Deformation of Elliptical Hollow Sections under Pure Bending – Using Reissner’s Differential Equations

The increased frequency in the use of glass facades coupled with aesthetical requirements of architectural design has amongst other factors required the use and subsequently the understanding of elliptical hollow sections behaviour. Up until now, approximate solutions have been employed for the design of elliptical hollow section. The behaviour of other cross sections, such as circular and rectangular has been well studied and the Brazier’s flattening effect verified. This work attempts to extend Brazier’s study to elliptical hollow sections under pure bending through the use of general differential equations formulation developed by Reissner for the behaviour of thin sections under pure bending. Corresponding cross section deformations were obtained and the deformed
shapes plotted for different curvature values. Simplified numerical modelling was employed to study the effect of increasing thickness on the elliptical hollow section failure mechanism.