Question

The state of stresses on an element is shown in the given figure. The value of stresses are ${\sigma }_x(=32MPa);{\sigma }_y(=-10MPa)$ and major principal stress ${\sigma }_1(=40MPa)$. The minor principal stress ${\sigma }_2$ is

• A. -22 MPa
• B. -18 MPa
• C. 22 MPa
• D. indeterminable due to insufficient data

Answer 1

The correct option is B -18 MPa

Centre of Mohr's circle,
$C=\frac{{\sigma }_x+{\sigma }_y}{2}=\frac{32-10}{2}=11MPa$
Major principal stress = C + r = 40
$\because$ r = 29 MPa
Minor principal stress = C - r
= 11 - 29 = - 18 MPa