Design and inelastic behavior of hyperbolic cooling tower

A design is performed for the hyperbolic cooling tower (Grand Gulf cooling tower) to check the design strength under a consistent design load; therefore, to verify the adequacy of the design algorithm developed. Based on the equilibrium consideration for the ultimate limit state of reinforcement in tension and cracked concrete in compression, an iterative numerical computational algorithm was developed. The design algorithm is implemented in a finite element analysis computer program developed by Mahmoud and Gupta. The amount of reinforcement is then determined at the center of each element by an elastic finite element analysis with the design ultimate load. Based on ultimate nonlinear analysis performed with the designed reinforcement, the analytically calculated ultimate load exceeded the design ultimate load from 26% to 63% for analyses with tension stiffening parameters of from 5 to 20. Since the effective tension stiffening would vary over the life of the shell due to environmental factors, a degree of uncertainty seems inevitable in calculating the actual failure load by numerical analysis. Even though the ultimate loads are strongly dependent on the tensile properties of concrete, the calculated ultimate loads are higher than the design ultimate loads for the design case. For the case designed, the design algorithm gives a lower bound on the design ultimate load with respect to the lower bound theorem. This shows the adequacy of the design algorithm developed, at least for the shell studied. The presented design algorithm for combined membrane and flexural forces can be evolved as a general design method for reinforced concrete plates and shells, through further studies involving the performance of many more designs and analyses of different shell configurations.