Design and ultimate behavior of RC plates and shells

Abstract

An iterative numerical computational algorithm is developed to design a plate or shell element subjected to membrane and flexural forces, which is based on equilibrium considerations for the limited ultimate state of the reinforcement and cracked concrete. Equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. To verify the design algorithm on the element level several experimental examples are designed. Nonlinear inelastic analyses are performed with the designed examples using the Mahmoud-Gupta’s computer program to show the adequacy of the design equations. The calculated ultimate strengths are from 3 to 18% higher than the ultimate strength obtained from the test results, except in one example. On the global structural level, a design is performed for a hyperbolic cooling tower to check the design strength to verify the adequacy of the design algorithm. Based on the ultimate nonlinear analysis performed with the designed reinforcement, the analytically calculated ultimate loads exceed the design ultimate load from 26 to 63% for analyses with various amounts of tension stiffening effect. Even though the ultimate loads are dependent on the tensile properties of concrete, the calculated ultimate loads are higher than the design ultimate loads for the cases considered. This shows the adequacy of the design algorithm developed, at least for the structures studied. The presented design algorithm for combined membrane and flexural forces can be evolved as a general design equation for reinforced concrete plates and shells through further studies involving the performance of many more designs and analyses of different plate or shell configurations.