vibration of dance floor

huangyhg

vibration of dance floor
i have seen people adding some percentages of live and superimposed dead loads to the mass of the floor. the model is then run (in etabs) to obain the eigenvalue, i.e. natural frequency. as we know natural frequency is not a function of external loads, what is the rationale of considering the live loads here?
thanks  
below is an excerpt from aisc design guide 11, which talks about magnitude of live load used for vibration analysis:
the supported weight, w, used in the above equations must
be estimated carefully. the actual dead and live loads, not the design dead and live loads, should be used in the calculations.
for office floors, it is suggested that the live load be taken as (11 psf). this suggested live load is for typical
office areas with desks, file cabinets, bookcases, etc. a lower value should be used if these items are not present. for residential floors, it is suggested that the live load be taken as 0.25 (6 psf). for footbridges, and gymnasium and shopping center floors, it is suggested that the live load be taken as zero, or at least nearly so.
thanks prsconsultant. at least, now i know what i see is a valid design procedure. but what is the rationale? by adding live loads to the mass of the structure, are we not artificially altering the true natural frequency of the structures?   
aisc criterion requires a close estimate of the natural frequency of the floor system under everyday loadings.
the guide recommends that the fundamental natural frequency
of the floor system be calculated using the beam (or joist) and girder deflections due to the weight supported. the dead and live loads used to calculate these deflections will significantly affect the estimated natural frequency.
a floor system will not exhibit annoying vibrations when fully loaded; problems occur when the system is lightly loaded. (for example, a number of problem floors have been reported in schools, not during the day when the children were there, but after school when only one or two people were in the classroom.)
the guide recommends the dead load should be estimated as 4 psf plus the weight of the floor deck and supporting   
here is a link to some additional information on effect of floor live load & damping on vibrations.
prsconsultant, i agree with a lot of your info, but will respectfully disagree about some of it.  you're typing mainly about office floors.  dance floors are a little different.
we need the ll for two separate reasons.  first to figure out the dominant natural frequency (big difference between this and the fundamental freq when one's using a program like etabs for this purpose--more on this later) in the bay that's being checked and then to determine the sinusoidal load to represent the activity.
to get the natural frequency.  the mass in etabs should be the absolute best estimate of the dl mass plus the realistic number of people who will be on the bay.  i asked one of hte ultimate authorities on floor vibe this question once and was told to estimate the weight of people on the area and smear that out as a uniform mass in the model.
use ch. 5 to get a sinusoidal uniform load.  it gives enough guidance to figure out how to use the *best estimate* live load from people (i.e. the one in the previous paragraph) to get this load.
now onto the big problem with using fea for an analysis like this.  etabs will probably spit 10 modes at you, all different because various bays are popped up instead of down, etc.  say you are checking one specific bay in the floor.  it is almost always totally impossible to look at the freq and mode shapes and figure out which one of these modes causes the bulk of the response to activity in that bay.  the *only* way to approach this problem is to use the program to predict the frequency response function.  sap2000 calls this type of analysis a "steady state" analysis.  it gives the frf magnitude or phase over a given frequency bandwidth.  look at this frf for load and accel measured in the given bay and *hopefully* one of the bays will have much more response than the others.  the lowest one that has significant response should be considered the dominant natural frequency in that bay.  you really cannot tell which mode to use without doing this.  before someone calls me out on the use of dominant natural freq versus dg11's "fundamental freq," dg11 uses a single degree of freedom approximation.  there is only one natural freq in that case -- fea is a totally different ballgame in this regard.
after you figure out which mode to use (in each bay--they'll probably be different), apply the sinusoidal uniform load and run a time history analysis to get the acceleration at whatever location you care about on the floor.
beware: this stuff gets pretty hairy.  fea for vibration is nothing like fea for strength and stiffness.  seemingly insigificant assumptions have very extreme effects on teh outcome.  to be honest, nobody really knows the *right* answer to lots of these questions, so it takes experience running analyses and testing the bldg to get an idea whether your assumptions are ok.  
the latest uk sci dg on floor vibrations has updated methods for doing this stuff.  keep in mind that dg11 is great, but it's 11 years old.  i'd say that more floor vibe research has been done in the last 7-8 years than in the entire time before 1997, probably by a fairly sizeable factor.  the sci dg was released about 6 months ago.
to get a real feel for the driving frequency on a dance floor, find your local royal scottish country dance society (rscds).  bring a stopwatch to one of thier balls, and you may see a couple of hundred dancers all rhythmecally jumping in the air and landing simultaneously.  if you look closely, you'll not only see the floor flex, you may even see the walls flex!  there is only a narrow frequency range in which dancers can jump up and down.  it doesn't matter what dance style (i've done them all), as it's all driven by gravity.  ask the band leader the range of possible rhythms, but keep in mind that dancers don't step to each beat of the music.
miecz, that's an interesting idea--rscds.
i worked on a project a few years ago that was a ballroom with a vibration problem.  if the folks danced at a specific beat, the floor moved up and down enough to open and close doors on the story below due to the air pressure changes!  
i also worked on a really funny one about 18 months ago.  it was a 100' cantilevered balcony which had a natural frequency of about 2.5 hz.  an un-named country/gospel band was there and played their signature song, which had a beat of about 1.25 hz.  people stood and clapped, but they bob once between each clap, so were right on the natural frequency.  usually, floors vibrate only 0.01-0.02" at the most, but this was enough to very clearly see on the audience cameras.  i'd guess it was moving about an inch, maybe two.  
resonance is the most awesome physical phenomenon i can think of.  i was able to stand out on the balcony tip with a metronome and bounce gently at the natural frequency and one of my pals was about 250' away, also on the cantilever tip.  he said the acceleration was uncomfortable all the way over there, probably 1-2%g.  i think it's beyond amazing that a 180-190 lb guy can get a multi-million pound structure moving that much.
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interesting stories. wish i could have been there to feel it myself.
thanks all for the valuable inputs to this tread.
i think to put it simply, the inclusion of a certain percentage of live load is to assume that these group of people are not atationary while the rest which are dancing will cause the excitation frequecy. we should then avoid the resonnace of frequency.
now, following this, any people has any knowledge what will be a good percentage of ll to be used then. (previous posts or guidance quoted seem to give absolute values only). in my analysis, i have adopted 25%.
  
  
if the question is, what percentage of the live load on a dance floor is stationary, the answer is, without question, zero.  any furniture, and the few resting dancers, will be at the edges of the floor, where they will have little impact on the natural frequency.