Non-linear finite element analysis of axially restrained steel beams at elevated temperatures in a fire

A method is presented for the analysis of the non-linear structural behavior of axially restrained steel beams at elevated temperatures, which employs the axis arc-length and section rotation of the deformed beam as basic variables. The novelty of the proposed formulation is an inclusion of a balance function that measures the error of the equilibrium between the internal- and external-forces in a cross-section of the beam. This strategy can easily deal with the geometric non-linearity and elasto-plasticity of steel at elevated temperatures. Each node for representing the section of the beam has two degrees of freedom in the proposed method. It is more computationally economical than the traditional beam element, which has three degrees of freedom. An example beam is studied to verify the proposed method. Parameters including the load ratio, axial restraint stiffness ratio, transversal and longitudinal temperature gradient, are studied. The middle-span’s deflection, axial force and moment, along with the strain and stress distributions across the section, are calculated at elevated temperatures. The comparison with results from the finite element method employing shell elements shows that the method presented here is precise.