7 .Al APPENDIX VII.A DERIVATIONS OF HOOP STRESS EQUATIONS VII . A.l: GENERAL REMARKS A derivation of the equations which determine membrane stresses in a capped cylindrical pressure vessel is presented in detail in (7.Al) . It is not the purpose of this appendix to reproduce such a detailed analysis. Rather, this discussion seeks to concisely demonstrate the reasoning behind some of this study's major structural calculations to those without a background in structural mechanics. Figure 7.Al is a free-body diagram isolating one half of a lateral se~tion of the hull. This semicircle is presumed for convenience to have a uniform depth of one meter. In order to remain in equilibrium, the radial forces exerted on the hull due both to the internal pressure and to the imposed centrifugal acceleration must be balanced by the stresses developed within the hull plate. This observation is the basis for the following calculation. VII.A.2: DETERMINATION OF HOOP STRESSES IN A SINGLE HULL Let F be defined as the total force per unit area directed radially outward and acting upon a single hull. The hoop stress developed in the hull by the action of this force is given by 0 8 . The force exerted by this stress over a specified section of hull is then given by the stress, 0 8 , multiplied by the longitudinal length of the section and the section plate thickness. For the situation illustrated in Figure 7.Ai: where Fp force due to hoop stress t hull plate thickness
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