walking induced Vibration of an elevated theater balcony 7

[IJR]

Pals

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

 

[ishvaaag]

I have in some 5 1/4 floppy disks some DOS programs of the eighties called dynamics or so, a set of programs that solved what happened to structures when a set of loads function of time were acting, both 2D and 3D. Maybe GSTRUDL also had this ability, and maybe SAP 2000 has some way to enter loads a function of time. More complex FEM packages surely will have (ANSYS, ABAQUS, MSC Nastran). In Visual Nastran 4D I think you can also enter F(t) forces, maybe I am wrong. Except for the strong FEM programs I think most will be unlikely to have some input or intelligence within (better) to ascertain how standing variable loads may be affecting the vibrations; in ANSYS and alike you may find how but surely requires competent use of the program.

 

[Lion06]

What I've typically done is modeled the floor system with nodes every foot or so. I then put mass loads at every node representing the actual DL and LL (per DG#11 or similar). The dynamic analysis will give you the period for the first 10 or so modes of the system. You can use that to get the frequency. Then use DG #11 to get accelerations based on that frequency.

 

[271828]

Yes, you can use a FEA program for this.

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.

 

[IJR]

27128

That was a very helpful post.

When you assign masses, what percent of live load do you assume, 10%?

respects
ijr

 

[271828]

Sorry, I wasn't clear. It's not even quite that simple.

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.

 

[271828]

Forgot something else for load definition. You might even consider the spatial distribution of people bouncing. For example, you might have 50% of people bouncing in the front, middle 1/4 of the balcony and 25% or less around the perimeter. To my knowledge, there is no data available on what % to use here or there, but common sense tell us that there is some distribution--a lot of folks don't participate or stay synchronized. For now, judgment is all we have for this part. Then again, how accurately do we know wind or seismic loads, LOL.

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...

 

[SteveGregory]

I think IJR was asking about walking induced and not rhythmic induced vibration. Correct me if I am wrong, but I think that in this case you would use 0% of the live load for the mass (worst case) and 65 pounds for the walking excitation force.

 

[271828]

Not sure why anybody would care about walking in that situation, but if that's to be evaluated, then let me know, IJR, and I'll type how to do that using FEA.

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.

 

[IJR]

271828

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

 

[drile007]

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.

 

[rowingengineer]

DG11 is the design guide published by AISC

http://www.aisc.org/store/p-1556-design-guide-11-floor-vibrations-due-to-human-activity-see.aspx

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?


Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it