ABSTRACT
Note that load at SLS can be more appropriately taken as gk + ψ2 qk. σs = (25.56/ 36.0) × (500/1.15) = 318 MPa ≈ 310 MPa assumed in the formula.
L/d = 11 + 1.5 × 5 × 0.005/0.0168 = 13.2 L/d = 13.2 × 0.8 = 10.6
Correcting for As, prov > As, reqd, L/d = 10.6 × 1.15 = 12.1 Actual L/d = 6000/305 = 19.7
Depth is too small. Deflection will exceed the permitted L/250. Redesign the beam:
L = 6 m, d = 6000/12 = 500 mm h = 500 + 25 (cover) + 8 (links) + 25/2 = 550 mm
d = 550 – 25 – 8 –25/2 = 504 mm Increase in moment due to deeper web = (0.55 – 0.35) × 25 × 1.35 ×62/8 = 30.38 kNm
k = M/ (b d2 fck) = (162 + 30.38) × 10 6/ (1800 × 5042 × 25) = 0.02 < 0.196
Provide 2H25; As = 982 mm 2
As, prov /As, reqd = 982/900 = 1.09 ρ = As/ (bw d) = 982/ (250 × 454) = 0.0087, ρ% = 0.87
ρ0 = 10 −3 ×√25 = 0.005, ρ0% = 0.5 < ρ%
Simply supported beam, K = 1 No compression steel, ρ' = 0
b/bw = 1800/250 = 7.2 > 3.0. Therefore L/d from equation is multiplied by 0.8.
