Figuring Rafter Thrust

[Don_P]

I saw a post that led me to think a ramble on rafter thrust might not be a bad idea. This seemed like it might be the most unobtrusive place to put this. I would be happy to answer questions here or in PM.
This picture should help describe what the vertical load on a roof is trying to do.

As the roof's weight pushes down vertically, the rafters try to push the walls out horizontally so that they can "snap through" and drop the ridge to the ground. A tie across from wall to wall in the diagram would arrest the horizontal component of the vertical thrust. The tie is usually a ceiling or second floor joist or the bottom chord of a truss. If there is a rigid triangle formed it is locked into shape, triangles do not change shape.

Another way to see rafter thrust is a tabletop experiment. Take a greeting card or piece of cardboard folded like a card and set it on a slick tabletop like a tent or roof. Push down on the ridge (the fold in the card). The card's feet slide out, that's the horizontal thrust. If the roof had been on top of walls it would have pushed the top of the walls out. Set the model back up but this time run a piece of thread from side to side across the bottom and tape it to each side. Push down on the ridge and the thread keeps the card from being able to spread. A bottom chord arrests the thrust. Since a piece of string worked we know it is a tension tie.

Before leaving that experiment there is another way to avoid thrusting the walls. Take the thread bottom chord off the card and set it up as a roof again. This time stick a pencil under the ridge and support it at each end on a stack of books or anything solid. Now push down on the ridge. The pencil supports the load as a beam, the roof hangs from the beam. Even though there is no tie, there is no thrust if a supporting ridge beam is used. If you push hard enough the pencil will snap. We would need to size and support that beam correctly. that's for another day.

The codebook has a table that gives connection minimums for the rafter heeljoint that is the simplest way to arrest thrust if you are within the confines of the table (R802.5.1(9)). That chapter is worth reviewing, I saw a roof on here recently that would fail inspection and is not particularly strong compared to what it could have and should have been. Most of the code structural provisions are minimums for life safety, they aren't there to line anyones pockets or to be mean, they have literally been written in blood. Something to think about when stepping below those minimums.

Back to calculating rafter thrust.
This calc is the easy way;
http://www.windyhilllogworks.com/Calcs/Sloped%20Rafter%20Design%20for%20Bending1.htm

For those who want the math behind it read on, I also have a handy chart that I could scan and email that takes the trig out;
Suppose I have a building 20' wide. I plan to set the rafters on 2' centers. 2'wide X 20' span = 40 square feet of roof bearing on each rafter pair. In my area we count on 20 lbs per square foot of snow and it is typical to design for 10 lbs per square foot for a conventional roof's self weight of rafters, plywood and shingles. Taking the 40 square feet X 30 lbs combined load per square foot = 1200 lbs vertical design load bearing on each rafter pair. 600 lbs on each rafter.

Lets put an 8/12 pitch roof on it... 8 divided by 12= .6666
arctangent of .6666= 33.69 degrees, the pitch is a 33.7 degree angle

Thrust = W {1-cos^2 (pitch angle)/2}/sin(pitch angle)
Working it: 600{1-.6923/2}/.5547
                600{1-.34615}/.5547
                600{.65385}/.5547
     Thrust=707.25 lbs

The connection between the rafter and its tie should be able to resist that thrust. I've included some nail sizes cross referenced by species in the calc above to figure how many nails to put in the connection. A real rough rule of thumb is that a 16 penny sinker is good for about 100 lbs in shear so 7 nails in the rafter/ceiling joist connection would work here. The AWC connections calc has many more combinations.

This calc goes into raised ties, definitely read the notes under the rafter span tables in the codebook and understand the nature of the increased loads on the rafters before going there;
http://www.windyhilllogworks.com/Calcs/raisedtiethrust.htm

[secordpd]

Don, do you think this truss plan is any good.








It came from Family Handyman/Readers Digest 

http://www.rd.com/50683/article50683.html   


Or do you think I would be better off with a rafter board and rafters, size to be determined.  Just wondering your opinion?   Thanx Helen

[Don_P]

Hi Helen,
Well it has some positives but there's probably better ways to get there. First off understand that someone could probably go into the Taj Mahal and pick it apart. So with that in mind I'll pick this apart and you can keep what makes sense.

The first thing that caught my eye is the use of carriage bolts. They are typically threaded all or most of the way so the shank of the bolt is compromised by the threads. A machine bolt is normally threaded on just the end so if the proper length is used the plane where the rafters and tie meet is bearing on a larger diameter smooth section of strong bolt. Carriage bolts are not recognized in the Nat'l Design Specification for Wood Construction (NDS) for this reason.

Next, If I remember from your other thread you are in a 60psf snow load area. The roof is generally assumed to have a self weight or dead load of 10psf for a total of 70 pounds per square foot. I quickly skimmed the article you linked to and it looked like these are spaced 4' apart. Let's see how much weight we are designing to support;
the roof is roughly 15' wide X 4' spacing=60 square of roof supported by each truss.
60 square feet X 70 pounds per square foot= 4200 lbs on each truss

This is drawn with a 6/12 pitch and when I go through the gyrations to figure out how much thrust must be restrained by the bolts in the tie/rafter connection its right around 2000 lbs. When I check in the NDS a 1/2" diameter bolt in double shear (the two rafters with the tie in between) each bolt is good for about 500 lbs in this orientation in SPF lumber, typical lumber at the big box. So you're looking at 4 bolts minimum in each end. They need to be at least 3-1/2" from the end of the tie, no closer than 2" to each other or any edges. If the truss fails this is going to be the place, take the time to sketch this out and improve those clearances if possible.

The rafters and tie are sufficient for the loads, the only reason to upsize them would be to get adequate connection room or to improve the spacing on the bolts.

You will need to tie these down to the supporting beam under the trusses with hurricane ties, there is a lot of roof wanting to lift off in the wind. Also since there is no X or Y bracing in the end wall the roof's tie into the existing roof is providing the sway bracing. Notice he switches materials at the valley all of this would need to be really well tied together, it isn't from what I can tell so a high wind stands a chance of twisting the end wall until it drops the roof. Some knee braces in that wall would help alot.

At that point the drawing in your article really falls apart. There is no support beam under the trusses so the load is being carried down to the deck on 2x4's. Including the overhang in the load there is 2333 lbs being supported by a single 2x4 with a 70" unsupported height in the center pane of the screen. The 2x4 can handle roughly 150 psi load without buckling, under a full load of snow you'll have triple that. So in a big snow this thing is probably going to collapse by those 2x4's buckling.

The deck underneath that is supporting the post loads on the rim as a beam rather than having posts lined up under the trusses. We've already got a problem above so I'll stop here but I suspect this won't work either.

So, I think we need to back up and punt at the truss support and work down from there if you want to pursue this plan.

For the deck itself you can find a good download here, DCA6;
http://awc.org/Codes/dcaindex.html#PostFramePubs

[Don_P]

I remembered this, its a fairly technical article on bolted connections but is worth looking at the pictures if nothing else to get an idea of how bolted connections fail in order to help get an idea of how to improve them.
http://www.awc.org/pdf/wdfAppendixE.pdf

[secordpd]

Thank you Don for so much info.(great pdf on deck building)  My feeling is I'm completely open to any design, but partial to a post and beam type frame.  I think that plan from Family Handyman is filed in the trash, and will start over. 

Well, it's back to the drawing board.  The good thing is it's going to rain for several days so that will give me some time to research more info. 

My only question is do you think it would be better to go with posts from roof to footing (like a pole barn) or build like modern manshed on beams?  And if I build on beams, what is the best way to attach beams to deck and girts or top plates.  I'm all for the simpson brackets ...

The building inspector suggested using pt 4x4 for footing instead of sonar tubes.  But my thoughts are sonar tube, attach 4x4 to them, and continue to top plate, then build rafters with dimensional lumber with a rafter board. 

Any thoughts?  H~`~`~`

[Don_P]

I'm not sure I'd chuck the plans, maybe fix the weak spots. Upsizing the tie to a 2x8 gave me plenty of room to get 4 bolts in;



then put a real post under each truss down to a footing. 4x4's are really for mailboxes, decks and porches should be on 6x6's minimum. If the total height from top of footing to bottom of carry beam is less than 16' then I prefer to do it with one timber. I prefer to notch in 2-1/4" deep for a double rim. This leaves a good amount of post remaining but is not strictly by the deck guide I linked to. It does calculate sufficient bearing for any situation I've been in, textbook is full bearing, 3" deep for a double rim. From there the posts continue up. This is a sketch I had, something along these lines


You've mentioned free standing and put up a link to an attached structure  No problem but if it is not attached to a rigid building then it should have some diagonal Y braces on the posts. Also making a steeper pitch decreases the tension in the bottom chord.

This is some hardware that might be interesting;
This could be used on the top of the tie to the rafter for a redundant connection if you wanted
http://strongtie.com/products/connectors/TS.asp

http://strongtie.com/products/connectors/T-L.asp
http://strongtie.com/products/APG/classic.html
http://strongtie.com/products/connectors/HLPC-HTPC_APG.asp

[secordpd]

Well, Don you got my mind a-churning.  I priced 6x6 today and I found a local lumber yard with pretty good prices.  I like your idea of transferring the weight to the footers from the rafters.  I am a little confused about

I prefer to notch in 2-1/4" deep for a double rim

.  If I double 2x?, that would be 3" notch.  Are you saying make a glued&nailed beam and only notch 2-1/4" into 6x6, which would leave 3/4" not supported in the notch?  Or am I missing something?

What would you use for the top plate?

And I understand if it's free standing, I need y supports.

One more thing, what is the best way to attach the 6x6 to the sonar tube footings - with this



or place 6x6 in hole with cement.  I thought I read some where that if the post was buried a certain depth, it would resist push-out more than just attached to footings?

Again, thanx so much for helping me, I always wonder about different building desgns, but never had the pros & cons laid out to me.

[Don_P]

well I had a post earlier and the darned computer ate it, lets assume it was highly enlightening but now you're stuck with this one  

I probably should have left the notch depth alone, 3" is probably going to pass with less raised eyebrows but since I didn't lets see how much weight my ply and a half notch can bear. Southern yellow pine, my treated lumber here, in #2 grade is good for 565 psi in compression perpendicular to grain, the side of the beam being crushed on the notch... in dry service. We had better call this wet service so we'll take 67% of that, 378.55 lbs allowed per square inch of bearing area. I'm proposing 2.25" X 5.5" X 387.55 psi=4684.55 lbs allowed. The typical design load for a deck is 40 psf live load + 10psf dead load so 4684.55 lbs/50 psf= 93.69 square feet. We can safely support up to ~94 square feet of floor on that notch. I'm typically supporting closer to half that area on a post. Recall that the deck guide calls for post spacing not to exceed 8'. It still leaves nearly a 4x6 or 4x4 of material left in a running or corner post respectively. I wouldn't want to give you advice that would give an inspector heartburn though, so use your judgement. BTW glue is not structural, but it won't hurt a thing.

 The top plate depends on the rafter/truss configuration. If the trusses are only over the posts then it won't take much of a top plate. If the plate is carrying trusses or rafters in its span then it needs to be designed as a beam capable of supporting that portion of the roof load. I've used 6x8's here pretty often on the typical post spacing. I've also let in dimensional lumber on one or both sides of the post top for the beam.

I don't care for sono tubes if I can avoid them. I prefer to either carry the post down to the frost depth footing or to build up something substantial enough to avoid tipping. If the porch is attached to a house then the sonotubes are laterally braced by the floor and roof diaphragms. If the structure is truly free standing then they would need to be adequately braced. Yes soil is a brace, of unknown quality.  Short of an engineering report I have to be conservative and call it zero. Those shallow post frame footings run from 4-8' deep depending on soil type and lateral load. I'd rather find a way to brace them with something I know can handle the work. If you do bury the posts they should be treated to .60 pcf or better, foundation grade is the best if available. They specify no heartwood in that grade, heartwood is impervious to treatment, so foundation grade is treated to the core.

[secordpd]

Hi Don,

Bad, bad computer, don't you hate that       and the second reply is never as good, cause you hate to write it again.......But thanx for your tenacity, you rock!!

I'm having second thoughts about the post from footing to rafter.  I just can't  imagine the cost of 16' 6x6 timbers, or the weight...  But I'm thinking of using 6x6 .60 foundation grade post (where can you buy them?), just to eliminate the hassle of the cement piers, then building beams on top  (like mountain Don did - w/16x16 cement footings ) or notched in. 

I have another question if you feel like answering: 

Does it matter which way the beams  or joists run in relation to the gable roof?

When you walk out of my kitchen's sliding glass door, that is the peak end of the gable roof.

I can only go out 12 or 14 feet as the sewer ejector pump tank is at about 16/17 feet.  So since my last deck was 12' deep and 16' wide, I was hoping to make it 2' or 4' wider.

With that in mind, (the rafters running the 16' or more), would it be more advantageous to run the joists one way or the other?

The reason I would like to run the joists 12' deep is because I was thinking of a bumpout on part of the 12' end to 14', covered with a little shed roof.

Any thoughts on that?

[Don_P]

I rocked today, but my name is mud tomorrow, gettin a raise anyway, its 20' up the scaffold

.60 is usually readily available and what I typically try to use. Since the switch to ACQ the treatment availability and contents have been all over the road. FG is usually special order and is used by permanent wood foundation people. If that style is common in an area then it is readily available otherwise I'd just go with regular .60. Depending on where you are I've been able to get 2.50 pcf CCA treated on the coast, wash yourself well after and cut over a plastic sheet so you can contain the dust and dispose of it.

When I can't run the post in one piece I let a piece of 1/4x3" plate steel into the back of the notch and run it up thru the decking and standing up 8" above the decking. I then use a 12"x1/4" drill bit to make a series of holes in the end of the post above. A sawzall with a 12" "Axe" blade is then inserted in the holes and hogs out the wood between holes. Drop the post over the steel and then bore thru the post and steel above and below. Bolt below catching the beam, steel and notched post. I pin the post above the deck with a smooth steel rod about 4.5" long and peg the hole with a wood plug, hidden uplift protection. Sounds like its attached to the house for lateral bracing, refer to page 14 under fig 21 in DCA6 "deck stability", good deal. Since the floor is a pretty rigid diaphragm attached to a fixed building this is considered to be braced.

Joist direction doesn't matter here as long as the beams and posts account for it. I think its time for a rough dimensioned sketch from your end, it can be in "paint" if you don't have any other program you prefer. It'll help keep this clear. Probably a plan view, from above, show me the house side in that,  and an elevation looking back at it and the house from out in the yard, give me some ideas about pitches and heights.

[secordpd]

Glad your getting a raise , not good about the mud.....

I'll start working on a sketch,  I haven't put one up cause I was trying to teach myself sketch-up, and wasn't good enough yet, but I'll find another way to get it on here...

Thanx Don, hope all works out for you....   Helen~`~`~`

[TimL]

I am resurecting this thread, because the question I have directly relates to Don's original post.
First, Don, thank's for the original post on calculating thrust. a nice simple explanation.

However, if the total load is 1200#, and you use 600 for your calculation, which results in the 707# thrust, does that mean that each rafter creates 707, for a total of 1414 axial tension in bottom member?

I have been reading a lot lately on this topic, and I do find differing oppinions.  please help me understand this, is the 600# used, just 'cuz thats how the formulae works??

Thanks in advance

Tim

[OlJarhead]

I'm still wondering about this myself. 

I have a 12/12 pitch with 2x6 rafters and 2x4 collar ties set at 5' from the top of the wall (2 feet from the ridge board).

The walls have loft joists 26" below the top of the wall.

I'll draw this out for visual but in the meantime I'm wondering if I might run into a problem of the roof spreading at the top of the walls (since the walls are tied together but below the top of the wall).

[OlJarhead]

That ought to show the roof design well enough I hope.

I want the loft space for a sleeping loft with a 2' knee wall to give more headroom.

I plan to install hurricane ties to each rafter however I found I cannot just nail them to the outside wall as they drop below the double top plates and inside won't work since it's a 2x6 wall with 2x6 rafters (so you've got a couple inches of 'shelf' on top of the wall.

[Don_P]

I am resurecting this thread, because the question I have directly relates to Don's original post.
First, Don, thank's for the original post on calculating thrust. a nice simple explanation.

However, if the total load is 1200#, and you use 600 for your calculation, which results in the 707# thrust, does that mean that each rafter creates 707, for a total of 1414 axial tension in bottom member?

I have been reading a lot lately on this topic, and I do find differing oppinions.  please help me understand this, is the 600# used, just 'cuz thats how the formulae works??

Thanks in advance

Tim

Axial tension in the tie is W/2 x run/rise. Of the 600 lbs on the individual rafter, half is supported by the wall. For an 8/12 rafter 300x1.5= 450 lbs axial tension in the tie.

Jarhead,    
your rafters are sitting tightly on the plate. Under roof load the birdsmouth will deliver load to the top of the wall immediately, either vertical or horizontal. The floor has been called a tie, has it been connected as one? The collar tie is nailed. At its elevation it will be handed 2-1/3 times the tension load of the floor ties. Nails have a certain amount of slip before they take load. Load goes to stiffness. Where's the stiffness in that scenario?

The wall studs are essentially a beam overhanging a support with a point load  on the end of the overhang. The highest bending moment is where the beam overhangs the support. In this case that is at the ledger, where they have been notched on their tension edge. As the kneewall height increases the bending moment on that notched area rises fast.

This might be another alternative to consider. Often in older balloon frames the top floor ceiling joists extend over the walls to form the overhang. A raising plate was nailed flat onto the top of that and the level cut rafters were attached to the raising plate. This method is not without problems. Fascia leaks can rot structure easier although cantilever trusses use basically this method. Dealing with the thrust in the connection to the plate needs to be considered. The cantilever has code limits.

[OlJarhead]

Mines built now -- framed anyway -- so can't make design changes too easily.

The loft floor is 2x8's hung on joist hangers nailed to the ledger which is notched into the 2x6 studs so I realize it's not the same as directly nailing to the rafter.

I guess the question is:  am I going to have a roof cave in? 

With collar ties every rafter pair and hurricane ties I don't have much of an option now other them maybe scrapping the catwalk and putting in two heavy beams on the top of the wall.  Of course then I'd have to have two ladders to get up to the lofts or have a raised catwalk that goes above those beams -- but that would be too much as they would be 2 feet plus the height of the beams above floor level in the loft...a 3 foot high catwalk would give only 4 feet of head clearance to the collar ties.


You can see the height of the knee wall here and the rafters sitting on the top of the wall as well as a collar tie I think.


Here you can see the loft ledgers notched into the studs with the loft hung on them with joist hangers (for 2x8's).

[OlJarhead]

This was taken the night before I did the work on the end wall -- but I think is a better show of my cabin framing right now.

[Don_P]

I guess the question is:  am I going to have a roof cave in?

I asked a similar question one time. "If you don't know the answer to that question an engineer does."

I'm no engineer and don't pretend to be one. I'm happy to pass along the snippets I've learned along the way but that is all it is. I've seen multiple references by experienced timberframers about the problems I've pointed out. When I do the math on the notched stud, I see their point. It is outside of prescriptive code. If you stay inside of code structurally I am quite confident you won't have any major problems. When you step outside of codebook prescriptions those portions of the building should be reviewed by an engineer or at least be very thoughtfully considered. I've drawn above what I believe would be a code compliant alternative to the design you show. It would not require an engineer and I would be more confident of its performance.

I've built large cathedral greatrooms with no structural ridge and no ties. They had intersecting wings whose walls and roof planes were buttressing the greatroom. You've proposed wrap around porches, bound to help. Someone described a kneewall truss the other day and I've built with a similar truss. The kneewall area is several feet deep and has a diagonal strut. They've built a buttressing post in the truss that required several feet of depth to satisfy the stresses.

While I had sketchup open, looking down, this pic shows how a post frame could be used. The posts extend from the wall top plate down to the footings, there is no hinge point at floor level.

[OlJarhead]

Thanks DonP -- very frustrating for me   I've seen several cabin pics here in the gallery of at least 3 cabins like this one, based on the 14x24, that show a knee wall that I just figured it was ok -- my goof.

I'll have to discuss with an engineer buddy of mine (he's an EE, ME and SE I beleive (holds 3 Engineering degrees)) and will look at it for free   But he's not a builder -- not of wood homes or cabins anyway -- but rather stuff in a nuke plant.  So he might not be the right guy, however I suspect he can steer me in the right direction.

My only real fear isn't snow but rather wind, since the pitch of the roof will keep the snow off.

[OlJarhead]

http://www.countryplans.com/nash.html

The Nash place was my original inspiration here at CountryPlans...and of course, as you can see it's built more or less the same as my place -- or should I say I built mine much like him -- except the foundation.

http://www.countryplans.com/lemay.html
The Lemay place is also done this way except he has beams (ok trees) that help keep the walls together -- but those tree beams are BELOW the loft floor so not up on the top of the wall where needed.

I think considerations also built this way and I seem to recall others -- so, it sounds like we're all risking some problems here.  The question now becomes what should we do to prevent issue?

I always thought it was the loft beams affixed to the walls that kept the walls from spreading and the roof coming down, but I never thought of the rafter coming out at the bottom where it meets the wall.

[Don_P]

This is some reading on and around the subject;
http://www.smandf.com/25-ConventionallyFramedRoofs-TheGabledRoofProblems&Solutions.pdf
This one is a classic from the 1880's and is a simple to follow explanation of thrust,
http://chestofbooks.com/architecture/American-House-Carpenter/78-Horizontal-Thrust.html
This one is relevent to the high tie comments and may also be of interest to Tim.
http://www.eng-tips.com/viewthread.cfm?qid=105386
(Tim, feel free to pm if you want)

If I understood correctly someone again just proposed this same setup, but with a 3' or 4' kneewall, to a new poster who lives in what I believe to be 60 psf snow country...  

If you followed the eng-tips discussion, what they referred to as the horizontal "kick" on the top of each stud would be 466 lbs. By my math the maximum safe bending moment on a notched 2x6 stud would be under 440 lb-ft (unnotched allowable stress would be 835 lb-ft). That's an 11" kneewall. The three foot kneewall proposed, 466 pounds pushing on a 3' lever=1398 lb-ft, to me looks pretty risky.

Keep raising the kneewall  . If the kneewalls get a bit higher the ties can drop to an effective height, thrust is restrained and the load is just vertical.

edit; another good article
http://www.coastalcontractor.net/pdf/2007/0707/0707desi.pdf

[GSPDOG]

Don has seen this before but this was my solution to this problem.



This is the design.  Couple of notes wood type and rating is important.  This is also being used for a metal roof with spray foam installation 3" - 5" thick.  It consist of a 2x6 rafters SYP #1's and 2x4 ties SYP #2's.   The ridge beam is 32 feet long and extends 2 feet out from the end walls.  16 Penny nails in a 2" pattern aligned with code nailing schedule which does not apply in my area but just because we have no codes is no excuse for not following them. in a 2 inch pattern means that they receive 8 nails per board. in a 2x2 pattern.  Ridge tied together with 2 3/4" 5 ply Plates. 36" long.  Cross nailed screwed and glued.

The 2x6 rafters are three 2x6's forming a U beam with 2x4 tying them together.  The interior close the U with a 1x8 dressing board that is not nailed but rather wooden 1/4 inch hardwood dow pins glued in place.

The 20 foot 2x6 raters are connected at the ridge beam  bird mouth at the knee wall connection in line with the foundation wall.  Finally they are connected to the 2x8 floor beam and the 6x6 porch post.  The extended floor rafters siting on the wall top plate, with 4 sets of hurricane straps. The porch beam is inset to the beam 1.5 inches so the porch beam connects all the porch post together.

It is over kill we could probably drive a truck across it if it were not for he 8ft spacing between the beams.  Here is a look at it before the roof went on and after.






So Hopefully that will be helpful to someone.