Tension of wire between posts with weight added to the wire

Click For Summary

Discussion Overview

The discussion revolves around calculating the tension in a wire that is tensioned between two vertical steel posts when a weight is applied to the middle of the wire. Participants explore the mechanics involved, including assumptions about wire stretch, angles, and material properties, while addressing the complexities of the problem.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Bob presents a scenario involving a wire tensioned to 400N and a 1000N weight applied at the center, expressing confusion about the tension dynamics.
  • bobbles22 calculates the tension in the wire to be approximately 7210 N, contingent on the wire's cross-sectional area and tensile yield strength.
  • Bob questions the calculation methods and presents an alternative estimate of approximately 24,000N based on wire elongation and angles.
  • nvn seeks clarification on the calculations and expresses confusion regarding the mechanics involved, particularly in contrast to solid structures.
  • Another participant provides a detailed calculation involving cable elongation and sag angle, arriving at a tension of 7210 N while requesting additional cable properties.
  • Bob reiterates the initial conditions and suggests a method involving triangular calculations and varying angles, noting that pretension affects vertical load capacity.
  • There is a disagreement regarding the effect of pretension on cable load capacity, with one participant asserting it increases capacity while another claims it decreases it.
  • Bob shares updated figures for cable properties, including Young's Modulus, and recalculates the tension to be 10867N, acknowledging a previous error in his calculations.
  • bobbles22 expresses that the new modulus of elasticity will significantly alter previous results and requests clarification on the cable's cross-sectional area.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and the effects of pretension on cable load capacity. There is no consensus on the correct tension value, as multiple calculations yield different results based on varying assumptions and methods.

Contextual Notes

Participants mention various assumptions, such as wire stretch, angles, and material properties, which may affect the calculations. The discussion highlights the complexity of the problem without resolving the differences in approach or results.

bobbles22
Messages
16
Reaction score
0
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
 
Engineering news on Phys.org
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.
 
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?
 
nvn: how do you get this figure, could you explain your working? I am 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
 
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:
bobbles22 said:
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

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.
 
alpha92 said:
Pretension increases the capacity of vertical load.
No, an increase in pretension decreases the cable load capacity.
 
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 into a radius, as I had a brain-fart!).
Thanks for everyones help. It is greatly appreciated.
Bob
 
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?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
9K
Replies
1
Views
12K
Replies
3
Views
3K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 3 ·
Replies
3
Views
5K
Replies
6
Views
6K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 9 ·
Replies
9
Views
5K