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Section 2-14 Thin-Walled Cylinders

When the wall thickness of a cylindrical pressure vessel is about one-tenth, or less, of its radius, the stress which results from pressurizing the vessel may be assumed to be uniformly distributed across the wall thickness. When this assumption is made, the vessel is called a thin walled pressure vessel. The stress state in tanks, pipe, and hoops may also be determined using this assumption.

In Figure [2-25] the inernal pressure p is exerted on the sides of a cylinder of thickness t and internal diameter D. The load tending to separate the two halves of a unit length of the cylinder is p*D. This load is resisted by the tangential stress, also called hoop stress, acting uniformly over the stressed area. We then have p*D = 2*t*sigma_t, or

     sigma_t = p * D / (2*t)             [2-51]

In a closed cylinder a longitudinal stress sigma_l will exist because of the pressure upon the ends of the vessel. The force acting upon the ends p*(pi()*D^2/4) must be equated to the longitudinal stress times the area over which the stress acts. Thus

     p * (pi()*D^2)/4 = sigma_l*(pi()*D*t)

     sigma_l = p*D / (4*t)                [2-52]