The figures below show the cross-section of a reinforced concrete beam, together with the (idealised) stress-strain diagrams for the concrete and reinforcing steel of which it is made.
a) Calculate from first principles the bending moment carried by the section when the compressive strain in the concrete top fibre is 0.0008, given that at this stage of loading the section has cracked, and the depth to the neutral axis is 157.1 mm.
b) Calculate from first principles the ultimate moment for this cross-section, given that at Mu the compressive strain in the concrete top fibre may be assumed to be 0.003, and the compressive stress distribution in the concrete may be approximated by a rectangle with a depth equal to 80% of the neutral axis depth, and a uniform stress value of 21 MPa. Hint: Assume that the reinforcement has yielded, check this assumption once the neutral axis depth is known.
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