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Ridge Beam & Statics?

Started by Wheels77PE, January 17, 2015, 10:53:08 AM

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Wheels77PE

I am designing a cathedral ceiling and having a difficult time wrapping my head around the structural ridge beam concept.  If we look at the statics of the sloped rafter member and draw a free body diagram, there is a vertical (Fy) and horizontal (Fx) component to the reaction.  I understand the ridge beam is designed for the vertical component.  How is the horizontal accounted for?
Many articles (including this forum) talk about the outward thrust not being present if the rafters don't move but even if the structure doesn't move, the load is applied.  If the load is applied the forces are there internally. To be in static equilibrium the reactions have to support the internal forces.
I would appreciate any clarifications! Thank You!

beenthere

Welcome to the Forestry Forum

I didn't design my cathedral ceiling, but do have a structural ridge beam 24' long holding up the 2x12 rafters that are over the 30' width of the room. The side walls are almost all glass.


  

 
south central Wisconsin
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Jim1611

How tall are those side walls?
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Ljohnsaw

WOW!  That is impressive - I don't see how it works but obviously it does!
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beenthere

QuoteHow tall are those side walls?

Std. 8' walls.

Some more of the build..


  

Addition extended on the old house which was a hip-roof style. Small windows at top sit above the old roofline and take in sun during the winter, and the moon on many moonlit nights. French doors replace the old sliding doors. The cedar beams on the cedar ceiling paneling are false and are boxed to hide wires for fans and any future hanging lights.
 

south central Wisconsin
It may be that my sole purpose in life is simply to serve as a warning to others

Den-Den

Quote from: Wheels77PE on January 17, 2015, 10:53:08 AM
  I understand the ridge beam is designed for the vertical component.  How is the horizontal accounted for?

The rafters on the other side of the ridge have an equal and opposite horizontal component.
You may think that you can or may think you can't; either way, you are right.

Magicman

Can't help but Welcome to the Forestry Forum, Wheels77PE.   :)
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razor

Hi Wheels. Full disclosure, i have no engineering training of any kind, and my physics education is limited to high school so feel free to educate me. 
i only have empirical evidence to go by but if your ridge beam is fixed, and your rafters are attached to each other at the peak, then there are only vertical forces at the rafter foot. For horizontal thrust to occur, the peak needs to come down. (Or, conversely, the feet would need to go up. Not an issue i would hope) 
So in my world, there is no horizontal with a ridge. I'd be interested to hear about the internal forces though.

Thehardway

Hey wheels,

Welcome to FF.  In a structural Ridgebeam and Ridgepost configuration, the ends of the rafters are notched and permanently secured and affixed to the ridgebeam with approved joinery or fasteners.  To have no horizontal thrust load, perfectly  even roof loading must occur.  In a computer model,  laboratory or theoretical setting this is possible and basically each side balances the other out and thrust is controlled at the ridgeline, with the eave wall having to carry only one half the shared vertical load per side.  Notice I said in theory as loading of a roof is almost never uniform and symmetrical.  Things like variance in lumber weight, wind load, and drifitng snow on the roof can all cause a stucture constructed like this to see horizontal load factors at the ridgebeam and at the eave. 

A ridgepost and ridgebeam construction is not ideal in my mind because it has a single point of catastrophic failure.  It is also subject to high load forces at the joints and potential failure should any racking occur.  I would reserve it for when no other traditional framing solution would work. Just my 2 cents.  This is in know way a criticism of what other have done.  Each must assess needs and risks and weigh them accordingly.
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Jeff

Kent, you don't happen to have your old drawings for that room do you?
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canopy

Very interesting discussion. Curious if a collar tie is added to each rafter pair, then what does that do or not do?

witterbound

My understanding is that a collar tie simply prevents sagging of the rafter.

beenthere

Located three pics to show the rafters, ridge beam and outside wall.

Gusset at the peak of the rafter pairs.  Some pieces scabbed on for safety in second pic.



  

  

 
south central Wisconsin
It may be that my sole purpose in life is simply to serve as a warning to others

D L Bahler

Of course, I cannot resist a discussion on Structural ridge beams!

I must disagree with the point made about the structural ridge not being ideal, due to a single point of potential failure. In practice this is a non-issue, unless of course you have a carpenter who has built such a system with no clue of how it works.

Essentially when you have a structural ridge beam, you exchange your typical means of calculating rafter loads with a totally new set of equations. It is beneficial to think of the rafters in this situation as being a completely different type of timber than are rafters without a ridge support. This is easy of course for me, because in German they have completely different and unrelated names (Rafen and Sparren) and are not thought of to be the same thing at all.

Remember that in roof loading, only the most basic physics are involved (though in a very complicated and dynamic way) so here this is a simple instance of Newton's law. We have for every action an equal but opposite reaction. So the rafters oppose each other at the peak. Other sorts of loading due to winds and asymmetry are handled by bracing. So for us, we would brace our ridge post to the cross beams and to the ridge to handle these forces. The building shown has no such bracing, rather relying on the great depth of the rafters to take care of this. What has been shown is a greatly simplified version of the structural ridge roof.

In central Europe, these forces are further alleviated by forgoing any attachment of the rafters to the plate, rather they extend over them without any type of seat or nailing or any such. As such, they are allowed to slide if need be.

Going back to the potentially catastrophic failure. This is true of you have a poorly designed ridge system. The building shown does certainly push the limits of design but does not yet exceed them, though I personally would probably not design a roof structure like that. The potential problem by this design is the massive span of the ridge without support. SO if that ridge fails at any point, the entire structure will topple in on itself. This sort of design fastens the rafters to the walls, which also serves to brace the walls in lieu of any sort of tying beam. So if the ridge fails or heavily deflects, not only will the rafters collapse but the walls will be pulled inward so the entire building fails.

The sort of system I am accustomed to is much more complex, involving cross beams in the walls, bracing, and intermediate support of the ridge so that failure at any one point will not cause the entire structure to collapse.

But obviously the poster is after a design like what we are shown. So for this I say, the design shown is perfectly reasonable as long as you design for these potential issues. These issues are not flaws as much as things you must be aware of and design for. They are only problems if you fail to consider them properly.

beenthere

QuoteThe building shown does certainly push the limits of design but does not yet exceed them

Which building are you referring to in your post?  Trying to follow what you are trying to say. ;)

If the building in the most previous pics, that ridge beam is four 1¾" x 18" microlams stacked side by each.
Over kill for sure.

And if the ridge beam fails, the walls will be pushed outward, not pulled inward. ;)
south central Wisconsin
It may be that my sole purpose in life is simply to serve as a warning to others

VTwoodworker

Hi Wheels,

You need to reconsider your free body diagram.  The loads on the rafters are vertical and the reactions from walls and the ridge beams are also vertical mostly equal and opposite.  The cathedral rafters do not act like a truss member which would behave as you are are assuming with a vertical and horizontal component to the reaction.  The rafter is just a beam that is not level and the ridge beam assuming it is sized correctly supports one end of the rafter.

If the ridge beam is not correct it will deflect and that will cause the walls to thrust and because the movement this is not the "static" condition.  The pics posted by beenthere looks like a good design to me the ridge beam is sized to carry the vertical load from the rafters.  And with a proper column to carry the load from the ridge beam to the structure. Too often people will use a 2x as a plate between the rafters and call that a ridge beam.  In that case the ridge beam can't carry any significant veritical load and the rafters require a collar tie or some other truss type configuration to take the resulting thrust.

Hopefully, my points make sense.  Bottom line is if you are designing a cathedral roof use a robust ridge beam that will carry the load without deflection and a load path for the ridge beam loads to get to the foundation.  Having said all of that I would put a couple of collar ties in to be conservative.

Good luck.

Wayne

D L Bahler

Beenthere, there is only one structure pictured on this entire post, I didn't think clarification was necessary

Say what you want, any free-span ridge beam of 24 feet is pushing design limits. That doesn't make it wrong, it just is. There is nothing wrong with pushing limits, as long as you are aware you are doing so and design accordingly.

four 1¾" x 18" microlams is not overkill, it's suitable design for the task. Try and figure out how much weight that ridge beam is carrying and you will see this is not at all excessive. It's right.

Also to be clear, all collar beams do is brace the rafters to each other. They are useful for resisting deformation due to unequal loading patterns (like prevailing winds, heavy snow one one slope but not the other, etc) by transferring the loads from one rafter into its opposite in the pair. They do not and cannot resist thrust in any meaningful way unless they are located below the bottom third of the roof.

Jim_Rogers

Quote from: D L Bahler on January 24, 2015, 07:13:05 PM
They do not and cannot resist thrust in any meaningful way unless they are located below the bottom third of the roof.

The engineers have proved this with their structural software that the "collar" doesn't "tie" the rafters together unless they are within 1 foot of the top of the plate. In most all positions above this they are in compression, holding the rafters apart from the sag of the loads mentioned above.

This is why I call it a "collar beam" and not a "collar tie." The word "tie" implies that is "tying" the rafters together, which in a lot of cases it is not.

Jim Rogers
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Wheels77PE

Thank you to all for the helpful replies. 
I think VTwoodworker clarified my original question best in that a regular roof w/ ridge board, rafters, collar ties & ceiling joists constitute a series of trusses; set at 16" o.c. They act together w/ horizontal and vertical forces.  I understand with a ridge beam only vertical forces are applied. 
As for the tangent the forum has gone off on regarding collar ties. It is my understanding that collar ties located in the upper third of the roof truss are for wind uplift forces and ceiling joists located in the lower third resist the outward thrust.
To D L Bahler
It is interesting to hear about construction in other parts of the world.  Speaking of wind uplift forces, what keeps the roofs in central Europe from being blown off the houses!? 

D L Bahler

A roof is very heavy. Its own weight is sufficient to hold it down, unless of course you happen to be in the middle of a category 4 hurricane.

Even on small structures, you don't have a problem with the roof getting torn off.

I get asked this question a lot, and I guess the best thing I can say is that maybe we are over-thinking the problem a bit too much. I can understand the rationality that would lead one to believe that such unattached roofs would be insecure, but practice has proven this concern to be unfounded. Remember too, we are talking about a region that is not exactly calm and easy. They have intense winds in the Alps that can do great damage. The only time I ever heard of a house like this losing its roof was when the storm Lothar -with hurricane force winds- came through around 2000, and cleared entire forests of of the sides of the mountains. Even then, most structures stood with their roofs intact.

So looking at the physics involved, I see where we could be worried. But remember these are often 4x6 rafters so they are not apt to go anywhere. The only concern we ever really have with wind getting under our roofs is in regard to ripping the coverings off of them, or stirring up the air in the attic and so causing a draft in the house. In the literature of the people who actually build roofs like this, I never have seen anyone seriously concerned with uplift moving the rafters.

As to collar ties -not so much uplift forces, as much as horizontal bending forces. So you have a wind load pushing against one side of the roof, the collar tie allows the unloaded rafter to bear a part of that load and so the whole roof is stiffer.

jwilly3879

The higher the "collar tie" the larger the rafter needs to be because it keeps the rafter from bending. I have seen buildings where the collar ties were raised to increase headroom and the rafters failed between the collar tie and plate.

From NYS Residential Code.

a. The tabulated rafter spans assume that ceiling joists are located at the bottom of the attic space or that some other method of resisting the outward push of the rafters on the bearing walls, such as rafter ties, is provided at that location. When ceiling joists or rafter ties are located higher in the attic space, the rafter spans shall be multiplied by the factors given below:



HC/HR Rafter Span Adjustment Factor
1/3 0.67
1/4 0.76
1/5 0.83
1/6 0.90
1/7.5 or less 1.00



where:

HC = Height of ceiling joists or rafter ties measured vertically above the top of the rafter support walls.

HR = Height of roof ridge measured vertically above the top of the rafter support walls.


ponderosae

Quote from: Wheels77PE on January 17, 2015, 10:53:08 AM
I am designing a cathedral ceiling and having a difficult time wrapping my head around the structural ridge beam concept.  If we look at the statics of the sloped rafter member and draw a free body diagram, there is a vertical (Fy) and horizontal (Fx) component to the reaction.  I understand the ridge beam is designed for the vertical component.  How is the horizontal accounted for?
Many articles (including this forum) talk about the outward thrust not being present if the rafters don't move but even if the structure doesn't move, the load is applied.  If the load is applied the forces are there internally. To be in static equilibrium the reactions have to support the internal forces.
I would appreciate any clarifications! Thank You!
Interesting topic, I was just reading this and thinking about it along the lines of force on the rafters myself. The way I look at a ridge beam is that the primary support it would add to the roof is to prevent it from collapsing at the apex, because the rafters are just hanging out there (butting heads and ready for a tug of war).

If you deflect a beam at the center, it pulls in on what it is attached to, and would collapse its supports inward with it (unless they were stable enough to resist that force), but if the supports were both strong and stable enough, then the beam would break in the center (if something had to give). Being that rafters are beams, then if only rafters are connected to each other at the peak, and you deflect them in the middle, they would be pulling the top of the roof inward and downward (or if rafters on one side of the roof deflect more than the other, then toward that side). When a ridge beam is supporting the rafters, they would push and pull against it instead of each other, and mostly downward. Now if the ridge beam deflects as a result, it would pull inward on the opposite walls, if attached there (or at least on the posts it was attached to), but if the ridge beam is stable and something has to give, some rafters may break (but that should be better than the whole roof collapsing).

Well, I'm looking at this in terms of what the extreme result of the 'vertical component' would be, because the way I picture it, there is typically only force coming down on a roof. The rest is about stability versus leverage (which would be the 'horizontal component', as a result of the angle of framing or its potential deflection). Basically, if the rafters are not stabilized by a supportive ridge beam, I think they would become unstable and collapse from the top before yielding in the middle, and the ridge beam also makes them less likely to break there (for distributing their load better).

Also I was reading about collar ties, and it was said that they can 'actually put a bending load on the rafters which can overdeflect them', if they were of minimum strength so as not to deflect otherwise. Beyond that, purlin beams (or underpurlins) seem related to this topic, as they would run along a roof like ridge beams, but go under the middle of rafters in order to effectively reduce their span, so that they would not deflect there. I'd think that both ridge beams and purlin supports would be ideal, although usually one or the other would be added (more often a ridge beam).







Don P

Hey ponderosae, welcome to the forum.

I had not seen this thread until now.
VTwoodworker's post is the one to study.

Think of a ridgebeam roof the same as a floor with a center girder in terms of the role of the ridgebeam and in sizing it.

As far as what happens if the ridgebeam deflects, this is where it differs. As the ridge sags the combined length of the rafter pair has to be accommodated somewhere, the walls are pushed outward.

The role of a collar tie, that is a horizontal tie in the upper third of roof height is to connect the rafter couple together in an uplift event. In the wake of hurricane Andrew when we saw on the evening news gable endwalls breaching the roofs unzipping at the ridge and the 2 planes of the roof sailing off, that is the role of the collar tie. For prescriptive construction there should be a collar tie at least every 4' or a metal strap over the rafters connecting the couple together as in a cathedral roof. It may act as a windbrace, or partial truss, generally if the rafters are improperly sized which was often the case with old houses.

The collar tie is often confused with the rafter tie, a horizontal tie in the lower third of the roof which when building a ridgeBOARD roof, absent a structural ridgeBEAM, ties the feet of the rafters together to prevent them from spreading.

As jwilley pointed out when someone uses a collar tie as a rafter tie the point of maximum bending moment is somewhere just below that tie. The rafter experiences an unexpectedly high bending moment and the tie connection easily becomes overwhelmed. One or the other is probably going to fail if it sees design load. Generally there and in the scenario you are trying to envision connections fail, but not always.


ponderosae

Thanks, I had read about the purpose of a ridge beam mainly being that it keeps the rafters from pushing out on the walls, and therefore substitutes for rafter ties (keeping the walls stable), but when I considered that rafters could do the opposite and pull in on the walls, when flexing (to possibly pull the roof down as well), it seems that the ridge beam does more than simply fill in for rafter ties.

In other words, I think the distinction to be made is that when down-force is put on a non-flexing rafter, it pushes out on the wall; however, when more down-force causes the rafter to flex, the opposite happens, and it pulls in on the wall. So the ridge beam helps keep the rafters from either pushing or pulling on the walls, and also keeps the rafters from being pushed flat, or pulling themselves down, where they are not supported at the rooftop.

Yet, in terms of 'statics', I haven't read much about it, though, as a metaphor, I'd imagine that the ridge beam keeps the rafters closer to a point of inflection (where they are not under compression on top or tension on the bottom), which tends to be in the middle of a beam, where no internal force exists. But I digress. Basically I'm just thinking it keeps the weight from shifting.

Don P

At maximum allowable rafter deflection how much do you think it could drag the wall inboard?

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