In-plane stability of uniform steel beam-columns on a Pasternak foundation with zero end-shortening

The linearized buckling response of uniform steel beam-columns resting on a Pasternak foundation type is dealt with in this work. The corresponding two-point boundary value problem depends on the two parameters associated with the foundation model, that is, shear layer constant and Winkler spring coefficient, as well as on the axial loading. The fourth-order differential equation of buckling and the consequent characteristic one yield exact values of the buckling loads, which may lead to shape functions, being either one sinusoidal waveform or the sum of two different waveforms. The former case is associated with a single-mode response, while the latter with mode coupling. The conditions for which each of these cases characterizes the beam-column behavior are fully assessed and the dependence on the combination of the aforementioned parameters on the response is discussed in detail. It is found that regardless of the order of coupling, the corresponding mode is not related to rational values of buckling loads and hence this unfavorable phenomenon is excluded in structural design.