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Unformatted text preview: PRESSURE VESSELS David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 August 23, 2001 Introduction A good deal of the Mechanics of Materials can be introduced entirely within the confines of uniaxially stressed structural elements, and this was the goal of the previous modules. But of course the real world is three-dimensional, and we need to extend these concepts accordingly. We now take the next step, and consider those structures in which the loading is still simple, but where the stresses and strains now require a second dimension for their description. Both for their value in demonstrating two-dimensional effects and also for their practical use in mechanical design, we turn to a slightly more complicated structural type: the thin-walled pressure vessel. Structures such as pipes or bottles capable of holding internal pressure have been very important in the history of science and technology. Although the ancient Romans had developed municipal engineering to a high order in many ways, the very need for their impressive system of large aqueducts for carrying water was due to their not yet having pipes that could maintain internal pressure. Water can ow uphill when driven by the hydraulic pressure of the reservoir at a higher elevation, but without a pressure-containing pipe an aqueduct must be constructed so the water can run downhill all the way from the reservoir to the destination. Airplane cabins are another familiar example of pressure-containing structures. They illus- trate very dramatically the importance of proper design, since the atmosphere in the cabin has enough energy associated with its relative pressurization compared to the thin air outside that catastrophic crack growth is a real possibility. A number of fatal commercial tragedies have resulted from this, particularly famous ones being the Comet aircraft that disintegrated in ight in the 1950s 1 and the loss of a 5-meter section of the roof in the first-class section of an Aloha Airlines B737 in April 1988 2 In the sections to follow, we will outline the means of determining stresses and deformations in structures such as these, since this is a vital first step in designing against failure. Stresses In two dimensions, the state of stress at a point is conveniently illustrated by drawing four perpendicular lines that we can view as representing four adjacent planes of atoms taken from an arbitrary position within the material. The planes on this stress square shown in Fig. 1 can be identified by the orientations of their normals; the upper horizontal plane is a + y plane, since 1 T. Bishop, Fatigue and the Comet Disasters, Metal Progress, Vol. 67, pp. 7985, May 1955....
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