DESIGN OF BEAMS By: Engr. Dr. Thevaneyan Krishta David Faculty of Civil Engineering Universiti Teknologi MARA (UiTM), SHAH ALAM
At the end of this week student should be able to: a)
Adapt the procedure in the EC2 to design the beam(CO2).
b)
Adopt new parameter to design the beam(CO2).
c)
Construct the detail of beam.(CO2)
Design Procedure Step
Task
Reference
1
Determine design criteria: Design life, Exposure class & Fire resistance
EN 1990 Table 2.1 EN 1992-1-1: Table 4.1 EN 1992-1-2: Sec. 5.6
2
Determine concrete strength
BS 8500-1: Table A.3 EN 206-1: Table F1
3
Select size of beam
EN 1992-1-1: Table 7.4N EN 1992-1-2: Table 5.5
4
Estimate actions on beam
EN 1990 Table A1.1 and A1.2
5
Determine action combination and arrangements
EN 1990 Table A1.1 and A1.2 EN 1992-1-1
6
Calculate min. cover for durability , fire and bond requirements
EN 1992-1-1: Sec. 4.4.1
7
Analyze structure to obtain critical moments and shear forces
EN 1992-1-1: Sec. 5
8
Design flexural reinforcement
EN 1992-1-1: Sec. 6.1
9
Check and design shear reinforcement
EN 1992-1-1: Sec. 6.2
10
Check deflection
EN 1992-1-1: Sec. 7.4
11
Check cracking
EN 1992-1-1: Sec. 7.3
12
Detailing
EN 1992-1-1: Sec. 8 & 9.2
Design working life EN 1990: Table 2.1 Design working life category
Indicative design working life (years)
1
10
2
10 to 25
Replaceable structural parts, e.g. gantry girders, bearing
3
15 to 30
Agricultural and similar structures
4
50
Buildings structures and other common structures
5
100
Monumental building structures, bridges, and other civil engineering structures
Examples Temporary structures
Exposure classes EN 1992-1-1: Table 4.1
Fire Resistance
EN 1992-1-2: Sec. 5.6
Material Strength BS 8500- 1
Concrete : In EC2 the design of reinforced concrete is based on the characteristic cylinder strength rather than cube strength and should be specified according to EN 206-1. or BS 8500: 2006
Material Strength EN 206-1
Material Strength Reinforcing Steel: EC2 can be used with reinforcement of characteristic strength ranging from 400 to 600 MPa. A characteristic yield strength of 500 MPa has been adopted by the UK reinforcement industry.
Beam Size The selection of beams sizes from structural viewpoint is often dictated by deflection control criteria. In practice, the overall depths of beams are often fixed in relation to their spans. Span to overall depth ratios of 13 to 18 are generally found to be economical in the case of simply supported and continuous beams. The recommended ratio of width to overall depth in rectangular beam section is in the range of 0.3 to 0.6.
Beam Size EC 2 Part 1-2 Tables 5.5 and 5.6, gives a method for determining the minimum dimension of beams for fire resistance requirements. EN 1992-1-2 Tables 5.5 and 5.6
Concrete Cover The nominal cover can be assessed as follows: Cnom = Cmin + DCdev Where Cmin shall be provided in order to ensure: •The safe transmission of bond forces
•The protection of steel against corrosion (Durability) •An adequate fire resistance And DCdev is and allowance which should be made in the design for deviation from the minimum cover. It should be taken as 10 mm. It is permitted to reduce to 5 mm if the fabrication subjected to a quality assurance system.
Concrete Cover EN 1992-1-1 Table 4.2 & Sec 8.9.1 Minimum cover for bond
Arrangement of bars
Minimum cover cmin,b*
Separated
Diameter of bar
Bundle
Equivalent diameter n = nb ≤ 55 mm Where nb is the number of bars in the bundle, which is limited to nb ≤ 4 for vertical bars in compression nb ≤ 3 for all other cases
* If the nominal maximum aggregate size is > 32 mm, cmin,b should be increased by 5 mm
Concrete Cover EN 1992-1-1 Table 4.4N Minimum cover for durability Exposure Class according to Table 4.1 EC 2
Structural Class
X0
XC1
XC2/XC3
XC4
XD1/XS1
XD2/XS2
XD3/XS3
S1
10
10
10
15
20
25
30
S2
10
10
15
20
25
30
35
S3
10
10
20
25
30
35
40
S4
10
15
25
30
35
40
45
S5
15
20
30
35
40
45
50
S6
20
25
35
40
45
50
55
Concrete Cover Minimum cover for fire resistance Rather than giving a minimum cover, the tubular method based on nominal axis distance is used. This is the distance from the centre of the main reinforcement bar to the top or bottom surface of the member.
a > Cnom + ď Ślink + ď Śbar/2 asd = a + 10 mm
Actions Actions that applied on a beam may consist of beams self-weight, dead and imposed loads from slabs, actions from secondary beams and other structural or non-structural members supported by the beam. The distribution of slab actions on beams depends on the slab dimension, supporting system and boundary condition. There are alternatives methods which consider various support conditions and slab continuity. The methods are, (i). Slab shear coefficient from Table 3.15 BS 8110, (ii). Yield line analysis and (iii). Table 63 Reinforced Concrete Designer’s Handbook by Reynold.
Analysis ď ą The primary purpose of structural analysis is to establish the distribution of internal forces and moments over the whole part of a structure and to identify the critical design conditions at all sections. ď ą The type of analysis should be appropriate to the problem being considered. The following may be used: linear elastic analysis, linear elastic analysis with limited redistribution, and plastic analysis. ď ą Linear elastic analysis may be carried out assuming cross sections are uncracked (i.e. concrete section properties), using linear stress-strain relationships, and assuming means values of elastic modulus.
DESIGN FLEXURAL REINFORCMENT EN 1992-1-1: Sec. 6.1 The design procedure for flexural design in figure below. The derived formula is based on the following simplified stress block.
DESIGN FLOWCHART OF FLEXURAL REINFORCMENT
FLEXURAL REINFORCMENT DETAILING EN 1992-1-1: Sec. 9.2.1
DESIGN SHEAR REINFORCEMENT EN 1992-1-1: Sec. 6.2 EC 2 introduces the strut inclination method for shear capacity checks. In this method the shear is resisted by concrete struts acting in compression and shear reinforcement acting in tension.
DESIGN FLOWCHART FOR SHEAR REINFORCEMENT
DEFLECTION EN 1992-1-1: Sec. 7.4 EC 2 has two alternative methods for checking deflection, either a limiting span-to-depth ratio or the theoretical deflection calculation. The span-to- depth ratio should ensure that deflection is limited to span/250.
DEFLECTION
DEFLECTION CHECKING FLOWCHART
CRACKING EN 1992-1-1: Sec. 7.3 Crack widths should be limited to ensure appearance and durability are satisfactory. In the absence of specific requirements (e.g. water tightness), it may be limited to the values given in Table 7.1N. The theoretical size of the crack can be calculated using expressions given in Section 7.3.4 EN 1992 or from “deemed to satisfy� requirements that can be obtained from Table 11, which is based on tables 7.2N and Table 7.3 N of Eurocode
CRACKING The limits apply to either the bar size or the bar spacing, not both.
DESIGN EXAMPLE 6.1 : Simply supported beam A rectangular reinforced concrete beam is simply supported on two masonry walls 250 mm thick and 8.0 m apart (clear distance). The beam has to carry a distributed permanent action of 20 kN/m (excluding beam selfweight) and a variable action of 10 kN/m. The materials to be used are grade C20 concrete and grade 500 reinforcement. The beam is inside buildings which subjected to 1 hour fire resistance and design for 50 years design life. Design the beam.
To be continued