## Deflection of tensioned wire rope

## Deflection of tensioned wire rope

(OP)

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.

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.

## RE: Deflection of tensioned wire rope

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.

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

I’m inclined to agree with HotRod10.

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

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.

## RE: Deflection of tensioned wire rope

A couple notes:

## RE: Deflection of tensioned wire rope

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

## RE: Deflection of tensioned wire rope

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.

## RE: Deflection of tensioned wire rope

Thanks

## RE: Deflection of tensioned wire rope

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 ?

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

## RE: Deflection of tensioned wire rope

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

My calculation is very close to your 2nd method.

## RE: Deflection of tensioned wire rope

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