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Reply to A. Roger Turk's Comments on Period Calculation for One Story Building
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- Subject: Reply to A. Roger Turk's Comments on Period Calculation for One Story Building
- From: <FEMCCLURE(--nospam--at)aol.com>
- Date: Sat, 13 Jun 1998 19:19:08 EDT
- Cc: 73527.13.56(--nospam--at)compuserve.com
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
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