Abstract

AbstractConstruction of concrete structures involves at least two different main materials: concrete and steel. Design of these structures should be based on cost rather than weight minimization. In this work, least cost design of singly and doubly reinforced beams is done by applying of the Lagrangian multipliers method (LMM) under ultimate design constraint beside other constraints. Cost objective functions and moment constraints are derived and implemented within the optimization method. The optimum solution comparisons with conventional design methods are performed and the result reported, showing that the LMM can be successfully applied to the minimum cost deign of reinforced concrete beams without need for iterative trials. Optimum design solution surfaces have been developed. Good and reliable results have been obtained and confirmed by using standard design procedures. The artificial neural networks (ANN) has been trained with design data obtained from optimal design formulas. After successful trials, the model predicted the optimum depth of the beam sections and optimum areas of steel required for the problems with accuracy satisfying all design constraints.