Analysis of structural system reliability with stochastic programming

The goal of this study is to provide a method for the identification of failure modes that contribute significantly to the estimate of the system probability of failure in rigid-plastic structures where axial force-moment interaction is considered. Mathematical programs are developed using the kinematic method of plastic analysis to determine the critical collapse mode and load factor when loads and resistances are deterministic. For structures where loads and resistances are random variables, nonconvex stochastic programs are developed using the kinematic method of plastic analysis to identify the least reliable mode. A decision rule is presented for the identification of failure modes in series systems based on their contribution to the system probability of failure. Application of this decision rule leads to the identification of failure modes that form an approximation of the system limit state. Stochastic programs based on this decision rule for failure mode selection are developed for the identification of failure modes in rigid-plastic structures. Examples illustrate the use of these mathematical programs in identifying significant failure modes in rigid-plastic structures where axial force-moment interaction is included.