Stresses and deformations in egg-shaped sludge digestors: discontinuity effects

In the first part of this study [J. Eng. Struct. 23 (2001) 1365–1372], detailed results for stresses and deformations throughout a hydrostatically-loaded egg-shaped sludge digestor were developed on the basis of the membrane hypothesis for shells. However, and as is well-known, such results are generally unreliable around the junctions of the shell components making up the digestor. A significant amount of bending and shearing will occur in the vicinity of these junctions. In this paper, a simplified but reasonably accurate approach for quantifying discontinuity effects is developed for general shells of revolution of a certain variation of thickness along the shell meridian, and applied to the present problem of the 3-region egg-shaped digestor shell, to yield explicit closed-form results for discontinuity, and hence net, stresses throughout the digestor. These results, being very general (all parameters are kept arbitrary), enable a quick and reasonably accurate estimate of stresses in egg-shaped digestors of the type considered, and will thus be useful to the structural analyst and designer. Any desired parametric studies may also be conducted on the basis of these analytical results. Numerical results are presented, enabling some observations to be made and design recommendations proposed for egg-shaped digestors.