What is the necessary gap width for thermal expansion of concrete sidewalks?

[Crimsonangel]

Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4 m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of 27 C°?

http://www.webassign.net/CJ/p12-20.gif (here is a picture)

I used the equation (deltaL=alpha*Lo*deltaT). So I knew alpha was 12*10^-6 and Lo was 2.4m and deltaT was 27 C°. I got deltaL to be 7.776*10^-4 m. So the concrete expanded and how has a length of 2.4007776 m. After that I wasn't sure what to do. I thought it would be 3 times 7.776*10^-4 but it wasn't. Could you please help? Thanks so much!

 

[Ja4Coltrane]

umm... maybe I'm being dumb but it seems like since it expands both ways with a total of .0007776 m that means that each way it goes half of that, and since there are two around each gap, I think the gap is just .00078m.

 

[OlderDan]

Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4 m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of 27 C°?

http://www.webassign.net/CJ/p12-20.gif (here is a picture)

I used the equation (deltaL=alpha*Lo*deltaT). So I knew alpha was 12*10^-6 and Lo was 2.4m and deltaT was 27 C°. I got deltaL to be 7.776*10^-4 m. So the concrete expanded and how has a length of 2.4007776 m. After that I wasn't sure what to do. I thought it would be 3 times 7.776*10^-4 but it wasn't. Could you please help? Thanks so much!

The 3 times 7.776*10^-4m gives you the total expansion of the three sections. You have two gaps that can be filled in by that increased length.

 

[jalpabhav]

my temperature for this question is 37 degrees Celsius...and i got deltaL to be 0.001066...i'm still not quite sure what to do with that

 

[OlderDan]

my temperature for this question is 37 degrees Celsius...and i got deltaL to be 0.001066...i'm still not quite sure what to do with that

I assume that is for one section. You have three sections that expand, and two gaps for them to expand into. The total expansion cannot be more than the total gap space.