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.

 

[slickdeals]

This might help

http://www.aisc.org/assets/0/544/546/670/0bc04a59-1c27-4360-94b4-849d1a3bf803.pdf

 

[JoshPlumSE]

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 But, keep in mind that the article was published in 1977 and is certainly superceded by the much more recent Design Guide.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.

 

[Lion06]

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

 

[Ron]

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.

 

[Lion06]

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?

 

[rowingengineer]

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

 

[msquared48]

What's a footfall? Never heard the term.

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

 

[STpipe]

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.

 

[rowingengineer]

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

 

[Lion06]

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).

 

[rowingengineer]

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

 

[Ron]

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

 

[msquared48]

Just outlaw music in the vicinity. No worries.

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

 

[JoshPlumSE]

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.

 

[271828]

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.

 

[271828]

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.

 

[Lion06]

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.

 

[slickdeals]

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.

 

[Lion06]

Slick-

I'll definitely do that.