Understanding the deflection of a cable under tension with a force applied in the middle

In summary, the conversation discusses the relationship between tension, force, and deflection in a cable with given properties. The force of 1000N is applied normally, and the length of the cable may affect the results. The concept of beam bending is mentioned, but it is noted that the cable can be treated as a beam due to its flexibility. Other factors such as the location of the force and the mass of the cable are also brought up. The conversation concludes with a reference to Lami's theorem and the triangle of forces.
  • #1
McLaren50
1
0
TL;DR Summary
I have a cable under tension. In the middle of the cable a force is applied. I want to understand the relationship between the force applied, the tension of the cable and the resulting deflection of the cable at the location of the applied force.
With the above in mind, I have a cable of E=60GPa, cross sectional area 7e-4m^2. I want to understand the relationship between the tension applied resisting the deflection of the cable when a force is applied so that the cable will not deflect more than 0.7m in this case. Take the force as 1000N.
Thanks
 
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  • #2
Would it be correct to say that the force is applied normal to the cable? Would you say that the length of the cable matters?
 
  • #3
Go to YouTube and search for 'cable deflection'.
 
  • #4
From "Roark's Formulas for Stress and Strain":

cable Roarks.jpg
 
  • #5
FEAnalyst said:
From "Roark's Formulas for Stress and Strain":

View attachment 259449
this applies to beam bending, not cable or wire stretching.
 
  • #6
Chestermiller said:
this applies to beam bending, not cable or wire stretching.

It's in the table of beam bending cases (with restricted horizontal displacement) but, as they say in the description, due to perfect flexibility this can be treated as a cable.
 
  • #7
FEAnalyst said:
It's in the table of beam bending cases (with restricted horizontal displacement) but, as they say in the description, due to perfect flexibility this can be treated as a cable.
Oops. Sorry. I mistook that A as an I.
 
  • #8
The fun comes when the load is applied at a location other than the center.
 
  • #9
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1. What is the equation for calculating the deflection of a cable under tension with a force applied in the middle?

The equation for calculating the deflection of a cable under tension with a force applied in the middle is:
d = (FL^3)/(48EI), where d is the deflection, F is the applied force, L is the length of the cable, E is the Young's modulus of the cable material, and I is the moment of inertia of the cable cross-section.

2. How does the deflection of a cable change with an increase in applied force?

The deflection of a cable increases proportionally with an increase in applied force. This means that as the force increases, the deflection also increases.

3. What factors can affect the deflection of a cable under tension?

The deflection of a cable under tension can be affected by several factors, including the magnitude of the applied force, the length and stiffness of the cable, and the material properties of the cable.

4. How does the position of the applied force affect the deflection of a cable?

The position of the applied force can greatly affect the deflection of a cable. When the force is applied in the middle of the cable, the deflection will be at its maximum. However, if the force is applied closer to one end of the cable, the deflection will be less.

5. How can the deflection of a cable under tension be reduced?

The deflection of a cable under tension can be reduced by increasing the stiffness of the cable, decreasing the length of the cable, or increasing the Young's modulus of the cable material. Additionally, using multiple cables or adding supports can also help reduce the deflection.

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