natural frequency limit of free-standing structure 1

[wngadam]

Does anyone have any comments/ advice on minimum natural frequency limits when desiging a free-standing carport or gazabo etc cantilevered from the base. I have been adopting 1.0 as a minimum but would like to see what other people are using.

Thanks.

 

[MikeHalloran]

Structures designed for deflection of ~1/360 of the span typically resonate around 4..6Hz. A natural frequency of 1.0Hz, if that's what you mean, implies unusual flexibility, which a layman might characterize as flimsiness.





Mike Halloran
Pembroke Pines, FL, USA

 

[vmirat]

I use ASCE 7 to determine natural frequency. Section 9.5.5.3.2 has a formula for calculating the approximate fundamental period (Ta) which is the inverse of natural frequency. I come up with a fundamental period of about 10 for an 8 foot high structure.

 

[GregLocock]

Does that (10s) seem reasonable to you? It doesn't to me.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[vmirat]

GregLocock,
Are you concerned that 10s seems too much? Keep in mind that the natural frequency is in Hertz, not seconds. Perhaps you're thinking of the fundamental period (T) which is measured in seconds. Since the period is the inverse of the frequency, the period for this particular example is 0.09s.

 

[UcfSE]

I think Greg appears "confused" because you said fundamental period in your 27 Mar 06 14:39 post. A fundamental period of 10s is unreasonable for most structures. Perhaps you meant the fundamental frequency is 10Hz?

 

[GregLocock]

10s = 0.1 Hz. yes, that seems very low indeed for a single story building.

I vaguely remember seeing 2 Hz for a much taller building.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[wngadam]

Thanks everyone for your responses. Let me try to clear up my question… The structure I am looking at is made up of two frames about 8 metres apart. Each frame has one single column that is cantilevered from the base. The base fixity of the two columns provides the only lateral stability for the structure. The structure is to be built in a cyclonic region in Australia however it is very well shielded.

I am more concerned about excitation caused by people shaking the structure than excitation caused by wind. I have modelled a single 2D frame in Microstran (the structural modelling software our office uses) and performed a dynamic analysis. The dynamic analysis calculates the natural frequency of the structure. The natural frequency depends on the steel sections selected and the gravity loads on the structure - additional loading i.e. wind does not come into it. To meet the structural design actions and deflection limits under wind loading and dead and live loading a nominal section like 75x75x3 square hollow section is more than sufficient. A 75x75x3 SHS gives the structure a natural frequency of just less than 1Hz (my gut feel is that this it a bit too low). However, to achieve around 7 Hz the member would have to be a 250x250x9 SHS (sorry, I am not familiar US sections, the first 2 numbers are the outside dimensions and the 3rd number is the wall thickness in millimetres).

To me it seems like extreme overkill to use a section that is more than 30 times stronger and 10 times heavier to increase the natural frequency to a value around 7 Hz.

I hope this makes sense. Thanks Adam.

 

[MikeHalloran]

Designing for high stiffness or high natural frequency typically produces structures that are way overdesigned for strength.

There is also the issue of incidental loading to consider. E.g., if you go with the 75mm tube, what happens the first time it gets hit by a car?



Mike Halloran
Pembroke Pines, FL, USA

 

[UcfSE]

You might not need excessive stiffness an order of magnitude above and beyond the call of duty. However, you should provide more than 1Hz imho. For flexible structures the dynamic nature of the wind plays a much more significant role than the very simplified static load we typically use. There are also the things you don't plan for, such as those mentioned by Mike or people you yourself mentioned, particularly kids.

 

[vmirat]

GregLocock,
Good grief! My tongue got tied on that one! You're absolutely right, I assumed that wngadam needed the period for seismic calculations such as used in ASCE 7, so I did that calculation, coming up with 0.09s. But then I converted it to natural frequency of 10Hz but got my wording wrong. Sorry for the confusion.

Adam, this sounds like a servicability issue. UcfSE alluded to the kid-effect and Mike mentioned damage by a car. Unless you know for sure that you have an environmental condition to consider (i.e. this is a gazebo located in a public playground where kids WILL climb on the thing, an attractive nuisance), then you design to what you know. I think you'll drive yourself crazy trying to design for all of the "what if's" that could occur. I doesn't seem fair and reasonable for you to be responsible for the irresponsible actions of others (i.e. someone shaking the structure back and forth).

You mentioned that you considered wind loading on the structure. Being in Australia, don't you guys have seismic loading also? The structure sounds like a flat roof canopy car port supported on two columns (inverted pendulum). I could see the seismic loading governing over the wind load, depending on the weight and vertical profile of the roof structure. If so, then that would give you the justification for the stiffness of 7Hz.

 

[wngadam]

Thanks everyone for their input. After discussions with some other guys from our office I have decided on a more empirical approach. I have sized the column by limiting the deflection to height/150 under the maximum drag force due to serviceability wind loads. Incidentally the natural frequency of the structure is now just less than 2 Hz. Due to the geographic location of the structure and its ductile properties, Australian Standards do not require specific design for earthquake loading.