How to move floor response spectrum to top of steel structure?

[IstvanSz]

Hello All!

I am looking for some help in connection with the topic of floor response spectra.
I have a task that I need to generate a local response spectrum from an available floor response spectrum. I need to transpose the floor spectrum to the top of a steel structure where an equipment will be located. The total mass of the steel structure and the future equipment on top is way less than the mass of the concrete floor it is located on.
I have a bit limited tools and I don't have experience doing this before.
I would like to ask you to give advice if the method I devised is good or if it needs improvement at some points.

The general idea is to generate a transfer function, T(f), so that I can get the local response spectrum as LRS(f) = T(f) * FRS(f), where f is frequency, LRS is the local response spectrum and FRS is the floor response spectrum.

I have an FE software that can calculate free vibration, can apply response spectrum as loads and can run a dynamic analysis with acceleration time history loading.

I am planning to take the following steps:
1) Run a free vibration analysis

2) Generate several single frequency harmonic loadings as time history loads (i.e. a sine wave):
- in the set of frequencies where the sine wave is generated I would include several frequencies near the resulting Eigen frequencies of step 1), and include few in between the result of step 1)
- the length of the load would be 10-20 cycles

3) For a given frequency calculate a point of T(f) as T(f) = a.max.result / a.max.timehist, where a.max.result is the maximum measured acceleration of a selected point on top of the steel structure, a.max.timehist is the maximum acceleration in the time history loading.
If I am not able to get the maximum acceleration as an output from the software then I will calculate the point of the transfer function as T(f) = f^2 * d.max.result / d.max.timehist, where d is the displacement.

4) repeat step 2) and 3) in the other 2 directions also

Can this work?
What do you think, the ideal length of the loading sine wave is?
Would it be best to seek some kind of convergence of the a.max.result?

I guess it is a natural question why I don't generate floor spectrum compatible artificial time history loading instead of the method described above. No doubt, that would be shorter way, but I don't know how to do that. If you can help me with a step-by-step guide in that topic or if you could tell me about some software that can do it, I would really appreciate that too.

Regards,
Istvan

 

[TLHS]

Assuming you are doing seismic work, is this a small piece of equipment? What's stopping your from using the non-structural component portions of the code for the design work, with the associated height factors?

 

[IstvanSz]

Could you be a bit more specific? I am not sure I fully understand which seismic code you are referring to. I am mostly familiar with EC8.

 

[TLHS]

I believe this formulation for non-structural elements is in EC8. It's pretty typical across a lot of codes. The red term is amplifying based on an assumed relationship between acceleration at ground level to acceleration at height.

It's a quick and dirty (and not necessarily all that accurate in all situations) floor spectrum.

You'd have to review your code to see if your application falls into the situation where you are allowed to use these provisions.