A B-splines-based GBT formulation for modeling fire behavior of restrained steel beams

An implicit finite element model based on the generalized beam theory (GBT) is developed to simulate the fire behavior of restrained steel beams. The model considers both material and geometric nonlinearities. A bilinear stress-strain curve is used to represent the material behavior at elevated temperatures. The GBT cross-section deformation modes are utilized to construct the mid-surface displacements of each wall, where the longitudinal variations of the mode amplitudes are approximated by the cubic B-splines. The bending related displacements are established by using assumptions of the Kirchhoff's plate theory. The Green-Lagrangian strain tensor is employed to represent the deformation at each quadrature point, and therefore the geometric nonlinearity can be included. A weak-form of the nonlinear equilibrium equations is derived by the Principle of Virtual Work and is solved by employing an implicit iterative procedure. The current model can capture local deformation because higher-order cross-section deformation modes are used. The fidelity of the developed GBT formulation has been evaluated by comparing the predictions with three benchmark results available in the literature, and case studies have been performed. It is found that the local buckling can influence the overall behavior of beams in fire, which is different to the finding of the conventional beam-element-based analysis. The current GBT approach is an alternative to the shell finite element formulation, but exhibits higher computational efficiency.