Reliability Based Optimum Design of Concrete Frames

A reliability based optimum design procedure as a rational approach to optimum structural design is presented. The reliability analysis is based on a first‐order second moment approach. Uncertainties in the structural strength and loading due to inherent variability as well as modeling and prediction errors are included in the formulation. The failure modes considered include failure due to bending, combined axial thrust and bending, and shear. The structural systems investigated are typical office buildings consisting of fourand ten‐story reinforced concrete frames. The procedure to obtain the optimal structure is based on a minimization of the total expected cost, and the optimal risk level is obtained as the value that results in the minimum total expected cost. The total expected cost is taken as the sum of the initial building cost and the loss due to failure. An iterative procedure is used to obtain member dimensions and reinforcing steel areas for prescribed risk levels ranging from ${10}^{-2}-{10}^{-6}\text{,}$ and upper, and lower bounds on the total expected cost are computed. For the buildings considered, the optimal risk level ranges from ${10}^{-4.1}-{10}^{-5.4}\text{.}$ The proposed optimization procedure can provide an accurate estimate of the optimal level of safety.