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Vibration Analysis for cantilevers
3

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.

RE: Vibration Analysis for cantilevers

Slickdeals gives an excellent article on the subject.  But, keep in mind that the article was published in 1977 and is certainly superceded by the much more recent Design Guide.  At least as far as "acceptance criteria" is concerned.  

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

(OP)
I'm comfortable with the acceptance criteria.  That article suggests using the transformed I for the entire length (even on the cantilevered portion) - interesting.

RE: Vibration Analysis for cantilevers

SEIT...not sure of the source of your vibration, but don't forget to consider lower amplitude, higher frequency vibrations in the spectrum.  These can be critical to fatigue failure.

RE: Vibration Analysis for cantilevers

(OP)
It is a footfall (65#).  I honestly can't say I've looked at fatigue from vibrations before, but I'm guessing that for a footfall, the forces are so small that it never reaches a stress where fatigue is an issue.  

Does that sound right?

RE: Vibration Analysis for cantilevers

I wouldn't consider footfall vibrations in my fatigue analysis, if the loading was well below ultimate.  

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

What's a footfall?  Never heard the term.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: Vibration Analysis for cantilevers

Footfall is just the term used to describe people walking, or the vibrations caused by a single step on the floor.  And from my limited experience, I would also agree with rowingengineer that footfall vibrations are generally not considered in fatigue analysis.

RE: Vibration Analysis for cantilevers

It is a term used to describe the loadings from people walking, I believe when SEIT state footfall 65 he meant 65 steps per minute which is just below a moderate walking speed. hopefully e will stop by as he is the local expert.

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

(OP)
I actually meant that the footfall force (the forcing function) is 65 pounds.  That's just right out of Design Guide 11 (it's 92 pounds for a pedestrian bridge).

RE: Vibration Analysis for cantilevers

Sorry SEIT, I am Aust, it would be 0.29 kN to me.

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

SEIT...I wouldn't consider foot traffic to be an issue either.  Just wasn't sure what was pushing the vibration.

RE: Vibration Analysis for cantilevers

Just outlaw music in the vicinity.  No worries.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: Vibration Analysis for cantilevers

Some comments:

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

65 lb is not the force due to walking, or a footstep.  Look closer at the explanation of the prediction method in Chapter 2.  The sinusoidal force inputs are more like 20 lb or less.

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

I would not use the stuff from the 1977 paper.  That's prehistoric by floor vibration standards and uses the very old reiher meister formulation.

RE: Vibration Analysis for cantilevers

(OP)
271828 -

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

SEIT:
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

(OP)
Slick-

I'll definitely do that.

RE: Vibration Analysis for cantilevers

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.

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."

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

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/
 

RE: Vibration Analysis for cantilevers

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.

RE: Vibration Analysis for cantilevers

(OP)
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?

RE: Vibration Analysis for cantilevers

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.

RE: Vibration Analysis for cantilevers

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.
 

RE: Vibration Analysis for cantilevers

Quote:

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.

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