Chance‐Constrained Optimization Model for Structural Design

Abstract

A mixed‐integer chance‐constrained optimization model is presented for structural design. The model incorporates the probabilistic nature of the loadings experienced throughout the life of the structure and can be used to investigate the trade‐offs between cost and the probability of failure. Design constraints are originally expressed as probability statements, in which the design parameters are considered to be random variables with established probability distributions. The chance constraints impose lower bounds on the likelihood or chance that specified failure criteria are exceeded for each structural member. Using the cumulative distribution function for each design parameter, the chance constraints may be expressed as deterministic equivalent constraints. Possible design solutions are limited to combinations of available standard sections using binary decision variables. An example is presented using a one‐story, one‐bay steel frame, and the results are compared with those obtained through conventional design procedures.