The cylindrical pressure vessel is fabricated using hemispherical end caps in order to reduce the bending stress that would occur if flat ends were used.The bending stresses at the seam where the caps are attached can be eliminated by proper choice of the thickness \(t_{h}\) and \(t_{c}\) of the caps and cylinder, respectively. This requires the radial expansion to be the same for both the hemispheres and cylinder. Show that this ratio is \(t_{c} / t_{h}=(2-u) /(1-u)\). Assume that the vessel is made of the same material and both the cylinder and hemispheres have the same inner radius. If the cylinder is to have a thickness of \(0.5 \mathrm{in}\)., what is the required thickness of the hemispheres? Take \(u=0.3\).

Transcribed Image Text:

In T