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Homework Help: Proving equations for a plane stress condition

  1. Jul 29, 2010 #1
    1. The problem statement, all variables and given/known data
    For a plane stress condition (stress z-axis = 0 ), prove the following relations if strain x-axis and strain y-axis are determined by experiments.




    σ_x = stress in x-axis
    σ_y = stress in y-axis
    ∈_x = strain in x-axis
    ∈_x = strain in y-axis
    E = modulus of elasticity

    2. Relevant equations

    Poission's ratio


    v=-lateral strain/axial strain


    3. The attempt at a solution
    I'm not sure which equations I should be using to solve the problem. Can I use Hooke's Law for multi-axial loading since it is a plane stress condition?

    I have tried rearranging Poisson's ratio equation with no luck.
  2. jcsd
  3. Jul 29, 2010 #2


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    Hooke's Law only applies to uniaxial loading of a rod. You might find generalized Hooke's Law useful:


    It applies in 3-D and in any isotropic material. More http://john.maloney.org/Papers/Generalized%20Hooke%27s%20Law%20%283-12-07%29.pdf" [Broken].
    Last edited by a moderator: May 4, 2017
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