# Calculating Expansion Cracks Width for Concrete Highway -30°C to +32°C

• Trizz
In summary, when working with temperature changes, Kelvin usually doesn't matter, but it did for the contraction equation you worked out because you should have got a negative when you had a positive. However, you should get in the habit of working with Kelvin in thermo.
Trizz

## Homework Statement

A concrete highway is built of slabs 12 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 +32°C?

________ cm

## Homework Equations

change in L = L original * alpha * change in temp

sorry i don't have symbols and stuff

## The Attempt at a Solution

I've tried it one way so far.

Basically, I just found the difference between the higher temp and the highway temp, and solved that as one equation. Then i found the difference between the lower temp and the highway temp, and solved that as one equation. Then i added the two answers.

change in L = 12m * 1200e-6(our teacher gave us this for alpha) * (32-20) = .1728

change in L = 12m * 1200e-6 * (20-(-30)) = .72

then i got .8928 cm

any help?

I don't think you care about how much they shrink as compared to how much the slabs expand. The big ouch comes if the slabs expand and hit each other, while if they shrink then the gap just gets a little bigger. I don't see any constraint on the overall gap size itself. Also, you should be working in Kelvin!

It seems like you shouldn't add the two. Just find the largest value (as Mindscrape said we only care about expansion) and that should be how much space you should put between the slabs. So the real problem it seems is finding the maximum value of

$$|x - 20|$$

On the range $$20 < x \le32$$

ok so something like...

change in L = 12m * 1200e-6 * 12 = .1728 cm

ohh and its 12 regardless if i work in celcius or kelvin

so does that seem better?

thanks guys i got it

Yeah, for changes in temperature the Kelvin scheme usually doesn't matter, though it did for the contraction equation you worked out because you should have got a negative when you had a positive. Get in the habit of working with Kelvin in thermo. You'll be sorry later if you don't.

Yep, that's good. Technically you should have in inequality in your answer.

Mindscrape said:
Yeah, for changes in temperature the Kelvin scheme usually doesn't matter, though it did for the contraction equation you worked out because you should have got a negative when you had a positive. Get in the habit of working with Kelvin in thermo. You'll be sorry later if you don't.

Yep, that's good. Technically you should have in inequality in your answer.

He actually would have gotten a negative delta T but he switched the final and initial temperatures.

## 1. How do you calculate expansion cracks width for concrete highways?

The width of expansion cracks for concrete highways can be calculated using the coefficient of thermal expansion (CTE) of concrete and the temperature difference between the lowest and highest expected temperature. The formula is: Crack width = CTE x Temperature Difference x Length of the highway.

## 2. What is the coefficient of thermal expansion for concrete?

The coefficient of thermal expansion for concrete varies depending on the type and composition of the concrete. However, the average CTE for concrete is around 10-12 x 10^-6 per °C.

## 3. How do you determine the temperature difference for calculating expansion cracks width?

The temperature difference can be determined by taking the difference between the lowest and highest expected temperature for the concrete highway. This can be done by consulting weather data or using a thermal imaging camera to measure the temperature of the concrete surface.

## 4. Is there a specific temperature range for calculating expansion cracks width for concrete highways?

The recommended temperature range for calculating expansion cracks width for concrete highways is from -30°C to +32°C. This range covers most weather conditions and ensures accurate results.

## 5. Can expansion cracks width be prevented in concrete highways?

While it is not possible to completely prevent expansion cracks in concrete highways, proper design and construction techniques can help minimize their occurrence. This includes using appropriate joint spacing, reinforcement, and control joints to accommodate for expansion and contraction of the concrete due to temperature changes.

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