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RE: Rigid plywood diaphragms
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- Subject: RE: Rigid plywood diaphragms
- From: Charles Greenlaw <cgreenlaw(--nospam--at)speedlink.com>
- Date: Sat, 21 Nov 1998 13:47:59 -0800
Thanks for stating a limited and clear technical question within a topic that has been of keen interest to me for more than 15 years. At 12:04 AM 11/20/98 -0800, you wrote: > >DO YOU THINK THAT IT IS APPROPRIATE TO ESTIMATE THE RELATIVE RIGIDITY OF >THE PLYWOOD SHEARWALL (OR CLOSE APPROXIMATION OF IT) BY USING THE PRODUCT OF >WALL'S RATED CAPACITY TIMES THE LENGTH? > In a one word answer, No. In a two word answer, Somewhat, depending.... What follows is a failed attempt to explain as clearly and succinctly as Judge Kenneth Starr did last Thursday in his opening statement to House Judiciary. (Not that anyone had been expected to change his or her views as to an ultimate outcome anyway.) First, get hold of UBC Standards or its APA source material on plywood shear wall deflections as a starting point. Some engineers now say this is no longer "proper data", but we still need a starting point. And get an APA Plywood Design Specification ("PDS") for its listings of sheathing structural properties if not in UBC. Second, let's agree that the model situation is a familiar 94 UBC Rw = 6 or 8, Zone 4 Seismic situation where design loads are less than actual earthquake loads and everything lurches back and forth vigorously. (Not Wind where nothing much is expected to happen inelastically.) But also, let's agree that the building is intended to perform with none of its shear walls reaching failure or breaking up, and that it indeed achieves this customary goal. (To simplify further discussion, let's assume all walls are the same height and on rigid foundations.) And last, let's agree that the wall's "rated capacity" is the familiar code-listed allowable shear load in lbs per foot, but "rigidity" for the purpose at hand is stiffness against deflection to a total shear force acting on a wall's length, not stiffness against a lbs per foot load. (To digress, your question reduces algebraically to, "Is relative rigidity approximately proportional to a wall's total capacity in lbs." But let's not go there.) Components of deflection: Let's examine each separate component of shear wall deflection in turn to see if it is consistent with your postulated rigidity relationship. Following along with free-body diagrams would help in verifying each separate condition. I doubt that merely reading along will work. There will be seen in the deflection formula at least four components that add up to the total deflection in a given shear wall. Of these, only one is BOTH linear elastic and independent of height to length aspect ratio. It is the shear deformation internal to the sheets of sheathing. For a given type and thickness of sheathing, the wall stiffness (against a total force) due to this component is proportional to the length alone, and would not vary according to the fastener- controlled rated capacity. Upgrading the sheathing as per listed wall rated shear capacities would change this only a little, so your proposition isn't met for this component of the total. Another component is leveraged axial stretch and compression of the vertical boundary studs or posts. For a given actual wall shear stress (or rated capacity) the axial force generated in the vertical boundary is a constant, regardless of wall length, and the vertical PL/AE figure therefore would vary only if the boundary member cross section changes, which it probably wouldn't be compelled to do with an increased rated capacity, now that 4x boundary members are routine. But happily, the wall deflection due to this component does vary inversely with wall length, so the resulting rigidity would once again be proportional to length, and again not proportional to increases in rated lbs per foot capacity. Note also that this component of deflection and rigidity is typically a minor one. A third component is the leveraged result of vertical hold down device stretch and of vertical downcrunch of the compression boundary member at its sole plate bearing, etc. The gross vertical forces at these locations are constant for a given actual shear stress or rated capacity, regardless of wall length. Presuming that higher design shears or rated capacities cause use of more robust hold downs (but not necessarily boundary members) vertical deformations probably hold about constant as rated capacity increases. But shear wall deflection for constant vertical hold down and downcrunch deformation decreases linearly with wall length, hence this component's rigidity to a total shear force increases proportional to wall length, with again little effect from changes in lbs per foot rated capacity. And now comes the "nail slip" component. Staying for the moment with older, non-cyclic data, wall length doesn't matter to wall deflection at a particular per foot shear stress. In other words, aspect ratio is not relevant to this component. But no way is nail slip and resulting wall deflection linear with variation in load for a given nail schedule. It is non-linear for the entire range of load, according to figures in UBC Standards I looked up and plotted years ago. But comfortingly, the "e-sub-n" nail slip value listed for every nail size was right on 0.030 inches at the nail shear corresponding to code-listed allowable wall shear stress for every nail size and spacing and plywood thickness and grade appropriate to that schedule. (Nail slip however was substantially less if seasoned framing was used.) Nail loads in excess of what gave 0.030 inches of slip gave rapidly increasing deformation, but not necessarily failure at any particular multiple of "allowable", nor at any particular value of nail slip. It appears that rated capacity for each combination was set at a figure giving about the same nail slip value. Where all of the shear walls are actually to be loaded by design to their rated capacity, even though that capacity varies from one wall to another, then deflection of all of them due to nail slip will be essentially the same, and not varying according to rated capacity. Each wall's rigidity to total shear load for this idealized but usually desired condition will therefore be proportional to wall length alone. And the proposed rigidity relationship again does not hold. Hence the one word answer, No. So much for looking at it with a hands-off policy. Now let's intervene and deliberately design in some alterations and see if useful things happen. Alterations from usual practice: If a wall has chosen for it (or for other reasons has) a rated capacity well in excess of the design shear it otherwise needs, big rigidity benefits in the form of reduced nail slip result. These benefits are not merely linear, so it would not be strictly true that rigidity would be directly proportional to the ratio of understressing the nailing, but the general tendency is there. So now one can reasonably say that rigidity is proportional to wall length, times some measure of surplus rated capacity, for this nailing component of deflection. One also can specify hold down devices that have low-deformation properties, and specify oversized examples of such devices to further reduce vertical deformations in the device and its fasteners. These benefits appear to be decidedly non-linear in a way similar to nail slip benefits. One can get this better hold-down rigidity as a by-product of designing all of the wall to a much higher rated capacity than the building design otherwise required, or one can specify super hold downs without comparably enhancing shear nailing. Improvements to specially limit downward deflection at shear wall boundary corners is of course also appropriate when acting to limit upward deflection at hold downs. This might consist of stouter end posts and thus less cross-grain bearing stress below, enhanced bearing provisions in framing below, etc. By using these interventions, one has grounds to say that for this component, rigidity is now somewhat proportional to a rated capacity surplus in boundary details as well as to wall length. Similarly, one can beef up vertical boundary members as a discretionary by-product of overdesigning the rated capacity of the whole wall, or as a separate act. The effect would be relatively linear, and rigidity for this component would improve according to the AE overdesign improvement obtained. Sheathing specification overdesign appears to offer minimal opportunities at first, because the listed "effective thickness" figures for structural plywood shear deflection purposes do not increase much until thicknesses approaching 3/4 inch are obtained. (I have specified 3/4 and 1-1/8 plywood for wall shear use on occasion, when this property and another one unrelated to shear were of advantage.) For ordinary thicknesses, Struct I has a listed shear modulus better than lesser grades. How OSB compares remains to be looked up. Enhanced sheathing really can help with rigidity, but the enhancement has to be well in excess of what mere overdesign in rated capacity would automatically obtain. Yet your proposed rigidity relationship is there in part with respect to the excess capacity. A provisional conclusion: With all four of the deflection components discussed so far, but still avoiding really narrow aspect ratios and cyclic loading results, it appears that rigidity is proportional to wall length alone for walls that fully employ rated capacity, and that rigidity is somewhat proportional as well to perhaps the ratio of rated capacity -to- actual design stress demand. But not proportional to straight rated capacity without respect to demand. Recent considerations: OK, what about narrow panels? As others point out, the leveraged effects of vertical deformations at boundary details really matter with a vengeance. Reliance on an Rw factor of 8 instead of 6 or less means the design overturning force couple falls that much further short of of the real thing, so that adverse deflection effects are worsened more than linearly. The obvious remedy is to depart from habit and design these features very conservatively for realistic forces and with superior devices and details to reduce shear wall deflection to a minimum. Pity, but code now prohibits trying this for ratios narrower than 2:1. Codewise, insult follows injury. And what about cyclic testing's lessons? One is that again, hold down performance and that of the other boundary sources of vertical deformation really matters. Another lesson is that as a panel nears failure, it begins to fail. Rigidity of a failing panel isn't very predictable, among other disadvantages. A remedy for this might be to build these things strong enough that they don't approach failure. That was one of the understandings set out at the beginning of this discussion. Another result of cyclic testing is that nails may wiggle and slip more than had been seen in one-directional testing years ago. This implies that the nail slip component of deflection and rigidity is an even greater proportion of the total, and even more non-linear. A compensation would be to not load those nails as much as has been customary, by having a higher ratio of rated capacity to design demand than formerly...yet another incentive for a more conservative nailing-based shear wall rated capacity. The two word "somewhat, depending..." answer came from these design intervention and overdesign possibilities. One more component of shear wall deflection has been ignored till now: slippage of the sole plate on its support due to looseness around anchor bolts or due to other anchorage deformations. The magnitude of this component can be large compared to the others and is subject to large variation according to workmanship and other imponderables. And rocking of the foundation was intentionally excluded but may contribute significantly. So how seriously should we take the task of calculating relative rigidities with precision? Given also that a shear wall loaded by more than its expected share incurs more nail slip and softens its relative rigidity in a self protective way, rather than exploding in anger, how accurate a rigidity analysis is worthwhile? The above addressed a single shear wall rigidity question, not horizontal diaphragms or the whole interacting system. But a general principle is offered: The main purpose of seismic-resistant design is that the building performs. It is a sideshow to nitpick how the designer himself performs, if the main purpose gets fulfilled. Charles O. Greenlaw SE Sacramento CA
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