Distributed plasticity model for analysis of steel structures subjected to fire using the direct stiffness method

Abstract

This article develops a temperature-dependent distributed plasticity model in a direct stiffness method (DSM) based formulation for coupled nonlinear thermo-mechanical analysis of steel space frames. The developed framework considers geometric and material nonlinearities, and performs coupled thermo-mechanical analysis by a two-level spatial discretization strategy. An isotropic hardening plasticity in combination with the von Mises yield criterion is considered, where the temperature-dependent yield function is derived from the stress-strain relations of Eurocode 3. The effects permanent plastic strains, large deformations and temperature-dependent material properties are directly incorporated in to the force deformation relations derived in a DSM based setting. Such a DSM based framework in conjunction with the distributed plasticity model facilitates higher computational efficiency. To ensure full coupling between mechanical and thermal solvers, thermodynamically consistent plastic heating term is added to the energy balance of the system. Also, connection flexibility is accounted for by developing a zero-length spring element integrated with 1-D beam-column elements. Five numerical examples are presented to demonstrate the efficacy of the developed framework. Within the numerical investigation, the importance of plastic heating coupling in the context of macro modelling based structural fire analysis of steel structures is quantified and the results indicate that such a coupling can be ignored in such macro scale structural fire computations.