Wire Tension Formula: Shape Expression w/ 3 Pivots

In summary, the OP is looking for an expression to represent the shape of a wire bent by three pivots. The term "elastica" is well defined and is the shape of a post-buckled column.
  • #1
Goinger
1
0
TL;DR Summary
If the wire is bent by three pivots, I want to find an expression that represents its shape.
If the wire is bent by three pivots, I want to find an expression that represents its shape.
There will be tension of wire and other physical factors.
How can it be expressed?
 
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  • #3
That does not sound like the elastica problem at all to me. The elastica is the shape of a post-buckled column, but OP is talking about a bending problem.
 
  • #4
Dr.D said:
That does not sound like the elastica problem at all to me. The elastica is the shape of a post-buckled column, but OP is talking about a bending problem.
The elastica is a more general field. You are considering only your experience and should also consider other things like meanders, splines and Bezier curves.

The "pivots" are control points or boundary conditions, while the elastic deformation is distributed through the elastic bending of the rod between the pivots.

Because the elastica problem can become complex, the OP needs to present a more complete description of the question. Maybe define "pivot" and "wire".
 
  • #5
Baluncore said:
The elastica is a more general field. You are considering only your experience
No, you are mistaken. The term elastica is well defined as the shape of the post-buckled column. For all the other items you mention, we have their own names to identify them.
 
  • #6
Dr.D said:
No, you are mistaken.
The Elastica is now a multidisciplinary field of applied mathematics. While it can obviously be applied to the shape of a slender column, it is not restricted to buckling failures in structural engineering.

As a narrow minded structural engineer you have no right to censor the OP, nor to deny the use of Elastica, for example, to biological structural membranes and their equilibrium positions.

I suggest you find and study a copy of “The Many Faces of Elastica” by Ivaïlo M. Mladenov and Mariana Hadzhilazova. 2017.
 
  • #7
Thread closed for Moderation...

After a Mentor discussion, the thread will stay closed.
 
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FAQ: Wire Tension Formula: Shape Expression w/ 3 Pivots

What is the wire tension formula?

The wire tension formula is a mathematical equation used to calculate the amount of force or tension exerted on a wire based on its shape and the number of pivots it has. It is commonly used in mechanical engineering and physics to determine the stability and strength of structures.

How is the wire tension formula derived?

The wire tension formula is derived from the principles of static equilibrium, which states that the sum of all forces acting on an object must equal zero for it to be in a state of rest or constant motion. By analyzing the forces acting on a wire with three pivots, the formula can be derived to determine the tension in the wire.

What are the variables in the wire tension formula?

The variables in the wire tension formula include the shape of the wire, the distance between the pivots, and the angles at which the wire is attached to the pivots. These variables are used to calculate the tension in the wire and can be adjusted to determine the optimal shape and configuration for a given structure.

How accurate is the wire tension formula?

The wire tension formula is a simplified model that assumes the wire is perfectly rigid and the pivots are frictionless. While this may not be completely accurate in real-world scenarios, the formula provides a good estimate of the tension in the wire and is widely used in engineering and physics calculations.

Can the wire tension formula be applied to wires with more than three pivots?

Yes, the wire tension formula can be modified to accommodate wires with more than three pivots. However, the calculations become more complex as the number of pivots increases, and the accuracy of the formula may decrease. In such cases, computer simulations or physical experiments may be necessary to determine the tension in the wire.

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