PHYSICS HMWK: HOW LARGE IS GAP... Thermal expansion of concrete highways?

Question

The Questions is:

A highway is made of concrete slabs that are 15 m long at 20.0degrees Celsius.

(a) If the temperature range at the location of the highway is from -20.0degrees Celsius to +40.0degrees Celsius, what size expansion gap should be left (at 20.0degrees Celsius) to prevent buckling of the highway?

(b) How large are the gaps at -20.0degrees Celsius?

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To get (a) I understand that

Delta L= 15 * 12E6 * (40-20)

after converting this = 3.6mm

Part (b) is where I am lost.......

Answer 1

You have it right.

Delta L= 15 * 12E-6 * (40-20)

after converting this = 3.6mm

For part (b), do the same thing, only plug -20˚ in:

Delta L= 15 * 12E-6 * (40-(-20))

ΔL = 15 * 12E-6 * (60)

ΔL = 10.8 mm

Answer 2

The chances the concrete actually buckling are slim due to the small coefficient of expansion of concrete. lol tell your teacher the gaps could be 1mm- 10000000mm due to the vagueness of the question. Should be the smallest gap allowed to prevent buckling, even then you would have to use the indeterminant buckling formula to find the stresses.