Question

A state of plane stress consists of uniaxial compressive stress of magnitude 10 kPa on a vertical surface, along with an unknown shear stress. If the largest stress is 12 kPa tension, the magnitude of unknown shear stress (in kPa, round off to two decimals) is___.

• A. 16.2

Answer 1

The correct option is A 16.2
Given, ${\sigma }_1=12kPa$
${\sigma }_x=-10kPa,\tau =?$
${\sigma }_1=\frac{{\sigma }_x}{2}+\sqrt{{\left(\frac{{\sigma }_x}{2}\right)}^2+{\tau }^2}$
$12=-\frac{10}{2}+\sqrt{{(-\frac{10}{2})}^2+{\tau }^2}$
$\tau =16.248\text{kPa}$