The Eiffel Tower is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (temperature of 31°C) and January (temperature of-4°C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.

I found ##11.55cm##

We need to consider thermal linear expansion. In this case I would try to find the coefficient of linear expansion of iron (from literature): Then we can say that the change in length ##Deltal## will be related to the original length ##l_0##, the coefficient ##alpha## and the change in temperature ##DeltaT## as:

##Deltal=alphal_0DeltaT## or with our data: ##Deltal=11.7xx10^-6*300*(-4-31)=-0.1155m## ]Cooling the tower it shrinks of ##0.1155m=11.55cm##