A thin-walled cylindrical can with rigid end caps has a mean radius R=100 mm and a wall thickness of t=5 mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction. Assume the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is __________ (correct to two decimal places).
Explanation
Hoop (circumferential) stress: σθ = pR/t. Total axial stress = pressure-induced axial stress + applied 50 MPa = pR/(2t) + 50. Setting σθ = σaxial: pR/t = pR/(2t) + 50 → pR/(2t) = 50 → p = 100t/R = 100×5/100 = 5 MPa.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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