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Re: Fwd: Period Calculation for One Story Building with Flexible Diaphragm, FEMA 310

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At 07:26 AM 6/11/98 EDT, you wrote:
  The 1994 Uniform Building Code, Section 23.22, has an equation for
>the calculation of a plywood diaphragm deflection, which includes a factor "A"
>for the area of the diaphragm chord.  In an existing tilt-up building, what is
>the diaphragm chord?  Is it the continuous steel 4" x 4" x 1/4 " angle which
>supports the roof construction at the face of the 5 3/4 inch reinforced
>concrete tilt-up wall?  Is it some portion of the 5 3/4 inch reinforced
>concrete tilt-up wall, say 5 3/4 " x 24", like the flange of a reinforced
>concrete tee beam? 
>It makes a big difference in the period, T,
>depending on how the diaphragm chord is defined.
>
>Frank E. McClure    FEMCCLURe(--nospam--at)aol.com
>
_________
Frank, I think first the FEMA 310 formula's origin should be questioned as
to whether it is based on the actual diaphragm deflection that would be
measured if the prescribed loading were applied, or only on a calculated
deflection that presumes certain conceptual assumptions and conventions will
be followed in the calculations.  If it is the latter, then those bases need
to be revealed, and they will answer your question.

But if actual deflections are intended, as seems likely, then the actual
deflection attributable to the "chord" component of the deflection formula
takes on the importance you point out. 

For this purpose the chord is what the building in its own pleasure decides
what the chord is. You and I don't get to dictate what parts are the chord
and what parts aren't. They will do what they want.

It appears that our burden shifts from one of control to one of
anticipation: We get to anticipate what might participate, and we get to
estimate the amount of participation among the several "roleplaying"
elements of the structure. The idea that there is a single, discreet,
exclusive chord is only a convenience in conceptualizing, that by now has
become habitual, but it was never a rigorous reality. (Same for the idea
that only shear stress happens in the sheathing between chords.)

If these notions are acceptable, then you get to proceed according to your
own estimates, drawn from your own sources and engineering judgment, for the
situation as you perceive it. This is one of those tasks where no single,
precise outcome can be had, no matter who is doing it.    

As for specifics in your example building, where all four walls are
substantially complete, it is likely that the walls have a huge effect. You
didn't say whether the panels are joined by poured closures. If they are,
their in-plane shear stiffness would be gigantic, and their axial tensile
stiffness very significant. The second part of this is obviously
chord-related. But the shear stiffness of the walls in which the chords are
active is also influential, perhaps less obviously.

If you chase through the statics and strength of materials principles, you
will find that the roof diaphragm as a flexural element is less like a
simple span plywood plate girder than it is like a fixed-ended one. Stiff
shear walls under the chords will not permit rotation of the diaphragm ends
in the way a simple span requires. If this end fixity effect were complete,
the chord component of deflection would be only one-fifth of that for a true
simple span.

Of course the l/w proportions of the diaphragm evoke deep-beam
complications, there are relative rigidity effects, and likely there is a
shear "lag" in the plywood diaphragm near the diaphragm ends. End wall
damage in this type of building at Northridge, near the corners, may have
been from the roof sheathing reasserting simple-span rotation on the end
walls, a ways in from the restraining side walls. Even if adjoining tilt-up
wall panels are not interconnected for much, each individual panel acting in
shear may act to cantilever upward the "chord" rigidity found in the floor
slab and/or perimeter foundation, to enhance that provided intentionally at
roof level.   

Hope this makes it clear and easy!  Happy engineering, your own way.

Charles O. Greenlaw, SE      Sacramento  CA