Stochastic Optimization of a Reinforced Concrete Element with Regard to Ultimate and Serviceability Limit States

Abstract

Main goal of the paper is to present an algorithm for stochastic optimization of a steel-reinforced concrete element’s cross section. Firstly, the deterministic problem is introduced and described. The description of uncertainties involved in the process and stochastic reformulation of the problem follows. Afterwards, the algorithm itself is introduced. This algorithm is based on internal cycle of deterministic optimization using reduced gradient method and external cycle of stochastic optimization using regression analysis. From the initialization state, the algorithm assess probabilities that ultimate and serviceability limit states are satisfied. Using regression analysis of these assessed probabilities, the algorithm finds new possible solution. The probabilities are assessed on orthogonal grid via modified bisection method. The paper concludes with presentation of the performed calculations and their results.