DISCUSSION
This problem will involve three components of normal stress (σx, σy and σz) and three components of normal strain (εx, εy and εz). Before starting the solution, consider which of the three components of stress and which of the three components of strain are known based on the statement of the problem.
Next write down the three Hooke’s law equations from lecture. These equations can be used to solve for the remaining unknown stress and strain components.
Recall the definition of strain in order to solve for Part (b).
Ask/answer questions in the discussion thread below.
I believe we’re supposed to assume $\sigma_{x} = -\frac{400\cdot10^{3}}{0.2\cdot0.4}$. The solution takes few steps and the equations are linear.
If assuming $\sigma_{x} = -\frac{400\cdot10^{3}}{0.2\cdot0.4\cdot(1+\epsilon_{z})}$, the equations are quadratic, and the final answers are very similar to the ones found in the first assumption.