Wood Diaphragm deflections - 3 sided walls with open side 4

[JAE]

I've gone through numerous online searches, book searches, and Eng-Tip searches to no avail.

My question first and then some background:

Question Does anyone have any formula or method of calculating the deflection of a wood diaphragm when it is supported only on three sides with an "open front" building?

Background
The NDS and IBC etc. provide an equation for a simple span diaphragm spanning between two resisting shear walls. The formula takes into account flexural type bending and shear deformation in the diaphragm, nail slip, etc. However, for a three-sided building with an open front (i.e. two side and one rear shearwall) the diaphragm will not "span" between two supports but will essentially cantilever off the rear wall with the two side walls assisting in taking the rotational effect of the missing shear wall.

This is more like a cantilever and not at all like the simple span that the diaphragm equation covers. We've talked over approximating the deflection using the IBC equation by using the analogy that a cantilever beam is like a half-span of a simple span in terms of deflections. But with the other aspects of diaphragm deformation included (nail slip, shear deflection, etc) we're not sure this is correct.

We have a building that exceeds the l/w ratio of 1:1 found in IBC 2006 2305.2.5 but can fall under the exception as long as we show calculations that "diaphragm deflections can be tolerated."

Anyone have any insight or references for this?

Thanks!

 

[msquared48]

http://books.google.com/books?id=Uf...n of a cantilevered plywood diaphragm&f=false

The author seems to model the cantilevered shear wall and cantilevered diaphragm the same, but I can't say that I agree. I would think that the equations for the diaphragm would be more complicated due to the torsional twist deflection of the diaphragm, which is not present in the shear wall. This gets into the lateral stiffness of the transverse end walls... and the rotational stiffness of the single wall - the whole system in fact.

Still looking...

Have you considered trying to model the system in RISA3D?

Mike McCann
MMC Engineering

 

[msquared48]

Might try this reasoning... relating to the statement "diaphragm deflections can be tolerated."

Calculate the diaphragm deflection according to the equations above neglecting any due to the torsion twist that would laterally deflect the walls. Claim that any deflection caused by the torsional twist is not a diaphragm deflection component, but actually a building deflection. Big difference here...

Mike McCann
MMC Engineering

 

[JAE]

Mike - RISA won't help as it is only a rigid diaphragm approach - so modeling the three shear walls and the diaphragm will give me the rotation twist in the diaphragm due to shear wall deflection - which is fine - but doesn't include any in-plane diaphragm distortion.

You say "calculate the diaphragm deflection according to the equations above..." That is the issue and question - I have no way of calculating deflection in a "cantilevered" diaphragm. That's what I'm looking for.

 

[msquared48]

JAE:

But that is my point from the article - you do - treat it as a cantilevered shear wall using the equations from the article. Relly, except for the rotational deflection, it is the same animal.

Mike McCann
MMC Engineering

 

[JAE]

Mike - thanks.

But I see the first term in the IBC equation - 5vL^3 / 8EAb which looks to me more like a simple span deflection equation - not sure you can just substitute the L for a simple span with an L from a cantilever and get the correct deflection.

 

[JAE]

Mike - attached is a rudimentary equation for basic diaphragm deflections for a simple span diaphragm.
Note that it uses Delta = qL^2 / 8G'B which is similar to the IBC equation 23-1 first term.

 

[OldPaperMaker]

JAE,
A book, The Analysis of Irregular Shaped Structures by R. Terry Malone and Robert W. Rice has a chaper 6 which is all about Open Front and Cantilevered Diaphragms.

In the first section of this chapter the authors refer to an APA publication (in 1982) titled Structural Panel Diaphragms, Design Example 3-Open End Buildings. This may be available on line at

http://www.apawood.org.

I hope that this helps

 

[JAE]

And attached here is a cantilever diaphragm with a point load at the end. This is a totally different equation form than the IBC.

It also might be somewhat useful but in our case instead of a point load at the end of the diaphragm we instead have a uniform load along the diaphragm span.

What I need is the corresponding equation for a cantilevered diaphragm deflection with a uniform load along its side.

 

[msquared48]

OK JAE...

But in the article I posted, the equation IS for a cantilevered shear wall, not a simple span shear wall, which the author claims can be modeled for a cantilevered diaphragm too.

The problem I see is quantifying the variables given.

In 1976, the APA put out a manual entitled "Plywood Diaphragm Construction" (14 pages), and they list on page 9 the equation for a simple span diaphragm condition, and on page 11 an equation for a shear wall (vertically cantilevered diaphragm) condition.

Do you have a copy of that manual?

Mike McCann
MMC Engineering

 

[JAE]

Mike - thanks again for your help - we've got that APA document - we discussed using the shear wall equation but again that is with a concentrated load on the top of the shear wall.... not a uniform load along the height of the "shear wall" which is what we'd have on our diaphragm with an open faced building.

Perhaps we could invent some adjustment factor based on comparing a cantilevered beam loaded at the end vs. a uniformly loaded cantilever and apply that to the shear wall deflection equation - but both of those are based on flexural theory (EI) instead of shear deformation theory (GA)

OldPaperMaker - thanks - I saw that book pop up on all our google searches. Perhaps we have to buy the book. I would rather hope to find the equation for the diaphragm as I think we have a good handle on everything except for

 

[msquared48]

JAE:

OK.

If the point load at the end was half the sum of a uniform load, the results should be the same, or very near the same, considering the different shear diagrams.

I really have never seen anything published for that specific condition... Just do an (JA)EWAG!

Mike McCann
MMC Engineering

 

[RFreund]

I just ordered the book mentioned by Papermaker (rregular Shaped Structures by R. Terry Malone and Robert W. Rice), I'm curios to see what they have to say. My guess is that it is similar to that mentioned by Mike. I'll let you know, but I don't think it gets here for a week.

EIT

http://www.HowToEngineer.com

 

[JAE]

RFreund - my fear on ordering that book was that they would go through all the process for analyzing the load paths but fail to deliver on the diaphragm deflection. I'm beginning to think that msquared48's (Mike's) view is that using the shear wall formula and adjusting for end load vs. distributed load is the only way to go.

 

[RFreund]

We're in luck. sorta. The book came early. I actually ordered it the other day unrelated to this, seems like a good book.

The book starts out saying that a rigid diaphragm is required for open front structures and that the rigidity of the diaphragm should be verified by calculation. However they do not show how to verify this by calculation rather they say that the prescriptive requirements provided by SDPWS should be met (which may need to be met by code anyway?), basically these are:
Cantilever length limited to 25ft (so from open front to back wall < 25') and the aspect ratio should be less than 1. SDPWS also says that L may be increased to L/W <= 1.5 when deflections can be tolerated and sheathing is in compliance with SDPWS Section 4.2.7.1 or 4.2.7.3. This would then seem to mean that if you have a L/W<1.5 than L can be whatever you like so long as you increase W and you would have a rigid diaphragm.

So the book example (and APA's) meet these requirements and the diaphragm is assumed to be rigid. In this case there is no bending term for the total diaphragm deflection as they not "APA noted that there was no bending deflection of the diaphragm because the chords were not restrained form bending". They also state then that the there would be no chord slip if the (chord) walls are full length, if partial length then they have drag struts which have slip. The book gives the equation for the total deflection of the diaphragm which includes shear, nail slip, rotation, end wall and side wall deflection. Chapter 7 shows an example as well.

So really there still seems to be no 'diaphragm deflection' or a way to get around the prescriptive requirements that I can see although the L/W <1.5 seems reasonable.






EIT
www.HowToEngineer.com

 

[wannabeSE]

JAE,
I don't know much about wood diaphragms. Will equations for bare metal deck diaphragms help (you will need to sort out the units. And, the formulas use a flexibility factor which is the inverse of G once all the units are sorted). See page 6 from the Verco ER attached

 

[UcfSE]

For the simple span, Delta = qL^2 / 8G'B uses a moment of M = qL^2/8, for M/G'B. For a cantilever, can you change the moment in the equations from simple span to cantilever, and same for shear force on the shear portion of the equation?

 

[msquared48]

JAE:

You might also look at the attached article, and pub from the APA.

http://cmec.wsu.edu/publications/CurtisEarlreport.pdf

Mike McCann
MMC Engineering

 

[JoshPlumSE]

I'm a little late to this topic. But, I would think you could still approximate the behavior using a RISA-3D analysis (or similar program). The key is to use a mesh of plate elements to represent the stiffness of the diaphragm. You have to figure how what E and G values to use for the diaphragm based on the properties of the sheathing. Then you want to soften up the plates if there is no blocking (by about a 50% reduction) and to account for anticipated nail slip (similar to the apparent shear stiffness concept given in the NDS special design provisions for wind and seismic).

If you do that, then you've got a semi-rigid or semi-flexible diaphragm. It's a useful procedure if you're doing a Master's Degree thesis on the subject... Or, if you have no other way of justifying the design or getting through plan check.

Note: These cantilever diaphragms have always scared me a bit. Then again, I came of age in the post-Northridge time frame. Where, if I remember correctly, these types of diaphragms were the cause of some apartment collapse fatalities. That's not to say that you can't properly design them, just that this is a system that requires extra caution / care.

 

[JAE]

JoshPlum - I thought of that but it seemed that this is such a simple geometry (cantilevered diaphragm with uniform load) that there should be - or ought to be - a basic equation for it similar to the shear wall equation. I think once we get this project going I'll see about using what others (UcfSE etc.) above have suggested for substituting into the existing equations.