Question

The three-dimensional state of stress at a point is given by
$\left[\sigma \right]=\left[\begin{array}{ccc}30& 10& -10\\ 10& 0& 20\\ -10& 20& 0\end{array}\right]MN/m^2$
The shear stress on the x-face in y-direction at the same point is then equal to

• A. zero $MN/m^2$
• B. -10$MN/m^2$
• C. 10 $MN/m^2$
• D. 20 $MN/m^2$

Answer 1

The correct option is C 10 $MN/m^2$

$\left[\sigma \right]=\left[\begin{array}{ccc}30& 10& -10\\ 10& 0& 20\\ -10& 20& 0\end{array}\right]$

$\left[\sigma \right]=\left[\begin{array}{ccc}{\sigma }_x& {\tau }_{xy}& {\tau }_{xz}\\ {\tau }_{yx}& {\sigma }_y& {\tau }_{yz}\\ {\tau }_{zx}& {\tau }_{zy}& {\sigma }_z\end{array}\right]$
Shear stress on the x-face in y-direction is represented by ${\tau }_{xy}$, Hence on comparing above two matrices
${\tau }_{xy}=10MN/m^2$