I was reading this topic, and this is what I Found:
Consider a rod of length $L$ which is fixed between to rigid end separated at a distance $L$. Now, if the temperature of the rod is increased by $Δθ$, then the strain produced in the rod will be:
Thermal strain,$$ε = \frac{ΔL}{L}=\frac{\text{Final length - Original Length}}{\text{Original Length}}=\alpha \Delta\theta,$$ where $\alpha=\frac{\Delta L}{L} \times \frac{1}{\Delta \Theta}.$
Now my doubt is that why are we taking Original Length as L and not as L = $L(1+\alpha\Delta\theta)$? Reason being that when we are considering a rigidly fixed rod , we can visualise that the wall/support has caused the rod to shorten or compress from its changed length of L(1+αΔθ) back to L, and so the value of strain $\epsilon$ should have been = $\frac{\Delta L}{L(1+\alpha\Delta\theta)}.$ So please explain me where I am wrong.