A thin cylinder has length L, diameter d, wall thickness t, Young’s modulus E and Poisson ratio μ. Find its change in length under internal pressure P.
For the intended closed-ended vessel, longitudinal stress is Pd/(4t) and hoop stress is Pd/(2t). Axial strain is $\epsilon_L=(\sigma_L-\mu\sigma_h)/E$. Multiplying by L gives $\Delta L=PdL(1-2\mu)/(4tE)=PdL(1/2-\mu)/(2tE)$. **A**.
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