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Elasticity: Determine zero normal stress plane

  1. Mar 8, 2014 #1
    Given the stress tensor in a point, determine the zero normal stress plane.
    .....2 3 0
    T= 3 2 0
    .....0 0 5
    ----------------------
    Eigenvalues: σ1=σ2=5, σ3=-1
    It must be simple, but I don't know how to determine the normal vector of that plane analytically.

    I know σ=0.
    t=Tn=σ+τ=τ
    If normal stress σ equals zero, ¿the shear stress will be the maximum value of τ ((σ1-σ3)/2)?

    Taking a look to Mohr's circle I think τ in that plane must be the intersection between the circunference and the τ axis, but that's not τmax.

    I'm confused.
     
  2. jcsd
  3. Mar 9, 2014 #2
    Okay, I think I got it.

    Using the equation of the mayor circunference of center (0,2) and radius R=3 from Mohr's circle, we make σ=0. Then we isolate the shear stress.

    (σ-2)2+(τ-0)2=32

    τ=√5

    Now that I have the modulus, I want to know the normal direction of the plane in which shear stress equals √5.
     
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