# Homework Help: Bridge expansion problem

1. Nov 28, 2007

### LostTexan07

1. The problem statement, all variables and given/known data
A concrete highway is built of slabs 28 m long (20°C). How wide should the expansion cracks be (at 20°C) between the slabs to prevent buckling if the range of temperature is -30°C to +56°C?

2. Relevant equations
[delta]L = aL[delta]T

3. The attempt at a solution
I tried to multiply the coefficient of linear expansion for concrete by the slab length and increase in temperature:
(~12x10^-6)(28m)(56-20)=0.012096=1.2x10^-2 or 1.2 cm

Then I did the same thing for the decrease in temperature:
(12x10^-6)(28m)(-30-20)=-0.016=1.6x10^-2 or -1.6 cm

I then added the expansions for the increase and decrease in temperature:
1.2 + 1.6 = 2.8 cm
But that is not the correct answer

2. Nov 28, 2007

### Shooting Star

The slabs will buckle only when they expand and push at each other. The max effect will be when two consecutive ones just touch each other at 56 C. For that, each slab will expand by half the dist between them, on either side.

Now I hope you can finish the calculation.