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Rigid vs Flexible Diaphragms - Some Comments
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- Subject: Rigid vs Flexible Diaphragms - Some Comments
- From: "Mark T. Swingle" <mswingle(--nospam--at)earthlink.net>
- Date: Fri, 07 May 1999 01:58:26 -0700
Thank you Bill Cain for putting the actual UBC wording regarding flexible vs rigid diaphragms (3 May 99, message #22 if in digest form). Here are my comments on the evolution of this provision and its use for buildings with wood diaphragms and wood shear walls. 1. FLEXIBLE vs RIGID I was told by a reputable source that the cut-off point between rigid and flexible (max diap deflection of TWO times the average story drift) was a number pulled out of a hat. I was told this during a SEAONC Code Committe meeting (approx 2 years ago) by someone who claimed to have participated in the development of this very definition. He claimed to be somewhat troubled by the fact that there was no technical justification for it, it was just a "gut feeling" (my words). He was trying to get someone to do some basic analyses to either justify it or adjust it. The idea was that a diaphragm stiffer than this is where the effects of redistribution and rotation start to occur. 2. DIAPHRAGM FLEXIBLE AND RIGID AT SAME TIME? Careful reading of this provision implies that if the building has interior shear walls, then EACH diaphragm section (between two adjacent walls) needs to be checked as to whether it is rigid or flexible. What do you do if, in one direction, some diaphragms are rigid and some are flexible! This can happen if the widths vary a large amount. Check it out! Yes, structural analysis can be made as difficult and complicated as your imagination allows. 3. DO THE EQUATIONS WORK? (IS A DIAPHRAGM ALWAYS A SIMPLE SPAN AND IS A SHEAR WALL ALWAYS A CANTILEVER?) In order to follow the code language and apply the test for a wood diap and wood shear wall building, one must use the deflection formulas in Volume 3 of the UBC. The only difference between the shear wall and diaphragm equations is that the diaphragm is assumed to be a simple span, and the shear wall is assumed to be a cantilever (check the coefficients). This would be fine for a one-story box with only perimeter shear walls. However, if the building has interior walls, then the diaphragm is a continuous beam, not a simple span. How does one use the equation to calculate deflection in this case? Furthermore, in a multi-story building, only the top floor shear walls would truly act as a cantilever, and even then only if the adjacent openings were full height! In actuality, if the shear walls have windows adjacent to them, then the stiffness will be significantly different due to the affect of the spandrels above and below the window. What is the effective height of the wall in this case? Ditto for the lower story walls which will be in reverse curvature, not be cantilevered. 4. WHAT ABOUT UNBLOCKED DIAPHRAGMS? The equation in the code for diaphragms is for BLOCKED diaps only. What does the CODE say about the deflection of UNblocked diaphragms? (Hint: nothing). How can a building official require a determination of flexible vs rigid if there is no code language. 5. NON-LINEAR EQUATION LEADS TO ITERATION!? In reference to the shear walls specifically, the deflection equation is highly dependent on the load per nail, in addition to other items, i.e. it is non-linear. Are we really expected to iterate through several cycles, revising the shear wall stiffnesses based on the previous assumption until it converges? Are you kidding? By this logic, we also need to distribute shears accordingly among the walls IN EACH LINE, because in the new way, the forces do not distribute linearly according to length IF THE LENGTHS VARY. 6. WHAT AND WHERE IS THE CHORD? In reference to diaphragms specifically, the deflection equation is dependent upon the axial stiffness of the chord member. Typically, the double top plates are assumed to be the chord for the purpose of this equation. However, would not the continuous rim joist and the sole plate of the wall above contribute? They certainly would in compression, and perhaps not in tension if not properly spliced. (And where is the diaphragm chord in a bulding with concrete walls?) My point in bringing up all of this is to point out that, IMHO, the idea of requiring this type of analysis is ridiculous, and cannot really be enforced by the building official because the UBC, as complex as it has become, still cannot address all of the possible factors in wood frame buildings, and lacks the necessary tools to accomplish it. Engineering judgement SHOULD still have a role in design. And until some entity comes up with defintive research on the subject, wood diaps are flexible, concrete diaps are rigid, and steel decking is rigid (perhaps flexible with no concrete fill??!!). What I have done in the past (on wood buildings with deep diaphragms) is to analyze for both rigid and flexible diaphragms, and take the worst case. However, my rigid analysis was crude, completely UNLIKE the ideas expressed above. I simply assumed that the diaphragm was a continuous beam of uniform EI and applied the loads. As you can imagine, all that happened was that for the rigid case, the INTERIOR walls received more load than they would for the flexible case. I would be very interested in your comments regarding the above. Mark Thomas Swingle, SE Oakland, CA
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