Question

A rod is 2 m long at 10 ºC. Find the expansion of the rod when the temperature is raised to 80 ºC. Take E = 10 kN/mm2 and α = 12 x 10-6/ ºC. *

Answer 1

Answer:

Free expansion of the rod =αLΔθ

=15×10

−60

C×2m×(50−20)

0

C

=9×10

−

4m=0.9mm

If the expansion is fully prevented, then

Strain=

2

9×10

−4

=4.5×10

−4

Temperature Stress = Strain ×Y

=4.5×10

−4

×2×10

11

=9×10

7

N/m

2

If 0.4 mm expansion is allowed, then length restricted to expand

=0.9−0.4=0.5mm

Strain=

2

5×10

−4

=2.5×10

−4

Temperature stress = Strain ×Y=2.5×10

−4

×2×10

11

=5×10

7

N/m

2