FTAO Shear Walls and the 4-Term Deflection Equation

[phamENG]

thread507-457014

bones - I hope you're around today. Ever hear back about this from anyone? I've got a building with lots of windows all around that are driving pier widths way down. There's enough that using strong walls for their better stiffness isn't really an option - I'd just have strong walls and roof trusses. So I'm trying to drill down deeper into this deflection calculation and, though the data appears to track nicely with the hystersis and backbone plots, I can't rationalize the application of hold down deflections to piers without hold downs.

 

[phamENG]

dirftLimiter - looks like you may be right. That would be upsetting if they embed Cd into the spreadsheet without telling anyone, though....what about all of us who don't care because we're doing wind design and even my 10 year MRI is about 10x the seismic load?

 

[driftLimiter]

Agreed that is upsetting. My sw spreadsheet has a toggle for lateral load source seismic vs wind that addresses this. Its funny how little I use the wind toggle, my turf is like Sds >= 1.0g all the time so wind rarely controls for me.

 

[phamENG]

Craig - I've been thinking on the averaging deflections question. I think it's appropriate in some applications. For instance, the SDPWS allows us to distribute loading based on capacity rather than stiffness if the an adjustment factor of 2b/h is used on all shear walls with a greater than 2:1 aspect ratio. If you're using stiffness, you can use 1.25-0.125h/b which results in less of a reduction. So I think it could be permissible to use the averaged deflections...but only if you're using 2b/h. Unfortunately, the APA spreadsheet lets you pick either and doesn't change the way it calculates the shear distribution.

 

[Craig_H]

Pham, interesting point. I should dig into this a bit more. I am unaware of a similar adjustment factor for shear walls under CSA O86. I guess that living in a snow globe has its benefits? My copy of the Wood Design Manual published by the Canadian Wood Council discusses both shear distribution methods, but recommends distributing forces based on stiffness. No mention of a reduction factor or capacity penalty for either choice. I sure hope that I'm not missing something.

 

[KootK]

KootK - I agree with your approach for a portal frame, or perhaps for the cantilevered beam method of FTAO design (though I haven't messed with that much), but not the more popular/common Diekmann method. Your model ignores the fixity that comes from the panels below the openings.

Certainly, I recognize that the fundamental behavior of these things is that of a vierendeel truss that is bastardized by a number of complexities, not least of which is general shear deformability. And in many respects, a Vierendeel truss is a pair of stacked portal frames with one of the frames flipped upside down.

I ignored the fixity deliberately in my previous sketch in order to simplify things and try to tease out a principle that I felt was not being recognized in the more complex models of the situation. That said, the same principles can be shown to hold true when considering the setup in all its Vierendeel glory. In words, for now:

1) Part of the action of the frame will be that of the entire frame rotating in rigid body fashion about the far compression chord in response to hold down elongation. This rotation will produce similar lateral drift in all of the piers of the Vierendeel frame. In this way, the physical hold down at the tension side pier will affect the lateral drift of all of the piers even though those piers do not, themselves, have physical hold downs.

2) Part of the action of the frame will be that of each pier rotating independently in rigid body fashion. This would more closely resemble classic Vierendeel behavior. This said, the top plates of the wall will ultimately make it such that the drifts of all of the frame piers will be made coincident, per my earlier sketch. This means that:

a) The shear in all of the piers will contribute to the tension demand in the physical hold down and;

b) The physical hold down will contribute to the drift in all of the piers.

In this way, again, the physical hold down at the tension side pier will affect the lateral drift of all of the piers even though those piers do not, themselves, have physical hold downs.

So we've got this interesting question here which is "why hold down terms for piers with no hold downs"? And two proposed explanations for that:

3) Mine: the physical hold down can, in fact, be shown to affect the drift of the piers that have no physical hold downs.

4) Yours: the developers of the method opaquely buried strap elongation in the guise of faux hold down elongation for some reason.

Of the two, is mine not the more logical place to start? Why the reach around of #4 when a more direct explanation stares us right in the face? Occom's razor and all that...

That fixity and the shear/bending behavior of that run of wall panels below the openings will dominate.

Sure. But, then, the run of wall panels below the openings is, itself, only rotationally retrained by physical hold down at the tension end of the frame. So that path too leads to the drift of all of the piers being impacted by the elongation of the physical hold down.

 

[bones206]

Pham - thnaks for taking the time. I'll have to debug my spreadsheet calc of the d[sub]a[/sub]'s. Btw, how did you manage to unlock their spreadsheet? The one I downloaded from APA is password protected.

Still don't get how the d[sub]a[/sub] values are exceeding the hold down rating but somehow it all works out.

 

[phamENG]

KootK - I do not disagree with your general description of the behavior of the wall. I agree completely about that. My trouble is with the application to the code based deflection equation.

If the design procedure followed that behavior, I would expect the deflections at each hold down and "virtual hold down" to be roughly equal to the global rigid body deflection plus the local rigid body deflection (rotation of the wall plus rotation of the pier in question). But it's not even close.

The deflection at the actual hold down is less than the global deflection at that point, meaning the local rigid body deflection would have to be going the wrong way.
The deflection at the middle "virtual hold down" is equal to the global rigid body deflection at the real hold down - this is plausible, though the local rigid body deflection would have to be almost as much as the global rigid body deflection at that point.
The deflection at the last "virtual hold down" is significantly greater than the global rigid body deflection, meaning there would have to be significant local rotation in the end panel. For that to happen, you'd need both lateral slip in the corner straps (which is not accounted for anywhere) as well as vertical slip, which I believe is already accounted for in the second term (Ga = apparent shear wall shear stiffness from nail slip and panel shear deformation).

So again, I don't dispute the behavior of the wall - I dispute the applicability of the simplified calculation method to that behavior. It doesn't add up, at least not to me.

As for why I put forward my thought for the deflection equation? Well, we have a pair of equations meant for solid walls without openings and hold downs on each end. So from the beginning, these equations are not directly valid for our configuration. So there are two choices that I can think of: come up with a new deflection equation to more accurately address the still somewhat debated behavior of an FTAO wall, or see if we can fit the 'tried and true' to the data. Turns out fitting the tried and true wasn't that hard, so it made sense to do it. It doesn't mean that it's right for the right reasons, it just means it fits the data. Good enough for run of the mill designs, but not so good for those of us with an innate curiosity that borders on being unhealthy.

bones - The interactive portion will still show you cell references - you just can't change them.

They exceed the hold down rating because it's a seismic example. If you look at the example sheet, the strength V is only 3750 (0.7E), and they do seismic deflection for seismic drift checks at E (3750/0.7) = 5357.

 

[bones206]

Regarding vertical slip, perhaps the wall deflection curve data was influenced by the bolts tilting at the simulated corner straps. I think the M410 research report alluded to that. I’m grasping at straws here.

Thanks again for the clarifications in the spreadsheet.

 

[phamENG]

Got an email back from an engineer at APA:

That factor of 4 is, in fact, the seismic deflection amplification factor. Modifying the deflection calcs to allow it to show up for wind design is something they are now considering for a future version of the spreadsheet.

The averaging of the deflections and distribution of the shears did not yield a satisfactory response. I'll decide tonight if that dead horse needs a fresh beating.

As for the virtual hold downs...KootK, we're both partially right. It's apparently a widely discussed topic within the halls of the APA. The equations assume a fixed sill/sole plate, which doesn't exist, so there is some deflection there, and this helps to account for that. But to quote:

APA performed a series of tests and attempted to adjust to traditional equations to account for the additional stiffness added by the sheathing around the opening....The equation is not perfect but is a fairly good match to the data collected during testing.