He's checking an expansion joint in a bridge.  Bridges are constructed with gaps in them on purpose, to account for changes in size they experience when temperatures go up and down.  Concrete is brittle, and it would crumble without these gaps.

The particles in the bridge move less in the winter, so the bridge contracts.  Likewise, the bridge expands in the summer.
 

VS.

Differing materials expand and contract at different rates.  A coefficient is used when predicting the effects of temperature changes on materials.

DL=LoaDT... says that the change in length depends on the material involved, its original length, and the temperature change
DL=Lf-Lo

Insert the second equation into the first one to get:

Lf=Lo[1+a(Tf-To)] where Lf and Lo are the final and original lengths, and Tf and To are the temperatures, and a is the expansion coefficient

How much longer is a 60m long aluminum plane when its temperature increases by 100°C?  a=24E^-6/°C

Here, we can just use DL=LoaDT because no original temp is specified...
 DL=(60m)(24E^-6/°C)(100°C)= .14m