Abstract:
Because of the absence of any specific code, the process of design of a free standing stair is
dependent on some approximate analytical methods. These methods fail to recognise the
variation of stress resultants across any cross section of the stair slab and require a lot of
computational works. Amanat[4] made an extensive study on free standing stairs using the
idealisation of Ahmad's[2] thick shell element and proposed a simplified guideline for easy
analysis of free standing stairs. His approach also recognises the stress variation across
different sections of the free standing stair, based on finite element analysis, and developed
seven empirical design equations.
If the loadings and the geometric conditions of the free standing stairs are symmetric, then,
only two redundants, namely the lateral shear and the bending moment at the mid landing
section are present. Hence, the number of empirical equations can be reduced to two for
finding the values of these two redundants. The moments and forces at the other critical
locations can be calculated by using equilibrium equations. With a view to developing a more
rational and realistic approach by reducing the number of equilibrium equations, and also for
increasing the range of applicability of Amanat's equations, this research was undertaken.
Sensitivity analysis of the different geometric parameters is carried out over an extended
range for two cases of loading. It is found that, in the higher range, the linear equations
proposed by Amanat fail to represent the moments and forces as seen from the results of
finite element analysis. Based on this study, two sets of empirical equations are developed for
two cases of loadings. Other necessary design parameters are obtained from' equilibrium
equations which reduce the total number of empirical relations, developed iby Amanat, from
seven to four. In this research, detailed study is carried out to select the equations which
nearly represent the actual situation. Ten prototype stairs are solved by using the proposed
equations, Amanat's equations, and finite element analysis. These results establish the
acceptability of the proposed equations.
The proposed method has made the calculations for forces and moments, required for design
of free standing stairs, very easy, and its estimation is found to be in the acceptable limits for
commonly used dimensional ranges of stairs. Recommendations regarding the reinforcement
layout have also been made.
