Deflection of a tensionned vertical cable

[1clown]

Hi Guys,
Does any body have a formula that I can use to determine the deflection of a cable due to a load applied horizontally a set distance from one end. The cable is hanging vertically and has been tensionned. All of my searching results in formulas for catenary type cables that are horizontal and have sag.
I remember that you used to be able to vote for people that had given helpful responses to posts. Can you still do this and if so how as I cannot remember how or find a tab to click on for a the replies to a post a couple of days ago.
Thanks
Kevin

 

[JAE]

1clown,
Try these threads and see if any help you. There are more - just use the search box at the top of the Eng-Tips page for "cable deflection".


thread507-111137

thread404-102006

thread507-323861

 

[rb1957]

"I remember that you used to be able to vote for people that had given helpful responses to posts. Can you still do this and if so how as I cannot remember how or find a tab to click on for a the replies to a post a couple of days ago." ... click the link beside the LPS (Little Purple Star) that shows up after each post.

follow JAE's links above.

i'd've thought that the cable would form straight lines between the load and the support; that the reactions would be as though the cable was a simply supported beam (static equilibrium), that the tension in the cable would determine the angles (to create these components), and the angles will give you the displacement (hoipefully the same displacement from both ends !?).

 

[Denial]

I think rb1957 is on the right track. If the cable is initially vertical, and if the eventual horizontal deflection of your load point is fairly small, then the "cable sag" that tends to dominate considerations of horizontal cables will not be significant (because the cable's self weight is acting parallel to the run of the cable rather than transverse to it).

HOWEVER a side effect of those preconditions (cable vertical, high initial tension) is that the axial extensibility of the cable will become a very important consideration. The problem remains highly nonlinear, but is amenable to hand calculation. The required algebra is not particularly demanding, and my recollection from times long past is that when you switch from algebra to arithmetic you end up with a cubic equation to solve for your deflection.

 

[JStephen]

I would think you could safely neglect the weight of the cable, which simplifies.

The effective modulus of elasticity for a cable can be obtained from reference books or manufacturers, and is not the same as for a bar of equivalent area or diameter.

For small deflections, I think you'd have an especially simply solution, otherwise, assume a deflection, calculate the corresponding strain, then the stress, then the lateral load required- should be quick and simple, more so with a spreadsheet.