 2
zcgi.II hp 129.979 mm
2 hp 1 1 1 h 3 Iy.iII Iy.HEB A HEB zcgi.II b eff h b eff h zcgi.II h p 2 12 n II n II 2
q kr.IIIn.et v kr.n q dl.III.et.a 10.442
hp
zcgi.II 267.521 mm
We consider the short-term load under which we understand 50% of the imposed load. The
q kr.III.et v kr.d
A i.II 0.03m
A HEB
Centre of gravity of cross section:
kN
III. Stage: self-weight of the beam + reduced short-term of imposed load
kN
2
Ideal area: A i.II A HEB b eff h n II
1 2 q dl.II.et b pl.d lp Ra lp 4
b eff 2.1m
h 75mm
1
22.16 m
q kr.IIIn.et 1.065
Ec
Sabah Shawkat ©
q nl.II.et v dl.n q nII.et
q dl.II.et.a
c
Ea
kN
Long-term component of imposed load (characteristic) II. stage:
concrete slab:
a
Cross-section characteristics II. stage:
kN
3.166 q dl.II.et
M max.III 109.003 kNm
Calculation of the composite structure:
2
m
Short-term imposed load: v kr.d 0.5 v d.red v kr.d 1.492 v kr.n 1.065
Maximum bending moment at the mid-span of the beam in III. Stage: self-weight of the beam
kN
kN
4 4
Iy.iII 7.823 10
m
Composite slab Composite slab
m
230 226
2 Determination maximum stresses in the extreme of the sheet: M plech with the Resulting cross-sectional characteristics II. stage: A i.II 0.03mchord zcgi.II 267.521 mm 4 4 fy I M m.max 10M sheet m y.iII 7.823 M W y.a W y.a Cross-sectional characteristics III.
M md.max fy M sheet W y.a M W stage: Ecm 32500 MPa y.a c 1.5 Ea 210000MPa
f ck 25 MPa M sheet 20.50 kN m
M slab
410MPa
fyd 356.522 MPa
1.15
Maximum bending moment infII. stage:
fycd 356.522MPa
cyl fcd 0.85 1.5
b eff
53.80 kN m
Ea The reinforcement will be designed in 4one rib, the ribs are spaced apart by 750mm, the moment Ec Ecm
Ecm 3.25 10 MPa
should be recalculated to a width of 0.75m.
n III 6.462
Ec
1
8
4
b str 4.2m
2
m
Lo lp
d Effective height of themoment concrete section:Qdl III Maximum bending incross III. stage: long-term load II. stage et.a220mm
The depth of the compression part of the concrete 1 10.442 q dl.III.et.a
kN
m x d
0.0774
Lo M slab.0.75 b eff 2 40.35 kN m b eff 2.1m 8
q dl.II.et.a 22.16m
lp 8.4m
kN
2 Distance from edge of along the axis of the reinforcement: the q dl.II.et bthe lp cross-section Ra lp M max.II M max.II 439.207 kNm pl.d concrete
b str if b eff b str b eff if b eff b str
n III
1
fctm 1.2MPa
R a 114.778 kN f cd 17 MPa
M p.max M sheet
Moment of inertia for the long-term component:
M max.III
8 x 0.017m
2 1 2 q dl.III.et.a lp q pr.d lp 8
Moment of inertia in stage I: Iy.iI Iy.HEB
b eff 2.1m
x u 0.8 x
z yia.I
d 0.22m
b d 0.825m
2
b d d of fcd Moment inertia in II. stage: Iy.iII 7.823 10 4 m4
h 75mm
h 205mm h s 360mm Input data: M doska.0.75 M dim M slab.0.75 40.351 p1 kNm 1 2 Ideal area: A i.III A HEB b eff h A i.III 0.03m M dim 40.351 kN m n II
M max.III 109.003 kNm xu 0.014 m
4 4
Iy.iI 4.32 10
Distance of center of gravity, point A in stage I: M dim
3 2 6 4 Iy.HEB 432 10 mm A HEB 18.1 10 mm to concrete ribs slab: Design of reinforcement
m
h p 0.5 z yia.I 180 mm
0.059
0.01737
Sabah Shawkat ©
h py 280mm
b py 75mm
h d 75mm
750 of mm Centrel stof gravity cross section: zcgi.III
l 7m
m
61.5 kNm fyd f 30 MPa max.I cylM
q dlII.eta long-term load II. Stage
Determination of M slab at 1 m linear: M slab
kN Material Characteristics: Maximum bending moment in stage I: qd long-term load of stage I q d 27.328
Distance A req b dof the d fcentre cd
l 7000mm hp 1 h b eff h h A HEB n III p 2 2
lst 0.75m
1 A HEB b eff h n III
h
2
h 2
zcgi.III hp 92.684 mm
m
Resulting cross-sectional III. stage: A 0.03m2 zcgi.III 304.816 mm Effective sheet width "bd": characteristics b dI min b d1 b d2 b d3 i.III 4 4
b d1 1 h d
Cross-sectional assessment: b d3 0.5 lst
b d1 0.45m
b d2 2 l
Assessment of steel beam: Point A
b d3 0.375m
b d 2 b d3 b py
d
u
cd
fyd m0 1.15
4 4
m 10 0.13 1Iy.iIII 6 9.348 2
4 4 inertia in III.area stage: TheMoment required of reinforcement willIy.iIII be: 9.348 10 m
The bcentre of gravity, point A in III. stage: x f
2 2 hp 1 1 1 h 3 Iy.iIII Iy.HEB A HEB zcgi.III b eff h b eff h zcgi.III h p 2 12 n III n III 2
Iy.iIII 9.348 10
zyia.II 267.521 mm
A st
zcgi.III 304.816 mm
p The ideal moment of inertia: zcgi.III 124.816 mm
2 of gravity, A req point 5.35 A cmin the second. stage: zyia.II zcgi.II
b d2 0.91m
zyia.III zcgi.III 2 2R20 A str A st 5.359 cm fy 204.348 MPa m0
zyia.III 304.816 mm 2 d 20 mm 6.28 cm
Check the degree of reinforcement of the concrete cross section: M max.I M max.II M max.III fy A zyia.I zyia.II zyia.III 204.348 MPa 1 fctm I Iy.iI m0 Ist.min b avrge 122.5mm y.iII y.iIII 3 fyd A 211.37 A str MPa st st 0.018 st.max 0.02 h py b avrage Mmax.I AI zyia.I Condition does not satisfied: AI 25.625MPa Iy.iI
The actual M depth of the compression part of the M concrete: max.III AIII zyia.III A str fyd Iy.iIII xu xu 15.94 mm b d fcd AIII 35.543MPa
b d 0.825m
Compositeslab slab Composite Composite Compositeslab slab
max.II zyia.II AII 149.27MPa Iy.iII 420 d MPa xu.lim 104.81 mm 525 MPa fyd
AII
xu.lim
A AI AII AIII
A 210.438MPa
231
Concrete Assessment: Point B
4
Distance of centre of gravity, point B in II. stage: zyib.III h p h zcgi.III z yib.III
130.184 mm
fIII
zyib.II h p h zcgi.II B
M max.II Iy.iII
bIII
bII
zyib.II 167.479 mm
M max.III 1 1 zyib.II zyib.III n II Iy.iIII n III
Mmax.III Iy.iIII Mmax.II Iy.iII
1 zyib.III n III
1 zyib.II n II
B 9.626
MPa
5 384
q kr.III.et b pl.d lp
B 9.581MPa
B bII bIII
f II 17.372 mm
4
Ea Iy.iIII
fIII 3.448 mm
Total deflection: fmax fI fII fIII lp Limit deflection: f lim 400
bIII 2.349MPa
bII 7.231MPa
3
q dl.II.et b pl.d lp Ra lp 1 5 fII 48 Ea Iy.iII Ea Iy.iII 384
fmax 21.615 mm
f lim 21 mm
Design of shear connection: we will consider rigid composite structure - shear connection is stressed by shear force
Marking the stress on the composite beam HEB 360
- we propose uniform distribution of shear connectors
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h - height of shear connectors and after welding (L - 5 mm) d – shear connectors diameter h tr 3.d
We suppose:
Lt – length of shear connectors, d – diameter of shear connectors, bo width of beam, hp1-height
of ribs above the beam:
d 12.7mm
Lt 50mm
b 0 300mm
h p1 1.5mm
h tr Lt 5mm
Assessment of the serviceability of limit state (SLS): fmax flim fmax
ls
Load capacity of shear connection:
400
fu 340MPa
fI fII fIII
Deflection of the first stage: steel-reinforced concrete slab: q d 27.328
kN
3.25 10
kN 2
1.492 q kr.III.et
fck 25 MPa
MPa
kN
1 fck Ecm v
2
RRd 0.29 d
m
Deflection in the third stage: reduced imposed:
4
1
m
Deflection in the second stage: floor layers + reduced imposed long-term load: 3.166 q dl.II.et
E cm
v 1.25
RRd 0.8 fu
d
2
m
Composite slab Composite slab
4
2
1 v
R Rd 33.729 kN
R Rd
27.565
kN
226 232
Reduce valueMof shear connection capacity: for ribs perpendicular to of beam Determination with the maximum stresses in the extreme chord the sheet: plech b h 0.7 0 tr 1 h fy kt M m.max hMsheet N r p1 p1
W y.a
M
maximum distance of shear connectors: 410MPa
3
kt 4.06 10 fy M md.max M sheet W y.a M W y.a
W y.a
1 kt 0.85 Nrat 12 m linear: M min kt of 0.7Mifslab Determination slab kt min kt kN 0.85 M sheet 20.50 m if Nr
M slab
Spacing of shear connectors: Material Characteristics:
PRd.x RRd kt
fycd 356.522MPa
PRd.x 23.43 kN
f cd
h 0.075m fctm 1.2MPa
17 MPa
Distance from the edge of the concrete cross-section along the axis of the reinforcement:
Thestage: reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment Vzrecalculated S.s should be to a width of 0.75m.
Effective height of the concrete cross section:
q dl.II.et 3.166
kN
kN q dl.II 13.296 m
q dl.II q dl.II.et b str
2
m
Design of reinforcement to concrete ribs slab: q dl.II L VzIIdata: Input 2 M doska.0.75
d 220mm
The depth of the compression part of the concrete 0.0774
Iyi 40.35 kN m
II. Stage:
fcyl fcd 0.85 1.5
6 h 450 mm fyd 356.522 MPa 2.5 d 31.75 mm
M p.max M sheet
53.80 kN m
T
1.15
minimum distance of shear connectors:
The longitudinal shear force per unit length: we have to calculate the force for II. Stage, III.
M slab.0.75
fyd
f cyl 30 MPa
x d
M dim
2
b d d fcd
M dim MkN 40.351 V zII kNm 46.535 slab.0.75
x u 0.8 x
x 0.017m
d 0.22m
b d 0.825m
xu 0.014 m
0.059
0.01737
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III. Stage: M dim 40.351
A req b d d fcd
kN m
kN kN q7000mm h pyq kr.III.et 280mm1.492bpy 75mmq kr.II h d q 75mm b str l kr.II 6.265 m kr.III.et 2 m l 7 m l st 750 mm VzIII 21.927 kN lst 0.75m
Cross Section II. stage:
TII
Iy.iII
1 n III kN
TII 95.324 m
kN Effective widthT"bd149.175 ": b dI T TIIsheet TIII m
1 6
2 0.13
b d1 1 h d
TIII
VzIII SyIII Iy.iIII
min b d1 b d2 b d3
b d3 0.375m
Composite roof slab using sheet metal profile TheDesign required reinforcement area will be:rib of slab: of shear reinforcement to the
2
h b eff h h p1 zcgi.III h s 2
Material b d characteristics: xu fcd 2 2 2R20 A st d A 6.28 cm A st 5.359 cm f Steel V 10425: fyd 375MPa str Steel R 10505: fcd 17.0MPa yd
1.602
L
SyIII 2.296L kN
TIII 53.851 m
b d1 0.45m
b d 2 b d3 b py
fcttm 1.2MPa
fycd 375MPa
20 mm fssd 450MPa
fsscd 420MPa
Check the degree of reinforcement of the concrete cross section:
Input data: width of the shear cross section " b q" f
b avrge
122.5mm
height of shear cross
stthe
A str
1 ctm st.min section " h q3" fydh q 280mm
b q 122.5mm
diameter of the bearing reinforcement of the support: " d s" st longitudinal 0.018 st.max 0.02
h py b avrage
d s 20mm
preliminary design of the diameter of the stirrups " d ss " d ss 8 mm The actual depth of the compression part of the concrete: The depth of the compression part of concrete cross-section " xu " xu 0.014 m
Number of shear connectors on 1m of the beam:
b d3 0.5 lst
q kr.II L
h 1 b eff h h p1 zcgi.II h p S yII SyII n II 2
Cross Section III. stage: SyIII VzII SyII
VzIII
2
A req 5.35 cm
b d2 T 2 l n tr PRd.x b d 0.825m
b d2 0.91m 1 n tr 6.367 m
xu
A str fyd
420 d MPa
xu 15.94 Cover reinforcement " tb" mm tb x22 mm u.lim 525 MPa fyd b d fcd
Cross-sectional characteristics: cross-sectional area " A b"
Composite Compositeslab slab Composite Compositeslab slab
xu.lim
104.81 mm 2
A b h q b q A b 0.034 m
233
- shear reinforcement coefficient
the distance of the centre of gravity of the drawn reinforcement from the edge of the cross-
s
section " ast "
bq, hq -the dimensions of the shear cross section
ast tb d ss d s 0.5
ast 40 mm
Effective cross-sectional height " h e"
h e h q ast
h e 240 mm
Level arm of internal forces " zb "
zb h e xu 0.5
zb 233.189 mm
Qbu
1 3
b q h q q fctm
q
h n f s
Shape cross-sectional coefficient " f " Cross sectional height factor " h "
We evaluate the shear from the external load:
h
1.4
-at a distance h / 2 from the front of the supports for the pre-stressed elements, wherein h is
the height of the cross-section near of the support
1.0 if h q 0.6m 2 3
h 1.213
1
hq m
Coefficient of normal force in the cross-section " n"
- in the support post (column) for the frame members
Shear reinforcement coefficient " s ":
- to the Qred value for the beam elements Reliability condition (shear resistance) of structure:
s
1 50 b stw stmin
stw
- shear reinforcement consisting of reinforcement intersecting the shear crack
stmin
- the minimum degree of the longitudinal reinforcement
Sabah Shawkat ©
Qu
- the transverse force on the bearing capacity in the examined section
kp 0
Qd
- transverse force from external extreme load qd
Area of tensile concrete reinforcement in the band 0.25*h from the tension chord of the
Qd
- increase or decrease the transverse force Qd in the section of the variable height
cross section " A st "
2
A st 5.359cm
2
A sw 0cm
element if the height does not change Qd = 0 Qpd
- the calculating transverse force on an oblique or curved pre-tensioning reinforcement
Area of longitudinal reinforcement in the band (+)(-)0.25h about the middle of the cross
Qbu
- load capacity of concrete
section height " A sw"
Qssu - bearing capacity of the stirrups
stw
Qsmu - load capacity of shear mesh Qu Qd Q d Qpd
Qd 145.154 kN
Q d 0kN
stmin
Qpd 0kN Qu
A st 2 A sw kp A p bq hq 1 3
Qbu Qssu Qsmu
Load-bearing capacity of concrete in an inclined shear crack:
stmin
1 3
fctm A st
kp A p Rpd p0t2 fyd A st kp A p A st kp A p
fctm
A st
3
stmin 1.067 10
fyd A st kp A p
h
- Load-bearing capacity of concrete in an inclined shear crack: h > 0.6m...h = 1.0
f
- cross section shape factor, case for us f = 1.0
Coefficient of effect of anchoring the longitudinal tensile reinforcement Ast behind the oblique
n
-coefficient of normal force in cross-section
shear crack " b"
Composite slab Composite slab
226 234
Determination the maximum the extremeb is chord the sheet: - if the reinforcement is anchored to lbd stresses then thein coefficient equalof"1.0" M plech with
- if reinforcement is not anchored lbd but ls is then a coefficient b calculates: M m.max M sheet M md.max fy M sheet W y.a M W y.a W y.a W y.a ls M
The force they have to carried by stirrups " Qs":
fy
b
1.0 if lbd ls
b
b 1
ls kN m M sheet 20.50 if l ls lbd of bd Determination M slab at
1 m linear:
M slab
s 0.728 M slab 53.80 kN m
s 50 b stw stmin
lbd
M p.max M sheet
n
f
concrete cross-section " Qbu"
1
Qbu b q h q q fctm Q bu Design of reinforcement to concrete ribs slab: 3 Qu Qd Q d Qpd Input data: M doska.0.75
c cmax if cof the cmax c 0.233m d 220mm Effective height concrete cross section: if c cmin The depthcmin of the compression part of the concrete c otherwise 0.0774 x d
s
MLoad 40.35of kNnon-reinforced m capacity slab.0.75
410MPa
Distance from the edge cross-section of the reinforcement: The minimum lengthofofthe theconcrete shear crack " cmin": along cmin the zb axiscmin 0.233m
s 1
should berecalculated to a width of 0.75m. h
Qs Qd Qbu Qs 128.507kN fyd 356.522 MPa fctm 1.2MPa 1.15 1.2 n b q fctm 2 4 c d c 2.214 10 m Length of shear crack " c": fcyl Qs f 17 MPa fycd 356.522MPa fcd 0.85 cd 1.5 0.18 fcd h q Maximum length of shear crack " cmax": cmax cmax 0.588m q fctm
fyd
f cyl 30 MPa
ThePartial reinforcement will be designed in one rib, the 750mm, the moment coefficient" f 1 ribs nare 1spaced b apart 1 by s 1 q" : h 1.213 q
SimpleCharacteristics: design of shear reinforcement: Material
x u 0.8 x
x 0.017m
xu 0.014 m
The force to be carried by the "n" shear stirrups " Nss ": Nss A ss fssd Nss 45.239 kN
16.647 kN
M dim
c b Nss0.825m
2 of the stirrups: s d Distance s b d d fcd
2.5 Qbu 41.617kN M dim M slab.0.75 40.351 kNm
Qs
d 0.22m s s 82.091 mm
0.059
0.01737
Sabah Shawkat ©
M dim
40.351
h py 280mm
floor s s A req b d ss d cm fcd
kN m
b py 75mm
Bearing capacity of stirrups:
l 7000mm
h d 75mm
The proposal on the minimum degree of stirrups:
l Minimum 7 m l st degree 750ofmm reinforcement lstThe 0.75m simplified ssmin
2
4 fssd
b d xu fcd A stQ u Qbu Qssu fyd
4
q.1
b avrge
4 if 450mm b q 2 tb d ss 900mm
s s 400mm
s s.max 0.18m
ss
2 0.13 b s
ssmin
q
s s.max min 0.75 h e 400mm
s s.max 0.75 h e
1A 6
b dI
min b d1 b d2 b d3
2
2
A ss 0.25 n d ss A ss 1.005 cm b d3 0.5 lst b d3 0.375m b d 2 b d3 b py
0.75h e 0.18m s s s s.max
2b b d1 1 h d bbd1 0.45m 2 l ssmin q s s 0.147 cm d2
s
Q ssu
131.865 kN
2 Q u 5.359 148.512 cm A st
kN 2R20
A str
2
6.28 cm
d
Qbu 16.647 kN
20 mm
st.min
122.5mm
1 fctm
3 fyd 18MPa if fcd 18MPa A str st fcd otherwise st 0.018 st.max 0.02 h py b avrage 1 Qumax b q h q fcd Qumax 194.367kN 3 Rbd
Structural principles for the positioning of the stirrups:
Effective "bd:": The areasheet of thewidth stirrups
ss
Check the degree of reinforcement of the concrete cross section: Assessment of limit capability of pressure diagonals: fcd 18MPa
n=2
2 if b q 2 tb d ss 450mm
s s 0.75 h e
Nss c
ssmin 6.667 10
The number of cuts relative to the width of the beam: n
Qssu
The required reinforcement area will be: Load capacity of the reinforced concrete cross section: Qd 145.154 kN
stirrups " ssmin"
method of calculation is considered beam:
fctm
2 s s 0.08m A req 5.35 cm
b d2 0.91m
Q d 145.154 kN
The actual depth of the compression part of the concrete: xu
A str fyd b d fcd
xu
15.94 mm
xu.lim
420 d MPa 525 MPa fyd
xu.lim
104.81 mm
We fasten the shear reinforcement at the top edge of the mesh slab.
b d 0.825m
Composite Compositeslab slab Composite Compositeslab slab
235
Composite Steel Concrete Ceilings
a) Reinforced steel profile 11 002R, reverse (concrete filled with narrow ribs)
Design and evaluate the composite steel-concrete ceiling on a span L, including the assessment of the sheet metal profile as a lost formwork. The distance of the ceilings is L1, the thickness of the concrete slab is h, the imposed load on the ceiling v, the ceilings are not supported during the construction.
b s1 84mm
b s2 116mm
4
b s1 s 4
3
Ia 131 10 mm
Characteristics of materials:
h 2 80mm
s 63.1 mm
h 2 80mm
3
h 2p
W ael 28.72 10 mm
h h 1 h 2p
2
h2 h 2p 0.02942m
b s1 b s2
h 1 50mm
3
h 0.07942m
b 25kNm
PENV 1994-1-1 – Concrete C25/30 f ctkom 1.40 MPa
fcko 10 MPa
fck 20 MPa
2
fctm fctkom
fck fcko
3
fctm 2.22 MPa
Scheme for calculating the mean thickness of the concrete slab
c 1.5
0.7 fctm fctk005
fctk005 1.56 MPa
fctk095 1.3 fctm
fctk095 2.89 MPa
Ecm 29 GPa
Dead - profile 12 101
Sabah Shawkat ©
Limit bending stress for concrete in compression: fcd 0.85
fck c
Steel 235: fyp 235MPa mo 1.1
Span:
L 7m
. The load is considered to be on width b of sheet profile: b = 1m
gosvsz 0.1133 kN m
fcd 11.33 MPa
1.35
godvsz gosvsz
g 0.15 kN m odvsz
2
The self- weight of the concrete mix (the measured rib thickness):
fy 235MPa
fu 360MPa
M1 1.1
a 1.15
g osc b h
E a 210 GPa
h def
L 24
gsstale gosvsz b gosc b
godc 2.68 kN m
vs 1.50 kN m
gdstale godvsz b godc b
1
g 2.83 kN m dstale
2
v 1.5
Mael Wael ULS assessment:
1
fyp a
vd vs v
vd 2.25 kN m
2
Mael 5.869 kN m
We calculate the elastic moment according to the old standard: Rd 190 MPa
Mel Wael Rd
Mel 5.46 kN m
The ratio between the old and the new standard is 7%: L1 2.0m Steel concrete ceiling
2
Live load during concreting:
h def 0.29167m
Scheme of ceiling loading
godc gosc
1.35
gsstale 2.1 kN m
L1 2.5m
2
g2 gdstale vd b
Composite slab Composite slab
g3 gdstale vd b
g1 g3
Mael Mel
1.08
L2 2.0m
L3 2.0m
g1 5.08 kN m
1
226 236
L L Material Characteristics: Profile 12 102: g osvsz g osvsz 1 2 2
Bending moments themaximum supports: stresses in the extreme chord of the sheet: Determination with the M plechabove Given
3
3
3
3
fy M m.max M md.max L1 M sheet L2 L2 L3 fy M c L2 g 1 g 2 2M b L1 L2 M M a L1 M b L2 g 2 g 3W 2M c L2 L3 M d L3 sheet 4 4y.a M W y.a 4 W y.a4 M W y.a Mb Mb 2.03 kN m Mc 2.03 kN m Find Mb Mc Mc 20.50 kN m M sheet
m1
53.80 kN m
1 2 g1 L1 8 2
Ma Mb 2
fcyl L L1 2 0.85 fycd 356.522MPa fcd 1.51.35 gosc gosc
1 40.35 kN2 m m3 g3 L3 8
Mb Mc
m2 0.51 kN m
Mc Md 2
m3 1.53 kN m
Input data:
gosc 3.97 kN m
Mb 2.03 kN m
M doska.0.75
40.351
h py 280mm
Mael Mb M dim
40.351 kNm
gosstale gosnosnik gosvsz gosc
Mel Mb Mel 5.46 kN m
gosstale 4.56 kN m
1
d 220mm
1 The gdepth compression of the concrete the godnosnik godvsz part godc godstale 6.15 kN m odstale of
L1 L2 2
dim
x u 0.8 x
x concreting: d x 0.017m during
vs vs M
v 1.4
vd v vs
b d 0.825m
2
b d d fcd
xu 0.014 m
vs 3 kN m
d 0.22m
1
1
vd 4.2 kN m
0.059 2
M sd g odstale v d L 8 2 A req 5.35 cm M sd W module: fy
Maximum bending moment:
M slab.0.75
A req b d d fcd
kN m
b py 75mm
Required cross-sectional
l 7000mm
h d 75mm
suppose IPE 270 TheWe required reinforcement area will be:
l st 750 mm
Assessment of the SLS (deflection only from dead load)
The calculation of bending moment over supports due to dead load: 1
2
gsstale L1
10 1 2 M2 gsstale L2 16
Mb 0.84 kN m
M1
1
11
M2 0.52 kN m
alebo
0.01737
xm L1
1
33
16
xm 0.84307m f
g sstale L1
4
st The
185Ea Ia
1
Max."bthe": allowable deflection will be: f L1 fmax 0.008m Effective sheet width b dI min b d1 b d2 b d3 max d 250 a) Beam:
Load:
b d1 1 h d Construction stage - the
b d1 0.45m
steel beam
Dead – self-weight (we suppose IPE 270)
b d3 0.5 lst
b d3 0.375m
gosnosnik 0.361 kN m
1
a
b d 2 b d3 b py
1.35
b d2 2 l
f fmax
b d2 0.91m
Msd 63.42 kN m 3
W 0.00031035m
6
4
Iy 57.9 10 mm 2 A str 6.28 cm
MplRd 98.9 kN m
A 4590 mm d
MplRd Msd
M Msd
A str
stress on the beam in extremecross-sectional fibres: stthe 0.018 st.max 0.02
h py b avrage
1 2 godstale L M 37.69 kN m 8
The actual depth of the compression part of the concrete: xu
M A str f yd d MPa hnmon 87.86462MPa 420 Rd hnmon xu.lim xu hnmon 15.94 mm W 525 MPa fyd b d fcd ely dnmon hnmon dnmon 87.86462MPa
b d 0.825m
1 godnosnik gosnosnik godnosnik 0.49 kN m
Composite Compositeslab slab Composite Compositeslab slab
20 mm
Msd 63.42 kN m
Check the degree of reinforcement of the concrete cross section: or
M
2 0.13
Wply fyp
1 fctm
f 0.00066m
1 6
MplRd
b avrge 122.5mm M Wely Rd M st.min 90.09 3kN fyd m
Maximum deflection at first span: xm 0.422L1 xm 0.844m
ULS:
2
gsstale L1 M1 0.76 m kN
1
1.15
3 3 3 3 xu f10 d 484 cd mm W 429 2 10 mm W b 2R20 A st ply A st ely 5.359 cm fyd
lst 0.75m
Mb
1
1
Sabah Shawkat ©
M dim
l 7m
17 MPa
Effective height of the concrete cross section:
Live 0.0774 loads
Design of reinforcement to concrete ribs slab: Mael 5.87 kN m
f
fctm 1.2MPa
cd g godc osc
2
godc 5.36 kN m
m1 1.53 kN m
m2 be recalculated g2 L2 to a width of 0.75m. should 8 2 M slab.0.75
fyd 356.522 MPa
Distance from the edge of the concrete cross-section along the axis of the reinforcement:
The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment 1
1.15 Concrete load due toydself-weight:
Determination of M at slab at 1 m linear: M slab Bending moments the mid-span of the beam:M p.max M sheet M slab
f
f cyl 30 MPa
g odvsz g osvsz
410MPa
Rd 104.81 210MPa xu.lim mm
2
237
Assessment of cross-section:
4
SLS: Deflection due to dead load: Maximum deflection: fmax
L
f
5 g osstale L
fmax 0.028m
250
f 0.01172m
Ea Iy
384
Carrying capacity of steel beam in shear: 2
t w 6.6mm h 270mm
f fmax
VplRd A v
2. The load due to service stage transfers to the composite beam
A a 4590mm
fy
2
A v 1.04h t w
A v 0.00185m
VplRd 218.65048kN
3 a
Load: Dead – Self-weight (estimate IPE 270): 1
1.35
g osnosnik 0.361kNm
g 0.23 kN m osvsz
g odnosnik g osnosnik
1
godnosnik 0.49 kN m
1
VSŽ 12 101: gosvsz gosvsz
godvsz gosvsz
b 24 kN m
3
Self-weight of concrete: gosc b h
Scheme of composite beam
L1 L2 2
0.5VplRd 109.32524kN
Qd 0.5VplRd
Effective width of the slab:
b eff 2
The beam is suitable
Sabah Shawkat ©
gosc 3.81 kN m
godc gosc
1.35
1
godc 5.15 kN m
gosstale gosnosnik gosvsz gosc gosstale 4.4 kN m
1
godstale godnosnik godvsz godc
1
godstale 5.94 kN m
vsdl 0.75 kN m
L1 L2 2
determined as the smallest value of the terms: b B
s 1.4
vddl vsdl s
vddl 2.1 kN m
2 L1 L2 vsuzitne 2 kN m 2
vduzitne 5.6 kN m
s 1.4
vduzitne vsuzitne s
1
B 2m
B L1
b 0.3L
gs gosstale vsdl vsuzitne
gd godstale vddl vduzitne
1
1
gd 13.64 kN m 1 2 Maximum bending moment: gd L Msd 83.54 kN m Msd 8
Maximum shearing force:
Qd
1 2
gd L
L 7m
0.3L 2.1m
for one row of composite connectors on the beam b 12 h 1 h 2p b n
b 12 h 1 h 2p b n 0.95304m
953 mm
When joining a concrete slab with a steel beam, the condition can be considered: b s1 s
In sum:
gs 9.9 kN m
1
b n 0m
- Service:
b eff 1.75m
8
The effective width of the plate-shaped perpendicular to the longitudinal axis of the ceiling is
1
Live load - long-term: floor, ceiling 2
L
h 1 kh.2
1 200
H
H h1 h2 h
Qd 47.73887kN
Composite slab Composite slab
kh2
h 2p
H 0.4m
h 2p 1 200
2
h2
b s1 b s2
H 0.002m
h 2p 0.02942m h 1 h 2p
1 200
H
h 1 h 2p 0.07942m
226 238
Determination Mplech with the maximum stresses in the extremefy chord of the sheet: Aa Position of the neutral axis ( shear capacity):
fy
M
M m.max W y.a
M sheet
M sheet
W y.a
a
x
x 0.04729m
M md.max fck fy 0.85 W y.a b effW y.a c M
M slab
M slab
410MPa Assessment of the deflection of the composite beam under the assumption of an elastic action. f
f cyl 30 MPa
f
356.522 MPa
f
1.2MPa
yd yd ctm 1.15 An effective modulus of elasticity of concrete is considered with the effect of creep of
concrete: fycd 356.522MPa
M sheet 20.50 kN m
Determination of M slab at 1 m linear:
Material Characteristics: SLS Serviceability limit state:
fcyl E´c cm fcd 0.5E 0.85 1.5
E´c 14500MPa f cd 17 MPa
Ea
M p.max M sheet
n´ 14.48276 Working coefficient: n´ E´c Distance from the edge of the concrete cross-section along the axis of the reinforcement:
53.80 kN m
Ea
The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment should be recalculated to a width of 0.75m. M slab.0.75
n k d 220mm - for short-term n k 7.77778 Effective height ofeffects the concreteEcross section: b 27GPa
The depth of the compression part of the concrete - for long-term effects 0.0774
40.35 kN m
x d E´b
cr 3
Stress distribution in cross section. Design of reinforcement to concrete ribs slab: Input data: M doska.0.75 40.351 kNm slab.0.75 x´ The depth of compression area according M todim old M standard:
M dim
x u 0.8 x
x 0.017m
1 1 cr
E´b 6750MPa
Eb
b 0.825m - according 2 to PENV 1994-1-1d
A a Rd
Eb
n d
d 0.22m
xu 0.014 m
Ea
n d 31.11111
E´b
0.059
0.01737
b d d fcd
Sabah Shawkat ©
M xdim
40.351
0.52991
b fcd
x´ 0.08924m
kN m
x´ 7000mm h pyThe 280mm 75mm 75mm pythe d the influence bof thicknesshof concretel slab and of
l terms 7 m of l st coefficients 750 mm :
lst 0.75m
1
H 1 600 0.002 mm
the reinforcement is calculated in 0.71429
E 2 a Epretv 13500MPa pretv A req 0.5E b d b d Efpretv A req n5.35 cm cd Epretv
To simplify calculations, thewill average The required reinforcement area be: value of the modulus of elastic modulus can be 1 1 considered: gosstale vsdl 5.9 kN m vsuzitne 4 kN m b d xu fcd
A st
fy a
h x 2
n
MplRd 231.07 kN m
Msd 83.54 kN m
MplRd Msd
1 6
b d3 0.5 lst
b dI
x´
2
min b d1 b d2 b d3
b d1 MplRd b d1 0.45m 1 hd 1.06365 satisfies M plRd´ b d3 0.375m
MplRd´ 217.24 kN m
b d 2 b d3 b py
A str
2
6.28 cm
d
b d2 2 l
b d2 0.91m
20 mm
n 21.68
st
A str
h py b avrage
h1 1 fctm h 1 h 1 h 2 h 1 b eff A 3 fyd a 2 n´ 2 (SLS): e 1 Aa h 1 b eff st 0.018 st.max 0.02 n´
st.min
e 0.12861m
The actual depth of the compression part of the concrete:
2 0.13
Beam IPE 270
122.5mm
Neutral Axis Position
MplRd´ Aa Rd h According to old standard: M 83.54 kN m
gosstale vsdl nd vsuzitne nk gosstale vsdl vsuzitne
2R20
Check the degree of reinforcement of the concrete cross section: b avrge
Beam IPE 270 is satisfactory
sd Effective sheet width "bd":
2
A st 5.359 cm
fyd
Bend assessment (at load bearing moment) according to ENV 1994-1-1 M plRd A a
n pretv 15.55556
xu
A str fyd b d fcd
b d 0.825m
Composite Compositeslab slab Composite Compositeslab slab
xu
15.94 mm
xu.lim
420 d MPa 525 MPa fyd
xu.lim
104.81 mm
239
the average value of the ratio of elastic modulus: n 21.68327
b 0.953m
A bi
PENV 1994-1-1 A bi´ h 1
b
2
2
A ik 10716.42857mm
The effective area of the welded mesh is neglected:
h1 h b h 1 A a h 1 h 2 n pretv 2 2 1
e´
1 n pretv
e
e´ 0.16894m
e´
b h1 A a
PENV 1994-1-1
h
2
2
A i A bi A a
A i 6787.54646mm
2
The average value of n:
Sabah Shawkat © 2
h 1 h 2 e´
2 h 1 b h 13 b h 1 e´ 1 n pretv 12 2
1
Ii 0.0002094m
4
Ii´ 0.00016436m
4
5
vsdl vsuzitneL
384
Ea Ii
5
vsdl vsuzitneL4
384
Ea Ii´
f 0.00391m
Ii
Ii´
fmax
L 300
h
2
h2
h1
Syd A bid rbo A a
h
h
2
b h1 nd
f fmax
A bik
h 2 0.08m
rbo 240mm
2
h h Syk A bik rbo A a 2 2
fmax 0.02333m
2
h 1 0.05m A a 0.00459m
centre of gravity of the steel part of the cross section of composite beam:
Syi A bi rbo A a f´ 0.00498m
b 0.953m
Distance of centre of gravity compression area of the concrete part of the cross section of the
1.27405
2
Ideal concrete area: short-term loads:
long-term loads: A bid
Static moment to axis y1:
rbo
PENV 1994-1-1 f´
2
4
Deflection due to imposed load: f
A i´ 7653.21429 mm
A i´ A bi´ A a
2 2 h1 h 11 3 Ii Iy A h 1 h 2 e b eff h 1 b eff h 1 e n´ 12 2 2
Ii´ Iy A
A id 6121.60714 mm
A id A bid A a
0.76131
Moment of inertia of ideal cross-section:
PENV 1994-1-1
2
A bi 2197.54646mm
n
A bi´ 3063.21429mm
n pretv
Location of the neutral axis: A ik A bik A a
PENV 1994-1-1
h1 b
h
2
h
3
Syk 1470342.85714mm 3
Syd 367585.71429mm
3
Syi 527411.14920767mm
2
PENV 1994-1-1
b h1 nk 2
2
Syi´ A bi´ rbo A a
h
2
A bik 6126.42857mm
h
2
Location of centre of gravity:
A bid 1531.60714mm
Composite slab Composite slab
3
Syi´ 735171.42857mm
Short- term load:
rok
Syk Aik
rok 137.20456mm
226 240
Long term load: Determination M plech with the maximum stresses in the extreme chord of the sheet: Syd M m.max M sheet rod rod 60.04726mm A id M W y.a W y.a
fy
Syi Mrmd.max ro fy o 77.70277mm M sheet Ai W y.a M W y.a
f 30 MPa cylW ybhk
H
M slab
M slab
rok
410MPa 1.15
3
fyd 356.522 MPa W ybhk 1635774.64736 mm
fctm 1.2MPa
fcyl fcd 0.85 1.5
cross-section of an ideal long-term:
M p.max M sheet
h Distance the edge of the cross-section along the axis of the reinforcement: y hd from rod y hdconcrete 0.07495m 2
The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment
Effective height of the concrete cross section: d 220mm Section modulus: for The depth of the compression part of theIydconcrete W yodd
n d 31.11111
should be recalculated to a width of 0.75m.
0.0774 x d 3 W yohd 1655016.90748mm
40.35 kN m
M dim beam: Composite
Design of reinforcement to concrete ribs slab: Input data:
2
fyd
fycd 356.522MPa
53.80 kN m
M slab.0.75
Iyk h
f cd 17 MPa The distance of the lower part of the steel fibres from the neutral axis of the composite beam
PENV 1994-1-1 M sheet 20.50 kN m Syi´ Determination of M slab 1 m linear: ro´ ro´ at 96.06048mm A i´
Material Characteristics: Composite beam:
W ybhd
2
b d d fcd
3
W yohd
W yodd 635989.75953482mm
y dd x 0.017m
x u 0.8 x
Iyd
xu 0.014 m
3
W ybhd 605251.99925704mm d 0.22m 0.059
b d 0.825m h H rod 2
0.01737
Sabah Shawkat ©
M dim
M doska.0.75
M dim
40.351 kNm
M slab.0.75
40.351 kN m Schematic diagram of the neutral axis of the ideal cross section.
h py 280mm Moment of
b py of the 75mm h d 75mm inertia ideal cross-section tol y-y7000mm centre of gravity:
l 7 m l st 750 mm 2 2 Iyk Iy A a rok A bik rbo rok lst 0.75m 2
Iyd Iy A a rod A bid rbo rod 2
Iyi Iy A a ro A bi rbo ro
composite b x beam: f
A st yh
4
Iyd 124048057.758mm
2
4
2
2
4
Iyi´ 163720223.436mm
2
ro
y d 0.2127m
2
A st 5.359 cm y h 0.0573m
2R20
2
A str
6.28 cm
d
Iyi 3 W yod W yod 674637.99689334mm 1 fctm y d st.min 3 fyd
A str 3 st W yoh 2504438.08776mm st 0.018 h py b avrage
st.max
W yoh
0.02
composite beam:
composite beam: Short-term Effective sheet width "bd": Section 2 0.13 for 1 6 Modules:
b d3 0.5 lst
d u cd h f ydro 2
n 21.68327 b avrge 122.5mm
The distance of the lower part of the steel fibres from the neutral axis of ideal cross-section of
n k 7.77778
yd
h
y hk b2.20456mm dI min b d1 b d2 b d3
The actual depth of the compression part of the concrete:
b d1 1 h d b d1 0.45m b d2 2 l Iyk 3 W yodk W yodk 767968.55641mm y dk b d3 0.375m b d 2 b d3 b py b d 0.825m
20 mm
Section modulus value)offor: Check the degree of(average reinforcement the concrete cross section:
Iyi 143497369.508mm
PENV 1994-1-1 Iyi´ Iy A a ro´ A bi´ rbo ro´
of composite beam:
2
A reqof the 5.35steel cm fibres from the neutral axis of ideal cross-section lower part
TheThe required reinforcement be:steel fibres from the neutral axis of ideal cross-section of distance of the upperarea part will of the
4
Iyk 209044542.292mm
2
A req distance b d d of fcd The the
Iyd y hd
b d2 0.91m Iyk W yohk y hk
Iyi W ybh A str fyd h H xro xu u 2 b d fcd
3
W yohk 94823742.04082mm
Composite Compositeslab slab Composite Compositeslab slab
15.94 mm
3
W ybh 766147.83983007mm 420 d MPa xu.lim xu.lim 525 MPa fyd
104.81 mm
Iyi yh
241
PENV 1994-1-1 W yod´
Iyi´
3
yd
Composite beam:
Iyi´
W ybh´ H
SLS (Design value): Short-term: vduzitne 5.6 kN m
h 2
8
3
W yoh´ 2857384.52707mm
yh
3
ro´
1
M1
2
M1 34.3 kN m
od 211.69847MPa
Rd 210MPa
od Rd
not satisfies
oh 121.22261MPa
Rd 210MPa
od Rd
satisfies
o´d dnmon d´
o´d 196.40241MPa
Rd 210MPa
Rd o´d
o´h hnmon h´
o´h 58.62704MPa
Rd 210MPa
Rd o´h
satisfies satisfies
The stress in the concrete slab:
Mpr 83.54 kN m
M pr
Sabah Shawkat © b
Normal stress on the composite beam:
d
M 1 34.3mkN
M1
h
W yodk
d 44.66329MPa
Long-term:
stresses in the lower part of the steel beam where the steel beam is composite:
PENV 1994-1-1
1 2 vduzitne L 8
M2 49.24 kN m
Mpr M1 M2
n k 7.77778
the lower part of the steel beam in the construction stage where only the steel beam and the
oh hnmon h
godstale vddl L
Short-term:
The total stresses in the bottom of the steel beam are calculated as the sum of the stresses in
od dnmon d
1
godstale vddl 8.04 kN m 1
Check the stress at the bottom of the steel beam:
Iyi´
W ybh´ 969105.52523959mm
Long-term:
M2
W yoh´
W yod´ 769713.64679246mm
d
M2
h
W yodd
d 77.43 MPa
M1
b
W yohk
h 0.36172MPa
M2
b
W yohd
h 29.75 MPa
M1
b 5.0289MPa
b 5.0289MPa
ad fcd
ad 8.09524MPa
According to NAD:
n k W ybhk
b 2.69597MPa
n W ybh
b´
M pr
b´ 5.54183MPa
n pretv W ybh´
b´ 5.54183MPa
b ad
satisfies
M2
nd Wybhd
b 2.62 MPa
Average value: d
M pr W yod
d 123.83384MPa
h
M pr
W yoh
h 33.35799MPa
b
M pr n W ybh
b 5.0289MPa
Calculation of composite:
PENV 1994-1-1 d´
M pr W yod´
d´ 108.53779MPa
Resulting cross-sectional stress.
For joining a reinforced steel sheet with steel beams, the steel connectors are welded together h´
M pr
W yoh´
h´ 29.23758MPa
b´
M pr n pretv W ybh´
with parallel welded profiled trapezoidal sheets. s 0.0631m
b´ 5.54183MPa
Composite slab Composite slab
h 2 0.08m
Rt 110MPa
m 1
r3 200mm
226 242
Material Characteristics: The spacing of the shear connectors will be half the width of the beam:
Determination with 2h 2 sheet: 4r3 of M h2 h 2 the maximum stresses in the extreme chord X the d if 2 1.0 plech 2 2.53566 then s M m.max
fy
Rt m s
s
L at 0.5 f MPa trnov cyl 30 N
M sheet
M md.max fy M W y.a 2 MMaximum W y.a bending W y.amoment: M 1 g sheet W y.a sd dL M Msd= 83.54 kN m 8 M sheet 20.50 kN m
1
Maximum shearing force: Qd g d L Qd 47.73887kN Determination of M slab at 1 m linear: 2 M slab M p.max M sheet M slab
PENV 1994-1-1
Qmin 0kN
d 0.02m
v 1.3
Qd Qmin
4 x d
Decides: 2
PRk2 M0.29d fck Ecm dim 2 b d d fcd
2
Vpriem 23.86943kN 40.351 kNm
A b h 1 b A b 0.04765m M dim M slab.0.75
p
o
Load capacity in full slab: Effective height of of the the connector concrete cross section: PRk1 0.8fu
40.35 kN m
r
PRk1 77.9115kN
X
1.31327m
x 0.017m
x u 0.8 x
PRk2 88.34297kN
PRk1 77.9115kN d 0.22m
b d 0.825m
2
d 220mm
2 The depth of the compression part of the concrete PRk1 d
0.0774
Average value of horizontal shear force Design of reinforcement to concrete ribs slab:
xu 0.014 m PRd 0.059
PRk1 v
PRd 59.93192kN 0.01737
Sabah Shawkat © 2 M doska.0.75
2 h py 280mm
2 b py 75mm
l st 750 mm
The required reinforcement area will be:
is determined depending on the construction procedure. For beams without temporary supports
lst 0.75m
in the construction stage: X
A st
kN
kt
Total horizontal shear force transferred by one shear connector: X r3
4r3 X 2h 2
0.01866m
1 m
11.86526kN
The area of one connector: A t
d 20mm
U
2
d
2
4
2h 2
r3
U "b13.62862kN A t Rt width U sheet Effective b dI d":
68.14311m kN min b d1 b d2 b d3
1N 6A R 2 0.13 b963.9kN 0.45m Nael d1 1 h d Nb bd1Nael ael a d
U
b d3 0.375m Ntrnov 70.72615
2R20
A str
r3
X
b d2F 2N l ct
b d 2 b d3 b py
kt 0.27606
PRdr PRd kt
fcd 1 f kNkt 1 ctm st.min MPa 1000 3 fyd
b
b d2 0.91m
2
6.28 cm
A str
st
0.018
st half of the beam: st.max The hnumber of pins on one py b avrage Qd
2.01MPa
xu
A str fyd Ntr n b d fcd PRdr
b d 0.825m
Composite Compositeslab slab Composite Compositeslab slab
xu
15.94 mm n 13.42
d
Ntr
0.02
1
L
s
xu.lim or
420 d MPa
Ntr f 525 MPa yd n Ntr1
20 mm
PRdr 16.54496kN
Ntr1 11.37543kN
2 x of the compression part of the2concrete: The actual depth b o H 2
The number of shear connectors on one half of the beam: b d3 0.5 lF stct Ntrnov U
2
A t 0.00031m
1
0.7 b o h t h p
d Ntr1 30.6 b avrge 122.5mm2 mm
Carrying capacity of one shearing connector: s
2
A st 5.359 cm
f
h h p reinforcement of the concrete cross section: Check the Ndegree of r p
The required diameter of the shaft: Rt m s
b d xu fcd
yd resistance of the ribbed slab: The reduced
1
X 59.32631m
n Iyi
A req 5.35 cm
l 7000mm
h d 75mm
The horizontal shear force per unit length of the steel and concrete sections of the cross section
Vpriem A b rb
2
A req b d d fcd
h 40.351h 1 kN m Mr dim h2 rb 0.1623m ro b
l 7m
17 MPa
fu 310 MPa
h t h 1 h 2 10mm
2
should be recalculated to a width of 0.75m.
Vpriem
f cd
fctm 1.2MPa
Distance from the edge of the concrete s 0.0631m N 1cross-section b s along the axish ofthe h reinforcement: h 0.08m
The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment
Input data:
fyd 356.522 MPa
fcyl fycd 356.522MPa fcd 0.85 Connector of diameter: 1.5
53.80 kN m
M slab.0.75
at 0.04949m 410MPa fyd 1.15
Ntr 221.98kN
xu.lim 104.81 mm n 19.51
243
b
2 bm
b
with
sheet
perpendicular
to
profiles
its
located
longitudinal
3
bk 2 bm 6
bk 2 bm h
h1 k h2
bm
Beam
l 10
2
Effective width of the concrete beams of the
b
edge beam (sheet profiles placed parallel to the beam axis).
axis The position of the profiles in the sheet plate
(1 - steel beam, 2 - sheet profile, 3 - concrete
B 2
bm
slab, 4 – shear connectors). 12.7 15.8 d 0.4 0.5 D 25.0 31.3 hD 8.00.3 8.00.3 d 3.0 0.1 4.0 0.1 1 0.2 0.2 1.5 v 1.5
0.3 12.0 0.1 4.0 0.2 1.5 18.2
0.5
31.3
Inner and outer beams with sheet profiles perpendicular to the longitudinal axis of the beams (1 - inner beam, 2 - end beam, 3 - sheet profile, 4 - concrete slab, 5 – shear
bs
bs
h
b bs 12
h
h1 k h2
Sabah Shawkat © connectors).
Effective width of the concrete beam of the Effective width of the concrete beam of the internal beam (sheet profiles perpendicular to edge beam (sheet profiles perpendicular to the longitudinal axis of the beam). the longitudinal axis of the beam).
b 6 h1 k h2
bn 2
b
bs 12
h1 k h2
Beam with sheet profiles parallel to the longitudinal axis of the beams (1 - steel
beam, 2 - sheet profile, 3 - concrete slab, 4 –
B3
shear connectors).
2
b 12 h1 k h2 bn b
1 2
B1 B2
b 0.3 l
Effective width of the concrete beam of the internal beam (sheet profiles arranged
Inner and outer beams with sheet profiles parallel to the longitudinal axis of the beams (1 -
parallel to the beam axis). b
inner beam, 2 - edge beam, 3 - sheet profile, 4 - additional sheet metal, 5 - ply profile, 6 -
0.3 l
concrete slab, 7 – shear connectors)
Composite slab Composite slab
226 244
Determination M plech with the maximum stresses in the extreme chord of the sheet: fy M
M m.max W y.a
M sheet
M sheet
W y.a
M md.max fy W W y.a y.a M
Determination of M slab at 1 m linear: M slab
M p.max M sheet Expansion of
concrete slab, 5 - thorn). The reinforcement will be designed in one rib, the ribs are spaced apart by 750mm, the moment should be recalculated to a width of 0.75m.
fyd 356.522 MPa
1.15
fcyl fcd 0.85 1.5
f cd
Concrete slab (1 - sheet profile, 2 - pre- slabs, 4 – shear connectors, 5 - reinforcements Input data: M doska.0.75 40.351 kNm M dim M slab.0.75 concrete layer of concrete slab, in ribs made of two profiles, 6 - reinforcement M3dim 40.351 kN m plate within the in ribs made of two profiles, reinforcement at - reinforcement of the
17 MPa
r1 3 d d 220mm
Effective height of the concrete cross section:
The depth of the compression part of the concrete x d
M dim
d 0.22m
b d 0.825m
2
b d d fcd
r1 40 mm
x u 0.8 x
x 0.017m
Axis distance of the shear connectors
(1 - steel beams, 2 - sheet profiles, 3 - concrete
fctm 1.2MPa
Distance from the edge of the concrete cross-section along the axis of the reinforcement:
0.0774
40.35 kN m
Design of reinforcement to concrete ribs slab:
r3 3 d
r2 1.5 d
r3 6 h
r3 40 mm
xu 0.014 m
0.059
0.01737
Sabah Shawkat ©
h pywidth 280mm of the l 7m
410MPa
Diameter of shear connectors
concrete slab (1 - beam, 2 -
sheet profile, 3 - additional sheet metal, 4 -
53.80 kN m
M slab.0.75
fyd
f cyl 30 MPa fycd 356.522MPa
M sheet 20.50 kN m
M slab
Material Characteristics:
top l the 7000mm
b py 75mm h d 75mm effective width b).
lst 0.75m
Location
shear connectors). The–required reinforcement area will be:
the
additional
partition
Length of sheet profiles.
reinforcement (1 - addition reinforcement, 2
2 0.13
b dI
b d1 1 h d
Length of connectors (1 - beam, 2 - sheet
min b d1 b d2 b d3
b d1 0.45m profile,
Effective width of the internal beam of the concrete beam (sheet sections parallel to the
2 l b d2 40.91m 3 b d2 - concrete slab, – shear
connector).
b d3 0.5 lst b d3 0.375m b d 2 b d3 b py beam axis) with additional sheet metal parts.
reinforcement of the slab, 5 – shear
2
2R20
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d
20 mm
Check the degree of reinforcement of the concrete cross section:
st
Effective sheet width "bd":
beam, 2 - profile, 3 - concrete slab, 4 -
A st 5.359 cm
fyd
b avrge
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surface of the concrete slab, 9 -
additional partition reinforcement).
l st 750 mm
A req b d d fcd Reinforced concrete
st.min
122.5mm
A str
1 fctm 3 fyd
st 0.018
h py b avrage
st.max
0.02
The actual depth of the compression part of the concrete: Cross-sectional area of the composite beam. xu
A str fyd b d fcd
xu
15.94 mm
xu.lim
420 d MPa xu.lim 104.81 mm 525 MPa The fydposition of the neutral axis of the cross-
section
b d 0.825m
Composite Compositeslab slab Composite Compositeslab slab
245
Reinforced concrete sheet with sheet metal profiles (1 - steel beam, 2 - sheet profile, 3 - concrete slab, 4 – shear connectors, 5 reinforcement in plate ribs, 6 - reinforcement
at the top surface of the concrete slab).
h
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f t Rd
fy
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-
Sabah Shawkat © Lightweight structures - Definition of lightweight structures - The art of tensegrity - Attachment of the stiffener to the steel beam - Detail of the support cables on the pylon - Detail of the support bearing cables on the pylon - Detail of the stiffener connection to column on the bar
-
Sabah Shawkat ©
-
248 248
Lightweight structures Lightweight structures Architects engineers executives of services to reap intellectual property of previous Architects andand engineers areare executives of services to reap thethe intellectual property of previous
constructions. clients' demands high nowadays, there a demand temporary, forfor temporary, constructions. TheThe clients' demands areare high nowadays, there is is a demand
generations. They studying, improving discovering. They creators new generations. They areare studying, improving andand discovering. They areare thethe creators of of new
transformable solutions offer sliding lightweight constructions ranging from simple transformable solutions thatthat cancan offer sliding lightweight constructions ranging from simple
spaces, forms structures constantly improving. This creative activity connects spaces, forms andand structures thatthat areare constantly improving. This creative activity connects
sliding marquee solutions staircases, which disappear pressing button (Khalifa sliding marquee solutions to to staircases, which disappear by by pressing thethe button (Khalifa
architects engineers their way to the of "Prof. Frei Otto. architects andand engineers on on their way to the art art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems being developed today NASA International Stadium). Tensile integrity systems areare being developed today forfor NASA andand
Lightweight structures used in various forms variations seen in broad spectrum Lightweight structures used in various forms andand variations cancan be be seen in broad spectrum useuse
form unprecedented options blame. form unprecedented options forfor blame.
current market. These structures, developed over years, together with advances on on thethe current market. These structures, developed over thethe years, together with advances in in
Talking about modern systems steel, wire membrane merit. And these Talking about modern systems of of steel, wire andand membrane hashas its its merit. And thatthat these
material engineering technology, continue progress now integral material engineering andand technology, continue to to progress andand areare now an an integral partpart of of
systems at the of the current building options. Limits given physical properties systems areare at the toptop of the current building options. Limits areare given by by thethe physical properties
architectural creation. architectural creation.
laws material construction system. These must fully taken account andand laws of of thethe material andand thethe construction system. These must be be fully taken intointo account
Architectural lightweight structures now seen in different shapes sizes. They may Architectural lightweight structures cancan now be be seen in different shapes andand sizes. They may
used creation modern system. practice, most often encounter andand used in in thethe creation of of thethe modern system. In In practice, wewe most often encounter thethe
internal, external, permanent, temporary, large, small, supported, membranes filled with be be internal, external, permanent, temporary, large, small, supported, membranes filled with air air
following issues: following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played important contemporary - are also very current. These unique forms have played an an important rolerole in in contemporary
• bars (struts) systems - stable problems of compressive bent bars, • bars (struts) systems - stable problems of compressive andand bent bars,
architecture, interior design various cultural events since time they first appeared in the architecture, interior design andand various cultural events since thethe time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving theory order, • cables systems - prestress, stiffness of the structure, necessity of solving thethe theory II. II. order,
1960s world-famous German architect engineer Frei Otto. 1960s by by thethe world-famous German architect andand engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions. • membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
present, light constructions designed constructed independently geographic At At present, light constructions areare designed andand constructed independently of of thethe geographic
location. They transform space have subtle elegant quality. addition location. They transform thethe space andand have so so subtle andand elegant quality. In In addition to to
providing basic functions such shading shutdown, they important functional providing basic functions such as as shading andand shutdown, they areare an an important andand functional element construction amphitheatres, sports stadiums, airports, courtyards, building element in in thethe construction of of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront interiors. facades, parks, seafront andand interiors.
Designing lightweight constructions to meet criteria a complex task. Every is visible Designing lightweight constructions to meet all all criteria is aiscomplex task. Every partpart is visible constructive, relying proper functioning of all parts. example, diaphragm fabrics andand constructive, relying on on thethe proper functioning of all parts. ForFor example, diaphragm fabrics developed to meet requirements high tensile strength, long with a high modulus areare developed to meet thethe requirements forfor high tensile strength, long lifelife with a high modulus elasticity. surface layer applied material ensures fabric resistance against of of elasticity. TheThe surface layer applied to to thethe material ensures fabric resistance against weathering dirt, provides resistance to UV radiation non-combustible properties. weathering andand dirt, provides resistance to UV radiation andand hashas non-combustible properties.
Tensile membrane architecture a highly sophisticated medium offers unique qualities Tensile membrane architecture is aishighly sophisticated medium thatthat offers unique qualities forfor architects, designers engineers therefore provides unlimited opportunities design as well architects, designers andand engineers therefore provides unlimited opportunities forfor design as well as experiment with form create alternative solutions to every design challenges. as experiment with form andand create alternative solutions to every dayday design challenges. This is made possible fundamental flexibility lightweight nature composite This is made possible duedue to to thethe fundamental flexibility andand lightweight nature of of composite membranes. Membrane structures often referred to textile as textile structures. However, actual membranes. Membrane structures areare often referred to as structures. However, thethe actual membrane construction is far removed from classic tent. main difference is its exact membrane construction is far removed from thethe classic tent. TheThe main difference is its exact geometric shape. functioning membrane structure, exact geometric criteria geometric shape. ForFor thethe functioning of of thethe membrane structure, thethe exact geometric criteria must computed. basic criterion is maintain to maintain concavity convexity main must be be computed. TheThe basic criterion is to thethe concavity andand convexity of of thethe main directions membrane surface. Following principle, about basic four directions of of thethe membrane surface. Following thisthis principle, wewe cancan talktalk about thethe basic four types of membranes: types of membranes:
think it important to explore new trends in lightweight constructions, among which WeWe think it important to explore new trends in lightweight constructions, among which wewe
saddle-shaped (hyperbolic paraboloid) 1. 1.saddle-shaped (hyperbolic paraboloid)
include: cancan include:
ridge-valley shape 2. 2.ridge-valley shape
1. Lightweight designs designed with regard to sustainability 1. Lightweight designs designed with regard to sustainability
arch shape 3. 3.arch shape
2. Modular light constructions 2. Modular light constructions
conical shape, 4. 4.conical shape,
3. Sliding light constructions 3. Sliding light constructions Designers benefits mass production simple structures, such "umbrella" Designers seesee thethe benefits of of mass production of of simple structures, such as as an an "umbrella" thatthat reproduciblecomponents. components.Savings Savingsfrom froma modular a modularstrategy strategylead leadto tocost-effective cost-effective hashasreproducible
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
249
with a specific shape. Thus, lightweight structures, in place of stiffness of the material, derive their resistance from their shape and may therefore be denoted as shape-active. One of the main design steps of lightweight constructions is therefore the design of a shape that is controlled by the required stress state. The specificity in the design of light structures is the fact that the result of the shape analysis (process shape search), the areas are curved in two directions, which are generally positively evaluated aesthetically and represent a very non-traditional form of revitalization of the public Another criterion of lightweight membrane construction is its prestress. The correct geometric
architecture in the Central European space. For this reason, the location of the planned
shape and prestress guarantees its stability, stiffness and dynamic resistance. At the same time,
workplace at AFAD is more than adequate. However, in many practical cases, in the world,
it allows the structure to resist the effects on which it was designed, rain, wind and snow.
lightweight and large-scale structures are the only structural layer of objects. Its role is, besides
The basic geometric shape of the membrane system emerges from the surface of the hyperbolic paraboloid
aesthetic criteria, to combine architectural, static and facade functions and, moreover, to provide a pleasant interior of the building. This step combines the role of architect and engineer, naturally deducting the requirement for multidisciplinary qualification of a designer. The unification of the role of architect and engineer in designing lightweight constructions is also a
Sabah Shawkat ©
top trend in top foreign workplaces and is known, for example, under the Archineer brand. The our archineer team aims to train such specialists, who will be able to apply in artistic and technical practice thanks to the interdisciplinary integration of knowledge.
The shell structures, once reinforced concrete, are now parameterized (Robotic Fabrications), converted to various non-traditional material concepts (Timber Shells). A great challenge for today's architects is global warming, membrane structures are increasingly seen in our territory and will be an integral part of sustainable climate solutions for public spaces, parks. We therefore consider this issue to be very topical and important. The ambition of the Engineering Cabinet is to prepare the basis for a new training program lightweight
construction,
which
is
not
yet
adequate
in
Slovakia.
Easy
constructions are specific by optimizing the built-in material. This is achieved by minimizing or completely eliminating bending stress. This special case can only be achieved on structures
Lightweight structures Lightweight structures
Lightweight structure-tensegrity shell
250 248
The naturestructures of the research and development of the project Lightweight Research will take place in a hybrid form of practical and theoretical approach. It will include Architects and engineers are executives of services to reap the intellectual property of previous analytical and design phase. generations. They are studying, improving and discovering. They are the creators of new
ParticipatingThe in workshops, lectures,are conferences and annotated will be for heldtemporary, constructions. clients' demands high nowadays, there istours a demand invited top professionals transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, formsIt and structurestothat are constantly improving. creative activity connects of Research: is necessary initiate a wide research activityThis focused on the concentration
sliding marqueeconstruction solutions tois staircases, disappear by pressing buttonbuilding (Khalifaand Lightweight one of thewhich popular architectural forms ofthetoday's International Stadium). Tensiletointegrity systems are being developed todayshape. for NASA and design. They appeal mainly their untraditional solutions and exceptional The concept
architects and engineers on theirdevelopment way to the artand of "Prof. Frei Otto. information on the historical the current state of the issue. Based on current research by researchers fromforms the foreign environment schools specializing Lightweight structures usedmainly in various and variations can beand seen in broad spectrum in usethis field. (ITKE University of Stuttgart Institute of Building Structures and Structural Design, on the current market. These structures, developed over the years, together with advances in ETH Zurich - Department of Civil, continue Environmental and Geomatic Engineering). Studies material engineering and technology, to progress and are now an integral part ofwill form the starting point for further research. architectural creation. Architectural lightweight structures candesign now be seen infor different shapes and sizes. They may Data Collecting: Collecting reliable methods light constructions will be confronted be with internal, external, permanent, temporary, large, small, supported, membranes filled with physical outputs in the form of models. The proposal methods will then be elaboratedairand or stretched. of these constructions structures, tensile-integrity structures presented New to thesubgroups professional public. The results- shell will be confronted at local and international - are also very current. These unique forms have played an important role in contemporary level. The Engineering Cabinet also has the task of elaborating and developing a generic architecture, interior design andlightweight various cultural events since time they firstboth appeared in theand methodology of designing constructions andthe offering it for academic
form options forisblame. of unprecedented lightweight construction particularly interesting for the needs of architects or designers from Form main of plussteel, of lightweight theirAnd ease,that airiness Talking aboutFinding. modern The systems wire and constructions membrane hasinclude its merit. theseand tremendous flexibility. Compared to traditional conventional designs, they make it easier systems are at the top of the current building options. Limits are given by the physical properties to withand a minimum number system. of support elements. Another significant advantage andoverlap laws oflarge the areas material the construction These must be fully taken into account is their design variability, which provides almost unlimited possibilities for searching and used in the creation of the modern system. In practice, we most often encounter thefor originalissues: and elegant forms. following
• bars (struts) systems - stable problems of compressive and bent bars, The main objectives of our project can be summarized as follows: • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order, - to focus on the field of design and implementation of light structures and to establish
Sabah Shawkat ©
1960s by the world-famous architect and engineerarchitecture. Frei Otto. commercial practice as anGerman alternative to contemporary At present, light constructions are designed and constructed independently of the geographic Lectures: They will be presented in an interactive way. Within lectures we will ensure a broad location. They transform the space and have so subtle and elegant quality. In addition to professional cross-section that will be guaranteed by professionals in the given field. providing basic functions such as shading and shutdown, they are an important and functional Workshops: The core of the research will be based on work with students of AFAD and CTU element in the construction of amphitheatres, sports stadiums, airports, courtyards, building in Prague. Than Practical lectures on lectures will be used by students to practice their new facades, parks, seafront and interiors. knowledge. Workshops will be led by lecturers who will direct students' thinking and creative Designing lightweight constructions to meet all criteria is a complex task. Every part is visible activity in the form of criticism and discussion. The outputs of the workshops will focus on and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics precise physical models, which will then be processed, analyzed and ranked in research outputs. are developed to meet the requirements for high tensile strength, long life with a high modulus
The collected input applied data willtobe the graphically and presented. Research of Exhibition: elasticity. The surface layer materialprocessed ensures fabric resistance againstthe work thatand willdirt, be provides taken from the workshops, the applied works and the work of the weathering resistance to UV radiation andsemestral has non-combustible properties. team of solvers, will be presented at the exhibition in the form of models and graphical outputs. We think it important to explore new trends in lightweight constructions, among which we
international cooperation in this field, resistance, large deformation solutions. • membrane systems - prestress, dynamic - to create a specialized training and consulting centre for both students and the professional Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for public, focusing on activities related to the correct design and realization of lightweight architects, designers and engineers therefore provides unlimited opportunities for design as well structures, as experiment with form and create alternative solutions to every day design challenges. - present the results at local and international conferences and workshops as well as create This is made possible due to the fundamental flexibility and lightweight nature of composite online outputs and organize events with the participation of top experts in the field, membranes. Membrane structures are often referred to as textile structures. However, the actual - to compile a book publication on lightweight structures for both students and specialists. membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes: 1. saddle-shaped (hyperbolic paraboloid)
One of the main goals of the project is the book publication of all stages and canPublications: include:
2. ridge-valley shape
phases research. 1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions Expert and Consultation Center: Creating a specialized expert group to serve as a source of 3. Sliding light constructions relevant information and consulting center in designing and constructing lightweight
4. conical shape,
constructions be oneofofmass the forms of final output andsuch willas bean a prerequisite for Designers see thewill benefits production of research simple structures, "umbrella" that phases ofcomponents. research on this issue. from a modular strategy lead to cost-effective hasfurther reproducible Savings
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
251
The art of tensegrity The members of a tensegrity structure are either always in tension or always in compression.
thought of as sections of rigid tubing which maintain the separation of two points. The tensile
The tensile members are usually cables or rods, while the compression members are strut
members are continuously connected to each other and to the ends of the compression members
sections. Key contributions to the early development of tensegrity structures appear to have
while the compression members are only connected to tensile members and not to other
come from several people. Some historians claim Latvian artist Karl Ioganson exhibited a
compression members.
tensegrity prism in Moscow already in the year 1920. Ioganson’s work was destroyed in the
The results of our design process are presented also graphically. In order to determine the
mid-1920’s by the Soviet regime, but photographs of the exhibition survived. The word
equilibrium position the lengths of the struts are specified, which are assumed to be all the same,
“tensegrity” (a contraction of “tensile-integrity”) was coined by the American entrepreneur
together with the stiffness of the top ties (assumed equal), bottom ties (assumed equal),
Buckminster Fuller. In the article "Snelson for the invention of Tensegrity" in Lalvani96,
connecting ties (assumed equal).
tensegrity pioneer Kenneth Snelson also quotes Russian constructivists whose members were loganson as inspiration for his work. Kenneth Snelson also remembered David Geiger's "Cabledome" technology and Matthys Levy's space triangulated tensegrity dome technology, which provided many creative and practical applications of tensegrity in practice. Campbell94 discloses a description of these two compositions which are dependent on the peripheral anchor for their structural integrity.
The qualities of tensegrity structures which make the technology attractive for human use are their resilience and their ability to use materials in a very economical way. These structures very effectively capitalize on the ever increasing tensile performance modern engineering has been able to extract from construction materials. In tensegrity structures, the ethereal (yet strong) tensile members predominate, while the more material-intensive compression members
Sabah Shawkat ©
All tensegrities are prestressed under tension; they are self–supporting and independent of
gravity. But the weight of the structure also adds to the prestress. All components are
are minimized. Thus, the construction of buildings, bridges and other structures using tensegrity principles could make them highly resilient and very economical at the same time.
dynamically linked such that forces are translated instantly everywhere; a change in one part is
I think that part of the reason that the beauty and construction of tensegrity did not come into
reflected throughout the whole structure.
practice, even in circles where there was a strong interest in the practical application of
The stability of prismatic tensegrity structures is not only determined by the connectivity
tensegrity, is the clear lack of professional and intelligent workers as well as the precise tools
manner of the members, but also sensitive to the height/radius ratio and the stiffness/prestress
for realizing their design and creation.
ratio.
The main shortcomings and problems of practical application of tensegrity technology for
Our team of structural designers started to deal with this kind of fine art of structure in the year 2008. Together with the students we try to bring fresh ideas into the field and create different
the practice these artists have identified are:
models of tensegrities. In this chapter could be found various model used for living and for
1. Low Load Response - "Relatively high deformation and low material efficiency compared
pleasure as furniture, table lamps or toys. We pay attention not only to the structure itself, but
to conventional, geometrically rigid structures."
also to details, aesthetic and the elegance of the models. Each node of the structures is connected by two horizontal cables within its own horizontal plane, and is connected by one vertical cable and one strut to nodes in the other plane. The thick and thin lines denote, respectively, cables that can only carry tension, and struts that carry compression. These structures are called super stable. In the model structures shown in this chapter, the tensile members are usually cables or rods,
2. The complexity of the production of details - spherical and domical structures are complicated in particular to produce details of joints as well as the selection of suitable material for their realization, these factories can lead to production difficulties. All the models shown in this appendix have been made by the author by means of Tensegrity elements.
while the compression members are sections of tubing or U profiles. The tensile members can be thought of as cables which pull two points together, while the compression members can be
Lightweight structures Lightweight structures
252 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective Tensegrity foot Bridge M1 over Morava river- Design systems- Parametric Modelling
Tensegrity foot Bridge M1 over Morava river- Design systems- Parametric Modelling
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
253
Sabah Shawkat © Tensegrity foot Bridge M2 over Morava river- Design systems- Parametric Modelling
Tensegrity foot Bridge M3 over Morava river- Design systems- Parametric Modelling
Lightweight structures Lightweight structures
254 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. fromrivera modular strategy Parametric lead to cost-effective Tensegrity foot Bridge M4Savings over Morava Design systemsModelling
Tensegrity foot Bridge M4 over Morava river- Design systems- Parametric Modelling
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
255
Sabah Shawkat © Tensegrity foot Bridge M5 over Morava river- Design systems- Parametric Modelling
Tensegrity foot Bridge M5 over Morava river- Design systems- Parametric Modelling
Lightweight structures Lightweight structures
256 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that Design systemsParametric tower has reproducible components. Savings from aModelling-Sightseeing modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
Design systems- Parametric Modelling-Sightseeing tower
257
Sabah Shawkat © Design systems- Parametric Modelling-Tensegrity structures Tensegrity art - Parametric Modelling
Lightweight structures Lightweight structures
258 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that Tensegrity art -Design systems- Parametric Modelling has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
Tensegrity art -Design systems- Parametric Modelling
withstand large structural shocks like earthquakes. Thus, they could be desirable in areas where earthquakes are a problem. Much interesting theoretical work has come from the University of 259
California at San Diego. Fuller's primary interest was adapting the technology to the development of spherical and domical structures with architectural applications in mind. He also used tensegrity structures to make some philosophical points. As an architect, Emmerich was also interested in architectural applications and designed at least one dome as well. An early exception to this dearth of information on tensegrity calculating was Hugh Kenner's excellent work Geodesic Math which went into an exact technique for the very simple tensegrity prism and outlined an approximate technique for dealing with some simple spherical structures. These domes could encompass very large areas with only minimal support at their perimeters. In a spherical configuration, tensegrity designs could be useful in an outer-space context as superstructures for space stations. Their extreme resilience makes tensegrity structures able to withstand large structural shocks like earthquakes. Thus, they could be desirable in areas where earthquakes are a problem. Much interesting theoretical work has come from the University of California at San Diego.
Sabah Shawkat © Tensegrity dome- Design systems- Parametric Modelling
Tensegrity dome- Design systems- Parametric Modelling
Tensegrity dome- Design systems- Parametric Modelling Lightweight structures Lightweight structures
260 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
261
Sabah Shawkat ©
Lightweight structures Lightweight structures
262 248
Lightweight structures Attachment of the stiffener to the steel beam
Bracing TR 168,3/10:
Architects and engineers are executives of services to reap the intellectual property of previous
d 168.3mm
t1 12mm
constructions. The clients' high nowadays, there is a demand for temporary, The depth of steel plate: demands t2 are 10mm
spaces, forms and structures that are constantly improving. This creative activity connects
transformable solutions that can offer sliding lightweight constructions ranging from simple Nsd A 3 2 0.063m 2.535 10 mm Height of steelsolutions plate: to staircases, h A sliding marquee which A disappear by pressing the buttonh (Khalifa
Input_Steel "Steel Son 235" if way Steel to "s architects and engineers their the235" art of "Prof. Frei Otto.
International Stadium). Tensile integrity m0 systems are being developed today for NASA and
Lightweight structures various "Steelused S 355"in if Steel forms "s 355"and variations can be seen in broad spectrum use
form unprecedented options for blame. Design of the welding attachment of the stiffener to the sheet metal plate:
"Nespravne triedy ocele !!!" otherwise on the current market. Thesezadanie structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are 0.9 at the top of the current building options. Limits are given by the physical properties
Enter_Steelcreation. "Steel S 355" architectural
and laws of the material and the construction system. These must be fully taken into account
generations. They are studying, improving and discovering. They are the creators of new
"Steel S 275" if Steel
t 40mm
"s 275"
E 210000MPa
t
fy
w
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
fy ( 235MPa ) ifpermanent, Steel "s 235" t 40mm be internal, external, temporary, large, small, supported, membranes filled with air
following issues: 0.85 if Steel
( 215MPa ) if Steel
"s 235" 40mm t 100mm
( 275MPa ) if Steel
"s 275" t 40mm
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also (very current. These unique forms have played an important role in contemporary 255MPa ) if Steel "s 275" 40mm t 100mm architecture, interior various t cultural 40mm events since the time they first appeared in the ( 355MPa ) ifdesign Steel and "s 355"
w
0.8 if Steel
"s 235"
0.9 if Steel
"s 355"
"s 275"
• bars (struts) systems - stable problems of compressive and bent bars, • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
1960s by
40mm tand 100mm ( 335MPa ) if Steel German "s 355" the world-famous architect engineer
Frei Otto.
a 3mm if t max-prestress, 10mm • membrane systems dynamic resistance, large deformation solutions.
At present, light constructions are designed and constructed independently of the geographic fu They ( 360MPa ) if Steel the"sspace 235" and t 40mm location. transform have so subtle ( 340MPa ) if Steel "s 235" 40mm t 100mm
and elegant quality. In addition to
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"s 275" t 40mm
element in( 410MPa the construction of amphitheatres, sports stadiums, airports, courtyards, building ) if Steel "s 275" 40mm t 100mm facades, parks, seafront and interiors. ( 510MPa ) if Steel "s 355" t 40mm
t criteria 100mm is a complex task. Every part is visible 490MPa ) if Steel "s 355" to40mm Designing (lightweight constructions meetall
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"s 355"
1.2 if Steel
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Steel "s 355"
fy 355MPa
m0 1.2
fu 510MPa
1. Lightweight designs designed with regard to sustainability
m1 1.2
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4mm if 11mm t max 20mm
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for 5mm if 21mm t max 30mm
architects, designers and engineers therefore provides unlimited opportunities for design as well 6mm if t max 30mm
as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact a 4 mm effective weld height Mw 1.5 geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main Stress due to force Nsd directions of the membrane surface. Following this principle, we can talk about the basic four Nsd types of membranes: Stress due to force Nsd: II 4 a l 1. saddle-shaped (hyperbolic paraboloid) fu
2. ridge-valley shape 3. arch shape Maximum permissible welding stress: 4. conical shape, L
The design of stiffener: Designers see strength the benefits of mass production of simple structures, such as an "umbrella" that
Nsd w Mw 4 a
fu
has The reproducible components. Savings N from a750kN modular strategy lead to cost-effective design strength of bracing: sd
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
3
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3
w Mw
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fu
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3
w Mw
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263
Welding evaluation by equalizing stress:
kol 0kPa
II
Nsd
Then we have to change the welding length, or decrease the angle between the bracing
II 218.11MPa
4 a L
member with beam, thus from 75o to approximately 25o. Design of the welding attachment of the stiffener to the sheet metal plate:
f
u 2 2 2 kol II kol w Mw
kol 0kPa
75deg
Nsd 750kN Verification
"weld is satisfactory"
"wel does not"
if
2 2 2 kol II kol w Mw
Nsd
rov 75deg
a 4 mm
a 2 L
0.707
a 2 L
kol
0.707
Fwy
2
2
kol 3 kol 3 rov
2
Fwx 194.114kN
Fwy
kol
fu
2
2
kol 3 kol 3 rov 853.884MPa
Verification
Fwy Nsd sin ( )
rov 132.563MPa
kol
Fwy 724.444kN
Fwy 2 a L
kol 181.111MPa
2 a L
0.707
Fwy Nsd sin ( )
Fwy 724.444kN
"weld is satisfactory" "weld does not"
if
Fwy 2 a L
fu w Mw
2
2
kol 3 kol 3 rov 367.024MPa
Verification
kol
kol 128.046MPa
w Mw
rov 308.408MPa kol 421.356MPa
2 a L
w Mw
L 0.215m
2
Nsd
fu
2
Sabah Shawkat © 2
Assessment of the welding:
rov
2
kol 3 kol 3 rov
Fwx 194.114kN
Fwx Nsd cos ( )
Nsd 750kN
2
Assessment of the welding:
fu
Design of welding of the connection plate to the beam:
Fwx Nsd cos ( )
L 400 mm
f
u 2 2 2 kol II kol w Mw
if
Verification "weld is satisfactory"
Design force:
a 5 mm
"weld is satisfactory" "weld does not"
0.707
kol 297.899MPa Verification "weld is satisfactory"
377.778MPa
fu fu 2 2 2 kol 3 kol 3 rov kol w Mw Mw
otherwise
Verification "weld does not"
Lightweight structures Lightweight structures
if
fu
w Mw
377.778MPa
fu fu 2 2 2 kol 3 kol 3 rov kol w Mw Mw
otherwise
264 248
Detail of structures the support cables on the pylon Lightweight
Design of tensile force: Nsd
Architects and engineers are executives of services to reap the intellectual property of previous Ocel "s 355"
Fsd.1 5200kN
t 40mm
E 210000MPa
generations. They are studying, improving and discovering. They are the creators of new spaces, forms and structures that are constantly improving. This creative activity connects Entry values: architects and engineers on their way to the art of "Prof. Frei Otto. Ocel "s 355" Lightweight structures used in various forms and variations can be seen in broad spectrum use fy 355MPa
fu 510MPa
on the current market. These structures, developed over the years, together with advances in
constructions. The clients' demands are high nowadays, there is a demand for temporary, The design normal force of the tensile cross-sectional load determined as less of the values transformable solutions that can offer sliding lightweight constructions ranging from simple Npl, Rd and Nu, Rd sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa International systems are being developed for NASAfrom: and The designStadium). of normalTensile force ofintegrity the unbroken cross-sectional load shalltoday be determined form unprecedented options for blame.
fy A Npl.Rd Npl.Rd 27031.771kN Talking about modern systems of steel, wire m0
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architectural creation.
systems are at the top of the current building options. Limits are given by the physical properties The design of bearing normal force of the weakened cross section is determined from: and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
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THYSSEN F be internal, external, permanent, temporary, large, small, supported, membranes filled with air cable 100 mm or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures
following issues:
m1 engineering 1.2 m2 and 1.3 technology, continue to progress and are now an integral part of material Mp 1.45
m0 1.2
diameter of the pin: - areThe also very current. These unique forms have played an important role in contemporary d 172mm
architecture, interior design and various cultural events since the time they first appeared in the
u.Rd
f net m2
u.Rd
pl.Rd - stable u.Rd problems t.Rd • barst.Rd (struts) systems of compressive and bent bars, N
min N
N
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- prestress, assessment "Conformes"stiffness if Nsd of N t.Rdstructure, necessity of solving the theory II. order, • cables systems the
Sabah Shawkat ©
Plate 1960s by thickness: the world-famous German architect and engineer Frei Otto. t = 85 mm At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional f
ysports stadiums, airports, courtyards, building element in the construction of Famphitheatres, Bruising plate pin: FbRd 5369.069kN bRd 1.5 t d Mp facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible assessment
"Conformes" if FbRd Fsd.1
and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics "does not"
otherwise
are developed to meet the requirements for high tensile strength, long life with a high modulus assessment The "Conformes" of elasticity. surface layer applied to the material ensures fabric resistance against
weathering and dirt, provides resistance to UV radiation and has non-combustible properties. Assessment of cross-sectional subjected to tensile stress: We think it important to explore new trends in lightweight constructions, among which we Design of tensile force: Nsd Fsd.1 can include: The width of plate: b p t 1. Lightweight designs designed with regard to sustainability The height of plate: h p 1075mm 2. Modular light constructions 2 A 0.091m area of unbroken cross-section: A b p h p 3. Sliding light constructions 2 The area of weakened cross-section: A net 0.077m A net A d t Designers see the benefits of mass production of simple structures, such as an "umbrella" that sd Nt.Rd has Nreproducible components. Savings from a modular strategy lead to cost-effective
"does not"
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2. ridge-valley shape F shape Fsd.1 sin ( ) 3. arch Vsd1
3
FVsd1 3.129 10 kN
4. conical shape, Partial safety factor:
Mw 1.5
Coefficient of strength class:
w 0.9
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
265
fu
design strength of the weld in the shear: fvwRd
3 w Mw
fvwRd 218.11MPa
Detail of the support bearing cables on the pylon Design of the K1 joint
effective welding height: a 6mm design resistance of the unit length of the weld: FvwRd fvwRd a Effective welding length: number of welds:
kN FvwRd 1308.661 m
Fsd.1 4100kN Fsd.2 4100kN Fsd.3 2000kN
lu1 2043mm
Fsd.4 1700kN
n 4
fu 510 MPa
components of individual stresses:
fy 355 MPa
Steel "s 355" t 40mm
FVsd1
II
m0 1.2
n
II 63.824MPa
lu1 a
M 1 FHsd1 e1
1
T
4 2
m2 1.3 1
2
Mp 1.45
Sabah Shawkat © W zvar
M 1 685.229kNm
M1
m1 1.2
W zvar
W zvar 4.174L
E 210000MPa
Cable THYSSEN 100 mm
FHsd1 lu1 a
6
a lu1
T T T 88.912MPa
T 88.912MPa
Screw core area
d 172mm
The thickness of the plate
t1 90mm
Comparative stress: 2
2
assessment
"Conformes" if "does not"
suppression the plate K1:
fu
2
T 3 T 3 II 209.385MPa
w Mw
377.778MPa
FbRd 1.5 t1 d
fu 2 2 2 T 3 T 3 II w Mw
otherwise
"Conformes" if T Mw
assessment "Conformes"
"satisfactory"
FbRd 5684.897kN
if FbRd Fsd.1 otherwise
Verification "satisfactory"
fu
"does not"
Mp
"does not change the design proposal"
assessment "Conformes"
assessment
Verification
fy
fu Mw
340MPa
suppression the plate K2
FbRd 1.5 t 1 d
otherwise
Verification
"satisfactory"
fy Mp
if FbRd Fsd.3
"It is inappropriate to modify the design of the joint" Verification "satisfactory"
Lightweight structures Lightweight structures
FbRd 5684.897kN
otherwise
266 248
Lightweight structures Assessment of cross-sectional tensile stress K1
Verification
"satisfactory" "does not"
if Nsd12 Nt.Rd
otherwise
Architects engineers Designand tensile force: are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
N F
F
3
N
8.2 10 kN
sd.2 spaces,sd12 forms sd.1 and structures thatsd12 are constantly improving. This creative activity connects
architects and engineers on their way to the art of "Prof. Frei Otto. Plate width: b p 90mm Lightweight structures used in various forms and variations can be seen in broad spectrum use The height of the platter in the considered location: h p 2300mm on the current market. These structures, developed over the years, together with advances in The area of not weakened cross-section: material engineering and technology, continue to progress and are now an integral part of 2
A 0.207m
A b p h pcreation. architectural
Architectural lightweight structures can now be seen in different shapes and sizes. They may The areaexternal, of weakened cross-section be internal, permanent, temporary, large, small, supported, membranes filled with air A
A A d t
0.192 m
2
netof these constructions - shell structures, tensile-integrity structures net or stretched. New 1subgroups
- are also very current. These unique forms have played an important role in contemporary Nsd12 Nt.Rd
architecture, interior design and various cultural events since the time they first appeared in the
Verification "satisfactory"
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa Assessment of cross-sectional tensile stress K2: International Stadium). Tensile integrity systems are being developed today for NASA and tensile force: formDesign unprecedented options for blame. 3
10 and kN membrane has its merit. And that these Nsd34 Fsd.3 Fsd.4systems Nsd34 Talking about modern of steel,3.7wire
systems are at the top of the current building options. Limits are given by the physical properties 90mm and Plate laws width: of the material and the construction system. These must bebpfully taken into account and used in the creation of the modern system. In practice, we most often encounter the The height of the platter in the considered location: h p 1745mm following issues: 2
A 0.157m Area of not weakened cross-section: A b p hp • bars (struts) systems - stable problems of compressive and bent bars, 2 Area of weakened cross-section: A net 0.142m A net A d t 1 • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order, Nsd34 Nt.Rd
Sabah Shawkat ©
Nsd12 1960s by the world-famous German architect and engineer Frei Otto. - design tensile force
At present, light constructions are designed and constructed independently of the geographic - the design normal force of the tensile cross-sectional load determined as less Nt.Rd location. They transform the space and have so subtle and elegant quality. In addition to of the values Npl, Rd and Nuas , Rdshading and shutdown, they are an important and functional providing basic functions such element in the construction of amphitheatres, sports stadiums, airports, courtyards, building
facades, parks,normal seafront and of interiors. The design force the not weakened cross-sectional load shall be determined from: Designing lightweight constructions to meet all criteria is a complex task. Every part is visible
- design tensile force Nsd34 Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for - the design normal force of the tensile cross-sectional load determined as less of Nt.Rd architects, designers and engineers therefore provides unlimited opportunities for design as well Rd and Nucreate , Rd alternative solutions to every day design challenges. The valueswith Npl, form as experiment and designpossible normal due forcetoofthe thefundamental not weakened cross-sectional load shallnature be determined fro ThisThe is made flexibility and lightweight of composite fy membranes. Membrane structures are often referred to as textile structures. However, the actual Npl.Rd A
Npl.Rd 46460.625kN
fy
m0 membrane construction is far removed from the classic tent. The main difference is its exact
m0
The design normal load force of the cross structure, section is the determined from: criteria geometric shape. For the functioning ofweakened the membrane exact geometric
A relying on the proper Npl.Rd and constructive, functioning 61237.5kN of all parts. For example, diaphragm fabrics Npl.Rd
are developed to meet the requirements for high tensile strength, long life with a high modulus of The elasticity. surface layerofapplied to the cross material ensures fabric resistance against design The normal load force the weakened section is determined from: weathering and dirt, provides resistance to UV radiation and has non-combustible properties. fu
Nu.Rd 0.9 A net Nu.Rd 67621.292kN We think it importantto explore new trends in lightweight constructions, among which we m2
can include:
• membrane systems - prestress, dynamic resistance, large deformation solutions.
fu basic criterion is to maintain the concavity and convexity of the main must be computed. The Nu.Rd 0.9 A net
Nu.Rd 49985.1kN
m2 directions of the membrane surface. Following this principle, we can talk about the basic four
types of membranes: N
min N
N
N
46460.625kN
pl.Rd u.Rd t.Rd 1.t.Rd saddle-shaped (hyperbolic paraboloid)
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
"satisfactory" if Nsd34 Nt.Rd Verification 3. arch shape
2. Modular light constructions
"does not" otherwise 4. conical shape,
Nt.Rd min Npl.Rd Nu.Rd
Nt.Rd 61237.5kN
3. Sliding light constructions N
N
3
N 8.2 10 kN
sd sd12 sd12 Designers see the benefits of mass production of simple structures, such as an "umbrella" that
Verification "satisfactory"
has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
267
Assessment of the corner welding on the joint plate at the terminal side K1: Eccentricity:
Verification
e1 123mm 40deg
Diversion of forces:
fu if T Mw
"It is inappropriate, modify the design "
otherwise
Verification "Satisfactory"
3
Design force:
"Satisfactory"
Nsd12 8.2 10 kN
Decomposition of force into individual directions y and z: Assessment of corner welding on the joint plate at the terminal side K2 and K3: FHsd1 Nsd12 sin ( )
3
FVsd1 Nsd12 cos ( )
3
Fsd.3 2 10 kN 3
3
FHsd1 5.271 10 kN
Fsd.4 1.7 10 kN
FVsd1 6.282 10 kN
Partial reliability factor:
coefficient of strength class
Mw 1.5
Design strength of the weld in the shear: Effective welding height:
fvwRd
fu 3 w Mw
- eccentricity: w 0.9
design force
f vwRd 218.11MPa
kN
number of welds:
lu1 2300mm
Components of individual stresses:
M 1 FHsd1 e1
II
n
a lu1
FHsd4 1.202 10 kN
F Vsd4 Fsd.4 cos 1
FVsd4 1.202 10 kN
FHsd3 1.813 10 kN
FVsd3 845.237kN
F Hsd4 Fsd.4 sin 1
2
II 136.556MPa
lu1 a
F Hsd3 Fsd.3 sin 2
F Vsd3 Fsd.3 cos 2
M 1 648.316kNm
Partial reliability factor:
2
Wzvar 8.817L
3
3
3
Mw 1.5
Design strength of the weld in the shear:
FHsd1 1 M1 T lu1 a 2 2 W zvar 2
Fsd.3 2000 kN
Decomposition of force into individual directions y and z:
m
FVsd1
6
F sd.4 1700 kN
2
T 107.021MPa
T T
fu 377.778MPa w Mw
2
3 II 318.993MPa T 3 T
T 107.021MPa
Effective welding height:
"Satisfactory"
if
2
2
fu
T 3 T 3 II w Mw
"It is inappropriate, modify the design " Verification "Satisfactory"
2
coefficient of strength class:
fvwRd
Effective welding length:
fu
w 0.9
f vwRd 218.11MPa
3 w Mw
a 8mm
Design resistance of the unit length of the weld:
Comparative stress: Verification
2 65deg
Sabah Shawkat ©
Effective welding length:
1
1 45deg
a 10mm
Design resistance of the unit length of the weld: FvwRd fvwRd a FvwRd 2181.101
W zvar
- diversion of forces: e2 389mm
e1 352mm
lu1 1745mm
FvwRd fvwRd a
kN FvwRd 1744.881 m
number of welds:
n 2
FVsd4 FVsd3
II
n
lu1 a
II 73.328MPa
otherwise M 1 FHsd4 e1
Lightweight structures Lightweight structures
M 1 423.133kNm
M 2 FHsd3 e2
M 2 705.107kNm
268 248
Lightweight structures W zvar
1
a lu1
Detail of the stiffener connection to column on the bar
2
W zvar 4.06L
6 engineers are executives of services to reap the intellectual property of previous Architects and
Entry values:The clients' demands are high nowadays, there is a demand for temporary, constructions.
generations. They are studying, and discovering. They are the creators of new Fimproving FHsd3 M2 1 M1 Hsd4 T T 174.599MPa improving. spaces, forms structures are This creative activity connects a constantly lu1 a W zvar W zvarthat lu1 2 2 and architects and engineers on their way to the art of "Prof. Frei Otto.
Steel "s 355" 40mm transformable solutions that tcan offer sliding lightweight constructions ranging from simple
f
u variations can be seen in broad spectrum use Lightweight structures used in various forms and 340MPa 174.599MPa T
T
T
Mw on the current market. These structures, developed over the years, together with advances in
material engineering Comparative stress:and technology, continue to progress and are now an integral part of architectural creation.
f
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa fy 355 MPa
m0 1.2
International Stadium). Tensile integrity systems are being developed today for NASA and m1 1.2 fu 510 MPa form unprecedented options for blame. 5
E 2.1 10 MPa
m2 1.3
Talking about modern systems of steel, wire and membrane has its merit. And that these systems are at the top of the current building options. Limits are given by the physical properties m0 1.1 if Steel "s 235" and laws of the material and the construction system. These must be fully taken into account 1.15 if Steel
"s 275"
u 2 2 2 Architectural lightweight structures can now be seen in different 377.778MPa shapes and sizes. They may T 3 T 3 II 371.579MPa
and used in1.2 theif creation the modern system. In practice, we most often encounter the Steel "sof 355"
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
w Mw
or stretched. New these constructions - shell structures, tensile-integrity structures Components ofsubgroups individualof stresses - are also very current. These unique forms have played an important role in contemporary architecture, interior design and various cultural events since the time they first appeared in the
1.1 if Steel
m1
"s 235"
1.15 if Steel
"s 275" • bars (struts) systems - stable problems of compressive and bent bars, 1.2 if Steel
"s 355"
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order, 1.3 if Steel
m2
"s 235"
Sabah Shawkat ©
1960s by the world-famous German architect and engineerf Frei Otto. 2
2
2
u
"Satisfactory" if T 3 T 3 II At Verification present, light constructions are designed and constructed independently of the geographic w Mw
location. They transform the space and and elegant quality. In addition to "It is inappropriate, modify thehave designso " subtle otherwise
providing basic functions such as shading and shutdown, they are an important and functional Verification "Satisfactory"
element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors. fu Verification
"Satisfactory"
Designing lightweight
if T Mw constructions to meet
all criteria is a complex task. Every part is visible
is inappropriate, modify the design " otherwise and constructive, "It relying on the proper functioning of all parts. For example, diaphragm fabrics
areVerification developed to meet the requirements for high tensile strength, long life with a high modulus "Satisfactory" of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties. We think it important to explore new trends in lightweight constructions, among which we
"s 275" dynamic resistance, large deformation solutions. if Steel • membrane 1.3 systems - prestress, 1.3 if Steel
"s 355"
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well Design of steel plate: as experiment with form and create alternative solutions to every day design challenges. ThisDesign is made possible due to the fundamental flexibility and lightweight nature of composite force o stiffener: Nsd 1500.0kN membranes. Membrane structures are often referred to as textile structures. However, the actual d 398mm Stiffener: TR159/8 t 70mm membrane construction is far removed from the1 classic tent. The main difference is its exact geometric shape.t For the functioning of the membrane structure, the exact geometric criteria Plate depth: 2 20mm must be computed. The basic criterion is to maintain the concavity and convexity of the main N
A 3 2 sd directions of the membrane wehcan basic four h the 0.127m A 5.07this 10principle, mm talk about Plate height: A surface. Following t fy types of membranes: m0
can include:
1. saddle-shaped (hyperbolic paraboloid) Design of the welding attachment of the stiffener to the steel plate: 2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical 0.85 shape, if Steel
w
3. Sliding light constructions
0.8 if Steel
0.9 if Steel
"s 235"
has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
Mw 1.5
3mm if t max 10mm 4mm if 11mm t max 20mm
"s 355"
Designers see the benefits of mass production of simple structures, such as an "umbrella" that w 0.9
a
"s 275"
5mm if 21mm t max 30mm
6mm if t max 30mm
t max max t1 t 2
269
Effective welds height:
Nsd
a 6 mm
Stress due to force Nsd:
II
II
Nsd
Maximum permissible welding stress: Nsd w Mw 4 a L1
II
3
4 a l
w Mw
3
Nper
w Mw
W h
L1 286.55 mm
L1 otherwise
Welding evaluation by equalizing the stress: Nsd
Nkol a Ls
M
z W 3
sin ( )
Nper 176.052kN
per 0kPa
W d
per 0kPa
I z3
I z1
h
W h 1.759L
d
W d 12.98L
Nsd
NII
I
Nper a Ls
Nper a Ls
4
1 12
cos ( ) NII 331.105kN
a Ls
M
3 4
3
I 2.726 10
m
5
h 1.102 10 kPa
Wh
M
3
d 4.003 10 kPa
Wd
5
Sabah Shawkat © per h 0.707
f
fu 377.778MPa w Mw
2 2 2 II 218.11MPa per per
if
2 2 2 per II 114.538MPa per
4
per h 0.707
per 7.79 10 kPa
fu 377.778MPa w Mw
f
u 2 2 2 per II per w Mw
f
u 2 3 2 3 2 per II per w Mw
f
u 2 2 2 per II per w Mw
Assessment
Assesment "confirmes"
Design of the welding of the connecting plate to the column:
Ls 1760mm
u 2 2 2 per II per w Mw
if
u 2 2 2 per II per w Mw
Assessment "complies"
z1 210mm
z2 385mm
f
"complies" if
"does not"
3 Design force: Nsd 1.5 10 kN
a 6mm
4
per 7.79 10 kPa
Comparative stress:
fu 377.778MPa w Mw
"confirmes" if
"does not"
28deg
4
II 2.181 10 kPa
u 2 2 2 per II per w Mw
Assesment
Nsd
3
40mm if L1 40mm
4 a L1
M 164.446kNm M Nper z1 NII z2
( 6 a) if 40mm L1 6 a
II
4
II 3.135 10 kPa
fu
Nsd
L1 286.553mm
fu
cos ( ) a Ls
4 a l fu
L1
4
z3 1550mm
Lightweight structures Lightweight structures
f
248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight structures Lightweight Lightweightstructures structures
Sabah Shawkat © Membrane structures Table properties of membrane structures Force density method Mohr circle of stress
Lightweight structures
272 248
Lightweight structures Prospect for European Guidance for the Structural Design of Tensile Membrane Structures
Euro code
The following table is are not executives a standard but a projecttomaster document. Architects and engineers of services reap the intellectual property of previous
for temporary, constructions. The of clients' demands are high nowadays, demand Strength values PVC-coated polyester fabrics not directlythere linkedistoa the stress verification in the
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple ULS
spaces, formsofand structures thatwith arePVC constantly Typology polyester fabrics coatingimproving. This creative activity connects
sliding marquee solutions to staircases, which Type disappear by pressing the button (Khalifa I Type II Type III Type IV
architects andType engineers on their wayIto the art of "Prof. II Frei Otto.
Standard integrity Value warp/weft warp/weft International Stadium). Tensile systems are beingwarp/weft developed today for NASA and Parameter warp/weft
III
IV
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame. EN 1875-3 Tear
Weightmarket. in g/m2These structures, 750/9001developed1050 1050/12501 on the current over the years, together with 1350/18501 advances in
1) 170/170 280/280 450/450 750/750 Method B Strength 1100/1100 Talking about [N] modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of 3) and weft lightweight in (N/5cm)structures 2800/2800 Architectural can now be 4200/4000 seen in different5600/5600 shapes and sizes.8000/7000 They may
systems are at the top of the current building options. Limits are given by the physical properties EN ISO 2411 100 110 120 130 Adhesion1) 140 and laws of the material and the construction system. These must be fully taken into account [N/5cm] and 1)used in the creation of the modern system. In practice, we most often encounter the
(kN/m)permanent, temporary, 56/56 112/112 160/140 be internal,and external, large, 84/80 small, supported, membranes filled with air
following issues: 2)
Tensile strength architectural creation.in warp
Tear strength in warp of these constructions - shell structures, tensile-integrity structures or stretched. New subgroups 3) (N/5cm)These 300/280 800/650 1200/1100 - are and alsoweft veryincurrent. unique forms have550/500 played an important role in contemporary
(62°) 4)2)
This values are given as mean values.
Accompanying the Euro code development, a new biaxial test standard is currently under
development in CEN/TC 248/problems WG 4 which aims to substitute the method • bars (struts) systems - stable of compressive and bent bars, of EN 1875-3 in the future.
andinterior (kN/m)design and various 6/5,6 cultural events 11/10since the time 16/13 24/22 architecture, they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
elongation German 15/20 15/20 Frei Otto. 15/25 1960s Ultimate by the world-famous architect and engineer
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Euro code
Sabah Shawkat © 15/25
(%)constructions are designed and constructed independently of the geographic At present, light
Minimum of thethe space and have so subtle and elegant quality. In addition to location. They width transform
weldsfunctions (cm) 3 4 they are an important 4 4 providing basic such as shading and shutdown, and functional element the construction Lightinpassing at 500nm, of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.13 translucent white colour
9.5
8
5
2 Every part is visible Designing lightweight to2meet all criteria task. Reaction to fireconstructionsM2 M22is a complexM2 M22
and 1)constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics The two values indicate an order of magnitude. are developed to meet the requirements for high tensile strength, long life with a high modulus 2) Classification according to French standards NF P92-503 and NF P92-507. Class M2 of elasticity. The surface layer applied to the material ensures fabric resistance against corresponds to class Bs2, d0 in EN 13501-1. weathering and dirt, provides resistance to UV radiation and has non-combustible properties. 3) Strength values are given as mean values.
PES/PVC-fabrics
Strength values architecture of PVC-coated fabrics directlymedium linked tothat the stress in the ULS Tensile membrane is polyester a highly sophisticated offersverification unique qualities for Parameter Standard Valuetherefore Type I Type II opportunities Type III Type IV Type V architects, designers and engineers provides unlimited for design as well warp/weft warp/weft warp/weft warp/weft warp/weft as experiment with form and create alternative solutions to every day design challenges. Mean
2750/2750
4000/4000
5500/5000
7500/6500
Strength
EN ISO
value
55/55
80/80
110/100
150/130
185/160
[N/5cm]
1421
5%
2500/2500
3500/3500
5000/4500
6750/6000
8500/7250
[kN/m]
fractal
50/50
70/70
100/90
135/120
170/145
Seam
percentage
Tensile
membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact
geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main strength at
EN ISO
of the
directions surface. Following talk about the basic four1) 23°Cof the membrane 1421 respective ≥ 90%this principle, ≥ 90% we ≥can 90% ≥ 90% ≥ 80% types of membranes:
tensile
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid) strength
can include:
2. Seam ridge-valley shape percentage
1. Lightweight designs designed with regard to sustainability
strength EN ISO 3. arch atshape
of the
2. Modular light constructions
1421 4. 70°C conical shape,
respective
3. Sliding light constructions
≥ 70%
tensile
Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
9250/8000
This is made possible due to the fundamental flexibility and lightweight nature of composite
strength 1)
Higher values might be possible, but maybe not economical.
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
≥ 70%
≥ 70%
≥ 60%
≥ 55%
273
The material model has five parameters: Ε 1:1 w and Ε 1:1 f are the reference values of warp
PTFE-coated glass fibre fabrics (Glass/PTFE-fabrics)
and fill Young’s moduli given for the 1:1 load ratio, ΔΕw and ΔΕf represent the variation of warp and fill Young’s moduli on the whole range of load ratios, and the Poisson’s ratio νwf.
French recommendations
All five parameters are estimated so that the difference between experimental and modelled
The following table is not a standard but a project master document.
data is minimized.
Table 2: Typology of glass fabrics with PTFE coating Type
I 2
Weight in g/m
Tensile strength in warp and
II
III
IV
800
1050
1250
1500
3500/3000
5000/4400
6900/5900
7300/6500
weft 2) in (N/5cm) and (kN/m)
70/60
100/88
138/118
146/130
Tear strength in warp and weft
300/300
300/300
400/400
500/500
6/6
6/6
8/8
10/10
in (N/5cm) 2) and (kN/m) Ultimate elongation (%)
3-12
3-12
3-12
3-12
Light passing at 500nm,
12-18
12-18
10-16
10-16
translucent white colour
Sabah Shawkat ©
Reaction to fire
M21)
M21)
M21)
M21)
NOTE Packing has an important impact on the properties of the material. 1)
Classification according to French standards NF P92-503 and NF P92-507. Class M2 is
correspondent to class Bs2, d0 in EN 13501-1. 2)
Strength values are given as mean values.
Estimated parameters for the non-linear material model
Manufacturer and reference EW 1:1 Ef 1:1 EW Ef wf (polyester type) (kN/m) (kN/m) (kN/m) (kN/m) (kN/m) Mehler Texnologies Valmex 653.2 444.5 521.2 403.7 0.327 FR700(I) Mehler Texnologies Valmex 882.0 679.6 803.8 437.6 0.263 FR900(II) Mehler Texnologies Valmex 1200.0 881.7 941.2 782.5 0.318 FR1000(III) Mehler Texnologies Valmex 1374.1 1003.4 1204.7 981.7 0.314 FR1400(IV) Ferrari Precontrant 702 (I) 635.3 661.9 295.0 168.5 0.196 Ferrari Precontrant 1002 (II) 830.2 976.0 766.7 123.9 0.213 Ferrari Precontrant B1617 (II) 865.8 707.5 662.9 662.5 0.308 An almost linear relationship was experimentally found between elastic moduli Ef and Ew (subscripts w and f represent the warp and fill directions)
Lightweight structures Lightweight structures
274 248
Lightweight structures Membranes
Geometric shape of the membrane
Architects andstructures engineersare areoften executives of to services to reap the intellectual property of previous Membrane referred as textile structures. However, the actual membrane generations. They areremoved studying, improving andtent. discovering. are the creators new construction is far from the classic The mainThey difference is its exact of geometric spaces, andfunctioning structures that aremembrane constantlystructure, improving. activity connects shape.forms For the of the theThis exactcreative geometric criteria must be architects andThe engineers on their way to the art the of "Prof. Frei and Otto.convexity of the main directions computed. basic criterion is to maintain concavity of the membrane surface. this principle, we can aboutinthe basic four types Lightweight structures used inFollowing various forms and variations cantalk be seen broad spectrum use of membranes: on the current market. These structures, developed over the years, together with advances in
temporary, constructions. The clients' are high system nowadays, therefrom is athe demand The basic geometric shapedemands of the membrane emerges surfacefor of the hyperbolic transformable solutions that can offer sliding lightweight constructions ranging from simple paraboloid. We can describe this area by mathematics: sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa 2
2
2
2
x Stadium). y International Tensile integrity systems are being developed today for NASA and z( xy ) a b options for blame. form unprecedented For an area with parallel curvature margins and a rectangular plan, we can define the following Talking about of modern systems andmarginal membrane has its merit. Andresult that these dimensions the areas Lx, Ly,offx,steel, and fywire . Under conditions: then they
material engineering and technology, continue to progress and are now an integral part of • saddle-shaped (hyperbolic paraboloid) architectural creation. • conical shape, Architectural lightweight structures can now be seen in different shapes and sizes. They may
systems are at the top of the current building options. Limits are given by the physical properties
Wave shape, be •internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues: then coefficients result
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures • vault shape. - are also very current. These unique forms have played an important role in contemporary Another criterion lightweight membrane its time prestress. The appeared correct geometric architecture, interior of design and various culturalconstruction events sinceisthe they first in the
Lx
formaterial xand the fx of the y construction 0 and zlaws system. These must be fully taken into account 2
and used in the creation ofLzthe modern system. In practice, we most often encounter the z
for
fx
y
2
x
0
• bars (struts) systems - stable problems of compressive and bent bars, •
2
a cables
2
Lx
systems 4 f x
2
b prestress,
Ly
2
stiffness of the structure, necessity of solving the theory II. order,
4 fy
Sabah Shawkat ©
shape guarantees its architect stability, and stiffness and dynamic 1960s byand the prestress world-famous German engineer Frei Otto.resistance. At the same time, it allows the structure to resist the effects on which it was rain, wind snow. At present, light constructions are designed and constructeddesigned, independently of theand geographic location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
4 f
4 f
x 2 ylarge 2 • membrane systems - prestress, dynamic z( xy ) resistance, x y deformation solutions. after fitting we get: 2
Lx
Ly
2
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for Let's take a look at the length coordinates that will then:
architects, designers and engineers therefore provides unlimited opportunities for design as well x
y
Lx
Ly
create alternative solutions to every day design challenges. as experiment with form and
This is made possible due to the2 fundamental flexibility and lightweight nature of composite 2 membranes. Membrane structures are often referred to as textile structures. However, the actual 2 2 After simplifying the expression we get:
z( )
fx fy
membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
275
Membrane Material Assessment
membrane in tension is 2,300-4,500 N / 5 cm. If glass fibres are used as the support material,
Modern membrane systems are manufactured from different types of textile membranes. These
the tensile strength of such a membrane will be 3,500-7,500 N / 5 cm.
are produced as composite materials and almost always consist of a bearing woven core and a surface film. The supporting core has a bearing function and therefore transfers the force to the membrane. The surface film has a protective function, ensuring waterproofness and tightness of the membrane.
General area of hyperbolic paraboloid
Sabah Shawkat © ETFE (Ethylene Tetrafluoroethylene)
ETFE is a fluorocarbon - a basic polymer (fluoropolymer) type of plastic. It has been designed as a material with high corrosion resistance and resistance over a wide range of temperatures. It was used for example for the pneumatic panels of the "Allianz Arena" football stadium, or for the "National Water Sports Centre" - the world's largest construction made of ETFE membrane. Also on panels of "Tropical Island" 20 000 m2 in Germany. Because ETFE has excellent mechanical stiffness and chemical resistance with which it can compete with polytetrafluoroethylene (PTFE). In addition, ETFE has high energy radiation resistance and can withstand moderately high temperatures for a long period of time. The strength of the ETFE
Textile membranes used in construction can be divided into several groups according to the
membrane in tension is about 1200 N / 5 cm and ETFE foil 430-500 N / 5 cm.
chemical composition: PVC (Polyvinylchloride) PTFE (Polytetrafluoroethylene)
Teflon is a synthetic fluoropolymer, has a very wide application in industry and construction. It has a high resistance to chemicals and an extremely low friction coefficient. The most famous PTFE membrane material is Gore-Tex. The largest PTFE construction can be termed the "Hubert H. Humphrey Metrodom" roof in Mineapolis with an area of approximately 80,000 m2 where a double-layered membrane with a glass fibre construction is used. Strength of the PTFE
PVC is less rigid and more deformable but also more resistant to mechanical deformations. It has a lower lifetime compared to PTFE material. The carrier material of these membranes is polyester or aramid fibre. The advantage is the lowest price of all materials used and lower flammability. Strength of PVC membrane in tension in combination with polyester carrier fibre is 3,000-9,800 N / 5 cm and aramid carrier fibre 7,000-24,500 N / 5 cm.
Lightweight structures Lightweight structures
276 248
Silicone Lightweight structures silicone is a very progressive material, used in combination with a glass fibre construction. It Architects and engineers are executives of services to reap the intellectual property of previous has a high service life of over 30 years, a third of the PTFE material and, as with the only generations. They are studying, improving and discovering. They are the creators of new material used, its smoke is not toxic. Silicone is mainly used in combination with glass fibre spaces, forms and structures that are constantly improving. This creative activity connects and the tensile strength of such a membrane is 3,500-6,000 N / 5 cm. architects and engineers on their way to the art of "Prof. Frei Otto. Lightweight structures used in various forms and variations can be seen in broad spectrum use Models forThese Modelling Membranes on Material the current market. structures, developed over the years, together with advances in material engineering andpatterns technology, to are progress and are nowmaterial an integral part ofand The material or work of the continue membranes the transfer of real behaviour architectural creation. the approximate view of their modelling. Due to the width of the range of materials used and Architectural lightweight structures can are nowmodelled be seen differ. in different shapes and maythe their design, the ways in which they The simplest waysizes. is to They interpret be membrane internal, external, permanent, temporary, large, small, supported, membranes filled with air material as isotropic material, with a constant modulus of elasticity and a Poison or stretched. New interpellation subgroups of these constructions shell structures, tensile-integrity constant. This has its significant -drawbacks mainly with regard tostructures the texture - are also very current. These unique forms have played an important role in contemporary structure. A more accurate model can be considered an anisotropic orthogonal - orthotropic architecture, interiorBy design events the time first appeared material model. this and we various are ablecultural to capture thesince distance of they material propertiesininthetwo
Advantages of a Tensile Fabric Building Structure (Pros and Cons of tensile Structures) 1. The installation tension membrane structures isthere oftenisfaster and more for cost-effective temporary, constructions. The clients'ofdemands are high nowadays, a demand in comparison to traditional structures. The other factor that clearly puts fabricsimple ahead of transformable solutions that can offer sliding lightweight constructions ranging from
other materials its staircases, clear span which capabilities, Sincebythepressing fabric has amazing tensile sliding marquee solutionsis to disappear thethis button (Khalifa capacity, the effect is to reduce the supporting framework to a minimum number International Stadium). Tensile integrity systems are being developed today for NASA and of supports, all working as a whole system. form unprecedented options for efficiently blame.
Talking about modern systems of steel, wire and membrane has its merit. And that these 2. Due to the translucency tensile fabric building structures provide an abundance of systems are at the top of the current building options. Limits are given by the physical properties daytime light underneath, making it an inviting and comfortable space below. The and laws of the material and the construction system. These must be fully taken into account unique properties of light reflectance and transmission also offer exciting possibilities and used in the creation of the modern system. In practice, we most often encounter the for lighting after dark. following issues: • bars (struts) systems - stable problems of compressive and bent bars, 3. Due to the unique flexible properties of the fabric membrane, tensile membrane • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order, structures offer architects, designers and engineers an a wide opportunity to investigate • membrane systems prestress, dynamicelegant resistance, deformation solutions. with shape -and create visually and large cone-shaped structures.
Sabah Shawkat ©
1960s by the world-famous perpendicular directions. German architect and engineer Frei Otto. At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
Hyper-elastic Materialsuch Model providing basic functions as shading and shutdown, they are an important and functional
element in the construction of amphitheatres, sports stadiums, airports, courtyards, building Hyper-elasticity is a phenomenon when the body returns to its original state after deformation. facades, parks, seafront and interiors. The dependence between tension and relative transformation can be described by a non-linear Designing lightweight constructions to meet all criteria is a complex task. Every part is visible curve. Both the load and the relief run along the same curve. Constitutive models for such and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics materials are derived from the deformation energy potential, based on the assumption of are developed to meet the requirements for high tensile strength, long life with a high modulus isotropic deformation. It is also necessary to consider that the hyper-elastic materials are almost of elasticity. The surface layer applied to the material ensures fabric resistance against incompressible thus their Poisson constant = 0.5. A typical example of hyper-elastic material weathering and dirt, provides resistance to UV radiation and has non-combustible properties. is rubber. It is also possible to model almost all carbon polymers, glass fibres and, last but not
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for 4. Tensile structures have demonstrated low maintenance projects architects, designersmembrane and engineers therefore provides unlimitedasopportunities for design as wellfor investors, but ifand properly and installed are virtually immune to damage and as experiment with form create engineered alternative solutions to every day design challenges. weathering. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual 5. Due to uniqueiscombination design properties, structure, and is environment, membrane construction far removedoffrom thematerials classic tent. The main difference its exact longevity andfunctioning durability of membrane structures beengeometric proven to criteria withstand geometric the shape. For the oftensile the membrane structure, thehas exact harsh and extreme climates and environments. must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
Weleast, thinkbiomaterials it important (blood to explore new trends in lightweight among which we vessels, muscles). The most constructions, commonly used constitutive material
1. saddle-shaped (hyperbolic paraboloid)
canmodels include: are:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability • Neo-Hook model, 2. Modular light constructions • Mooney-Rivlin model, 3. Sliding light constructions
3. arch shape 4. conical shape,
• Ogden's Designers seemodel. the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
277
Sabah Shawkat ©
Lightweight structures Lightweight structures
278 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
279
Sabah Shawkat ©
Lightweight structures Lightweight structures
280 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
281
Sabah Shawkat ©
Lightweight structures Lightweight structures
282 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweight Lightweightstructures structures Lightweight Lightweightstructures structures
283
1. Iteration step
Force density method- updated reference strategy Determine iteratively the equilibrium position (xp, yp) of the point p using the Force Density Method, as initial trial position for the iteration and do 3 iteration steps. xk 7m
Evaluation the force density for each element (cable) Si
h
qi
yk 3m
li
li
h
2
x h x y h y i i k k
h
2
l i
xk xi 2 yk yi 2
2. Draw a convergence diagram for: -The xp coordinate
S´i
q i
-The yp coordinate
qi
li
0.596
Horizontal axis: iteration steps, vertical axis: respective entity
i 1 2
x1 5m
xi
Boundarie
0.606
-The resulting cable forces
x2 10m
yi
y1 5m
y2 3m
li
kN
8.246
Note that the quantities xp, yp, l1, l2 refer to the still unknown equilibrium configuration. The coordinates xp and yp are the independent variables (unknowns). Solve the equations granting the equilibrium in both vertical and horizontal directions
Sabah Shawkat © 5
m
10
Cable force:
5
m
Equilibrium conditions:
3
xk
cos i
S´1 5kN
S´2 4kN
S´i 5 4
kN
li
y h y i k
h
sin i
h
cos i
li
-0.97
1.043
-0.894
Sicos i qi xk
h
h
i
Ry
Sisin i qi yk
Rxi
h
h
yk 3 m
-0.576
h
sin i
xi
h
yi
Ryi
i
-0.576
li
i
qi xk xi
Rxi
xk
i
i
Initial trial point:
cos i
h
sin i
0.849
Rx
xk 7 m
m
6.708
m
kN
Ryi -8.428 -8.428
Lightweight structures Lightweight structures
qi yk yi i
kN
yk yi li
284 248
Iterate steps 1. And 2. until convergence Lightweight structures
Evaluation of the new force densities:
Architects and engineers executives of services to reap the intellectual Equilibrium conditionsare using the assumption of constant force densities:property of previous generations. They are studying, improving and discovering. They are the creators of new K xp yp xk 7 m spaces, forms and structures that are constantly improving. This creative activity connects
architects and engineers on their way to the art of "Prof. Frei Otto.
Given structures used in various forms and variations can be seen in broad spectrum use Lightweight
xk x1market. q 2 These xk xstructures, 0 xk Find xk years, together q 1 current on the developed over the with xk 7.479 m advances in 2 material engineering and technology, continue to progress and are now an integral part of Rx q1 xk x1 q2 xk x2 yk 3 m architectural creation. Given Architectural lightweight structures can now be seen in different shapes and sizes. They may q 1 yk y1 q 2 yk y2 0 yk Find yk yk 4.008m be internal, external, permanent, temporary, large, small, supported, membranes filled with air
or stretched. New subgroups of these 2 2 constructions - shell structures, tensile-integrity structures xk xi yk yi l i - are also very current. These unique forms have played an important role in contemporary li qi architecture, interior design and various cultural events since the time they first appeared in the 2.67 m kN 0.606 1960s by the world-famous German 2.715architect and engineer Frei Otto. m 0.596 At present, light constructions are designed and constructed independently of the geographic
constructions. S´i The clients' demands are high nowadays, there is a demand for temporary, q i qi transformable l i solutions that can offer sliding lightweight constructions ranging from simple kN sliding marquee solutions to staircases, 1.873 which disappear by pressing the button (Khalifa m 1.473 International Stadium). Tensile integrity systems are being developed today for NASA and form unprecedented options for blame. xk yk yi cos i sin i cos i sin i Talking about l imodern systems of steel, l i wire and membrane has its merit. And that these
2.801
-0.371
2.755
0.371
systems are at the top of the current building options. Limits are given by the physical properties and laws of the material and the construction system. These must be fully taken into account andEquilibrium used in theconditions: creation of the modern system. In practice, we most often encounter the following issues: xk 7.479m • bars (struts) systems - stable problems of compressive and bent bars, Given
Rx q1systems xk x1- prestress, q2 xkdynamic x2 resistance, ylarge m • membrane deformation solutions. k 4.008
q 1 systems xk x1 -prestress, q 2 xk stiffness x2 0 of the structure,xk Findofxksolving thexktheory • cables necessity II.m order, 7.202
Sabah Shawkat ©
location. They transform the space and have so subtle and elegant quality. In addition to Actual cable forces Si q i l i Si providing basic functions such as shading and shutdown, 1.619·103they N are an important and functional 3 1.619·10 element in the construction of amphitheatres, sports stadiums, airports, courtyards, building
facades, parks, seafront and interiors. 2. Iteration step Designing lightweight constructions to meet all criteria is a complex task. Every part is visible andUpdate constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics of reference configuration: are developed to meet the requirements for high tensile strength, long life with a high modulus The deformed configuration of the last step is now the reference configuration. of elasticity. The surface layer applied to the material ensures fabric resistance against xk 7.479 m has non-combustible properties. weathering andmdirt, provides resistance to UVyradiation k 4.008and
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2.715
1. Lightweight designs designed with regard to sustainability 2. Modular light constructions
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3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
285
Determine iteratively the equilibrium position (xp, yp) of the point p using the Force Density
xp 4 yp 2
x1 2m
x2 6 m
x3 4 m
y1 2m
y2 4 m
y3 7 m
2. Draw a convergence diagram for:
A ( 2 2)
xi 2
yi
m
2
x3 y3
6
4
4
7
S´2 6kN
S´3 5kN
S´i
kN
5
Initial trial point:
P xp yp
A ( 4 2)
xp 4m
yp 2 m
l i
h
yp yi li
xi
h
i
Sisin i qi yp
h
h
h
yi
i
q i xp xi
Ryi
Rxi
qi yp yi i
Ryi
-0.243
kN
sin i
cos i
kN
-9.243
li
h
xp xi 2 yp yi 2
2
q i
S´i li
h
2
(h
1.414
-0.707
-0.243
-9.243
0.8
-1
Given
2 2.121 1
kN m
0 q1 xp x1 q2 xp x2 q3 xp x3
2
xp 4.047m
yp 3.805m
xp Find xp
Rx
yp 2 m
m
xp 4 m
q 1 xp x1 q 2 xp x2 q 3 xp x3
xp xi 2 yp yi 2
iteration)step
li
P xp yp
0
2
kN m
qi 2.121
yp Find yp
1
qi
0
-9.243
l i
x x y y i i p p h
2
-0.243
q 1 yp y1 q 2 yp y2 q 3 yp y3
Define the force density for each element (cable)
li
h
Given
1. Iteration step
h
Sicos i qi xp
3. Iterate steps 1. And 2. until convergence:
6
qi
-1
C ( 4 7)
4
Si
0.8
i
m
sin i
li
Sabah Shawkat ©
B( 6 4)
Cable force: S´1 4kN
h
0 -0.707
Rxi
x1 y1
xp
cos i
h
sin i
i
respective entity
X1 1
li
1.414
Ry
Horizontal axis: iteration steps, vertical axis:
h
i
The resulting cable forces
sin i
2
Rx
-The xp coordinate -The yp coordinate -
x2 y2
li
y h y i p
h
cos i
i 1 3
Boundaries:
xp
cos i
Method, as initial trial position for the iteration and do 5 iteration steps.
Si q i l i
2.828
Si 5.459·103 4.163·103
5
3.196·103
Solve the equations granting the equilibrium in both vertical and horizontal directions
Lightweight structures Lightweight structures
N
li 2.729 1.962 3.196
m
286 248
2. Iterationstructures step Lightweight
3. Iteration step
2
2
Architects andm engineers executives of lservices reap the intellectual property xp 4.047 yp are 3.805 m l i of previous xto i p xi yp yi 2.729 m of new generations. They are studying, improving and discovering. They are the creators 1.962
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3.196
2.76
S´istructures used in various forms and variations can be seen in broad spectrum use Lightweight q i qi l i market. These structures, developed over the years, together with advances in on the current kN 1.466 material engineering and3.058 technology, m continue to progress and are now an integral part of
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1.565
Architectural lightweight structures can now be seen in different shapes and sizes. They may Solve the equations granting the equilibrium in both vertical and horizontal directions be internal, external, permanent, temporary, large, small, supported, membranes filled with air xp subgroups of these yp constructions yi or stretched. New - shell structures, tensile-integrity structures cos i sin i cos i sin i l l i forms have played an important role in contemporary - are also very i current. These unique 1.483 0.661
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1.328
0.672
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1.639
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• membrane systems - prestress, dynamic resistance, large deformation solutions.
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Given
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yp 3.805m
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2.76
1. Lightweight designs designed with regard to sustainability Si l i q i Si 2. Modular light constructions 3. Sliding light constructions
4.993·103
1.565
architects, Given designers and engineers therefore provides unlimited opportunities for design as well
This is made possible due to the fundamental flexibility and lightweight nature of composite
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1.811
3. arch shape 4. conical l i q i shape, Si
N
Si
4.602·103
4.368·103
4.319·103
5.073·103
Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
4.857·103
N
287
4. Iteration step xp 4.807m
yp 4.443m
xp xi 2 yp yi 2
l i
5. Iteration step
li 3.721
m
1.273
xp 4.951m
yp 4.45m
xp xi 2 yp yi 2
l i
2.682
q i
qi
li
1.075 4.715
kN m
S´i
q i
qi
li
xp li
xp 4.807m
5.257
sin i
yp yi
cos i
li
kN m
1.837
Solve the equations granting the equilibrium in both vertical and horizontal directions
sin i
1.292
0.656
3.777
0.348
1.792
-0.954
cos i
xp
sin i
li
yp yi
cos i
li
sin i
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0.639
4.338
0.394
1.819
-0.937
xp 4.951m
0 q1 xp x1 q2 xp x2 q3 xp x3
q 1 xp x1 q 2 xp x2 q 3 xp x3
xp Find xp
Rx
yp 4.443m
xp 4.951m
Given
0 q1 xp x1 q2 xp x2 q3 xp x3
q 1 yp y1 q 2 yp y2 q 3 yp y3
xp xi 2 yp yi 2
li 3.835
0
qi
m
1.075
1.141
4.715
2.722
Si l i q i
Si 4.123·103
yp Find yp
yp 4.45m
q 1 xp x1 q 2 xp x2 q 3 xp x3
xp Find xp
Rx
yp 4.45m
Given
Given
l i
1.043
Solve the equations granting the equilibrium in both vertical and horizontal directions
m
1.141
1.865
Given
3.835 2.722
S´i
cos i
li
q 1 yp y1 q 2 yp y2 q 3 yp y3
l i
xp xi 2 yp yi 2
kN m
li 3.883
0
qi
m
1.043
1.052
5.257
2.779
1.865
Si l i q i
Si 4.05·103
N
5.531·103
5.381·103
5.106·103
5.075·103
Lightweight structures Lightweight structures
yp Find yp
1.837
N
kN m
xp 5.036m
yp 4.421m
288 248
6. Iterationstructures step Lightweight
Determine iteratively the equilibrium position (xp, yp) of the point p using the Force Density
2
2
Architects andm engineers executives of previous xp 5.036 yp are 4.421 m lproperty lof xp toxreap ypintellectual yi i services i the i 3.883 m generations. They are studying, improving and discovering. They are the creators of new 1.052
spaces, forms and structures that are constantly improving. This creative activity connects 2.779
architects and engineers on their way to the art of "Prof. Frei Otto.
S´istructures used in various forms and variations can be seen in broad spectrum use Lightweight q i qi l i market. These structures, developed over the years, together with advances in on the current kN 1.03 material engineering and technology, continue to progress and are now an integral part of m 5.703
architectural creation. 1.799 Architectural lightweight structures can now be seen in different shapes and sizes. They may Solve the equations granting the equilibrium in both vertical and horizontal directions be internal, external, permanent, temporary, large, small, supported, membranes filled with air or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures ypforms yi have played an important role in contemporary - are also veryxpcurrent. These unique cos i sin i cos i sin i li i architecture, interior design and variouslcultural events since the time they0.624 first appeared in the 1.297
Method, as initial trial position for the and do 5 there iteration constructions. The clients' demands are iteration high nowadays, is asteps. demand for temporary, transformable that can offer sliding lightweight constructions ranging from simple xp 4 ypsolutions 4 sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa 2. Draw a convergence diagram for: International Stadium). Tensile integrity systems are being developed today for NASA and -The xp coordinate -The yp coordinate form unprecedented options for blame. -The resulting cable forces Talking about axis: modern systems of vertical steel, wire Horizontal iteration steps, axis:and membrane has its merit. And that these systems are at the top of the current building options. Limits are given by the physical properties respective entity and laws x1 and 2the m construction x2 5msystem. These must be fully taken into account i of 1 the 5 material and used in the creation of the modern system. In practice, we most often encounter the x3 5m x4 3 m x5 2 m following issues: y1 2m y2 2m y3 8m • barsy(struts) systemsy- stable 11m 8mproblems of compressive and bent bars, 4
5
Boundaries: x1 yof ( 2 2) necessity of solving the theory II. order, • cables systems - prestress, structure, X1 1 stiffness 1 the A
Sabah Shawkat ©
4.786 Frei Otto. 1960s by the world-famous German architect and engineer 1.812
0.4
-0.928
At present, light constructions are designed and constructed independently of the geographic
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5.703
2.829
1.799
1. Lightweight designs designed with regard to sustainability Si l i light q i constructions Si 2. Modular 4.029·103 N 3. Sliding light constructions 3
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11
2
8
as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite
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2
1. saddle-shaped (hyperbolic paraboloid) S´i 2. ridge-valley shape 3 kN
3
4
3. arch shape 5
4 4. conical shape, 5
5.621·10
6
3
Designers see the benefits of mass production5.09·10 of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Initial trial point:
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
P xp yp
A (4 4)
xp 4 m
yp 4 m
5
289
1. Iteration step Define the force density for each element (cable) Si
h
qi
li
li
h
2
x h x y h y i i p p
h
xp xi 2 yp yi 2
l i
S´i
q i
1.061
kN m
0.97
2.828
m
2.236
xp
cos i
li
cos i
0.97
0
xp 3.635m
yp 4 m Given
yp yi
yp 5.204m l i
q 1 yp y1 q 2 yp y2 q 3 yp y3 q 4 yp y q 5 yp y5 4
yp Find yp
xp xi 2 yp yi 2
0
qi 1.061
li
2.236
kN m
Sabah Shawkat © 1.342
S cos h i i
i
q h x h x i i p
Sisin i qi yp
h
i
h
yi
q i xp xi
Ryi
i
-7.603
qi yp yi
7.787
3.112
3.019
5.831
4.123
3.239
4.346
h
qi
cos i
sin i
1.414
0.707
2.305
-7.603
1.789
0.894
2.305
-7.603
0.97
-0.97
2.305
-7.603
0.566
-0.99
2.305
-7.603
0.894
-0.894
Iterate steps 1. And 2. until convergence
3.815
kN
2. Iteration step Define the force density for each element (cable)
i
kN
Si
3.483
i
Ryi
m
3.597
i
h
Si q i l i
li
-0.894
kN
0.97
-0.99
2.305
0.707
-0.97
0.894
Rxi
0.894
0.566
Rxi
li
0.707
1.789
Ry
li
h
sin i
sin i
1.414
Rx
sin i
h
cos i
q1 xp x1 q2 xp x2 q3 xp x3 q 4 yp x4 q 5 yp x5
Rx
4.123
Solve the equations granting the equilibrium in both vertical and horizontal directions xp
xp Find xp
li
4.472
1.342
q 1 xp x1 q 2 xp x2 q 3 xp x3 q 4 xp x4 q 5 xp x5
7.071
0.707
y h y i p
xp 4 m
h = iteration step
2.236
h
Given
2
qi
li
P xp yp
q i
Si li
h
S´i li
li
2
x h x y h y i i p p
h
qi 0.834 1.436
kN m
1.286 0.858 1.852
Lightweight structures Lightweight structures
2
li 3.597 3.483 3.112 5.831 3.239
l i
m
xp xi 2 yp yi 2
290 248
Solve the equations Lightweight structures granting the equilibrium in both vertical and horizontal directions Architects and engineers are executives the intellectual property of previous h y h y of services to reap xp yp yi xp p i cos i are the creators of new generations. improving and idiscovering.sinThey cos i They aresinstudying, i h h li li spaces, formsliand structures thatli are constantly improving. This creative activity connects
h S"Prof. h h cos i and engineers sinon architects tox the art of i their way R i Otto. qi xp xi icos Frei 1.011
0.891
i
i
Lightweight in various forms and variations can be seen in broad spectrum use 1.044 structures used 0.92
2
2
q i high nowadays, l i xp The xi clients' yp demands yi l i there is a demand for temporary, constructions. are kN 4.475 m 0.834lightweight transformable solutions that can offer sliding constructions ranging from simple 4.515 m 1.436 sliding marquee solutions to staircases, which disappear2.354 by pressing the button (Khalifa 1.286
4.783 International Stadium). Tensile integrity systems are being developed today for NASA and 0.858 2.276 form unprecedented options for blame. 1.852
0.623 -0.994 material engineering and technology, continue to progress and are now an integral part of
q i l i modernSsystems Si about Talking of steel, wire and membrane has its merit. And that these i 3.732 kN systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
-0.899 structures, developed over the years, together with advances in on the 1.168 current market. These 1.122
-0.863
6.482 3.026
h beseen in different shapes and sizes. They may Architectural lightweight S sin h structures q hcan now Ry i i i yp yi be internal, iexternal, permanent, temporary, large, small, supported, membranes filled with air i
and used in the creation 4.102 of the modern system. In practice, we most often encounter the
or stretched. tensile-integrity structures Rxi New Ryi yp structures, yi qsubgroups q- ishell i xp xi of these constructions - are also very played an important role in contemporary i current. These unique forms have i Rxi interior design the time they firstsin i in the Ryand cos isince i various cultural events architecture, appeared 1.222 kN -6.472 kN 1.011 0.891 1960s by the world-famous German architect and engineer Frei Otto.
3. Iteration step Define theproblems force density for each element (cable): • bars (struts) systems - stable of compressive and bent bars,
following issues:
4.217
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
1.222
-6.472
1.044
0.92
At present, are designed and constructed independently of the-0.899 geographic 1.222 light constructions -6.472 1.168 1.222 location. They 1.222
transform
the-6.472 space -6.472
and have so
0.623 and subtle 1.122
elegant quality.
In-0.994 addition -0.863
to
providing basic functions such as shading and shutdown, they are an important and functional
element in the construction of amphitheatres, airports, courtyards, building 3. Iterate steps 1. And 2. until convergence sports P xpstadiums, yp xp 3.635 m facades, parks, seafront and interiors. Given
Designing all criteria is a complex task. Every part is visible q 1 xp lightweight x1 q 2 constructions xp x2 q 3to xmeet 0 p x3 q 4 xp x4 q 5 xp x5 and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics xp Findtoxpmeet the xphigh 3.44 m strength, long life with a high modulus l i requirements are developed for tensile
3.597 m of elasticity. The surface layer applied to the material ensures fabric resistance against 3.483
weathering and dirt, provides resistance to UV radiation and has non-combustible properties. 3.112 5.831
We think it important to explore 3.239 new trends in lightweight constructions, among which we can include: Rx q1 xp x1 q2 xp x2 q3 xp x3 q 4 yp x4 q 5 yp x5 1. Lightweight designs designed with regard to sustainability yp 5.204m 2. Modular light constructions
3. Sliding Given light constructions q 1 yp y1 q 2 yp y2 q 3 yp y3 q 4 yp y q 5 yp y5 0 4 Designers see the benefits of mass production of simple structures, such as an "umbrella" that
Sisystems -h prestress,hdynamic 2 2 • membrane solutions. h 2 2 x x resistance, y h y large deformation li qi l i xp xi yp yi i i p p h li Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for
architects, designers and engineers therefore provides unlimited opportunities for design as well S´i q i q i and create alternative l i solutions to every day design challenges. as experiment with form li kN 4.475 m This is made possible due fundamental flexibility and lightweight nature of composite 0.67to the 4.515 m membranes. Membrane1.107 structures are often referred to as textile structures. However, the actual 2.354 1.699
4.783 membrane construction is far removed from the classic tent. The main difference is its exact 1.045
geometric shape. For the functioning of the2.276 membrane structure, the exact geometric criteria 2.636 must be computed. The basic criterion is to maintain the concavity and convexity of the main Solve the equations granting the equilibrium in both vertical and horizontal directions directions of the membrane surface. Following this principle, we can talk about the basic four h types of membranes: y h y xp xp i p cos i cos sin 1. saddle-shaped (hyperbolic paraboloid) i i h h li li li 2. ridge-valley shape Rxi sin i cos i q i xp xi 3. arch shape 0.769
0.947
1.461
-0.749
0.719
-0.996
1.511
-0.775
4. 0.762 conical shape, 0.938
has yreproducible Savings from a modular strategy lead to cost-effective yp 6.237 m p Find yp components.
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
i
sin i Ryi
yp yi li
q i yp yi i
291
Rxi
Ryi
kN
0.842
-5.089
sin i
cos i
kN
0.769
0.842
-5.089
0.762
0.938
0.842
-5.089
1.461
-0.749
0.842
-5.089
0.719
-0.996
0.842
-5.089
1.511
-0.775
3. Iterate steps 1. And 2. until convergence
P xp yp
4. Iteration step Define the force density for each element (cable):
0.947
Si
h
qi
li
h
q i
xp 3.44m
li S´i
2
x h x y h y i i p p
h
qi
li
0.586 0.957
Given
li
kN m
5.225 1.98
xp Find xp
li 4.475
1.69
3.551
xp 3.322m
m
4.065
1.23
0
xp xi 2 yp yi 2
l i
m
5.122
2.02
q 1 xp x1 q 2 xp x2 q 3 xp x3 q 4 xp x4 q 5 xp x5
2
Solve the equations granting the equilibrium in both vertical and horizontal directions
4.515 2.354 4.783 2.276
cos i
li
h
cos i
yp 6.237m Given
q 1 yp y1 q 2 yp y2 q 3 yp y3 q 4 yp y q 5 yp y5 4
yp Find yp
l i
0
sin i
qi 0.67 1.107 1.699 1.045 2.636
Si 3.433
kN
kN m
li
li
cos i
h
Rxi
sin i
0.649
0.966
0.636
0.947
1.678
-0.531
0.817
-0.997
1.966
-0.623
Rxi
yp 6.948m
xp xi 2 yp yi 2
Si q i l i
y h y i p
h
xp
yp yi
sin i
li
li
Sabah Shawkat ©
q1 xp x1 q2 xp x2 q3 xp x3 q 4 yp x4 q 5 yp x5
Rx
xp
0.872
-3.212
kN
i
0.649
-3.212
0.636
0.872
-3.212
1.678
5.225
0.872
-3.212
0.817
1.98
0.872
-3.212
1.966
m
qi yp yi
cos i
0.872
5.122
Ryi
i
Ryi
kN
qi xp xi
4.065 1.69
3. Iterate steps 1. And 2. until convergence: P xp yp
xp 3.322m
Given
5.786 3.365 4.249
q 1 xp x1 q 2 xp x2 q 3 xp x3 q 4 xp x4 q 5 xp x5
4.454
Lightweight structures Lightweight structures
0
292 248
Lightweight structures xp Find xp
xp 3.218m m Architects and engineers are executives of services to reap the intellectual property of previous
li
5.122 5.225
cos i
Rxi
sin i
0.588 constructions. 0.572
The
0.975 clients' 0.948
qi xp xi
Ryi
q i yp yi
i for temporary, demands arei high nowadays, there is a demand
generations. They are studying,1.98 improving and discovering. They are the creators of new 4.065 spaces, forms and structures that are constantly improving. This creative activity connects
transformable solutions that can offer sliding lightweight constructions ranging from simple
architects and engineers on their way to the art of "Prof. Frei Otto.
2.317 Stadium). -0.48 International Tensile integrity systems are being developed today for NASA and
1.69
Rx q1 structures xp x1 used q2in xvarious q3 and xp variations x3 q 4can x4 inqbroad x5 use 5 yp p x2 forms Lightweight spectrum ypbeseen
on the current market. These structures, developed over the years, together with advances in yp 6.948m material engineering and technology, continue to progress and are now an integral part of Given architectural creation.
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures 2 2 Si q i l i Si l i xp xi yp yi q i li - are also very current. These unique forms have played an important role in contemporary
Architectural y2 q 3can ypnow y3beseen q 4 in yp different y qshapes y5 sizes. 0 They may q 1 yp ylightweight 1 q 2 ypstructures 5 yp and 4 be internal, external, permanent, temporary, large, small, supported, membranes filled with air yp Find yp yp 7.333m
kN 5.47 m 3.204 kN 0.586 5.623 5.381in the architecture, interior design and various culturalm events since the time they first appeared 0.957
1.691
-0.351
sliding0.876 marquee solutions -0.998 to staircases, which disappear by pressing the button (Khalifa form unprecedented options for blame. Ryi cos i Rxi sin i 0.895 kN -1.609 kN 0.588 Talking about modern systems of steel, wire and membrane has its0.975 merit. And that these 0.895
-1.609
0.572
0.948
systems0.895 are at the top of the current Limits are given by the physical properties -1.609 building options. 1.691 -0.351 0.895 0.876These must be -0.998 and laws of the material and-1.609 the construction system. fully taken into account 0.895 -0.48 and used in the creation of-1.609 the modern system.2.317 In practice, we most often encounter the
following issues: 3. Iterate steps 1. And 2. until convergence Given
P xp yp
xp 3.218m
• bars (struts) systems - stable problems of compressive and bent bars,
q 1 xp x1 q 2 xp x2 q 3 xp x3 q 4 xp x4 q 5 xp x5 0 • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
1.903 1960s by the world-famous German architect 2.02 and engineer Frei Otto.
3.844
3.674
4.519
1.23 and constructed independently of the geographic At present, light constructions are designed 1.389 4.931 3.551 location. They transform the space and have so subtle and elegant quality. In addition to
providing basicstep functions such shading andfor shutdown, they (cable): are an important and functional 5. Iteration Define the as force density each element
element in the construction of amphitheatres, sports stadiums, airports, courtyards, building Si 2 2 h h h h 2 2 facades, li and interiors. xp xi yp yi qi parks, seafront l i xp xi yp yi h l Designing lightweight constructions to meet all criteria is a complex task. Every part is visible i S´i and qconstructive, relying of all parts. For example, diaphragm fabrics q i on the proper functioning li i l i are developed to meet the requirements for high strength, long life with a high modulus kN 5.47 tensile m 0.548 5.623 m of elasticity. The surface layer applied to the material ensures fabric resistance against 0.889
1.903
weathering and dirt, provides 2.102 resistance to UV radiation and has non-combustible properties. 1.361
3.674
1.389 We think it important to explore new trends in lightweight constructions, among which we 4.321
can include: Solve the equations granting the equilibrium in both vertical and horizontal directions 1. Lightweight designs designed with regard to sustainability
xp Find xp x 3.121m li • membrane systems - prestress, dynamic presistance, large deformation solutions. 5.47 m 5.623 Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for 1.903
architects, designers and engineers therefore provides unlimited opportunities for design as well 3.674
as experiment with form and1.389 create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite Rx q1 xp x1 q2 xp x2 q3 xp x3 q 4 yp x4 q 5 yp x5 membranes. Membrane structures are often referred to as textile structures. However, the actual
membrane construction is far removed from the classic tent. The main difference is its exact yp 7.333 m geometric shape. For the functioning of the membrane structure, the exact geometric criteria Given
must be computed. The basic criterion is to maintain the concavity and convexity of the main y1 membrane q 2 yp surface. y2 q 3Following yp y3 this q 4principle, yp y we qcan y5 0 basic four q 1 ypof the 5 ytalk directions the p about
4
types of membranes: y Find yp yp 7.507m 1.p saddle-shaped (hyperbolic paraboloid)
2. ridge-valley shape
h h 2. Modular light xp yp yi xp constructions yp yi cos i sin i sin cos 3. Slidingi light hconstructionsi h li li li li Designers see the benefits of mass production of simple structures, such as an "umbrella" that
l i arch shape xp xi 3.
2 yp yi 2
4. conical shape,
has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
qi 0.548 0.889 2.102 1.361 4.321
kN m
li 5.62 5.819 1.943 3.495 1.224
m
293
Si q i l i
Si
6. Iteration step Si
h
qi
h
q i
5.62
5.175
5.819
4.084
1.943
4.756
3.495
5.29
1.224
2
x h x y h y i i p p
h
xp 3.041m
m
2
l i
xp xi
2
yp yi
2
0.534 0.859
li
kN m
5.62
m
Given
5.819
3.495
1.431
1.224
4.901
q 1 yp y1 q 2 yp y2 q 3 yp y3 q 4 yp y q 5 yp y5 4
1.943
2.059
yp Find yp
yp 7.584m
h
cos i
li
h
sin i
y h y i p li
0.555
Rxi
0.98
0.536
0.946
1.606
-0.254
0.893
-0.999
2.549
-0.402
Rxi 0.78
kN
xp cos i li
h
sin i
cos i
Ryi
q i xp xi
Ryi
i
0.534
li
0.859
cos i
qi yp yi
0.536
0.946
1.606
-0.254
0.78
-0.754
0.893
-0.999
0.78
-0.754
2.549
-0.402
3. Iterate steps 1. And 2. until convergence Given
4.123 4.887
0.98
P xp yp
5.494
xp 3.121m
q 1 xp x1 q 2 xp x2 q 3 xp x3 q 4 xp x4 q 5 xp x5
0
Lightweight structures Lightweight structures
5.681 5.918 2.003 1.121
4.901
Si
li
3.416
1.431
sin i
0.555
kN m
2.059
5.085
-0.754
qi
3.032
-0.754
xp xi 2 yp yi 2
i
0.78
l i
Si q i l i
kN
-0.754
yp yi
sin i
0.78
0
Sabah Shawkat ©
Solve the equations granting the equilibrium in both vertical and horizontal directions xp
q1 xp x1 q2 xp x2 q3 xp x3 q 4 yp x4 q 5 yp x5
Rx
yp 7.507m
qi
li
li
Define the force density for each element (cable): li
li S´i
xp Find xp
kN
3.082
kN
m
294 248
Mohr´s circle of stress Lightweight structures
max
2
b
b 4 c 2 The
2
min
max 7.202
b b 4 c
min 0.798
demand for temporary,
Architects and engineers are executives of services to reap the intellectual property of previous
constructions.
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
clients' demands are high nowadays, there is
2a
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary architecture, interior design and various cultural events since the time they first appeared in0 the 1 Solution of the principal stress eigenvalue problem: 0 I n 0 n n 1960s by the world-famous German architect and engineer Frei Otto. 0 At Characteristic present, light polynomial: constructions are designed and constructed independently of the geographic
• bars (struts) systems - stable problems of compressive and bent bars, • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
location. They transform the space and have so subtle and elegant quality. In addition to
11 2basic 22 6 such 12 2.5 and 12 12 they21 12important and functional providing functions as shading shutdown, arean
element in the construction of amphitheatres, sports stadiums, airports, courtyards, building
facades, parks, seafront and interiors. 11 0 12 2 det ( lightweight 0 I) ( 11 22 ( 12) part is visible 02all criteria 0 11 22 Designing constructions is a) complex task. Every 21 22 0to meet and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus 2 ) 0 layer 11 22applied ( 12) to det fabric 0 of elasticity. surface resistance against 02 (11The 22 the 2 tr 0ensures 0material weathering and dirt, provides resistance to UV radiation and has non-combustible properties. Analytical solution. Principal stresses: We think it important to explore new trends in lightweight constructions, among which we can include: Characteristic polynomial of the eigenvalue 1. Lightweight designs designed with regard to problem: sustainability
• membrane systems - prestress, dynamic resistance, large deformation solutions. Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes: Analytical solution. Principal stress directions: 1. saddle-shaped (hyperbolic paraboloid) 2. ridge-valley shape
2. Modular light constructions 3. Sliding light constructions 11 12 n 0 n 0 b ( 11 22) b 8 det ( 0 I) det I 0 0 n 21 22 0 n Designers see the benefits of mass production of simple structures, such as an "umbrella" that
0 Ishape n 0 min 0.798 3. arch 4. conical shape, n 11 12 1 0 1 min 21 22 0 1 n2
has reproducible 2components. Savings from2 a modular strategy lead to cost-effective 11 22 ( 12)
c 11 22 ( 12)
c 5.75
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
I
n 0 0 n
min I n
0
11 12 1 0 1.202 2.5 min 0 1 2.5 5.202 21 22
n 1 1
295
1 n2
( 1.202 2.5 )
1
n min
b
2
2
1 n2 1 2
2
1 n2
n min
0
0.901 0.433
1.202 1 2.5 n 2
1 n2
1.202
n 2
0
a
2.5
Plan stress state and principal stresses: A membrane is subjected to a shear deformation. The material itself can be assumed to behave linear elastic (the stress - strain relationship can
1 2
n 2 0.481
2
1 n2
a 0.901
be described with the Hooke an law for the plane stress state.) Material parameters: Strain state at point P referring to the given local coordinate system:
n 2 b 0.433
reference configuration
n max
b a
or
n max
0.433 0.901
11 0.01
11 22 22 0.02 0.05
2 12
12
21 0.4 E 0.200
kN 2
mm
1. Determine the stress state at point P referring to the given local coordinate system
Sabah Shawkat © 2. Evaluate the principal stresses and their directions 3. Determine the principal strains
(Hint: A principal strain state is defined by vanishing shear deformation. You can use the
inverse relationship of the Hooke an law to determine the principal strains from the principal stresses)
Extra question: Are the realistic?
(Consider the characteristic mechanical behaviour of membranes) Hooke an law for the plane stress state: 1. Determine stresses:
11 22
C
or
11 22 2 12
C
0 1 0 1 2 1 1 0 0 2 E
11 22 12
C is the so called constitutive or elasticity matrix (in general it is a fourth-order elasticity tensor) E represents the Young´s modulus
Lightweight structures Lightweight structures
296 248
The Plane Stress Problem
Lightweight structures ν the poisons ratio Architects of services to reap the intellectual property of previous 0 1 are executives 11 and engineers 11 4.286 11 They 0 1 E generations. and discovering. are the creators of new 22 They are studying, improving 22 22 5.714 MPa 2 1 This creative structures 0 0 spaces, that are constantly improving. 3.571 12forms1 and activity connects 2 12 architects and engineers on their way to the art of "Prof. Frei Otto. The invers relationship is as follows: Lightweight structures used in various forms and variations can be seen in broad spectrum use 11 11 1 over0 theyears, together with advances in on the current market. These structures, developed 1 1 0 C C 1 22 22 and are now an integral part of E material engineering and technology, continue to progress 2 0 0 2 ( 1 ) 12 12 architectural creation. The strain in the thickness direction can be determined as: Architectural lightweight structures can now be seen in different shapes and sizes. They may be internal, 33 external, temporary, small, supported, membranes filled with air permanent, large, E 11 22 1 11 22 or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures 2. Determine principal stress: - are also very current. These unique forms have played an important role in contemporary 0 and 12 various 11design architecture, interior appeared in the 2 cultural events since the time2 they first 2 det 0I 0 11 22 0 1122 12 0 tr0 det 0 1960s by the world-famous German 22 0 architect and engineer Frei Otto. 21 2 location. space and have so subtle and elegant quality. In addition to 0 They 22 0 the 11 transform 11 22 12 0 providing basic functions such as shading and shutdown, they are an important and functional
element in the construction of amphitheatres, 2sports stadiums, airports, courtyards, 2building B 10 MPa C 11.735MPa B 11 22 C 11 22 12 facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible B
2
2
B 4 C
B B 4 C
8.642 MPa 02 diaphragm 1.358 MPa fabrics 01 and constructive, relying on the02 proper functioning of all parts. For example, 01 2
2
are developed to meet the requirements for high tensile strength, long life with a high modulus 3. Determine principal stress directions: of elasticity. The surface layer applied to the material ensures fabric resistance against
is a 2D problem. The stresses in the z direction are considered to be negligible. sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa zzsystems yz are 0 International Stadium). Tensile integrity developed today for NASA and xz being The stress-strain compliance relationship for an isotropic material becomes: form unprecedented options for blame.
Talking about modern systems of steel, wire and membrane has its merit. And that these xx 1 options. 0 Limits 0 0 given building byxxthe systems are at the top of the current are physical properties yy 1 0 0 0 yy and laws of the material and system. These must be fully taken into account the construction 0 0 0 0 zz 1 most often encounter the and used in the creation of the modern system. In practice, we 0 0 0 yz 0 0 0 1 0 0 0 following issues: 0 1 0 0 zx 0 0 1 0 0 0 xy • bars (struts) systems - stable of compressive and bent bars, xyproblems The three zero stress entries in the stress vector indicate that we can ignore their associated • cables systems - prestress, stiffness of (i.e. the structure, solving theory II. order, columns in the compliance matrix columns necessity 3, 4, andof5). If wethe also ignore the rows
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic 2
The plane stress analysisdemands refers to are the high problems where there the thickness of thefor structure is very temporary, constructions. The clients' nowadays, is a demand small compared to other of the structure in the XY plane. The planefrom stresssimple problem transformable solutions thatdimensions can offer sliding lightweight constructions ranging
8.642 MPa
4.286 MPa
5.714 MPa
3.571 MPa
01 11 resistance to UV 22 12 weathering and dirt, provides radiation and has non-combustible properties.
We think to explore new trends in lightweight constructions, among which we 11 itimportant 12 1 0 n 1 0 11 12 1 0 4.356 3.571 MPa 01 01 0 1 can include: 12 22 12 22 0 1 n 2 0 3.571 2.928 1. Lightweight designs designed with regard to sustainability 4.356 MPa n n 1 1 4.356 MPa n 1 3.571 MPa n 2 0 2. Modular light constructions
n 2
1
( 3.571 MPa )
n 2 1.22
3. Sliding light1constructions n1 0.634 0.773 n 01 n 01 n 02 n2 0.773 2 2 0.634 of mass production of simple structures, n 1 the nbenefits Designers see such as an "umbrella" that 2 has reproducible components. Savings from a modular strategy lead to cost-effective
associatedsystems with the- prestress, strain components with z-subscripts, the compliance matrix reduces to a • membrane dynamic resistance, large deformation solutions. simple 3x3 matrix, Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for xx 0 xx 1 unlimited provides opportunities for design as well architects, designers and engineers therefore 1 1 0 yy yy E as experiment with form and create alternative solutions to every day design challenges. 0 0 0 xy xy This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane are often referred as textile However, the actual The stiffness matrix structures for plane stress is found by to inverting thestructures. plane stress compliance matrix, and is given by, membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning structure, the exact geometric criteria of the membrane xx xx xx 1 0 xx and convexity of the main E must be computed. The basic criterion is to maintain the concavity 1 0 yy yy yy yy 2 of 1the principle, membrane directions this we can talk about the basic four Following 0 0 1 surface. xy xy xy xy types of membranes: 1. saddle-shaped (hyperbolic paraboloid) If: xx 0.015 0.025 xy 0.022 2. ridge-valley shape yy
0.4
E 0.200
kN 2
mm
Stresses: in-plane stress field forms a tensor defined by three independent components: 3. arch The shape xx , yy and xy 4. conical shape, xx 1 0 xx E 1 0 yy yy 1 2 0 0 1 xy xy
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
xx
yy
xy
5.952
7.381 MPa
3.143
297
The force density method The Force Density method is popular among space structure designers and the method was developed at the end of the 1960s by German engineers Linkwitz and Schek for the determination of cable net structures or for the initial equilibrium problem of the cable roofs at the Olympic Games in 1972 hosted by Munich. Their goal was to determine a geometry that would be sufficiently rigid without the addition of load ballasts, geometry that would be built easily and would efficiently carry the loads over long distances using subtle elements. This method became very popular rapidly and designers began to work on researches from various countries, which caused expansion and variation. Prestressed cable-nets structure and textile membranes are characterised by the inherent interaction between their geometry and stress distribution. This relationship between the form and forces makes it impossible to directly design such structures as is the case with conventional structures.
Sabah Shawkat ©
Assumption for using this method is that, that the creating elements of the analysed structure, must be straight and must be pin-joined to each other or to the supporting structure, which is fulfilled in this case. First, a graph of a network is drawn and all nodes are numbered from 1 to Ns, and all the elements are numbered from 1 to m. The Nf nodes which are to be fixed
points are taken at the end of the sequence. All the other nodes N are considered as free. Thus the total number of nodes is Ns= N + Nf. Then the connectivity matrix Cs is constructed with the aid of the graph. Each element j has the node numbers k and l (from k to l).
Looking at the geometric model of a typical node of the net, it is clear that this node will be in a steady position, if the resulting force effect of the members will be in equilibrium with the external load in the node. On this basis, it is possible to construct the equilibrium rule for the node as follows: The element between the nodes i and j will be denoted by (i, j). The nodes that are linked with elements by the node i will be called "neighbours" to node i, and the set of their labels will be denoted by Ni. Nf ∪ Ns means the set of those elements which are either in Nf, or in Ns, or in both
Nf ∩ Ns means the set that contains all those elements that Nf and Ns have in common
Lightweight structures Lightweight structures
298 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
299
The equilibrium equations for the free nodes for the x-, y- and z-directions are written as T
( C ) ( U ) ( L)
1
S
F x
T
( C) ( V) ( L)
1
Fy
S
T
( C) ( W) ( L)
1
S
Fz
By using the force-to-length ratios for the elements, i.e. the force densities, are written as: T
( C) ( U) q
Fx
T
( C) ( V) q
Fy
Fz
T
( C) ( W) q
where the vector q, of length m. is described as: (q )
( L)
1
( S)
We write down the matrix expression of equation of equilibrium to the shape: The connectivity matric Cs for the structure is define by (i = 1,2,…Ns).
( U) q
( Q) ( u)
( V) q
( Q ) ( v )
( W) q
( Q) ( w)
at the stage when we have a single initial set geometry, it is necessary to create the connectivity matric Cs. This matrix represents. the number of columns are the number of nodes and the
we can translate equations of equilibrium into shape:
number of rows is the number of members, each row will have 1, -1 and 0, depending on the
Sabah Shawkat ©
node in which the node starts its 1 and its end we denote -1. all other cells in the row will be zero.
For purposes of a further calculation, it is convenient to note that the connectivity matric Cs is
based on two partial C-matrices, including nodes that can change their position during the
T
Fx
T
Fx
T
Fx
(C) (Q)(C)(x) (C)(Q) Cf xf
( C) ( Q) ( C) ( y) ( C) ( Q) Cf yf ( C) ( Q) ( C) ( z) ( C) ( Q) Cf zf
calculation, and Cf that contains only nodes re-assisting the support.
By defining the positioning vectors xs, ys, zs from which are again based on the partial vectors related to the free node x, y, z and related to the fixed node xf, yf, zf , we can calculate the vector
after the introduction of substitution
(D)
Df
T
(C) (Q) (C)
T
( C) ( Q) Cf
displacement of each node, in all directions of the global coordinate system,
Cs
continue to shape
C Cf
(D) (x)
where C and Cf contains the free and fixed nodes, respectively. Denoting the vectors containing
u
Cs xs
C x Cf xf
v
Cs ys
C y Cf yf
w
Cs zs
C z Cf zf
( D) ( y)
Fy Df yf
( D) ( z)
Fz Df zf
from which we express the node's final position
the coordinates of the n free nodes x, y, z, and similarly for the Nf fixed nodes xf, yf, zf, the coordinate differences for each element can be written as:
Fx Df xf
( x)
Fx Df xf ( D)
( z)
Fz Df zf ( D)
Lightweight structures Lightweight structures
1
1
( y)
Fy Df yf ( D)
1
300 248
The equilibrium equations described above represent the linear system of equations, after the Lightweight structures solution we obtain the equilibrium of the position of the nodes. By introducing a force density Architects and engineers are executives of services to reap the intellectual property of previous coefficient (q) a set of otherwise non-linear equations was modified to allow it generations. They are studying, improving and discovering. They are the creators of new solution in one computed step. However, this method of solution is spaces, forms and structures that are constantly improving. This creative activity connects highly difficult for programming. architects and engineers on their way to the art of "Prof. Frei Otto. The force structures density method commonly used incan engineering find spectrum the equilibrium Lightweight used in(FDM), various isforms and variations be seen intobroad use shape of a structure consisting of a network of cables with different elasticity properties on the current market. These structures, developed over the years, together with advanceswhen in
2
2
2
xj xi yj yi zj zi l ( i j ) l xi yi zi xj yj zj constructions. The clients' demands are high nowadays, there is a demand for temporary, transformable solutions that can offer sliding lightweight constructions ranging from simple zj zi xj xi yj yi sliding marquee (Khalifa Si j solutions to0 staircases, which Si j disappear 0by pressingthe Si jbutton 0 l l l i j i j i j Stadium). integrity systems International Tensile are being developed j Ni j Ni j Ni today for NASA and
form unprecedented options for blame. -- Si,j is the force value in the element (i, j), with positive orientation from the node i toward Talking about the node j, modern systems of steel, wire and membrane has its merit. And that these
stress engineering is applied. While shape analysis of tensile structures is anow geometrically material and technology, continue to progress and are an integral non-linear part of problem, the FDM linearizes the equations analytically by using the force density ratio for each architectural creation.
systems at γi,j the top the current building options. are of given the physical properties -- αi,j,are βi,j, are of angles between coordinate axesLimits and axis the by element (i, j), oriented from
cable element, q = S /L,structures where S and are the forcein and length of a cable element respectively. Architectural lightweight canLnow be seen different shapes and sizes. They may method relies permanent, on the assumption that large, the ratio of tension forcemembranes to length offilled eachwith cableaircan be The internal, external, temporary, small, supported,
and used in the creation of the modern system. In practice, we most often encounter the
be constant, transforming a system of non-linear- shell equations to a set of linear equations which or stretched. New subgroups of these constructions structures, tensile-integrity structures can be solved directly. - are also very current. These unique forms have played an important role in contemporary architecture, interior and density various cultural since the timestudied they first appeared in thethe The properties of design the force method events were subsequently thoroughly and 1960s by the world-famous German architect and engineer Frei Otto. method could be implemented in an efficient way by applying special sparse matrix techniques
andi toward laws ofj,the material and the construction system. These must be fully taken into account following issues: • bars (struts) systems - stable problems of compressive and bent bars, • cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
At for present, light are designed and to constructed independently of theup geographic solving theconstructions resulting equations. It proved be a powerful tool for setting and solving
location. They transform the space have so networks subtle and elegant quality. In addition to the equations of equilibrium for and prestressed and structural membranes, without providing basic functions such as shading and shutdown, they are an important and functional requiring any initial coordinates of the structures. element in the construction of amphitheatres, sports stadiums, airports, courtyards, building The essential ideas are as follows. Pin-joined network structures assume the state of equilibrium facades, parks, seafront and interiors. when internal forces S and external forces F are balanced Designing lightweight constructions to meet all criteria is a complex task. Every part is visible
the compilation of on a computational program, of equations equilibrium be converted andFor constructive, relying the proper functioning all parts.ofFor example, can diaphragm fabricsinto following arethe developed to form: meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against
Equilibrium free node i resistance to UV radiation and has non-combustible properties. weathering and of dirt, provides We think it important to explore new trends in lightweight constructions, among which we j ∈ Ni means j is an element of the set Ni can include:
1. Lightweight 0 0 Si designs Stoi sustainability j cos i designed j j cos i j with regard 2. Modular j Ni light constructions
j Ni
Si j cos i j
• membrane systems - prestress, dynamic resistance, large deformation solutions. Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite
of thestructures element (i,j). li,j is the length membranes. Membrane are often referred to as textile structures. However, the actual The nonlinear algebraic equation system obtained membrane construction is far removed fromwill thebeclassic tent. The main difference is its exact xj xiof the membrane geometric shape. For the functioning the exact geometric criteria structure, Si j 0 must be computed. The basic and convexity of the main 2 criterion is2 to maintain2 the concavity xj xi yj yi zj zi j Ni directions of the membrane surface. Following this principle, we can talk about the basic four
j Ni
3. Sliding light constructions xj xi yj yi zj zi cos i see cos i production cosstructures, j the benefits of mass j i j Designers of simple as an "umbrella" that l i j l i j l i such j has where reproducible components. Savings from a modular strategy lead to cost-effective
types of membranes:
y yi 1. saddle-shaped (hyperbolicj paraboloid) Si j 2 2 2. ridge-valley shape xj xi yj yi zj zi j Ni
0
3. arch shape
4. conical shape,
j Ni
Si j
Lightweight Lightweightstructures structures
xj xi 2 yj yi 2 zj zi 2 zj zi
i ∈ Nf means i is an element of the set Nf
Lightweightstructures structures Lightweight
2
0
0
301
If the relationships Si,j / li,j in the equilibrium system are denoted qi,j, the system becomes Si j
q ( i j )
xj xi yj yi 2 zj zi 2 2
are called force densities
q i j zj zi
q i j yj yi
j Ni
0
q i j xj xi
0
j Ni 0
j Ni
Force densities qi,j can be set instead of force values Si,j.
qij. xj xi qik xk xi qil xl xi qim xm xi Fxi
0
Sabah Shawkat ©
qijxj qijxi qik xk qik xi qilxl qilxi qimxm qimxi Fxi
xi qij qik qil qim qijxj qik xk qilxl qimxm Fxi
xi qij qik qil qim
xi
0
0.
qijxj qik xk qilxl qimxm Fxi
qijxj qikxk qilxl qimxm Fxi qij qik qil qim
what is possible for the general network topology write as follows: n
xi
n
xj qij Fxi
j1
yi
n
qij
j1
n
zjqij Fzi
yj qij Fyi
j1
zi
n
j1
qij
j1
n
qij
j1
This suggests that the equilibrium position of each node in the space is a function of the average position of its neighbours, where the great coefficient is the force density of the bristles seizing the solved nodes.
Lightweight structures Lightweight structures
302 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous To illustrate the properties of the linear force densities a simple example will now be given. generations. They are studying, improving and discovering. They are the creators of new Consider the structure bellow with all fixed nodes in the x-y plane. spaces, and Initialforms position of structures free nodes that are constantly improving. This creative activity connects architects and engineers on their way to the art of "Prof. Frei Otto. 0 1 0 1 2 0 structures used forms and variations can be seen in broad spectrum use Lightweight in various x 0 y 0 z 0 on the current market. structures, 1 0 These 0 developed over the years, together with advances in 1 material 2engineering and technology, 0 continue to progress and are now an integral part of architectural creation.of fixed nodes (supports): The initial position Architectural 0 lightweight 2 structures 2can now be seen in different shapes and sizes. They may 0 0 0 be internal, external, permanent, temporary, large, small, supported, membranes filled with air xf y f zf 2 2 0 or stretched. of these 2constructions - shell structures, tensile-integrity structures 2 New subgroups 0 - are also very current. These unique forms have played an important role in contemporary architecture, interior design and various cultural events since the time they first appeared in the
constructions. The clients' demands are high nowadays, there is a demand for temporary, Matrix of continuity transformable solutions that can offer sliding lightweight constructions ranging from simple 1 0 0 0 0 0 0 1 0 disappear sliding marquee solutions to staircases, which by pressing the button (Khalifa 0 1 0 0 0 1 0 0 0 International Stadium). Tensile integrity systems are being 1 0 0 0 0 0 1 0 0 developed today for NASA and 1 0 1 0 options 0 0 0 0 form unprecedented for blame. 0 0 1 1 0 0 0 0 0 0 Talking about has its merit. And that these 0 and 0 0 systems of steel, wire 0 1 0 modern 0 membrane 1 0 C Cf 0 are given by the physical properties 0 0at 0the 1top0of the current building 0 1 0Limits systemsare options. 1 1 0 0 0 0 0system. and laws 0of0 the material and the construction These must be fully taken into account 0 0 1 0 1 0 0 0 0 in the creation of the modern system. and used In practice, we most often encounter the 1 0 0 0 0 0 0 1 0 following issues: 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 • bars (struts) systems - stable problems of compressive and bent bars, External Load of Free Nodes:
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
Sabah Shawkat ©
1960s by the world-famous German architect and engineer Frei Otto.
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible
and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics A simple cable structure with zero external loads. The arrows indicate the directions of elements. are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties. We think it important to explore new trends in lightweight constructions, among which we can include: 1. Lightweight designs designed with regard to sustainability 2. Modular light constructions
0 0 systems - prestress, 0 resistance, large deformation solutions. • membrane dynamic 0 0 0 Fx membrane Fyarchitecture 0 Fzahighly Tensile is 0 0 sophisticated medium that offers unique qualities for 0 0 0 architects, designers and engineers therefore provides unlimited opportunities for design as well 0 0 0 as experiment with form and create alternative solutions to every day design challenges.
Force Density Coefficient of Prestress:
This is made possible due to the fundamental flexibility and lightweight nature of composite 0 0 0 0 0 0 0 0 0 0 1 0 Membrane membranes. structures are often referred to as textile structures. However, the actual 0 1 0 0 0 0 0 0 0 0 0 0 membrane construction is far removed from the classic tent. The main difference is its exact 0 0 1 0 0 0 0 0 0 0 0 0 0 shape. of the membrane structure, the exact geometric criteria geometric 0 0 1 For 0 0 the 0 0functioning 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 is to maintain the concavity and convexity of the main must be computed. The basic criterion 0 0 0 0 0 1 0 0 0 0 0 0 directions Q of the membrane surface. Following this principle, we can talk about the basic four 0 0 0 0 0 0 1 0 0 0 0 0 types ofmembranes: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 (hyperbolic 0 0 1 0 0 0paraboloid) 1. saddle-shaped 0 0 0 0 0 0 0 1 0 0 0 0 2. ridge-valley shape 0 0 0 0 0 0 0 0 0 0 1 0 3. arch shape 0 0 0 0 0 0 0 0 0 0 0 1 4. conical shape,
3. Sliding light constructions
Designers see the benefits of mass production of simple structures, such as an "umbrella" that
has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
303
Design stiffness matrix:
3 0 T D C Q C 1 0 0
0 1 0 3 1 0 1 4 1 0 1 3 0 1 0
0
1 1 T Df C Q Cf 0 0 0
0 1 0 3
1 0 0 1 0
0
1 0 0 1
Calculation of new position of free nodes
0 0 1 1 0
Calculation of new position of free nodes:
0.333 1 1 x D Fx Df xf 1 1 1.667
For different force density values we get different resulting shapes of this structure. it is seen that
1 1.667 1 y D Fy Df y f 1 0.333 1
1 1 1 D Fz Df zf 1 1 1
Design stiffness matrix
i 1 12
q 1 i
q1 q2 df 0 0 0
q
3
0
0
q
0
0
q 0
7
0 q
0 q 11 q 12 0 0
6
10
3 1 0 1 4 1 0 1 0
of that element. the opposite holds for decrease in the force density, even more emphasised with negative values. For elements 1-3, 5-12 have q = 1 and element 4 has q = 9 q
3
0
0
0 0 q 11 q 12
Sabah Shawkat ©
0 1 0
0 1 3
for a single element an increase in the force density relative to the others results in a construction
q 1 q 2 d f 0 0 0
0 q1 q3 q4 q q q 0 2 5 6 q q q d 4 5 4 0 0 0 0
3 0 d 1 0 0
0.333 1 1 1 1.667 1 1 1 1 x d Fx d f xf 1 y d Fy d f y f 1 z d Fz d f zf 1 1 0.333 1 1.667 1 1
0
0 1 0 3
q q
5
q q
1 1 df 0 0 0
8
q
9
8
q q q
8
7
8
0
9
1
0
0
0
1
0
0
0
0
1
0
1
0
1 1
q 9 0 q q q 9 10 12 0
0
q q q 5
0
0
4
11
0
q
0
0
q
7
0
6
0
q
10
0 q1 q3 q4 q q q 0 2 5 6 q q q d 4 5 4 0 0 0 0
11 0 d 9 0 0
0
9
0
0
3
1
0
0
1 12 1 1 0 1 3 0 0 1 0 3
Lightweight structures Lightweight structures
q q
5
q q
8
q
9
7
8
0
9
1 1 df 0 0 0
8
q q q
8
1
0
0
0
1
0
q 9 0 q q q 9 10 12 0
0
q q q 5
0
0
4
0 0 0 1 0 1 0 1 1
11
304 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous Calculation of new position of free nodes generations. They are studying, improving and discovering. They are the creators of new 0.6 1 1 0.911that are constantly improving. 1.667 This creative activity 1 connects spaces, forms and structures 1 1 1 x d and Fxengineers d f xf on 0.733 y dto the Fyart dof 1 Otto. z d Fz d f zf 1 way architects their f y"Prof. f Frei 0.911 0.333 1 in various forms and variations Lightweight structures used use 1.578 1 can be seen in broad spectrum 1 on the current market. These structures, developed over the years, together with advances in material engineering and technology, continue to progress and are now an integral part of For elements 1‐3, 5‐12 have q = 1 and element 4 has q = ‐0.2 architectural creation. 0 q 1 q 3 0 lightweight structures Architectural can now be seen in different shapes and sizes. They may q 2 0 q 6 0 temporary, large, small, supported, membranes filled with air be internal, external, permanent, 0 0 0 d f 0 or stretched. subgroups of these constructions - shell structures, tensile-integrity structures New 0 q 0 q 7 11 - are also very current. These 0 0 q 10 q 12 unique forms have played an important role in contemporary architecture, interior design and various cultural events since the time they first appeared in the 0 0 0 q q q qthe 3 4 4 1960s by German architect and engineer Frei Otto. 1 world-famous 0 q 0 0 q q q light constructions 2 5 6are designed 5 and constructed independentlyof the geographic At present, q q q q q q q q d In addition to 5 4 and 5 have 8 9so subtle 8 and elegant9 quality. location. They 4 transform the space 0 0 q q q 0 q providing 7 8 they 11 are an important basic functions such as shading8 and shutdown, and functional q q q courtyards, 0 of amphitheatres, q airports, 0 elementin the0 construction sports stadiums, building 9 9 10 12
constructions. The clients' demands are high nowadays, there is a demand for temporary, For interior elements 4-5, 8-9 have q = 1 and edge elements 1,2,3,6,7,10,11,12 have q = 6 transformable solutions that can offer sliding lightweight constructions ranging from simple 0 0 q 1 q 3 solutions sliding marquee to staircases, which disappear by pressing the button (Khalifa q 2 0 q 6 0 International Stadium). Tensile integrity systems are being developed today for NASA and 0 0 0 0 formdfunprecedented options for blame. 0 q 0 q 7 11 Talking about of steel, wire and membrane has its merit. And that these q systems 0modern q 0 10 12 systems are at the top of the current building options. Limits are given by the physical properties and laws of the material and the construction system. These must be fully taken into account 0 0 0 q q q q 1in the 3 creation 4 and used of the modern4 system. In practice, we most often encounter the 0 q 0 0 q q q issues: 2 5 6 5 following q q q q q q q q d 4 5 4 5 8 9 8 9 • bars (struts) systems - stable problems of compressive and bent bars, 0 0 q q q 0 q 8 7 8 11 theory II. order, q q the 0 - prestress, 0 stiffness of the qofsolving q structure, necessity 0 • cables systems 9 9 10 12
Sabah Shawkat ©
facades, parks, seafront and interiors. 0 0.2 0 0 1 0 0 1.8lightweight 1 to Designing constructions meet all criteria is a complex task. Every part is visible 0 3 1 0 0 1 0 1 0 on the proper functioning and dconstructive, relying of all parts. For example, diaphragm fabrics 0.2 1 2.8 1 1 d f 0 0 0 0 are developed tensile strength, long life with a high modulus 0 0 to1meet 3 the 0 requirements 0 1 for 0 high 1 1 surface 0 3 layer 0 1 to 1 the material ensures fabric resistance against 0 0 The 0 applied of elasticity. weathering and dirt, provides resistance to UV radiation and has non-combustible properties. Calculation of new position of free nodes
We think it important to explore new trends in lightweight constructions, among which we 0.167 1 1 can include: 1.167 1.667 1 1 1 1 d f xf designed y dregard Fy to dsustainability x d Fx designs 1.5 with 1. Lightweight f y f 1 z d Fz d f zf 1 1.167 0.333 1 2. Modular light constructions 1.833 1 1 3. Sliding light constructions
• membrane systems - prestress, dynamic resistance, large deformation solutions. 13 0 1 0 0 6 6 0 0 0 13 1 0 0 6 0 6 0 Tensilemembrane architecture is a highly sophisticated medium that offers unique qualities for d 1 1 4 1 1 df 0 0 0 0 architects, designers and engineers therefore provides unlimited opportunities for design as well 0 0 1 13 0 0 6 0 6 and create alternative as experiment with form solutionsto every day design challenges. 0 0 1 0 13 0 0 6 6 This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual
membrane construction is far removed from the classic tent. The main difference is its exact Calculation of new position of free nodes geometric shape. For the functioning of the membrane structure, the exact geometric criteria
must be computed. The basic criterion is to maintain the concavity and convexity of the main 0.077 1 we can talk about the 1 basic four directions of the membrane surface. Following this principle, 1 1.923 1 types of membranes: 1 1 1 x d Fx d f xf 1 y d Fy d f y f 1 z d Fz d f zf 1 1. saddle-shaped (hyperbolic paraboloid) 1 0.077 1 1.923 1 1 2. ridge-valley shape
3. arch shape 4. conical shape,
Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
305
The calculation of stiffness and stiffness matrix.
Assemble the bar elements 1 and 2 in one stiffness matrix according to figure in a: k1 0 u1 k1 k1 k1 k2 k2 u 2 0 u k2 k2 3
F1 F2 F 3
According to the figure in b, then the stiffness matrix we can indicate as: k1 k1 0 u 1 k1 k1 0 u 2 0 0 0 u3
According to the figure in c, then the stiffness matrix we can indicate as:
k1 k2 k2 u2 k2 k2 u 3
F2 F3
Boundary conditions figure in c, then the stiffness matrix we can indicate as:
Sabah Shawkat ©
k k ( A E) 11 12 1 L k21 k22 0 ( A E)
Fi
L ( A E)
Fj
L
Fi Fj
u ( A E) 1 1 i L 1 1 u j
Fi Fj
k1 k2 k2 u2 k2 k2 u 3
0 P
ui uj
u i u j
Element 1- bar element: ( A E) L
k1 k1 u 1 k1 k1 u 2
F1 F2
k1 u 1
F1
k2 u 2
F2
k1
F1 u1
Element 2 - bar element:
k2 k2 u 2 k2 k2 u 3
F2 F3
k2
F2 u2
Lightweight structures Lightweight structures
306 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
At present, light constructions are designed and constructed independently of the geographic According to a location. They transform the space and have so subtle and elegant quality. In addition to
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for
Sabah Shawkat ©
1 functions such as 1 shading providing basic and shutdown, they are an important and functional u N u N u N N 1
2
2
2
1 1
2 2
element in the construction of amphitheatres, sports stadiums, airports, courtyards, building Cantilever beam- Example facades, parks, seafront and interiors. u
0 mm
u
10 mm
1 lightweight constructions 2 Designing to meet all criteria is a complex task. Every part is visible
and constructive, on the proper functioning of all of parts. example, diaphragm if we want relying to find the displacement in the middle the For Cantilever beam where fabrics 0 Each node has athe shape function for high tensile strength, long life with a high modulus are developed to meet requirements
of elasticity.1 The surface layer applied to the material ensures fabric resistance against N1 0.5 N1 weathering and2 dirt, provides resistance to UV radiation and has non-combustible properties. N2
1
N2 0.5
architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
2 We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include: Value of shape function varies from 0 to1, sum of all shape functions is 1
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
N1 N2 1
Shape function = 1 at its node, =0 at all other nodes 3. Sliding light constructions u 5 mm of simple structures, such as an "umbrella" that u see N1 uthe N2 u 2 of mass production Designers 1 benefits
has reproducible components. Savings from a modular strategy lead to cost-effective
Lightweightstructures structures Lightweight Lightweight Lightweightstructures structures
307
Sabah Shawkat ©
Lightweight structures Lightweight structures
308 248
Lightweight structures Architects and engineers are executives of services to reap the intellectual property of previous
constructions. The clients' demands are high nowadays, there is a demand for temporary,
generations. They are studying, improving and discovering. They are the creators of new
transformable solutions that can offer sliding lightweight constructions ranging from simple
spaces, forms and structures that are constantly improving. This creative activity connects
sliding marquee solutions to staircases, which disappear by pressing the button (Khalifa
architects and engineers on their way to the art of "Prof. Frei Otto.
International Stadium). Tensile integrity systems are being developed today for NASA and
Lightweight structures used in various forms and variations can be seen in broad spectrum use
form unprecedented options for blame.
on the current market. These structures, developed over the years, together with advances in
Talking about modern systems of steel, wire and membrane has its merit. And that these
material engineering and technology, continue to progress and are now an integral part of
systems are at the top of the current building options. Limits are given by the physical properties
architectural creation.
and laws of the material and the construction system. These must be fully taken into account
Architectural lightweight structures can now be seen in different shapes and sizes. They may
and used in the creation of the modern system. In practice, we most often encounter the
be internal, external, permanent, temporary, large, small, supported, membranes filled with air
following issues:
or stretched. New subgroups of these constructions - shell structures, tensile-integrity structures - are also very current. These unique forms have played an important role in contemporary
• bars (struts) systems - stable problems of compressive and bent bars,
architecture, interior design and various cultural events since the time they first appeared in the
• cables systems - prestress, stiffness of the structure, necessity of solving the theory II. order,
1960s by the world-famous German architect and engineer Frei Otto.
• membrane systems - prestress, dynamic resistance, large deformation solutions.
Sabah Shawkat ©
At present, light constructions are designed and constructed independently of the geographic
location. They transform the space and have so subtle and elegant quality. In addition to
providing basic functions such as shading and shutdown, they are an important and functional element in the construction of amphitheatres, sports stadiums, airports, courtyards, building facades, parks, seafront and interiors.
Designing lightweight constructions to meet all criteria is a complex task. Every part is visible and constructive, relying on the proper functioning of all parts. For example, diaphragm fabrics are developed to meet the requirements for high tensile strength, long life with a high modulus of elasticity. The surface layer applied to the material ensures fabric resistance against weathering and dirt, provides resistance to UV radiation and has non-combustible properties.
Tensile membrane architecture is a highly sophisticated medium that offers unique qualities for architects, designers and engineers therefore provides unlimited opportunities for design as well as experiment with form and create alternative solutions to every day design challenges. This is made possible due to the fundamental flexibility and lightweight nature of composite membranes. Membrane structures are often referred to as textile structures. However, the actual membrane construction is far removed from the classic tent. The main difference is its exact geometric shape. For the functioning of the membrane structure, the exact geometric criteria must be computed. The basic criterion is to maintain the concavity and convexity of the main directions of the membrane surface. Following this principle, we can talk about the basic four types of membranes:
We think it important to explore new trends in lightweight constructions, among which we
1. saddle-shaped (hyperbolic paraboloid)
can include:
2. ridge-valley shape
1. Lightweight designs designed with regard to sustainability
3. arch shape
2. Modular light constructions
4. conical shape,
3. Sliding light constructions Designers see the benefits of mass production of simple structures, such as an "umbrella" that has reproducible components. Savings from a modular strategy lead to cost-effective
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G. N. Vanderplaats - Multidisciplinary design optimization. Vanderplaats Research & Development, Inc., 2007
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Lightweight Steel Structures ©
Assoc. Prof. Dipl. Ing. Sabah Shawkat, MSc, PhD. 1. Edition 2019 Published by Tribun EU, s.r.o. Cejl 892/32 Brno tel.: +420 543210089 ISBN 978-80-263-1458-5 Printed in Czech Republic