Vibration of Dance Floor 1

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 members, unless a heavy ceiling and/or unusual ductwork is present. For live load, the Guide recommends 11 psf for offices and 6 psf for residences.

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.

271828-

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.

sgdon,

A few words of caution here.

The majority of comments posted here have been from an office/domestic point of view. While the fundamentals are still the same the specifics are completely different.

The major issue with dance floors is that the excitation is caused by a large number of people dancing to the same beat(i.e. the same frequency), as opposed to offices where the excitation is usually due to a very small fraction of the live load (one or two people).

I agree with miecz that zero live load should be included as there could be no stationary people/furniture to provide this (they could be all jumping up in the air at the time).

I have read an article on the excitation frequencies for modern music and I will see if I can find it for you. This will be a completely different frequency to those that are critical for an office.

It is worthwhile to note that in this situation, it will likely be vibration that will drive the design, and strength should be checked after you reach the optimum solution.

Good luck.

Guys, look at DG11 Page 38 and the subsequent examples.

Including 0 psf in the natural frequency calc is unconservative and wrong.

"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%."

Follow-ups like this one make me wonder why I bother. Sorry I'm a little grumpy, but I spent a fair amount of time typing that first post and it was apparently either ignored or disregarded as wrong.

AGAIN: estimate the mass of the people who will be on the floor. This will be different depending on the occupany (a kindergarten dance room versus a banquet for sumo wrestlers, for example).

Read Design Guide 11. It spells out most of what is needed.

Hi 271828

Your effort in response is definitely appreciated and definitely not gone unnoticed. Thanks also to the rest who are willing to share your knowledge and experience in this tread, or others in the Forum.

I am not able to get hold of DG11 or Design Guide 11 in my office. But i am able to extract very valuble information from this tread.

Cheers

sgdon,

You cannot check anything against vibration unless you have a reference such as DG11. You should not be trying to do this without it. If you know a member of the AISC then you can get them to download it from the AISC website.

271828,

It surprises me that they do suggest using some live load, obviously the authors havent been to as wild concerts as I have!

csd72, I think part of the reason is that the excitation is the 2nd or 3rd harmonic, not the first. This is only my guess, though.

Agreed about DG11. Get it, get the SCI DG, or don't do this. DOing this project without one of these is exactly like trying to design a steel bldg without a steel spec.

csd72, well, after thinking about it an hour or so, I'm sure I know why the LL is included in the fn calcs. Think about it this way. Say the floor response is mostly from the mode with a natural frequency of 7 Hz. The worst case is if the crowd bounces at 7 Hz / 3 = 2.33 Hz (7 Hz / 2 = 3.5 Hz is too fast for most activities, although not all of them). That means the floor is vibrating up and down 3 times in the amount of time it takes for the crowd to land and leave the floor. They ARE on the floor for some of the cycles, although not all of them.

The whole subject of structure - human interaction is a very difficult one and I can only think of a few (mostly poorly done) experimental studies done on the subject. In this case, the actual answer is far more complicated and I doubt that anybody really knows it. The best thing to do, in that case, is just include the mass of the people.

Now I feel better, LOL.

According to Equation 5.1 of DG11, the minimum natural frequency increases with participating live load. Simply stated, Eq. 5.1 says "the more dancers you have, the stiffer your floor needs to be", which is what you would expect. Though DG11 is not clear on this, I believe that non participating dancers, and furniture, should be included in w[sub]t[/sub], but not in w[sub]p[/sub]. The more total weight you have, w[sub]t[/sub], the lower your natural frequency is, and the lower it needs to be. Looking at the formulas, it seems to me that it would be conservative to estimate the non participating dancers and furniture as zero.

The floorvibe demo may help to do your prelim:

miecz, it's always a tradeoff between the following:

Higher mass --> lower fn --> higher excitation forces and it's easier to actually hit resonance.

Higher mass --> a=F/m, so lower acceleration FOR THE SAME force.

Just have to run the calcs to be sure. It is definitely not always conservative to exclude mass in these calcs. I'm *almost* completely sure it's always conservative to include the LL.

Every calc I've ever run got better with higher fn.

Anyway, the answer, like csd72 typed, is to get a copy of FloorVibe. It's also possible to use ETABS, SAP, etc., but that requires quite a bit of specialization in the subject.