Question

A thin steel ruler having its cross-section of 0.0625 cm x 2.5 cm is bent by couples applied at its ends so that its length / equal to 25 cm, when bent, as a circular arc, subtends a central angle $\theta ={60}^o$. Take $E=2\times {10}^{6}kg/c{m}^2$. The maximum stress induced in the ruler and the magnitude is

• A. $2618kg/c{m}^2$
• B. $2512kg/c{m}^2$
• C. $2406kg/c{m}^2$
• D. $2301kg/c{m}^2$

Answer 1

The correct option is A $2618kg/c{m}^2$


$L=R\theta$

$\therefore R=\frac{L}{\theta }=\frac{25}{\left(\pi /3\right)}=23.8732cm$

Maximum bending stress,

${\sigma }_{max}=\frac{E}{R}.y_{max}=\frac{2\times {10}^6}{23.8732}\times \frac{0.0625}{2}$

$=2618kg/c{m}^2$