Derivation of spring constant k: Where can I find it?

[redoubt]

Folks---

I want a reference(text or journal article) that presents the mathematical
derivation of the following formula for the spring constant k of a coiled,
ideal spring.

k = G*d^4/(8*n*D^3)

A Google search was unsuccessful.

 

[redoubt]

Spring Constant Derivation: Where can I find it?

Folks---

I want a reference(textbook or journal article) that presents the mathematical derivation of the following formula for the spring constant k of a coiled, ideal spring.

k=G*d^4/(8*n*D^3)

A Google search was unsuccessful.

When this question was asked in the General Physics Forum several weeks ago, there were 81 views, but no replies. I believe this derivation is a classic in linear elasticity theory, but I can't locate it.

 

[TVP45]

If this is not a homework type question, you might try Eng-Tips to see if anyone on there knows.

 

[Andy Resnick]

Where did you find the formula?

I found this:
http://www.sussex.ac.uk/engineering/documents/sm_lecture_19.pdf

but no obvious derivations...

 

[ok123jump]

Folks---

I want a reference(textbook or journal article) that presents the mathematical derivation of the following formula for the spring constant k of a coiled, ideal spring.

k=G*d^4/(8*n*D^3)

A Google search was unsuccessful.

When this question was asked in the General Physics Forum several weeks ago, there were 81 views, but no replies. I believe this derivation is a classic in linear elasticity theory, but I can't locate it.

This constant comes from the derivation of the deflection of a coiled spring. By deriving the deflection, one can extract the spring constant k from the equation.

The derivation of the equation for the deflection of a spring comes from Castigliano's theorem.

See A. C. Ugural "Mechanical Design: An Integrated Approach" McGraw-Hill Professional (2003): pg. 565