On November's eve - the fifth,In the year of '84,Three hardy sons of StaffordshireTo labour went once more'Mid the furnace light and glare,'Twas indeed a busy scene;Those sons of toil they little knewOf the danger - then unseenA sudden crash! A peal like cannon's roar!Good God! What can it mean?Alas, their earthly toil is o'er!While destruction reigns supreme.They wrought and toiled as EnglishmenKnow only how to do.And at the post of duty fell, Mourned by all who knew.

Thin wall pressure vessel

Explosion at Wolverhampton, England, November 5th 1884

Three men killed

Pressure vessels are subject to loading from all directions. The analysis can be relatively straight forward if the walls are thin (less than 1/10 of the radius of the vessel). We will cover cylindrical and spherical vessels.

Away from the ends the force in an annular section of the vessel must balance the force due to the pressure in the vessel.

Cross sectional area of section through hoop is tdy and the stress in the hoop is 1. The force due to the pressure is distributed across the entire inner area of the section. This area is 2rdy.

t

pr

rdyptdy

1

1 022

t

pr

rprt

22

02 22

t

pr

rprt

22

02 22

For a spherical vessel the result is the same as for the top of a cylinder.

There is also a radial stress that we have neglected – it falls from P inside to 0 outside the vessel. The thin walls will be compressed in the radial direction. For this analysis we will neglect this because it is small if t/r is greater than 10.

The gas pipe line is supported every 20 ft by concrete piers and also lays on the ground. If there are rigid retainers at the piers that hold the pipe fixed, determine the longitudinal and hoop stress in the pipe if the temperature rises 60° F from the temperature at which it was installed. The gas is at a a pressure of 600 lb/in2. The pipe has an inner diameter of 20 in and thickness of 0.25 in. The material is A36 steel (E=29,000 ksi; alpha=6.6 x 10-6 /°F)