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Re: ASCE 7-05: RSA Procedure per 12.9

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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.

Daniel Popp, S.E.

From: "bill(--nospam--at)" <bill(--nospam--at)>
To: seaint(--nospam--at)
Sent: Thursday, February 19, 2009 1:20:26 PM
Subject: ASCE 7-05: RSA Procedure per 12.9

Okay, I'm trying to slog my way through this, and I'm corn-fused.

12.9.4 says that I must scale the "design values of combined response," and proceeds to talk to me about calculating a base shear V according to 12.8 (which I thought I was escaping by using the RSA in the first place), and then comparing it to Vt, the base shear from the RSA. This is supposed to done in each orthogonal direction.

Now, my first question is, What IS the Vt in a given orthogonal direction? For instance, when I run the RSA for my current problem, using the first twenty modes, and then look at the summation of the reactions for the RSA in the X-direction and then in the Z-direction (the plan directions, since positive Y is "up"), I actually get forces in X AND Z (and Y, for that matter), in each case. They are close (about 3% difference) so I guess I'm doing something right.

But is the Vt ONLY the summation of reactions in the particular direction of interest, or is it, perhaps, the vector sum of the reactions in both X and Z in each case?

I hope I've made myself clear - I'm easily confused and assume others are as well.

I just cannot seem to find anyone around here, in the flesh, who knows diddly-squat about any method other than "equivalent static force."