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Given: A thin-walled cylindrical pressure vessel with radius R = 1.0 ft and wall thickness t = 0.25 in. is simultaneously subjected to both an internal pressure p = 30 psi and a compressive force F at the ends. Req'd: Determine the magnitude of the force F such that sL = -sH (i.e., the wall of the cylinder is in a state of pure shear). |
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Sol'n: For the wall of the pressure vessel to be under pure shear, the longitudinal and hoop stresses must be equal and opposite. The hoop stress is:
sH = pR/t = (30 psi)(12 in.)/(0.25 in.) = 1440 psi
The stress in the longitudinal direction is equal to the superposition of the stresses due to the pressure (positive) and the compressive force (negative)
sL = pR/2t – F/[(2pR)(t)] = (30 psi)(12 in.)/2(0.25 in.) – F/[2p(12 in.)(0.25 in.)]
sL = 720 psi – 0.053F
Setting the negative of the longitudinal stress equal to the hoop stress and solving for F gives:
F = (1440 psi + 720 psi)/(0.053)
F = 40.7 kips
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