Response Spectrum Analysis?

[Backcheckrage]

Hello community!

I have been reading the forums as well as my seismic design book regarding RSA. There are plenty of comments and literature on what to do with the results (i.e. scaling it based on some comparison of RSA shears versus some percentage of static linear static analysis shears).

But I still have trouble answering this basic question: What information does a RSA give you about your building model that a simple linear static analysis won't give you? In other words, why and when would anyone want to perform a RSA?

Thanks in advance.

 

[jdgengineer]

A linear static analysis assumes the response of the building is first mode dominant (inverted triangle). This is generally true for relatively short regular structures. Tall buildings, and those with structural irregularities have other modes that contribute significantly to the seismic response of a building (torsion or whipping). By using the linear static approach you are neglecting the contribution from these modes and therefore may be drastically under-designing your structure.

For a short regular structure, it's my understanding that a RSA analysis can achieve a more economical solution. As the analysis is more thorough the code allows you to peel back some of the conservatism in the linear static approach. ASCE 7-05 allows you to design for forces as low as 85% of the linear static approach when the RSA approach is used. While depending on your structure you may not end up with lower forces in some instances you will. Other codes, such as ASCE 41, have no such limit and allow you to design only including the RSA approach even if the forces are significantly lower than the linear static approach.

Hope that helps.

 

[Backcheckrage]

Thanks for your reply, jdgengineer.

It appears to me if I am going to perform any 3d computer modeling of a building, I might as well perform an RSA because it is easy enough. According to my local code (New Zealand), I have to use at least 80% of the static analysis for my RSA (i.e. 0.8*V_s / V_rsa is my scale factor when running my RSA). So would it be true to say that a RSA only distributes this vertically in a more realistic matter compared to the first mode, this means I have to increase the number of modes ETABS uses to analyze the model in the Dynamic Analysis Form. Any thoughts on this?

I do notice that my particular software (ETABS) does NOT permit a non-linear RSA. My situation is that I have compression struts within an infilled frame structure... I suppose I could artificially reduce the stiffness of the "tensioned" members to trick the program into using compression only, this just seems hokey. Does anyone have thoughts on this?

Modeling is fun! Yay box shaking!

 

[jdgengineer]

I agree if you are doing computer analysis you might as well use RSA. As different frequencies of vibration excite different modal masses your distribution of forces (vertically and horizontally) and total force will be different between this and the equivalent force method.

Per code requirements you need to increase the total number of modes in order to meet your minimum modal mass participation (90% in asce 7-05)

I could be wrong on his, but I don't believe RSA theory applies to nonlinear systems. RSA is essentially taking the linear response of the different fundamental frequencies of vibration and adding them up to determine the total response. For nonlinear analysis one typically uses a pushover curve (nonlinear static analysis) or time history analysis (nonlinear dynamic analysis). Both of these, to an extent, can be done in ETABS. Although Perform would bet the more common software for this.

 

[JoshPlumSE]

JDengineer is correct. RSA theory only applies to linear systems.

I have used the "hokey" method you describe.... But, only for pairs of braces. Essentially, I just use 50% of the stiffness for each brace in a tension / compression brace pair. That way, the lateral stiffness of the structure is constant and I can do an RSA analysis. Now, I will generally need to design the brace for twice the force that I get out of my analysis. But, otherwise, the analysis should be pretty good.

 

[Backcheckrage]

That makes too much sense, JoshPlum. Thanks for the tip.