Most solid materials change size when their temperature changes, and this effect is called thermal expansion. In bridges, rails, pipelines, and building frames, even a small fractional expansion can become a large motion over long distances. Engineers must predict this motion so parts do not buckle, crack, jam, or tear loose.
Expansion joints give structures controlled space to move safely as the temperature rises or falls.
For a uniform bar, the change in length depends on its original length, its temperature change, and its coefficient of linear expansion. If a part is free to expand, it changes length with little internal stress, but if it is restrained, thermal stress can build up. This stress is caused by the material trying to expand or contract while supports prevent the strain from happening.
In design, engineers combine expansion calculations with material strength limits to choose joint gaps, support locations, and safe operating temperatures.
Key Facts
- Linear expansion: ΔL = αL0ΔT
- Final length after heating: L = L0 + ΔL
- Thermal strain for free expansion: εthermal = ΔL/L0 = αΔT
- If expansion is fully restrained, thermal stress magnitude is σ = EαΔT
- Tensile or compressive force from thermal stress: F = σA
- Steel has a typical coefficient of linear expansion of about α = 12 x 10^-6 1/°C
Vocabulary
- Thermal expansion
- Thermal expansion is the increase in size of a material caused by a rise in temperature.
- Coefficient of linear expansion
- The coefficient of linear expansion, α, measures how much a material's length changes per unit length for each degree of temperature change.
- Thermal strain
- Thermal strain is the fractional change in length caused by temperature change, given by ε = αΔT for free expansion.
- Thermal stress
- Thermal stress is the internal stress produced when a material is prevented from expanding or contracting freely.
- Expansion joint
- An expansion joint is a gap or flexible connection that allows a structure to change length without building up damaging stress.
Common Mistakes to Avoid
- Using the final length instead of the original length in ΔL = αL0ΔT. The formula is based on the starting length before the temperature change.
- Forgetting that ΔT is the temperature change, not the final temperature. Use ΔT = Tfinal - Tinitial, and keep the sign if direction matters.
- Calculating thermal stress for a freely expanding part. A free part expands without significant thermal stress, while stress appears when expansion or contraction is restrained.
- Ignoring units for α and temperature. If α is given in 1/°C, then ΔT must be in °C or K since temperature changes have the same size on both scales.
Practice Questions
- 1 A 25.0 m steel rail has α = 12 x 10^-6 1/°C. If its temperature rises from 10°C to 45°C, how much does its length increase?
- 2 A steel beam with E = 200 GPa and α = 12 x 10^-6 1/°C is fully restrained while its temperature increases by 40°C. What thermal stress develops, and is it tensile or compressive?
- 3 A bridge deck has expansion joints at regular intervals, while a short steel bracket bolted tightly between two rigid walls has none. Explain which one is more likely to develop large thermal stress during a hot day and why.