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Reply to A. Roger Turk's Comments on Period Calculation for One Story Building

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A. Roger Turk,

Thank you for your reply to my June 11, 1998 email message:  How to calculate
the period, T, of a one story tiltup building with a flexible diaphragm, using
FEMA 310, Section 4.2.2.1.1, equation (4-1), on page 4-3.

You raise the question: Does it really make that much difference if you use
various selected values of "EA" for the diaphragm chord on the resulting
building period?  

At first blush, it would appear that it would not make that big a difference.
However, in a tiltup concrete building there are two diaphragm chords, one on
the tension side of the diaphragm - in the example in my June 11, 1998 posting
- it could be the 4 x 4 x 1/4 steel angle. However, on the compression side of
the diaphragm it could be the 4 x 4 x 1/4 steel angle plus a portion of the
reinforced concrete titltup wall acting in compression.  In other words, the
effective compression flange would be the A steel + A concrete x E conc./ E
steel = A equivalent steel area.  The tension A steel area and the compression
A equivalent steel area could be used to calculate a moment of inertia, I, to
be used in the flexural deflection calculation:
5*W*L**3 / 384*E*I to calculate the flexural deflection.  I have not prepared
such a calculation because I do not know how much of the tiltup concrete wall
I can assume will be part of the compression chord.  However, the compression
chord in the actual performance of the diaphragm will be more than the 4 x 4 x
1/4 angle acting alone.

To the flexural deflection of the diaphragm, you would need to add the shear
deflection and the diaphragm deflection due to the plywood nail slip.  The
shear deflection calculation is relatively straight forward using the 1994
UBC, Section 23.222 formula. However, the calculation of the diaphragm nail
slip is not so straight forward, because the diaphragm loading is in
accordance with FEMA 310, Section 4.2.2.1.1, not the 1994 UBC seismic loading.
The FEMA 310 diaphragm loading is discussed below.

In the FEMA 310, equation (4-1) calculation, you are to use the loading to the
diaphragm  "...due to a lateral force equal to the weight TRIBUTARY to the
diaphragm in the direction under consideration."  It is my understanding that
the "weight TRIBUTARY" means the total weight of 1/2 the weight of the two
tiltup concrete walls  that frame perpendicular to the direction of the roof
diaphragm deflection  plus the weight of the roof construction.  In other
words, it would be the seismic loading to the roof diaphragm from a base shear
equal to V = 1.0 W.

The maximum roof diaphragm shears for the "weight tributary" horizontal force
will be much greater than the maximum roof diaphragm shears using the 1994 UBC
seismic forces.  For the 1994 UBC, if  V = .186 W, the "weight tributary" roof
diaphragm shears would be approximate 5 times the 1994 UBC roof diaphragm
shears.

The nail slip values in the 1994 UBC are for plywood roof diaphragms shear
values, according to the 1994 UBC, not the roof diaphram shear values for the
"weight tributary", V = 1.0 W, horizontal diaphragm shear forces.  The dauting
question is how can we calculate the nail slip diaphragm deflection at the
high roof diaphragm shears resulting from the "weight tributary" horizontal
forces.

>From my point of view, the calculation of  "a more realistic" fundamental
period, T, - not the default period values, T, using the 1994 UBC or NEHRP
equations, for a one story building with a flexible roof diaphragm, which is
to be used to calculate the "Pseudo Lateral Force Base Shear", according FEMA
310, is not that straight forward and generally agreed upon procedure.

If we can not agree on how to calculate the fundamental period, T, for a
single story building with a single flexible roof diaphragm, then it will be
difficult for different engineers to evaluate and design the retrofit of an
existing building in a consistent manner, using equation (4-1) in FEMA 310.
This lack of consistent understanding,  application and enforcement would
result in poor public policy concerning the evaluation and retrofit of these
type buildings.

I believe that Charles Greenlaw's postings to the SEAOC List Server, date June
11, 1998 and June 13, 1998 present some very important statements concerning
the use of FEMA 310, equation (4-1).



Frank E. McClure   FEMCCLURE(--nospam--at)aol.com