Simplified analysis and design of free standing stairs resting on partially rigid support

Abstract

Conventional design of a free standing stair is dependent on some approximate analytical methods. The conventional methods fail to recognize the variation of stress resultants across any cross section of the stair slab. Amanat (1993] made an extensive finite element study on free standing stairs and proposed a simplified but rational guideline for easy analysis of free standing stairs based on seven semi-empirical equations for direct evaluation of forces and moments at critical locations. His approach recognizes the stress variation across different sections of the free standing stair .. Later, in the study of Zahid (1999], two equations were developed for two redundants, namely the lateral shear and the bending moment at the mid-landing section. The moments and forces at the other critical locations can be calculated using equilibrium equations. In all these studies, supports were assumed completely fixed at floor levels. In the present study, two sets of empirical equations are developed for three cases of loading for stairs resting directly on the floor slab which can provide only partial rigidity as support. Other necessary design parameters are obtained from equilibrium equations. Ten example stairs are solved by using the proposed equations and. finite element analysis. Comparison of these results establish the acceptability of the proposed equations. The proposed method has rendered the calculations of forces and moments very easy, and the estimation is found to be within the acceptable limits for commonly used proportions of stairs.