Statics of the laterally loaded shear-flexure beam with hinged end and elastic interior supports

Abstract

Applying the principle of the minimum complementary energy a simple method is developed for the determination of the response quantities of the shear-flexure beam with hinged laterally fix end supports and laterally elastic interior supports subjected to lateral loads at the nodes. For up to seven-span beams closed-form solutions are derived, whilst for beams with eight or more spans formulas are given for the coefficients and load-terms of the compatibility equations system, so that the response quantities can easily be obtained. The general method includes, as limit or special cases, the solutions for the shear beam with elastic supports, the flexure beam with elastic supports and the simple shear-flexure beam without interior supports. As practical applications of the developed theory, flat-roofed diaphragms in the form of either stressed-skin deckings or longitudinal trusses and grid structures are dealt with and the corresponding stiffnesses defined. A numerical example of a typical industrial building illustrates both the general and the special-case approaches and a discussion of the results points out the effect of the system's parameters onto its response. The paper intends to contribute to an easier design and preliminary and simple final analyses of some spatial building structures.