Question

A steel rod of length 6.0 m and diameter 20 mm is fixed between two rigid supports. Determine the stress in the rod, when the temperature increase by 80°C if

(a) the ends do not yield 

(b) the ends yield by 1 mm.

Take Y = 2.0 x 10⁶ kg/cm² and α = 12 x 10^-6 per°C

Answer 1

Given, length of the rod l = 6 m = 600 cm

Diameter of the rod d = 20 mm = 2 cm

Increase in temperature t = 80°C

Young's modulus Y = 2.0 x 10⁶ kg/cm² and thermal coefficient of linear expansion

 α = 12 x 10^-6 per°C When the ends do not yield 

Let, 

σ₁ = stress in the rod

Using the relation σ = αtY

When the ends yield by 1 mm

Increase in length due to increase in temperature

of this 1 mm or 0.1 cm is allowed to expand . Therefore, net compression in the rod

or compressive strain in the rod

Substituting the values,