cathedral ceiling rafter thrust load

huangyhg

cathedral ceiling rafter thrust load
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.

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.
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.   
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   
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.
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.  
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.  re  
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   
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.  
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.
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