Optimal design of dynamically loaded reinforced concrete frames under displacement and rotation constraints

The paper deals with reinforced concrete beams and frames subjected to short-time, high intensity dynamic pressure. The shape and geometry of the structure and the layout of the longitudinal reinforcement are given and the areas of reinforcement are design variables.The determination of the plastic displacements and deformations caused by pressure is based on the plastic hinge theory and on the assumption that during the dynamic response the structure undergoes stationary displacements. The problem is to minimize the total amount of reinforcement such that the plastic displacements do not exceed the allowable displacements prescribed at certain points of the structure, or alternatively, that the plastic rotations in the plastic hinges do not reach the limits at which brittle failure occurs.A variational formulation of the problem is presented and the solution is based on the optimality criteria approach which requires an iterative procedure. A few examples illustrate the application of the method.