# dynamic behaviour of lighting columns

In the calculation of lighting columns, you must take dynamic behaviour into account. It's done by a factor on the wind loads, that depends on the
period of vibration of the column. The European EN 40 standard committee says this period must lie between 0 and 3.5 seconds.
the standard: " ... factor .... takes into account the increase in the load resulting from the dynamic behaviour of the lighting column cause by wind gusts".
Now, when I calculate the period of vibration of a 6 meter pole-with- bracket by means of matrix method (eigenvalue problem with distributed mass matrix) I get LOWEST eigenvalues that result in maximum periods of vibration way higher than 3.5 seconds, and a load factor that is unacceptably high (and not in line with experience).
The questions: Which eigenvalue should I use to determin the period of vibration ? (A column has A LOT of eigenfrequencies...) How should the relation with "wind gusts" be interpreted ?
Here is the array of typical eigenvalues from my calculation: array(24) { => float(1.81673652086) => float(1.82377482274) => float(41.8565929569) => float(43.8413395721) => float(138.031662251) => float(233.428272113) => float(519.636228268) => float(710.793797493) => float(2776.57589519) => float(4218.21507698) => float(8078.78449371) => float(9531.15538271) => float(11888.6098069) => float(18685.6311882) => float(24678.9208868) => float(25294.8476091) => float(40684.7831304) => float(73070.7945844) => float(83898.8774131) => float(95870.9738707) => float(137719.85692) => float(277530.743338) => float(368154.480533) => float(633315.738033) }
(So the eigenfrequencies in rad/s are the sqrt from these values.)
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I am certainly missing something, using your values and method. Start with array = 1.82 sqrt (1.82) = 1.35 rad/s 1.35 X 2pi = 8.5 Hz
array(25) ??????? = 633316 sqrt(633316) = 796 rad/s 796 X 2pi = 5kHz
??? Brian Whatcott Altus OK
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On Fri, 04 Jan 2008 20:59:26 -0600, Brian Whatcott

I certainly was missing something: 1.35 rad/s = 0.21 Hz T = 4.7 sec
...and so on
[Please don't tell me I screwed up twice running :-)
Brian W
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On Fri, 04 Jan 2008 21:09:26 -0600, Brian Whatcott wrote:

yeah, sure... That part I knew... but before that, I have to **choose** one for the determination of the load factor. Which one ?
for one: all eigenvalues are related to a degree of freedom. Wind is in the z-direction, so I only consider those eigenvalues related to that z-direction, right ? But only translation along the z-axis or the ones related to rotation about the x-axis too (this rotation results in a displacement along the z-axis) ? Then, why should I use the **lowest** eigenfrequency ? Why is that one related to the worst-case scenario ?
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Ddear Osiris:
...

This will carry the most energy, generate the highest displacement (before column failure), and is closest to the forcing function ("near zero"). If you knew you had a forcing function near 5 kHz, then you could look for harmonics there. (Say you were supporting or stabilizing an engine...)
David A. Smith
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On Mon, 07 Jan 2008 06:08:42 -0700, N:dlzc D:aol T:com \(dlzc\) wrote:

thnx. What about the karman-frequency then ?
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Dear Osiris:

...
David A. Smith
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-

I'll take a shot at this.... If a rough empirical equation for vortext shedding frequency is given by F = 0.2V/d
For F = frequency V = air speed d = pole diameter
Then a low wind speed corresponds with the lowest vortex shedding frequencies. (Unsurprisingly!) But low wind speeds carry the lowest energy, so for a pole's limiting structural stiffness (expressed as a resonance frequency which should be higher than some limit value, which implies a limiting periodic time which should be shorter than some limit value) a wind speed low enough to excite a pole resonance via vortex shedding, will have insufficient energy to cause damage.
Brian Whatcott Altus OK