Linear Expansion Problem: Finding Optimal Crack Width for Highway Slabs

[yossup]

linear expansion problem...urgent!

Homework Statement

A concrete highway is built of slabs 12m long (20 degrees C). How wide should the expansion cracks between the slabs be (at 15 C) to prevent buckling if the range of temperature is - 30 C to 43 C?

Homework Equations

change in length = (coefficient) (initial length) (change in temperature)

coefficient = 12 * 10^(-6)

The Attempt at a Solution

So first I solved the length of the slabs at 15 C =

coefficient (12m) (-5 degrees C) = -7.2 * 10^(-4)

so (12m - 7.2 * 10^(-4)) = 11.99m

so at 15 degrees C, the slab is 11.99m

Then I solved how much it would expand/contract at 43C/-30C

basically

change of length from 15C to 43C = .00403m

change of length from 15c to -30c = -.00648

since in an expansion crack, there are slabs on both sides which would BOTH expand, I thought the answer would be .00403m + .00403m but it's wrong.

I've tried

.00403m + .00648m

.00403*2 + .00648*2

but these are all wrong.

What am I missing? No matter how much I think about it...I don't get what about my calculations are wrong. Thanks!

 

[tiny-tim]

A concrete highway is built of slabs 12m long (20 degrees C). How wide should the expansion cracks between the slabs be (at 15 C) to prevent buckling if the range of temperature is - 30 C to 43 C?
…
change in length = (coefficient) (initial length) (change in temperature)
…
coefficient = 12 * 10^(-6)since in an expansion crack, there are slabs on both sides which would BOTH expand, I thought the answer would be .00403m + .00403m but it's wrong.

I've tried

.00403m + .00648m

.00403*2 + .00648*2

but these are all wrong.

Hi yossup!

Why are you going down to -30C?

The question only involves expansion from 15C to 43C.

(and you only need to consider one slab, not two)

 

[yossup]

so the answer is simply =>

(coefficient_concrete) (11.99m) (28C) ?

why only one slab? don't you need to consider two since if two slabs next to each other both expand for example, .1m. then if they are expanding towards each other...in order for them not to buckle, there would have to be .2m of space between them.

 

[tiny-tim]

why only one slab? don't you need to consider two since if two slabs next to each other both expand for example, .1m. then if they are expanding towards each other...in order for them not to buckle, there would have to be .2m of space between them.

ah … but imagine ten slabs with 9 gaps of .01m = 120.09m total.

If they each expand by .01m, then they take up 120.1m …

so it's only one slab that has to be accounted for at both ends …

and if the highway is infinitely long, you don't even have to bother about that!