Spline Finite Element Methods for Analysis of Axially Restrained Steel Beams Subjected to Elevated Temperatures in Fire

Abstract

A spline finite beam element for analysis of axially restrained steel beams subjected to elevated temperatures in fire is presented. Both geometric nonlinearity and material nonlinearity are integrated in the proposed method. Governing equations of the beam are established according to the internal-force and external-force equilibriums at each node of the elements representing the beam, and the nonlinear equations system is solved by the Newton-Continuation method. This strategy can avoid the building of the elemental and globe stiffness matrix, which may be complex when involves the second-order effect of axial force and elastic-plasticity of steel at elevated temperatures. Numerical examples of using the method proposed are presented. The influence of non-uniform temperature distributions is discussed. The structural responses, which include the deflection, axial force and moment at middle-span of the example beam, are calculated using both the presented spline finite element method (SFEM) and general finite element method (FEM) with shell elements. Comparisons of the results show that the spline finite beam element method is computationally economical and precise.