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

AI Thread Summary
The discussion centers on finding a reference for the mathematical derivation of the spring constant formula k = G*d^4/(8*n*D^3) for coiled springs. Despite a Google search yielding no results, participants note that this derivation is a fundamental concept in linear elasticity theory. A suggestion is made to consult A. C. Ugural's "Mechanical Design: An Integrated Approach" for relevant information. Additionally, the derivation of the spring constant is linked to the deflection of a coiled spring, which can be derived using Castigliano's theorem. The quest for a definitive source continues, highlighting the challenge in locating academic references on this topic.
redoubt
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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.
 
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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.
 
If this is not a homework type question, you might try Eng-Tips to see if anyone on there knows.
 
Where did you find the formula?

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

but no obvious derivations...
 
Last edited by a moderator:
redoubt said:
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
 

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