Relationship of spring constant and torsion constant?

[NoviSad]

Homework Statement

I'm trying to find a relationship between spring and torsion constants for an experiment but am not sure what it is and am struggling to find it.

Homework Equations

Torque = Torsion Constant * Angle of Twist

Force = Spring Constant * Extension

Shear Modulus = Force*Length/Area*Extension

The Attempt at a Solution

I have absolutely no idea.

 

[SteamKing]

The spring constant and the torsion constant measure different actions on a body. The spring constant is fundamentally related to the axial compression of the spring, while the torsion constant measures the effect of twisting on the spring.

AFAIK, the two constants are not related.

 

[unscientific]

The variables involved are orthogonal to one another ($r$ vs $\phi$), so they are independent of one another.

 

[AlephZero]

If you are asking about a straight wire, the two material properties (Young's modulus and shear modulus) are independent of each other. There is a formula that connects E, G, and Poisson's ratio for isotropic materials, but any two of those three constants are independent.

If "spring constant" means you are talking about a coil spring, there is a complicated relation between the extension and torsion stiffness which involves the geometry of the spring (turns per unit length, diameter of the wire, and diameter of the coils) as well as the shear modulus of the material. But most real-world springs are meant to be used either in extension or in torsion, but not both together.

 

[NoviSad]

If you are asking about a straight wire, the two material properties (Young's modulus and shear modulus) are independent of each other. There is a formula that connects E, G, and Poisson's ratio for isotropic materials, but any two of those three constants are independent.

If "spring constant" means you are talking about a coil spring, there is a complicated relation between the extension and torsion stiffness which involves the geometry of the spring (turns per unit length, diameter of the wire, and diameter of the coils) as well as the shear modulus of the material. But most real-world springs are meant to be used either in extension or in torsion, but not both together.

Strange, I was seemed to be made to believe there definitely was one. Talking about a rubber band by the way.

 

[NoviSad]

1. Homework Statement
Does extension affect the torsion constant in any way?

Known data: Extension, Force, Time Period
2. Homework Equations

Time Period of a Torsion Pendulum = 2PI sqrt(Moment of Inertia/Torsion Constant)
3. The Attempt at a Solution

Having a very hard time, unsure what to do to figure this out, even with the data.

 

[her]

what is the relationship between the spring constant and the outer diameter of the spring?

 

[haruspex]

The terminology for springs is confusing.
An everyday helical spring under tension or compression works by torsion of the material. As you pull the ends and stretch out the spring, the wire undergoes torsion. If a spring of N coils, fully closed when relaxed, is pulled completely straight (and the ends of the wire not allowed to rotate the applied load) it will have a net strain of 2πN along its length.
To figure out the algebra, it might be easiest to start with a simple loop of wire, cut at some point. If the two ends of the cut are displaced from each other by one wire thickness they now form one loop of a fully compressed spring. Through what angle will the two cut ends have turned on their core axes?

There are also "torsion springs". In this case, a torque is applied along the main axis of the helix, tightening or expanding the spring diameter. As far as the wire is concerned, this is a bending moment, not torsion. See https://en.wikipedia.org/wiki/Torsion_spring.

A third way to use a helical spring is to bend it sideways. This again produces torsion in the wire, but unevenly.