How to Calculate Natural Frequenecy of Steel Structure

[rogerroll]

Machinery's Handbook, Roark's Formulas for Stress and Strain, etc. All these books help to find strengths, moments and frequencies of simple-ish beams. But what about support structures with braces and cross-bars? What's the procedure for determining the Natural Frequency of an assembly that's bolted to a rigid object? If anyone dares, please visit my site and if you'd like to help, that'd be great!

Thanks,
Roger

http://homepage.mac.com/rogerroll/seismic_roge/

 

[MikeyP]

I'm afraid that the simplest way of dealing with a structure like that is to use Finite Element software (there are simple Shareware packages available)

The tricky part is defining the actual model in the FE software. Finding the natural frequencies is relatively easy once that is done (usually a single command).

For an FE expert this is not a time (or brain) consuming task. However, if you want to include the effects of liquid sloshing about in the tank then it becomes a much more difficult problem.

Looks like you might have to hire someone after all.

M

--
Dr Michael F Platten

 

[tomirvine]

I agree that the finite element method may be required.

In addition, here is a reference book that goes beyond the Machinery Handbook and Roark's:

R. Blevins, Formulas for Natural Frequency and Mode Shapes, Krieger, Malabar, Florida, Reissue 1995.

This book even has a chapter on fluid systems and slosh.

Tom Irvine

http://www.vibrationdata.com

 

[zzy]

For a little complicated parts, it is very hard, if not impossible, to find a closed-form of natural frequency. Finding natural frequency in FEA is very easy. It is probably the easiest type of analysis in FEA. If you need help, let me know.

 

[rogerroll]

I appreciate all your help, guys!

I tried a demo of Cosmos DesignStar (FEA) Wow, it's expensive! $10,000!
Which FEA software do you guys know/use/recommend?

Thanks!

 

[GregLocock]

You'll have more luck asking that on the Finite Element Analysis forum, but the current consensus seems to be that NE Nastran is a good cheap alternative to the usual contenders, and I sort of got a price of $4000.

Bear in mind that an uncorrelated model is really no better than a back of envelope calculation!

Cheers

Greg Locock

 

[cab1990]

Hello roger roll,

I generally agree with the responses you have gotten. I have been using finite element software for 20 years now and it is my preferred method of solving problems like this one. However, if I were you, with a limited budget, and limited knowlege, and wanting to get just a ballpark feeling, I would do this:

I would create a lumped mass model(get Shaum's outline for vibrations at Waldenbook) with the tank and water comprising the mass. Neglect the mass of the supports. they are small in comparison. To this mass, I would attach a vertical spring and a lateral spring calculated from the stiffness( to calculate stiffness get Shaum's outline for mechanics of Materials at.. you guessed it, Waldenbooks) of the supports. Then I would calculate the natural frequency in the vertical and lateral direction.

........
xxxxx-| Mass |
........
|
x
x
x

See if these numbers meet your 25 Hz requirement. If they do, then you must calculate the first rotational mode which is a little more complicated. If you do the previous, I'll explain the latter.

The reason this will work is that you are interested in the lowest vibrational modes. These are characterized by the global mass and stiffness. The other modes are higher frequency have have less energy to cause damage at your supports.

Good luck, and I mean realy...good luck.

cab

PS If you or anyone will perform the calculation by hand, I'll verify it by FEA...for free of course.

 

[ibrahimdemir]

Roger,

A structure should be stable for static analysis before going for dynamic analysis. I believe, the vessel and/or content of it have very high masses. As far as I can see from the diagrams, the structural system does not have lateral brace to stabilise the system under horizontal wind or seismic loads in the longitudinal direction of the vessel. So, non of the analyses will give you an answer without a stabiliser member in the longitudinal direction of the vessel or a brace in horizontal direction to a fixed point.

Second, I would not recommend very high saddle under the vessels as far as the seismic loading concern. If the saddles are short, the bending moment on vessel connections of the fixed saddle(s) which are introduced by the loads in the longitudinal direction of the vessel will be smaller. Here, I consider rigid type saddle connections which are required for load transfer under the seismic loads.
(For rigid and sami-rigid definitions of the saddles you need to read some background papers of BS5500 Annex G.)
If the vessel content elevation is important, you need to rise the structural members to the underside of base plate elevation of the vessel by making them stable under the lateral loads that introduced by the vessel base plate.

So, you need to check if the vessel is stable staticly under the wind and seismic loads to see the necessity of introducing bolts. If the vessel is stable with shear pads only under the static analysis by considering a g factor for the seismic load ,I believe, this analysis will be satisfactory if there is no sloshing effect in the vessel. The sloshing effect still can be solved seperately to check if the system is stable without bolting the vessel onto the structure ( introduction of shear pads are always necessary by considering thermal movement of the vessel if available ). If there is a thermal movement, you need to use sliding pads under the saddle base plate(s) and introduction of the bolts between base plate and structure may not be working due to high shear loads and bending moments on the bolts. So bending moment action on the bolts should be eliminated by the shear pads and bolts can take only uplift forces if the vessel is not stable without them.

To me without large amount of sloshing effect ) which can be eliminated within the vessel by introducing breakers into the vessel ) there is no need to go further dynamic analysis or dynamic frequency analysis. You'd better solve the problem staticly first. If you still get problems go for dynamic analysis.

Hope this help.

Ibrahim Demir

 

[rogerroll]

Thanks to everyone!
I am presently trying CadrePro to see if I can learn something about FE!
Chances are I'll have more questions!

Roger