Natural/Fundemental Frequency of Structure 1

[ARS97]

Perhaps I'm making this too difficult, but I have a question regarding load application and the resulting natural frequency of a structure. Keep in mind - I don't get to deal with even moderate levels of seismic design in the areas that I typically deal with, so my knowledge/experience with structure frequency isn't probably what it should be.

I understand that the natural (or fundemental) frequency of a building is the lowest frequency of the structure. I'm a bit confused though on how to obtain this lowest value and what impact the applied load has on it.

For a given structure, let's say you apply several load cases that are based on different degrees of the structure's selfweight to mimic a range of lateral loads, such as:
LC 1 = 0.001W
LC 2 = 0.001W
LC 3 = 0.1W
LC 4 = 1.0W
LC 5 = 10.0W

If you use computer software (Staadpro) to calculate the frequency of the structure under each of those load cases (Rayleigh method in this case) and you plot the load (X) versus the frequency (Y), you'll see that the frequency approachs zero as the load % increases. For this example, I was checking a storage bin with unbraced legs:

Frequency for LC 1 = 188.66 cps (or Hz)
Frequency for LC 1 = 59.66
Frequency for LC 1 = 18.87
Frequency for LC 1 = 5.96
Frequency for LC 1 = 1.67

In my above example, an infinite increase in load makes the frequency approach zero. I know this isn't how it's done.....so where am I going wrong here? Do I need to limit the upper range of the loads to a reasonable limit? Do I need to calculate the frequency just based on the actual load? (On a side note, correct me if I'm wrong, but calculating the frequency of a structure under a certain load case isn't necessarily the NATURAL (lowest) frequency of the structure......that's simply how the structure is responding to THAT load. Maybe that's all I need.....I'm not sure.)

Any help is appreciated.....

 

[structSU10]

What is W in this case? self weight of the structure? To get the correct natural frequency you must use the correct mass of the system. frequency is directly related to the mass and stiffness of a structure SQRT(K/M), with K being stiffness and M being mass. As you can see, as mass increases, frequency decreases, so it should approach zero as mass goes to infinity.

 

[ARS97]

W is the selfweight. So if I'm interpreting correctly, natural frequency should be based on (1.0 * selfweight of structure), applied in the desired direction?

 

[ARS97]

In the above example, the natural frequency should be taken as 5.96 Hz (load case 4: 1.0 * selfweight)....correct?

 

[structSU10]

That is correct.

 

[ARS97]

Thank you.......

 

[Bagman2524]

Here's a similar thread.

http://www.eng-tips.com/viewthread.cfm?qid=28892

 

[Bagman2524]

Another way of looking at it is the more deflection the lower the frequency: f = (1/2*Pi)*SQRT(g/delta).

http://www.fabreeka.com/documents/file/papers/isolation_theory.pdf

 

[amec2004]

My reply as the followings

1. The load you input will be converted to mass by STAAD internally. There shouldn’t be so many load cases as you mentioned above. Normally there will be only one or two load cases, such as operating or empty case, defined specifically in one direction of X,Y,Z to work out the frequency in that direction by using Rayleigh Method. See attached PDF
1) You shall only input the load in one direction in one load case
2) You shall not input negative value as it will cancel the positive value and you get less mass
3) You shall use a specific load case for frequency calc and shall not mix with other loads such as wind load

2. Modal Calculation Method will give you more accurate result with frequency in 6 directions. You have to determine the STAAD output f1, f2, f3 … fn belong to which direction based on the mass participation ratio

How to Find the Structure Frequency in STAAD

There are two methods: Rayleigh Method and Modal Calculation. See attached PDF

Rayleigh Method

The Rayleigh frequency is based on the statically deformed shape created by solving the load case.
To get a Rayleigh frequency for a combination of two or more load cases, you must create a primary load case (not a Load Combination) using the Repeat Load command and include the Calculate Rayleigh command within the load case.
In most instances, the loads in a Rayleigh case should be in the horizontal direction in order to approximate the first bending mode. You should have one load case with Rayleigh for forces in one horizontal direction, then another load case with Rayleigh for forces in the other horizontal direction.
You should not have the MODAL CALC command in these Rayleigh cases.



anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[ARS97]

Very helpful guys. I will take a better look at this tonight when I get a chance. Much appreciated. This confirms what I was expecting, but getting verification by others is a big help.

 

[ARS97]

Here's a related question. Let's say you've determined the natural frequency of a small structure in a certain direction. The small structure supports a centrifuge/decanter that has an operating speed of 3600 rpm (60 hz) that can produce vertical and horizontal dynamic loads. When looking at the frequencies, do you:
a) Compare the operating frequency of the decanter (3600 / 60 = 60 hz) with the natural frequency (much lower), or
b) Compare the structure's frequency under the machine's imposed load with the natural frequency

If it's (a), then coming up with a structure that has suffiicent rigidity to stay above the machine's operating frequency (say by 30%) will not be easy. (I suppose a "low tune" could be considered, but I think that opens up the problem of the start/stop events causing resonance when it passes through the lower frequency of the structure.) If it's (b), much different story.

?

 

[amec2004]

This is the first time I use my newly purchased Microsoft Surface Pro tablet to prepare sketch for Eng-Tips.com.
In the past I have to sketch on a paper and then scan into PDF. Now I can just free sketch on tablet screen and share these brilliant ideas with my engineering friends all over the world!

Please refer to attached PDF for the sketch. [red]Please bear with my bad handwriting though.[/red]

>> Compare the operating frequency of the decanter (3600 / 60 = 60 hz) with the natural frequency (much lower)

Yes we do.

We normally tune the structure’s natural frequency to be +/- 20% away from the machine’s operating frequency. It’s not an easy task in the reality as for block type foundation there are natural frequencies in 6 DOFs with different values crossing a big range which can easily overlap the machine’s operating speed, and for flexible type machine supporting structure there can be easily over 20 natural frequencies with significant participation ratio in 6 DOFs. The machine can also have two or three rotors with different operating speeds. In many times it’s not realistic to get full range of structure's different natural frequencies all staying away with the machine operating speed or multiple speeds with multiple rotors completely, let alone the +/-20% requirement. In this case we normally check the amplitude criteria only. The resonance frequency clearance check is a bonus, but in many times it’s difficult to meet this criteria.

>>Compare the structure's frequency under the machine's imposed load with the natural frequency

This statement seems not quite logic.

In your statement the structure's frequency under the machine's imposed load and the natural frequency refer to the same thing. What you are talking is similarly to comparing Obama with current White House owner and you are talking about the same person !

>>the start/stop events causing resonance when it passes through the lower frequency of the structure.)

Yes but for short period of time.



anchor bolt design per ACI 318-11 crane beam design

http://www.civilbay.com

 

[ARS97]

amec2004 - thank you for that info.....that's a very helpful post.......