## Wood Diaphragm deflections - 3 sided walls with open side

## Wood Diaphragm deflections - 3 sided walls with open side

(OP)

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

My question first and then some 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!

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!

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

buildingdeflection. Big difference here...Mike McCann

MMC Engineering

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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.

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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.

## RE: Wood Diaphragm deflections - 3 sided walls with open side

Note that it uses Delta = qL^2 / 8G'B which is similar to the IBC equation 23-1 first term.

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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 www.apawood.org.

I hope that this helps

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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.

## RE: Wood Diaphragm deflections - 3 sided walls with open side

Butin 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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

EIT

www.HowToEngineer.com

## RE: Wood Diaphragm deflections - 3 sided walls with open side

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

## RE: Wood Diaphragm deflections - 3 sided walls with open side

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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

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

Mike McCann

MMC Engineering

## RE: Wood Diaphragm deflections - 3 sided walls with open side

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.

## RE: Wood Diaphragm deflections - 3 sided walls with open side