Shells of revolution

Rules for the design of shells of revolution under internal pressure differ from the Division 1 rules, particularly the rules for formed heads when plastic deformation in the knuckle area is the failure criterion. Shells of revolution for external pressure are determined on the same criterion, including safety factors, as in Division 1. Reinforcement for openings uses the same area-replacement method as Division 1 however, in many cases the reinforcement metal must be closer to the opening centerline. 

A shell of revolution is the form swept out by a line or curve rotated about an axis. (A solid of revolution is formed by rotating an area about an axis.) Most process vessels are made up from shells of revolution cylindrical and conical sections and hemispherical, ellipsoidal and torispherical heads Figure 13.3. 

The analysis of the membrane stresses induced in shells of revolution by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected. 

Consider the shell of revolution of general shape shown in Figure 13.4, under a loading that is rotationally symmetric that is, the load per unit area (pressure) on the shell is constant round the circumference, but not necessarily the same from top to bottom. 

Figure 13.4(a)(6). Stress in a shell of revolution (c)(d). Forces acting on sides of element abed... 

The radial (diametrical strain) will be the same as the circumferential strain e2. For any shell of revolution the dilation can be found by substituting the appropriate expressions for the circumferential and meridional stresses in equation 13.36. 

The final element which influenced the room shape selection was volumetric efficiency. To provide a given room floor area and overhead clearance requires a much larger volume for a shell of revolution than is required by a more typical rectangular-shaped room. The unusable extra floor space and volume to be ventilated in a spherical or cylindrical shell are significant penalties. 

The form of microcapsules is frequently expressed by an ellipsoidal hollow shell of revolution rather than a spherical shell. In the case of a thin oblate ellipsoidal shell, the form factor is represented by... 

Koussios S, Bergsma O K and Mitchell G (2005) Non-geodesic filament winding on generic shells of revolution, Proc I Mech E vol. 291, Pari I J Materials Design and Applications, DOI 10.1243/ 146442005X10184. 

A shell is a curved plate-type structure. We shall limit our discussior to shells of revolutions. Referring to Figure 5.1 this is denoted by an angle cp, the meridional radius and the conical radius T2, from the center line. The horizontal radius when the axis is vertical is r. 

The above two equations are the results for a general shell of revolution. Two specific cases result ... 

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