vibration for dancing and concert

[MDjajasaputra]

I need to do vibration analysis for dancing and concert. Attached is my problem.

Structure consists of the following
- big trusses at lines A and B (L span = 6x28ft) with support at line 1 and 7.
- 7 columns at line C
- 7 lines of trusses spanning between big trusses and columns at line C
- Floor loads supported by filler beams and then transferred to trusses.

I'm thinking to simplify my problem assuming a bay of 168ft (= 6x28ft) by 70ft with trusses at line 1 to 7 as a beam and big trusses at line B as girder. I will follow the design guide 11 procedure with these assumptions. Is this the right approach? Need some inputs. Thanks.

 

[Lion06]

I think that is a reasonable approach. I would make sure you account for the filler beam deflections in the frequency calculation even though you're not technically using it in your slightly adjusted bay. I would also make sure you account for the increased deflection of a truss when using the conventional deflection equations - I believe using 0.85Ichords with the standard deflection equation properly accounts for the shear deformations that are more pronounced in a truss.

I did vibration looks for similar framing not long ago - it was 20' deep trusses spanning 140' supporting two floors. I will just say that it is exceptionally difficult to get the trusses stiff enough to work for vibrations. I'd be interested in your results when you work through this.

 

[MDjajasaputra]

Thanks StructuralEIT - Did you use transformed moment of inertia? Just trying to figure out to calculate the composite section properties for the trusses. How did you do yours? DId you do finite element model? Thanks for your input.

 

[Lion06]

I did a hand calc to get the I of the truss (including the composite slab), then reduced it appropriately to account for the truss (I think it is a 0.85 factor). Then I used RAM Advanse to model the floor. For the truss I input a generic beam section with an I to match the I from the hand calc. I did this because in order to do a dynamic analysis you need to break the members into small sections and apply mass loads along the length. Mass loads can't be applied to member, only nodes; so in order to approximate a uniformly distributed mass load I break the members into roughly 1' sections and lump the masses at the nodes. This works pretty well. This makes it very time consuming to model a truss in this fashion, which is why I made a custom section with the appropriate I, but as a beam section.

 

[MDjajasaputra]

For the transformed section - you just use the top and bottom chord of truss plus the slab with beff = min(spacing, 0.4x span length). Correct?
You use the FEM program to get the natural frequency? My first time to do this kind of vibration analysis. What size of the top and bottom chords do you use?

 

[Lion06]

Yes, I used RAM Advanse just to get the natural frequency. I then used that along with DG #11 to get an acceleration. I did use the effective slab width along with the both chords, but I was supporting a floor on two levels. I would limit beff to what you show, but limit the span length to the panel point spacing otherwise you can end up with a huge beff that is unrealistic.

I sized the chords based on strength, while neglecting the composite slab action. We weren't counting on that for strength, but you can count on it for vibrations even if it isn't a true composite slab because the loading at which vibrations are considered is much lower than ultimate strength levels and deck welds and friction will do the trick. I had very heavy W14's for the chord. Somewhere in the nieghborhood of W14X500 (I don't think 500 is a real weight, but it was VERY heavy).

 

[MDjajasaputra]

Did you have your frequency > fn required? I think we need to have the natural frequency to be above the frequency of the activity in order to use the design guide formula.

 

[Lion06]

No, fn,required is based on an initial acceleration limitation. There are two components to the vibration check. The first is resonance. You need to ensure that fn is high enough to not be in resonance with the first (and possibly the second) harmonic of the activity that you're designing to. I don't remember off the top of my head what it is for dancing.
The second is accelerations. The acceleration needs to be checked regardless of fn. It is a function of fn and of the forcing function (somewhere in the neighborhood of 7psf for a lively concert) - which I believe to be a bit conservative for your condition (and the condition I was dealing with). I believe it's difficult to get 7psf acting together over such a large area.

I'm surprised we haven't heard from 271828 yet. He must not have logged in recently. He is the resident vibrations expert.

 

[rowingengineer]

While i have no comments on the fn or a, I would recommend inculding foundation stiffness in your modelling.

When in doubt, just take the next small step.

 

[Lion06]

rowing-

Do you have any papers that sugges this? For a truss this long, with this much load at full service level loads, I would expect to see piles or some other deep foundation for which the stiffness would not be an issue.

 

[rowingengineer]

StructuralEIT,
The design guide 11 has a small but significant revision can't remember when it happened now, but for rhythmic excitation column deflection and foundation parameters were included in the basic equations. If the building has deep piles these need to be treated as columns and included in cals. My rule of thumb is if you have column/pile lengths in excess of 15m then you need to included this deflection, more from experience than anything.






When in doubt, just take the next small step.