walking induced Vibration of an elevated theater balcony
walking induced Vibration of an elevated theater balcony
(OP)
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Design guides for simple beams and simple floors are available. In these simple beams and floors, modeshapes are in the vertical plane and are related to static deflections under gravity loads. Latest practice is to limit accelerations to some empirically determined values.
In balconies(usually large slope) gravity loads introduce sways too and modeshapes take on those sways. Design guides do not help much then
Is there a general finite element method, eg apply a dynamic load somewhere and study accelerations.
Can you point out some printed reference?
respects
IJR
Design guides for simple beams and simple floors are available. In these simple beams and floors, modeshapes are in the vertical plane and are related to static deflections under gravity loads. Latest practice is to limit accelerations to some empirically determined values.
In balconies(usually large slope) gravity loads introduce sways too and modeshapes take on those sways. Design guides do not help much then
Is there a general finite element method, eg apply a dynamic load somewhere and study accelerations.
Can you point out some printed reference?
respects
IJR






RE: walking induced Vibration of an elevated theater balcony
RE: walking induced Vibration of an elevated theater balcony
RE: walking induced Vibration of an elevated theater balcony
1. Model the balcony as accurately as you possibly can with the time you have.
2. Assign your absolute best guess of the mass to the shell elements, nodes, members, etc.
3. Run the modal analysis to get the first few natural frequencies--say 10-15 of them up to maybe 15 Hz. You'll have to somehow determine which of these modes would give the maximum acceleraiton if excited at resonance. This isn't easy in most cases. Look for modes that have the entire balcony deflecting up and down like a diving board. Depending on your balcony, you might be able to find it visually.
4. Apply a sinusoidally varying load to represent crowd motions. Compute the psf of humans that are assumed to be moving--this is like wp in DG11 Table 5.2. How many are moving? Your guess is as good as anyone's. Determine the applicable type of load from DG11 Table 5.2 and which harmonic of the load can match the natural frequency from Step 3.
For example, if fn=4.5 Hz and you are designing for a lively concert, the second harmonic causes resonance if the forcing frequency (equal to the first harmonic freq) is 2.25 Hz, making the second harmonic frequency 2*2.25 Hz = 4.5 Hz. Say you've determined that you think you have 15 psf of moving humans over some portion of the balcony. Your sinusoidal load has an amplitude of (15 psf)(0.05)=0.75 psf using the dynamic coeff from Table 5.2 for second harmonic of lively concert loading. Create a sinusoidal load of 0.75 psf that has a frequency of 4.5 Hz.
5. Run a time history analysis using the load from Table 4. Set the time stepping increment to something like 0.01 to 0.005 sec.--just something fine enough that your sinusoids don't have their peaks chopped off. Set the damping ratio to 0.06 per DG11 Secton 5.2, last paragraph. Run the analysis for as many seconds as you think a crowd could keep up a very synchronized movement. I'd pick something like 4 sec. With a damping that high, it won't matter much anyway if you pick 3 sec. or 10 sec.
6. Compare the peak acceleration from Step 5 to values from Table 5.1.
RE: walking induced Vibration of an elevated theater balcony
That was a very helpful post.
When you assign masses, what percent of live load do you assume, 10%?
respects
ijr
RE: walking induced Vibration of an elevated theater balcony
For mass calculations: consider the actual weight of everything attached to the slab. This includes people (assume 168 lb / person) at the actual seat spacing.
For load definition: consider the assumed number of people participating in the synchronous movement. For example, if you assume 50% participation and the total weight of humans is 15 psf, then you'd have 7.5 psf going into the load calculation.
RE: walking induced Vibration of an elevated theater balcony
One probably could get a better guess at the % from someone who frequents concerts than the average structural engineer or even vibration specialist! I wonder if any eng-tips members are frequent concert attendees...
RE: walking induced Vibration of an elevated theater balcony
RE: walking induced Vibration of an elevated theater balcony
Keep in mind that someone might run like heck down the stairs also and that causes a lot more trouble than walking on a flat surface.
RE: walking induced Vibration of an elevated theater balcony
Walking induced vibration governs because the balcony will not be subjected to rythmic activity, but has a long front aisle, and it is a long span structure(30m,100ft) with limited girder depths(architectural needs). When people walk on the aisle, I am going to have trouble given my shallow girders. I would like to handle that.
The balcony however, having modeshapes that include a large lateral sway(sway on plan), seems to need analysis that you recommended, as an enhancement to DG11. I remember reading Farzad Naeims notes some time and he mentioned how bad x/y vibrations can be to someone sleeping and thought I should consult friends here, before blindly using DG11.
(And under this balcony, there will thousands of lights, shadows caused by them may amplify any small movement significantly and are likely to cause additional sensitivity).
respects.
IJR
RE: walking induced Vibration of an elevated theater balcony
Sorry, but don't know what is DG11 Table 5.2...can someone attach it?
Thanx
PS: Additional star for 271828 for his very helpful posts.
RE: walking induced Vibration of an elevated theater balcony
http:/
Worth having in the collection if you want to look at vibrations for less complex systems then discussed above.
e- Oxford, Martin Williams and his mob were doing some research into crowd behaviour in stadiums, as well as damping by passive people. I don't know whether this is published yet, might hold the key to the percentages, but again might not. Do you know when/if any publications have come of this?
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