Cathedral Ceiling Rafter Thrust Load 3

[kxa]

Is there horizontal force at the heel of the rafters for a cathedral ceiling when using a structural ridge beam. I have collar ties halfway up on a 7/12 pitch. My analysis for dead and snow loads show a good amount of kickout force where rafters meet the wall but a couple of people I spoke with say that when using structural ridge beam there is very little horizontal force.

 

[bjb]

With a structural ridge beam, the rafters have vertical support at the ridge and the wall, so equilibrium can be reached without horizontal forces at the wall and ridge. However, when the ridge beam deflects, the rafters will move with it, and there would be some resulting horizontal deflection imposed at the top of the wall. To minimize this, I design stiff ridge beams. You also need properly designed posts and footings to support the ridge beam.

If you don't have a structural ridge beam, it's been my experience that collar ties are not very effective because they tend to be located too far away from the top plate. The tension force in the collar ties often requires alot of nails, or the use of bolted conncetions. Also, there is a lot more bending in the rafter because of the collar tie. If this isn't accounted for, the rafters can be undersized, and over time they can creep and cause the walls to kick out. I have seen this on several existing buildings that I have checked. This problem becomes worse with decreasing roof pitches.

It's also been my experience that a lot of architects (and some engineers) don't really understand what is necessary for a sloped roof using rafters to stand up and not kick the walls out. If you don't have a reliable load path to resolve the horizontal forces with rafters, then the rafters require two points of vertical support for equilibrium. An inadequate design for this system is the number 1 problem that I have seen when investigating sloped roofs with cathedral ceilings. Unfortunately, trying to design this system properly can result in battles with the architect, because they may not like the ridge beams, and may not understand the difficulties with collar ties.

 

[samdamon]

Rule of thumb for collars is that they have to be at least within the lower third of the rafter span to be effective at all, and bjb's comments about the forces and connections of the collars to the rafters are spot on. I frequently see collars placed too high, with inadequate connections, and spaced so that only every third or fourth pair of roof rafters is restrained. Mostly see it in residential and older commercial or farm buildings. The roofs in these structures stand but the walls typically spread at the top.

When using a structural ridge beam you will have no horizontal force at the rafter low end connection due to gravity loads, but there will be wind and seismic forces (both vert and horizontal) that will need to be considered because the roof rafter is laterally bracing the top of the wall, and the wall is holding down the rafter end.

 

[bjb]

SamDamon raises an excellent point about the roof bracing the wall. The way that I have looked at it, as the horizontal forces are applied to the wall, a reaction is provided between the roof framing member and the wall. The load in the roof framing member is trasfered into the roof diaphragm, and the reactions that the roof diaphragm is looking for are provided by the shear walls. At the gable end, there is a problem if you have platform construction because there is a discontinuity bettween the wall studs and the roof diaphragm. If possible, going full height with your wall studs at the gable ends can geta around this.

The most important thing is to make sure that you have a relaible load path that you have designed that allows for the transfer of applied loads to the elements that resist them. Cathedral ceilings with stick framing can be tricky. A good reference that gets into load paths for wind is the Windstorm Mitigation Manual for Lightframe Construction, I think you can get it from FEMA.

 

[HouseBoy]

Based on the description of the roof construction, I think the rafter tails will have thrust (considering the vertical load case only).
The horizontal component will be in compression as it resists the inward bowing of the rafters (albeit slight). This compression will be counteracted by the horizontal (outward) force applied at the top of the wall.
Consider the free body diagram.
If the horizontal piece could be eliminated or somehow connected to the rafters in a way that it only supports the vertical load (of the ceiling) the thrust at the tials would go away.

 

[kxa]

Thank you all for your input.I must say however that I agree with houseguy. when you load the rafters with DL & LL or SL, the rafters produce compression in the collar ties and the ends of the rafters sitting on the walls are forced down and outward. Therefore, the rafter tails produce both horizontal and vertical loads on top of the walls. When you analyze the unbalanced snow load condition, this becomes even more obvious.
I think of it as an 'A' frame structure that the sides are being pushed in and down. The legs tend to want to move outward. If you think my logic is not right, I would like to hear yours.

 

[bjb]

I don't think it's correct to look at it as an A frame because you have a structural ridge beam that provides vertical support. Look at the free body diagram for a sloped rafter loaded vertically only with reactions at the ridge beam and the wall. Snow load and live load acts on the horizontal projection, not perpendicular as with wind. Equilibrium is achieved without any horizontal reaction. Even if you break the vertical loads into components that are perpendicular and parallel to the rafter, the resultatnt reactions at the ends are stil vertical. Remember that at the wall, the rafters are birdsmouthed so you have a horizontal surface of the rafter sitting on the horizontal top surface of the wall. If you did not birdsmouth the rafter, and had a bevelled top plate, then you would be inducing horizontal load into the wall. See Example 2.6 in the fifth edition of Design of Wood Structures by Breyer. Only vertical reactions at the rdige and wall are shown.

Any outward push by the rafters resulting from either their deflection or the deflection of the ridge beam is self limiting. If these elements are stiff enough, it shouldn't be a problem. Also, with a properly designed ridge beam system, you don't need collar ties. I don't think that collar ties are the way to go in anything but a small building with a steeply pitched roof. The connection forces become so large they can be hard to deal with.

 

[HouseBoy]

bjb:
Just so we're clear about this, I would expect that the conditions described in the original thread could work well, but the points about horizontal thrust and/or outward spread of the rafter tails need to be corrected.
First of all, the fact that the bottoms of the rafters and the tops of the walls are flat does not in and of itself prevent thrust or movement. The rafter tails will slide out if there is nothing there to prevent them from moving outward and if the rafters are birdsmouthed at the plate they will push out on the walls. That pretty much is the definition of thrust!
I looked at the example in Breyer and I noted one significant difference, the example has no horizontal component between the top plate and the ridge! As I stated in my original post, it is this horizontal component that causes the thrust at the tails. (I am neglecting the component of thrust caused by deflection of the ridge beam as does the example).
If the horizontal component is there, it WILL cause the tails to thrust outward or (if they are restrained) there will be horizontal force at the bottoms of the tails.
I'm not sure what you mean by "self limiting". I guess that if the elememts are stiff enough, it shouldn't be a problem but the question is about whether or not there is thrust. There is in the case where a horizontal member is used.

 

[bjb]

Houseguy, maybe we're not on the same page, so I will try to clarify my position. It's not my intent to have a battle with you. With a structural ridge beam, you do not need collar ties. The collar ties are redundant because equilibrium is acheived by the vertical reactions at the ridge and the wall.

If you do add collar ties to a system that has a structural ridge beam, I do agree that the collars will be loaded by the deflection of the rafter. The collars will be in compression; as a result the rafter tails will tend to push on the wall. This also happens as a result of the deflection of the ridge beam. As I mention in my first post, the ridge beam deflects downwards, which has the effect of pushing on the walls. My point about this being self limiting is that the push is only occuring because of the flexibility of the system. If the system is vertically stiff, any induced horizontal deflections of the wall are minimized. Theoretically, it the system were infinitley stiff, there would be no induced horizontal deflection. Yes, I know that infinte stiffness is not possible, I use this to illustrate my point.

The bottom line that I am trying to establish is that with a structural ridge beam, static equilibrium is achieved for vertical applied loads with only vertical reactions at the ridge and wall. Therefore, you don't need collar ties as they are redundant. Why use them then? If they are there for some architectural reason, I don't think you need to consider them as part of your load path. Any induced horizontal movement at the wall should be managed by designing you ridge beams and rafters with adequate stiffness.

 

[HouseBoy]

That is fine bjb. We are in agreement.
The problem I am sometimes confronted with involves the case where the owner and/or architec wants the ceiling profile described (with a flat section about halfway up the rafters). Since the horizontal piece doesn't work well as a collar tie (for reasons we already agree upon) I find that I frequently can get a structural ridge to work. The "problem" then becomes trying to resist the added thrust caused by the ceiling joist! As we agree, it's not needed to hold the roof up but it does cause forces or spread that must be accomodated. It sometimes makes the wall construction more complicated. That is why I wanted to be clear about the point of whether or not thrust is there.

 

[bjb]

I understand where you are coming from houseguy. If we were having this conversation face to face, I'm sure any misunderstanding would not have happened. I usually try to design members as stiff as I reasonably can when faced with this issue. I came up with a calulation template that predicts how much horizontal movement results from a given vertical displacement. So far I have had success with this, although dealing with the arch's is tough, especially if I calc a big ridge beam.

It's been my experience that a lot of arch's and some engineers don't really understand what goes into making a cathedral ceiling work. When I am hired to check out a distressed wood building, by far the number 1 problem that I see is improperly designed and built cathedral ceilings. The bad ones usually hold up for dead load, so people go away with the idea that what they did works. Throw in some snow load and time for creep and you get walls kicking out. When they see what I consider to be a properly designed ridge beam system, they often have a problem with it.

My concern in my posts was that the original poster may have had an incorrect understanding of the statics involved with a structural ridge beam. That is why I was harping on it. The trickier statics case is when you don't have a ridge beam, and you do need the horizontal forces from prefereably a ceiling joist, or a collar tie.

 

[bylar]

I think that there may be a misconception of collar ties.
They are not to restrict the horizontal thrust (as most agreed) The IBC requires collar ties. They are required to be in the upper 1/3 and therefore are useless in resisting horizontal thrust. I believe they were orignlaly required to prevent the spread of the rafters from the ridge (board or beam) due to wind loads.
I think they are useless and there are easier ways to prevent this uplift seperating the rafter but in our area the inspectors require collar ties regardless of the engineering because it is in the code.

 

[TFL]

I agree with Bylar. collar ties help to hold the ridge together under wind suction. though i never count on it, they also help to theoretically cut the span on the rafters under symetrical live load. read snow load.

 

[Slowzuki]

I just finished going through some of this myself designing our own post and beam shop.

I agree that using a structural ridge beam to limit deflection to say 1/180 of the span in a wood ceiling can cause noticable spreading of a wall. Designing to 1/360 would be better. Both result in a massive beam or flat truss when any kind of span is involved. (I live in Canada, 52 lb/ft2 flat roof snow load in our area).

In our place the size of this beam would be too large for any pitch of roof I was considering. We had to move to a moment frame type design with collar ties and haunch bracing and moment resisting wall members.

By doing this the collar ties and hauch bracing can be used to reduce effective spans drastically reducing the size of the members. In our particular span I believe we went from 2x12's 24" on centre for a cathedral ceiling ridge beam system to 6x6 posts and beams on 8 ft centres for a moment resisting construction.

The draw back of course is now we have a pair of 2x6 haunch braces every 8 ft in our living space. I'm ok with that since we are exposing our construction.

 

[bjb]

I agree that collar ties are not the way to resist spreading of the rafter tails. I also don't think they should be counted on to reduce the span of the rafters. There are some people that do consider them effective to resist the horizontal spreading of rafter tails. Unfortunately, on many of the buildings that I have looked at that have a cathedral ceiling, there is no other load path. The result is usually walls that have been pushed outwards. When I design a wood roof with a cathedral ceiling, the architect usually tells me that collar ties will resist spreading of the rafters. I have also heard this from other engineers.

In my area, snow loads are not quite as bad as 52 psf. I have done similar things slowzuki. Sometimes we would have trusses at a spacing where we could have a reasonably sized ridge beam spanning between.

 

[Slowzuki]

bjb, re the reducion of span, I'm not talking about literally using span tables, rather using a truss/moment frame analysis software and determining the attainable spans of the complete assembly.

The code does allow span reductions for light framed buildings with collar ties I believe.

The structural supplement to our building code doesn't have really severe unbalanced loading cases for simple roof shapes. We did have a recent change to the requirments for quonset hut style roofs for unbalanced loading due to a few collapses.