Catenary wire tension with spring ends

[bnickeson]

I've got a fairly unique problem. I'm designing a structure with wire cables that is to have LED Christmas lights hung on it from a tall tower. The tower has a ring beam attached at the top and there is a ring beam of larger diameter at the bottom that is anchored to the ground with columns. Stretching between these two ring beams are 84 wire cables in a circle with LED's on them that form a Christmas tree of lights. Each wire is approximately 78 feet long. I am analyzing the "tree structure" in RISA to determine ring beam forces, column forces and uplift, and tension in the wires. Unfortunately, since RISA isn't a non-linear program it won't do catenary action of the wires, so I am forced to basically fake this force in using thermal loads to create the tension. This is all fairly well and good until I get to the wind forces. Catenary tension and cable deflection is pretty easy to determine as long as you have fixed ends on either side of the cable. However, in my case since the ring beams have some flexibility and there is a spring on one end of each wire, the determination of the catenary tension and its equivalent thermal load isn't as easy.

With a fixed end condition, the cable develops 625 pounds of tension under a 2.2 plf load and 32" deflection. My question is fairly simple: if I effectively have springs on the end of this cable, will it still have the 625 pounds of tension due to the same wind load? Intuitively, it doesn't seem like it would since your y_max (deflection) would get larger thus your P (tension) would get smaller assuming the same distributed load. But since this is a horizontal force on a fairly vertical wire (and ignoring self weight) I wasn't sure if that was necessarily the case from an outside force. I couldn't find any literature that addresses spring end conditions

Basically what I'd like to do is to take a wire into a separate RISA model, determine the thermal load required to create a 625 pound load with fixed ends, then apply that exact same thermal load to all of the wires in the tower model. Obviously, since those wires have springs on the end you will not develop a 625 pound tension load in the wires, but I don't know if that is realistically accurate or not when a wind load is applied. Does anyone know if this is an acceptable way of modeling this problem? Or I suppose, could anyone check this in SAP2000 or another non-linear analysis program?

Thanks.

 

[BAretired]

How much do the springs elongate under a tension of 625#? How much does the wire stretch? How much does each ring deform?

Under wind load, 84 wires are not going to behave identically, so the rings will have asymmetric loads resulting in asymmetric deformation.

Why are you ignoring the dead weight of the wire and LED lights? What kind of precision are you looking for? Can't you make an educated guess using hand calculations?

BA

 

[paddingtongreen]

Before you try to run this through RISA, you need to understand what is going on.
You say, "With a fixed end condition, the cable develops 625 pounds of tension under a 2.2 plf load and 32" deflection." Is this 32" deflection calculated from the load, length and wire properties, or assumed?

What initial tension are you using for the wire?

If the spring is more flexible than the wire in tension, of course it makes a difference.

Worry less about Risa and more about the behavior under load.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[bnickeson]

BA: We only know somewhat vague information about the springs so far, but it would appear they elongate somewhere in the neighborhood of 2" at 625#. The ring has varying deflections at each point around the circle. It's supported by eight columns, so at those eight columns the deflection is essentially zero. Between the columns though the ring beam will deflect so the effective spring stiffness at those locations is less than at the columns. Thus the issue that prompted this post. And I realize that 84 wires are not going to behave identically under a given wind load, but for analysis purposes I'm not sure what other assumption you could make other than applying the calculated wind load to all of the wires. And I meant we were ignoring self weight only for the consideration of the wind load case for our catenary problem on what is very nearly a vertical wire. For the wind load case only, this is a catenary cable with zero pretension and a perpendicular load. The dead load and pretension will be included in all of the load combinations and will apply an additional tensile load to the wires.

paddington: I am trying to understand what is going on, which is the reason I asked about this! The 32" deflection was calculated using the P = wl^2/8y equation, then verified using y = l*(3wl/64EA)^1/3 equation from Roark and by geometry. The initial tension will be between 100# and 200#. The folks who will be erecting it couldn't be more specific so I've assumed 200#. And I assumed the springs would make a difference in the tensile load in the wires as I mentioned above, but had nothing to quantify it other than the RISA model and fake thermal loads. My main question is whether the thermal loads will accurately model this reduction in tension due to the springs on the ends of the wires and the effective springs due to the flexibility in portions of the ring beam. I believe it does, but have no way to verify it other than an extremely complex iterative analysis.

 

[BAretired]

If the wires and rings can take it, why not just be conservative and design for the 625#, ignoring any potential reduction?

If you need more precision than that, I don't see why the thermal loading wouldn't provide the correct result provided the temperature was selected to account for the total strain of all the elements.

An approximate method would be to divide the span into four equal parts, assign a deflection of 32" to the middle point and 24" to the quarter points. Then determine using Pythagoras' theorem how much the sag increases with the known change in length. And if you want more precision than that, divide the span into eight equal parts and do the same, assigning initial sag in the form of a parabolic curve.

BA

 

[dhengr]

Bnickeson:
Show us a sketch with some approx. sizes, dimensions, wire rope dia. and wt., etc., so we have a better feel for the proportions of this thing. What is the center tower or pole? You should have some say in how this thing is built, as you learn and understand how it works; not just be checking their ideas, if they don’t work or detail well. Although, if they have done these before and they have worked, I’ve seen set ups like this before, you have a good starting point. Is each of the 84 wires a single wire, or are they each a light wire rope, size, wt. per ft., etc.? What kind of end hardware is contemplated? Are the springs tension (extension) springs or compression springs under the bot. ring, which cause wire tension, but can bottom out, can go solid? The wire tension will be limited to (or by) the spring force which will lead to the wire shape, catenary shape. What are the spring sizes, lengths, spring constants, etc.? Why not let the bot. ring hang vert. within limits, moving up and down, maybe be weighted by some amount, so thermal affects go away. Tie the entire bot. ring down to the ground with springs. You may have a catenary tension problem, but it is a strange one since the chord slopes are darn near vert., at least very highly sloped. It seems to me that wind loading and potential vibration problems might be the biggest issue. Maybe you want some spacers (a spacer ring, light wire truss), all around btwn. the vert. wires, at the quarter points of the 78' wire length. Otherwise, the wire rope is loaded by self weight and spring tension which is almost all along the axis of the wire, only a small perpendicular component, maybe negligible. Where do the 625lbs. tension, 2.2plf loading and 32" deflection come from? I can’t imagine that much potential deflection not tangling every other wire up with its neighboring wire and lights. I’m just throwing out some ideas here, I’ve not run any calcs.

You might do well to take a look at design methods and criteria for electrical power transmission wires. These systems have many things in common with your tree design. Although, I think I would try to do most of the early (prelim.) design by hand, there are reasonable methods in the literature. I just don’t think you even know how to model this system correctly, even if you do have a fancy FEA program. Either by hand calcs. or simple FEA, how does a single vert. wire react to wind load, including self weight and ice loads. Now, move this wire 10 or 15̊ away from vert.