Beam span for a pavilion roof

[marimbob]

Hi,

Can anyone help me with beam sizing/substitution?
I purchased plans for an 18' x 18' pavilion. It calls for 2 2x12 Hem/Fir boards at the top on all 4 sides, with 4' diagonal braces. I have 2x6 Hem/fir boards available, which I want to use as I have no budget for more wood. Is there a way to substitute 3 or 4 2x6s per side, and still have structural integrity? BTW, I'm actually building it at 15' 6" square, so the span between the posts is 15' 6". The posts are 6x6 and are about 112" tall. For the roof, I'll be using engineered trusses with corrugated, galvanized roofing panels.

-Bob

[Don_P]

Doubtful... you can try.
1st check section modulus of the 2x12's... bd^2/6=31.64 each, moment of inertia for each is 178... bd^3/12
so you have a section modulus of 63.28"^3 and a moment of inertia of 356"^4

Notice how the equations either square or cube depth... depth means a powerful amount in the strength and stiffness of a beam.

A 2x6 has a section modulus of 7.563, and an I of 20.80
start with bending 63.28/7.563=8.36... so nine 2x6's wide will equal two 2x12's in bending strength if species and grade are the same

Next check deflection 356/20.8=17.11.. it'll take eighteen 2x6's wide to equal the stiffness of a pair of 2x12's.

Short answer, rethink your plan 

[Don_P]

Breaking the 15'6" span in half with another post is one option, 6 posts.

rather than try to reverse engineer a beam that I kind of doubt was engineered to begin with... what is the pavilion overhang width (I'm assuming you are talking about a simple gable roof built of trusses), and local snow load?

[marimbob]

Hi Don,

Thank you for your responses. It's been a while since I was in advanced algebra/ trig. so I had to spend a little time decoding your equations, as well as getting a (very) basic understanding of the terminology. I was sure your numbers were right, so I kept at it until mine came out the same.

The city code here in Olympia WA specifies a snow load of 25 PSF, unless it's a low slope as in a carport. The trusses I have are just shy of 4/12 (3.8/12) and there is a 2 foot overhang on each side of a single gable. Seismic Design Category: D IBC 1613

I was hoping not to resort to a 6 post structure, mainly to give it a more open feel. I would rather wait until I can fit the necessary beams in my budget.

The plans I bought call for 2x6 rafters with gussets, but (oddly) no ridge beam, on 24" centers, and the roof "sheathing" is 50 2x6x20' boards. That seems really heavy to me, and doesn't include roofing.

What I have to use are trusses made of 2x4 stock, and 2'x10' panels of metal roofing. 9 trusses and 16 panels should only weigh a fraction of the weight of 1220 feet of 2x6s, so the  2x12s may actually be over kill.

I tend to reverse engineer projects because I try to use the materials I have on hand. One day I'd like to make a complete materials list, go to the lumber store, and say "deliver this to my place" and be done with it.

[Don_P]

There is a difference between a ridgeboard and a ridgebeam. Typically what you see is a ridgeboard that is non structural, it is simply something to nail the rafters to and carries no load. A truss or gusseted together rafter set accomplishes the same thing structurally. A ridgebeam is heavier and typically is supported at each end and often along its' length by posts. Doesn't have to be, but that is typical.

I can't help with the seismic, you are likely going to be required to have this fully engineered when you permit this.

For the gravity loads the front end way to size the beam is;
Take half the building width plus overhang, 9.75', times the span ~15'. This gives us the tributary area in square feet loading each beam... half the roof over that span. Times the load (25 psf dead +10psf live)=5118 lbs
There are beam design equations at awc.org, their publication DA6
I've written some of those equations into javascript to make it easier
http://www.timbertoolbox.com/Calcs/beamcalc.htm
Enter load, span (I used 180"),actual dimensions (I used 3 x 11.25), Fb 1124, E 1.3, Fy 172.5
This is the beam in your plan... it fails miserably, looked kind of dubious. This is why its not a good idea to reverse engineer a plan. Anyone can sell a plan, we don't know the source but I'd take that as a note of caution on what you have.

I finally passed at 4 ply 2x12 in #2 Hem/fir. LVL's or a glulam beam are other options. The truss shop might be able to help with design as well. Bracing this structure needs a lot of thought. Scabbing on some 2x's probably isn't going to keep it upright if the ground is moving under it.

[ChugiakTinkerer]

Marimbob, welcome to the forum!  The beam you're describing is essentially the header over a two-car garage door in a load-bearing wall.  Assuming there will be some permit required for construction, you will likely have to comply with a code of construction.  If you update your profile to show your general location, folks may be able to assist you in determining what the reference code is for your area.

Most states and counties have adopted the International Residential Code.  The IRC has been developed as a cookbook of sorts, so that if builders follow the requirements then homeowners can be assured that their house will withstand the local conditions for wind, snow, earthquakes, etc.  The 2015 version of the code is online at http://codes.iccsafe.org/app/book/toc/2015/I-Codes/2015%20IRC%20HTML/index.html

Chapter 6 has requirements for wood wall construction.  The nice thing about the IRC is if you follow it you don't have to get wrapped up in a lot of complex engineering calculations.  Scrolling down a ways, you'll see Table 602.7(1) shows the allowable header spans for exterior bearing walls.  You'll see there that for a 20' wide building (yours is actually 15.5') with a 30 psf ground snow load, the longest span for 2 2x6 is a mere 5'-5".  The 4-ply 2x12 beam in this instance can only span 14'-1".

Your permitting authority, if it exists, will tell you whether or not the pavilion requires a permit, and if so what code requirements there may be.  Frequently small utility structures are excluded.  Check first with the county or other permit authority where you live to know what will be required.  Occasionally one can build a build a structure and there will be no formal code requirement or inspection.  Even if that applies in your case, you will want to build a structure that is strong enough to withstand anticipated snow and wind loads as well as potential ground movement.  So even if you're not required to build to code, you should do so for the safety of you and your family and any other future users of the pavilion.

Within the IRC there is another table, Table 602.7(3), that shows allowable header spans for open porches.  Assuming that your pavilion falls under this category, you'll see that a beam made of two 2x6 can span up to 7-6" whereas a beam made of two 2x12 can span up to 14'-4".  I am assuming here that the pavilion is essentially two open porches butted together, so I am looking at a porch depth of 7'-9".  If you have a building inspector for this project they may or may not agree with my assumption.

If the porch assumption applies, I see two obvious ways you can build your pavilion.  The first is to insert a post in the middle of the bearing wall side like Don_P suggested, to you reduce your header span.  I should mention here that the unsupported span is exactly that.  It mans the portion of the beam that has nothing below it.  For a structure that measure's 15'-6" from outside edge to outside edge, the unsupported span will be reduced by the width of each post.  If an actual 6", then your span would be 14'-6".  If using dimensional lumber, the 6x6 is really 5.5 inches each side so the unsupported span is 14'-7".  The second method is to use two 2x12 to form the beam and adjusting your design so that the unsupported span does not exceed 14-4".  You could do that by moving the posts a couple inches closer, or by using bigger posts such as 8x8.

I should mention that I don't build or design for a living, I'm just someone trying to understand the code better so that I can have a safe and solid cabin.  I think your next step is to contact your county permitting authority and see what requirements they will have for what you want to build.

Edit: I see you're in Olympia, WA.  Thurston County has an informative web site on their codes here: http://www.co.thurston.wa.us/permitting/bldgcodes/bldgcodes-title14-readcode.html

[marimbob]

Thanks Chugiak!  I'll check out those IRC charts. Safety and code compliance are my top priority, whether I'm doing a project requiring a permit or otherwise. That's why I'm doing my due diligence here and elsewhere. This roof will cover a deck that is 16x12, the deck is adjacent to, but not connected to the 16' wide slab of my house. The roof will also be adjacent to, but not connected to the house. I believe a permit is required, due to the size of the roof, and the proximity of the house. I'm trying to determine what I need in terms of design before I pull a permit or hire an engineer.

Don,   I think I'll go ahead and add two more posts, to shorten the spans. I put the numbers into your calculator as follows:


Load on Beam(pounds)   
2559 (I divided your load figure in half)
Span of Beam (inches)   
52  (That's the maximum, not necessarily the actual)
Width of Beam   
6
Depth of Beam   
5.5
Maximum Allowable Fiberstress in Bending (PSI)   
550
Modulus of Elasticity (million PSI)   
1.3
Maximum Allowable Horizontal Shear (PSI)   
100
Show result  Reset
Fiberstress in Bending      Deflection      Horizontal shear
Max Moment (ft-lbs)   
1386.125
Deflection (inches)   
0.043322915101427495
Shear (PSI)   
58.15909090909091
Section Modulus Required   
30.242727272727272
Max 1/360 (Floor)   
0.14444444444444443
Section Required   
19.1925
Section Modulus Input   
30.25
Max 1/240 (Roof)   
0.21666666666666667
Section Input   
33
Section Modulus Pass/Fail   
Pass
Deflection Pass/Fail   
Pass
Shear Pass/Fail   
Pass

Question: If I bolt the diagonal braces to the inside edges of the posts, and up under the beams, is that a legitimate way to shorten the beam span. i.e. if the span between the posts is 82" and the braces each attach 24" from the posts, that would leave a span of 34" between the braces....The numbers I used in the above calculator shows a maximum span of 52" with 4 2x6s for the beams.

[NathanS]

If you stick frame instead of using trusses you could probably afford more 2x12s and still come out ahead cost wise.

[marimbob]

Thanks for the reply Nathan, how does a stick built roof work?

[NathanS]

Most common would be ceiling joists, with rafters tied to them. This is like a 'site built' truss.

The other option is in addition to the 2x12 built up beams you'll need, you'd need another one up at the ridge of the roof to carry half the load of the roof.

If you frame a ridge beam, you don't need joists - which is often chosen for aesthetic reasons.

It may be worth your time to read some framing books to learn more on how these systems work. Choices and options can become overwhelming and there is a lot to learn. One issue with trusses is that they are unwieldy for one or two people to install.

[Don_P]

Braces do not decrease the span. By the time they actually "hook up" and take load the beam they are supposedly helping is already getting significant full span stress. If you can insert a shoulder of the brace into a ledge or pocket in the post and beam it will stiffen the frame considerably.

For this use I've been getting design values from this spancalc... the same folks that create the code span tables;
http://awc.org/codes-standards/calculators-software/spancalc
The correct source is their publication  "Supplement, Design Values for Wood Construction" which is a free download.
Anyway, for a hem-fir 2x6, #2, Fb-1461, E-1.3, Fy-172.5, considerably higher than the numbers you used. I'm getting a pass at 90" span with 3 ply 2x6's

Another way is several built up trusses over each post with rows of horizontal purlins between.

[marimbob]

That's great info Nathan, thanks again!

I already have the roof trusses, and corrugated metal roof panels. Right now I'm leaning towards biting the bullet, as it were, and just buying 8 2x12x16s for my beams. The cost is about the same as buying the posts and other materials to put in 2 more posts.

[marimbob]

Don,
I like the idea of notching the posts and beams to strengthen the bracing. As you can see, I'm trying to decide if I'd rather plan two more posts or buy the 8 2x12x16s for an unbroken span. I'm leaning towards the 2x12x16 option, because it's more in keeping with my original vision. It seems to me that it would be strongest to set the beams on top of the posts so the load transfers directly onto them. If so, would the 6", 18 gauge, post caps sold at Lowes be sufficient connectors? Is there a better way to attach the 2x12s?

[Don_P]

You don't need anything on the gable ends, the trusses are spanning the ends, the beams are needed for truss support. Whatever you put there is gravy, you do need to brace that direction... braces do not need to hit the post at the same elevation.
I'm barely failing at 169" span with a triple #2 Hem-fir 2x12.
With a select structural dougfir beam I'm barely passing at 2 ply 2x12.
The way I would build it would be the SS dougfir notched into the 6x6 posts, a 6x6 brace that has the bottom point bobbed flat and a ~47* angle so that the flat inserts in the post and then angles back out to full post dimension (that was mud, holler if you need a pic) Notch the top of the brace to fit around the dougfir beam and run 2 bolts @ 1/2" through brace and beam... 2" from edges, etc.

Just as a minor point, correctly span is the clear distance between supports plus half the required minimum bearing length at each end. We tend to neglect that extra few inches but think about it when pushing around the limits.

[ChugiakTinkerer]

...
Just as a minor point, correctly span is the clear distance between supports plus half the required minimum bearing length at each end. We tend to neglect that extra few inches but think about it when pushing around the limits.

Thanks heaps for that, i appreciate the correction.

[marimbob]

That's great Don! Yes a picture would be good. I'd need to know what the shape of the brace is, how deep the notch is, and what the minimum bearing length is, but 169"is plenty! Would the 2x12's need to be connected with wood screws, lag bolts, glue and dowels?

[Don_P]

I drew the notch into the post at 1", that would be about the max I would go into the post. The post top and top end of the brace are notched 3" deep to fully catch the beam.

Check on availability of the beam material. LVL is another option if you can't get select structural dougfir.

I'd bolt the post to beam and brace to beam with 1/2" bolts, 2 per connection, no closer than 2" to edges. Lag or timber screw the brace to post, this is a compression brace, so they need to act in opposing pairs, they have no tension capacity. They only act to keep the angle from becoming more acute, in a wind or shake the brace at one end of the beam is working the brace at the other end is in tension and isn't really working. Nail the beam plies together, I typically angle rows of 3 nails about 12-16" apart. Do use hurricane ties to connect the trusses to the beam and make sure the posts are well connected to the footings, uplift is a real potential with large open roofs.

[marimbob]

Hi Ron,

thanks for the picture! when you said 'brace' in you previous post, I was still thinking about metal connectors, so I couldn't figure it out at all! I checked with my favorite local lumber yard, and they stock the 2x12x16s, so that's easy.

Thank you very much for your help and advice! This is going to look fantastic when it's finished. My original plan, before I acquired the trusses, was to design it with a 'cathedral style' roof. That's what the plans with the gusseted rafters I bought have . Would that work with the design you've given me if I add beams of the same dimensions at the gable ends?

[Don_P]

The load path changes with a cathedral. There needs to be a ridge beam that supports half of each side of the roof, so half the roof load. Your side beams then only support 1/4 of the roof load each. The best way to support the ridgebeam is directly on a post that runs straight down to the ground. I doubt you want that. If the gable end beam is strong enough to support the ridge beam post landing smack dab in the center of it with half of the ridge beam load carried by the gable beam at each end. So 1/4 of the roof weight as a point load at midspan on a 169" span.

Just walking and talking through it, this should be fun, the eave beams support the rafter ends spaced evenly along the 169" span and carry 1/4 of the roof load. 5118/4 =~1280 lbs. I'm going back to #2 hemfir design values Fb 977 (non repetitive member), e 1.3, Fv 173. a single ply beam on the eaves works.
http://www.timbertoolbox.com/Calcs/beamcalc.htm

The ridgebeam is carrying half the roof load, 2560 lbs. Fb will bump up to 1124 lbs because this will be a multi-ply beam. I'm passing with a double 2x12 ridge beam in #2 Hem-fir

The gable beams also carry 1/4 of the roof load but as a concentrated point load at midspan. The bending moment is double on a point loaded beam as compared to a uniformly loaded one. There is also the upper half of the gable overhang 560 lbs added to 1/4 of roof load=1840 lbs point loading the gable end beam
http://www.timbertoolbox.com/Calcs/beamclc_ctrptld.htm
I'm just failing at 2 ply #2 hemfir. It can be 2 ply in #1 or dougfir.

[marimbob]

That's awesome Don! I'm glad you have fun with it; I do too, I just don't have the chops to know the right numbers to put in. Out of curiosity, why does this need a ridge beam rather than a ridge board, or gusseted rafters (as in the plans I have)? How would the gable end 2 ply 2x12x16 beams and the 1 ply eave beams be attached to the posts?

[Don_P]

The mental exercise that usually does the AHA! moment... Take a greeting card and set it on a smooth tabletop like a tent. This is a roof. Push down on the "ridge". The "feet" should slide out. Notice as the pitch gets lower the force required to create that outward thrust is lower. In a house the walls bow out and the roof snaps through.. a toggle.

Now run some tape or thread some string across the bottom of the card from side to side, locking the triangle to prevent the roof bottom from spreading. Push down on the ridge again... AHA! This is the role of rafter ties or ceiling joists. If you move that tie upwards it becomes less and less effective and also induces a bending moment in the roof. This is the reason rafter ties should be in the lower third of roof height and as the ties rise the rafters often must also be bigger. That is a conventional roof.

If we want to eliminate the ties we still need to prevent that spreading tendency. Take the greeting card and slide a stick or pencil under the ridge and prop it up solid at each end from the table. Push down, no spreading action, the card is now hanging from the ridge beam, AHA! This is how a cathedral roof is usually framed. If the ridge cannot sag there is no spreading thrust.

The designer of your plans has sent up another red flag, the stresses are too high for what I'm envisioning as a gusset.

I would probably notch the post tops 3" deep on the gable faces and 1.5" deep on the eave faces leaving roughly a 2x4 to attach to... you are asking for a lot of connections in a small area, make sure this is good clear wood in that area. Weave the 2x12's to give good nailing of the beam corner A timberframer would drop the gable beams below the eave beams to avoid removing so much wood in one area. Spaced 3 post corners also look good but get into the wallet pretty quick.

[marimbob]

Ok, I thought there might be too much risk of spreading in those plans; I was thinking about adding collar ties.

What size would the mid gable beam posts need to be to hold up the ridge beam?

[Don_P]

Terminology; A roof should have collar ties in the upper third of roof height or straps over the ridge connecting opposing rafters together for wind uplift.
Absent a ridgebeam it should also have rafter ties across the lower third of the rafters to prevent spreading. The lower the better.

We should check the ridge support post, and all, the beam to post contact surfaces for crushing... compression perpendicular to grain.

A column should also be checked for buckling. Since these will be relatively short that shouldn't take much. Let's start there...
We have an 1840 lb load
http://www.timbertoolbox.com/Calcs/columncalc.htm
enter the post length
I tried with a 4x4 so entered 3.5, 3.5
compression strength parallel to grain, 900 psi (this is end grain bearing capacity for "western woods"
E 1.0 (stiffness of western woods)
Load 1840 lbs

You can alter post lengths to find the fail point but I think that should work fine for most reasonable lengths. Any bigger is gravy structurally, bigger might look better for instance.

Now lets check for crushing of the post into the ridge or gable beam. Assuming they are 2 ply, 3" thick total x 3.5" wide=10.5 square inches of bearing contact between post and beam.
Divide 1840 lbs/10.5 square inches=175 pounds per square inch of pressure from the post into the side grain of the beams. We know the post is fine, it can handle 900 psi on its end grain. The side grain capacity of western woods is 335 psi, we've got 175 lbs of pressure... check.

Half of the 1840 carried by the gable beam is supported on each 6x6 end post. No matter how you cut it I think you'll have at least 12 square inches of bearing... check

Lets check column capacity of the 6x6, another calc walks through the same math a little differently, might help things click. This one is set up for heavy timber, which is wood 5x5 and larger so we can check our 6x6 using that one;
http://www.timbertoolbox.com/Calcs/Simple_column.htm
You can back out the example and type in your inputs in the boxes.
For total load on the 6x6 posts we know we have half of 1840 lbs from the ridge post, 920 lbs. We also have half of the eave beam,1280/2=640 lbs
920+640=1560 lbs total post load
I would use #2 dougfir P&T, I think the rest of the inputs should make sense. I'm not worried about the 6x6 posts.

Eave beam crushing... 640 lb load, bearing capacity of at least 335 psi, our notch will give 1.5x4" of bearing surface.. looks good.

[marimbob]

Nice! The plans call for 2x6 rafters. Since you've raised serious concerns regarding those plans, is that necessary, or would 2x4 rafters work here? How deep can a bird's mouth notch be on a 2x4?

[Don_P]

For that I would go here, this is where the code tables come from;
http://awc.org/codes-standards/calculators-software/spancalc
I checked #2 spf 2x4's 24" on center, rafters (snow) l/180 deflection, 25+10 loading

Technically you cannot birdsmouth and run a tail off a 2x4... you need to leave at least a 2x4 of material above the birdsmouth to carry up to a 2' overhang. I would stick with 2x6 and not notch more than 25% deep.