Tolerance limits for geometric imperfections in hyperbolic cooling towers

The imperfection forces, due to a meridional imperfection in the form of a cosine curve, are calculated using a series solution to the classic elastic thin-shell theory for hyperboloid cooling tower shells. The closed-form solution is extended to include the effects of reduced hoop stiffness due to vertical cracking and yield in the circumferential steel. Subsequently, tolerance limits are derived to predict the maximum permissible radial deviation at any level in a cooling tower shell assuming orthotropic behavior due to vertical cracking and extended to include yielding in the circumferential direction, assuming the shell can safely strain in the circumferential direction to twice the yield strain of steel without progressive failure. The tolerance limits derived permit larger radial deviations in the more critically stressed zones near the base of a cooling tower than the limits published by Croll and Kemp and Al-Dabbagh and Gupta in 1979 and can accommodate imperfections of very short length characteristic of a kink in the perfect meridian.