A 4m long steel bar of square cross section of 40mm side is heated through $75^oC$ with its ends clamped before heating. - i. If the clamps do not yield - ii. If the clamps yield by 0.6mm - Take E = 210GPa and $α = 11.5 × 10^-6/^oC$ -

Mumbai university > MECH > SEM 3 > Strength Of Materials

Marks: 10M

Year: June 2014

$$T = 75^oC \ \ \ \ \ \ L = 4m = 4000mm$$ $$B = 40mm \ \ \ \ A = 40^2 = 1600mm$$ $$E = 210GPa \ \ \ \ α = 11.5 × 10^-6/^oC $$

When there is an increase in the temperature, the bar expands and exerts a force on the clamps. The stress or strain in the material is caused by the expansion or the contraction prevented.

$[Free Expansion – Induced Contraction] = Expansion Allowed$

$[αTL - \frac{PL}{AE}] = Expansion \ \ Allowed$

Putting in the values, we have,

$[11.5 × 10^-6][75][4000] - \frac{P[4000]}{[1600][210 × 10^-6]} = Expansion \ \ Allowed$

$[3.45] - \frac{P}{84 × 10^3} = Expansion \ \ Allowed$

i) If the Clamps do not yield,Expansion Allowed = 0mm

$[3.45] - \frac{P}{84 × 10^3} = 0$

$P = 289.8 kN$

This is the value of the thrust that the bar exerts on the clamps, when the clamps do not yield.

ii) If the clamps yield by 0.6mm, Expansion Allowed = 0.6mm

$[3.45] - \frac{P}{84 × 10^3} = 0.6mm$

$P = 239.4 kN$