Thermal Expansion Concrete Problem

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Homework Help Overview

The problem involves calculating the size of expansion gaps needed for concrete slabs on a highway, considering temperature variations from -20.0 degrees Celsius to +40.0 degrees Celsius. The original poster presents specific values and options for the required gap sizes.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the thermal expansion formula but questions whether they are using the correct temperature difference. Some participants suggest reconsidering the temperature range used in calculations.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the reasoning behind temperature choices. There is a mix of attempts to clarify the calculations and the underlying assumptions about temperature effects on concrete.

Contextual Notes

There is a discussion about the implications of temperature changes on concrete expansion and contraction, with some participants questioning the necessity of gaps during contraction. The original poster expresses uncertainty about the calculations and the provided answer options.

Mr. Goosemahn
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Homework Statement


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

1. 3.8 mm
2. 1.6 mm
3. 3.6 mm
4. 4.2 mm
5. 2.6 mm

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

1. 9.5 mm
2. 11.7 mm
3. 11.0 mm
4. 12.7 mm
5. 10.8 mm

Homework Equations


L=L0*a*T

The Attempt at a Solution


I plugged in the values I have and I got:

L=15*(12*10-6)*40 and got .0072 meters, or 7.2 millimeters, but that isn't one of the options.

I can't do 'B' until I have A.

Am I plugging in the values incorrectly?

Help?
 
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I tried the problem again and still get 7.2 millimeters. Does anybody know what exactly I'm doing wrong?
 
Do I have to divide the 7.2 by 2? That's the only possible relation that I see between what I'm getting and the possible answers, being 3.6.
 
Why did you use 40 for the temperature difference? The hottest it gets is 40 degrees, so the maximum possible temperature difference is 20 degrees.
 
ideasrule said:
Why did you use 40 for the temperature difference? The hottest it gets is 40 degrees, so the maximum possible temperature difference is 20 degrees.

But wouldn't it be 40 since the difference between -20 and 20 is 40?
 
But the concrete contracts when temperature is lowered, so you wouldn't need to leave a gap. You'd need to leave a gap when it expands.
 
ideasrule said:
But the concrete contracts when temperature is lowered, so you wouldn't need to leave a gap. You'd need to leave a gap when it expands.

Ooohhhh, that makes sense. Yeah, 3.6 worked. Thanks for the help, I really appreciate it.
 

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