Shells as Tanks

Shells often don’t just resist their own self-weight, they can also be used to retain liquids. Large-scale water towers are a typical example! Liquid retaining structures have to resist internal hydrostatic pressure and perhaps even overpressure due to retained gasses if they’re sealed from the atmosphere.

Spherical Tanks

In this section, we’ll consider this load case in detail by evaluating the membrane forces in a spherical tank. Although we’ll limit our exploration to spherical tanks - you can take what you learn in this section and apply it to any of the other shell geometries we explore in this course.

The focus here is not really the shell geometry but how we handle the hydrostatic pressures induced by a retained liquid or gas.

Hydrostatic Pressure

The first task is to determine an expression for the normal pressure which is a function of the fluid depth and any overpressure present. Our spherical geometry makes this marginally more involved than for a tank with vertical side walls - but understanding how to handle this more complex geometry leaves you well-placed to handle simpler geometries later.

Membrane Forces

With our expression for the normal pressure established, we move on to evaluating the membrane forces that develop when the tank is full to the top.

From here, we’ll introduce the slight complication of the tank not being full to the top. This time, we’ll parameterise the fluid depth and re-run our analysis. In the end, we’ll see that this doesn’t actually complicate matters that much after all.

Don't forget about superposition

In this section, we’ll only focus on the membrane forces induced by the tank contents. A more complete analysis that accounts for the tank self-weight and any vertically imposed external load can be achieved by using superposition and the material we’ve already covered.