Structural Icons for Architects part.1 by Archineer

Structural Icons for Architects

Sabah Shawkat © Sabah Shawkat

Sabah Shawkat ©

Reviewer:

prof. Ing. arch. Julián Keppl, CSc. prof. Dipl. Ing. Ján Hudák, PhD. MSc. Nastja Dzavik Dr. Salahaddin Yasin Baper

Cover Design: Editor: Technological Support: Software Support: Publisher:

Peter Nosáľ Richard Schlesinger Marek Vaško asc. Applied Software Consultants, s.r.o., Bratislava, Slovakia Tribun EU, s.r.o. Cejl 892/32, 60200 Brno, Czech Republic Tribun EU, s.r.o., Brno, Czech Republic

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Publishing of this book was financially supported by the Ministry of Education,

Sabah Shawkat ©

Science, Research and Sport of the Slovak Republic ( KEGA 002VŠVU-4/2019)

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.

Structural icons for architects ©

Sabah Shawkat 1. Edition, Tribun EU, s.r.o. Brno, Czech republic 2021 ISBN 978-80-263-1624-4

Sabah Shawkat

Richard Schlesinger

Sabah Shawkat is a structural designer, specializing in lightweight structures, such as tensile structures, tensile integrity structures, grid shells and reciprocal frames. He focuses on transforming these beautiful structures into design components such as chairs, tables, illuminated lamps or hammocks for interiors, gardens or public spaces.

Richard Schlesinger works as an assistant professor at the Engineering Room of the Academy of Fine Arts and Design in Bratislava. He defended his dissertation on design and technological procedures used in monument protection at the Department of Architecture, Faculty of Civil Engineering of the Slovak University of Technology.

Sabah Shawkat is also a passionate expert in traditional fibre reinforced and prestressed structures. He has published numerous articles in professional journals and has written several books.

Richard Schlesinger teaches students of architecture several structural engineering subjects such as Introduction to Structural Engineering and Construction in Architecture. Moreover, he regularly organizes workshops and exhibitions of student projects and construction models. He is also actively involved in projecting, building construction and reconstructions as well as modernisations of buildings.

Sabah Shawkat ©

He teaches students of architecture and building engineering. Moreover, he regularly organizes workshops for students and exhibitions of his own as well as student projects and construction models. He is also actively involved in projecting and building constructions as well as reconstructions and modernizations of buildings.

A B C D E F G H I J

PROPERTIES OF F IB R E R E IN FOR CE D CON CR E T E , REINF ORC ED C ONC R E T E A N D H IG H P E R FOR M A N CE CON CR E TE STRUC TURA L LOAD S

Sabah Shawkat © METHODOLOGY OF S T R U CT U R E S REINF ORC ED C ON CR E T E PREC A ST C ONC RE T E

BONDED AND UNBON D E D P R E S T R E S S IN G T E N D ON S STEEL STRUC TUR E S TIMBER STRUC TU R E S C REATIVITY IN ST R U CT U R A L D E S IG N TERMINOLOGY

CONTENTS

TABLE OF

INTRODUCTI ON

PROPERTIES OF FIBRE REINFORCED CONCRETE, REINFORCED CONCRETE AND HIGH PERFORMANCE CONCRETE

B1-B56

STRUC TURAL L O A D S

C1-C104

METHODOLOG Y O F S T R U CT U R E S

D1-D152

REINF ORC ED CON CR E T E

PAGES

TABLE OF

A1-A72

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E1-E52

PREC AST C ON CR E T E

F1-F76

BONDED A ND U N B O N D E D P R E S T R E S S IN G T E N D ON S

G1-G74

STEEL STRUC T U R E S

H1-H54

TIMBER STRU CT U R E S

I1-I147

C REATIV ITY IN S T R U CT U R A L D E S IG N

J1-J31

TERMINOLOG Y

“ Your su cce ss will n o t d e t e rmin a t e b y y o u r g e n d e r o r b y y o u r e t h n ic ity b u t only b y the sco p e of yo u r d re a ms . “ Z a h a Ha d i d

Sabah Shawkat ©

The book you are holding in your hands is an excursion of construction icons for architects and designers from the field of conventional and modern lightweight structures. I do not consider it as the only source of information for understanding the behaviour of construction during their lifetime, as well as their service. This book presents two worlds, one is traditional, the second is lightweight structures, personally I always try to show the difference between these worlds in a simplest way possible.

These systems are characterized on the basis of the philosophy of Frei Otto where he says that the „form follows force”, it follows that, the stresses and deformations of the structure are known and we are looking for the final form of the structure which is a function of iteration, the self-weight is several times less than the imposed load, this ratio will take us to the area of dynamics behavior where the influence of static load ceases to meet the conditions, and we must focus on other parameters such as the frequency of the structure, the frequency due to the excitation force, resonance, damping and maximum amplitude. Because we will assess the design for its entire useful life to serve people and at the same time to be comfortable.

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- The philosophy of conventional structures is constructed on the basis of le Corbusier as a “form follows function”, where the shape of the structure is clear and we look for deformations and stresses in the structure, while the actual self-weight of the structure several times exceeds the imposed load.

- Lightweight structures, which is a set of creative and elegant construction systems such as, tensile integrity structures these are created according to the idea of Karol Ioganson, Buckminster Fuller and Kenneth Snelson, reciprocal frames based on the idea of Leonardo Da Vinci, transparent membrane structures which are designed based on the idea of Frei Otto and anti-gravity tensegrity structures.

My excursion as I mentioned presents the designers, diagrams of materials such as concrete, steel, fiber-concrete, wood, prestressed tendons, where their quality has a great influence on the ultimate limit state and serviceability limit stat. I hope this book will serve you and offer simple ideas for realizing your creative designs, while I would be grateful if you would feed me back in case you needed an explanation or found errors. Sabah Shawkat, Bratislava, 31.10.2020

Sabah Shawkat © A I Properties of fibre reinforced concrete, reinforced concrete and high performance concrete

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A3 Concrete is a mixture of cement, aggregate and water. The addition of water to the concrete mix starts a chemical reaction called hydration that results in the binding of the sand and aggregate to produce a sandstone conglomerate. Concrete is placed in forms prior to hardening. As concrete dries and cures, fine cracks are produced from thermal effects caused from shrinkage. Concrete reaches about ninety percent of its full strength in 28 days. Other materials called admixtures are added to concrete to improve strength, workability and frost resistance, and to reduce shrinking, cracking and permeability.

strength, the stiffness and the cracking of the normal weight, normal strength concrete is basically governed by the properties of the mortar and the ability of the interface to mobilize the strength and stiffness of the aggregates. Properties of the mortar and the interface are in turn governed by the water/cement ratio; the lower w/c ratio the stronger the mortar and interface stage. Consequently, decreased w/c ratio improves the interaction between the mortar and the coarse (gross) aggregate phases. Introduction of superplasticizers in concrete technology has made it possible to produce concrete with extremely low w/c ratio, resulting in the production of concretes with very strong mortar phase and interface.

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The most important mechanical properties of bulding materials are their weight, tensile strength, yield strength, shear strength, compressive strength, ductility, toughness, impact resistance, fatigue resistance, elasticity and creep under load. Other important mechanical properties are their strain capacity and their resistance to rain and moisture penetration. Some properties, for example the compressive strength of concrete, depend on the way the test is done and may reflect other, more fundamental properties.

In the simplest case concrete can be regarded as a three phase material consisting of a continuous phase (mortar) and a particle phase (coarse aggregates). The described phases interact through a third phase, namely the interface. The

The use of fibres to strengthen materials which are much weaker in tension than in compression goes back to ancient times. when probably the oldest written account of such a composite material, clay bricks reinforced with straw occured. At about the same time period, approximately 3500 years ago, sun baked bricks reinforced with straw were used to build the 57 m high hill of ‚Aqar Quf‘. The first widely used manufactured composite in modern time was asbestos cement, which was developed in about 1900 with the invention of the Hatschek process. Now, fibres of various kinds are used to reinforce.

A4 In differ to the normal strength concrete, the crack trajectory does not avoid the coarse aggregates, but it may pass through them. The concrete‘s shear strength is about one-third the unit compressive strength, whereas, tensile strength is less than one-half the shear strength. The failure of a concrete slab subjected to a downward concentrated load is due to diagonal tension. However, web reinforcement can prevent beams from failing in diagonal tension. The concrete‘s tensile strength is such a small percentage of the compressive strength that it is ignored in calculations for reinforced-concrete beam. Instead, horizontal steel bars well embedded in the tension area provide tensile resistance. The tensile strength of a bar, is the stress, calculated as force divided by the original area of the bar, which causes fracture of the bar in tension. The yield stress, is the stress at the yield point, the yield point is the point at which plastic flow of the material begins to occur. Below the yield point the material is elastic and is able to recover its original shape when the load is removed. Above this point the material is said to be plastic and undergoes a permanent deformation, which remains after the load is removed.

concrete structures, in general, it is an important characteristic for the development of cracking and therefore, for the prediction of deformations and the durability of concrete. Other characteristics such as bond and development length of reinforcement and the concrete contribution to the shear and torsion capacity are closely related to the tensile strength of concrete. Bond Strength is the measure of effective grip between the concrete and the embedded-steel bar. The design theory of reinforced-concrete beam is based on the assumption that a bond develops between the reinforcement and the concrete that prevents relative movement between them as the load is applied. How much bond strength develops depends largely on the area of contact between the two materials. Because of their superior bonding value, bars having a very rough surface (deformed bars or rebars) have replaced plain bars as steel reinforcement

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The tensile strength of concrete is neglected for the strength of reinforced and prestressed

The bond behavior of a reinforcing bar and the surrounding concrete has a decisive importance regarding the bearing capacity and the serviceability of reinforced concrete members. This knowledge is an indispensable requirement to give design rules for anchorage and lap lengths of reinforcing bars, for the calculation of deflections taking into account the tension-stiffening effect, for the control of crack width, and, thus, the necessary minimum amount of reinforcement.

A5 (Shah, S. P.)

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Sabah Shawkat © The steel used for making steel fibers are generally carbon steels or alloy steels; the latter are used primarily for corrosion-resistant fiber, in refractory applications and marine structures. Steel fibers may be produced in a number of ways:

- pulling and successive cutting of wires, milling, shearing sheets producing fibers by the hot melt extraction process, in which a rotating wheel is brought in contact with the molten steel surface, lifting off some liquid metal.

Steel fibres may be produced in a number of ways, ( Mindes, S. & Bentur, A.)

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In figures are schematically presented deformations around the fibre before and after loading and distributions of the elastic shear stress at the interface and tensile stress distribution, ( Mindes, S. & Bentur, A.)

A10

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Types of fracture process zone. Diagrams at the bottom show the trends of the stress distribution along the crack line. Hillerborg’s Approach The Cohesive Crack as a Constitutive Relation

A11 (Mindes, S. & Bartos.)

Sabah Shawkat © There are three different types of fiber orientation in the hardened concrete mass. Most common are randomly oriented low fiber volume or randomly oriented high fiber volume. Less common are uni-directional fiber composites consisting of non-metal fibers.

There are three different types of fibre orientation in the hardened concrete mass. Most common are randomly oriented low fibre volume

A12

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Mechanics of Fibre Reinforced Composites, OA. The cracks initiate at a very low load , A Cracks begin, AB With further straining, B Above mentioned process leads to the homogenisation, (Mindes, S. & Bentur, A.)

A13

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Length Effects and Interpretation of Pull-Out Curve, OA - Intact interface, AB – Gradual debonding, BC – Debonding completed, C- Stick-Slip behaviourand strain softening behaviour, (Imam, Mindes, S. & Bentur, A.)

A14

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A15

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Different forms of steel fibres, (Mindes, S. & Bentur, A.)

A16

Sabah Shawkat © The fracture properties are characterized by three parameters: - fracture energy Gf , - uniaxial strength ft ,- width of the crack band wc The role of fibers in the concrete is to transfer the load from the matrix. There are two cases, which can occur and the stress transfer effects between the fiber and matrix are different in: - the pre-cracking case, - the post-cracking case Here is presented the simple pull-out geometry.

Bažant & co-workers’s Model - Crack Band Model, ( Bažant, Z. P. & Oh, B. H.)

A17

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A18

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A19

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Length Effects and Fibre-Matrix Interaction, simple pull-out geometry

A20

Sabah Shawkat © In HPC, however, the paste and the transition zone are generally much denser and stronger than in NSC, thus providing good stress transfer between aggregate and paste. In another words, the aggregates participate more

actively in the concrete’s mechanical responses. Researchers and practitioners alike are coming to recognize the vitally important role that aggregates play when it comes to making HPC.

High strength concrete, calcium hydroxide (Ca(OH)2), Ca(OH)2 crystal formation and calcium silicate hydrates (CSH) (Walraven J.C.)

A21

Sabah Shawkat © In this respect, two points that assume some significance are the aggregate strength and the strength of the interface, i.e.., the bond between the aggregate and matrix. The strength of the bond between HCP and aggregate is a function of the amount of Ca(OH)2 crystal formation.

Normal strength concrete, Ca(OH)2 crystal formation and calcium silicate hydrates (CSH), High strength concrete, calcium hydroxide (Ca(OH)2), Ca(OH)2 crystal formation and calcium silicate hydrates (CSH), (Walraven J.C.)

A22

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Geometry, loading and deformation of cracked hinge according to MCMOD Calculation of deﬂection FRCB

A23

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Modelling of Flexural Behaviour, The curve 0 presents plain concrete. Curves 1 and 2 characterized weakly reinforced specimens, For curves 3, Stress vs strain of NSC and stress vs strain of HPC, (Banthia & Sicard) (1989)

A24

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Bending – Axial – Load Interaction of fibre reinforced concrete

A25

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A26

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Crack mouth opening , applied load P and crack mouth load Pm. MCMOD

A27

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A28

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Crack opening in concrete contribution and fibre contribution and stress vs opening cracks relationship, Illustration of the multi-linear stress-crack opening relationship, ( Bažant, Z. P. & Oh, B. H.)

A29

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Deﬂection in FRC and diagram of FRC in tension, Illustration of the bi-linear and multi-linear stress-crack opening relationship, (Rossi & Casanova)

A30

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(Rossi & Casanova)

A31

Sabah Shawkat © It is important to recognize that, in general, fibre reinforcement is not a substitute for conventional reinforcement. The role of fibres is to control the cracking of FRC. In the Figure is shown typical stress-strain curves of FRC. As can be observed, the fibres improve the ductility‘ of the

material or more properly, its energy absorption capacity. The interaction of a crack, propagating in the matrix, with a fiber, can be quite complicated, often resulting in extensive micro cracking in the vicinity of the fiber, and deboning at some distance away from the actual fiber-matrix interface.

Determination of the equivalent ﬂexural strength by the bending testing on the simple, DBV Merkblatt ”Bemessungsgrundlagen fur Stahlfaserbeton”, Diagram of FRC, (Rossi & Casanova)

A32

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Load-Deﬂection Diagram, (ACI, JCI method, Barr, ASTM, & Jonsen)

A33

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Diagram of FRC and load deﬂection relationship, (Belgian standard NBN B15-238)

A34

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The general ﬂexural behaviour of different types of FRC in different levels of load (I, II, III –as an ultimate limit state) , (Mindes, S.; Edginton & Allen )

A35

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Bending – Axial – Load Interaction diagram of FRC

A36

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Belgian standard NBN B15-238 (1992). Distribution of stresses, when the ultimate load is reached

A37

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Tension softening diagram, diagram stress vs strain of FRC, (Design guidelines for DRAMIX)

A38

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(a) Three-point bend with arbitrary SD ratio (b) reduction to a reference beam with fixed SD = 4 subjected to a combine MCMOD

Decomposition for the general case

A39

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Simplified approach by Pedersen

A40

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Determination of stresses in FRC, (Marti, Casanova & Rossi)

A41

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A42

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Fracture energy vs water cement ratio, tensile strength vs water cement ratio, characteristic length vs water cement ratio of FRC

A43

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Fracture zone and real crack in FRC, (Hillerborg, P. E., Int. J. Cem. Comp., 1980)

A44

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FRC Four phases of stress distribution in elastic layer of hinge Phase 0 = state of stress prior to cracking; Phase I – III = states of stresses during crack propagation (Marti, Casanova& Rossi)

A45

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Crack extension resistance

A46

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Graphical illustration of the forward (a) and inverse (b) analysis

A47

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A48

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Possible operating toughening mechanisms in a FRC. Fictitious crack in fibre reinforced concrete

A49

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Softening, hardening and tensile stress vs tensile strain of FRC

A50

Sabah Shawkat © (a, b) cohesive crack model for ductile- brittle materials (c, d) cohesive crack model for quasibrittle materials (concrete) (e, f) quasibrittle material

Stress distribution and softening curves, ( Wecharatana, M.; Shah, S. P & Hillerborg, P. E )

A51

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The effect of superplasticizer on strength of FRC, (Bažant, Z. P. & Oh, B. H)

A52

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The state of equivalent of forces in FRC, (Chan, S.Y.N.; Anson, M.; Koo, S. L.)

A53

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Wacharatana & Shah’s Model (COD Crack Opening Displacement), fibre bridging length over real crack in FRC

A54

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(Hillerborg, P. E)

A55

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A56

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RC rectangular beams subjected by two concetrated loads and design of fictive truss analogy system

A57

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Deﬂection analysis due to concentrated load on FRC beam, SBT program

A58

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what is strain? change in size or shape relative to original state, e.g. change in length relative to original length ε = ΔL / L - dimensionless Is steel? 1. elastic? yes - it has a linear relationship between stress and strain up to the yield stress 2. plastic? yes - after the elastic range it becomes plastic until ultimate failure 3. brittle? no What is the advantages and disadvantages of the steel when used as structural materials? advantages • high strength - yield stress 250-300MPa up to

• good in tension and compression

• high Modulus of Elasticity 200000 MPa - small deformations

• small variability - lower factor of safety • can be easily manufactured in many shapes - rolled, cast

disadvantages • heavy: 7800 kg/m3 • non-flammable but loses strength under heat - needs to be fireproofed • rusts - needs protection (stainless steel possible but expensive) • buckling may be a problem - thin elements • expensive - use eﬃciently e.g. I-beams

1000MPa for high strength wires

Diagrams stress vs strain of prestress steel, conventional steel and concrete

A59

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Diagrams, moment vs curvature and shear force vs shear strain to determine the bending and shear stiffness

A60

Diagonal failure is usually investigated by testing reinforced concrete beams under two-point load. This testing arrangement has the advantage of combining two different test conditions-pure bending between the two loads and constant shear force in the end section.

the formation of inclined cracks. If no shear cracks exist (state I in shear), the shear deformations are usually small and can in most cases be neglected. After the full development of inclined cracking (state II in shear), shear deformations can be quite large, even larger than deformations due to flexion.

Theoretical and experimental analysis of the influence of the short term stationary load on deformation properties of reinforced concrete rectangular beams at different load levels is given. Deflections due to bending moment and shear force were calculated from deformations of the fictitious truss system, using a method based on Williot-Mohr translocation polygons.

The behaviour of reinforced concrete structures under service conditions can be considerably different from linearly elastic behaviour due to the cracking of concrete which, even though it arises only in a limited number of cross sections, modifies the stiffness of the structural elements and therefore leads to non-negligible redistribution of the stress resultants. Reinforced concrete elements subjected to bending are characterized when the bending moment is higher than the first cracking moment, by the formation of cracks which lead to transferring the tensile loads to the reinforcing bars while the concrete comprised between two consecutive cracks is still reacting. This effect is usually referred to as tension stiffening.

measured by means of deform meters, while the lengths of the bases were 140 mm for the upper and lower chords, 203 mm for the diagonals and 140 mm for the verticals.

Sabah Shawkat © The evaluation of the deflection of reinforced

concrete beams is strongly affected by the cracking of concrete. In order to develop a correct calculation of deflection, it is necessary to define an adequate tension-stiffening model and the exact prediction of the values of shear and bending stiffening. The magnitude of the shear strain is highly dependent on

Strains of the upper and lower chords and the diagonals of the truss analogy system were

From the ratio of the geometrical dimensions

L/h = 5.6 (where L is the span, h is the depth of the test beams) it is evident, that the influence of the shearing deformation on the total deflection will be significant.

A61

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Geometry parameters of beams. Reinforced concrete beams subjected to concentrated load

A62

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Determination of the deﬂection of reinforced concrete beams by the means of deformation coeﬃcients and by the author

A63

Sabah Shawkat © The stress - strain diagram for concrete (the conventional stress distribution in the compression zone) is presented normally by the parabola - rectangle curve. According to the design concept with partial safety factors the maximum stress value is α fcd . The factor α = 0.85 takes account of the concrete strength under sustained load which is smaller than the strength

under short term loading. The non-proportional interdependence between stress and strain of the concrete in the compression zone represents an approximation to the real stress distribution in the ultimate limit state. In these cases, only a part of the parabola - rectangular diagram gives the stress distribution in the compression zone which is limited by the relevant strain at the upper fibre.

States in diagram stress vs strain of traditional concrete

A64

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The depth of neutral axis as a function of diagrams, stress vs strain of steel and concrete

A65

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The evaluation of deflections of reinforced concrete beams is strongly affected by the cracking of concrete. It is clear that the crack development directly influences the calculation of the deflection and strain energy.

The bending cracks first appear in the region of the maximum moment, then follows the development of cracks in the shearing forces region. These cracks slightly incline in the direction of principle stress compression trajectories and finally a shear crack (from a new or bending crack)

is formed which prolongs to the compression region and to the tension beam end. In this cracks appears a failure which is called a critical crack. Character of shear crack formation in the zone of shear force acting can have two forms: a) Cracks begin from the tension side of elements as a normal crack in bending region and they further develop in the direction of principle stress compression trajectories. b) Shear cracks appear solitary in the middle zone along the element depth

The development of shearing cracks in RCB

A66

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Three types of diagrams of steel and two diagrams of concrete to define reinforcement in reinforced concrete cross-section

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Using diagram of concrete to define the concrete stress in compression zone

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Diagram stress vs strain of reinforced concrete

A71

References [1] Hillerborg, A. (1980) “Analysis of fracture by means of fictitious crack model, particularly for fibre reinforced concrete.” The Int. J. Cem. Comp. 2(4), 177-184 [2] Jenq, Y. S. and Shah, S. P. (1985) “Two parameter fracture model for concrete.” J.Eng. Mech.-ASCE, 11(10), 1227-1241. [3] Petersson, P.-E. (1981) “Crack Growth and Development of Fracture Zone in Plain Concrete and Similar Materials.” Report No. TVBM-1006, Division of Building Materials, Lund Institute of Technology, Lund, Sweden.

[7] “ Fracture energy and strain softening of concrete as determined by means of compact tension specimens.” Mater. Struct., 21, 21-32. [8] Mindes, S. & Bentur, A.:”Fibre Reinforced cementitious Composites”, 1990 Elsevier Science Publishers Ltd [9] European pre-standard: ENV 1992-1-1: Eurocode 2: Design of concrete structures – part 1: General rules and rules for buildings.

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[4] Hillerborg, A. (1985) “Numerical methods to simulate softening and fracture of concrete.” Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, G. C. Sih and A. DiTomasso, eds., Martinus Nijhoff, Dordrecht, 141-170.

[5] Wittmann, F. H., Roelfstra, P. E., Mihashi, H., Huang, Y.-Y. and Zhang, X.-H. (1987) “Influence of age of loading, water-cement ration and rate of loading on fracture energy of concrete.” Materials and Structures, 20, 103-110. [6] Balaguru, P. & Kendzulak, J.:“ Mechanical properties of Slurry Infiltrated Fiber Concrete (SIFCON). American concrete Institute, Detroit, 1987

[10] Design of Concrete Structure, Norwegian Standard NS3473 (1992), Norwegian Council for Building Standardization, Oslo, 1992 [11] Rossi, P. “Mechanical Behaviour of Metalfibre Reinforced Concretes.” Cement & Concrete Composites 14 , pp. 3-16, 1992 [12] Moranville-Rgourd, M.:“Durability of High Performance Concrete : Alkali-Aggregate Reaction and Carbonation“, High Performance Concrete: From material to structure, 1992 E & FN Spon [13] Hassanzadeh, M.; Haghpassand, A.:”Brittleness of Normal and High-Strength Concrete”, Utilization of High Strength Concrete, Proceedings, Symposium in Lillehammer, Norway, June 20-23, 1993

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[14] Zhou, F. P.; Barr, B. I. G.:” Effect of coarse aggregate on elastic modulus and compressive strength of High Performance Concrete”, Cement and Concrete Research, Vol. 25, No. 1, 1995 Elsevier Science Ltd. [15] Casanova, P. and Rossi, P. (1996) “Analysis of metallic fiber-reinforced concrete beams submitted to bending.” Materials and Structures, 29, 354-361. [16] Holzmann, P.: “ High strength concrete C 105 with increased Fire-resistance due to polypropylen Fibres”, Utilization of High Strength /High Performance Concrete, Proceedings, Symposium in Paris, France, May 29-31 1996

[20] Stang, H. and Olesen, J. F. (2000) “A fracture mechanics based design approach to FRC.”in P. Rossi and G. Chanvillard (eds.), Fiber-Reinforced Concretes (FRC), BEFIB’ 2000, RILEM Publications S.A.R.L., ENS – 61 Av. Pdt. Wilson, F-94235 Cachan Cedex, France, 315-324, proceedings of the Fifth International RILEM Symposium. [21] RILEM-Committee-TDF-162 “Test and Design Methods for Steel Fiber Reinforced Concrete. Recommendations for Uni-axial Tension Test.” (2000), Mater. Struct.,.

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[17] Muller, H. S.: “Creep of High Performance Concrete – Characteristics and Code-Type prediction Model.” Fourth International Symposium on the Utilization of High Strength / High Performance Concrete, 1996, Paris, France [18] Casanova, P. and Rossi, P. (1997) “Analysis and design of steel fiber reinforced concrete beams.” ACI Structural J., 94(5), 595-602.

[19] Stang, H. and Olesen, J. F. (1998) “Evaluation of crack width in FRC with conventional reinforcement.” Cement & Concrete Comp., 14(2), 143-154.

[22] RILEM-Committee-TDF-162 “Test and Design Methods for Steel Fiber Reinforced Concrete. Recommendations for Bending Test (2000).” Mater. Struct., 33, 3-5. [23] RILEM-Committeee-TDF-162 “Test and Design methods for Steel Fiber Reinforced Concrete. Recommendations for Design Method.” (2000), Mater. Struct., 33(3), 75-81.

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B I Structural Loads

B2 Loads You can give four types of load, from which the load cases are combined, namely dead load, snow load, wind load and live load. Dead Load As dead load are considered the constructions own weight and permanent installations, as insulation, roofing and smoke hatches. Snow Load The snow load can be divided into two parts (depending on the selected norm): 1. permanent snow load 2. live snow load

If the mobility is = 0%, all the snow is considered permanent. On the other hand, if the mobility is = 100%, the entire snow load is considered a live load. Wind Load The wind load can at most consist of four load cases. Normally the two following cases suffice (the order has no influence, case 1 can also be suction): 1. wind pressure 2. wind suction Both cases are calculated as a wind load acting on the total length of the construction, where one is acting on the profile sheet as a pressure against the supports, the other as a suction pulling the sheet from the support.

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The permanent snow load is handled as a load case affecting the whole length of the construction. This is taken into consideration when calculating force entities and deflections only if the entity in question increases because of the load.

The live snow load is handled as a separate load case for each span. This means, that the influence of the live snow load on each span on the entity under consideration is separately calculated. For instance the greatest field moment is found in a combination, where the live load is added in the calculated span and the adjoining spans are without live snow load. The division of the total snow load in permanent and live snow loads is given with the feed data mobility (%).

Densities of selected construction materials Materials Density[kN/m3] Metals aluminium 27 copper 87 steel 77 zinc 71 Other materials glass, in sheets 25 Plastics: acrylic sheet 12 polystyrene, expanded, granules 0,25 slate 29

Imposed loads Imposed loads on a building are those arising from occupancy and are principally modelled as uniformly distributed loads. Characteristic values for these are tabulated in relation to building use. In special cases concentrated loads may be relevant, and these are also specified. Imposed loads are generally classified as variable and free. Loads due to moveable partitions and services which may be repositioned are treated as imposed loads. The characteristic values of imposed loads are composed of long-term, medium-term, and short-term components. In practice there is often no need to distinguish between these except where materials are sensitive to time-dependent actions. For example, concrete is subject to creep, and load duration may therefore need to be considered in some aspects of the design of composite structures.

Building occupancy categories A Residential (including hospital wards, hotel bedrooms etc) B Office areas C Assembly areas (subdivided into 5 sections depending on likely density of occupation and crowding) D Shopping E Storage areas The characteristic values of the impose load for areas in residential, social, commercial and administration buildings are provided in table below divided into categories according to their specific uses

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Building occupancy is defined in five categories (A-E) with some sub-divisions as shown in Table below and corresponding characteristic imposed floor loadings are specified. These are identified in Table below. In general, roofs with access should be designed for the same level of imposed load as for floors, but garage and vehicle traffic areas are treated separately

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B10

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B11

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B12

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B13

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B14

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Wind pressure calculation in case of simplified procedure (this refers to such structures which are not sensitive to dynamic excitation and to maximum 200m high buildings): External pressure: wE = qref*ce(ze)*cpe Internal pressure: wi = qref*ce(zi)*cpi where cpe, and cpi are the external and internal pressure factors. where qref reference mean wind velocity ce(ze) exposure coefficient; the function of height from above ground and terrain roughness categories I-IV; The coefficient also modifies the mean pressure to a peak pressure allowing for turbulence ze,zi reference height for local pressure cpe external pressure coefficient

Negative and positive wind pressure on the surfaces of the structure

B15

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Legend for saddle roofs

B16

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Calculation of the positive and negative wind pressure forces on individual walls and roofs of the building.

B17 wind normal to the large face

wind normal to the small face

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Calculate the value of γ0 from the graph due to wind load acting on the two directions, large and small face of the building.

B18

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Action on structures

B19

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The definition of normal and extreme pressure loads on structures

B20

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Coeﬃcients ξ vs T

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Coeﬃcients τ vs H

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Dynamic pressures

B23

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Closed construction with saddle roof and open construction with vaulted roof

B24

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The value of q for Bratislava region depending of height above ground level.

B25

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B26

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B27

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Wind on facade m1

B28

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Wind on facades

B29

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Calculate the horizontal load on individual columns in the industrial hall

B30

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Conception of latice beam

B31

Lateral stiﬀening The wind loads in the side wall of the building are transferred to the stiffening lattices in the end wall through the horizontal lattice in the roof parallel to the side walls. However, the horizontal force of the side wall wind columns is transferred to the primary columns through the roof profile. This way, the eaves section of the side wall can be made lighter. The joints of the stiffening profile must be checked for the loads created by the horizontal forces.

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Design the bracing elements of the end wall. The horizontal load is divided evenly in the end walls, as the building is symmetrical and the bracing in the end walls is similar. In the pressure coefficient of the wind load, the effect of negative pressure must also be taken into account, so Cp=0.6+0.3=0.9. Thus the following value for the horizontal force of the end wall is obtained:

In the building area, the wind velocity is νref. The reference mean velocity pressure qref is determined from the formula: Lateral stiffening

The forces on the columns are determined simply by the area of the load carried. The resistance must be checked separately for two different load combinations, since at this stage it is not known whether the dominant load is the snow load or the wind load.

Roof bracing, horizontal stiffening in the model building, and a beam with semi-rigid joints

B32

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Exposure coeﬃcients Ce when Ct =1 (building stands on level ground), connecting the bracing, the forces on the columns, pressure coeﬃcients for the wall

B33

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Transformation of loads from inclined surfaces into a horizontal direction

B34

Seismic Loads In some parts of the world earthquakes are a very important design consideration. Seismic actions on structures are due to strong ground motion. They are a function of the ground motion itself and of the dynamic characteristics of the structure.

rigidity elements. The links must be able to transmit the horizontal inertia force.Strong ground motion can be measured by one of its parameters, the maximum ground acceleration being the parameter most usually adopted for engineering purposes. These parameters are expressed on a probabilistic basis, i.e. they are associated with a certain probability of occurrence or to a return period, in conjunction with the life period of the structure.

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Diaphragms in a building are the structures which transfer horizontal inertia forces, resulting from the motion applied to the masses of floors and their loading, towards the structures able to contain them. Diaphragms must be structures of low deformability and capable of efficiently distributing the horizontal action between the various vertical resistant structures. Diaphragms may be provided in many ways: concrete slabs, composite slabs, trusses, frames. Diaphragms must be properly linked to the vertical

Euro code 8 (EC8) is a modern design standard for the determination of seismic loads and structural details.The soil movements induced by earthquakes produce vibrations in buildings and, thus, inertial forces in the structures also. These forces are called seismic loads. To bear seismic loads, the building should be able to withstand vertical movements without loosing strength.

The conception behaviour of reinforced concrete frames due to seismic load

B35

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- Possible mechanism of post-elastic deformation for equivalent monolithic moment resisting frames of buildings during severe seismic loading

- Shows mechanisms of post-elastic deformation that could occur in equivalent monolithic moment resisting frames and structural walls due to the formation of plastic hinges during a severe earthquake. The static mechanisms of give designers a reasonable sense for the actual situation. If yielding begins in the columns of a moment resisting frame before it begins in the beams, a column sides way mechanism can form. In the worst case, the plastic hinges may form in the columns of only one

story because the columns of the other stories are stronger. Such mechanism can make very large curvature ductility demands on the plastic hinges of the critical story, particularly for tall buildings. - On the other hand, if yielding begins in the beams before it begins in the columns, a beam sides way mechanism will develop, which makes much more moderate demands on the curvature ductility required at the plastic hinges in the beams and at the column bases. Therefore, a beam sides way mechanism is the preferred mode of post elastic deformation, particularly because ductility can be more easily provided by reinforcing details in beams than in columns.

The conception and behaviour of precast reinforced concrete frames due to seismic load

B36

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The values of dynamic coeﬃcients Cd for a- steel structure, b- concrete structure, ccomposite steel concrete vs steel structure, d- pedestrian bridges

B37

Thermal effects were practically ignored by bridge engineers until the 19th century. With the development of railway construction, long steel bridges have been built, and their behaviour under thermal effects must be considered. Complex joint and support systems were then conceived for these structures to prevent the effects of restrained thermal movements.

In the 20th century, concrete bridges are being built with increasing large spans as a result of the development of design methodologies and construction techniques. The concern with durability problems and the use of more accurate methods of analysis led, in the preceding decades, to the design of these structures with reduced numbers of joints and bearings. With this tendency for more monolithic bridges, the thermal effects began to play an important role in the design and construction process. Several accidents due to inaccurate thermal analysis of bridges have been reported (Moorty and Roeder 1990; Thermal Effects in Concrete Bridge Superstructures 1985)

development of heat of hydration during construction. Exposed structures such as bridges may be subject to significant temperature variation which must be taken into account in the design. If it is not provided for in terms of allowing for expansion, significant forces may develop and must be included in the design calculations. In addition, differential temperatures, e.g. between the concrete deck and steel girders of a composite bridge, can induce a stress distribution which must be considered by the designer. The increase of the temperature of steel and concrete in composite steel-concrete elements, leads to a decrease of mechanical properties such

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as yield stress, Young‘s modulus, and ultimate compressive strength of concrete. Thus, when a steel or a composite structure is submitted to a fire action, its load bearing resistance decreases. If the duration and the intensity of the fire are large enough, the load bearing resistance can fall to the level of the applied load resulting in the collapse of the structure.

Concrete bridge structures are subjected to thermal effects due to the interaction with the environment conditions or due to special effects, like the placement of the hot asphalt on the deck or the

Temperature effects

B38

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The behaviour of fixed beam due to temperature

B39

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Box-Girder cross-section calculation of curvature due to temperature

B48

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Unequal course of temperature along the height of the cross-section of the structure creates the necessary suﬃcient deformation state and subsequent stress of the structure.

B49

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Statically indeterminate beam

B50

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Ununiforme temperture, the cross section of the structure acts on it as an ununiforme load.

B51

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The effect of temperature as structural load on continue reinforced concrete beams and frames

B52

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More dangerous effects usually occur when the temperature changes ununiforme over a short period of time, without much redistribution of stresses across the cross section.

B53

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Free deformation due to temperature

B54

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Deformations due to temperatures

B55

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Secondary effect of temperature

B56

References [01] Deutscher Ausschuss fur Stahlbeton – DafStb (1994): Richlinie fur Hochfesten Beton, Supplement a DIN 1045, DIN 488 and DIN 1055, Berlin, Germany [02] Eibl, J.: Concrete Structures. Euro - Design Handbook. Karlsruhe, 1994 – 96 [03] Edward, G., Nawy, P.E.: Prestressed Concrete A fundamental Approach. Part 1, New Jersey, 1989 [04] Elvery, R., Shafi, M.: Analysis of shrinkage effect on reinforced concrete structural members. ACI Journal, Vol. 67, 1970

[09] Goulet, J.: Résistance des matériaux. aide mémoire, Bordas, Paris, 1976 [10] Grandet, J.: „ Durability of High Performance Concrete in Relation to ‚External‘ Chemical Attack“, High Performance Concrete: From material to structure, 1992 E & FN Spon [11] Grigorian, C. E., Yang, T.-S., and Popov, E. P., ‘Slotted Bolted Connection Energy Dissipators,’ Earthquake Engineering Research Center, University of California, Berkeley, Report No. UCB/ EERC-92/10, July, 1992.

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05] Elliot, K. S.; Torey, A. K.: Precast concrete frame buildings, Design Guide. British Cement Association 1992

[06] FIP Recommendations ´Design of multi-storey precast concrete structures´. 1986 [07] Goto, Y.: Cracks Formed in Concrete Around Deformed Tension Bars, Journal of the ACI, No. 68, April, 1971 [41] Gregor, J. G.: Reinforced Concrete, New Jersey, 1988 [08] Gvozdev, A. A.: Novoje v projektirovanii betonnych i železobetonnych konstrukcij. Moskva, 1978

[12] Gupta, A. K.: Unified Approach to Modelling Postcracking Membrane Behavior of Reinferced Concrete, Journal of Structural Engineering, Vol. 115, No. 4, April, 1989 [13] Gupta, A. K.: Postcracking Behavior of Membrane Reinforced Concrete Elements Including Tension-Stiffening. Journal of Structural Engineering, Vol.115, No. 4, April, 1989 [14] Grigorian, C. E., Yang, T.-S., and Popov, E. P., ‘Slotted Bolted Connection Energy Dissipators,’ Earthquake Engineering Research Center, University of California, Berkeley, Report No. UCB/ EERC-92/10, July, 1992

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C I Methodology of structures

The chapter offers a simple, comprehensive, and methodical presentation of the basic concepts in the analysis of members subjected to axial load, tension, bending, and pressure. The rational design procedure and its applications to axially loaded and twisted bars and beams is described in order to make clear the relation of mechanics of materials to design.

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These graphical presentations are used to make critical evaluations of the load-deformation relations of the strength of materials. The diagrams attempts to fill what the author believes to be avoid in this regard. Emphasis is placed upon the illustration of important principles and applications through diagrams. Above all, an effort has been made to provide a visual interpretation of the fundamental principles, basic equations, concept of stress and the means of which the loads are resisted in typical members.

Bending

Arch

Compression + Tension

Catenary Cable

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Grid

2.Layer Cable Net

Space Dome

Space Frame

3.Layer Cable Net

Shell

Slab

Membrane

Behaviour of conventional and lightweight structures

Calculation of bending according to Clapyron method

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C6 Determination of Internal forces in frame reinforced concrete structure

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Analysis of reinforced concrete walls

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C10 Reinforced concrete footing

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C11 Retaining Wall

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C12 Combined Footing

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C13

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C14 Columns

Punching problem

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C15

Determination of shear connectors

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C16

Steel structure

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C17

Shear stress

Shearing force

Static moment

Sabah Shawkat © Deﬂection due to shearing forces

Deﬂection due to bending moment

Wood

C18

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C19

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C20

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C21 The authors of this methodology, which I present in this chapter are Prof. Schlaich and Prof. Schäfer from Stuttgart. For the first time in the concrete calendar 1984, these methods were presented by the authors and their suggestions concerning the presented methodology were well received, even by the commission for the new version of the CEB Model Code. As we know from the literatures construction in reinforced concrete is first and foremost the implementation of the results of the static calculation and the dimensioning in formwork. The simplifying assumptions on which the static calculation and dimensioning were based must also be taken into account. The construction is not limited to those cross-sections that are examined in the static calculation, but includes all areas of a structure. The purpose and function of the planned supporting structure throughout its entire service life, as well as the production technology and economy, must be considered and processed to a good compromise. In particular, the structure must also be established for actions that have not been calculated.

in the design, not in an incorrect static calculation or standard dimensioning. This is especially true if you also pay for the inadequate construction work due to unnecessarily complicated details. This method should be applicable to all details and be compatible with the standard design methods in order to avoid contradictions and misunderstandings. One of the main principles of this method is that, the load transfer through internal forces in the entire structure must be as uniform as possible.

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The result of the construction and consequently the quality of the structure depends on the experience and care of the engineers involved, on the subjective love of detail. These subjective influences may be the reason why the most frequent cause of damage and deficiency still lies

The designer should recognize that good constructive designing and training can only develop from an intimate understanding of the course of the internal forces in the structure and that this understanding can and must be learned systematically. Consequently he must observe numerous principles and rules that are essentially based on experience. In this way, he contributes to the fact that the supporting structure, manufactured according to his formwork and reinforcement plans, meets the quality requirements with regard to durability, feasibility and economic efficiency. The quality of a building depends on many small details that the designer should not leave to chance or the construction site.

C22 The reinforcement of the concrete has several purposes: - The reinforcement should absorb the tensile forces that occur in the structure as a result of the external loads. The steel inserts thus serve the load-bearing capacity or stability of the structures. - The reinforcement cannot prevent the formation of cracks in the concrete. but it should have an effect. that the cracks in the concrete remain fine under the working loads. It is generally measured so that the greatest crack width does not exceed about 0.3 mm in a dry environment and about 0.2 mm in a moist environment. In the case of an aggressive environment or exposed concrete that is subject to high demands, even smaller crack widths should be aimed for.

The bars must be held securely in their intended position during concreting and compacting. In particular, the concrete cover of the reinforcement must be secured to the formwork using suitable spacers. The reinforcement nets in walls must also be braced against one another so that the concrete cover cannot become too large. The chapter offers a simple, comprehensive, and methodical presentation of the basic concepts in the analysis of members subjected to axial load, tension, bending, and pressure.

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- The reinforcement should provide the structure for the influences that cannot be calculated, for example from differential settlement, fire and other catastrophes. It is used to limit the crack widths from internal or forced stresses, such as those that occur with temperature changes, or shrinkage. - In compression members, the reinforcement serves to increase the load-bearing capacity under pressure or to secure the component against unintentional bending moments and buckling. Pressure reinforcement reduces creep. and shrinkage deformations.

The rational design procedure and its applications to axially loaded and twisted bars and beams is described in order to make clear the relation of mechanics of materials to design.

C23

Figure shows the spread of a central load concentrated on the width a in a strip with the width l. The load spreads practically within a limited (D-) area Dl, which is about the same as long. The intensity of compressive stress and tension stress depends on the ratio of the load application width a to the distribution width l. choice of tension rods.

Sabah Shawkat © The calculation of the value Z can be

This formula also results from the simple model c with the assumption z = l/2. The diagram a/l vs ν shows this approximation in comparison with Z from an elasticity-theoretical calculation

C24

Sabah Shawkat © Area D1 (a) Principal stress image from linear-elastic Finite element calculation; (b) transverse tensile stresses (condition II: (c) and (d) framework models: (e) Bar forces and strut inclination

C25

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For loads F in the corner area D2 they reach a size up to Z1 = F / 3.

Area D2 (a) Stress curve (state I); (b) Framework model, Truss model

C26

Sabah Shawkat © The stress on area D3 is related to that of D1 and is divided into two with large d/l separate D1 areas. The same applies to areas D4 and D2. The area D5 is by far the most common area next to D1.

Area D3 (a) Principal stress pattern; (b) Stress curves (state I); (c), (d) and (e) Framework models; (f) Bar forces and inner lever arm z

C27

Sabah Shawkat © Area D4 (a) Principal stress pattern; (b) Stress curves (state I); (c) and (d) Framework model

C28

Sabah Shawkat © Area D5 (a) Principal stress pattern; (b) Stress curves (state I for d / l = 1; (c) and (d) frame models; (e) bar forces, inner lever arm z and compression angle ν

C29

Sabah Shawkat © The lever arm z of area D6 with attached load does not diff er from that of area D5, if elastic behavior is used as a basis.

Area D6 (a) Principal stress pattern; (b) Stress curves (state I); (c) and (d) Framework models; (e) Bar forces, inner lever arm z and strut angle ν

C30 Reinforced wall subjected to concentrated load

Sabah Shawkat © In the area D7, it can be useful to use a refi ned model according to D7d instead of the simple model in D7e, in order to make the transverse tensile forces Z2 from the spread of the pressure trajectories; in the simpler model, the transverse tensile forces are taken into account as part of the pressure, so that both models ultimately come down to the same thing. With increasing d/l D7e and f, the transition to area D1 (top) and D5 (bottom) gradually takes place.

Area D7 (a) Principal Stress Image; b. Stress curves (state 1); (h) bar forces and internal lever arm z, (c) to (g) bar models, (h) bar forces and inner lever arm z3

C31

Sabah Shawkat © The model for areas D8 is obtained by combining two models D5c, when the ratio d> 2l. With smaller d / l, the compressive forces can no longer be evenly distributed over the entire width of the wall support; from d / l <1/2 the left and right side separate into two areas D4.

Area D8 (a) Principal stress image; b. Stress curves (state 1); (c) and (d) Frame models

C32

Sabah Shawkat © The model for areas D9, combines the modules D1c and D5c.

Area D9 Principal stress pattern; b) Stress curves (state I); c) Framework model; d) The length of the D9 area in relation to the. Edging of the entire wall; (e) Bar forces and inner lever arm z

C33

Sabah Shawkat © Correspondingly, in area D10, the models of areas D3d and D8c can be found again. From d/l> 2, the upper and lower halves of D10 are identical to D9. The models and forces in D9 and D10 only apply to the middle spans of a multi-span wall trimmed either by F or p Rigid D9d. In the area of the lateral edge, the models and bar forces depend signifi cantly on the projection lK and the unevenness of the load. These disturbances „in the vicinity of the lateral edge have an eff ect on the length d into the middle spans.

Area D10 (a) Principal stress pattern; (b) Stress curves (state (c) framework model

C34

Sabah Shawkat © a single D-area (typical area D5) occurs in many diff erent structures, four examples are given here The propagation of cable forces in the top chord plate of a bridge, a wall with large openings. a hollow box girder with forces from the introduction of the clamping force and a detail of the internal forces of a rectangular beam, which shows that the stirrups must be closed.

C35

Forces from prestressing (anchor forces V, defl ection forces u, friction forces R). (a) forces on the tendon; (b) Forces on the concrete

It is advisable to take a fundamental approach to the preload; this approach helps to better understand the real behavior of prestressed structures. Artifi cial forces are generated by the prestressing with the help of hydraulic presses, on the one hand these forces act as a load on the prestressing steel, on the other hand as a load on the reinforced steel concrete construction). The loads on the prestressing steel and on the reinforced concrete are equal, but act in the opposite direction. The engineer selects the tendon direction and the type and size of the prestressing, then these artifi cial loads infl uence the load paths and sectional sizes or stresses as a result of the external loads (dead weight, structural loads, etc.) favorably and as eff ectively as possible.

they cause. In these load cases, the prestressing steel also contributes to the resistance of the crosssections or structural members.

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It is now proposed, that these prestressing loads as permanent loads, that never change again, after the jack has been removed. All tension changes in the prestressing steel. that arise after removing the press, are assigned to those load cases, which

The idea that the prestress itself changes under live loads because the stress in the prestressing steel increases or decreases as a result of the bond with the concrete is misleading. The stress changes in the prestressing steel due to creep are corresponding Shrinkage and relaxation (often referred to as „loss of tension“) and they can be treated as a separate load case. B area - Bernoulli - Navier hypothesis, with linear process D area- Static discontinuity or geometric discontinuity, with non-linear process

C36

Sabah Shawkat © Similar loads in diff erent structures a) Wall-beam support on 3 supports („bend“); b) End of a girder or a wall with the anchorages of 3 tendons (split tension „and“ edge tension „)

RC Wall subjected to uniform loads from above, model; dotted lines indicate pressure and solid line indicates tension, diagram of stress in tension and in compression, model for the fracture state.

C37

Sabah Shawkat © Wall panel with load attached below, Double wall panel model with inner lever arms according to elasticity theoretical stress distribution, simplifi ed model and the fi gures shows area of infl uence of loads to be suspended (dead weight and loads below), From the pictures we understand that the lines

that are marked as interrupted will represent a reinforcement that will be designed based on the calculation of compressive stress and solid lines will represent the proposed tensile reinforcement based on the calculation of tensile stress of reinforced concrete walls

C38

Sabah Shawkat © RC Wall with extension: two models for various loads

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Sabah Shawkat © RC Wall with large opening, loads acting on the upper side of wall, Load path with tension and compression lines.

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Sabah Shawkat © Framework models of typical D areas of a box girder prestress bridge. Bridge supported by Pillar with a central bearing

C41

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Openings in panels of a box girder bridge, simplifi ed models

C42

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Diagram of deﬂections on beams due to uniform and concentrated load

C43

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Deﬂection calculations for a cantilever beam by the conjugate beam method

C44

Sabah Shawkat © A simple beam that works to carry the shear stress must also be designed for the bending moment. The failure due to bending moment occurs as the beam defl ects and either the bottom fi bres pull apart and fail in tension or the top fi bres crush and fail in compression. This is illustrated in Figure for Bending Moment. A beam carries load (usually horizontally) from fl oors and roofs to columns. A simple beam must be designed to resist both shear and bending moments.

Shear stress in a beam goes to failure along a plane, perpendicular to the beam, in which the load side of the beam displaces downward See Figure below. Shear for an illustration. It is important to understand that shear failures tend to happen quickly, without much notice or warning (i.e. not much movement, creaking, defl ection, etc.). Therefore, building codes tend to require a higher factor of safety against shear failures when stipulating the allowable stresses.

Deformations due to bending Moment, shearing force and Normal force in beam structure

C45

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When a beam is loaded, it defl ects. The new position of its longitudinal centroid axis is called the elastic curve. At any point of the elastic curve, the radius of curvature is given by R=EI/M Where M= bending moment at the point, E = modulus of elasticity, I = moment of inertia of the cross-section about the neutral axis. Since the slope dy/dx of the curve is small, its square may be neglected, so that, for all practical purposes, 1/R may be taken equal to d2y/dx2, where y is the defl ection of a point on the curve at a distance x from the origin of coordinates, hence, R=EI/M may be rewritten

M=EI(d2y/dx2). in which θA and θA are the slopes of the elastic curve at any two point A and B. It should be noted that the integral represents the area of the bending-moment diagram between A and B with each ordinate divided by EI. Since the defl ection at mid-span for this loading is the maximum for the span, the slope of the elastic curve at the centre of the beam is zero, i.e., the tangent is parallel to the undefl ected position of the beam. Hence, the deviation of the either support from the midspan tangent is equal to the defl ection at the centre of the beam.

Simply supported beam subjected to concentrated load - uniform load

C46

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Calculation of bending moments over supports B and C due to diﬀerent uniform load cases

C47

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Stresses and deformations of structural members due to uniform and concetrated load

C48

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States of stability and failure in frame structure

C49

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Forces in suspention bridge

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A tale of lightweight structures

C51

25N

If there is a larger angle in the tension

Sabah Shawkat © in opposite directions then it will take more load tohold weight, and if the

angle is smaller, then it will take less load to hold the same weight.

The funicular concept can be best described and visualized with cables or chains, suspended from two points, that adjust their form for any load in tension or also be compressed like arches, where the form of cable becomes the form arch upside-down.

in tension, but are unstable under wind uplift, for stabilizing the system we provide anticlastic curvature shape because increased curvature increases stability. Also cable trusses evolved from need to stabilize suspension structures against wind uplift and unbalanced gravity loads.

Suspended structures are used for longspan roofs, where the horizontal thrust is resisted by a compression ring or by infrastructures. This type of structures eff ectively resists gravity load

A minimal surface may be anticlastic or fl at covers any boundary with a minimum of surface area, equal and opposite curvature at any point, and uniform stress throughout the surface.

Structural principal, ropes helds by tension

C52

l=L(1+8/3(d/L)2) H=(qL2/8d) T=H(1+(64.d2.x2)/L4)1/2 ∆l=(H l/AE) (1+(16/3)d2/L2) ∆d=∆l/ (16/15)(d/L)(5-24d2/L2 ) ∆d= ∆L (15-40 (d2/L2)+288 (d4/L4)) /16 (d/L) (5-24(d2/l2 ))

Mmax =0.161 PL2 (4/α( Eld/q L4))1/2 where α is the equivalent modulus of foundation, approximately 1100kN/m2

Sabah Shawkat © Mmax occure when 2a/L= π/4 (4/α (Eld/q L4 ))1/2

The structural system of the cable-stayed bridge or suspension bridge, by decreasing the distance between the cable supports, the deck can be made slenderer as the bending moments are reduced. Therefore, the structural designer greatest goal is always to make the deck as slender as possible, because at the end its design will be elegant and aesthetically pleasing. Cable supported bridges, which can be built in a great variety of forms and with considerable elegance, have great potential.

Suspension structures

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The eﬀect of tension force on simple supported beam

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The eﬀect of compression force on simple supported beam

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The principle of structural reciprocity

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Sabah Shawkat © Structural models have three scales 1. Geometric scale relates model dimensions to original dimensions 2. Force scale relates models forces to original structure 3. Strain scale relates model strain (displacements) to strain in the original structure

Diagram of reactions in frame structures

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Calculation of bending moments and shearing forces on continuous beam due to uniform load

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Sabah Shawkat © Diagram in which bending moment is plotted along the span is called a bending-moment diagram. Consider the simply supported beam or continuous beam subjected to a downward-acting, uniformly distributed load gd (units of load per unit length). The support reactions Ra and Rb may be determined from equilibrium equations, Ra may then be found from equilibrium of vertical forces. The

distribution of stress within a beam of any material depends on the confi guration of the applied load. The action of a uniformly distributed load is to bend the beam downwards and cause tensile stress to be set up in the lower half of the cross-section and compressive stress in the upper half.

The calculation of bending moments over continuous beam due to uniform load

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Caculation of deﬂections and stiﬀness due to concentrated and uniform load over simple supported beam

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Procedures for calculation of equivalent loads

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Arch bridge

C63 The terminology for arch bridge, L is span, f is rise, support area is springing line, pick point of arch bridge is crown. We can have divided the arch bridge as conventional arch bridge with road way supported above arch or tied arch with suspended roadway. The girder can be design to resist the horizontal component of the arch reaction; this arrangement is called a tied arch. Suspending the roadway from the arch may be an appropriate solution for low-level crossings or when suitable foundation material for conventional arch abutments is not available. Economy and elegance are nevertheless diffi cult to achieve when this type of the bridge is built of reinforced and prestressed concrete. Arch bridges with suspended roadway can be more successfully designed in structural steel. For this reason, we show the calculation of an arch steel bridge as example to understand the process and to fi nd the forces in relation with angles of the members.

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The arch, columns, and deck girder constitute a frame system. The moments in the frame system can be divided into two components: fi xed system moments and fl exible system moments. Fixed system moments are produced when vertical deformations of the arch are restrained and are thus equal to the continuous beam moments in the girder. Flexible system moments correspond to vertical displacements of the arch and are, in general, shared by arch and girder.

Two idealized limiting cases are possible: stiff arches, which resist the entire fl exible system moment with no participation of the girder, and deck-stiff ened arches for which the entire fl exible system moment is resisted by the girder. Moments due to arch displacements can be further divided into dead load and live load components.

Arch bridge

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Simply supported

Gerber type

Continuous beam bridge

Frame bridges

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Cable stayed bridge

Suspension bridge

Main types of bridges

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Cable Stay and Suspension Bridges

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Calculation of M,M´

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Inﬂuence lines

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Inﬂuence lines

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Inﬂuence lines

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Inﬂuence lines

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Inﬂuence lines

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Inﬂuence lines of Gerber beam

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Inﬂuence lines

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The pictures show structural elements that are loaded by a horizontal force such as the wind, also the way of loading that acts on the structure tends to turn and destabilize the whole structural system. The occurrence of a reaction in the supports and the creation of the opposite moment which will rotate in the opposite direction by the moment which creates the result of external loading in our case is a horizontal force due to wind or earthquake.

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The load that acts on the structure tends to reverse and destabilize the entire structural system. The construction will be stabilized when the moments reach the same value and the opposite sign.

Stability of structures subjected to lateral forces

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Transformation at an inclined sectional grades to the inclinations m/m

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Sabah Shawkat © Verifi cation of stresses in individual structural elements which are loaded with uniform and concentrated force. A simple beam with a uniform load, a column which is a load by a concentrated force, and a shell or an arch beam which is loaded with a uniform load.

The dimensioning of the element

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States of static schemes in bridges design

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Calculation of bending moment at point B, due to uniform continuous distributed load and uniform declining distributed load on beam ﬁxed at one end and supported at the other

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Calculation of bending moment at point B, due to partily uniform continuous distributed load, and load increasing to one end, on beam ﬁxed at one end and supported at the other

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Calculation of bending moment at point B, due to concentrated load at any point and triangle uniform load on beam ﬁxed at one end and supported at the other

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Calculation of bending moment at point B, due to load increasing uniformly at centre, triangle uniform load at any length on beam ﬁxed at one end and supported at the other

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Caculation of bending moment due to uniform load and concentrated load at any point on beam ﬁxed at both ends

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Calculation of bending moment at B, due to concentrated load at any point and moment on beam ﬁxed at one end and supported at the other

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Calculation of bending moment at A and B, due to uniform continuous distributed load and partly uniform distributed load and uniform declining distributed load increasing to one point on beam ﬁxed at both ends

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Write bending moments expression due to load increasing at the mid-span of the beam and partly uniform distributed load at any length on beam ﬁxed at both ends

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Write bending moments expression due to concentrated load at any point on beam ﬁxed at both ends

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Calculation of bending moment at A and B, due to uniform continuous distributed load, partly uniform distributed load, uniform declining distributed load on beam ﬁxed at both ends

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References [1] Comité Euro-International du Béton (CEB): Concrete Reinforcement Technology. Bulletin d‘Information N „140, 1983.

[8| Collins, M. P. and Vecchio, F.: The Response of Reinforced Concrete to Inplane Shear and Normal Stresses. Publication No. 82-03, University of Toronto, März 1982.

[2] Euro-International du Béton Committee (CEB): Industrialization of Reinforcement in Reinforced Concrete Structures. Bulletin of Information No. 164, 1985.

[9] Design of Concrete Structures for Buildings. CAN3-A23.3-M84. Canadian Standards Association, Rexdale, Ontario, 1984.

[3] ACI-Committee (H. Hllsberg): Formwork of Concrete. Journal of the American Concrete Institute.

[10] Schlaich, J. and Schäfer, K.: Zur Druck Querzug- Festigkeit des Stahlbetons. Beton- und Stahlbetonbau 78 (1983), Heft 3, S. 73-78.

[4] Konig, G.: Control of Cracks in Reinforced Concrete and Prestressed Concrete. Abhandlung I des 10. Intern. Kongresses der F1P in New Delhi New Delhi. 1986, pp. 259-268.

[11] Collins. M.-P. and Mitchell, D.: Shear and Torsion: Design of Prestressed and Non Prestressed Concrete Beams. PCI-Journal Vol.25, no. 5, Sept./ Oct. 1980. pp. 32-100.

[5] Schlaich. J. and Scheef, H.: Beton- Hohlkastenbrucken. Structural Engineering Documents N ° ld. 1VBH. Zurich. 1982.

[12] Nilsson, I.H. E.: Reinforced concrete corners and joints subjected to bending moment. National Swedish Building Research. Document D7, 1973. [13] Leonhardt. F. and Walther. R.: Wandartige Träger. DAIStb., II. 178. Verlag W. Ernst and Sohn. Berlin, 1966.

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[6] Marti, P.: Basic tools of reinforced concrete beam design. ACI-Journal, V. 82, Jan. - Febr. 1985. S. 4656. [7] March. P.: Truss Models in Detailing. Concrete International. Vol7, N ° 12, Dec. 1985, pp. 66-73.

[14] Schlaich. J. and Leonhardt. F.: Flat conical bowls for antenna plate shapes on sendetiurmen. Beton- und Stahlbetonbau 62 (1967), 11.6, pp. 129133.

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D I Reinforced Concrete

Reinforced concrete (RC) is one of the most important building materials and is widely used in many types of engineering structures. The economy, the efficiency, the strength and the stiffness of reinforced concrete make it an attractive material for a wide range of structural applications. The ultimate objective of the designer is to create a structure that is safe and economical.

instead of being uniformly distributed. The concrete beam strength is increased greatly by embedding steel in the tension area. When steel reinforcements in concrete help carry imposed loads, the combination is reinforced concrete. What are the advantages and disadvantages of the reinforced concrete when used as structural materials:

The choice of building materials depends on various factors, such as strength, spanning capabilities, environmental conditions, economy, and aesthetics. However, the structural performance of a material is primarily dictated by strength and stiffness. Concrete is strong in compression, but relatively weak in tension. The reverse is true for slender steel bars. When concrete and steel are used together, one makes up for the deficiency of the other. The most common type of steel reinforcement employed in concrete building construction consists of round bars, usually of the deformed type, with lugs or projections on their surfaces.

Advantages - medium strength - yield stress 20-50 MPa - medium Modulus of Elasticity 20000 - 30000 MPa - medium deformations - non flammable - good sound proofing - use for sound isolation

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The purpose of the surface deformations is to develop a greater bond between the concrete and the steel. From the structural engineering viewpoint, the three main elements that support live loads in a building are tension members, compression members, and bending members called beams. Beams command the most study, because the bending stress varies over the beam cross section,

(floors) - can be formed into many shapes - waterproof if made properly - else needs protection - generally inexpensive - forms the fabric.

Disadvantages - heavy: 2400 kg/m3 - large variability - lower factor of safety - slow construction. Usage - medium spans - frames, slabs, shells, footings, retaining walls.

Sabah Shawkat © To understand how structures work, a few basic concepts must be explained. A structure must be designed to resist the likely forces it will encounter and not fail or deflect too much. The common forces are snow load, wind load, earthquake load, dead load (the actual weight of the structure itself) and live load (people or stored materials). The building code generally sets the limits for those various design loads.

But the best place to begin an understanding of simple structural analysis is not in the building codes and the stipulated loads, but in knowing how simple structural elements work and fail. Columns are defined as vertical structural elements. Column transfer load from a roof or a floor down to a foundation. For a simple column, most of that load is an axial force that transfers downward. That axial force (which may be caused by snow, dead and live load) will given in kN.

Topology of reinforced concrete members

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Positioning the neutral axis of reinforced concrete

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Positioning the neutral axis of reinforced concrete

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Preliminary design cross-sectional thickness of reinforced concrete slab structures uniform loading (dimensions rounded to 10mm)

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Preliminary design cross-sectional dimension of reinforced concrete beams and frames structures uniform loading (dimensions rounded to 50mm)

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Boundary conditions of columns and design of reinforcement to RC frame

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Calculation of bending moments on continuous beam according to 3M Claperon method

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Permissible stresses - example

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Permissible stresses - example

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Permissible stresses - example

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Permissible stresses - example

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Sabah Shawkat © Curved Beams Structural members, such as arches, crane hooks, chain links, and frames of some machines, that have considerable initial curvature in the plane of loading are called curved beams. Unlike the condition in straight beams, unit strains in curved beams are not proportional to the distance from the neutral surface, and the centroid axis does not coincide with the neutral axis.

Hence the stress distribution on a section is not linear. - Curved beam subject to uniform load over the full span of end moment fixed beam (gd + vd ) [kN/m]. - Concentrated load at midspan of end moment fixed beam P [kN] - Circle Closed Beam on n Supports

Circle closed beam on n supports

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Sabah Shawkat © Uniaxial tension Fibers having a length l and a circular cross section with a diameter d corresponding to a volumetric reinforcement ratio Vf are considered. In the Figure are presented assumptions valid for aligned fibers:

• the embedded length L of the shorter ends of the fibers bridging the crack occurs between 0 and l/2 => the average embedded length = l/4 • a constant frictional bond strength τfu is acting along the embedded shorter ends of the fibers

Cracks and design of reinforcement to the corner of RC frame to prevent the cracks

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Sabah Shawkat © The cracks that forming a reinforced concrete beam can be due to flexure or a combination of flexure and shear. Flexural cracks start at the bottom of the beam, where the flexural stresses are the largest. Inclined cracks, also called shear cracks or diagonal tension cracks, are due to a combination of flexure and shear. Inclined cracks must exist before a shear failure can occur. In most reinforced concrete beams, however, flexural cracks occur first and extend vertically in the beam. These alter the state of stress in the beam and cause a stress concentration near the tip of the crack. In time, the flexural cracks extend to become flexure-shear cracks.

Cracks and diagram of bending moments of RC frames

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Cracks vs stresses in reinforced concrete frames

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Sabah Shawkat © Almost all compression members in concrete structures are subjected to moments in addition to axial loads. Although it is possible to derive equations to evaluate the strength of columns subjected to combined bending and axial loads, the equations are tedious to use. For this reason, interaction diagrams for columns are generally computed by assuming a series of strain distributions, each corresponding to a particular point on the interaction diagram, and computing the corresponding values of Nsd and Msd. Once enough such points have been computed, the results are summarized in an interaction diagram.

Critical zone and design of reinforcement to RC columns

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Diagram of concrete and steel for calculation of compression zone

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Diagram of shearing forces and diagram of moment vs curvature in reinforced concrete beams

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Interaction diagram, axial load vs bending moment of RC members

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Interaction diagram of concrete column Strain compatibility method - Point 1- is the top point on the interaction diagram represent the maximum axial compression usable load, where the corresponding moment will be zero (M=0). - Point 2- corresponds the point where the force in tension reinforcement is equal zero (zero tension), so the strain at the level of reinforcement εs = 0 at once face and crushing of concrete at the other.

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- Point 3 - is balance failure- where the strain of concrete εc reaches the maximum value of compression strain εc = 0.0035 and the tensile strain at the level of tension steel at opposite side reaches the yield value εs = fyd/Es

- Point 5- illustrates the stage where the concrete in tension zone is ignored due to cracks and the strain at the level of reinforcement reach his yield value, and the strain εc of concrete reach the maximum value εc = 0.0035.

- Point 6- represent the pure tension in concrete the section is completely cracked, where the force of concrete is neglected completely so the axial tensile capacity of the corresponding moment will be zero, and the total force acting at centroid of section is divided by the reinforcement at upper and lower of concrete section. For a symmetrical section the concrete is ignored.

Interaction diagram of RC member cross-section and diagrams steel and concrete

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Transverse Reinforcement

Longitudinal Reinforcement

1. The spacing of the transverse reinforcement along the column should not exceed the lesser of the following three distances: - 20 times the minimum diameter of the longitudinal bars

This clause deals with columns for which the larger dimension h is not greater than 4 times the smaller dimension b. Bars should have a diameter of not less than 8mm.

2. The diameter of the transverse reinforcement (links, loops or helical spiral reinforcement) should not be less than 6 mm or one quarter of the maximum diameter of the longitudinal bars, whichever is the greater. 3. The transverse reinforcement should be anchored adequately.

The area of reinforcement should not exceed 0,04 Ac outside lap locations unless it can be shown that the integrity of concrete is not affected, and that the full strength is achieved at ULS. This limit should be increased to 0,08Ac at laps. For columns having a polygonal crosssection, at least one bar should be placed at each corner. The number of longitudinal bars in a circular column should not be less than four.

Reinforced concrete column with critical zone

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Sabah Shawkat © Structural members include beams, columns, girders, walls, footings, and slabs. Each of these different structural members interacts with one another to a considerable degree, thus forming a monolithic whole.

2. In structural language, the loads are said to stress the structure which strain under stress. 3. A structure will always choose to channel its loads to the ground by the easiest of many paths available.

Structural systems 1. The purpose of structure is to channel the loads on a building to the ground.

4. Since all structural actions consist of tension and /or compression, all structural materials must be strong in one or both.

Structural system of reinforced concrete members

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The minor and major axes of the ellipses coincide with the directions of maximum compression and tension at each location. This allows the directions of the maximum tensile and compressive stresses (the principal stresses) to be plotted Figure a. Thus, at mid-span the direction of stress is parallel to that of the beam. Towards the ends of the beam the direction of the tensile and compressive stresses become progressively more inclined to the axis of the beam and the tensile and compressive stress lines cross each other. The material in these regions is stressed simultaneously in tension and compression in two orthogonal directions.

Failure eventually occurs due to the formation of a diagonal crack which is not crossed by the reinforcement. This type of failure is called a shear failure because the degree of inclination of the principal stress lines causes a shearing action on the cross-section rather than a simple bending action. Shear failure can be prevented by shaping the reinforcing bar. The beam depicted in Figure eventually fails due to the formation of an inclined crack at the end of the beam which is not effectively crossed by the reinforcement. This type of failure is called a shear failure.

The shear load capacity of reinforced concrete beam

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The shear load capacity of reinforced concrete beam

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Sabah Shawkat © Permissible ratio of effective height of span to effective depth of beam resp. slab for simplified analysis of deflection limit

Design of reinforcement to reinforced concrete cross-section

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Bending moment diagrams of one-way and two-way RC slabs subjected to uniform load

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Diagrams of bending moment due to uniform load in RC slabs

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Diagrams of moment due to uniform load in circle RC slabs

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Diagrams of moment due to uniform load in circle RC slabs

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Sabah Shawkat © A two-way slab is a concrete panel reinforced for flexure in more than one direction. In case of the simply-supported on four sides and carries a uniformly distributed load, in additon to the bending moments, the slab elements are also subject to twisting moment. In this case the torsion in the slab elements would cause the four corners of the slab to lift off from their supports. In practice floor

slabs in multi span structures are usually continuous from one span to the next and integral or firmly held down on their lines of supports so that lifting of the corners cannot occur. The fixing of the slab at the supports and the effect of the torsion considerably reduces the bending moment at the center of the slab compared to that in the simply supported slab.

Diﬀerent types of boundary conditions in RC slabs subjected to uniform load

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One-way RC slab-ribbed, RC waﬄe slab, RC ﬂat slab and two-way RC slab

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Sabah Shawkat © A one-way reinforced concrete slab is a flexural member that spans in one direction between supports and is reinforced for flexural only in one direction. If a slab is supported by beams or walls on four sides, but the span in the long direction is more

than twice that in the short direction, most of the load will be carried in the short direction; hence, the slab can be designed as a one-way slab. One-way slabs are generally considered to be a series of shallow beams of unit width (1m) where is no torsion.

The calculation of bending moments in one-way RC slab and in cantilever RC slab

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The calculation of bending moment in RC T beam

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Finite element analysis is a powerful computer method of analysis that can be used to obtain solutions to a wide range of one- two- and three-dimensional structural problems involving the use of ordinary or partial differential equations. For the majority of structural applications, the displacement FE method is used, where displacements are treated as unknown variables to be solved by a series of algebraic equations. Each member within the structure to be analysed is broken into elements that have a finite size. For a 2D surface such as a flat slab, these elements are either triangular or quadrilateral and are connected at nodes, which generally occur at the corners of the elements, thus creating a ‘mesh’. Parameters and analytical functions describe the behaviour of each element and are then used to generate a set of algebraic equations describing the displacements at each node, which can then be solved. The elements have a finite size and therefore the solution to these equations is approximate; the smaller the element the closer the approximation is to the true solution.

Lord, and in 1930 the use of flat slabs was codified in the 1930 London Building Act4. The term ‘flat slab’ has no universal definition. Euro-code 2 defines flat slabs as slabs supported on columns. For the purpose of this guide, a flat slab is considered to be a reinforced concrete slab of constant thickness, which could include drop panels. However, this guide does not specifically discuss how to model drop panels. If the area of the column has been modelled, then realistic shear stresses can be obtained, but some engineering judgement may be required in using them because there will be peaks which may exceed the design limits in the codes. Some software can undertake the punching shear checks and design of the reinforcement.

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The flat slab was conceived as a structural system in the earliest days of reinforced concrete development. Credit for inventing the flat slab system is given to Claude Allen Porter Turner, and his system was described in Engineering News in October 1905. Further development of the flat slab method was carried out by Robert Maillart and Arthur

The design of flat slab floors is usually governed by the serviceability requirements. Deflection is influenced by many factors, including the tensile and compressive strength of the concrete, the elastic modulus, shrinkage, creep, ambient conditions, restraint, loading, time, duration of loading, and cracking. With so many influences, and many which are difficult to accurately predict, the deflection calculation should be regarded as an estimate only.

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Sabah Shawkat © Reinforced concrete slabs with long spans extending over several bays and only pointsupported by columns, therefore without any beams, are designated as flat slabs. This type of constructions offers a variety of advantages, from the case of constructions (formwork and reinforcement) through to their flexibility in application. In a flat in which all tendons are concentrated along the column lines and cross in the idealized punching cylinder (support strip

method), the bending moments mx can be computed using the elastic theory of thin plates by means of a finite Element program. In the zone of the supports, not only large bending moments occur but also very large vertical forces. The combination of high bending moments and punching forces limits the application of conventionally reinforced slabs. Prestressing improves the structural behaviour of a flat slab structure considerably.

Calculation of bending moments in RC ﬂat-slab

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Sabah Shawkat © Brackets and corbels are cantilevers having shear span to depth ratio, zh / hc, not greater than unity. The shear span zh is the distance from the point of load to the face of support, and the distance hc shall be measured at face of support. The corbel shown in Figure below may fail by shearing along the interface between the column and the corbel, by yielding of the tension tie,

by crushing or splitting of the compression strut, or by localized bearing or shearing failure under the loading plate. The depth of a bracket or corbel at its outer edge should be less than one-half of the required depth hc at the support. Reinforcement should consist of main tension bars with area Ast and shear reinforcement with area Ash

Corble beam and critical section in RC ﬂat slab

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Sabah Shawkat © The slab with shear reinforcement also displays spalling of the concrete cover after failure. However, the slab is in this stage primarily carried by the bent-down bars which intersect the failure shear crack. The residual load capacity is, thus, governed by the bent-down bars. The load in the post-punching stage could have increased until the yield stress is reached in all bent-down bars. Hence, the use of shear reinforcement consisting of bent-down bars not only improves the ductility and the punching

shear strength, but also improves the residual load capacity of the slab after punching failure. Where punching shear reinforcement is required it should be placed between the loaded area/column and 1.5d inside the control perimeter at which shear reinforcement is no longer required. It should be provided in at least two perimeters of link legs. The spacing of the link leg perimeters should not exceed 0,75d.

Design of reinforcement in critical section to prevent the punching in reinforced concrete ﬂat slab

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Sabah Shawkat © In modern construction, where there is generally a requirement to minimise depth, the use of wide, shallow band beams is common. The beams, which are either reinforced or post-tensioned, support the one-way or two-way spanning slab and transfer loads to the column.

large spans can be economically constructed. The one-way spanning ribbed slab provides a very adaptable structure able to accommodate openings. For long two-way spans, waﬄe slabs give a very material-efficient option capable of supporting high loads.

For longer spans the weight of a solid slab adds to both the frame and foundation costs. By using a ribbed slab, which reduces the self-weight,

Diﬀerent types od reinforced concrete slabs

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The flat plate is the simplest form of twoway slab - simplest for analysis, design, detailing, bar fabrication, placing, and formwork. A flat plate is defined as a two-way slab of uniform thickness supported by any combination of columns, without any beams, drop panels, and column capitals. Flat plates are most economical for spans from 4,5 to 7,5 m, for relatively light loads, as experienced in apartments or similar building. Transfer of Shear and Moments to Columns: Lateral loads, as well as unbalanced gravity loads, cause transfer of moments between the slab system

and supporting columns. This total unbalanced moment Mf must be resisted by the columns above and below the slab in proportion to their stiffness. A portion, Mfb of this total unbalanced moment, is considered to be transferred to the columns by flexure and the second portion Mfv through shear. The lateral distribution of moment become: - for positive moment, column strip 60 %, middle strip 40 % - for negative moment at the edge column, column strip 100 % - for interior negative moments, column strip 75%, middle strip 25 %

Deﬁnition of column strip in reinforced concrete ﬂat slab

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Sabah Shawkat © To obtain the load effects on the elements of the floor system and its supporting members using an elastic analysis, the structure may be considered as a series of equivalent plane frames, each consisting of vertical members – columns,

horizontal members - slab. Such plane frames must be taken both longitudinally (in x-direction) and transversely (in y-direction) in the building, to assure load transfer in both directions.

Deﬁnition of equivalent strip load in RC ﬂat slab

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Sabah Shawkat © In the vicinity of columns, the load tends to punch through the slab - the cracking occurs along the surface of a truncated cone or pyramid in the slab around column. The shear force Vsd , causing punching shear may be computed as the net upward

column reaction less the downward load within the area of slab enclosed by the perimeter of the critical section. The critical section for punching shear is at the distance d, from the face of the support.

Failure due to punching in critical section of RC ﬂat slab

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The area of punching in ﬂat reinforced concrete slab

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Tools to prevent the punching in reinforced concrete ﬂat slab

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Sabah Shawkat © Stairs and their Types: Stairs lead from floor to floor. They are of several types. The common ones are: (1) a sloping slab spanning from one floor to a landing or another floor (2) a sloping slab carried on sloping beams from one floor to another or to a landing.

Typical reinforcement details are given for these staircase on Figures below. The load for which these staircase is designed varies with the type of building. There are a number of other types such as stairs cantilevered from a side wall, spiral stairs with sides cantilevered out from a central column and free-spanning spiral stairs. They can be easily designed and detailed.

Design of reinforcement in reinforced concrete stairs

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Sabah Shawkat © The loads acting on all structures erected on the ground have to be transmitted to the supporting soil. The part of structure, usually built below the ground surface, which interacts with soil base and effects the transfer of loads from the parts above (superstructure) to the soil is identified as the foundation structure or substructure. In reinforced concrete structures, the loads from the superstructure are brought to the foundation level mostly through

compression members such as columns, walls and piers. The average service load stresses in these compression members are usually in the range of 7-20 MPa, whereas the allowable bearing pressure on the soil base may range from 200 to 500 kPa and may be even less. Thus the safe transfer of the high intensity loads to the relatively weaker soil is the function of the foundation structure.

Circul and hexagonal reinforced concrete footings

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Sabah Shawkat © Combined footings carry two or more columns that are either so close to each other that their individual footings would overlap or where a column is too close to the property line and would cause a large rotation on the single footing due to eccentric action. The shape of the combined footing

should be designed do that only uniform pressure is generated. In other words, to avoid rotation and unequal soil pressure, the centroid of the bearing area of the combined footing should coincide with the resultant of the loads acting on the footing.

Combined footings, design of ﬂextural reinforcement

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Sabah Shawkat © If the bearing capacity of the upper soil layers is insufficient for a spread foundation, but firmer stratum is available at greater depth, piles are used to transfer the loads to these deeper stratums. Piles are generally arranged in groups or clusters, one under each column. The group is capped by a spread footing or cap that distributes the column load to all piles in the group. Reactions on caps act

as concentrated loads at the individual piles, rather than as distributed pressures. If the total of all pile reactions in a cluster is divided by area of the footing to obtain an equivalent uniform pressure, it is found that this equivalent pressure is considerably higher in pile caps than for spread footings. Thus, it is in any event advisable to provide ample rigidity that is, depth for pile caps in order to spread the load evenly to all piles.

Deep foundations

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RC foundations

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Design of steel head to prevent the punching, in RC ﬂat slabs

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Diagram of bending moment on combined footings

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Diagram of stresses under isolated footings

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Diﬀerent types of deep foundations

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Diﬀerent types of reinforced concrete foundations

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Diﬀerent types of isolated footings

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Diﬀerent typs of RC footings on piles

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Isolated footings - design of reinforcement and the development of shear cracks

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Sabah Shawkat © Isolated footings are rectangular pads which spread a column load over an area of soil that is large enough to support the column load. The soil pressure causes the footing to deflect upward and the projection on each side of a column acts as a cantilever slab in two perpendicular

directions. The soil pressure causes tension in two directions at the bottom and the critical sections where the maximum moment occurs, are at the faces of square and rectangular concrete columns or pedestals. There is required to place the flexural reinforcement in both direction across the full width of the footing.

Isolated footings with critical area for punching in shear area

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Isolated footings on piles

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Lay-out of foundations

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RC ﬂate slab and ﬂat concrete as a RC foundations

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RC isolated footings combined with strap reinforced concrete beam

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Veriﬁcation of ultimate limit state ULS of RC piles

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Shallow foundations

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Sabah Shawkat © In a flexible footing the contact stress distribution derives not only from its displacement and rotation as a rigid unit, but also from its bending deflection. The theory of beams on elastic foundation is based on the assumption that the soil reaction of each point is proportional to the vertical displacement

of the contact face. The deflection curve of the beam of the constant stiffness EI on elastic foundations of the constant modulus of subgrade reaction C is determined by the differential equation. In case of the beam subjected to a combination of loads, can be used the method of superposition.

Soil pressure under RC footings

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Sabah Shawkat © If foundations and columns are cast separately, pocked foundations are employed. The pocket in which the columns are seated, formatting a fixed base to the column, are shaped like a truncated pyramid tapering towards the bottom of the pocket. This enables the formwork for the pocket to be lifted out in one piece. The depth of the pocket is usually set at 1,5 times the largest dimension of the column cross-section. As pocket foundations are very easy to handle on site, they are also used for pin-joined column bases. In this case the pocket does not need to be as deep.

Pocket foundations can also be constructed in precast concrete.in dealing with the structural analysis of pocket foundations, most publications place the axial force centrally in the base of the pocket. But this ignores the fact that the fixed part of the column twists due to the horizontal force or the bending moment, and therefore causes the axial force to act eccentrically.

Traditional RC foundations vs RC pocket precast concrete footing

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The analysis or design of any geotechnical structure is fundamentally based on the need to prevent failure (the limit state) in the broadest sense of the word (i.e. loss of function) by satisfying the equation:

Resistance (Capacity) > Loads (Demand) Historically, civil engineers have satisfied Eq. by increasing the resistance side of the equation. The loads, generally dictated by nature either directly or indirectly, are accepted as is and material is added to the structure. According to the principle of Limit States Design, the design criterion is simply to design for equilibrium in the design limit state of failure. The design criterion could be expressed in the following way: Rd ≥ Sd

The design resistance effect Rd which in the case of the design of a footing is the design ultimate bearing capacity. The purpose of a retaining wall is to hold back a mass of soil or other material. As a result, concrete masonry retaining walls must have the structural strength to resist imposed vertical and lateral loads. The footing of a retaining wall should be large enough to support the wall and the load of the material that the wall is to retain. The reinforcing must be properly located as specified in the plans. Provisions to prevent the accumulation of water behind retaining walls should be made. This includes the installation of drain tiles or weep holes, or both.

Sd is the design load eﬀect

Cantilever reinforced concrete retaining wall

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These can be designed including corners as L shaped reinforced walls to resist horizontal forces from ground to roof level. They have to be properly designed and may restrict openings to corners unless other measures are taken. Concrete walls have many uses including retaining earth walls, tank walls, shear walls in multi-story buildings, etc. A properly installed cast-in-place concrete wall achieves excellent structural strength, fire resistance and an attractive finish. Walls carrying vertical loads should be designed as columns. Shear walls should be designed as vertical cantilevers, and the reinforcement arrangement

should be checked as for a beam. Where the shear walls have returns at the compression end, they should be treated as flanged beams. As a general rule, the exterior walls of a reinforced concrete building are supported at each floor by the skeleton framework, their only function being to enclose the building.The wider range of walls being designed. Three basic categories, Bearing walls, Non-bearing walls, Shear walls Figures below illustrates the design and detailing requirements for diagonal reinforcing.It is desirable that during a several earthquakes most of the coupling beams will yield before the walls thereby minimizing wall damage.

RC Walls - cracks and diagonal reinforcement due to seismic forces

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Deformations and displacements in shear walls

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Design of reinforcement in reinforced concrete walls

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The distribution of lateral loads to several shear walls depends on the rigidity of the floor and the rigidity of the shear wall. A rigid floor with flexible shear walls is one extreme case and a flexible floor with rigid shear walls is another extreme case. In the first case, the lateral force is distributed to the shear walls depending on their relative levels of rigidity. In a case where the floor is supported by three shear walls of equal rigidity, each of these walls carries a third of the lateral load. However, if the inner wall is not located at the centre, a torsion component is also developed. In the other extreme case, the floor may be regarded as a continuous multi-span

beam over the supporting shear walls or two noncontinuous single-span beams extending between two shear walls.The assumption of a perfectly rigid floor should only be used if the floor plan dimension ratio is close to one. The end reinforcement of shear walls, as well as the bottom plate, should be anchored to the foundations to resist uplift forces (upwards) and sliding forces (horizontal). In a multi-storey house these anchoring forces should be considered from storey to storey as these accumulate towards the bottom storeys.

Frame structure walls with stiﬀ coupling

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Shear walls diﬁnition, with ﬂexible coupling beams

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Walls contains openings and walls supported by columns

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Walls with number of openings

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Design of reinforced concrete members

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Design of reinforced concrete members

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Design of reinforced concrete members

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Design of reinforced concrete members

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