Tension and Compression Stability and Second-Order Analyses of Three-Dimensional Multicolumn Systems: Effects of Shear Deformations

The stability and second-order analyses of three-dimensional (3D) multicolumn systems including the effects of shear deformations along the span of each column are presented in a condensed manner. This formulation is an extension to an algorithm presented recently by the writer in 2002 and 2003 by which the critical load of each column, the total critical load, and the second-order response of a 3D multicolumn system with semirigid connections can be determined directly. The proposed solution includes not only the combined effects of flexural deformations and shear distortions along the columns in their two principal transverse axes, but also the effect of the shear forces along each member induced by the applied end axial force as the columns deform and deflect (as suggested by Haringx in 1947 and explained by Timoshenko and Gere in 1961) in their two principal transverse axes. The extended characteristic transcendental equations (corresponding to multicolumn systems with sidesway and twist uninhibited, partially inhibited, and totally inhibited) that are derived and discussed in this publication find great applications in the stability and second-order analyses of 3D multicolumn systems made of materials with relatively low shear stiffness such as orthotropic composite materials (fiber reinforced plastic) and multilayer elastomeric bearings used for seismic isolation of buildings. The phenomenon of buckling under axial tension in members with relatively low shear stiffness (observed by Kelly in 2003 in multilayer elastomeric bearings, and recently discussed by the writer in 2005) is captured by the proposed method. Tension buckling must not be ignored in the stability analysis of multicolumn systems made of columns in which the shear stiffness ${\mathrm{GA}}_s$ is of the same order of magnitude as ${\pi }^{2}EI∕h^2$ .