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Discussion Starter · #1 ·
OK guys, here's my dilemma. I know it sounds stupid, but i can't figure it out. The really sad part is that someone here WILL KNOW THIS!!

I need to build an OCTAGON. It has 8 sides, of course. The octagon must be 10 feet from one side to the other. What i need to know is this:
1) how long should each side be?
2) what angle should the joints be?

I have a few ideas...
does 4.1422 feet sound about right, and how about 135 degrees?


I wont tell you what this is going to be until my numbers have been verified.

I can fly a plane, save a life, or rebuild an engine...but this geometry stuff is above my head!

thanks a million, guys...

-mike

Give me Jeep or Give me Death!!!

(Will trade functioning organs for CJ-7 or flatfender)
 

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I assume that you are building a gazebo. . .

The process to find out the length is a long mathematical process that would take up a page of BBS and about four or five sketches too /wwwthreads_images/icons/crazy.gif!

Since I couldn't sleep and it is 0325, I would double check these figures by cutting eight strings to length, form them into an octagon, and then check the length of your sides. Or if you have a concrete slab large enough, just chalk it out with your chalk box and check it. Measure twice, cut once - remember?

Your length of the sides will be 5' 3 3/8" from outside tip to outside tip and your angle (the inside angle that you cut to butt the ends of the header joists together) will be 67.5º. In fact, your angle won't change no matter how large or small your octagon is - remember that!

I would suggest purchasing a "adjustable speed square." Stanley makes a nice one that is black with yellow lettering. It is a triangle with an arm that sweeps through it. It has a little knob on the end of the arm that you can tighten to set the arm at graduated angles. It will make marking your angles much easier, much faster, and more accurate when you lay this out. You will need it when you start cutting those rafters! I used to be able to mark these angles with a regular framing square - but that was back when I had something to prove to the crusty old farts on the job site /wwwthreads_images/icons/blush.gif. When I got out on my own and hired my own crew, I have all but forgot how to pick one up /wwwthreads_images/icons/laugh.gif.

In doing this calculation, I assumed two things: First, that you meant 10' from the outside edge of your header joists and not the inside edge. Second, that you meant 10' from the outside edge of your header joists on the flat side of the octagon - and not the corners.

Hope this helps. It should be close enough for you to tweak it from here.

Now I am going to get some sleep. Naaah. It's 0335 now - I might as well brew a pot of coffee and get busy!

When you come to the end of your road, get out and lock the hubs in . . .
 
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Discussion Starter · #5 ·
4'-1 3/4 " sides, the corners are 45 deg, so each piece has a 22.5 deg. on each end, 10'-9 7/8" from corner to corner or 5'-4 15/16" from the center to any corner...love that autocad : )

looks like you had it right

 

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Mike - My hand at autocad says that your numbers are right on. 49.7" sides at 135 degree angles.

80 CJ7 258 T176
36X12.5 Swampers
Fiberglass body
 

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Just because I had two minutes before work, I ran it in Cad and got the same as above.

pbm
74 cj5,304,t18,2.46 ts d20,30f,44r,soa,MORE buggy front,35's,Rci's,5pt,full cage,air,etc.
78 J10,360,727,d20,44f,44r,35's,4" lift,etc.
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For the AutoCad guys:

Thanks for the correction on the length of the sides. /wwwthreads_images/icons/blush.gif After a few hours of work and a pot of coffee, I see where I made my error in calculation. /wwwthreads_images/icons/blush.gif BUT . . . Your program is measuring the angle of one header joist to the next - kind of like the angle of one side of the stop sign as opposed to the next. AutoCad is using this fomula: x = [(n-2)* 180 / n)] (where n = the number of sides.) Now to translate your angle into a real life cut to butt two pieces of wood together at a 135º angle, you need to divide that amount by 1/2: 67.5º. This is where your 45º comes in. The 45º is the inside angle at the center of the piece of pie.

Here is how you can see it in real life: draw a stop sign, then draw lines in from each corner to the center - kind of like cutting it up like a pie. Those corners that intersect in the middle of the pie are the 45º angles (NOT 45º CUTS THOUGH!!), and those outside corners where each slice comes together at the edge of the pie are the 67.5º angles.

Mike - just use my angles and their measurements and you should come out all right!

When you come to the end of your road, get out and lock the hubs in . . .
 

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Looking back at the posts, if the side were 5'-3 3/8" at the outside edge, the overall circumference would be 13' 2 1/4", not 10'-0". So far the winner is 4'-1 1/16" sides (outside edge length) with 135 degree angles total, each piece mating the joint gets a 67.5 degree cut. There I had seven minutes at work to play.

pbm
74 cj5,304,t18,2.46 ts d20,30f,44r,soa,MORE buggy front,35's,Rci's,5pt,full cage,air,etc.
78 J10,360,727,d20,44f,44r,35's,4" lift,etc.
Support Search and Rescue.......Get Lost!
 

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Forgot the damn pic

pbm
74 cj5,304,t18,2.46 ts d20,30f,44r,soa,MORE buggy front,35's,Rci's,5pt,full cage,air,etc.
78 J10,360,727,d20,44f,44r,35's,4" lift,etc.
Support Search and Rescue.......Get Lost!
 

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Discussion Starter · #13 ·
8 x 45 is 360 ...I don't know if he is building a deck or what, but my skil saw wont cut 67.5 deg. , it will cut 22.5 tho. , so thats how I descrided it...180 - 45 = 135...
90 45 = 135...45/2 = 22.5

If I'm wrong, there must be 1000 houses out there in the twilight zone, cause I've used those figures for 25 years, framing, triming or designing the bastids.
 
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Discussion Starter · #14 ·
that is supposed to say 90 plus 45 = 135...the freekin puter won't post the plus sign ! wtf ?

 

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Your right, drawing it in segments at 45 degree angles give you the same thing as 135 degree inside angles/2 =67.5, Another difference in the comparison between the way you look at things. Anyway I think he'll be able to get it built.

pbm
74 cj5,304,t18,2.46 ts d20,30f,44r,soa,MORE buggy front,35's,Rci's,5pt,full cage,air,etc.
78 J10,360,727,d20,44f,44r,35's,4" lift,etc.
Support Search and Rescue.......Get Lost!
 

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I'll throw in my .02

You didn't specify if 10' was from flat side to flat side or from point to point in the angles.

If it is side to side then the length of the long points on your boards should be 4'1-11/16"(4.14') the angle is 67.5. Using these measurements the entire octagon will fit inside a 10'9-13/16" diameter circle.

If it is point to point then the length of the long points on your boards should be 3'9-15/16"(3.83') the angle is 67.5. Using these measurements the entire octagon will fit inside a 10' diameter circle.

Solved with pencil and paper using a calculator (5 minutes).

Hope this helps. What are you building??

Later,

http://home.off-road.com/~tom85cj7/home.htm
 

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I also like the pen and pencil method, heck, I just love math in general. Here is the proof completed.

JEEPN
Winter Harbor, Maine
'81 CJ-8 Scrambled, It's a Jeep, Chevy, IHC kinda thing!
'88.5 Zuki, 5" Calmini, Locked, Swamped, Rolled, and just generally broken in right!
 

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Discussion Starter · #18 ·
Hey, I think I worked on a rafter crew with you guys in Houston ('77)... We would debate the math for 2 hrs. before we cut a board...rotfl... old memories

 

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Hell, with Pro/E you should have had time to model it, render it, get a bill of materials and run stress analysis on it :)

pbm
74 cj5,304,t18,2.46 ts d20,30f,44r,soa,MORE buggy front,35's,Rci's,5pt,full cage,air,etc.
78 J10,360,727,d20,44f,44r,35's,4" lift,etc.
Support Search and Rescue.......Get Lost!
 
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