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Tension of wire between posts with weight added to the wire

  1. Sep 25, 2009 #1
    I have a problem with a design at work. We have a wire tensioned to 400N between two vetical steel posts 7m apart.

    What would the tension be in the wire if someone of about 100kgs (1000N for the sake of the calcualtion) sat on the middle of the wire. Assuming there is almost no stretch to the wire as it is spun steel rope of reasonable thickness (4mm).

    I'm confused as the tension is horizonal, but the force is vertical with no horizontal component, but you know that it is pulling the posts together more as a result of the added force.

    Any help greatly appreciated.

    Bob
     
  2. jcsd
  3. Sep 25, 2009 #2

    nvn

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    bobbles22: Assuming your cable has an equivalent solid circular cross-sectional diameter of 4.0 mm, it currently appears the tension on your loaded cable would be roughly 7210 N. If you could give us the exact solid cross-sectional area of your cable, and the tensile yield strength of your cable material, it might be helpful.
     
  4. Sep 25, 2009 #3
    Thank you for that NVN. Could you explain how you reached that answer. I got approx 24,000N. I worked on the basis that I knew the wire would stretch about 7mm, worked out the angle of the bend from horizontal, then took the 1000N acting down and worked out the horizontal compoment of it. Have you got an easier way?
     
  5. Sep 25, 2009 #4
    nvn: how do you get this figure, could you explain your working? Im not doubting you, i am just getting confused with this problem - all of my mechanics problems have always used solid steel structures, but this problem is confusing me a bit?

    Cheers
     
  6. Sep 25, 2009 #5

    nvn

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    Using the assumption stated in post 2, I currently got a cable elongation of 19.0 mm (9.5 mm per side), neglecting your cable pretension. This gave me a cable sag angle of theta = 4.21 deg. Therefore, T = 0.5*P/sin(theta) = 6811 N, where P = 1000 N. I then added to this the cable pretension stated in post 1 (400 N), as an approximation, thus giving cable tension T = 7210 N.

    If you could provide the cable properties mentioned in post 2, and the cable modulus of elasticity, it might be helpful.
     
    Last edited: Sep 26, 2009
  7. Sep 25, 2009 #6
    Solve as a triangle with point load at the bottom node, assume hinge at ends. Angle theta will increase with reduction in rope diameter and reduction in rope tension. Pretension increases the capacity of vertical load. You can compute a table for theta ranging from 5 deg to 20 deg.
     
  8. Sep 26, 2009 #7

    nvn

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    No, an increase in pretension decreases the cable load capacity.
     
  9. Sep 28, 2009 #8
    Thanks for everyones help with this. So you are aware, the figures I have put in are 7000mm initial length, 8mm extension (rounded up from 7.96mm) using Diameter 4mm (therefore radius 2 of course), Young's Modulus is 70,000N/mm2.
    Using this 8mm extension, I found the angle to be 2.74 degrees and therefore the force to be 10467N along the wire (acting as the hypotenuse) then added the 400N original force, giving 10867N total in the wire.
    Obviously, this uses the stated exact figure of Young's Modulus of 70,000 and this is likely slightly higher than the figures used by others. I have also found out my error on the original calculation (basically, I forgot to change the diameter in to a radius, as I had a brain-fart!).
    Thanks for everyones help. It is greatly appreciated.
    Bob
     
  10. Sep 28, 2009 #9

    nvn

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    bobbles22: Thanks for the modulus of elasticity. That new value will change my previous results, greatly reducing T. But we will get into that later.

    First, your results appear to be far off, unless I am misinterpreting what you wrote. What is the cross-sectional area of your cable?
     
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