Plastic Limit Temperatures of Flexibly Connected Steel Frames: A Linear Programming Problem

A linear programming (LP) formulation is proposed for the evaluation of the plastic limit temperature of flexibly connected steel frames exposed to fire. Within a framework of discrete models and piecewise linearized yield surfaces, the formulation is derived based on the lower-bound theorem in plastic theory, which leads to a compact matrix form of an LP problem. The plastic limit temperature is determined when the equilibrium and yield conditions are satisfied. The plastic mechanism can be checked from the dual solutions in the final simplex tableau of the primal LP solutions. Three examples are presented to investigate the effects of the partial-strength beam-to-column joints. Eigenvalue analysis of the assembled structural stiffness matrix at the predicted limit temperature is performed to check for structural instability. The advantage of the proposed method is that it is simple, computationally efficient, and its solutions provide the necessary information at the limit temperature. The method can be used as an efficient tool to a more refined but computationally expensive step-by-step historical deformation analysis.