THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Thermal expansion
Only the heating after contact creates stress
An initially stress-free 0.80 m rod can slide into a 0.24 mm axial gap before reaching a rigid stop. Its α is 15 × 10⁻⁶ K⁻¹ and Young’s modulus is 120 GPa. The uniform temperature rises by 50 K. Assume straight elastic deformation without buckling or yielding.
What is the final compressive stress magnitude?
Organize the givens & assumptions
- L0 = 0.80 m
- Gap = 0.24 mm
- α = 15 × 10⁻⁶ K⁻¹
- Y = 120 GPa
- ΔT = 50 K
Uniform temperatures and the stated expansion coefficients; small thermal strains and first-order expansion unless a retained ratio is explicitly requested. Free expansion except for the named axial constraints. Constrained rods remain straight and linearly elastic; no buckling, yielding or moving supports.
- A
- B
- C
- D
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