Optimal Expansion Gap for Concrete Highway in Varying Temperatures

[liz_p88]

Homework Statement

A highway is made of concrete slabs that are 15 m long at 20.0°C. (a) If the temperature range at the location of the highway is from -20.0°C to +40.0°C, what size expansion gap should be left (at 20.0°C) to prevent buckling of the highway? (b) How large are the gaps at -20.0°C?

Homework Equations

Coefficient of Linear Expansion for concrete is 12 (10^-6 K^-1)
Change in length = (coefficient of linear expansion)(initial length)(change in temp)

The Attempt at a Solution

(a) I did {(12 x 10^-6 K^-1)(15m)(40C)} = .0072 m or .72 cm
{(12 x 10^-6 K^-1)(15m)(20C)} = .0036 m or .36 cm
.72 + .36 = 1.08 cm

(b) .72 cm

 

[gneill]

For (a), why did you add the length changes for 40C and 20C?

For (b), where did 0.72 cm come from?

 

[liz_p88]

I'm a bit confused. I added them thinking that the total expansion would vary, going up from 20 to 40 and down from 20 to -20. But what I'm thinking is that maybe when it heats up, it expands and when it cools down to -20, it contracts? I really have no idea what I'm doing and posted it on here for help.

 

[gneill]

Okay. The coefficient of expansion is positive, so the concrete will expand when heated, and contract when cooled.

The stated temperature for the initial length is 20C. If the temperature gets cooler than 20C then the slab will contract and the gap will widen -- no fear of crumpling if the gap gets wider. On the other hand, when the slab gets warmer than 20C it will expand, acting to close the gap. So it seems that if you pour the concrete at 20C you only need to make allowance for the +20C rise to 40C.

 

[liz_p88]

That makes sense. So would I only have to account for the temperature increase and disregard the contraction when solving for (a)? And did I calculate it correctly?

 

[gneill]

The value for the increase in length that you obtained looks good.

 

[liz_p88]

Awesome thank you for your input!