Another vibration question

[Lion06]

I am doing a vibration analysis of a wood floor system supported by a concrete wall at one end and a WF at the other. There are currently (2) support columns that need to be moved to increase the clear span from 15' to 25'. I have the strength/deflection issues worked out, but I'm concerned about vibrations. This is a basement girder that supports the first floor, and a bearing wall supporting the second floor. The attic and roof span exterior wall to exterior wall (i.e. the interior wall is not a bearing wall). The issue I have is that DG #11 (obviously for steel) talks about how vibrations in floors is a bay phenomenom nad not applicable to individual beams. Does this hold true for wood floor systems?
Here is the approach I was going to use, please feel free to comment and let me know your opinions.

1. I have a few papers on vibrations in wood floors, but they're not nearly to the technical level of DG #11. I plan to follow them, but add additional criteria. The first criteria in the one paper is to keep a fn>14Hz. The equation given accounts for the joist and girder, but just one joist - it doesn't give an approach for considering the entire floor. I would think that this would be conservative given that you are only counting on the stiffness of one joist. Do others see it this way, too?

2. I also intend to determine an acceleration based off of the frequency of the floor per step 1.

3. I am going to determine the frequency/acceleration of the WF alone to verify it's within acceptable limits.

Does anyone have any other recommendations?

 

[Tmoose]

resonant frequency of SDOF systems is related to static deflection.

15 Hz ~0.04 inch or 1 mm

http://www.veco-ny.com/theory.htm

 

[Lion06]

tmoose-
That depends on the length of the member and what is supporting it.

 

[ishvaaag]

I would proceed in the following way.

I would make a model of the substructure of interest in RISA 3D or ETABS. If only the floor substructure is of interest, you may model the joists pinned at one end and supported in the girder at the other, itself simply supported. Create an hypothesis for the participating mass for the case; usually would be the weight of the people to be moved by the vibrating force, so a fraction of the live load, say from 0.1 to 0.3 of LL for rooms but might be the full live load for a big hall. Make a dynamic analysis.

From there you have your fundamental frequency, that would meet requirement or not. I think for myself a fundamental frequency bigger than 14 times a second is a very stiff structure. Since men usually impart the dynamic significant loads through the feet, it is quite unlikely they will constitute a forcing vibration agency of frequency very far apart from 1 Hz as much, 1 time per a second. You can't jump 5 times a second, sorry. So, the enormous difference between the natural frequency and the forcing vibration makes statistically the magnifier impact factor negligible, 1.004, an IMPACT factor that would magnify a static load of the value of the participating mass, easily seen for almost all cases where the participating mass is less than 100% entirely subsumed in other hypothesis with ordinary safety factors.

1 mm deflection under significant live loads... it is unlikely that except on sturdy concrete floors/slabs or purposely built structures for such behaviour be seen. This is simply too stiff to be generally economical.

Say now you are not restricted to some specific natural frequency. The same process above described can get for you an impact factor, itself a function of ratio of the frequency of the forcing vibration to the fundamental frequency f1 of the structure. Hence, if your forcing vibration is very close to the natural frequency you may get an impact factor of say, 6, and then the hypothesis of vibration being considered may overcome the requirements of strength and deflection and be the controlling one, forcing a redesign of the structure to make it more stiff, and hence, have a lower impact factor.

For these general concepts

Structural Dynamics in Practice
A quide for professional Engineers
Arthur Bolton
Mc Graw Hill International UK 1994

I found enlightening.

What above doesn't adress the comfort issues, that must be tackled by any normative or tecnical text. The well known text of Tamboli on steel structures has at least a quite good chapter on this.

 

[BAretired]

The National Building Code of Canada has a simplified static analysis method of calculating vibration-acceptable spans for wood joists. It considers subfloor sheathing thickness, bridging and method of connecting sheathing to joists.

BA

 

[ishvaaag]

More on what I have labeled above an Impact factor (and behaves like that)...

It is really named the dynamic magnifier, a value that gives the ratio of amplitudes of vibration when the force is applied at some forcing frequency to statically. So it applies only to the force being applied rythmically (what causes the deflection amplitude), that, by the way, need not necessarily coincide with the weight of the mass vibrating conjointly with the structure (you may have people dancing and seated, or people within a building and wind vortex shedding ryhtmically outside, or a boy pulling the top of a pole with a given mass atop at different frequencies. So one thing vibrates with the structure and takes part in the determination of the natural frequency, and the usual assumption is other part constitutes the actual force imparting vibration.

For vertical live loads such in a dancing room such separation is not entirely clear since for sure some people will be quite static, some others will have taken full contact with the floor and transmited to it all their fall energy not preserved in their muscles as spring deformation, and some others are just about to make contact; these will have to move not only the seated people and the structure but also those that are at that moment in contact with the floor. Everything in contact with the floor has to be vibrated and so takes part on the determination of the ongoing natural frequency. These niceties and of course following the true course of the dynamically acting forces and reactions are summarily dispatched by assuming some part of the live load being applied at some forcing frequency; this is of course a simplification, and so examining a range of other forcing frequencies and mass participation should be a cautionary sound practice.

For actual structures following numerically the process of the effect of the dynamically applied loads at given times, rythmically or not, there's structural software (with some usual simplifications in the structural field) and I have some even from the DOS era in 5 1/4" floppy disks. I however only perused them (was a family of programs) because my practice rarely touched (and touches) these problems, for we are accustomed here to stout RC structures and except for those that meet a specific case in their practice, the stiffness is such that vibration is not a controlling problem.

Furthermore, other than earthquake effects and fatigue cycles, the codes were only aware of vibration for walking bridges, and only recently 2005 to present or so vibration figures in the general building regulations in express way.