The elastic stability of partially-restrained plates under compression and in-plane bending

Conventional stability analysis of plates under combined compression and in-plane bending is based on the assumption that the plate is free to move laterally and hence the restraints imposed by the attached elements are ignored. If the plate is considered, more realistically, to be restrained against in-plane motion, a set of destabilizing forces appears that results in a lower buckling load and possibly a different buckling mode from the free in-plane case. The paper illustrates the influence of this restraint on the stability of plates under compression and in-plane bending. The unloaded edges are assumed to be partially-restrained against rotation and in-plane translation, while remaining straight, and the distribution of the reactive forces acting on the plate is shown. A generalized formulation for the buckling coefficient is first derived in terms of given functions that describe the longitudinal and transverse displacement profiles. Using the prescribed formulation, a closed form expression is derived for the computation of the K factor for plates partially-restrained against rotation and in-plane translation. Numerical verification is then undertaken using the Galerkin method to check the accuracy of the derived expression for the limiting conditions of simply-supported and clamped boundaries. It is shown that the difference ranges from 0 to 4%. A comparison is also made with the predictions of the buckling load calculated from various formulae available in design specifications, which are based on free in-plane motion, and numerical values based on the fully-restrained condition. A difference of up to 34% is found in the predictions of K and different buckling modes are observed. Finally, the transition of the buckling coefficient, K, from pinned to clamped boundaries for various plate aspect ratios and lateral restraint intensities is also presented.