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Re: ASCE 7-05: RSA Procedure per 12.9

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Bill,

If you have not done so already, download FEMA 450-1 and FEMA 450-2.  These are the NEHRP Provisions, and more importantly a detailed commentary, which were the base documents for the current IBC/ASCE Seismic requirements.  These are free downloads from FEMA and below is their website:

http://www.fema.gov/library/viewRecord.do?id=2020

Think of the 85% rule as just a minimum code value without trying to read much else into it.  Also remember that your RSA analysis is suppose to be a more accurate representation of your structure, especially for structures with significant irregularities, and can capture some of the higher modes that your ELF can not.  That said, in the commentary of FEMA 450-2 it states the following, "Where modal analysis predicts response quantities in excess of those predicted by the ELF procedure, this is likely the result of significant higher mode participation and reduction to the values obtained from the ELF procedure is not permitted".

You have to be very careful with words and use of "scaling" as the way RISA uses the term is NOT the same as the code uses it.  There are actually two scalings going on here.  One is to include R and I into the Response Spectra curve and another to bump the results if you are lower than 85% of the ELF.  The expectation of the code is that you would "scale" your response spectrum by R/I before you start your analysis.  This is so you are comparing apples to apples in your final results (i.e. both your RSA and ELF need to include or exclude R and I).  Since most computer programs do not allow for this "upfront" R/I scaling, unless you input your own response spectrum curve, most engineer just scale the final results.

If I understand your RSA orthogonal direction issue correctly, I would perform the RSA in one direction and then calculate the scaling factors for just that direction.  Once you input this scaling factor it will apply to all the resulting directions of that analysis.  The vector sum will be taken care of by checking the X and Y Direction Analysis.  As a side note, be sure you have checked the box for Use Dominant Mode for Signage.  Hard to explain but it helps keep the signs (+/-) for the other directions and will likely reduce your large vertical results.

As for the 100%/30% orthogonal effect, this should be handled within your load combinations.

Hope this help,

Thomas Hunt, S.E.
Fluor




bill(--nospam--at)polhemus.cc
02/20/2009 06:17 AM
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Re: ASCE 7-05: RSA Procedure per 12.9





Thanks for your reply, Daniel.

Yes, I understand the part about combination of the modes. As you state, most software can handle this auto-magically (I'm using RISA-3D, it seems to do a good job of it). Please note that this is a fairly simply structure, a steel-frame platform raised about 8 feet off the ground, moment frames in all directions. The plan-view is kind of "funky," hence the RSA is required because of the "irregular plan."

In my case, I ran the first 20 modes, and it adds up to about 97% of the total mass - so, okay.

My problem is that the sum of the reactions for each of the X-direction and Z-direction modal analyses, gives me forces in all orthogonal directions.

For example:

When I look at the results for the X-direction RSA, I get the following (in kips)

SUM Rx = -5.961 (Horizontal)

SUM Ry = -11.912 (Vertical)

SUM Rz = -5.723 (Horizontal)

Then, the results for the Z-direction RSA is:

SUM Rx = -4.122

SUM Ry = -11.567

SUM Rz = -6.892

So you see, I have reactions showing up pointing in each of the orthogonal directions for each case.

My question is, should the "base shear" from RSA (Vt in ASCE 7 parlance) in each case actually be the VECTOR SUM of the total horizontal reactions in each direction? Am I understanding it correctly?

In this case, since I've got a "short, stiff" structure, the RSA shears are probably larger than 85% of the Equiv. Static base shears (V) - although the numbers I'm giving are NOT reduced by division by R/I as mentioned in 12.9.2. Should they be, for comparison? It isn't clear to me from the text of ASCE 7.

You guys who "grew up" with this stuff have no idea how difficult it is to glean this from reading. too many unspoken assumptions, I think.

  Bill,

Refer to the previous section (12.9.3) for the combination of the modes.  It states that the value for the "parameter of interest" (base shear in your case) calculated for the various modes shall be combined using the SRSS or the CQC method.  The CQC (complete quadratic combination) is generally recommended for this purpose.  Most analysis programs (e.g. ETABS) do this automatically.  The number reported for the response spectrum base shear should be the final combined number (verify this with the program help), which must be no less than 85% of the equivalent lateral force base shear.  This must be checked in both the X and Y directions.  The upshot is that you do have to run the equivalent lateral force numbers to give you a baseline for evaluating the response spectrum results.

My understanding of this lower bound is that it prevents engineers from reducing the stiffness of the structure to an unrealistically low level, which would reduce the dynamic base shear to a potentially unconservative value.  The 85% limitation keeps you from getting too far away from reality.  For short, stiff structures, you are likely to be above this lower bound anyway, and may even be better off using the equivalent lateral force method directly.

A final note:  the 85% limitation applies to base shear only, not overturning moment.  For taller buildings, the response spectrum analysis can reduce the story shears at higher levels due to the higher mode shapes, greatly reducing the overturning moment at the base.  I have seen reductions in overturning moment of up to 80% in certain taller structures.

Regards,
Daniel Popp, S.E.


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