flexible diaphragm why analyze as simple span

huangyhg

flexible diaphragm why analyze as simple span
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?
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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.
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.   
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...
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:
the diaphragm doesn't specifically act like a flexural beam.
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.

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.
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...
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.
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.
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
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 re