Structure II Course Code: ARCH 209 Dr. Aeid A. Abdulrazeg

Preliminary Sizing of Members The analysis and design of concrete structures is essential a trial and error process. The magnitude of permanent gravity loads, for instance, is dependent on member sizes is required before structure can be analysed. If the final dimensions required to resist, say bending moment in a member differ from the initial estimate of the member size, then the design process must be repeated with revised member dimensions until these initial assumptions are satisfied. The more accurate the initial size estimates, the less iterations will be involved as the solution will converge more rapidly to precise requirements.

Preliminary Sizing of Beams Effective Depth of the Beam The strength of the beams in flexure is governed principally by the effective depth, that is , the depth from the extreme compression fiber of the beam to the centroid of the tension steel . A large effective depth results in a relatively small required quantity of reinforcement. However, deeper beams at each floor level increase the permanent gravity load to the columns and result in a higher building overall which requires extra cladding.

Table 1 The different possibilities of steel arrangement 5

Consider a simply-supported beam of rectangular cross-section supporting a distributed load as shown in Figure : The deflection can be expressed as a fraction of the span by dividing both sides by L.

The limitations on deflection are governed by satisfying the basic (span/effective depth) ratio from Table 3.9 (BS8110), modified accordingly for tension and compression steel using Table 3.10 (BS8110) and Table 3.11 (BS8110). The ratios are given for both rectangular and flanged sections and are based on limiting the total deflection to ≤ (span/250). This should ensure that any deflection occurring after construction of finishes and partitions ≤ (span/500) and ≤ (20 mm).

Example 2 A rectangular concrete beam 250 mm wide × 475 mm overall depth is simply supported over a 6.0 m span. Using the data given, check the suitability of the beam with respect to deflection. Data: Characteristic strength of concrete (fcu) 40 N/mm2 Characteristic strength of main steel (fy) 460 N/mm2 Area of reinforcement steel required 897 mm2 Assume the distance to the centre of the main steel from the tension face is 50 mm Design ultimate moment at mid- span 150 kN. m

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Breadth of Beams The breadth of rectangular concrete beams and webs in flanged beams has a much lesser effect on the resistance of a beam to bending moment than does effective depth.

Breadth is governed by the practical consideration of simply fitting all the reinforcement into the section while avoiding congestion.

The minimum practical breadth for a design in accordance with EC2 is: b = 2 (cover to main reinforcement) + 2 Dim. Stirrup+ 5Ømax S = hagg + 5 mm S = Ømax.

Breadth is a major influencing factor on the shear strength of beams. The preliminary breadths is determined by limiting the shear stress in beams to 2.0 N per mm2.

T or L beams occurs where the beams are cast integrally with the floor slab. End beam or L-Beam Intermediate beam or T-beam Floor Slab L-beam T-beam

Fig. Isolated T and L beam sections Due to the integrity of beams with the floor slab a part of the slab has to be considered in the design of the beam. The part of the floor slab integrated with the beam is called flange and the rest of the beam is called the web. The T and L shaped beam is shown in Fig. along with the dimension used. Fig. Isolated T and L beam sections The intermediate beam show in Fig. will have a floor slab at its top from both sides and hence has a T shape, while the end beam has a floor slab from once side and hence has an L shape.

The effective breadth “bf “ of the flange is given in BS 8110 part-1 clause 3.4.1.5 as follows: 1. T-beam or centre to centre between beams whichever is less 2. L -beam or ½ of centre to centre distance between beams where: bw : the width of the web Lz : the distance between points of zero moment (point of inflection) in the beam. where: In continuous beams of length L, Lz = 0.85L for external span , 0.7L for internal span and 2.0L for cantilevered.

Example: for the beam shown in figure the total factored ultimate loading is 43 kN per m and the total depth is 800 mm. Find: Preliminary web breadth. The effective flange breadth. Given: T- section continuous beams. Total design load is 43 kN per m Total depth 800 mm Area of tensile reinforcement 950 mm2 Characteristic strength of concrete 30 kN/mm2

10 mm 25 mm

the effective depth: Assuming each span be simply supported, the shear force at the ends of each member:

thus the minimum web breadth is 200 mm the minimum web breadth required all bars on one level is given by: the minimum web breadth required for fire resistance. 200 mm. thus the minimum web breadth is 200 mm

(b) The effective flange breadth. the distance between points of zero moment in span BC is Hence, the effective flange breadth is