Deflection of tensioned wire rope 4

[alexpazolinid]

Hi,
I have searched for this topic and found similar questions but they are not applicable to my case.
I was wondering if I could get some help to find the deflection of a 7x7 wire rope upon vertical loading.
Scenario: A 10-meter 7x7 wire rope with diameter still to be decided (for now I am using 30 mm) fixed support on each end with a load of 2000 kg acting right on the middle (worst case scenario). I assumed no sag as the cable will be pre-tensioned with 300 kgf of tension on each side.
Problem: I have used two sources for calculating the deflection of this 7x7 wire rope and the values differ considerably. (Please find attached references in case needed)
Results:
• Design of Prestressed Barrier Cable Systems ( by James D. Roger) page 4 , eq 5 = 500mm
• Tiger Wire Rope Engineering Handbook page 18 , eq 26 = 2003mm
I found interesting that Wire Rope Engineering Handbook does not consider the youngs modulus of the wire rope and the other source does not take into account the pretension of the cable. Also, to verify these results, I conducted an FEA model and the result is giving even less deflection of the cable, around 30mm which I don't believe is right.

 

[JStephen]

Assume a deflection value.
From geometry, you can figure the change in length, thus the strain, then the stress, which is additive to the prestressing stress
From that stress and the geometry, you can figure the corresponding force.
Repeat and adjust as necessary.
The wire rope will have reduced effective E due to the construction, see the wire rope literature. So not the same as a bar.

 

[BridgeSmith]

So you're going to put 300 kgf pretension into a 8mm cable and then add a 2000 kg vertical load to it? Calculating the deflection is easy - it's infinite, since it will break instantaneously.

 

[3DDave]

Twisted wire rope has some internal movement as the strands move over each other. I expect the FEA model did not include the factor and treated it as a single rod.

 

[MIStructE_IRE]

For context, thats a taught wire, 8mm thick, 10m long with a Mercedes E Class hanging out of it.

I’m inclined to agree with HotRod10.

 

[Tomfh]

I made a zip line for my kid using 10mm cable. It had 5% initial drape. I load tested it by lifting end up the end of my car. I wouldn’t like to repeat the experiment lifting the whole car with a short, taut 8mm cable.

 

[alexpazolinid]

Funny how I typo changes the situation a lot hahah
Yeah, an 8mm diameter is more house wire balustrade than a construction purpose wire rope... not even 150 kilos on it would do.
Anyway, I have this spreadsheet for calculating the deflection using the equations from my post sources' so an iterative calculation would be a little bit of a pain but that might work. Thanks for advice JStephen.

 

[CANPRO]

JStephen has given you good advice to get started. I checked your scenario with my spreadsheet and got a deflection value of around 400mm, assuming 30mm cable, effective area of about 0.6*gross, and an effective modulus of about 0.5*steel, and a self weight of 3.4 kg/m.

A couple notes:
[ul]
[li]You can't assume zero sag. Cut the cable in half and draw the free body diagram - zero sag = infinite pre-tension, this condition does not exist. With your condition (span and pretension) and the assumptions I've stated above, I get an initial sag of about 140mm[/li]
[li]Per JStephen's advice, assume an initial sag or pretension - these two values are directly related (see free body diagram above). You can use this to calculate your initial cable length[/li]
[li]Once you have an initial cable length, you can start to look at your loaded condition. With the point load applied, assume the cable takes straight lines from the supports to the applied load (forming a triangle)[/li]
[li]Based on this triangle, calculate the tension in the cable, the additional strain, and the new cable length - this gives you a new triangle with new tension values - this is where the iteration comes into play.[/li]
[/ul]

 

[rb1957]

the cable will deflect, and the cable will develop tension. The vertical component of the tension reacts the applied weight.



another day in paradise, or is paradise one day closer ?

 

[BridgeSmith]

Excellent summation of the approach, CANPRO, and your area, effective modulus, and final deflection look about right.

I haven't run the numbers myself, but if CANPRO's numbers are correct, the tension in the cable is well beyond the working strength for a high strength wire rope of that size (I didn't find the 7x7 construction in anything close to that size, mostly 6x36) and about halfway to the breaking strength. A larger cable or more sag may be necessary to meet safety factor requirements.

 

[alexpazolinid]

Thanks CANPRO and JStephen. It has been my first time looking at deflection in wire ropes and this is also a parallel work I need to do for a much bigger project. Anyway, I was also wondering how is this new value for tension reacting with the pretension applied to the cable? Through T=Load applied/2*sin(angle) I found the tension which is generated by the load. Is this new tension contributing positively to 250 N I had previously? Also, I found a sag value of around 120 mm (I had to adjust some initial inputs) and my solution does not differ much for the case were I neglected it. I approached this in a slightly different way than JStephen by assuming a deflection value -> change in length from 5m and deflection -> strain -> stress -> applied force as F/A -> T=F/2sin(initial theta) -> Goal Seek
Thanks

 

[rb1957]

cable tension is cable tension. The pre-tension gives the cable some stiffness to resist sag.

once you've applied load, you need cable tension to react this, as you're working out. btw, it'd help us understand your problem and solution and capability if you included that sentence about solving deflection for cable tension to react the load.

another day in paradise, or is paradise one day closer ?

 

[alexpazolinid]

After a few weeks working on this project, I came up with two calculations which are driving me nuts. They give different values for the deflection and I believe it is a matter of working around with sag and strain for the wire rope. Can anyone comment on these two calcs I have attached as a spreadsheet ? Cheers

 

[TLHS]

Is this in a climate controlled space? thermal effects can be significant on a span of that length.

 

[alexpazolinid]

Yes, it is... thermal effects are not a concern for now

 

[CANPRO]

Alex, with the cable and span properties shown in your attached spreadsheet, I get the following values from my spreadsheet:

Initial Sag = 32mm, Loaded Sag = 658mm, Loaded Cable Tension = 2010 kg

My calculation is very close to your 2nd method.

 

[rb1957]

why the difference in row 30 "change in length" ? wouldn't the larger assumed? hori. deflection have the larger change in length ?

another day in paradise, or is paradise one day closer ?