A uniform bar is heated uniformly but prevented from expanding in any direction. What type of internal stress develops as a result?
Compressive stress
When a bar is heated uniformly:
- Free to expand: length increases by ΔL = α·L·ΔT (no stress)
- Completely restrained (fixed at both ends): the bar cannot expand, so internal compressive stress develops
The compressive stress σ = E·α·ΔT, where E = Young's modulus, α = coefficient of thermal expansion, ΔT = temperature rise.
This is because the constraint acts like a compressive force being applied at both ends to prevent the natural expansion. The bar would have expanded but is pushed back, so it's in compression.
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