How Is Cable Deflection Modeled Under Uniform Wind Loads?

[bouferrouk]

Anyone has come across the problem of a cable deflection (static) under the effects of wind? Iam looking into the problem of the deflection of the electric contact wire of a train (the wire above the train from which it extracts electric energy) under the effects of side winds and I wonder how to model this problem and solve it statically. You may assume the wind is acting uniformally along the cable. One possible solution i thought about is to treat the cable deflection in the same way as a "catenary" which represents the deflection of a chain or cable under its own weight. But Iam not sure...Any help is greatly appreciated...Does anyone know of an expression for cable deflection under uniform load if the cable is fixed at two ends?

 

[FredGarvin]

I don't think the catenary (cosh function) is the way to go in this case. Since the deformation is not due solely to it's own weight, I would treat the cable as a cantilever beam with a uniformly distributed load.

I'm not really familiar with the make up of one of these cables. Are they relatively rigid? What is the construction like?

 

[bouferrouk]

Thanks mate. Although the cable has stiffness and could be treated as a cantilever beam it has a long length (60m)...sorry i should have said this before. Hence, I thought I should treat it as a flexible cable as it will be in a slack condition. I think the contact wires for train overhead lines are made of copper (E = 120*10^3;) and each cable hungs between two vertical masts a repeated fashion.

The point about the catenary was to as follows. For a flexible cable or chain the weight is uniformally distributed along the cable and it will sag under its own weight (well the catenary!). Now under wind effects, I will ignore the weight effects and only treat the uniformally distributed wind force which I assume will have a similar effect on cable displacement and hence may be treated as a catenary problem. Or I can combine both the effects of cable weight and wind force which are uniformally distributed and take the cable to behave as a catenary?


Anyway, to be honest Iam looking for another way. There must be an expression (somewhere!) for a cable displacement when it is supported at both ends??


Let me know.

 

[FredGarvin]

I see what you're meaning now. I would think that you could solve each different scenario separately and superimpose the two results to obtain the final combined loads. That does assume a linear combination is an acceptable assumption.

You may want to see if you can purchase or get a hold of this paper:
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMOEEX000123000001000043000001&idtype=cvips&gifs=yes

 

[AlephZero]

I would think that you could solve each different scenario separately and superimpose the two results to obtain the final combined loads. That does assume a linear combination is an acceptable assumption.

I would be wary of making that assumption, because

1. The wind loading depends on the deformed shape of the cable

2. There is a difference in shape between a free hanging cable (a catenary) and a cable with uniform load per horizontal length (a parabola), so these assumptions do make a difference.

I've no personal experience of analysing this sort of cable problem, but AFAIK the ABAQUS finite element program can handle this type of problem - for example modeling deep-water mooring cables and long tow ropes including the effects of water currents, etc.

 

[FredGarvin]

I would be wary of making that assumption, because

1. The wind loading depends on the deformed shape of the cable

Good point. I completely over looked that.

 

[bouferrouk]

Ok guys thanks very much for your replies and suggestions so far. Not sure if the linear superposition is acceptable as the problem of cable deflection under own weight and external uniform load would mostly be nonlinear (from common sense anyway).

I am looking for a simple case to start with. From what I have read around there seems to be a great deal of difference on whether a flexible cable under uniform external load, apart from its own weight, would behave as a catenary or a parabola. If I neglect the effects of own weight and so take the initial cable to be 'straight', and consider an external uniform load over a cable supported at both ends, what would the cable displacement equation look like? I am hoping textbooks or whatever have these somewhere...

Many thanks.

 

[jim mcnamara]

You may want to consider sag due to ambient temperatures, which will change the "shape" of your beam - cable sag is not trivial.

#0 transmission wire (copper) over 60m will move vertically a non-trivial distance from 0 C to 35 C. At any rate the length of the "catenary" or whatever you consider will change with temperature.

 

[bouferrouk]

Ok I have found the following link which talks about the deflection of a cable that under a uniform loading and supported at both ends.

http://www.ecf.utoronto.ca/apsc/courses/civ214/Lectures/Cables_carrying_uniform_load.html


However, not sure how cable deflection under its own weight is taken care of? Can some1 verify if the working presented applies to my case?


Cheers.

 

[kach22i]

The cable will be in tension similar to a Post-Tension rebar or cable found in a concrete plank (like in a long-span stadium), right?

There must be a side force to be calculated in these elements as the tension does not do all the work independent of all other forces acting on the beam.

Just take away the concrete tee.

EDIT:
I just clicked the link provided. Remember that if you are not terminating the connection at each and every end you just might have a continuous beam with multiple supports which is very different than a simple span. I'm not sure you will get the same kind of moment in a cable though.

http://www.necs.fr/gb/illu_precontrainte.php
http://www.necs.fr/photos/prec_maillage-deformees.jpg

 

[bouferrouk]

Ok guys found this link in which a differential equation is given, as part of a question, for the transverse deflection of a cable due to uniform wind loading q (Question number 4)

http://numericalmethods.eng.usf.edu/mcquizzes/08ode/finite_dif_method.html

Would anyone verify that the differential equation is correct. I assume the boundary conditions are zero deflections at wire ends (x=0 and x=L) which would help to solve for a general expression of wire deflection under uniform loading. Notice it has the cable tension and cable flexural stiffness involved which makes sense.

Any help is appreciated.