A steel rod oflength 6 mand diameter 20 mm is fixed between two rigid supports as shown in Fig. `Y= 2 xx 10^(6) N//cm^(2), alpha =12xx10^(-6)//""^(@)C` and change in temperature is `80^(@)C.`

Options

A. Stress in the rod is 1920 `N//cm^(2)` when the ends do not yields
B. Stress in the rod is 1587 `N//cm^(2)` ' when the ends do not yield
C. Stress in the rod is 1800 `N//cm^(2)` when he ends do not yield
D. Stress in the rod is 1587 `N//cm^(2)` when the ends yield by 1 mm

Answer

A, D

Explanation

Stress = Y `prop Delta theta =2xx 10^(6) xx 12 xx 10^(-6) xx 80 = 1920 N//m^(2)`
Strain `= (S)/( Y) = (1920)/(2 xx 10^(6)) = 0.00096 = (l)/(L) :. L=0.00576m`
Since it is elongated by 1 mm = 0.001 , r = 0.00576 - 0.001 = 0.00476
The new stress = `(1920xx 0.00476)/(0.00576) = 1586.67 N//m^(2)`