Chapter 8 Applications of Plane Stress (Pressure vessels, Beams ...

F horiz = 0 (2 r m t) - p ( r 2 ) = 0the tensile stresses in the wall isp r 2 = CCC2 r m tfor r >> t (r > 10 t), r m j r thenp r = CC2 twhen we cut through the center of the sphere in any direction, we canconclude that the sphere is subjected to uniform tensile stress in alldirections, they are known as membrane stressesStresses at the outer surfacethenp r 1 = 2 = CC 3 = 02 tStresses at the inner surface p r max = C = CC2 4 tp r 1 = 2 = CC2 t 3 = - p + p p r p p rthen max = CCC = CC + C = C (C + 1)2 4 t 2 2 2tLimitations of thin-shell theory1. r > 10 t or more2. internal pressure must exceed external pressure2