Natural Frequency of a Steel Chimney using Excel Spreadsheet

[mmagg]

I require a method to calculate the natural frequency of a steel chimney with multiple diameters using an excel spreadsheet. All the methods I have used to date work well for constant diameter and tapered structures but do not provide accurate results for stepped structures. I am considering using a dynamic approach but solving for eigenvalues is difficult without resorting to VBA.

Any advice would be much appreciated.

Thanks,

 

[OzEng80]

mmagg - i had a similar problem problem with a steel crucifix. You might find some of the responses in that thread useful.

http://www.eng-tips.com/viewthread.cfm?qid=239563&page=1

 

[enginerding]

An option you could use would be to lump the mass of each steel section (or portion of each steel section) and apply a series of lateral loads at each lumped mass. Find the deflections at each of the lumped masses. Then use equation 15.4-6 in Chapter 15 of ASCE 7-05.

| n |
| SUM (w[sub]i[/sub] * (delta[sub]i[/sub])[sup]2[/sup] |
T = 2 * pi * SQRT| i=1 |
| ___________________ |
| n |
| g* SUM (f[sub]i[/sub] * delta[sub]i[/sub]) |
| i=1 |


ASCE defines f[sub]i[/sub] as "any lateral force distribution in accordance with structural mechanics." And the delta[sub]i[/sub] are the elastic deflections "calculated using the applied lateral forces f[sub]i[/sub]." Although it doesn't define it in this section, w[sub]i[/sub] are the weights attributed to each level.

 

[Qshake]

I'm intrigued by your statement that approximate methods do not provide accurate results for stepped structures. What are you comparing the results to?

Whether you are dealing with a tapered chimney or a stepped chimney, the method and results should be very similar. You have discretize your structure into lumped mass for either tapered or stepped and can fashion your stiffness parameters for each of the lumped masses.

Also, what is your intended use of this value. If it is for earthquake loading, then the first 3 modes are likely to be sufficient for your purpose. If your purpose is to investigate stability of the sections then you will require higher modes that will cause vibration in the walls themselves rather than the whole structure acting as a cantilever.

More information would be helpful.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[mmagg]

enginerding, I am using the formula you posted and my results are fine for a straight stack but for a stepped structure the result is scewed. After some testing of various heights and diameters I believe my issue has to do with the calculated deflection at each section.

I currently calculate the moment due to self weight from the tip at each section of the stack and use the data to generate a third order polynomial. That equation is then intergrated twice to provide an equation that relates the lateral displacement of the stack as a function of elevation. This method is fine for straight structures but does not work when there is a change in diameter as there is no equation that can follow the step changes accurately.
I require a different method to define the deflection of the stack as a function of elevation.

Qshake, I require the natural frequency (1st and 2nd) to calculate the gust factor for wind loading and stack stability calculations.

 

[GregLocock]

Check out Rayleigh Ritz methods. Thomson "Theory of Vibrations" is the book to have.

You could also probably use Holzer's method.

However I'd agree with Qshake, a tapered beam solution would be a good enough approximation given the many unknowns in reality.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[enginerding]

When you are calculating the deflection of each section, you have to make sure that you are following the slopes correctly. For example, the deflection will cause the top pipe to deflect - curvature, angular and lateral displacement. the pipe below it also deflects likewise. But the total deflection is not simply the sum of the individual member displacements because the pipe below has a rotation at its end. Deflection will be the individual member deflections, plus the deflection due to the rotation at the bottom times the length.

I am not sure if this makes sense as written. It is much more clear in my head. Maybe I will see if I can sketch this better and upload it later today...