Nonlinear analysis of reinforced concrete plane frames exposed to fire using direct stiffness method

This article presents a framework based on the direct stiffness method for nonlinear thermo-mechanical analysis of reinforced concrete plane frames subjected to fire. It accounts for geometric nonlinearity, material nonlinearity, and nonlinear thermal gradients and incorporates two-way coupling between thermal and structural analyses. Force deformation relations are derived from classical Euler–Bernoulli beam theory and are expressed in terms of temperature-dependent stability and bowing functions. This is one of the unique features of proposed framework and allows a coarser spatial discretization to be used as opposed to full finite element–based approaches (such as SAFIR [registered trademark of the software SAFIR developed at the University of Liege]). The cross sections of the structural members are discretized with two-dimensional meshes for thermal analysis while structural analysis utilizes a line element based on direct stiffness method. Equivalent bending and axial rigidities of this line element are computed using several fibers along the length of the member, passing through the nodes of the two-dimensional mesh used for thermal analysis. The total strain at each fiber is decomposed into mechanical, thermal, creep, and transient thermal components. A discrete damage parameter is introduced at fiber level to ensure irreversibility of crushing and cracking in accordance with relevant constitutive laws. Five numerical examples are presented to demonstrate the accuracy and efficacy of the developed framework with respect to theoretical solutions, experimental observations, and some of the existing macro- and micro-finite element–based approaches. It is found that the developed framework can predict the response of reinforced concrete structures very well.