Geometrically and materially nonlinear analysis of reinforced concrete shells of revolution

Abstract

Reinforced concrete dome shell roofs are often used to provide a light, efficient structure spanning over a large clear space. Examples include auditoria, gymnasia, water tanks, and storage structures. These domes generally have a conical, spherical or ellipsoidal meridian, but they may have a complex meridional profile and a continuously varying thickness. When the shell is thin and the radius of curvature is large, they are susceptible to axisymmetric snap-through buckling or collapse. The collapse of a shell in this manner instigated the work described in this paper. Existing solutions for snap-through buckling are often used in current design, but they are generally of limited value because they relate to elastic shells of uniform thickness. However, the non-uniformity of the shell thickness, and the cracking and yielding in reinforced concrete have strong influences on the snap-through collapse load. In this paper, a general finite element formulation is presented for the large deformation and collapse analysis of reinforced concrete doubly-curved axisymmetric shells. The nonlinear behaviour of concrete is modelled using a rigorous concrete plasticity model. It includes the effects of flexural, stretching, thermal and shrinkage cracking. The analysis is applied to an example dome roof which fails by snap-through buckling.