Test Academy | A 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 𝑡 . The corresponding change in the wall thickness of the cylindrical portion, i.e. 100 × (𝑡 − 𝑡)/𝑡, is _____

Question

A 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 𝑡 . The corresponding change in the wall thickness of the cylindrical portion, i.e. 100 × (𝑡 − 𝑡)/𝑡, is ______%. (round off to 3 decimal places).

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Answer :

Correct answer is : -0.06

t = wall thickness, r = nominal radius, μ = 1/3,

change in nominal (circumferential) perimeter: hoop strain = 0.1 %

changed wall thickness due to nominal strain(due to radial strain) = t̅

change in the wall thickness of the cylindrical portion $\frac{δ t}{t}$ = (t̅ − t)/t

$ϵ_{h} = \frac{p d}{4 t E} (2 - μ)$ = 0.1/100

$\frac{p d}{4 t E} = \frac{0.001}{2 - \frac{1}{3}}$ =

Radial strain : $\frac{δ t}{t} = \frac{1}{E} [σ_{3} - μ (σ_{1} + σ_{2})]$

since σ3 = 0, σ2 = σ1/2, $σ_{1} = \frac{p d}{2 t}$

$\frac{δ t}{t} = - \frac{1}{E} μ \frac{3 σ_{1}}{2}$ = $- 3 μ \frac{p d}{4 t E}$

$δt/t = - 3 \times \frac{1}{3} \times \frac{0.001}{2 - \frac{1}{3}}$

δt/t × 100 = - 0.06 %

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