Recommended period for a steel umbrella structure 2

[Orellandres]

Hi Community,
I have a roof structure (image attached). Where can I find information about recommended natural periods of vibration?
The height of the structure is 5m and an approximate radius of 5m. The surface supports glass.

 

[3DDave]

That is mainly a cantilever beam (vertical) with a large mass on the top that will put the beam in bending.

The simplest formula looks like this:

https://vlab.amrita.edu/?sub=3&brch=175&sim=1078&cnt=1

for a rough approximation. Since there are diagonal stiffeners, the bending of the beam won't be uniform so it might be taken as if the mass is concentrated at that joint with a separate calculation as if the structure is shortened and bends only about that joint.

However you are likely to see that the broad umbrella resists rotation via inertia and will have an effect that further lowers the natural frequency. There is easily a mode where the umbrella tilts in opposition to the bending, making the beam deflect into an S-shape.

 

[dik]

Is this what it looks like in plan?

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[Just Some Nerd]

dik, I think you're missing 3 more diagonal stiffeners coming out of the centre. Looking at orellandres' picture it looks like they're attached to the closest corner of the smallest hexagons (the ones in the centre of the larger hexagons).

----------------------------------------------------------------------

Why yes, I do in fact have no idea what I'm talking about

 

[SWComposites]

Presumably the required minimum natural frequencies will be related to wind loading requirements and the need to avoid aerodynamic forced displacements and vibrations.

 

[dik]

like this?

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[GregLocock]

In addition to the bending mode there will be a very exciting torsional mode to think about.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Orellandres]

I was wondering If there is a limit on natural period, my main objective is control it the vibration to avoid problems of service. The structure have a 0.5s of period for first mode, it's a traslational mode.

 

[drawoh]

Orellandres,

Vibrations should be something like third year mechanical engineering. Have you gotten this far? Are you headed there?

Vibration analysis is fairly counter-intuitive. A good crude, practical assumption is that you have masses and springs. If the masses are low and the springs are stiff, you have high natural frequencies, and no problems. If you have something heavy sitting on a soft spring, you could be in trouble.

Regard your entire structure as a bunch of springs.

--
JHG

 

[GregLocock]

We can't give you hard and fast numbers because you really haven't said what standard it needs to meet. But, so the wind is blowing and this thing is swaying once per 2 seconds. That is very floppy indeed. I can't give you a target that can be justified, but 5 Hz would seem none too high.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[driftLimiter]

You could check out ASCE 7-16 Ch 26 Section 11 on gust effects.
This has to do with the periods of structures related to wind loading. TBH I haven't really had to use this area of the code very much but It might help.

Also The period of this structure may impact its seismic design force, ASCE7-16 Ch 13. should be sufficient (perhaps Ch 15).

 

[buildinggalileo]

What an interesting project, thanks for sharing!

 

[drawoh]

Orellandres,

This may be water under the bridge, but I have given this further thought.

The infamous Galloping Gertie was flexible. Under wind pressure, it was capable of rotating enough to change its aerodynamic characteristics. On a windy day, it rotated back and forth. On the final day, this rotation occurred at the natural frequency of the bridge, and it self destructed.

If your structure is mechanically rigid, it will not move significantly in response to wind loads. There will be no change in behaviour in response to wind loads, and therefore, no oscillation at any frequency. If your structure is permanent, there is no need for light weight. Make it big and forget it. Your stiffer structure will have a higher natural frequency.


--
JHG