Thermoelastic buckling and post-buckling of weakened columns

Structural columns in engineering practice may weaken over time as a result of corrosion, erosion, impact, fatigue cracking or similar effects that reduce their effective cross-section. The effect of the degradation of the cross-section may then lead to premature flexural buckling. This paper presents a solution for the buckling and post-buckling behaviours of such weakened columns under thermal loading. The method of minimum total potential is employed to derive the differential equations for the buckling, as well as those for the post-buckling response, and the boundary value equations with variable coefficients that govern the behaviour are solved using a shooting procedure. The buckling and post-buckling responses of weakened columns are investigated parametrically, and it is found that the weakening of the column may affect the buckling temperature significantly. Comparisons between the solutions of the problem that account for, and do not account for, the axial deformation are also given, and the results indicate that the effects of axial deformation need to be considered under thermal loading. A Rayleigh–Ritz solution for weakened columns is also presented, and it is found that the proposed simplified formulation can predict the buckling and post-buckling responses of weakened columns under thermal loading quite accurately.