Stress analysis of buildings under horizontal load. Part 2: Load distribution

Abstract

Having established the governing differential equations for buildings under horizontal load of trapezoidal distribution in Part 1 of this study, closed-form solutions are presented here for the determination of the load distribution among the bracing elements, the shear forces, bending and torsional moments and the normal and shear stresses in the bracing elements. After eliminating the hyperbolic functions by tabulating their values, simple formulae and diagrams are given for the calculation of the maximum shear forces, bending moments and Saint-Venant torsional moments. It is shown that torsion plays a crucial role in the three-dimensional behaviour. The most important geometrical and stiffness characteristics are identified and their role in the global behaviour is analysed. Guidelines are given on how to improve the structural performance of building structures. In addition to sizing the elements of the bracing system, the technique is potentially useful both at the concept design stage and for final analysis for checking of structural adequacy, assessing the suitability of structural layouts, verifying the results of other methods, evaluating computer packages, facilitating theoretical research and developing new techniques and procedures. Worked examples demonstrate that the calculation of the characteristic global deformations, load distribution, shear forces, bending and torsional moments only takes a couple of minutes.