Question

In a plane stress condition, the components of stress at a point are ${\sigma }_x=20$ MPa, ${\sigma }_y=80$ MPa and ${\tau }_{xy}=40$ MPa. The maximum shear stress (in MPa) at the point is

• A. 20
• B. 25
• C. 50
• D. 100

Answer 1

The correct option is C 50

${\sigma }_{1,2}=\frac{1}{2}\left[\right({\sigma }_x+{\sigma }_y)\pm \sqrt{({\sigma }_x-{\sigma }_y{)}^2+4{\tau }_{xy}^2}]$
$=\frac{1}{2}[100\pm \sqrt{(60{)}^2+4\times {40}^2}]$
${\sigma }_1=100MPa$
${\sigma }_2=0$
${\tau }_{max}=\frac{{\sigma }_1}{2}=\frac{100}{2}=50MPa$