Question

In a thermal expansion, when do you include stress and strain?

For example, if a brass bar and a copper bar are next to each other, and you want them to both expand until the total length of both bars added together is 40cm. Do you include the young's modulus with stress and strain? Will they deform? Or is this only applicable if the two bars have walls next to them?

Answer 1

The stress produced due to heat is known as Thermal Stress
and the respective strain is Thermal Strain.... BUT there are certain cases for Thermal Stress to play its role as given below :-

Explanation:

Case 1 : When both ends of the bar are free to move -

Then the Thermal Stress = Zero.
and Thermal strain = Zero.

Case 2 : When both ends are rigidly clamped -

Then Strain`= αΔT`
and Stress `= YαΔT`

`NOTE:-`

1. Here `α` is the Coefficient of Linear expansion of the given Bar.
2. `Y` is the Young's Modulus of the material of the Bar.
3. `ΔT` is the change in temperature due to heating of the Bar.

`Conclusion :-`

I hope this clears your doubt ie. the Themal Stress comes into play only when there is some force which resists the bar to expand or contract in order to compensate with the change in Temperature `(ΔT)`.