Flanged beams
Flanged beams can be treated in much the same way as in BS 8110. The main differences compared with BS 8110 are that the assessment of the flange width is more sophisticated (see Figures 9 and 10) and that Eurocode 2 contains a check to confirm that the shear stress at
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Figure 6
Procedure for assessing deflection
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Determine basic l/d and K from Figure 7 |
Determine Factor 1 (F1) For ribbed or waffle slabs F1 = 1 - 0.1 ((fcf/fcw) - 1) 2 0.8+ (bf is flange breadth and bw is rib breadth) Otherwise F1 = 1.0
Determine Factor 2 (F2) Where the slab span exceeds 7 m and it supports brittle partitions, F2 = 7/ieff < 1.0 Otherwise F2 = 1.0
Where os = Stress in reinforcement at serviceability limit state (see Figure 8) 0*5 may assumed to be 310 MPa (i.e. F3 = 1.0) Note: As,prov < 1.5 -As req'd (UK National Annex)
+ The Eurocode is ambiguous regarding linear interpolation. It is understood that it was the intention of the drafting committee that linear interpolation be used and this is in line with current UK practice.
Figure 8
Determination of steel stress
320 300
rf 280
IS 260
Tu 240
t5 o
E 220
200 180
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To determine stress in the reinforcement (os), calculate the ratio Gk/Qk, read up the graph to the appropriate curve and read across to determine osu. os can be calculated from the expression: os = osu ( As,req ) (—) Figure 7 Basic span-to-effective-depth ratios 36 34 32 30 28 IT 26 c ro 0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% Percentage of tension reinforcement (ASireq'd/bd) Notes 1 This graph assumes simply supported span condition (K = 1.0). K =1.5 for interior span condition K =1.3 for end span condition K = 0.4 for cantilevers. 2 Compression reinforcement, p, has been taken as 0. 3 Curves based on the following expressions: Figure 11 Procedure for determining flexural capacity of flanged beams START Carry out analysis of beam to determine design moments, M (see Table 3) Determine lo (see Figure 9) and beff from: beff = (bw+ beff1 + beff2) where beffi = (0.2bi + 0.1 lo) < 0.2 lo < bi beff2 = (0.2b2 + 0.1 lo) < 0.2 lo < b2 Note: The flange width at the support will be different from that at mid-span. For symbols refer to Figures 9 and 10 Determine K from K = where b = bw at support b = beff in span bd2 fck Determine K' from Table 4 or K' = 0.60 d - 0.18 ô2 - 0.21 where d < 1.0
Neutral axis in flange. Design as rectangular section (Figure 2) and then check longitudinal shear (Figure 14) Neutral axis in web Calculate moment capacity of flange from:
Figure 9 Definition of lo, for calculation of effective flange width
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