Cylinder

where y = R and 7= moment of inertia. For a cylinder: I = TÍ (D4 - (f)/64 in.4

Figur$ 4,! 6 Cylinder comparison of thickness for a flat end and a hemispherical end

Figur$ 4,! 6 Cylinder comparison of thickness for a flat end and a hemispherical end

This stress must then be considered in addition to the longitudinal stress already presented because of internal pressure. If the end closures are in the form of flat plates, bending stresses due to the internal pressure are introduced as:

where ?/ = thickness of end. This necessitates the wall of a flat disc-type end being extremely thick compared with a hemispherical end which is found to be the most efficient shape where the stress in the wall is:

Fig. 4.16 compares the thicknesses and corresponding volumes of the two types of ends for varying values of r (assuming p = 2,000 psi and ultimate stress in the wall material of 100,000 psi).

The volume of the flat end is found to be approximately four times the volume of the hemispherical end for any given radius of tube, resulting in increased weight and material cost. Other end shapes such as ellipse will have a volume of weight somewhere between the two, depending on the actual shape chosen.

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