Membrane Reinforcement in Saddle Shells: Design versus Ultimate Behavior

Abstract

In current practice, stresses from elastic analysis are used to design reinforcement in concrete shells based on pointwise limit state behavior. This practice may be justified in view of the lower bound theorem of plasticity and the fact that elastic stresses are equilibrium stresses. Reinforced concrete, however, is not a perfectly plastic material, and the lower bound theorem cannot be strictly applied. To verify the adequacy of current practice, therefore, an analytical program was undertaken at North Carolina State Univ. A finite element computer program, which accounts for cracking of concrete and yielding of reinforcement, and that incorporates a cracking model consistent with the limit state design equations, was developed. The program was used to analyze various plane stress and shell problems. Many cases of hyperbolic paraboloid shells were also studied and are reported in this paper. It is shown that in all the saddle shell cases analyzed, the calculated ultimate capacity exceeded the design ultimate capacity. This proves the adequacy of the current practice at least for the saddle shells studied. Other conclusions of the parametric studies performed are also presented.