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Re: Wind question
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- Subject: Re: Wind question
- From: TJ Fu <tzujfu(--nospam--at)gmail.com>
- Date: Sat, 25 Jun 2011 16:38:48 -0400
Jeremy,
I am not familiar with the Structuralpedia Forum, so I’ll response here.
Question in Structuralpedia …
When designing a non-building structure for wind, it is necessary to determine if it is flexible or rigid. To do so, you need to determine the natural frequency. ASCE 7 does not lend much help to figure this out.
I'm going through old text books and reference material now to try to determine this but I'd be happy if someone pointed me in a more precise direction.
ASCE7 determines the Gust Factor (G) based on whether the structure is flexible or rigid.
Let: ω = Natural Frequency (Radians/second) = (k/mass)^{0.5}= [k/(W/g)]^{0.5} = (kg/W)^{0.5}
K = Spring Constant = 1^{k}/∆” = the load that produces unit deflection (1“)
∆ = Horizontal deflection at C.G. structure due to 1 kip horizontal load (in)
g = Acceleration of Gravity = 386 in/dec^{2} = 32.2 ft/sec^{2}
W = Weight of Structure (kips)
T = Natural Period of Vibration (sec/cycle)
Then: T = 2π/ω = 2π(W/kg)^{0.5 }= 2π(W/386k)^{0.5} = 0.32(W/k)^{0.5}
Flexural Structures: T > 1 sec/cycle
Rigid Structures: T ≤ 1 sec/cycle
For non-building structures, you could refer to…
“Seismic Design for Buildings”, Air Force Manual No. 88-3,
Chapter 13, Appendix G – Structures Other Than Buildings.
It is based on Work = Energy Theory
Procedures to determine Spring Constant of the structure (k)…
1: Apply 1.0 kip load at C.G. of structure
2: Apply Work = Energy Theory to calculate k value
Work = (0^{k }+ 1^{k})/2 x ∆” = ∆/2 k-in
Energy = Ʃ[(0^{k}+P^{k})/2xδ] = Ʃ(P/2 x PL/AE) = Ʃ(P^{2}L/2AE)
Where: P = Member force due to 1^{k} horizontal load (kips)
δ = Elongation or shorting of the member (in) = PL/AE
A = Area of the members (in^{2})
E = Modulus of Elasticity of steel = 29000 ksi
So, Work = Energy
∆/2 = Ʃ(P^{2}L/2AE)
∆= Ʃ(P^{2}L/AE)
K = 1^{k}/∆” = Ʃ(AE/P^{2}L)
We then can calculate the Natural Frequency or Natural Period of the Structure from k (Spring Constant) value.
TJ Fu, PE
We have a wind question in the structuralpedia forum if anyone is interested...
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