Closed-Form Solutions for Initial Thermal Postbuckling Response of Axially Restrained Columns

Closed-form equations for the initial thermal postbuckling response of axially restrained elastic columns with six well-known sets of rotational and lateral end restraints are presented. These equations, which are consistent with the conventional beam-column (Euler–Bernoulli) theory, are based on the assumption that the column axial force remains constant at the buckling level in the postbuckling phase, i.e., the (additional) thermal axial extension because of the increased temperature above the buckling temperature is converted into the column’s lateral deflection via the bowing effect. The equations consider the effects of partial axial restraints as well as the degradation of elastic material properties with rising temperatures. To evaluate their accuracy, the postbuckling response predicted by these approximate equations is compared to the exact (elastica) solutions available in the literature and to the finite-element solutions. The results of these validation studies indicate that these relatively simple closed-form equations can predict, with a high degree of accuracy, the initial thermal postbuckling response of axially restrained columns with the various rotational and lateral end restraints considered in this paper.