Correct Answer - Option 1 : No stress
Explanation:
Consider a prismatic steel bar of 5 mm. If the above bar is rested over frictionless surface, then on increasing the temperature of bar by T⁰C, the uniform thermal strain is given by,
ε = αT
If above bar is free to expand, then there will be no thermal stresses. Let us assume bar is constrained between fixed supports. In this situation thermal stress will be induced in the direction constrained.
- As we know when the temperature of anybody is changed it causes it to expand or change its dimension and this tendency of changing the shape, area, and volume of the body is called the thermal expansion of that body.
- Whereas because of this change in temperature if the length of the body is increased then it can be termed as linear thermal expansion of that body.
Whereas this change in length can be expressed as
ΔL = L α Δ T
i.e., \(Thermal~strain=\frac{\text{ }\!\!\Delta\!\!\text{ }L}{L}=\alpha \text{ }\!\!\Delta\!\!\text{ }T\)
And due to this thermal expansion, the thermal stress developed in a material can be expressed as
\(E=\frac{Thermal~stress}{Thermal~strain}\Rightarrow ~Thermal~stress=E\times \alpha \text{ }\!\!\Delta\!\!\text{ }T\)
Where,
ΔL = changes in length,
L = original length,
ΔT = change in temperature of the body
α = the coefficient of linear expansion.
E = Elasticity modulus
