Correct Answer - Option 4 : All of these
Explanation:
- When the temperature of material changes there will be a corresponding change in dimension.
- If a member is free to expand or contract due to the rise or fall of the temperature, no stress will be induced in the member.
- If the member is constrained (i.e. body is not allowed to expand or contract freely), change in length due to rise or fall of temperature is prevented and stresses are developed in the body which is known as thermal stress.
- The change in length (ΔL) due to change in temperature is found to be directly proportional to the length of the member (L) and to change in temperature (ΔT).
ΔL ∝ L ΔT
ΔL = αLΔT
where α is known as the coefficient of thermal expansion.
So Strain due to change in temperature,
\(\epsilon=\frac{Change\ in\ Length}{Original\ Length}=\frac{α LΔ T}{L}=α Δ T\)
From hook's law,
\(σ=\epsilon E=α Δ TE\)
where σ = Thermal stress, E = Modulus of elasticity of the material
Hence it clear that thermal stress is directly proportional to change in temperature (ΔT), Coefficient of thermal expansion (α), and modulus of elasticity (E).
