Linear Thermal Expansion

δ_{T} = α Δ T L ε_{T} = α Δ T

A free bar changes length by α ΔT L. Handbook steel α ≈ 6.5×10⁻⁶ /°F (11.7×10⁻⁶ /°C); concrete is a little smaller (~5.5×10⁻⁶ /°F); aluminum is about twice steel. If the member is free, thermal strain produces no stress. If fully restrained, σ = E α ΔT (mechanics of materials).

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

Step-by-step solved example

Steel α = 6.5×10⁻⁶ /°F, ΔT = 100°F, L = 40 ft. Find the free expansion.

Free thermal expansion δ = α ΔT L.

1. Product
δ = α ΔT L = 6.5e−6 × 100 × 40 = 0.026 ft.
$δ_{T} = 0.026 ft$
2. Inches
0.026 × 12 = 0.312 in.
$δ_{T} = 0.312 in$

Answer: δ_T = 0.026 ft = 0.312 in

10 practice questions

0/10 correct

1.Free thermal expansion is

2.Steel α = 6.5×10⁻⁶ /°F, ΔT = 100°F, L = 40 ft. δ is

3.Handbook α for structural steel is about

4.Concrete α compared with steel is typically

5.If the bar is free to expand, thermal stress is

6.A fully restrained bar develops

7.Steel α in SI is nearest

8.Aluminum α is roughly

9.L = 30 m, α = 12×10⁻⁶ /°C, ΔT = 40°C. Free δ is

10.A temperature drop (ΔT < 0) in a free bar