Suspended pendulum-like structure 3

[sekwahrovert]

Consider the design of a suspended structure idealized in the attached sketch. The suspended structure is fairly rigid and suspended by 2 cables (or 4 in a 2x2 grid). How would one determine the natural period of such a system? Is it a simple formula containing the dimensions A, B, and/or C?

I can elaborate on the real-world structure that this model represents as needed, but I'll keep it simple for now. Thanks in advance for any input.

 

[WARose]

It doesn't matter what the period is because it is unstable (for a permanent structure). It can not safely resist lateral loads.

 

[sekwahrovert]

Thanks for responding, WARose, but I don't agree. ASCE 7-10 Sections 13.5.1 and 13.6.1 address architectural, mechanical, and electrical components "which are supported by chains or otherwise suspended from the structure." Further reading in these sections makes it pretty clear (at least to me) that such suspended items need not be braced against lateral movement if certain criteria are met.

 

[WARose]

Thanks for responding, WARose, but I don't agree. ASCE 7-10 Sections 13.5.1 and 13.6.1 address architectural, mechanical, and electrical components "which are supported by chains or otherwise suspended from the structure." Further reading in these sections makes it pretty clear (at least to me) that such suspended items need not be braced against lateral movement if certain criteria are met.

Ok.....your OP didn't include the fact this was some type arch/mechanical support.

If I needed the period, I'd just treat it like a inverted pendulum.....the period then depending on the stiffness of the column and the mass supported.

 

[JStephen]

For small deflections/ small angles, the cables act as springs in the horizontal direction, with force proportional to deflection. So you can apply an assumed (small) lateral load, calculate deflection, and get the period from Eq. 15.4-6 in ASCE 7-10 or similar.

I assume if actually suspended from cables or chains, damping could be just about zero, so I'm not sure how the overall design would work out. That would enter into the gust response as well.

 

[sekwahrovert]

JStephen,

Thank you for the reference. Equation 15.4-6 seems overly complex for what seems to be a simple system. For simple pendulums, T = 2*pi*sqrt(L/g). I would think a similar equation would exist for my system that doesn't require forces and deflections as input. The assumption of small deflections/angles is reasonable. The suspended structure is indoor, so wind isn't a consideration. I'm considering the possibility that seismic shaking of the building structure could have significant effects on the suspended component due to similar natural periods.

 

[JStephen]

Take dimension A as L, and that should give you the same result as Eq. 15.4-6.

 

[BAretired]

I would think that the length of pendulum L should be taken as A+C, i.e. distance to the center of gravity of the system.

BA

 

[JStephen]

That extra dimension doesn't rotate, so it wouldn't enter into the problem.

 

[Denial]

I'm with JStephen on this.[ ] Because the two cables are parallel and of equal length the suspended body does not rotate, and it moves through an arc of radius A.[ ] An additional consequence of the fact that the the suspended body does not rotate is that you can ignore its rotational inertia, and so use the "simple pendulum" formula.[ ] (If, say, the two cables formed an isosceles triangle, apex at the top, L=A+C used in the same formula would not apply because you would also have to allow for the rotational inertia of the suspended body.)

 

[BAretired]

Okay, I see what you are saying.

BA

 

[WARose]

Thanks for responding, WARose, but I don't agree. ASCE 7-10 Sections 13.5.1 and 13.6.1 address architectural, mechanical, and electrical components "which are supported by chains or otherwise suspended from the structure." Further reading in these sections makes it pretty clear (at least to me) that such suspended items need not be braced against lateral movement if certain criteria are met.

Note to the OP: I'd be careful with this. I've looked at the section of ASCE cited and it says: Components supported by chains or otherwise suspended from the structure are not required to satisfy the seismic force and relative displacement requirements provided they meet all of the following criteria...

By that, yes, you might be able to satisfy seismic criteria with this set up.....but I'm not sure it works in terms of serviceability. Unless there is lateral support elsewhere (i.e. at another support), this is probably ill-advised. I have been asked in the past (especially in a industrial setting) to provide lateral support for all sorts mechanical/electrical components (even lightly loaded cable tray) where there is too much movement on a day to day basis.

If this is a trapeze approach (and even if it meets the requirements of Chapter 13: i.e. lightly loaded)......and no lateral support anywhere.....I'd question that for the reasons I stated.

My 2 cents.