| Practice Problem 7-1 |
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Given: A thin walled cylindrical pressure vessel with radius 1.0 ft and a wall thickness of t = 0.25 in is simultaneously subjected to both an internal pressure of, 30 psi and a compressive force F at the ends. Req'd: Determine the magnitude of the force F [kip] such that sL = -sH (i.e., the wall of the cylinder is in a state of pure shear). |
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Solution: For the wall of the pressure vessel to be under pure shear, the longitudinal and hoop stresses should be equal and opposite. The hoop stress is given by: sH = pR/t = (30 psi)(12 in)/(0.25 in) = 1440 psi The stress in the longitudinal direction is equal to the stress due to the internal pressure minus the stress due to the compressive force: sL = pR/2t - F/[(2pR)(t)] = (30 psi)(12 in)/2(0.25 in) - F/[2p(12 in)(0.25 in)] = 720 psi - 0.053·F sL = (30 psi)(12 in)/2(0.25 in) - F/[2p(12 in)(0.25 in)] = 720 psi - 0.053·F Setting the negative of the longitudinal stress equal to the hoop stress and solving for F gives: F = (1/0.053)(1440 psi + 720 psi) = 40.7 kip |
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