A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10^–5 °C^–1.

Question

A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10^–5 °C^–1.

Philoid · Accepted Answer

Given:
Temperature at which rod is unstrained: T₁= 20 ° C
Increased Final Temperature : T₂ = 50 ° C
Change in temperature : Δ T = T₁ – T₂ = 30 °C
Coefficient of linear expansion of steel: α = 1.2 × 10^–5 °C^–1.
Formula used:
Now we know that formula for linear thermal expansion of a body is:
Where ΔL is the Change in Length and L is the initial length at T₁.
Substituting ,

But, Strain is Change in length divided by original length:

Hence, Longitudinal strain developed in the rod is 3.6 x 10

A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10–5 °C–1.

A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10^–5 °C^–1.