Mixed Fiber Elements and Incremental-Iterative Algorithm for Shakedown and Limit Fire Analysis of 3D Frames

This work presents an efficient fiber analysis for evaluating the shakedown safety factor of 3D frames under multiple load combinations. Mixed beam elements are employed for an accurate discretization of the structures. A continuation method, similar to an incremental elasto-plastic analysis, is used at structural level. It evaluates a fictitious equilibrium path made of a sequence of safe states with a converging non-decreasing load factor. Each point of the path is obtained by finding kinematic variables corresponding to self-equilibrated stresses satisfying Melan’s condition for the current load factor to be safe. The stress admissible domain is defined at fiber level as a function of the load factor using the maximum and minimum effect due to all loads. The overall analysis allows a direct application of the Newton method easily implemented in commercial codes. The same numerical strategy can solve also a different problem, named limit fire analysis. It consists in evaluating for an assigned external load the maximum time of fire exposure that leads to the structural collapse as a consequence of the strength reduction of the materials.