Topic: Strength of Materials
For a body subjected to direct stresses $\sigma_x, \sigma_y$ and $\sigma_z$ the direct strain $\epsilon_x$, in x direction is (where E and $\gamma$ are Young's Modulus and Poisson's ratio respectively)
- A. $\epsilon_{x}=\frac{1}{E}\{\sigma_{x}+\gamma(\sigma_{y}-\sigma_{z})\}$
- B. $\epsilon_{x}=\frac{1}{E}\{\sigma_{x}-\gamma(\sigma_{y}+\sigma_{z})\}$
- C. $\epsilon_{x}=\frac{1}{E}\{\sigma_{x}-\gamma(\sigma_{y}-\sigma_{z})\}$
- D. $\epsilon_{x}=\frac{1}{E}\{\sigma_{x}+\gamma(\sigma_{y}+\sigma_{z})\}$
Answer: B. $\epsilon_{x}=\frac{1}{E}\{\sigma_{x}-\gamma(\sigma_{y}+\sigma_{z})\}$
Explanation: Let E and $\gamma$ be Young's modulus and Poisson's ratio. The strain in the x-direction in a 3D body is derived using generalized Hooke's Law: $\epsilon_{x}=\frac{1}{E}[\sigma_{x}-\gamma(\sigma_{y}+\sigma_{z})]$.