Cable deflection with 1000N midpoint load and tension to limit sag to 0.7m

[McLaren50]

TL;DR

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

 

[Chestermiller]

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?

 

[AZFIREBALL]

Go to YouTube and search for 'cable deflection'.

 

[FEAnalyst]

From "Roark's Formulas for Stress and Strain":

 

[Chestermiller]

From "Roark's Formulas for Stress and Strain":

View attachment 259449

this applies to beam bending, not cable or wire stretching.

 

[FEAnalyst]

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.

 

[Chestermiller]

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.

 

[Dr.D]

The fun comes when the load is applied at a location other than the center.

 

[Baluncore]

Welcome to PF, and the triangle of forces.

https://en.wikipedia.org/wiki/Lami's_theorem
Don't forget the mass of the cable.