Irregular rectangle L1 calculation at every foot

matrixebiz

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Hello, I am building a Carport off the side of my house (sorry for the MS Paint sketch) but basically I want to measure and cut all the roof beams on the ground ahead of time so I'm not trying to tape measure each one (that would be very time consuming) I was wondering what the formula would be to calculate each beam length for me - L1a through to L1f if I'm setting them at every 12 inch centers from L1.
Measurements are just to illustrate approximate values, I'll plug in the actual values into the formula. Thank you
 

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lev888

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15-12=3
The 3 foot difference is divided into how many equal segments? (assuming everything is spaced equally)
L1a is shorter than 15 by one segment
L1b is shorter than 15 by .........
 

matrixebiz

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Lets say there are 21 beams in total if W1 is 20' instead of 20.5', so what do you mean by segments?
Are the segments, how many 'beams' excluding the 2 end ones (L1 and L2) since we already know the measurement of those ones?
19 segments?
3/19= 0.157
So L1a is 15' minus 5/32 of an inch?
 
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lev888

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Lets say there are 21 beams in total if W1 is 20' instead of 20.5', so what do you mean by segments?
Are the segments, how many 'beams' excluding the 2 end ones (L1 and L2) since we already know the measurement of those ones?
19 segments?
3/19= 0.157
So L1a is 15' minus 5/32 of an inch?
Draw vertical lines through right ends of the beams. These lines divide the portion of L1 that's greater than 12 feet into segments.
Do you see what I mean by "L1a is shorter than 15 by one segment"?
How long is one segment?
L1a = L1 - x.
L1b = L1 - ??
 

matrixebiz

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No, I'm not following :( I don't know how long one segment is.
 

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lev888

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matrixebiz

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Like this?
 

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HallsofIvy

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Since the right side is a straight line, each length goes from 12 feet to 15 feet in equal steps.
15- 12= 3. There are 7 equal steps (6 internal and the top) so each step is 3/7 foot. Since a foot is 12 inches 3/7 foot is (3/7)(12)= 36/7= 5.14 inches.
The bottom is 12 feet
The first above it is 12 feet 5.14 inches.
The next is 12 feet 5.14+ 5.14= 12 feet 10.28 inches.
The third is 12 feet 10.28+ 5.14= 12 feet 15. 42 inches= 13 feet 3.42 inches.
The fourth is 13 feet 3.42+ 5.14= 13 feet 8.58 inches.
The fifth is 13 feet 8.4+ 5.14= 13 feet 13.54 inches= 14 feet 1.54 inches.
The sixth is 14 feet 1.54+ 5.14= 14 feet 6.68 inches.
The top, as a check, is 14 feet 6.68+ 5.14= 14 feet 11.82 inches- 0.18 inch less than 15 feet because of roundoff.
 

lev888

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matrixebiz

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Okay, so if I wanted each beam 12 inches on center away from each other, so basically 21 equal beams (Steps) how would that calculate out?
 

matrixebiz

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Got it, thanks.
 
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