There are many examples of thin shells employed as structural components. In this chapter, attention is given to the membrane stresses taking place over the entire wall thickness. The general analysis of stress and deformation in several typical members is treated, applying equations derived for plates and shells as well as the principle of superposition as needed. A comparison of the bending and membrane stresses for tanks with a vertical axis is made. The expressions derived for thin cylindrical vessels are valid for those under internal pressure. They pertain equally to cases of external pressure if the sign of p is changed.
It should be noted that the stress formulas developed here are valid only if the pressure is not significant such as to cause failure by elastic instability. That is, when a vessel such as a vacuum tank is to be constructed to withstand external pressure, the compressive stresses produced by this pressure in the shell must be lower than the critical stresses at which buckling of the walls might occur. Some relationships employed in the design of plates and shell-like structures are introduced. The chapter concludes by presenting a case study on filament-wound cylindrical pressure vessels.