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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.

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This article develops a fully coupled hydro-thermo-mechanical formulation based on the direct stiffness method for analysis of steel and reinforced concrete structural space frames. The superiority of the developed formulation lies in developing the direct stiffness method for fire analysis, which enables use of a much coarser spatial mesh when compared to existing fire analysis frameworks. Effects of temperature-dependent material properties, damage due to fire and pore pressure, nonlinear thermal gradients, and large deformations of structural members are directly integrated into the stability and bowing functions in the construction of the member stiffness matrix. This alleviates the need to perform element-level numerical quadrature, typically required by all existing finite element–based approaches. Full coupling between the pore pressure, thermal and mechanical solvers is considered through a two-level spatial discretization strategy with a staggered scheme for the numerical solution procedure. Five numerical examples are presented to demonstrate the accuracy and efficacy of the developed formulation in analysis of steel and reinforced concrete structural members and frames.