(Solved): 1. Consider the section cut shown below. The origin is centered on the cut. The cut extends fro ...

1. Consider the section cut shown below. The origin is centered on the cut. The cut extends from -b/2 to b/2 in the x-direction and similarly from $-\mathrm{h}/2$ to $\mathrm{h}/2$ in the $\mathrm{y}$-direction. There are no body forces, $\mathbf{b}$. The stress distribution on the cut is given by: $\overleftrightarrow{\sigma }=\left[\begin{array}{ccc}5& 5xy& -5xz\\ 5xy& -2.5y^2& 0\\ -5zx& 0& 2.5z^2\end{array}\right]\mathrm{MPa}\text{. }$ a) Does this represent an equilibrium force distribution? b) What is the total force acting on the cut? c) What is the total moment acting on the cut? Note that: $\hat{n}=\frac{1}{\sqrt{2}}(\hat{ı}+\hat{ȷ})$, where $\hat{ı}$ and $\hat{ȷ}$ are unit vectors in the $x$ - and $y$-directions respectively. The dimensions are $h=5\mathrm{cm}$ and the width $b=10\mathrm{cm}$. Note because of the angle of the cut the area is larger than bh by $\sqrt{2}$.