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Re: Building Natural Frequency

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Building Natural Frequency
• From: Daryl Richardson <h.d.richardson(--nospam--at)shaw.ca>
• Date: Mon, 08 Jul 2002 16:00:42 -0600

Zchary,

The National Building Code of Canada, Section 4.1.9.1.7) permits the use of one of the following formulae for determining the  fundamental period, T, for calculating seismic response factors (which suggests that they may not be much good for anything else).

T = 0.085*h^0.75 for steel moment resisting frames,

T = 0.075*h^0.75 for concrete moment resisting frames,

T = 0.09*h/D^0.5 for other frames,

where h and D are in meters,
h is the height,
D is the dimension in the direction being considered.

Now I've never used these formulae because whenever I've needed such information I've always had the structure already loaded on computer or had the means to use a Rayleigh method of analysis which I can do on my old HP programmable desk top calculator.  This program is, admittedly, quite antiquated compared to what is available in today's programs; but the science behind it (the Rayleigh method) is still valid if you want to develop a spreadsheet to do this.

The Rayleigh method is described in "Introduction to Structural Dynamics" by Biggs: but there are probably many other sources as well.

Regards,

H. Daryl Richardson

Zachary Goswick wrote:

I am curious how everybody comes up with the natural frequency of a building.
Does everybody have to input every building into a structural software
package to get this? All of the new codes I have seen require frequency in
order to calculate wind and seismic loads.  Even the simplified methods
require this.  How does everybody handle this for small buildings, or where
an existing building needs to be modified?

I know the equations and theory behind finding the natural frequency.  I
am just looking for how this is found practically.  Since the natural frequency
is (k/m)^1/2, I can find the mass of the building fairly easily, but the stiffness
of the whole building is much harder.  You almost need to input it into some
sort of structural package to get this.  How do others handle this?

Zachary Goswick, P.E.
Structural Engineer
Angus-Young Associates, Inc.
555 South River Street
Janesville, WI  53545-4827
Phone: (608)756-2326
Fax: (608)756-0464
Email: zachg(--nospam--at)angusyoung.com