Minimum cost design of concrete beams with a reliability-based constraint

The optimum cost design of under-reinforced concrete beams is considered by treating all the design parameters as random variables. The design is considered to be safe and adequate if the expected moment capacity of the beam exceeds the design moment capacity by a certain number of standard deviations. The optimum cost design problem is cast as a nonlinear mathematical programming problem and is solved as a sequence of unconstrained minimization problems. Numerical examples are presented to illustrate the effectiveness of the method. The resulting computer program is used to examine the characteristics of optimum designs as effected by changes in the cost coefficients and the design parameters.