How does the length of a bridge change with the seasons?

Harnessing my inner 10 year old, I think bridges are completely rad. The fact that we can build such huge structures across great distances safely is pretty awesome So, given my fascination with bridges, I figured I’d take a closer look at the physics that bridge builders have to consider when planning and putting together these remarkable pieces of engineering. For the sake of ease of calculations, I’m considering only the effects of temperature, not any other weather factors. I’m also assuming that the bridge will respond in a linear fashion to the changes in temperature.

The bridge I’m considering is essentially a solid slab of steel spanning a river. I’m going to take a look both at winter and summer effects of temperature on the bridge.

SUMMER

ΔT = +30^oC

α = 12x10^{-6 o}C^-1

L_o = 200m

ΔL = ?

ΔL = αL_oΔT

ΔL = (12x10^{-6 o}C^-1)(200m)(30^oC)

ΔL = 0.072m = 7.2cm

WINTER

ΔT = -20 ^oC

α = 12x10^{-6 o}C^-1

L_o = 200m

ΔL = ?

ΔL = αL_oΔT

ΔL = (12x10^{-6 o}C^-1)(200m)(-20^oC)

ΔL = -0.048m = -4.8cm

As a means of comparison, what if it was an aluminum bridge?

SUMMER

ΔT = +30 ^oC

α = 25x10^{-6 o}C^-1

L_o = 200m

ΔL = ?

ΔL = αL_oΔT

ΔL = (25x10^{-6 o}C^-1)(200m)(30^oC)

ΔL = 0.15m = 15cm

WINTER

ΔT = -20 ^oC

α = 25x10^{-6 o}C^-1

L_o = 200m

ΔL = ?

ΔL = αL_oΔT

ΔL = (25x10^{-6 o}C^-1)(200m)(-20^oC)

ΔL = -0.10m = -10cm

Guess it’s a good thing we make bridges out of steel and not aluminum!