Diaphragm Design for Dutch Gable Wood Roof

[KootK]

Per the sketch below, I'm trying to work out shear transfer through a dutch gable wood framed roof. I've been considering it as three discrete, connected diaphragms:

1) The hip roof segment at the left end.
2) The main gable roof in the middle.
3) The hip roof segment at the right end.

The trouble is this: conceived this way, diaphragms one and three have aspect ratios of about 8:1 (sketch is poorly scaled). That's a no go per North American wood codes which usually limit diaphragm aspect ratios to around 4:1. I'm having a hard time seeing a away around this.

The only workaround that I've come up with is to consider all three diaphragms, and the vertical plywood at the gable trusses, as a single diaphragm. Basically, I take the five diaphragm surfaces -- three horizontal-ish and two vertical -- and fold them out flat in the east west direction. Then I use that fictional diaphragm for calculating deflections and aspect ratios. My logic for this is that all of the sub-diaphragms are shear connected to one another and jointly span between two drag elements (shear walls) at the far ends. Thus, one diaphragm for all intents and purposes.

Anybody buy this? Got a better idea? Please advise. There is some irony in the fact that, two decades ago, I was the truss guy framing out five or so of these roofs a month. Luckily, I wasn't the EOR and I had no concept of lateral loads whatsoever. A little less lucky for society I suppose.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[asixth]

I work under different codes than the one's you mentioned but whenever I come up with something that falls outside the prescriptive codes, I provide an engineered design working it out from scratch.

For that detail I would call up a horizontal truss. Roof trusses in my location are a deferred item usually design by technicians who have no idea about engineering principals. So we normally need to give a design loads and provide schematic details for transferring the lateral forces into the shearwalls.

 

[XR250]

Has anyone ever observed a diaphragm failure in a roof of this type?

 

[KootK]

@asixth: In a previous thread (Link) I pitched that very idea as a wishlist concept. Just scroll down to the sketch. Trouble is, there are literally tens of thousand of these structures out there that have no truss and seem to be performing. It'll definitely raise some eyebrows if I specify a horizontal truss. Not that that is a valid reason to shirk my engineering duties. To make matters worse, the main run of gable trusses is scissored. No ceiling help to speak of.

@Excel: I see where you're headed and I agree: no failures and lots of data points. Still, I have to find some reasonable narrative here regarding load path. It'll be equally problematic for wind the other way.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[jayrod12]

Do you need the 8:1 aspect ratio part of the diaphragm to make it work?

Can you just ignore it and use only the conventional portions (between the gables)? That would likely be my first place to start if it's a capacity issue.

 

[KootK]

@Jaryod: without the 8:1 bits, how would the shear in the gables make its way out to the shear walls?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[jayrod12]

It's wood, it will all work itself out.. haha..

I didn't pay close enough attention to your detail. A lot of the dutch gables I have done have the main floor wall running in line with the gable wall (truss) above and the lower roof portion is more for show.

I would say your original post seems reasonable. At the interface of the 8:1 piece and the vertical piece I would have a shit-ton of blocking for both pieces to ensure good shear transfer capacity at that joint.

Although my first comment was made in jest, it's not wholly incorrect. The flexibility of wood structures to redistribute load as required astounds me. The issue is it's generally impossible to quantify.

 

[KootK]

Maybe the gable should line up with the shear wall. It's not likely to hear though as there is some decorative stuff going on that I didn'tmention.

I agree with your overall opinion of wood construction. I often feel as though I'm wasting my time trying to design wood systems for lateral in detail. Some prescriptive stuff would suit me just fine.

I'm thinking to taking a swing at this horizontal ceiling truss business. Two options:

1) I align the bottom of the truss with the tops of the walls. The heel heights of the jack trusses, corner sets, and ridge rafters will all be messed with.

2) I align the top of the truss with the tops of the walls. The framing is unaffected but the ceiling will be lowererd by 1.5" and drywall will be affected. It's non-standard wall heights here anyhow.

Which of the two options do you guys think is best?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[jayrod12]

Preferably option 2. Especially since the drywall is only slightly affected and easier to manipulate than the framing above.

 

[woodman88]

2009 IBC Section 1602
1 "Diaphragm. A horizontal or sloped system acting to transmit lateral forces to the vertical-resisting elements...."
2 "Diaphragm chord. A diaphragm boundary element perpendicular to the applied load that is assumed to take axial stresses due to the diaphragm moment."

Unless you are designing the ridge blocking to act as a diaphragm chord, without any interior shearwalls you have only one diaphragm.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[KootK]

The only workaround that I've come up with is to consider all three diaphragms, and the vertical plywood at the gable trusses, as a single diaphragm. Basically, I take the five diaphragm surfaces -- three horizontal-ish and two vertical -- and fold them out flat in the east west direction. Then I use that fictional diaphragm for calculating deflections and aspect ratios. My logic for this is that all of the sub-diaphragms are shear connected to one another and jointly span between two drag elements (shear walls) at the far ends. Thus, one diaphragm for all intents and purposes.

@Woodman: I was hoping that you'd surface for this. I'm not clear on your response however. Are you agreeing with the approach outlined above? My "one diaphragm" would include the main gable roof, the vertical face of the sheathed gable trusses, and the skirts? The 8:1 bits would not be considered separate diaphragms in their own right?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[woodman88]

I define a horizontal diaphragm by the shearwalls, disregarding any slopes or breaks in the slopes. So your diaphragm ratio would be w/h.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[medeek]

I don't know if this is the correct way to look at it or not but here is my take...

The roof is loaded in the transverse direction (perp. to ridge). Treat the main diaphragm between the two gable/girder trusses as a regular diaphragm, ignore the jack stud corner pieces for simplicity and to be conservative. Then this main diaphragm is transferring all of its shear load into the two gable end girder trusses. The girder trusses are themselves acting as mini shearwalls in a sense. Then somehow the shear force they are withstanding has to be transferred into the shearwalls below, this will be through the hip roof segment. The aspect ratio though would be 1:8 and not 8:1 so your ratio is fine. You should have plenty of strength with that ratio and your unit shear will be okay, even though I don't have the numbers.

A confused student is a good student.

 

[medeek]

I'm not sure if this makes sense but here is a FBD of what I'm trying to explain in my previous post:

A confused student is a good student.

 

[medeek]

Correction, my treatment of the shears was not rigorous enough. The correct values would be:

R₂ = R₁ = (wL₁)/2

R_1swl = R₁ + wL₂

v₁ = R₁/b₁

v₂ = R_1swl/b₂

I think that makes more sense.

A confused student is a good student.

 

[KootK]

@ Woodman: thanks. I'll take your approval as the next best thing to code official okay.

@ Medeek:

1) If you ignore the jack stud corner pieces, how do you connect the 8:1 diaphragm ends to the shear walls at the north and south sides of the building? Without those connections, I think that the 8:1 diaphragm would not be able to achieve rotational equilibrium.

2) I'd considered the 8:1 vs 1:8 ratio thing too. I find it confusing where the diaphragm is really a transfer element rather than an element receiving directly applied lateral load. I may need to revisit that as I suspect that you're probably right. It'll turn into an 8:1 for wind in the other direction unfortunately. But that's an issue for another day. Or perhaps this afternoon.


The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[KootK]

I responded before I read your latest batch Medeek. Thanks so much for your attention to this. You nailed it. Terry Malone would give you a hug if he saw this.

My only concern: your D1/D3 chord forces need to pass through the corner sets as shear to make it back to D1 & D3.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[medeek]

Here is the corrected diagram:

A confused student is a good student.

 

[medeek]

I guess one could simplify this and consider the corner diaphragms as part of D2 and D3, then b₂ = b₁ and the unit shear diagram will essentially be identical to the unit shear diagram if the entire roof were considered one diaphragm. Otherwise your correct in that the chord forces need to resolve back into the corners somehow to complete the model. I'll have to give it some more thought.

A confused student is a good student.

 

[medeek]

I would be curious to see how one would model this up in RISA. Modeling the trusses, rafters and joists as beam elements is pretty simple but how to correctly model the sheathing?

A confused student is a good student.