Question

A steel rod of length 6.0 m and diameter 20 mm is fixed between two rigid supports. The stress in the rod ( in kg/cm${}^2$) is........., when the temperature increases by 80${}^o$C. (take Y $=$ 2.0x10${}^6$ kg / cm${}^2$ and $\alpha =$12x10${}^{-6}$ per${}^o$C )

a) the ends do not yield
b) the ends yield by 1 mm

• A. 1587,1920
• B. 1920, 1587
• C. 1000,2000
• D. 2000, 1000

Answer 1

The correct option is B 1920, 1587

$\Delta T={80}^{0}C$

$\Delta L=L\alpha \Delta T=6\times 12\times {10}^{-6}\times 80$

$=57.6\times {10}^{-4}m.=5.76mm$

$A=\frac{\pi \left({10}^2\right)}{10}=\pi \times {10}^{-4}{m}^2,L=6m.$

(a) ends do not yield.

$stress=\frac{F}{A}=\frac{y\Delta L}{L}=2\times {10}^6\times \frac{5.76}{6000}$

$stress=1920kg/c{m}^2$

(b) ends yield 1 mm, i.e. now $\Delta Lis(5.76-1)$

$=4.76$ mm

$stress=\frac{y\Delta L}{L}=2\times {10}^6\times \frac{4.76}{6000}$

$=1587kg/c{m}^2$