Roof Rafter Collar Tie Calculations/Design 2

[mfstructural]

I haven't done a calculation for roof rafters/collar ties in a while and I'm a little rusty. I'm trying to run some calcs on an existing roof that has 2x6 rafters @ 16". The rafters are about 14'-6" in length, roof pitch is 6:12. 2x6 collar tie is located about 30" below the bottom of the ridge board. Previously, these 2x6 members were at the top plate level acting as ceiling joists/rafter ties, but it's been opened up to create an open space. How would I approach this? Does the collar tie reduce the span of the rafter? or do you assume the rafter is spanning the full 14-6"? A 2x6 rafter spanning that far will not work for 25 psf snow and 10 psf DL. I'm not sure how to approach it calculation wise?
Thanks

 

[mfstructural]

I ran some hand calcs which I posted last week. Over the weekend I created 2 models. one with a roller support at one end and one with a pin. The I had to use 2-2x6s in the model because the le/d exceeded 50. The collar tie is set as a tension only member.

For the pin model, the rafter ICs are below 0.805 and are adequate for strength. The deflection of the rafters is around .35". I'm not understanding why the IC of the collar tie is coming up at 0.0 though. We've been talking about the difference between the pin and roller in the model and how that translates to the actual condition. The horizontal thrust at the walls (from the pin model) is .869. It's a 2x4 wall. A 2x4 wall is not going to take 869 pounds every 16 inches. Is there a way to take that thrust out by reinforcing that connection? I go to a lot of houses and there are vaulted ceilings with 2x6 rafters, so I'm trying to understand why those walls aren't blowing out from the thrust.

I also modeled it with a roller, and obviously there was no thrust, but the ICs shoot up and the moment of 3,254 lb*ft lines up with what BAretired calculated above. I think in real life this falls somewhere in between the pinned and rolled condition and the walls can take some thrust, particularly if hurricane ties are installed at the rafter to wall connection, no? image of the model attached also.
And thanks for everyone's help again! I just wanting to really understand this.

 

[Celt83]

For the pin model, the rafter ICs are below 0.805 and are adequate for strength. The deflection of the rafters is around .35". I'm not understanding why the IC of the collar tie is coming up at 0.0 though.

There is no tension in the collar tie because the rafters cannot spread in the pin-pin model. Without a change of length of the tie, elongation in this case, there is no axial force, tension in this case. Did you review the axial, shear, and moment diagrams for each model. If you are just reviewing the interaction numbers then that is a bad habit that you need to break, the fastest way to see if the model is behaving as you intended is to look at the diagrams.

...particularly if hurricane ties are installed at the rafter to wall connection, no? image of the model attached also.

What does the presence of a vertical tension tie, in my experience the hurricane ties primarily provide uplift resistance, at the rafter wall interface have to do with the horizontal force that would be applied by the rafter in the pin-pin state of the model.

I think in real life this falls somewhere in between the pinned and rolled condition and the walls can take some thrust

Agree it is somewhere in between but I disagree that the wall is doing much of anything to resist the thrust. I think in real life your getting a lot of help from the roof sheathing and the top plates working to span to any perpendicular element that are attached to them.





Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[mfstructural]

Yes, the hurricane tie won't do anything. Looking at the moment diagrams (attached), it's behaving as expected. The issue is that the ICs are over 2 for the rafters and deflecting over 3" at midspan. And this is with 2-2x6. So basically, sistering a 2x12 to the existing 2x6 may work (have to check it). As someone said above the other issue is going to be the connection between the rafter tie and rafters...the tension is 1.6 kips. What is the preferred method for attachment? screws or through bolts?

 

[BAretired]

What the heck is IC? I strongly dislike acronyms and abbreviations. I assume the C is "capacity" but I'm darned if I know what the I stands for.

IC usually stands for "integrated circuit" but that makes no sense here.

BA

 

[mfstructural]

Interaction coefficient. Same thing as UC in RISA. I have a habit of calling it IC from a while back.

 

[BAretired]

I don't use RISA and would not have known what UC meant either. Neither of these terms is standard structural jargon and should be avoided or defined before use.

BA

 

[Celt83]

...deflecting over 3" at midspan. ..

Keep in mind that we've agreed the wall cannot resist the thrust so you need to limit the spread as well as the vertical deflection. While things like the sheathing and wall top plates will by their own nature aid in resisting the thrust I would not rely on them in my design, the aid they provide can be hard to quantify if at all.

What is the preferred method for attachment? screws or through bolts?

I'd personally start with nails/screws, then a proprietary screw like Simpson's SDS, and then a thru bolt if needed.
Edit:If these connections are going to be exposed I'd ask the client sometimes thru bolts will both give them the look they want and and the capacity you need.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[BAretired]

I agree with Celt83. You cannot rely on the roof deck and wall top plate to provide beam action as there is no way of knowing whether or not they are adequately built to provide beam action in the plane of the roof. They could hold up under dead load, then collapse when loaded with snow.

The pin/pin model cannot be used. Instead, the pin/roller model must be used. That means the rafters are seriously over-stressed. It is unfortunate that the ceiling joists/rafter ties were removed before the analysis had been completed. It appears that remedial measures are necessary. It may be necessary to reinstate some tension ties at the level of the wall top plates.



BA

 

[mfstructural]

Yes, it is unfortunate that they went and did all this without doing an analysis before. After several conversations with the owner/carpenter, he finally understands that this will not work so he's agreed to lower the collar ties. I modeled it with collar ties located for a 9' ceiling. The model results show that 2x10s are over stressed (image attached), however, they will be sistered to the existing 2x6 rafters so I don't think that will be an issue. The spread deflection (at the roller) is shown as .331" under full load (DL, snow, and wind). The tension in the collar tie is 1.23 kips, so the connection between the collar tie and rafter must be designed for this tension. Bending does not need to be designed for since the member was modeled as tension only correct? I don't have to account for any moment in the connection.

The only thing I am unsure about is the thrust reaction at the roller. The thrust reaction is 527 pounds so it will be about 270 pounds at each wall right? Under wind loads that may not be the case but I don't think all of it will go to one wall. I feel like the double top plate can take out 270 pounds at 16" on center. I can add a simpson roof tie since those are capable of transferring some lateral load.

The interesting thing though is that I modeled the original condition with a roller, with the rafter tie at the top of the wall, and the thrust reaction was 1.086 kips, which is higher than the horizontal reaction with collar tie higher. Does that seem reasonable? I though it would be lower. The joint deflections are much lower, almost non existent, but the reactions are higher. Also, when I modeled it with 2x6 rafters it showed the rafters were way over stressed...but the roof has been there for 40 years with no issues. That's what I'm trying to wrap my head around.

Lastly, the model gives me errors for le/d>50 for the rafters unless I reduce unbraced length. I set the unbraced length as 4'. My questions is in practice there is no blocking at 4' so are we assuming that the sheathing is laterally bracing the rafter? I go into attics all the time and don't see blocking and 2x10s spanning 20' and the rafters are not buckling.

 

[Celt83]

..so I don't think that will be an issue.

I feel like the double top plate...

This is going to sound obnoxious, but there are established methods to check these things so hopefully you mean that you feel these things will be ok but plan to run the numbers to verify rather than just saying you feel these will be ok so they must be and not actually checking them. Hopefully that's not taken the wrong way I've had some recent experiences where the latter statement ended up being true for some folks who really didn't have the experience level to make that kind of "gut" decision.

The interesting thing though is that I modeled the original condition with a roller, with the rafter tie at the top of the wall, and the thrust reaction was 1.086 kips, ...

confused by this if your running the model with a roller and vertical loads there should be no horizontal reaction. If you talking about wind pressure then the x direction force will be transmitted thru the roof diaphragm to the lateral resisting elements, you should verify this load path.

Lastly, the model gives me errors for le/d>50 for the rafters unless I reduce unbraced length. I set the unbraced length as 4'. My questions is in practice there is no blocking at 4' so are we assuming that the sheathing is laterally bracing the rafter? I go into attics all the time and don't see blocking and 2x10s spanning 20' and the rafters are not buckling.

For bending with the top of the rafter in compression yes it is common to assume the sheathing provides bracing, for wind suction, compression in the bottom fibers, the unbraced length would be the full length of the rafter.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[BAretired]

Sorry, I have been away from my computer for a few days.

The only thing I am unsure about is the thrust reaction at the roller. The thrust reaction is 527 pounds so it will be about 270 pounds at each wall right? Under wind loads that may not be the case but I don't think all of it will go to one wall. I feel like the double top plate can take out 270 pounds at 16" on center. I can add a simpson roof tie since those are capable of transferring some lateral load.

The thrust reaction at the roller must be zero. That is the definition of a roller. I don't know where 527# came from. Nodes N1 and N5 indicate "By combination" but I don't know what you are combining.

If we were to assume 527# is correct (I don't believe it is), then each wall would take 527# at 16" centers, not 270#. Unless the wall is a sturdy cantilever, it will not be able to do that. Normal practice is to assume pin/roller where neither wall takes any horizontal thrust.

You seem to be making a fundamental error in your statics. You must get it straightened out before using your analysis in the actual structure.

BA

 

[BAretired]

@mfstructural,

Please bring us up to date on this file.

BA

 

[North2South]

Neither top of wall connection can provide a horizontal restraint. In my office, we set the in plane horizontal restraint at the ridge. The roof diaphragm provides this restraint. The tops of the walls are modeled as rollers. Under loading, both walls should spread evenly. You need to check deflection at the top of the wall for H/240 or whatever you deflection criteria is in addition to the ridge deflection.

I inspected a house a couple years ago that had similar geometry. The ridge had settled and the walls were leaning outward. We had to come back with new tension ties to stabilize the roof.

 

[BAretired]

@Fletch10,

Good points. Instead of Pin/Roller at walls, use Roller/Roller with Horizontal restraint at ridge. That gives the horizontal deflection for each wall directly.

New tension ties will be required, but not necessarily at every 16" rafter spacing. If used, say at every four feet, would need top plate (possibly reinforced) to distribute horizontal reaction to each rafter.

BA