Problem $1.$

Design a simply supported rectangular beam to carry a live load of $1500l\frac{b}{f}t.$ The span of the beam is $22$ ft $,$ the compressive strength of concrete is $4000$ psi and the yield stress of steel reinforcement in flexure is $60000$ psi. Design the beam for flexure in tension$-$controlled failure. Find the dimensions of the cross section and the steel reinforcement required. Check for the minimum reinforcement requirement.