Optimal shapes of cylindrical concrete water tanks

The optimal wall shapes of circular cylindrical concrete water tanks are treated herein. The tanks have piecewise linearly tapered wall thicknesses. The internal radius and height of the tank are maintained constant while the thickness of the wall is varied along the axis so that the critical bending and hoop stresses attain values as close as possible to their allowable values. For the analysis a procedure which combines the Runge-Kutta method of solution of ordinary differential equations with a numerical minimization method is used. This procedure is then imbedded into a minimization routine to deal with the design problems. The results of the study show that the major saving in material is achieved by one slope itself. While two slopes improve the saving in material for some tanks, it does not seem reasonable to increase the number of slopes beyond two.