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 (read aloud: delta-L equals alpha L-nought delta-T). is the growth in length — what you are solving for: is alpha, the material's expansion coefficient per °C, is said “L-nought”, the length before the warmth, and is the temperature rise in C°. For steel, : twelve millionths of its length, per degree.
Twelve millionths sounds like nothing — until is a hundred-metre bridge deck and 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.
- = Change in length (length)
- = Linear expansion coefficient (thermal expansion coefficient)
- = Original length (length)
- = Temperature change (temperature difference)