Water Standpipe

Free Body Diagram

One type of water tank for a municipal water supply system is a standpipe. If the standpipe is 120 ft tall and the diameter is 30 ft, calculate the stress in the 0.5 in. thick steel plates at the bottom of the tank. Assume both ends are spherical and the tank is completely filled with water. Ignore minor pressure variations in curved ends.

The dimensions of the standpipe are:

     120 ft tall
     d = 30 ft or r = 15 ft
     t = 0.5 in

Water pressure (hydrostatic pressure variation) at the bottom of the standpipe

    p = γ_w z = (62.4 pcf)(120 ft)
       = 7,488 psf = 52.0 psi

From the free body diagram, for equilibrium F_s = pA
For unit thickness (pressure variation negligible in the limit): σ_h (2r π) (t) = p (πr²)

The hoop stress is calculated as

     σ_h = pr / 2t = (52 psi)(15 ft)(12 in/ft) / [2 (0.5 in)]
         = 9,360 psi = 9.36 ksi

Note 1: the tensile strength of steel is on the order of 40 - 80 ksi, so 0.5 in. is sufficient thickness.

Note 2: final plate thickness used in design must consider wind and/or earthquake loads.