Question

The state of stress at a point is given by ${\sigma }_x=-6MPa,{\sigma }_y=4MPa$, and ${\tau }_{xy}=-8MPa$. The maximum tensile stress (in MPa) at the point is

• A. 8.43

Answer 1

The correct option is A 8.43
${\sigma }_1=\frac{{\sigma }_x+{\sigma }_y}{2}+\sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}$
$=\frac{-6+4}{2}+\sqrt{{\left(\frac{-6-4}{2}\right)}^2+(-8{)}^2}$
$=-1+\sqrt{25+64}$
$=-1+\sqrt{89}=8.43MPa$