How to implement a SeismModal Response Spectrum Analysis combined with AISC's Direct Analysis Method 2

[jochav5280]

Hello All,

Does anyone have experience with applying a Modal Response Spectrum Analysis combined with AISC's Direct Analysis Method (DAM)?

Per Chapter 12 of ASCE 7-10, certain horizontal and vertical structural irregularities disqualify the use of the Equivalent Lateral Force Method (ELFM) for generating seismic loads. In my experience, most of my colleagues don't check the irregularities and used the ELFM on everything they design. I find this is largely due to ignorance of the code requirements as well as due to the simplicity of the ELFM.

We use STAAD for analysis/design, and I've found that while it will perform a Modal Response Spectrum Analysis (MRSA), you can't directly combine the results with an iterative analysis such as P-Delta or the DAM. STAAD's technical help has indicated that the only way to combine the MRSA results directly with DAM is to combine them via superposition, which ignores the P-Delta effects associated with the DAM.

STAAD's technical support has tried to help me come up with a method in which I manually create a static load case that represents the results of the MRSA, but I'm finding that this will be very labor intensive. I'm responsible for explaining how to implement the MRSA with the DAM to my colleagues, and am afraid that this manual creation process will be criticized for it's difficulty and labor intensity.

That said, could someone help me understand how the MRSA results should be combined with DAM? I don't believe we can ignore the P-Delta effects, especially since my seismic loads are the controlling lateral loads, which would lead to the greatest P-Delta effects.

I'd appreciate any insight you could give me. Among the (20) engineers I work with, nobody knows what to do here.

Thank you very much in advance,

jochav5280

 

[Rabbit12]

RISA 3D seems to have the same issue. It'll do a RSA but doesn't do a P-delta analysis with the RSA. My company is also trying to come up with a way to deal with that issue.

 

[mike20793]

I believe both ETABS and RAM SS can do it.

 

[KootK]

It seems to me that the process would have to go:

1) Analyze each mode individually, accounting for P-delta effects.
2) Combine the modal results per standard RSA procedures.

Is there a technological impediment to such a process? I'll happily confess that I may not be fulling grasping the complexity of the situation.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

There are two issues here.

1) Use of P-Delta analysis when combined with Response Spectra Loading.
Whether or not P-Delta analysis is included in the Response Spectra Solution is dependent on how the P-Delta analysis is accounted for. If the program uses a Geometric Adjustment to the Stiffness matrix then this is accounted for. Though you will have to specify a load combination that forms the basis of the geometric adjustment.

If the program uses "Woods Method" or "Secondary Shear" method, then this will not generally be accounted for in Response spectra analysis results.

Now, ASCE gives you some guidance on when the P-Delta effect is allowed to be neglected for seismic loads based on the Theta calculation. This can be used to justify the lack of P-Delta in the RSA calculations. They also give you a method of amplifying your results manually. You could use this method to amplify the RSA results as well. This would be similar to applying a B1-B2 method to amplify your final results.

Lastly, as a dramatically more challenging method, you could seek to implement an approximate "geometric" modification of the stiffness matrix by selectively decreasing the properties of certain members. I'm going off of memory here, but I believe the seismic design handbook (2nd edition) has some suggestions on how to do this.

2) The use of Direct Analysis Method Stiffness Adjustment in an RSA Analysis.
You are not required to use the DA Method stiffness adjustments for an RSA analysis. In fact, you probably shouldn't. The DA Method is not intended to change the loading on your structure at all. So the RSA forces applied to your structure really shouldn't change.

And, if use a reduced stiffness for your buildings, your natural periods would change, resulting in reduced loads.

I believe the AISC engineering journal had an article maybe 5 years ago, written by Shankar Nair and James Malley that talked about combining DA Method and Seismic design and give general recommendations. This is probably the best place to start. 3rd Quarter Engineering Journal, 2011

 

[sticksandtriangles]

I am certainly no expert on this topic either but I will throw my thoughts/experiences into the ring. (I just took a dynamics class at the University of Cincinnati and I would hope I would have gained a stronger grasp for the concepts I was learning . I feel like I would need to take another 2 classes before I truly started to understand the principles behind dynamic analysis as I often felt myself just becoming a matrix manipulator with no sense of the equations I was working.)

I too find myself in the same situation, where colleagues seem to ignore MRSA and use ELFP at all times.

Few things come to my mind:
Are the results from a Modal Response Spectrum Analysis results like that of a of the ELFP, being that you can calculate an equivalent static force being applied to the center of mass of a diaphragm after combining all the modal responses? I do not think so, have to dig through my dynamics book.
I have done 1 MRSA design at my current office that utilized RAM, and it has output for applied story shears, but not applied story forces while utilizing the MRSA procudure. Utilizing an ELFP in RAM, applied story forces can be found in the output. I would have to dig through the manual to see the difference in nomenclature. I think this is the issue with the DAM and MRSA results, the results from MRSA do not yield static forces that can be applied to the diaphragm and combined with other load combinations that can then be iteratively run to account for P-Delta and P-little delta. I need to dig through my Chopra book to recall how the results from a MRSA are found. Again I think that the results do not equate to a static force which can be easily combined with other applied forces.

I felt comfortable ignoring the P-Delta effect on the one job I did because the lateral system was CMU shear walls.

Let me know your thoughts, I will dig through my dynamics book tonight and see what I can find on the MRSA.

 

[KootK]

Free access to some of the excellent information that JoshPlum mentioned: Link

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

Sticks and Triangles -

The MRSA analyses start by calculating a response for each mode. Each individual mode could be represented by static forces.

Once the individual modal results are calculated, they are combined together using some statistical procedures (SRSS, CQC, or such) to give final results for the overall analysis. The combinations of modes cannot be represented by equivalent static forces.

It is technically possible to apply a P-Delta solution (with P-little delta) to each individual modal result first. But, you have to have good idea of the axial force in the members. That's why a geometric stiffness matrix reduction when based on a reasonable load combination for axial force will give you a good representation of the P-Big Delta result. However, it doesn't usually give you much information on the P-Little Delta component.

Note:
The P-Little Delta should be a small part of the overall effect on most structures. It's usually only moment frames with really slender columns where this starts to become a major issue. Or, maybe cantilever column structures.

 

[jochav5280]

Thank you all for your responses,

I will have to digest all of this in hopes of finding a solution. In speaking with the folks at SAP2000, they indicated that their program takes the results of the Modal Response Spectrum Analysis (MRSA), and converts it into an equivalent static load case so that the results can be combined with the Direct Analysis Method (DAM), which is essentially what I'm after as this is brain damage to complete manually in STAAD.

JoshPlum, in regards to Point-2 of your first post, I was trying to communicate that the resulting loads from the MRSA need to be used by the DAM to perform the structural analysis; I understand that the MRSA shouldn't be using a reduced stiffness from the DAM to determine it's results. Thanks for the resource, I'll hopefully be able to digest their recommendations and turn them into a solution. As mentioned initially, I'm tasked with assembling a "work instruction" for how to carry out a MRSA and perform the structural analysis using DAM to determine the design member forces.

Best regards,

jochav5280

 

[sticksandtriangles]

Once the individual modal results are calculated, they are combined together using some statistical procedures (SRSS, CQC, or such) to give final results for the overall analysis. The combinations of modes cannot be represented by equivalent static forces.

Mind explaining what you mean? Why do the combination of modes after SRSS or CQC lose equivalent stitic force representation?

 

[KootK]

When you perform the combination, you're fancy-averaging peak response values that do not occur at the same instant in time and do not nessecarily even have the same algebraic sign. The result is an envelope of response values rather than a single set of forces in equilibrium.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

Statics don't necessarily match up with a response spectra analysis. Meaning if you sum all the member forces and reactions at a joint, they don't necessarily equal zero. Also, the deflected shape you get from a response spectra analysis will also look odd. We wrote a couple of RISANews blog topics on the subject awhile ago.

http://risa.com/news/why-dont-response-spectra-reactions-satisfy-statics-risa3d/

http://risa.com/news/why-does-deflection-plot-response-spectra-solution-look-strange/

Now, if you extend that same concept, it explains why you can't replace the RSA analysis with a single set of equivalent static forces. Actually, you could certainly do this for a model that is controlled by a single mode. However, when the results for multiple modes are combined together statistically, it doesn't work.

You can come up with an statistically valid story shear for each individual level. But, that's not going to produce the same forces, reactions and displacements at the other joints.

 

[sticksandtriangles]

Thanks for the links Josh.

If one were to use the CQC method, I am guessing that the set of equivalent static forces could be utilized.

I know that the CQC method is quite conservative though.

Thanks!

 

[jochav5280]

Thank you JoshPlum,

So if I have to report foundation loads for an RSA to my foundation engineer, is it still okay just to give them the reactions from the RSA? Are there any implications for their load combinations when they run their foundation design?

Additionally, when would you use a single mode for an RSA? For instance, ASCE 7-10 requires 90% mass participation, so this would seem very unlikely to obtain in a single mode for most structures.

Wouldn't it be possible to determine the story shears at each level per the results of the RSA and then create an equivalent static load case that could be used to perform a P-Delta analysis with?

Lastly, could you comment on why/how use of the Geometric Stiffness matrix is a acceptable way for accounting for P-Delta effects, without actually performing a second order analysis. The document Kootk gave us a link to in his second post indicated this in a foot note on page-203 of the Engineering Journal portion. I understand that the main stiffness matrix is multiplied by this matrix to account for the axial softening effect produced by members with axial loads, however, I'm not understanding how this is an acceptable replacement of a second order analysis.

Many thanks in advance!

 

[JoshPlumSE]

So if I have to report foundation loads for an RSA to my foundation engineer, is it still okay just to give them the reactions from the RSA? Are there any implications for their load combinations when they run their foundation design?

This is one of the tricky parts about doing an RSA analysis. If you've got a moment frame, where one column should be in compression when the other one is in tension, the RSA results will not necessarily show that. The magnitude of each force is correct, but the relative signs of the forces may not be.

If you give the X, Y, and Z reactions for a single joint that should be fine. It's more conservative than what you'd get if you had run a time history analysis. But, that's not really possible with code design spectra.

Additionally, when would you use a single mode for an RSA? For instance, ASCE 7-10 requires 90% mass participation, so this would seem very unlikely to obtain in a single mode for most structures.

Generally you wouldn't, I was merely trying to draw a comparison between an individual modal result (which obeys statics and can be converted into equivalent static loads) and what happens when you use statistical procedures to combined multiple modes. That being said, you often have a case where one mode that dominates over other modes. Say you've to 75% mass participation for one mode. RISA (possibly other programs as well) allow you to use the relative signage of this dominant mode. Doing this will mean that your RSA results will approximately obey statics.

Wouldn't it be possible to determine the story shears at each level per the results of the RSA and then create an equivalent static load case that could be used to perform a P-Delta analysis with?

No. For all the reasons already discussed.

Lastly, could you comment on why/how use of the Geometric Stiffness matrix is a acceptable way for accounting for P-Delta effects, without actually performing a second order analysis.

A geometric stiffness adjustment will change the stiffness matrix of a member based on the loading in that member. So, the lateral stiffness of a member is reduced due to the presence of the axial force. That's the P-Big Delta effect. So, if you use a reasonable load combination, you will get a good P-Big Delta effect for the overall structure.

There are limitations to this, however. The axial force in the members used to reduce the stifffness is based only on the gravity loads. That's reasonable for overall frame behavior, but for unsymmetric structures it can miss localized buckling when say one column get a large compression due to purely from the RSA load. For reasonably symmetric structures, this is balanced out by a tension on another column, and the overall P-Big Delta effect is the same.

It also doesn't usually account for P-Little Delta effect. We'll call this the effect of member end rotation. The reason is that the end rotations that you see during a gravity load combination are different from the end rotations you see during a lateral load combination. Therefore, using a gravity load combination to estimate the change to the stiffness matrix doesn't really work for the little-delta effect of an RSA.