Vibration Analysis for cantilevers 3

[Lion06]

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.

 

[271828]

I think it's pretty easy as vibration analyses go. (Check out the European formulations!! You'd almost have to be a ME to understand them.) I've used very similar methods on lots of floors. I don't believe there is any way to do an approximate DG11-ish analysis on something other than a regular rectangular floor bay or some other limited situations. One could get some kind of answer, but would have zero clue whether it's reasonable or not.

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.

 

[271828]

"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."

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.

 

[slickdeals]

http://www.arcelormittal.com/sections/index.php?id=133

 

[slickdeals]

Also look at Anthony Barrett's thesis from Virginia Tech. His research was with Dr. Murray.

http://scholar.lib.vt.edu/theses/available/etd-09062006-184827/

 

[IDS]

There has been a lot of work done on this in the UK in recent years, particularly in relation to sports stadiums and other large public performance buildings, and the effect of rythmic jumping. The Institution of Civil Engineers Structures and Buildings Journal has several papers on the topic.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[271828]

Oops, I missed this one.

"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.

 

[Lion06]

271828-

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?

 

[STpipe]

SEIT,

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.

 

[271828]

Glad there was no offense. It's always cool when someone ventures out of the comfort zone and learns new stuff.

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.

 

[271828]

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.

NOt true. Your sentence right before that one tells how to determine the location of max response.