Reliability of Portal Frames with Interacting Stress Resultants

A general formulation based on mathematical programming and structural reliability theory is given for the analysis and synthesis of portal frames where yield with respect to plastic collapse is governed by several stress resultants. The mechanism compatibility equations are formulated using the generalized mesh description. The elasto-plastic material is assumed to satisfy Drucker's postulate of stability. The stochastically most important modes of the reliability assessment problem are found by minimizing a quadratic concave function over a linear domain. Mathematical programming techniques that include recent developments in concave quadratic minimization are presented. The paper also describes a first-order second-moment reliability-based approach to the optimum design of ductile frames. It involves an iterative process, which is repeated until the best reliability-based design is obtained. This design has a preassigned reliability level against plastic collapse and simultaneously minimizes the prescribed objective function. Examples are solved by employing the proposed computational techniques.