Compression Roof 2

[TORCHMAN]

First time posting here - always use this forum when searching for info and finally decided to join the community. Let me know if you need more info.

I am looking to design a compression roof with no ceiling joists/ties, or structural ridge beam. I am hoping to use a ridge board and collar ties. Is this possible?
I have 2 of these to design but the one I am most concerned about has a low pitch of 3/12, dimensions are about 6m wide x 1.5m tall
My concern is that the walls kick out due to heavy snow loads (2.3kPa).

Diagram below and a website delving into the issue.

https://inspectapedia.com/structure/Roof_Framing_Specifications_Canada.php

I am trying to model this roof on FTool but having a difficult time understanding if I am analyzing correctly. I tried playing around with height of collar tie and even adding a ceiling joist but unable to reduce the lateral load to something acceptable which tells me my model is not acting right.

Model:
Modeled with high collar tie:

https://files.engineering.com/getfi...37705&file=sloped_ceiling_high_collar_tie.ftl

Also, the way I picture the load transfer is that the lateral load has to be carried by the top plate of the wall (double 2x6) it bears on. And that the top plate acts as a beam from shear wall to shear wall. The top plate will run 4m from shear wall to shear wall and a double 2x6 is not that strong so the load would have to be quite minimal. Am I analyzing this correctly?

 

[JAE]

Collar ties are difficult to use and get to work correctly. The challenge is the connection between the collar and the sloping rafters.
Secondly - your image shows correctly that the rafters (and walls) will deflect significantly depending on the geometry.

For collar ties to work efficiently, they should typically be halfway up the slope or lower.
Higher ties can be done but the deflections sometimes get nasty and the connection are signficant.

 

[KootK]

At anything proportioned like that sketch, what you want is probably:

1) A ridge beam rather than a ridge board and;

2) Using the collar ties only for uplift resistance.

That's the traditional way of using that system.

Back when I was a truss designer, we'd occasionally do "tail bearing trusses" as shown below as a way to produce a coffered ceiling look. This is about the best possible version of collar tie as tension tie. 2x8 chords and high capacity toothed plates for the connection.

Even that setup would tap out with an overhang of 24" - 48" in snow country. It's just a crap load of bending on the cantilevered overhangs.

 

[SWComposites]

am looking to design a compression roof with no ceiling joists/ties, or structural ridge beam - Nope, even an aircraft stress guy knows this won't work in snow country. Add the structural ridge beam.

 

[GeorgeTheCivilEngineer]

Scissor trusses worth considering.

Compression roofs do work but if you look at traditional oak framed buildings, which sometimes use this approach, the eaves beam (to differentiate it from a wall plate) could be a 8x8" D30 solid oak, if not larger.

The connection into the shear wall would need to be designed and creep effect considered. I'd also consider how to manage the horizontal midspan deflection at the centre of the eaves beam. A continuous eaves beam with semi-fixed connections at the corner (eg with dragon ties) will all help minimise deflections.

 

[Eng16080]

I am looking to design a compression roof with no ceiling joists/ties, or structural ridge beam. I am hoping to use a ridge board and collar ties. Is this possible?

Sure it's possible, but probably not reasonable.

I don't have the software needed to view the model you attached above (a picture might be better), but unless the ties are located somewhere within the bottom third, I doubt you'll get anything reasonable to work. To verify your software model, you should draw a free body diagram and create a simple spreadsheet to solve for the collar tie force. You'll find that the force approaches infinity as you move up the rafter. A tie located half way up the rafter height will have about double the tension force than if it were located at the bottom (wall plate). This force will cause the rafters to want to snap at that location.

I can think of the following solutions considering "no ceiling joists/ties, or structural ridge beam":
[ol 1]
[li]Use steel rafters with the connection between both pieces fully rigid (moment connection).[/li]
[li]Design a beam at the wall top plate location capable of resisting the outward thrust. As you already noted, the 2x6 top plates alone likely won't work. Maybe you could sandwich a steel plate between the wood top plates.[/li]
[li]If there's some other way to resist outward thrust at the top of the wall, that could also work. Like having exterior counterforts bracing the wall (like you see with those municipal salt storage sheds).[/li]
[/ol]

If there are shear walls at 4m apart, I would try to use a ridge beam spanning from wall to wall. I suppose you have a reason why you can't do that though.

 

[GeorgeTheCivilEngineer]

Also - are purlins an option? Or is the same issue stopping a ridge beam meaning purlins can't be installed?

 

[TORCHMAN]

Thanks for all the great answers, folks. Your suggestions are great, I am glad I joined this community. It is just a matter of cost/constructability. You see, this is a project in which the home owner already did much of the work but was stopped by the municipality due to not having structural drawings. He called me to check the work and provide advice as to what is required to make his work structurally safe. He is very open to having to rework whatever is required so it is really a matter of finding the most cost effective way to a sound design.

The low pitch roof is 60+ years old and was there when the house was purchased. I am not sure about what the owner did - currently it stands with no ceiling ties, he added posts on both ends of what looked to me to be a 1 ply ridge board, reinforced the roof rafters by sistering new 2x8s to what were existing 2x6s, not realizing the lateral load it could cause to the walls.

A bit of a messy project. From a cost perspective, I believe that framing a truss or just adding ceiling joists are the best solutions. If a ridge beam was added, it does not have a clear vertical path down to the fnd. wall, it would have to get picked up by another beam that is already built and not strong enough, though can also be reinforced.

Thanks again for all the help.

And just so I can get a better understanding of the system,

To verify your software model, you should draw a free body diagram and create a simple spreadsheet to solve for the collar tie force.

Is this what the FBD is supposed to look like?

 

[Eng16080]

By free body diagram, I meant to look at the forces specific to the tie. The picture you show is a model of the full truss. Regarding your model, if you're trying to analyze the scenario whereby the tie is resisting the outward thrust and the walls are not, then you should use a roller (not a pin) for one of the supports. For the force required to be resisted by the walls, then modeling as you have it shown is fine.

 

[Eng16080]

Here's what I meant by Free Body Diagram:

Rather than using your loads in the free body diagram, I solved for the tension force (Fx) in the tie for any general case of roof pitch (S), uniform load (w), and tie height (h). This makes it easy to mess around with the tie location to see how screwed you are trying to make this situation work.

For your specific case then, using w = 1.60 kN/m, L = 6m, and S = 3/12 = 0.25, we get:
Fy = wL/2 = 4.8 kN
I'm not sure exactly what the distance of the tie to the bottom of the rafters is, but it looks like it's around 0.6m
Fx = wL*L / 8*(SL/2 - h) = 48 kN
Interestingly, the force on the tie is exactly ten times the vertical reaction at each support.

So, for this to work, the tie would need to resist the 48 kN force (doable), the rafters would also need to resist this point load (unlikely), and finally you would need to design a connection between the two capable of transferring this force (unlikely). Technically, there's also an axial force acting on the rafters (which is usually ignored in rafter sizing).

Now, if you were curious what the force with the tie at the wall plate height would be, then use h = 0. This also gives you the horizontal force that the top of the walls would need to resist if there were no tie.

 

[JAE]

TORCHMAN:
Your model is incorrect. The two base pin supports are shown as fixed horizontally.

In reality they both are able to move outward horizontally as the top of the wall has no stiffness to resist the lateral thrust of the roof frame.

Your should model one support as a roller - exactly like what Eng16080 shows in the sketch.

This will make sizeable changes in the frame behavior and forces.

 

[Compositepro]

I see rollers under one support.

 

[JAE]

Compositepro - on Eng16080's sketch yes. Not on the OP's computer model rendering.

 

[TORCHMAN]

Gents,

My model was like ENG16080 had suggested, to yield forces for my wall to resist. Which I now know the top plate will not work.

ENG16080, I Checked FBD. Seems like the force I got is much lower and confirmed by the model once roller was added on the other side, maybe a doable connection with 2 collar ties.

Now I wonder about the physical connections and deflection. The deflection the model yields (using SLS loads) is about 42mm which is too high I wonder what the acceptable deflection would be? In reality, would this deflection be split on each side? Also, would the connection between rafter and top plate look like since it should not be fixed horizontally? Just the rafter bearing on the top plate with no screws?

 

[GeorgeTheCivilEngineer]

If the ridge beam can't be located due to inadequate support on the gable, would the use of large section purlins not be feasible? They would be offset and so avoid the weak beam in the gable?

Otherwise reinforce the gable beam and use a ridge beam. Raised ties, especially on shallow pitched roofs, is just a heap of headaches.

 

[phamENG]

I'd say this is a fool's errand. There's a reason the code doesn't allow this - it doesn't work! For very small roofs, sure, but for a typical house it just doesn't. Elements may be 'strong enough' but the deflection (either short or long term) will be a huge problem. Just because it stands now with no live/ snow load and a negligible wind load doesn't mean it will continue to stand when actually loaded.

There is a method called folded plate that could be employed, but with a 60 year old roof the diaphragm may not be up to it. Do a search here for it, though, and you'll find some interesting information.

 

[HouseBoy]

Seems like the connection from the tie to the rafter will be very tough to do.
Also seems like bending in the rafter will be problematic.
Regarding the 42mm deflection, you indicate that is horizontal. What is the vertical deflection?

 

[Eng16080]

ENG16080, I Checked FBD. Seems like the force I got is much lower and confirmed by the model once roller was added on the other side, maybe a doable connection with 2 collar ties.

Your analysis is mostly in agreement with mine. The difference in value is due to:
[ol 1]
[li]I had assumed the tie was nearly at the top of the rafter, based on the picture of the model you provided. In your FBD above, you show it half way up the roof, instead, which results in a much lower tension force which also happens to be exactly double the vertical reaction.[/li]
[li]In your FBD, your roof pitch is actually 6:12, not 3:12 as you stated initially.[/li]
[li]Also, you apply your snow load to the length of the rafter (3.35m), whereas you should use the horizontal projection of the rafter instead (3m). Using the full length is slightly conservative and probably ok if this is what you intended to do. You would use the full length for dead loads (which you should also be accounting for). If your 1.6 kN/m load is snow plus dead, then I can see the logic in what you did to avoid having to separate the loads.[/li]
[/ol]

Accounting for those differences, my calculation matches yours based on the tie height and roof pitch. The tension force is now much more reasonable in terms of getting a solution to work. You may still have trouble getting the rafters to work with the massive point load at midspan and designing a connection to work.

The deflection the model yields (using SLS loads) is about 42mm which is too high I wonder what the acceptable deflection would be? In reality, would this deflection be split on each side?

How are you determining that the deflection is too high if you don't know what the acceptable deflection would be? I would compare the vertical deflection using only the snow load to L/360 or L/240 if there are no brittle finishes applied to the roof/ceiling. Your L would be 6m or the full width of the roof.

Also, would the connection between rafter and top plate look like since it should not be fixed horizontally? Just the rafter bearing on the top plate with no screws?

PLEASE CONNECT THE RAFTERS TO THE TOP PLATE! In the idealistic model that you've created of the roof, we're making the assumption that the top of the wall is not capable of resisting any outward/horizontal force. Technically it will have some capacity in this respect, although minimal. Any small capacity that the wall has should add to the overall strength of the roof and provide redundancy.

Beyond that, the roof definitely needs to be connected to the walls for reasons not discussed here, like wind/seismic forces which will create lateral and uplift forces needing to be resisted at that junction. In a structure, every structural element should be connected.

 

[TORCHMAN]

Thanks again ENG16080!

Yes, you're right, I adjusted my design so that the forces worked. What I ended up doing is proposing a couple of solutions to the client:
1) Reinforce the ridge beam and its supports and have no compromise on ceiling height
2) Collar tie near top + rafter tie 0.5m above wall. So there is a compromise in ceiling height.

PLEASE CONNECT THE RAFTERS TO THE TOP PLATE! In the idealistic model that you've created of the roof, we're making the assumption that the top of the wall is not capable of resisting any outward/horizontal force. Technically it will have some capacity in this respect, although minimal. Any small capacity that the wall has should add to the overall strength of the roof and provide redundancy.

Yes sir! Another local engineer I brought this problem to told me the best way to idealize it would be with a spring, which I think makes sense.

How are you determining that the deflection is too high if you don't know what the acceptable deflection would be? I would compare the vertical deflection using only the snow load to L/360 or L/240 if there are no brittle finishes applied to the roof/ceiling. Your L would be 6m or the full width of the roof.

The deflection I am referencing is horizontal. I typically use L/500 for horizontal deflections from floor to floor - the ceiling will be drywalled: 3000mm by 500 = 6mm. Using option 2 mentioned above, adding the collar tie at the top and a low rafter tie, I got the deflection down to 20mm total, so 10mm each side. But with the idea that the top plate of the walls have some resistance and are really springs, I imagine that the deflection will be much lower.

 

[JAE]

I would not count on the wall having "some" lateral stiffness when you are determining strength designs (members and connections).
You might try to guesstimate a spring constant AFTER design to check deflections - but even then - not sure how you can estimate any spring constant even remotely accurate.

Two points:
1. I've framed up walls before and mid-way between intersecting walls I can move the wall with my fingertips pushing sideways on the double top plate.
2. The spring stiffness won't be constant along the wall but would be stiffer near corners and intersecting walls and less stiff (or nothing) midway between depending on the wall length.