Shell analysis of an inflatable arch subjected to snow and wind loading

A ¯exible material, such as a woven or braided fabric, may be tailored to form an arch when in¯ated. Such arches have been used as the framework for transportable shelters and are analyzed in this paper. It is assumed that the cross section of the pressurized arch is circular and that only in-plane (membrane) stresses are present. An analytical solution for these initial stresses is given for an arbitrary arch centerline shape. Then external loads are applied, and the additional stress resultants include bending and twisting moments. The linear thin-shell theory of Sanders is used to formulate the governing equations, including the e€ect of the initial membrane stresses. The material is linearly elastic, nonhomogeneous, and orthotropic. Approximate solutions are obtained using the Rayleigh±Ritz method. In the examples, the centerline of the arch is a semi-circle, the ends are ®xed, and the material is homogeneous and isotropic. Four loads are treated: a symmetric (`fullʹ) snow load, an asymmmetric (`halfʹ) snow load, a wind load symmetric with respect to the plane of the arch centerline, and a distributed load acting sideways. The resulting de¯ections are computed and plotted. 7