Question

At a certain point in a strained material, the intensities of stresses on two mutually perpendicular planes are $150N/m{m}^2$ (tensile) and $70N/m{m}^2$ (tensile). If the maximum shear stress is $60N/m{m}^2$. The shear stress on these planes will be nearly

• A. $40N/m{m}^2$
• B. $92.19N/m{m}^2$
• C. $44.7N/m{m}^2$
• D. $60N/m{m}^2$

Answer 1

The correct option is C $44.7N/m{m}^2$

${\tau }_{max}=\sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}$

${\sigma }_x=150N/m{m}^2\left(Tensile\right)$

${\sigma }_y=70N/m{m}^2\left(Tensile\right)$

${\tau }_{max}=6N/m{m}^2$

${\tau }_{xy}=?$

$60=\sqrt{{\left(\frac{150-70}{2}\right)}^2+{\tau }_{xy}^2}$

$60=\sqrt{(40{)}^2+{\tau }_{xy}^2}$

${\tau }_{xy}^2={60}^2-{40}^2$

${\tau }_{xy}=44.72N/m{m}^2$