Simplified method for Analysis and Design of Helical Stairs

Abstract

The design of reinforced and prestressed concrete helicoidal stairs has recently very famous among the architect. Bergman suggests an approximate method of analysis, which reduces the analysis to that of a horizontal bow girder. More accurate pro- cedures based on an analysis of the longitudinal elastic axis of the girder as a three dimensional indeterminate structure have been presented by Fuchsteinner, Gedizli, Cohen,and Holmes. Analysis of helicoidal stairs require long and complex equations. The aim of Present study is to develop a simpli ed method for analysis of helicoidal stairs. Normally, he- licoidal stair is an indeterminate to the six degree. But in this report a simpli cation such as symmetrical loading condition is made in such a way that it reduces to two degree. Also it is further assumed that torsional modulus is taken as one half of the elastic modulus by neglecting poisson's ratio of the material and Ix/Iy is neglected due to stair slab width is very wide as compare to its thickness. Based on above as- sumption a stair with equal under symmetrical loading, displacement are calculated from virtual integral with application of principle of least work and two redundant are determined by solving the elastic equation and then moment and shear force are calculated. Analysis and design of helical stair is carried out using Simpli ed method and Scordelis method. The comparison of Simpli ed method and Scordelis method is also presented. Moment and force are consider as unknown redundants. For di erent values of angle the table is provided to get values of unknown redundants. A spread sheet programme is developed to calculate design moment and forces. Design example is presented and structural detailing is provided.