A steel rod of length 1 m and area of cross-section

Question:

A steel rod of length 1 m and area of cross-section 1 cm2 is heated from 0oC to 200oC without being allowed to extend or bend. What is the tension produced in the rod?

Solution:

Young’s modulus of steel, Y = 2.0 × 1011 N/m2

Coefficient of thermal expansion, α = 10-5 oC-1

Length, L = 1 m

Area of cross section A = 1 cm2 = 1×10-4 m2

Rise in temperature = 200oC

Tension produced in rod by the compression is

Y = (T/A)/(∆L/L)

T = 4 × 104 N

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