Project ForgeA thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson's ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became t̄. The corresponding change in the wall thickness of the cylindrical portion, i.e. 100×(t̄−t)/t, is ___________% (round off to 3 decimal places).
Explanation
Hoop strain εθ = ΔC/C = 0.001 (perimeter ∝ radius). For a closed thin cylinder, σθ=pr/t, σz=pr/2t, σr≈0. Thickness (radial) strain εt=−(ν/E)(σθ+σz)=−(ν/E)(3pr/2t), while εθ=(pr/Et)(1−ν/2). So εt/εθ = −(3ν/2)/(1−ν/2) = −9ν/5. With ν=1/3: εt/εθ=−0.6. εt=−0.6×0.001=−0.0006=−0.06%.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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