Discontinuous chords in wood framed building @ dormers
Discontinuous chords in wood framed building @ dormers
(OP)
Hello,
I am working on a new wood framed building. There are several dormers where the double top plate will have a discontinuity. Please see the attached sketch.


Based on diaphragm design, the chord force is around 2.5 kips. My question is the following, how do I connect the plates at these locations. My first idea was to install a steel frame at these openings, weld a strap to the end of each steel post and nail the other side of the strap to the next continous double plate.
Any other ideas would be greatly appreciate it.
Regards
I am working on a new wood framed building. There are several dormers where the double top plate will have a discontinuity. Please see the attached sketch.


Based on diaphragm design, the chord force is around 2.5 kips. My question is the following, how do I connect the plates at these locations. My first idea was to install a steel frame at these openings, weld a strap to the end of each steel post and nail the other side of the strap to the next continous double plate.
Any other ideas would be greatly appreciate it.
Regards






RE: Discontinuous chords in wood framed building @ dormers
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
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RE: Discontinuous chords in wood framed building @ dormers
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
Thank you JAE, Im still trying to digest the idea of only using one side of the roof and ridge beam as a chord.
RE: Discontinuous chords in wood framed building @ dormers
Regards.
RE: Discontinuous chords in wood framed building @ dormers
Many engineers would argue that, for E-W load when the function is that of collector rather than chord, the collector does not need to be continuous as a chord does. Yet another shade of grey. What bothers me about the use of a partial diaphragm is that it can imply rather a lot of axial strain in portions of the diaphragm outboard of the chords. This is rough stuff though so I try not to get too up tight.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
RE: Discontinuous chords in wood framed building @ dormers
You have a diaphragm with intermediate offsets (notches). If you are looking for a more in-depth analysis of how to design the transfer wood diaphragms around the notches, check out 'The Analysis of Irregular Shaped Structures - Diaphragms and Shears Walls' by Terry Malone. Most cases only require some additional strapping, blocking, and tighter diaphragm nailing near the notches. I also agree with XR250 that this usually does not get addressed for residential construction.
RE: Discontinuous chords in wood framed building @ dormers
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RE: Discontinuous chords in wood framed building @ dormers
While I agree that it's almost certainly not a huge issue, or even a small one (I'm with XR philosophically), the fuse concept doesn't ring true to me. First off, you usually want a fuse to be ductile. Secondly, I think that the mechanically correct way to look at strain on the un-chorded side of the diaphragm would be something like this:
1) Estimate curvature based on the properties of the chorded, structural diaphragm.
2) Project the curvature from #1 out to the unchorded edge to estimate strain there.
3) Look at what the strain at the unchorded edge means for sheathing joints in flexural tension where the fastening would tend to split the supporting framing perpendicular to grain.
Designated or not, you're likely to have unintended chord out at the "non-chorded" edge, between dormers, whether you want it or not. Therefore:
1) sheathing tensile strain surely is not a problem between dormers.
2) Any real potential for strain incompatibility issues would surely arise at the "notches" created by the dormers. And that could be detailed accordingly.
Just as nac521 proposed essentially.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
For a 3 story wood framed building - maximum preferred lateral drift is perhaps L/400.... (3 stories)(12 ft/story x 12"/ft)(1/400) = +/- 1 inch.
You would design your half-diaphragm then to limit the lateral drift (at the outer eave) to 1"... (i.e. no extension out to the edge is necessary since you are back-calculating the drift at the edge to begin with.)
A 1" deflection in a longer diaphragm - say 60 ft long - would not amount to much strain along the eaves....think a 60 ft. long arch with a 1" offset.
The dormers are "open" so any spread in their sidewalls would be quite minuscule.
We're talking wood framing here - very ductile.
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RE: Discontinuous chords in wood framed building @ dormers
Agreed. Just theoretical sport worrying.
But drift is not strain. For example, with the same diaphragm center line deflection, a deeper diaphragm will have more strain. So while half diaphragm drift and eave drift may be the same, half diaphragm chord strain and eave strain will not. The eve strain will be amplified.
There`s no need to project out to the eave if drift is your only concern. However, as I explained above, strain is another kettle of fish and the projection to the eve would be necessary in order to work it out.
And there`s the rub. It`s a one inch offset at the diaphragm center line. If your 60ft diaphragm were 40ft deep, the offset that matters would be 241" as it pertains to in-plane diaphragm strain at the eves.
Agreed. My concern, if I really had one, would not be the sidewalls but, rather, the integrity of the diaphragm immediately surrounding the "notch". Particularly the re-entrant corners. Rationally, it's another solid argument for some offset chord elements there for reinforcing.
In what sense are you thinking? As I understand it, the overwhelming majority of wood members and connections fail via some permutation of brittle tensile fracture. It's just the nature of an imperfection riddled materiel. The main exception that I'm aware of is diaphragm performance due to fastener slip. The in-plane diaphragm strain that I envision is shown below and, certainly, very little ductility could be expected there.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
The 1" drift is at the outer edge of the building - depth of diaphragm doesn't matter.
You would design your diaphragm to limit the building drift (I haven't even talked about shear wall deflection so your actual diaphragm deflection would be really, even less.
From that you back calculate the diaphragm deflection from the limit of drift at diaphragm midspan. So whatever depth of diaphragm you have - be it 12 feet or 12000 feet, the arc of the outer edge of the diaphragm is still just 1" or so and the strain in the diaphragm is still based on the difference in length of the straight diaphragm eave line and the arc length of the deflected diaphragm. Hoooke's Law forever.
The sketch you show assumes that the strain is all concentrated at some brittle connection where in reality you have all sorts of fuses along the line....think about the additional deflection we add to our shear wall deflections due to nail slippage. Also the dormers are giving up a huge amount of stiffness through the length so any possible build up of strain will be simply lost in the dormers.
A 3" lateral diaphragm deflection on a 100 ft. long diaphragm eave results in a net gain in arc length of 1/64" approximately.
The strain from that is very small (1.3 x 10^-5). Waste of time to even bother with it.
You would still have double top plates, continuous blocking or a collector of sorts along the edges between the dormers to help pull the thing together where it can - but the strain is nothing.
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RE: Discontinuous chords in wood framed building @ dormers
Mike McCann, PE, SE (WA)
RE: Discontinuous chords in wood framed building @ dormers
Nope, still kicking up dust. Please review the sketch below, in particular the details of the strain diagram at the bottom.
As I see it, per the sketch below, eave strain will be 3X peak structural diaphragm strain precisely because of the width of the outstanding diaphragm.
There's nothing to back calculate. Per the sketch below, the magnitude of the drift at the eave will be identical to the magnitude of the drift at the structural diaphragm center line. It's the strain that will differ.
.
Again, I believe this to be your fundamental source of error. The arc formed by the 1" displacement is only part of the story. The far ends of the eave also spread further apart which add more axial strain. Vastly more. This is quite analogous to, say, reinforcing a wide flage beam with a WT on the bottom. The WT isn't just displaced downwards, it's stretched. And that composite stretching is the source of our VQ/I stuff.
And what would these fuses be? All I see is some axially stiff sheathing panels and some nailed joints. Do you really think that you'll get meaningful nail plowing action through the plywood prior to the tension perpendicular to grain failures that I illustrated above? I don't.
The eave strain between dormers will be unaffected by the presence of the dormers. Eave strain at any location in the non-structural diaphragm will simply be a linear amplification of the strain in the structural diaphragm as I've shown below. And the structural diaphragm isn't notched.
I'd be happy to play along but we'd have to assign a width to this diaphragm in order to calculate meaningful results, for the reasons mentioned above.
Rationally, I feel that one must acknowledge the presence of meaningful strain at the edges of diaphragms. For that strain is also the strain in our diaphragm chords. So if there's not meaningful strain in our diaphragm chords, how do our chord forces come about? 1/64" in 100 ft is a strain of 0.00015. That's not going to generate any chord force.
I acknowledged these practical realities myself in my previous post (11 Jan 17 19:28). Logically, however, I don't think that they should be included in the current, theoretical discussion. It seems patently inconsistent to follow this path:
1) Design a partial diaphragm to avoid the complexity of dealing with at notched full diaphragm.
2) Ignore the problematic aspects of the partial diaphragm because we actually have a notched full diaphragm.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
"there's nothing to back-calculate"..... that isn't true. You START with a limit on lateral drift for your building. You include in that deflection the shear deformation caused drift and also include any diaphragm deformation that adds to drift between shear walls. If you START with L/400....or L/360 or whatever, you have a limit as to how much deflection you can tolerate in your diaphragm at its midspan.
Even with your not-correct flexurally deformed diaphragm, you'd still work backwards to find a half-roof diaphragm stiffness that would limit that arc. I use the term back-calculating to suggest that you'd start with the limit on deflection and then back-determine the necessary diaphragm stiffness to accomplish that.
For a usual range of 3-story wood framed buildings, that drift limit really minimizes the resulting arc length of the eave edge.
Wood is a very VERY forgiving material in construction and the use of a half diaphragm in this particular case, just isn't that big of a concern. I've even done this on other designs and with no problems.
As you mentioned..."1/64" in 100 ft is a strain of 0.00015. That's not going to generate any chord force."
What Mike says above, adding a collector of sorts to the top of the dormers, could be considered as well...just more cost and to accomplish what, though.
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RE: Discontinuous chords in wood framed building @ dormers
You could think of the strapping and blocking as a continuous top plate - just relocated to the point where the roof diaphragm wants to tear. From that lone, the forces travel down the sloping roof diaphragm that can be considered a sloping shear wall, all to the vertical shear walls below.
A little over the top, but it works...
Mike McCann, PE, SE (WA)
RE: Discontinuous chords in wood framed building @ dormers
If the notched diaphragm can't calculate because the dormers take out too much area I'd try and develop some collector / continuity across the dormers with "transfer columns" strapped at roof diaphragm and dormers to tie discontinuities together.
This all assumes high seismic forces.
RE: Discontinuous chords in wood framed building @ dormers
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RE: Discontinuous chords in wood framed building @ dormers
While I agree that wood diaphragms undergo significant shear deformation, the assertion that my flexural analysis is meaningless or incorrect is seriously flawed.
1) Just because shear deformations exist, that's no reason not to bother looking at flexural stresses strains.
2) If flexural stresses and strains are not important or relevant, then why bother with chords? We certainly don't bother with them to deal with shear deformation.
3) Shear deformations are additive to flexural deformations. As such, you'll see the 3X strain shown in my sketch and then some more drift as a result of shear deformation.
Ok. But you're calculating the arc length incorrectly by ignoring the role that diaphragm depth plays. So your back calculation, by merely enforcing a drift limit, isn't enforcing any particular limit on in-plane diaphragm strain. Less drift begets less strain, obviously, but strain is not quantified by your suggested procedure.
While I agree with the conclusion, I still contend that your estimation of the resulting arc length is flawed as I discussed previously.
I agree and have acknowledged as much several times here. I do a version of the same thing myself, sometimes even in steel. This expanded discussion is theoretical only in my opinion. That said, I think that there's presumption in suggesting that a short history of successful performance represents a glowing endorsement of the half diaphragm method. Roof diaphragms essentially never have problems. And that includes all of the real world diaphragms that have discontinuous chords, no heel blocking, no ridge blocking, and no properly detailed colledtors. They work because these systems are often heavily redundant, not because of the spiffy tricks of structural engineers.
Sure. I was the first to suggest this strategy up at the top.
I would say that:
1) In theory, it accomplishes a design that gives proper credence to realistic deformations and strain compatibility. It also produces a design in compliance with the methods that seem to be becoming the state of the art in our industry.
2) In practice, it probably accomplishes nothing at all except, perhaps, to spare the diaphragm some localized damage at the re-entrant corners of the notch during a very extreme event.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
You state that "my estimation of the resulting arc length is flawed". Perhaps I haven't done a rigorous analysis of an actual diaphragm...but my assertion that the arc length results in small strains is correct regardless of the share of deformation between flexural or shear based deflections.
I even said that even at 3 x the deflection (your incorrect assertion of a flexural only deformation) the strains were small...that is still true.
Providing a chord (like (2) 2x6 top chords) isn't going to change the strains in other elements of the diaphragm or dormers anyway. The total deformation of a diaphragm isn't affected by the chords all that much as a larger proportion of your diaphragm deformation is shear-based. The chord does nothing to reduce that.
This is getting a bit tedious so I'm signing off this thread. All I'm saying is that you could use a half diaphragm successfully. I've done it before. It works.
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RE: Discontinuous chords in wood framed building @ dormers
The code has implied safety factors associated with design procedures which translates to maximum acceptable probabilities of collapse. Just because the structure doesn't have problems doesn't mean it meets the intent of the code provisions or acceptable probabilities of collapse potential.
Food for thought -- In SF Bay Area I could have designed structures without any seismic design principles and not have had any problems for past 27 years. Not exactly something I would take comfort in.
RE: Discontinuous chords in wood framed building @ dormers
I think JAE is saying that you would need to design the LFRS such that your drift displacement is small, so that even when you project this displacement out to the outside edge of the dormers it is a small strain at this point.
KootK is saying well when you project it out it is larger than what you had calculated at the point you calculated it at.
Both seem to be saying that:
Unless your diaphragm that was "going along for the ride" was much much deeper than your diaphragm "doing the work" you're probably ok. And if it was much much deeper then you would violating diaphragm ratio limits.
And also saying that it would be nice to have a better load path like the blocking and strapping mentioned by M^2.
EIT
www.HowToEngineer.com
RE: Discontinuous chords in wood framed building @ dormers
I agree strongly with this. I would, however, argue that similar reasoning should lead one to conclude that wind loads are just as important as seismic loads. All of the elements of risk and reliability are already baked into the cakes that are our code specified wind and seismic loads. Beyond that, load paths are load paths and strain is strain.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
RE: Discontinuous chords in wood framed building @ dormers
I was interested in studying in-plane axial strains in the diaphragm. That was the scope of my analysis. Given a particular diaphragm load, flexure contributes to in-plane axial strain and shear does not. Therefore, my diagram was 100% correct for the purpose for which I created it.
If one starts with a limit on drift and some of that is eaten up by shear does that mean that there will be less drift going into the flexure bucket? Yeah, of course. Does that invalidate my analysis of the fexural strain component? Not at all. Note that nothing about my sketch contradicted the notion that shear contributes to diaphragm deformation. I simply did not choose to study that nuance. If you want a sketch that does speak to shear deformation, I suggest that you create one of your own.
You seem to be getting stuck on the magnitude of the strain. I don't care about the magnitude of the strain. In almost every one of my posts here, I've repeated clarified that:
1) I, like you, think that the magnitude of the strain is small.
2) I, like you, suspect that the strain is not a serious concern in practice.
We do not need to continue faux-debating whether or not the strain is small or whether or not it's a serious issue in practice. We've agreed on that from the start.
So why bother with chords then? Is the state of the art really that much in the wrong? And I would argue that how much of a diaphragm's response is shear based is very much a function of the diaphragm aspect ratio. And, in fact, by going with the half diaphragm approach, one is creating an analytical diaphragm in which the influence of flexure is actually increased relative to the influence of shear. In the OP's example, it appears that we might even be getting close to code limits in that regard.
I'm sorry that you feel that way. I've been enjoying the discussion and was hoping to tease a bit more understanding out of it yet. However, years of experience has taught me that you're first and foremost a practical fellow. And you prefer not to get bogged down in technical minutia, which I get.
Yes, and I have not really disputed that. I merely mentioned a slight concern, of my own, for strain beyond the designated structural diaphragm. And I feel that I've done a reasonable job of legitimizing that concern here.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
Exactly right. At least that's what I started with.
There is one fundamental disagreement that should not be overlooked. We clearly disagree on how chord/diaphragm strain should be calculated. I think that diaphragm depth factors into it in a big way. JAE doesn't think that it comes into play at all (my interpretation of his comments). That's kinda huge.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
What I said was that if you design a half-diaphragm the resulting design checks (which you correctly advocate) can determine that the outer arc strains on the eave are under control, or limited.
The true diaphragm drift is a combination of shear deformation (roughly shown here):
AND Flexural deformation - that you illustrated in your sketch above.
I commented that your sketch was not really correct - and it is not - it ONLY shows the flexural deformation of the diaphragm and ignores the significant share of shear deformation.
You provided that flexural deformation sketch to support the notion that the depth of the diaphragm affects the resulting arc length at the eave, which it does - but not 100% as you implied.
I agreed that there was additional strain at the outer eave but again - not due to 100% of the flexural deformation (the 3 times value you showed) but the TRUE eave strain would be somewhere below that amount.
The influences of both are present. For most diaphragm sizes in wood construction, the shear deformation tends to be more influential in the total deformation than flexural but then I even conceded that if the 3 times amount you incorrectly showed was present, you'd still have small amounts of strain in the chord, which you agreed.
I see that this discussion seems to be devolving into an "I can out-quote you last" so I'll concede the thread and let you have your way with your quote machine. But my really only point here is that a half-diaphragm can be designed to control drift in buildings and with most simple wood framed structures (like apartment buildings) the resulting strains at the outer edge are (under service conditions - not extreme seismic conditions) manageable and don't result in long term issues.
jdgengineer - I agree that a contractor statement depending on past results isn't purely a true engineering statement but we were talking about serviceability issues (cracks at the dormers) not life safety issues.
28 years is a pretty long time to see results, even with wind...but you're correct - it wasn't 50 or 100 years.
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RE: Discontinuous chords in wood framed building @ dormers
Personally, I would still put in the line of strapping as Mike mentioned at the top of the dormers. If you all don't then great, you can tell the contractor you are more economical :). Wouldn't change my approach, personally.
To follow-up on the 28 year comment. I don't agree. In ASCE 7-10 Category II structures are designed for 700 year MRI wind event, and Category III and IV are designed for 1700 MRI wind event. In my opinion, I don't believe 28 years is adequate time to say the structure is "tested". If the reference was in regards to my comment about the SF Bay Area, the point I was trying to make was that we have not had a major earthquake since 1989. Therefore, you could have ignored seismic detailing completely and not have had a problem since 1989. That time spans the career of a lot of engineers, but I think we could all agree that the 27 years is not adequate time to say the structure is tested in a seismically prone area.
I'm not trying to be argumentative, sorry if I am coming across that way.
RE: Discontinuous chords in wood framed building @ dormers
RE: Discontinuous chords in wood framed building @ dormers
I do not accept your assessment that my sketch was incorrect. It was utterly correct with respect to what I was attempting to convey: the nature of flexural strain here. My diagram was, perhaps, incomplete with respect to what you wanted to see acknowledged: the influence of shear deformation on felxural strain in a limited drift scenario. How about that?
My sketch did not say that 100% of the drift manifested itself as flexural deformation. My sketch said that eave flexural strain would be 3x half diaphragm flexural strain. And that is true.
Please don't be put off by the quoting. I know that it feels like a personal attack at times (that's how ego endowed creatures are built) but I really just do it because it's an efficient way for me to thoroughly and systematically process all of the points of contention. I'm an engineer after all. I find that when others don't quote, that's when in depth discussions really devolve into pitiful messes.
We've known each other for a while now. I would hope that you would think better of me than to assume that I'm engaging in some kind of petty "quote arms race". If I bother to say something, it's because I feel that it has substance. If you want to be done here, then be done. You can't expect me to stop discussing things with you when you're still discussing them with me however. I like it after all.
While I suspect that you will not be interested, I still think that there's an important point to be resolved regarding the calculation of chord diaphragm strain. Given my druthers, I would like to:
1) Have you supply your calculation for the 1/64" elongation number.
2) I'll do my best to produce a calculation doing it my way.
That way, we can objectively attempt to resolve something meaningful. How about:
1) 100 ft X 30 ft diaphragm.
2) 3" midspan deflection based on a parabolic flexural curve.
3) You specify the percentage of deflection attributed to shear based on your original calc.
I'll invest the time if you'll share your stuff.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Discontinuous chords in wood framed building @ dormers
Hell no I'm not laughing. I'm jealous that your market can support high quality structural engineering solutions. I actually interviewed with a few firms in California last spring. And my very specific intent was to be able to practice in a region where:
1) Folks know good structural when they see it and;
2) There's half ways decent regulation and;
3) There's at least a modicum of hope for getting paid for #1.
I practice in a hopeless backwater in this regard.
Thanks for sharing your solution.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.