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Balcony Floor Vibration

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I have a balcony with a 28 foot cantilever. The backspan varies from 30 to 
45 feet. I'm trying to design for floor vibrations per AISC design guide 
11. The balcony is for a church, and my thinking is that my natural 
frequency should be at least 6 based on chapter 5 and my peak acceleration 
should be less than 0.5% g based on chapter 4.

The problem is that this requires enormous beams, something like W36x230 at 
5 feet on center just to get in the ballpark, way more than required for 
strength.  The problem seems to be the large deflection I calculate for the 
cantilever, that results in a very low natural frequency.

Has anyone run into anything similar? Maybe I could use the deflection at 
some point other than the end of the cantilever. Maybe 3/4 or 2/3 the 
cantilever length, although even this doesn't help as much as you might 
expect. Past experience I have had with this design guide is that almost 
any floor I check doesn't work.

Any advice or comments would be appreciated.


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