Flexible Diaphragm Why Analyze as Simple Span 3

[Greatone76]

We have a situation where we have 3 frames roughly equally spaced with a fexible roof diaphragm connecting them. It seems the typical approach is to use a situation of 2 simple span beams between the frames. Why isn't a continuous beam spanning over 3 supports used?

When we run the continuous beam the middle support or frame get signicantly more load them if we do two simple span beams. And as expected the loads on the ends spans are less than when use use 2 simple span beams. What makes it correct to ignore the continuity of the deck over the middle support? Does it have something to do with the stiffness of the deck?

Is the standard engineering approach to use 2 simple span beams? Our unoffically conclusion is to take the worst loads produced by each case. Does this seem reasonable?

 

[rdbse]

I understand your question. However, you should think of the flexible diaphragm in terms of force distribution based on tributary widths to the frame/shearwall.

It would be conservative to take the worst case from your simple/continuous beams models, but if you feel better using this than go for it.

In computer models with rigid diaphragms, lateral forces unload into stiffer elements and leave less stiff lateral elements with very small forces. I often design the less stiff elements for a minimum force based on their tributary width. This works well for me, so do what makes you feel comfortable.

 

[Greatone76]

I guess our question behind this post boils down to why we use a simple span or tributary width to distribute wind loads on a flexible diaphragm.

Doesn't the deck have continuity over a middle frame?

Maybe there is an assumption I'm missing when thinking about flexible diaphragms. Perhaps the deck can't hold both negative and positve moment over a single span?

We are curious if the convention to go with simple span beams is simply because 30 years ago it was more difficult to find the reactions of continuous beams.

 

[youngstructural]

The convention probably does have it's birth in simpler analytical times, however it also is logical, simple and easy, while resulting in a system with a total capacity to take the loads applied.

That said, I don't normally use it, and I will explain why. Rdbse touched in stiffness, and that's exactly right. The force distribution depends on the stiffness of the diaphragm and of the supports.

Let's look at the diaphragm first: Don't immediately think beam, first try to picture what would happen if the diaphragm was actually infinitely rigid. The loads would distribute purely from tributary widths. So, in a beam it is actually the deflection of the beam, which allow the outside edges to rotate, which causes the centre support to take additional load. The continuity accross the centre support in effect acts like a propped cantilever.

So our first decision is whether or not our walls are approximately equal in their ability to support the diaphragm (stiffness). After that we're free to assume simply or continuous beam model for our force distribution, confident in the fact that as one or more walls deflect the loads will redistribute to match our assumption.

Now that really does require relatively equal stiffness walls and probably that you aren't in a high seismic area. Let's look at the relative wall stiffness to see why:

If you have three walls and the outside two are full height 200 (8inch) thick without openings and the middle wall is 150 (6inch) thick with several nearly full height large openings, you won't get half of the load being carried by the middle wall. It will deflect and carry less load.

Personally I will usually design for the relative stiffness of the walls and the diaphragm, including the structural eccentricities and secondary torsional forces which occur due to the layout and relative stiffness of bracing elements. I posted the basis of my design procedure in a thread about hand analysis methods. I guess now I've posted my logic behind it as well.

Appologies for the length of the post, but I wasn't up to the task of explaining it with fewer words this time on a Sat morning.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[JAE]

Time warp - here in middle US it is still Friday!

youngstructural - most of what you say makes sense, but I would try a different tack to answer the question:

[red]The diaphragm doesn't specifically act like a flexural beam.[/red]

It rather acts as a diaphragm with the stiffness/deflection behavior based more on shear distortion rather than flexural distortion. For thinner, less stiff diaphragms the continuity doesn't matter as much because it is more based on shear modulus and shear deflection instead of E and flexural deflection.

 

[haynewp]

It's still Thursday where I am.

JAE, don't you mean for thicker, more stiff diaphragms the stiffness is based more on shear deflection instead of flexural deflection? The less stiff the diaphragm the more towards flexural based stiffness it leans, but still the majority is shear deflection.

 

[youngstructural]

My post doesn't depend on how the diaphragm deflects but rather that it does or does not. The beam modelling is what is under discussion, but you've quite right: for a thorough understanding you really do need to consider that it is combined shear and flexural bending, governed by shear type. Also your analysis must include both terms to be as acurate as possible.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[JStephen]

If the diaphragm in question is two-dimensional in stiffness, you have plate bending, not beam bending, and assuming any kind of 1-way beam action is a gross approximation. If the diaphragm is flexible enough, it will begin to support loads through tension action rather than bending. Or if it fails in bending under the maximum load, then the reactions will be re-distributed accordingly.

I think a bigger issue, though, is the accuracy of the applied loads. You can use a building code to calculate loads to 8 decimal places, yet the actual loads the structure will see in its lifetime are very approximate, probably +/- 50% or more. And you may have a uniform load in the building code when real loads simply won't be uniform. With this in mind, it seems to me to be questionable if you really gain much from a more accurate distribution of your assumed loads into the structure.

 

[JAE]

haynewp,

I always undertood that shear deflection vs. flexural deflection in a member is more based upon the span/depth ratio rather than the thickness or stiffness of the member.

Any member has both going on at one time...it's just that for most diaphragms, the flexural behavior (based on the direct compression/tension deformation in the "beam") is much smaller than the shear distortions occurring over the full depth of the diaphragm.

 

[msquared48]

Professionally speaking, I have a real problem with calling any plywood diaphragm rigid as it places it in the same category of stiffness as a concrete or metal deck infill diaphragm. To me, by nature, these are totally different structural animals, and act as such.

The concerete diaphragms have continuity across all supports that is generated both by a continuous pour, but also the steel reinforcing. If needed, this continuity can be broken with a cold joint or some other mechanism.

A plywood diaphragm, however, is made up of many small pieces, loosely tied together with nails, sometimes glue, some steel straps, and the killer for deflection - spacers - that allow for more movement between the plywood panels. Moreover, the panels are amaximum of only 12 feet long, and with the staggering, are continuous over the supports every other or two out of three panels, and not by much.

I could never see full rigidity here for plywood, but might consider up to 25% if my arm was severly twisted.

Mike McCann
MMC Engineering

 

[haynewp]

JAE,

I agree, I actually had depth in mind rather than "thickness". Generally, I think of stiffness as being a member that is deep compared to its length anyway. There is also the E/G ratio as well as the L/d ratio. If I remember correctly, the E/G of wood is a lot higher than for steel or concrete.

 

[Lion06]

Please forgive the ramblings of an EIT, but I have a few questions on this topic.
It was my understanding that the difference between a flexible diaphragm and a rigid one is that a flexible diaphragm acts as a beam (distributing lateral forces to frames/shearwalls as a beam would to supports) and a rigid diaphragm acts as a rigid body (distributing lateral forces to frames/shearwalls based on the relative stiffnesses of the supports (frames/shearwalls)).
Is that accurate?
If not, why?
If it is, why does a rigid diaphragm need chord steel if it is not acting as a beam?

 

[haynewp]

Yes.

Theoretically I guess if it was exactly rigid it would not need chord steel. But it is not exactly rigid so we put it in anyway, or it is already often there in the form of a perimeter floor beam in a composite floor system, or pour stop angle at the perimeter, for example.

 

[cap4000]

Check out this nice link for a comparison of rigid vs flexible.

http://www.arch.virginia.edu/~km6e/arch721/content/lectures/lec-03/home.html

 

[youngstructural]

Excellent resoure cap!
Certainly a more clear explanation than my long-winded post. I particularly like how clearly the diaphragm "plan" view shows the rotation of the "prop" support and the cantilever-like deflections in a flexible diaphragm.

JStephens: With respect I have seen some good and useful posts from you, however the issue of load accuracy is well off topic. Unfortunately Structural Engineering is much too complex to give us much better load approximations than +/- 50%. We can refine them to more like +/-5%, but only at tremendous cost (wind tunnels, FEA environment modelling, etc) and almost never is doing so economical.

Pointing out that the codes are fatality flawed with regards to precision on estimating the actual loads is not going to help. Discussing alternative methods of distributing loads just might.

That said, you are quite right about diaphram actions, if we were dealing with a homogeneous material of contant cross section, but we aren't. Given concrete, timber or concrete on steel deck pan, beam modelling applies well enough. Particularly when we are talking about the total capacity of the system and bearing in mind that with only rare exception the system will deflect to distribute our loads in keeping with our assumptions.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[msquared48]

Makes sense from the link above that if the diaphragm does not have the stiffness to transfer the load to the interior support(s), then it would be termed more flexible than one that did.

Also makes sense, as with a stong beam weak column analogy, that if the stiffness of the diaphragm is great in relation to the supports (that are not truly "rigid supports" here if you note), that the relative rigidities of the suopporting structures determine the loads that the diaphragm will transfer to them.

A star for the link. This is a good one for students, let alone old timers.

Mike McCann
MMC Engineering

 

[OzEng80]

This is a concept I still haven’t got my head around yet. The link addresses the flexible diaphragm well by showing the ‘panelized’ deflection between frames. I assume this rotation at internal frames could have significant damage to the diaphragm?

I have a question about diaphragm behavior associated with frames with (considerably) varying stiffness.
The flexible diaphragm concept requires frames be designed with a tributary area loading. What happens when you have adjacent frames with a large difference in stiffness. Say one frame deflects span/150 in service conditions and the immediately adjacent frame only deflects span/500? Even a ‘flexible’ diaphragm would offer resistance to a tributary area allocation of load with this arrangement. Is there a maximum allowable diaphragm deflection (frames spacing/500)? that should be followed for flexible diaphragms?

How is a cantilevering flexible diaphragm handled?

Many thanks!

 

[msquared48]

There are limits in the code as to the maximum square footage and limit of projection from the main structure. The lateral load is applied to the cantilever and it is treated as a cantilever beam with a moment at the juncture with the face of the building or main diaphragm. Tension/compression ties have to be added at the limits of the cantilever diaphragm to tie it into the main diaphragm.

As to a maximum diaphragm deflection, that is one of the two numbers figured into your story drift limitations, the other being the relative shearwall deflections.

Regarding the other questions, just look at the diagrams a little longer and try to get a feel for it. It does make sense.

Mike McCann
MMC Engineering