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Rigid vs Flexible diaphragm discussion[Subject Prev][Subject Next][Thread Prev][Thread Next]
- To: seaint(--nospam--at)seaint.org
- Subject: Rigid vs Flexible diaphragm discussion
- From: "Martin W. Johnson" <MWJ(--nospam--at)eqe.com>
- Date: Tue, 10 Aug 1999 08:52:36 -0700
Most of the comments about this topic have seemed to me to have been missing the real issue of how we are designing diaphragms versus how they in fact behave. Analysis approaches such as used for flexible and rigid diaphragms are only basic approximations of what goes on. We also do many things that don't fit into either approach, such as allowing short walls to "rock" and clustering a series of adjacent short walls on either side of a corridor together as a group (which, by the way, assumes that the short width of diaphragm between them is "rigid", a word many of you abhor). But the main thing that is not being recognized is that we are designing using "imaginary" forces. Consider the following situation. A wood diaphragm has plywood shearwalls on each side. On the right side, two 4-foot long shear walls are provided. On the left, a single 12-foot long shear wall is provided. We design the diaphragm and walls using the diaphragm Vpx forces in the code, and determine the required nailing using the WSD tables in the UBC. But both the forces we are using and the defined strengths of the components are "imaginary" WSD values. The real strength of the plywood diaphragm and walls is around 2.5 to 3 times larger than the "allowable" shears. Hence the structure will ACTUALLY tend to transmit interia forces at the REAL strength of the structure, which, in Blue Book Terms, would have a base shear of around Ro x V. But here is the problem. The short 4-foot long shear walls on the right side of the diaphragm have got foundation systems that were only designed using a factor of safety of 1.5 against overturning. In other words, the "real" strength of the short shear walls will never be attained, because the walls are going to rock. So only half of the expected inertia force will be resisted on the right side. Where does the rest of the inertia go? IF the diaphragm is wide enough and flexible enough, the inertia will only go into unexpectidly large lateral displacements along that end of the diaphragm, and the wall on the left side won't notice much. But if the diapragm is not wide, but perhaps as wide as being square, the "left over" inertia force is going to be transferred to the wall on the left side. That wall is longer and will not rock. So after the earthquake we will look at the structure and see that the short walls do not have much structural damage, but perhaps considerable nonstructural damage, while the long wall has visible structural damage - bent nails, etc. And we will say, "Aha! Rigid diaphraghm behavior!". I guess the point of this is that, first, there seems (to me) to be some merit in "considering" the effects of rigid diaphragm behavior in structures, "second," that thinking of the code in a manner that it is a "recipe" which must be followed step-by-step causes us to overlook all of the judgemental design assuptions we make, and third, that both of the analysis approaches we are discussing - rigid and flexible- are ficticious. The only "real" way to consider the behavior of structures is at the "strength" level, considering the plastic behavior of the structures. And I do not advocate that, except for important structures where the fees are better. My recommendation is to "consider" the effects of rigid diapragm behavior on structures, but have a mechanism to neglect it in instances where it becomes obsessive, such as very wide diapragm spans or very small (i.e., residential) structures. Oh, and by the way, what about all of the plywood floor diapragms that have got lightweight concrete topping on them? Isn't that pretty rigid, even though we ignore the strength contributed by the concrete??? Best regards to you all, Martin.
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