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

  1. Feb 1, 2008 #1

    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.
     
  2. jcsd
  3. Feb 8, 2008 #2
    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.
     
  4. Feb 8, 2008 #3
    If this is not a homework type question, you might try Eng-Tips to see if anyone on there knows.
     
  5. Feb 8, 2008 #4

    Andy Resnick

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    Science Advisor
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    2016 Award

    Where did you find the formula?

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

    but no obvious derivations...
     
    Last edited by a moderator: May 3, 2017
  6. Feb 8, 2008 #5
    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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