Question

For a state of plane stress ${\sigma }_1={\sigma }_x=40MPaand{\sigma }_2={\sigma }_{y}MPa$. What are the values of the maximum in-plane shearing stress and absolute maximum shearing stress?

• A. $(\pm 10,20)MPa$
• B. $(\pm 10,10)MPa$
• C. $(\pm 20,10)MPa$
• D. $(\pm 20,20)MPa$

Answer 1

The correct option is A $(\pm 10,20)MPa$

Maximum in-plane shearing stress

$=\pm \frac{{\sigma }_1-{\sigma }_2}{2}=\pm 10MPa$
Absolute maximum shearing stress is based on major principle stress

$=\frac{{\sigma }_1}{2}=\frac{40}{2}=20MPa$
Absolute maximum shearing stress is obtained from major principal stress applied without minor principal stress.