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Principal Stresses, Calculating Stress in the x and y direction and working out shear

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data

    The principal stresses at a point in a material are 50 MN/m^2 and 30 MN/m^2 , both in tension. If the angle between the Ox axis and the direction in which the greater stress acts is 40º measured anticlockwise from the direction of the greater principal stress, find σx and τxy.
    τx’y’ = 0.

    2. Relevant equations

    σn =1/2(σx +σy) + or - 1/2(σx −σy)cos2φ+τxysin2φ
    τn =+ or - 1/2(σx −σy)sin2φ+τxycos2φ

    tan2φ=(2τxy)/(σx −σy)

    σ1 or σ2 = 1/2(σx +σy) + or - ((1/2(σx -σy))2+τxy^2)^(1/2)


    3. The attempt at a solution

    I have rearranged this equation to give

    x=σ1 or σ2. I am not sure if this is right and not sure how to start this or what equations to?use.
     
  2. jcsd
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