Angles on gambrel roof

[Jackhammer]

I would appreciate any information on the angles of each cut for a gambrel roof with a lower span of 16'. I also need to know the length each board should be cut with the lower board having a 6" overhang.

The sidewalls are 8' 1 1/4" from the floor to the top of the top plate. I will be using 2'X4' rafters on 16"oc.

I will not be using a ridge board. If possible I would like both the upper and lower boards to be about the same length by maintaing a 4/12 upper and 15/12 lower pitch.

Hopefully I have provided you with the information needed in order to make a calculation.

[Joe Bartok]

I can't help much here, as my experience with standard framing methods is limited, and a gambrel roof nil. There are other guys here a lot more qualified to help you out, especially with detailed calculations, and I'm awaiting their responses as well.
Meanwhile, try this website for now (selected at random):
http://www.taunton.com/finehomebuilding/pages/h00130.asp
Your angles measured from level are:
arctan(4 ÷ 12) = 18.43495°
arctan(15 ÷ 12) = 51.34019°
To keep the two boards the same length, I'd assigning a unit lengths to the boards, giving:
cos 18.43495° + cos 51.34019° = 1.57338.
This can be factored to give the actual board length. I'm taking half of the span = 8 ft. plus the 6 ft. overhang = 14 ft. (If I'm reading your question wrong and the 14 ft. is incorrect, just substitute your own numbers).
Board length = 14 ft. ÷ 1.57338 = 8.89084 ft.
The rises are:
8.89804 sin 18.43495° = 2.81381 ft.
8.89804 sin 51.34019° = 6.94820 ft.
giving an overall rise of 9.76201 ft. for the 14 ft. overall run.
Sorry, that's not much help, and wait until you get a response from the pros before you start cutting anything, because I'm on the "learning curve" myself.

[Jackhammer]

Joe, thanks for the reply. I am trying to figure this out with the formulas but I'm getting stumped. Rather than the 6' overhang it will be 6".

What does the term "sin" mean? I never was proficient in math.

Can Grumpy and the rest of the pros help me out here?

[giddonah]

sin is the sine function in trigonometry. It is used to find lengths and angles in right triangles.

Ever hear sohcahtoa in a math class?
http://www.mathwords.com/s/sohcahtoa.htm

If you don't understand that page and want to, let us know and we'll help.

[Jackhammer]

giddonah, I don't think sohcahtoa was even a word when I went to school. I bearly got through the adding, subtraction, division, and multiplication. This seems to be way over my head.

Is there some sort of graft or table that will tell a person what I need to know?

Will the same angle change if 2X6 were used rather than 2X4?

Pretty complicated to me. I guess thats why I'm not a developer. What you think?

[Jackhammer]

Rich, Maarass, Cole 21, Grumpydasmurf, Dragon, and Valent. Can I get your input?

[Rich]

Take a peek at this page and scroll down to Gambrel Roof - http://www.berryvalesoftware.com/easyraft.htm

As far as the sohcahtoa - I learned it a little different oh-ah-oa corresponds to sin cos tan - same thing just a little different.

[Joe Bartok]

learning, I no sooner posted last night’s response and logged off when it occurred to me that I’d made a grave error. I believe I used a 6 foot (???) overhang in last night’s calcs :shock: , and there’s no way that can work! A scale drawing or detailed calculation shows that the 15 ÷ 12 rafter is supported by nothing but fresh air. That should have been 6 inches, exactly as you posted; I should have known better and I think I should get my eyes checked.
The procedure for scaling out the total run for equal lengths as shown in Unit Rafters is valid, but dimensions of the Drawing to Scale must be revised. Substitute the correct value for the 14 feet and use the sketches and the calculations as a pattern.
Also posted is a sketch of what I don’t understand and do understand; more don’ts than do’s, sad to say. I’m obviously out of context so I’ll just sit back and watch how this is done. Question for anyone: Is it better to lap or sister the rafters, or use gussets?
PS: This was created last night when I was offline; you've already answered some of my questions, but I don't have time to change anything. BTW, angles and ratios always remain the same, regardless of the dimensions of the material. Gotta go, be back tomorrow! :)

[Jackhammer]

Thanks Joe, and to everyone else who contributed.

[Dragon]

The easiest way to do this is to literally draw it out on the floor.

[Joe Bartok]

Now there's a thought. Time for a dumb question, but bear with me.
The sidewalls are 8' 1 1/4" from the floor to the top of the top plate. I will be using 2'X4' rafters on 16"oc.
Are roofs actually framed with 2 by 4 rafters?
I did a rough estimate of the bending moment, and came up with 2 by 8's. That's using local values for snow loads, the value for stress at extreme fibre from an engineering program, and rounding the result up as a safety factor.
Still fooling around with dimensioning as well, and 2 by 4's aren't leaving much wood to work with after cutting the bird's-mouth.

[bkrahmer]

I'm with Joe. (again...)

[Joe Bartok]

These notes were going in my computer’s Recycle Bin, then thought I’d post them in the hope they’ll do more good than harm.
The bird’s-mouth dimensions are based on 3-1/2 inch wide plate, the rafter depth is 7-1/2 inches, different values than you are using. However, my dimensions begin at the working point shown, are on the insides of the rafters, and follow the triangles. If you use Dragon’s excellent suggestion and do a layout on the floor, you will find that everything will work out itself out regardless of the rafter depth. The angles in the drawing should also help. As for the overlap between rafters, if you find it’s not needed, just disregard it.
Good luck! And keep in touch as to which methods work the best.

[Joe Bartok]

Here's the sketches I meant to post on Saturday. (Saturday's drawings were done with invisible ink, and the calculations used imaginary numbers. That's why you can't see the attachments :D).

[Jackhammer]

Joe, these are pretty impressive calculations. I believe I'll be able to work with these.. Thanks

[Dragonrider99]

Hello Learning. I just now saw your post and was curious as to how you made out with your shed. I just finished mine and I think it came out pretty good. I had never built any kind of large structure before and designed the whole thing myself. The angles on the roof actually were quite easy to work out once I figured out the secret easy way lol. The angles that needed to be cut on each roofing member was simply 22.5 degrees ( or 67.5 degrees, depending on your reference). The sides of my roof are exactly the same length. The only measurement that is critical is the width (span). My shed has a full loft with flooring (sitting on 2x6 joists). The trusses I made myself using the design I made and are 2x6 joists with 2x4 roofing members and wooden gussets. If you build it with a truss and joists then it is fairly easy. My shed has a 6 inch overhang as you can see by the picture. Anyway, I wish you luck. If you have any questions, please feel free to ask.

[Jackhammer]

Hey Dragonrider99, that's a pretty impressive building.
I'm still working on mine. I decided to go with a gable roof rather than the gambrel due to height.

Thanks for the info and pictures.

[Cole]

Nice Work, Dragonrider99!!!

[TnAndy]

The easiest way to do this is to literally draw it out on the floor.

Yep I agree, and that is exactly the way I do it too.

You can get all math complex about it, or just lay it on the floor to angles that suit you, then mark the angles directly and cut a pattern from that.

KISS principle.