Least cost design of a prismatic simply supported singly reinforced rectangular concrete beam

In this paper least cost design of a prismatic simple supported singly reinforced rectangular beam with varied spans of 5m, 7m, 9m, 11m and 13m and uniform concentrated load of 100KN based on flexural constraint of the American Concrete Institute (ACI 318/95) is reported. The cost function of the beam was developed based on the unit costs of 1:2:4 concrete mix, formwork, steel and link reinforcements. The unit cost of 1:2:4 concrete mix used was 30,000 per m3 of concrete, 1,000 per m2 of formwork, 300 per kg of steel reinforcement. The unit cost per kg of link reinforcement was assumed to be half the unit cost of steel reinforcement. The design variables were the depth and steel reinforcement ratio. The width of the beam was kept constant as 0.225m. The deign variables were appended to the Lagrangian multiplier which was used an the optimization process and a FORTRAN program was used to facilitate the needed optimal solutions. It was shown among other findings that the depth of the beam decreased as the steel ratio increased but the total cost per unit length reduced showing that it is cheaper to increase the area of steel reinforcement and reduce the depth