Buckling analysis of non-uniform Timoshenko columns under localised fire

The buckling analysis of non-uniform steel columns with various boundary conditions under localised fire is investigated based on the Timoshenko beam theory (TBT). The temperature-dependent (TD) material properties are taken into account. First, based on the differential quadrature (DQ) method, the temperature field in the column is determined by solving the heat transfer equation considering the convection and radiation boundary conditions. Then, a segmented model is presented to solve the stability problem for the column with the variable flexural rigidity resulting from the non-uniform temperature distribution and cross-section. The transfer-matrix method is employed to obtain the critical buckling load and corresponding buckling mode. Finally, an example is conducted to study the temperature field and buckling response of tapered circular hollow steel columns under localised fire. The feasibility of the present method is verified by comparing the present results with those predicted by the finite element (FE) method and those reported in the literature. Numerical results show the influences of the localised fire and shear deformation on the buckling response of the column.