Natural frequency of high rise building

[nathan7]

Hi all,

To estimate the natural frequency of a tall structure, literature suggest to use the formula 46/H.

This is a general formula derived from tests on real structures. This formula is valid for structure which have been designed to perform under service and ultimate loads.

When I'm undertaking a preliminary design and I'm checking if the core structure is big enough i need to calculate the period based on the size of the core (which might be too small) and on the square root of k\m

Does anyone know a formula to work out the natural frequency of a tall structure simply base on mass and stiffness?

Regards

 

[KootK]

If the core is your only lateral force resisting element and your floor masses are fairly regular, you could use the Rayleigh Ritz method. To be honest though, I'm not sure that would be any more accurate than code formulas once foundation flexibility and wall cracking are accounted for. What are you using the period for? Strength wind / EQ or occupant comfort?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Guest262653]

I've just recommended these books from Zalka yesterday in this forum, but here they go again:

"Global Structural Analysis of Buildings" -

http://www.amazon.com/Global-Structural-Analysis-Buildings-Karoly-ebook/dp/B000FBFF0O

"Structural Analysis of Regular Multi-Storey Buildings" -

http://www.crcpress.com/product/isbn/9780415595735

 

[yakpol]

The vibration period can be estimated by formula N_floors/10. For better precision you will need to estimate the stiffness and to use vibration formulas from a text book.

 

[asixth]

The H/46 is from the Australian Earthquake code and is in metres so it is similar to Floors/10.

What I have found is the Australian Code formula is slightly conservative and will result in high base shears.

For a core building I find the response of the building to be a little more flexible when the building is modelled using ETAB's.

You can do a quick dynamic run in SpaceGass or Microstran, whichever frame program your using. Build up a cantilever with the stiffness properties and lump a mass at each level.

 

[nathan7]

Hi kootk

I knew about the method that you are referring to but it's quite complex and it will require mathcad to process the calculation. I also don't have a full calculation example (do you have one?).

I want to calculate the period to be able to asses acceleration during schematic design simply based on the stiffnesses of the core witch is reflected on the frequency of the structure (k\m).

I've done extensive researches and I came to the conclusion that there is no a proper formula to calculate the frequency. The worldwide formula use to estimate the frequency of the first mode of vibration is 46/h. To work out the correct frequency computer software must be use

Thoughts?

 

[KootK]

I've attached an example for where the stories are modeled as lumped masses. When I first encountered the method, I was stuck by how easy it is to apply. The development of the method is all calculusy but the application to discrete systems is not. For your case, the assumed shape function would come from the formula for cantilever bending under uniform load.

If you have many stories and the masses are fairly uniform, you can simplify your solution by treating it as a uniformly massed cantilever. For that, closed form solutions are available: Link

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[nathan7]

Hi Kootk

Thank you for the tips. I had a look at the book and it seems very good. I will go through the example and see if it can be adapted for more than five story.

Thanks