Question

A thin cylindrical tube with closed ends is subjected to:
1. Longitudinal stress ${\sigma }_1=14N/m{m}^2$
2. Hoop stress ${\sigma }_2=2N/m{m}^2$
3. Shearing stress $\tau =8N/m{m}^2$
Then the maximum shearing stress is

• A. $14N/m{m}^2$
• B. $12N/m{m}^2$
• C. $10N/m{m}^2$
• D. $8N/m{m}^2$

Answer 1

The correct option is C $10N/m{m}^2$

Thee cenre of Mohr's circle
$C=\frac{{\sigma }_1+{\sigma }_2}{2}=\frac{14+2}{2}=8N/m{m}^2$
Radius of Mohr's circle
$\sqrt{{\left(\frac{{\sigma }_1+{\sigma }_2}{2}\right)}^2+{\tau }^2}=\sqrt{{\left(\frac{14+2}{2}\right)}^2+8^2}$
$=10N/m{m}^2$
Maximum shearing stress $=$ Radius
$=10N/m{m}^2$