Thermal Expansion

δ_{T} = α Δ T L

Free thermal change in length. α is the coefficient of linear expansion. If the bar is free, thermal strain αΔT produces no stress. If fully restrained, σ = E α ΔT (compression on heating for a bar between rigid walls).

$δ_{T}$ (m): Free thermal length change
$α$ (1/°C): Coefficient of linear expansion
$Δ T$ (°C): Temperature change
$L$ (m): Original length

Step-by-step solved example

Steel α = 12×10⁻⁶ /°C, ΔT = 40°C, L = 10 m, free to expand. Find δT.

Free expansion δ = α ΔT L along the bar.

1. Free expansion
δT = α ΔT L = 12e−6 × 40 × 10 = 4.80×10⁻³ m = 4.80 mm.
$δ_{T} = 4.80 mm$
2. Stress
Free expansion → σ_thermal = 0.

Answer: 4.80 mm (σ = 0)

10 practice questions

0/10 correct

1.α = 12×10⁻⁶ /°C, ΔT = 50°C, L = 2 m. δT =

2.Fully restrained bar: thermal stress magnitude is

3.Free thermal expansion produces

4.Aluminum α is about

5.ΔT = 80°C, α = 12×10⁻⁶ /°C, L = 5 m. δT =

6.Cooling (ΔT < 0) a free bar

7.Free thermal strain αΔT is

8.Units of α are

9.Steel E = 200 GPa, α = 12×10⁻⁶, ΔT = 25°C, fully fixed. σ =

10.If supports yield slightly, thermal stress is