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Complex stress problem

  1. Apr 10, 2009 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data

    In an element of material, subjected to general two-dimensional stress one axial stress is 66N/mm2 (tensile) and the shear stress is 48N/mm2. Calculate the values and directions of the principal stresses and the normal and shear stresses on planes equally inclined to the axes if the other axial stress of 22N/mm2 is a) tensile and b)compressive.

    2. Relevant equations

    [tex]\sigma_n=\frac{1}{2}(\sigma_x+\sigma_y)+\frac{1}{2}(\sigma_x-\sigma_y)cos2\theta+\tau_{xy}sin2\theta[/tex]

    [tex]\tau_n= \frac{1}{2}(\sigma_x-\sigma_y)sin 2\theta-\tau_{xy}cos2\theta[/tex]

    3. The attempt at a solution

    Well I used the fact that the principal stresses are given by

    [tex]\sigma_1,\sigma_2=\frac{1}{2}(\sigma_x+\sigma_y) \pm \sqrt{(\sigma_x-\sigma_y)^2+4\tau_{xy}^2[/tex]

    and got the values to be 96.8 N/mm2 and -8.80N/mm2

    Then I used the fact that

    [tex]tan2\theta=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}[/tex]

    and got [itex]\theta=32.69[/itex]. That part I got out, but I don't know how to get the normal and shear stresses on planes equally inclined to the axes.

    I am not sure about what the question means by equally inclinded to the axes.

    EDIT:solved.
     
    Last edited: Apr 10, 2009
  2. jcsd
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