Question

A mild steel bar is subjected to an axial force P, resulting in an axial stress ${\sigma }_x=100N/m{m}^2$. What would be the normal stress ${\sigma }_n$ on a plane n-n making an angle $\theta =45°$ with its axis?

• A. 25 $N/m{m}^2$
• B. 40 $N/m{m}^2$
• C. 50 $N/m{m}^2$
• D. 100 $N/m{m}^2$

Answer 1

The correct option is C 50 $N/m{m}^2$

${\sigma }_n=\frac{{\sigma }_x+{\sigma }_y}{2}+\frac{{\sigma }_x-{\sigma }_y}{2}\cos 2\theta$

$\therefore {\sigma }_n=\frac{100+0}{2}+\frac{100-0}{2}\times \cos 90{}^{\circ }$

$\therefore {\sigma }_n=50N/m{m}^2$