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Math Help - Help with determining quantity of road asphalt required.

  1. #1
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    Help with determining quantity of road asphalt required.

    Hi

    Here is my problem. I've been given this project and I'm really not sure how to approach it. The image shows a road intersection. I need to figure out the quantity of road asphalt required to pave this roadway with 50mm of asphalt. The corner radius have been given to me as '4m radius' and the asphalt density as 2.5. The circle is imaginary, I've simply included this to help me with my calculation.

    1st I calculate the total road area less the radius.
    6 x 14m =84m2
    4 x 6m=24m2
    4 x 6m=24m2
    Total area 132.0m2

    2nd I calculate the radius for 1 corner.

    4 x 4m = 16m2
    less the area of the circle 3.1416 x 2 x 2 = 12.5664m2
    the radius area = 3.4336m2 x 4 = 13.7344m2 + 132.0m2

    Grand Total Area =145.7344m2

    Now I need to calculate the quantity of asphalt to cover this area at 50mm. So I need to covert the 50mm to meters(?)
    50mm/1000 = 0.05

    Now this is where I get lost. Is this the formula I use? area x depth x density?

    145.7344 x 0.05 x 2.5 = 18.2168 mg

    Any help will be greatly appreciated.

    Attachment 22057
    Attached Thumbnails Attached Thumbnails Help with determining quantity of road asphalt required.-intersection.jpg  
    Last edited by bronte; August 14th 2011 at 09:48 AM.
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  2. #2
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    Re: Help with determining quantity of road asphalt required.

    Couple of things:

    What does density have to do with it? Does it settle or form or something?
    The drawing in confusing. Exactly what is being paved?
    It's not clear at all what the circles have to do with anything.
    It's lovely to see how wide the roadway is, but the distance from the intersection appears to be inconsistent.

    Let's getter a better definition of the problem, shall we?
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    Re: Help with determining quantity of road asphalt required.

    Thanks for the reply.

    The mass density or density of a material is defined as its mass per unit volume.

    I've updated the drawing...please keep in mind this drawing is not to scale. The area being paved is coloured.

    As I mentioned previously the circle is simply a tool I've used to try and calculate the radius of the corner(s) to determine area. All corner radius are given a 4m and each corner will be exactly equal or the same.

    It's lovely to see how wide the roadway is, but the distance from the intersection appears to be inconsistent....sorry I don't quite understand what you mean by this.

    Thanks..
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    Re: Help with determining quantity of road asphalt required.

    Your area calculation is not quite correct:
    Quote Originally Posted by bronte View Post
    1st I calculate the total road area less the radius.
    6 x 14m =84m2
    4 x 6m=24m2
    4 x 6m=24m2
    Total area 132.0m2

    Wilmer: Correct!

    2nd I calculate the radius for 1 corner.
    4 x 4m = 16m2
    less the area of the circle 3.1416 x 2 x 2 = 12.5664m2
    the radius area = 3.4336m2 x 4 = 13.7344m2 + 132.0m2

    Wilmer: Do not multiply by 4; 3.4336 is what you need (4 quarter circles).

    Grand Total Area =145.7344m2

    Wilmer: 132 + 3.4336 = 135.4336
    Looks like you're trying to overcharge your poor customer
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    Re: Help with determining quantity of road asphalt required.

    Bronte,

    You haven't given us enough information. What is the value of the distance marked "?" below?
    Attached Thumbnails Attached Thumbnails Help with determining quantity of road asphalt required.-untitled.gif  
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    Re: Help with determining quantity of road asphalt required.

    Quote Originally Posted by awkward View Post
    Bronte,
    You haven't given us enough information. What is the value of the distance marked "?" below?
    That value is "apparently" 4; Bronte gave it to us in this calculation he shows:
    "4 x 6m=24m2"
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    Re: Help with determining quantity of road asphalt required.

    Assuming the value is 4 meters, then my calculation agrees with Wilmer's: 135.4 square meters.

    [edit] If you have to cover that area with 50mm = 0.050m of asphalt, then you need 135.4 x 0.050 = 6.77 cubic meters of asphalt. [/edit]
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    Re: Help with determining quantity of road asphalt required.

    Yes you're right--I now see where I was wrong. 3.4336 is the total of the 4 corners and of course in this example I require all 4...thank you
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    Re: Help with determining quantity of road asphalt required.

    Quote Originally Posted by awkward View Post
    Assuming the value is 4 meters, then my calculation agrees with Wilmer's: 135.4 square meters.

    [edit] If you have to cover that area with 50mm = 0.050m of asphalt, then you need 135.4 x 0.050 = 6.77 cubic meters of asphalt. [/edit]
    Okay seems reasonable and correct to me. I've now been given a slight twist to the problem, before I asphalt the intersection I now have to grind/mill 50mm of existing asphalt and replace with 50mm of fresh asphalt (density 2.5) so not to change the existing grade of the road. Density of asphalt provided by the consulting engineer. Okay so now I'm going to illustrate what I think the formula should be, please correct me if I'm wrong, I need to understand this clearly.

    A = 135.43m2 x 0.05 = 6.77m3 x 2.5 = 16.93 tonne of asphalt.
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    Re: Help with determining quantity of road asphalt required.

    This is where I was headed earlier. Just what does density have to do with it? Fresh vs. newly milled vs seasoned after pouring. These all have different densities? I'm thinking the simple calculation would give the fresh density, but once it is seasoned, it won't be as thick as desired. How much compression is there after pouring? There is more than meets the eye when pouring real substances. The ideal calculations rarely cut it.
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    Re: Help with determining quantity of road asphalt required.

    Quote Originally Posted by TKHunny View Post
    This is where I was headed earlier. Just what does density have to do with it? Fresh vs. newly milled vs seasoned after pouring. These all have different densities? I'm thinking the simple calculation would give the fresh density, but once it is seasoned, it won't be as thick as desired. How much compression is there after pouring? There is more than meets the eye when pouring real substances. The ideal calculations rarely cut it.
    The consulting engineer has provided the calculation for density of the asphalt, this I think has more to do with the design mix at the asphalt plant. For this project I have been instructed to use '2.5' This is all I know but can consult with the engineer tomorrow.
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