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Re: ASCE 7-05: RSA Procedure per 12.9

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Bill,

Your confusion is understandable after looking through the RISA implementation of the RSA.  I'm familiar with the ETABS approach, which is much more straightforward.  To combine the X and Y directions, you can use the SRSS method (the Z direction is independent).  Your base shear for the RSA would then be 7.247 kips in the X-direction.  The response reduction factor R and the importance factor I should be used, so this number can be multiplied by I/R.  The result should be compared to the equivalent lateral force base shear and only increased if it is below 85% of that value -- you cannot scale it down.

In ETABS, it looks like this:  the response spectrum is non-dimensional, so the scale factor must include the acceleration due to gravity (g).  R and I are also included, so the input scale factor for R = 4 and I =1 would be 386 in/s^2 * 1.0 / 4.0 = 96.5.  This value is the minimum scale factor; it must be increased such that the RSA base shear is no less than 85% of the ELF base shear.  So there are essentially three scale factors combined into one number:  g, I/R, and 0.85V/Vt (>= 1).

RISA offers a spreadsheet for calculating the scale factors.  If you have the load combination spreadsheet open, there should be a "SF" button on the toolbar to the left of the "Solve Current" button.  This will open the "Spectra Scaling Factor" dialog, which may be useful to you.  The help file also has an extensive section on RSA.

Best of luck,
Daniel


From: "bill(--nospam--at)polhemus.cc" <bill(--nospam--at)polhemus.cc>
To: seaint(--nospam--at)seaint.org
Sent: Friday, February 20, 2009 4:17:07 AM
Subject: 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.