Vibration Analysis for cantilevers
Vibration Analysis for cantilevers
(OP)
I'm doing a vibration analysis for a cantilevered floor system. I'm using software to model the floor in order to get the fundamental natural frequency and using that along with Design Guide 11 to determine the accelerations.
My question is this - would you determine, for the DL and LL suggested in DG 11, the inflection point and use composite section properties for the positive moment portion only? Would you only count on bare steel for everything (I realize this is the conservative route, but I'm trying to be as accurate as possible so I don't get very deep beams)?
Would anyone count on the WWR in the slab and determine the cracked I of the "composite" beam to get an increased I for the negative moment portion? I know we would never do this for strength, but the loads where vibrations are considered are so low that it doesn't seem completely unreasonable.
My question is this - would you determine, for the DL and LL suggested in DG 11, the inflection point and use composite section properties for the positive moment portion only? Would you only count on bare steel for everything (I realize this is the conservative route, but I'm trying to be as accurate as possible so I don't get very deep beams)?
Would anyone count on the WWR in the slab and determine the cracked I of the "composite" beam to get an increased I for the negative moment portion? I know we would never do this for strength, but the loads where vibrations are considered are so low that it doesn't seem completely unreasonable.






RE: Vibration Analysis for cantilevers
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RE: Vibration Analysis for cantilevers
That beig said, it should give you some idea about to model the stiffness of the beam for composite or non-composite behavior.
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
Does that sound right?
RE: Vibration Analysis for cantilevers
An expert is a man who has made all the mistakes which can be made in a very narrow field
RE: Vibration Analysis for cantilevers
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
An expert is a man who has made all the mistakes which can be made in a very narrow field
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
An expert is a man who has made all the mistakes which can be made in a very narrow field
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Vibration Analysis for cantilevers
1) I believe the reson why you use the transformed area for the entire length is because the amplitude of vibration is assumed to be very small. Meaning that the friction resistance of the slab/steel interface is enough to ensure composite behavior. We're talking serviceability considerations, not ultimate failure loads.
2) The design guide has additional criteria that you'll want to look at (minimum stiffness and such). I do not believe these are covered in that early (1977-ish) paper. But, the design guide will cover them.
RE: Vibration Analysis for cantilevers
Josh is right about his #1 and #2 in the post right before this one.
I'd be hesitant to use a program to get the frequency and then plug that into the Chapter 4 acceleration equation. That equation has lots of assumptions in it that don't apply here. Like the effetive mass being W for example--that's for a sinusoidal mode shape. There's also the R=0.5 adjustment factor embedded that helps to create 65 lb.
There was a NASCC 2010 presentation by Davis and Murray that showed a finite element method. It's not the only such method out there. I'd go that route. Do a time history to predict the acceleration.
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
Thanks for the input - much appreciated, as always.
I wasn't intending to use the method from the 1977 paper, just the fact that it says to use the composite section along the entire length.
I took a look at the presentation by Davis and Murray. It looks extremely involved. There were a few things I wasn't clear on, as well. I looked at the slides only, and did not listen to the presentation.
Some things of note:
1) It recommends modeling the slab as a shell element. I've typically only modeled the composite beams, and left the slab out.
2) The increased EI of spandrels (by a factor of 2.5) to account for stiffening from the cladding was interesting.
3) It recommended modeling of the entire floor. This seems onerous, since every single node needs to be assigned mass to evenly (and accurately) distribute the mass.
4) I had a hard time extracting what the footfall force should be. The state it should be a function of bodyweight (168 #), but I wasn't able to find out where they ran through the calc and come up with a number. One of the graphs seemed to show +77# or -110#.
5) I didn't see anywhere that it talked about the "real" effective mass to use.
RE: Vibration Analysis for cantilevers
Once you are done, you should try to document the steps for the benefit of the users of this forum. I hope that is not too much to ask.
RE: Vibration Analysis for cantilevers
I'll definitely do that.
RE: Vibration Analysis for cantilevers
1. Build a model of the floor. Slabs are modeled with shells and beams are modeled using transformed sections from DG11. Just apply a smeared-out mass over the entire floor. Don't try to go to each node and apply a mass. Can't just model the beam unless you're just going to predict freqeuncies. Don't try to model every little beam, especially around openings, stairs, etc. Just model the big typical stuff. The analyses aren't that accurate anyway and nobody knows what happens due to the partitions at openings, etc. Some copying and pasting should make it pretty fast. I usually build the model for a typical floor in a couple of hours.
2. Run a modal analysis to get the mode shapes and natural frequencies.
3. Apply the 4-term Fourier series load to represent the footstep forces. This is a very old approach an is definitely nothing new. Select the Fourier series term frequencies so that one of them matches the natural frequency to be excited. See the example on Slide 32. In that example, the four Fourier series terms had amplitudes of 77 lb @ 1.9 Hz, 13.5 lb @ 3.8 Hz, 11 lb @ 5.7 Hz, and 9.56 lb @ 7.6 Hz.
4. Run the time history analysis to predict the response and compare the peak acceleration to 0.5%g or whatever.
RE: Vibration Analysis for cantilevers
Couldn't hurt, but I don't see the point. The NASCC presentation already does most of this, and has some research to back up the approach. Not sure why the approach taken by a random guy on his first attempt (no offense StrlEIT) is of interest. If the approach is unclear, one could write into the AISC SSC and ask some questions.
RE: Vibration Analysis for cantilevers
RE: Vibration Analysis for cantilevers
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RE: Vibration Analysis for cantilevers
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Vibration Analysis for cantilevers
"5) I didn't see anywhere that it talked about the "real" effective mass to use. "
In their approach, Davis and Murray never compute the effective mass. It's automatically embedded in the first analysis method with time history stuff. In the second method, it's buried in the FRF peak magnitude. It could be backed out of the FRF peak mag, though, using the following, if anybody cares:
aSteadyState=F/(2*Damping*M)
FRF peak magnitude is aSteadyState/F in acceleration/force units, and this is computed using SAP2000. Back-solve for M and that's the "effective mass." For their methods, there's no need to get it, though.
RE: Vibration Analysis for cantilevers
No offense taken - I'm by no means a vibe expert and certainly don't proclaim to be. I do have a couple more questions for you, though. This method requires modeling of the entire floor, so where in the floor system are you getting the accelerations for? I'm imagining the accelerations will be different at different locations - is that a fair statement?
Also, have you done this before? Has it been with SAP 2000 or another program? I use RAM Elements and even using shell elements you can't assignment a uniform mass to the floor, you need to assign mass to nodes. This seems like it would be more onerous and time-consuming.
Finally, Say you have a system of beams such that the effective slab width is half the spacing. Does that mean that the I of the slab is 0? If you use a transformed I for the beams and then use the slab I, are you not double-dipping on that stiffness?
RE: Vibration Analysis for cantilevers
To answer you first question, with my limited experience with floor vibrations, your statement concerning the accelerations being different at different locations would be correct. The mode shape amplitudes at various locations of the floor would also affect what accelerations you get. So if you're modeling an entire floor, you would have to extract the response at every single node, and find the location where the maximum response occurs, and what that value is.
RE: Vibration Analysis for cantilevers
Accel will be different in lots of places. Monitor the acceleration wherever you're interested in it. If there's no place in particular, then look for the worst. Remember that response is proportional to mode shape amplitude, so that tells you where to look. If it's a cantilevered system, then the max acceleration will probably be at the cantilever tip. Response will be worst if someone is walking near that max mode shape amp also.
I've done these types of analysis using SAP. Any program that'll do time history analysis should work. In SAP, it's possible to superimpose a point mass on a node, a line mass on a frame element, or an area mass on a shell. RISA allows this kind of thing too, but didn't do time history analysis the last time I checked.
When you're computing the beam transformed MOI for DG11 calcs, the MOI has four terms: the beam's MOI about its own axis, the beam's parallel axis term, the slab's MOI about its own axis, and the slab's parallel axis term. When doing this in SAP, the third of those four is already in the shell EI. Therefore, just don't include that term in the beam's transformed MOI.
Again, I'd suggest writing to the SSC. They'll probably get the question to one of the authors and I bet they'd step you right through the process.
RE: Vibration Analysis for cantilevers