Question

Figure 3 shows the cross-section of a reinforced concrete beam which incorporates a services duct on the compression side. The concrete has the following properties: f'c =32 MPa, y = 0.82, and Ec = 28,500 MPa. Calculate the ultimate moment, Mu, for this section from first principles. Please note that the reinforcement yield stress for this question is 460 MPa and Ast = 4800mm. You may use the usual equivalent rectangular stress block and the limiting strain criterion (EU = 0.003). Assume initially that all reinforcement yields before Mu; this assumption must be checked. 400 100 1200 1150 Figure-3

Answer 1

Ce 28,500 MPe 32 M Pa o 82x B2 26.24 400 C 0. a 160 Dst 4800mm depdn aris at Bssume neudrol CE T. conerala x svers dme C Brea of a)- 200x200 x 26. 24 Prsumng dre Steel h be T = 460 x 40 oo c=T 320a- 460x480 o= ] 40000 26. 24 = 38 7.9SMM

level of steel かrain chedeing dnargle Simila vang Sians cormpresin dbre 0.002 at dne Pulnne er dreme 0.003 382.95 O.00 2 38フ.95 762.04 150-3829S e = 0.00ら89 762.04 >460 2x105 ansumphon of sted Hence de con aet 19 = N Tx (d-0.sa2) 460×4全Dox (1150-0.e x38フ、45)Nmm 2196.56ヒNつ 1