Question

For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in the figure.
By how much angle $\left(\theta \right)$ in degrees the stress element should be rotated in order to get the planes of maximum shear stress ?

• A. 26.6
• B. 48.3
• C. 31.7
• D. 13.3

Answer 1

The correct option is C 31.7

Coordinates of
$C=(\frac{80-20}{2},\frac{25-25}{2})$

$=(30,0)$

In $\Delta$ABC,
BC = 80 $-$ 30 = 50 MPa
AB = 25 MPa

$\alpha =ta{n}^{-1}\left(\frac{25}{50}\right)={26.56}^o$

$\therefore \theta ={90}^o-\alpha ={63.44}^o$
Angle to be rotated
$=\frac{\theta }{2}=\frac{63.44}{2}={31.7}^{\circ }$