Lessons · Engineering · thermal expansion

Thermal expansion: heat makes it longer, and holding it makes it stressed

A bar warmed by ΔT grows by δ = α L ΔT. If it cannot grow, that same strain becomes a stress σ = E α ΔT.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

A 30 m steel pipe run was welded to the wall at both ends in January. In July it was 18 mm longer than the wall allowed, and the bracket that lost was the one nobody thought was loaded.

How to think about it

Coefficient times length times temperature change gives the free growth. Ask whether anything stops it. If so, the strain it cannot take becomes stress through E, and that stress does not care how thick the bar is.

Worked example

δ_T = α × L × ΔT

Growth is coefficient times length times temperature rise.

Steel α = 12e-6 per °C; a 30 m pipe run warms by 50 °C

The numbers that arrive on the job.

δ_T = 12e-6 × 30 × 50 = 0.018 m = 18 mm

Eighteen millimetres. A bracket has to let that happen.

Held so it cannot grow: σ = E α ΔT = 200,000 × 12e-6 × 50 = 120 MPa

Half of yield, from temperature alone, with no load on the pipe at all.

Your turn

A 12 m aluminium bar, α = 23e-6 per °C, ΔT = 25 °C. Write the growth.

δ_T = 23e-6 × 12 ×  = 0.0069 m

The trap

Mixing °F data with a per-°C coefficient. A rise of 50 °C is 90 °F, and α per °F is five ninths of α per °C. Use one system all the way through or the growth is off by nearly double.

Practise thermal expansion on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.