How Wide Should Expansion Cracks Be Between Concrete Slabs to Prevent Buckling?

[LostTexan07]

Homework Statement

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?

Homework Equations

[delta]L = aL[delta]T

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

 

[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.

 

[ogb p]

.

Your approach is on the right track, but there are a few things to consider in order to find the correct answer. First, you need to take into account the fact that the expansion will occur on both sides of the slab, so you should double your calculations for the increase and decrease in temperature. Additionally, you should use the absolute value of the temperature differences (|56-20| and |-30-20|) to ensure you get a positive value for the expansion. Finally, you should also consider the fact that the expansion cracks need to be wide enough to accommodate the maximum expansion, so you should take the larger value between the two calculations.

Therefore, the correct calculation would be:
(2)(12x10^-6)(28m)(|56-20|)=0.033984=3.4x10^-2 or 3.4 cm
(2)(12x10^-6)(28m)(|-30-20|)=0.0384=3.8x10^-2 or 3.8 cm

The larger value between 3.4 cm and 3.8 cm would be 3.8 cm, so the expansion cracks should be at least 3.8 cm wide to prevent buckling.