Thermal buckling and postbuckling of columns accounting for temperature effect on material properties

Thermal buckling and postbuckling of columns are analyzed accounting for the effect of temperature on “material constants,” i.e., the modulus of elasticity, the coefficient of thermal expansion, and the yield stress. The columns are simply supported, and fully or elastically constrained in the axial direction. Solutions are obtained by two methods. One of these methods is using “real-time” values of material constants corresponding to buckling and postbuckling at prescribed temperatures and neglecting the history of loading. The other method takes the effect of the history of loading into account using polynomial property-temperature relationships throughout the evolution of temperature. It is demonstrated that buckling temperature calculated by these methods may vary, although the trends found by them are in a qualitative agreement. Contrary to postbuckling behavior of mechanically compressed columns, in the case of thermal loading the column exhibits a noticeable resilience, i.e., temperature can significantly increase over the buckling value prior to the collapse. It is observed that since material constants are continuous functions of temperature, they can always be presented in the form of polynomials. Accordingly, the solution can be extrapolated to any material employing experimental polynomial property-temperature relationships as is illustrated in the paper.