Question

A rod is 2m long at temperature of 10oC. Find the expansion of the rod, when the temperature is raised to 80oC. If this expansion is prevented, find the stress induced in the material of the rod. Take E = 1.0 x 105 MPa and α = 0.000012 per degree centigrade.

Answer 1

Answer:

ΔL = 1.68 mm

σ = 84 MPa

Explanation:

Thermal expansion is:

ΔL = α ΔT L

Thermal stress is:

σ = α ΔT E

Given:

α = 1.2×10⁻⁵ /°C

E = 1.0×10⁵ MPa

ΔT = 80°C − 10°C = 70°C

L = 2 m

ΔL = (1.2×10⁻⁵ /°C) (70°C) (2 m)

ΔL = 0.00168 m

ΔL = 1.68 mm

σ = (1.2×10⁻⁵ /°C) (70°C) (1.0×10⁵ MPa)

σ = 84 MPa