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1、Chapter 8 Applications of Plane Stress (Pressure Vessels,Beams,and Combined Loadings)Mechanics of Materials8.3 Cylindrical Pressure VesselsCylindrical pressure vesselsExamplesIndustrial settings:compressed air tanks and rocket motors;Homes:fire extinguishers and spray cans;Countryside:propane tanks
2、and grain silos;Pressurized pipes:water-supply pipes and penstocks.Normal stresses in a thin-walled circular tank1,2:membrane stresses,principle stresses=0:no shear stresses1:circumferential stress,hoop stress2:longitudinal stress,axial stressCircumferential stresst:thickness of the tank;r:inner rad
3、ius of the cylinder.Disregard the weight of the tank and its contents.resultant of 1 resultant force P1 Longitudinal stressr:inner radius of the shellresultant of 2 resultant force P2 Note:a longitudinal welded seam in a pressurized tank must be twice as strong as a circumferential seam.Stresses at
4、the outer surfaceBiaxial stressPrinciple stresses:Maximum in-plane shear stresses:Maximum out-of-plane shear stresses:Absolute maximum shear stress:Stresses at the inner surfaceTriaxial stressPrinciple stresses:Maximum shear stresses:disregarded when the shell is thin-walledDisregard the presence of the compressive stress in the z direction,the stresses at the inner surface become the same as the stresses at the outer surface.End