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Lesson 45 · The stretch of summer
Why the bridge has gaps
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Why the bridge has gaps

Warm a solid and it grows — every metre of it, by a tiny fixed fraction per degree. The machine is ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T (read aloud: delta-L equals alpha L-nought delta-T). ΔL\Delta L is the growth in length — what you are solving for: α\alpha is alpha, the material's expansion coefficient per °C, L0L_0 is said “L-nought”, the length before the warmth, and ΔT\Delta T is the temperature rise in C°. For steel, α=12×10−6 /∘C\alpha = 12 \times 10^{-6}\ /^{\circ}\mathrm{C}: twelve millionths of its length, per degree.

Twelve millionths sounds like nothing — until L0L_0 is a hundred-metre bridge deck and ΔT\Delta T is a Canadian summer. A tiny fraction of a very long thing is real millimetres, which is why decks ride on expansion joints and rails are laid with gaps. Mind the units on the way out: the machine answers in metres, and the question usually wants millimetres — cross the ×1000 bridge last.

αΔTL0ΔL

ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T

  • ΔL\Delta L= Change in length (length)
  • α\alpha= Linear expansion coefficient (thermal expansion coefficient)
  • L0L_0= Original length (length)
  • ΔT\Delta T= Temperature change (temperature difference)
Thermal Linear Expansion solver →