What size ridge beam would I need to support a cathedral gable roof that is about a 4:12 pitch, 14′ long and spans 16′ wall-to-wall? The live load would be about 40 PSF. Three-tab asphalt shingles. No ceiling finish (This is a porch roof.)
Where did you find the information?
Thanks!
Al Mollitor, Sharon MA
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A good local lumber yard should have that info. If you are going with an engineered beam, the company that makes them has all the charts on stress loads and will tell you. I did an addition on my own house with a similar size room with a cathedral on a 10 pitch and I used a 3" by 14" LDL by Tru Joist I believe...I know it seems overkill but the faces of the 10"rafters on such an angle had to have full contact against the ridge. I had to use 10" for the R-value.
It looks like I got the job, so I want to bump this up in case someone out there can help me out.
I appreciate the suggestion to check with my LVL supplier and I may do that, but for now, I'm hoping something like a 2x10 or 2x12 will do.
Al Mollitor, Sharon MA
Al,
Give National Lumber a call ( I know you've heard the radio commercials out here!). They'll give you an answer right quick and you'll know it satisfies MA code. I've got a great lumber salesman that I use over there, Mike Fucci, I can put you in touch with him if you like.
here are the basics (from any basic eng. structural textbook), numbers rounded up
Z=b*h^2/6 = w*l^2/(8*sigma)
16'span, 14 ft long, 40psflive, est 6 psf dead
So if you use sigma=1200 psi DF or SYP,
w=(0.5*16)*(40+6)/12=6.2 #/inch load
Moment = w*length^2/8= 0.125*6.2*(14*12)^2= 21,900 inch -pounds
Moment = sigma*Z,
where Z is the section modulus = width *height^2/6 for rectangular section
1200 *Z=21900, so Z needs to be 18.25
Pick a 12" height, so 18.25 = b*(11.25^2)/6, thus b is less than 1.5" so a 2X12 will work.
If you tie your 8 ft rafters together at just the one the sheathing joint (center of length of room or 8 ft from one end with a piece of 1/8" aircraft cable, now you have a truss and it will carry lots more, ask Boss about that.
Better yet, even just staggering the roof sheathing end joints, you have a dynamic structure to analyze, but it will be also much stronger (much more complicated calculation, can't do that in my head right now)
I don't come anywhere close to your numbers.
I always used the formula: span squared * loading (PLF) over 8 to get the moment in foot-pounds. In this case, that would be 14 squared * 368/8, or 9,016 foot pounds. That would be equivalent to 108,192 inch-pounds - a long way from the 21,900 you got.
Also - 6 PSF is pretty light for a roof dead load. I never use less than 10 on a shinge roof.
Since I don't really follow your formula, I'm not sure how you cam up with your numbers. But they don't look right.Rigid flexibility is the key to indecision.
Thanks to Boss and Junkhound for your input. I hope the discussion continues since this is interesting stuff, although way over my head. I don't know anything about structural engineering, but I can read a table. My code book has no table for this situation, however.
I just want to point out the obvious: A good portion of the roof load will be carried by the walls. The ridge beam (as I understand this) serves primarily to keep the walls from spreading. Also, the gable end will be resting on the end wall and the rafters butting up to the exterior wall of the existing house will be nailed to the studs of that wall. I may be using 3/4 cdx for the roof sheathing, not for strength, but to reduce the amount the roofing nails stick through the underside. Hmmmm...If I use 3/4 cdx, maybe I should go to 24" o.c. rafter spacing.
Thanks to the comment by Junkhound, I am beginning to see how the sheathing will help keep the roof from sagging. I will pay careful attention to how it is arranged and nailed.
Al Mollitor, Sharon MA
"The ridge beam (as I understand this) serves primarily to keep the walls from spreading."
The only way a ridge beam can keep the walls from spreading is if it hold up the ends of the rafters.
Ridge boards and ridge beams are often misunderstood.Not one shred of evidence exists that life is serious.
In a roof with a structural ridge beam, there is not lateral thrust, i.e. the rafters aren't trying to push the walls out. The roof load is carried on the ridge and on the walls, and there is no need for collar ties or ceiling joists to resist lateral thrust.
In a roof with a ridge board, there is lateral thrust. The ridge board is not designed to carry any roof load, and the only way it works is as a triangle with rafters descending both ways from the ridge and collar ties/ceiling joists connecting them. The collar ties are in tension.
Once in a while you get someone who wants a cathedral ceiling so they go in with a sawzall and cut out a bunch of collar ties and hang sheetrock on the underside of the rafters. If they don't also install a structural ridge then they get sagging, leaning, possible collapse, etc.
Won't even try to do the numbers in the 5 minutes I have right now, but you can 'evolve' your gable into a V without even a ridge board and then into a hip, then a dome.
Look at it this way, say 40#/inch load at the ridge, look at your 3/4 sheathed roof as a big 8 ft high, 3/8" thick beam laid flat down to a 4/12 slope, an eyeball number (you better check) shows that a less than 1000psi plywood would be sufficient with staggered middle edges and 2x6 rafters to keep'em flat - -- however, you then have about 6000 pounds of lateral thrust at each end wall to deal with. To easily deal with the end wall thrust, go to a hip roof, and wrap the top with a 1/4" by 1" steel strap. Viola, no ridge at all, less overall wood usage, etc. From there it is a simple step to a dome.
The old Roman designers (e.g. pantheon) apparently used this iterative technique to evolve structures, so it sure ain't new.
Thanks for the input, Dave. I understand the function of a structural ridge beam. It's the size I'm trying to figure out. So far, I'm having a little difficulty believing that I really need a triple 2x12 beam for this little porch roof, but I want to get this right the first time, so I'm keeping an open mind.
Al Mollitor, Sharon MA
Well, I just got a calc for a beam to support about 17 feet of ceiling joists/attic floor. I need a 6x14 DF#1 or a fairly large manufactured beam. I had been hoping for a 4x12... but they're not really that strong.
Don't you wish there was a place we could go to read those posts that got deleted?!
Whoever posted #16 and deleted it , ROTFALMAO
I always miss the good ones!
Day late and a dollar short again.
In a no-tie roof, the ridge is picking up half of the total loading from each rafter, and the walls where the rafters bear on their low ends pick up the other half.
Thus, each lineal foot of the ridge is picking up 40 psf of roof live load times the 8 sf of tributary area. Let's add in about 12 psf for the dead load of lumber, sheathing, and roofing. That's plenty.
So, we need a structural member that will handle a plf total loading of 8 x (40 +12), or 416 pounds per lineal foot, at a length of 14 feet. The TrusJoist website will give us a member size. I'll go there now and revise this post when I get back.
. . .
I'm back. I looked in the roof tables for snow country (115% load duration) to be safe.
A 1-3/4 x 11 7/8 1.9E LVL is a little borderline, and while handling the load OK at full live, offers a little too much deflection for me. I would go one size up at 14 deep.
Edited 5/22/2004 11:23 pm ET by Bob Dylan
Thanks, Bob! My next step is to call the people that sell the LVL's I use. It will be interesting to see if they come up with the same answer.
Al Mollitor, Sharon MA
Just to let you know that your contribution was appreciated...I checked with the engineers for the LVLs I use. They recommended a double 1-3/4 x 11-7/8 beam. They included the possibility that snow may fall off the roof from the house that this new roof will be attached to. That beam may be going up tomorrow.
Thanks!
Al Mollitor, Sharon MA
w=(0.5*16)*(40+6)/12=6.2 #/inch load (NOT) ! -- how about 30.6!!! #/inch, then M = same as Boss's numbers.
Thanks Boss!
Whoops, can't do math in my head that early in the morning anymore, only 1 2x12 did seem awful light. Heck, I can't even figure out now how I came up with the 6.2 number, unless I was just testing <G> ?
which means don't ever trust somebody else's numbers - or even your own when 3/4 asleep, etc. You need about 3 2x12s, not one. And, as Boss also said, you need to vertically support the ends, not just set them between rafters .
Put that cable in tension across the middle on the rafters at the sheating joint and you could still get away with 1 2x12 yet though.