• question_answer Hoop stress and longitudinal stress in a boiler shell under internal pressure are $100\,\text{MN/}{{\text{m}}^{\text{2}}}$ and $50\,MN/{{m}^{2}}$ respectively. Young's modulus of elasticity and Poisson's ratio of the shell material are $200\,\text{GN/}{{\text{m}}^{\text{2}}}$ and 0.3 respectively. The hoop strain in boiler shell is: A) $0.425\times {{10}^{-\,3}}$                B) $0.5\times {{10}^{-\,3}}$C) $0.585\times {{10}^{-\,3}}$                D) $0.75\times {{10}^{-\,3}}$

${{\sigma }_{\theta }}=100\,\text{MN/}{{\text{m}}^{\text{2}}}\text{,}$ ${{\sigma }_{t}}=50\,G\text{N/}{{\text{m}}^{\text{2}}}\text{,}$ $E=200\,M\text{N/}{{\text{m}}^{\text{2}}}\text{,}$ $v\text{ }=\text{ }0.3$ ${{E}_{\theta }}=\frac{1}{E}[{{\sigma }_{\theta }}-v{{\sigma }_{1}}]$ $=\frac{1}{200\times {{10}^{3}}}[100-0.3\times 50]$ $=42.5\times {{10}^{-\,5}}$or$0.425\times {{10}^{-\,3}}$