Lateral Stiffness - Building frequency 1

[blue82]

Hi,

I'm trying to get an idea of a buildings frequency, i've got a 70m high tower with a concentrated mass at the top.

Is there a rule of thumb when first considering its sway sensitivity?

Can i use f=1/2pi * sqrt k/M ? How do i go about determining it's lateral stiffness?

 

[briancpotter]

Lateral stiffness, based on Hooke's law, is the force divided by deflection (F = kx, or k = F/x). For a concentrated mass on top of a tower, k = 12EI/h^3.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[blue82]

Thanks for the response, and nice blog!

 

[briancpotter]

Whoops, that should actually be k = 3EI/h^3 (looked at the wrong diagram)

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[blue82]

Out of interest, what is an acceptable frequency? I'm getting around 0.4Hz

 

[briancpotter]

The frequency is a determinant of the wind and seismic forces, so in part your lateral force resistance will determine what's acceptable. Otherwise you'll have to examine whatever code you're using for frequency/deflection requirements for towers.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[wannabeSE]

Structure Magazine has a article on Building periods that you may find helpful:

http://www.structuremag.org/Archives/2008-6/C-CS-BuildingPeriods-Jacobs-June08.pdf

. Note that different approximate periods (inverse of frequency) are used for wind and seismic. ASCE 7-10 has some equations for both. The equations depends upon what type of lateral force resisting system is used. These could be used as a starting point. What percentage of the total building mass is concentrated at the top?

 

[blue82]

Thanks for the information,

It's an airport control tower, so its basically a 70m stairwell and then 3 cabs at the top.