Material yielding by both axial and bending spring stiffness at elevated temperature

Material yielding is typically modeled either by plastic zone or plastic hinge methods under the context of geometric and material nonlinear finite element methods. In fire analysis of steel structures, the plastic zone method is widely used, but it requires extensively more computational efforts. The objective of this paper is to develop the nonlinear material model allowing for interaction of both axial force and bending moment, which relies on the plastic hinge method to achieve numerical efficiency and reduce computational effort. The biggest advantage of the plastic-hinge approach is its computational efficiency and easy verification by the design code formulae of the axial force-moment interaction yield criterion for beam-column members. Further, the method is reliable and robust when used in analysis of practical and large structures. In order to allow for the effect of catenary action, axial thermal expansion is considered in the axial restraint equations. The yield function for material yielding incorporated in the stiffness formulation, which allows for both axial force and bending moment effects, is more accurate and rational to predict the behaviour of the frames under fire. In the present fire analysis, the mechanical properties at elevated temperatures follow mainly the Eurocode 3 [Design of steel structures, Part 1.2: Structural fire design. European Committee for Standisation; 2003]. Example of a tension member at a steady state heating condition is modeled to verify the proposed spring formulation and to compare with results by others. The behaviour of a heated member in a highly redundant structure is also studied by the present approach.