NON-LINEAR ANALYSIS OF ELASTICALLY AXIAL-RESTRAINED 2D STEEL BEAMS AT ELEVATED TEMPERATURES IN FIRE BASED ON ARC LENGTH COORDINATE METHOD

A method is presented to study the non-linear structural behaviour of elastically axial-restrained steel beams at elevated temperatures in a fire, which employs the arc-length and section rotation of the deformed beam as basic variables. Governing equations are formulated based on the internal- and external-force equilibrium at every discrete node. This strategy can easily deal with the geometric non-linearity and elastic-plasticity of steel at elevated temperatures. Each node has two degrees of freedom in the proposed method. It is computationally more economical than the beam element in traditional finite element methods, which needs three degrees of freedom at each node. An example beam is studied using this method to verify the presented method. Parameters, including load-ratio, elastically axial-restrained ratio, transversely and longitudinally non-uniform distribution temperature, are studied. The middle-span deflection, axial force and moment, together with the strain and stress distributions across the section, are calculated at different temperatures. Comparisons to results obtained through general finite element method employing the shell element show that the presented method is precise.