Question about Response Spectrum Analysis 1

[3doorsdwn]

I have a structure where I am attempting to do a response spectrum analysis (as per the code: ASCE7-02 in this case). For the force at each level (i.e. the vertical distribution), ASCE7 gives the following equation (on p.151): Cvx=Wx(?xm)/?Wx(?xm). Where Wx=weight at each level/node; ?xm = displacement amplitude for a structure (on level x) in a orthogonal direction vibrating in its mth mode. To me, the most logical thing to do is to just use the weight of the whole floor and the average of the displacement amplitude(s) (?xm) for each node (and mode) for each orthogonal direction. (And then combine the results as per the SRSS or CQC method.) It doesn’t make much sense to find the tributary mass for each node at a level (where there may be hundreds of nodes) and then combine all that with the amplitude, when you would probably get just about the same thing using an average.

Thoughts?

 

[UcfSE]

"Nodes" is not listed in this equation. The lateral deflection at a given x^th level will be the same at any node in that floor, so I don't know what you're referring to. Remember that modal analysis is analyzing a MDOF system using SDOF system tools, so you only have one "node" per floor or level where the lumped mass is located.

If you have any periods that are close together, i.e. more than one dominant mode, you may get less than good results from SRSS. If you have time I would check CQC along with SRSS. Calculating the sum of the absolute values would provide an additional sanity check as an upper bound to your results.

In general, if you have a new idea, give it a shot and compare it to the traditional or "known" method for several cases. Maybe you'll stumble onto something good or helpful.

 

[3doorsdwn]

""Nodes" is not listed in this equation. The lateral deflection at a given xth level will be the same at any node in that floor, so I don't know what you're referring to. Remember that modal analysis is analyzing a MDOF system using SDOF system tools, so you only have one "node" per floor or level where the lumped mass is located."
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That's kind of what I am referring to here: in any FEA model of a building you are going to have a great deal of nodes per floor. So if you (logically) decide to calculate the mass for the whole floor (rather than the tedious task of figuring the attributable mass to each node) you have to decide which amplitude to use for that level. And that is what I was trying to decide: using the max. or the average.

"If you have any periods that are close together, i.e. more than one dominant mode, you may get less than good results from SRSS. If you have time I would check CQC along with SRSS."
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Right. Two consecutive modes are considered closely spaced if their corresponding frequencies differ from each other by 10% or less (of the lower frequency).

 

[UcfSE]

Are you getting significantly different lateral deflections at your floor levels for each node?

What does your mode shape matrix [φ] look like?

Either way, if your max is similar to your average, it may be good enough to pick one and proceed.

The point I was trying to make about modal analysis is you are already assuming an SDOF for each mode. So there is no consideration for deformation at each node; there's only one per floor and only one degree of freedom per mode (per orthognal direction). You should be able to get the properties you need from your model (T,[φ]) and the seismic weight and then go to the code and calculate your load effects and put those back into your model and check it.

 

[3doorsdwn]

I’d have to say there isn’t a great deal of difference between the amplitudes for the nodes. As you said: it may be logical to use an average (especially if it is close to the max.).

Thanks.