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Homework Help: Princiap Stress and Strains

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data

    For a plane stress state, show that the principal stresses and strains occur in the same direction?

    2. Relevant equations

    Hookes Law for PLane Stress States
    Principal Stress is tan(2θ)=2δ/([itex]\sigma[/itex]x-[itex]\sigma[/itex]y)
    Principal Strain is tan(2θ)=[itex]\gamma[/itex]xy/([itex]\epsilon[/itex]x-[itex]\epsilon[/itex]y)

    3. The attempt at a solution


    I cannot see how to get rid of (1+v)/E, can anyone help me out please.
  2. jcsd
  3. Oct 12, 2012 #2
    What do the Hooke's law equations for each of the stresses explicitly in terms of the strains reduce to when σz is set equal to zero?
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