Chapter 8 - Imperfect shallow shells

Abstract

The stress resultants in shallow shells are sensitive to the presence of small deviations in the geometry. This chapter describes simple solutions and numerical results for shallow shells commonly employed as roofs in industrial or sports buildings. It presents the equivalent load equations, in which the solution of the bending equations is made using a Ritz technique. The advantage of this solution is that it yields explicit equations for displacements and stress resultants of the imperfect shell. It is noted that the solution presented is linear in the amplitude of imperfection, and is also restricted to the first order equivalent load. This approximation can be enough to get an estimate of the stress levels in an imperfect shallow shell. The chapter also presents the results for an elliptical paraboloidal shell to illustrate how important the stress is in a practical situation. It is observed that the main difference between a flat plate and a shallow shell is the geometric curvature of the shell.