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Mechanics of Materials II - Mohr's Circle

  1. Apr 19, 2007 #1
    1. The problem statement, all variables and given/known data

    For an element [Stress Block], determine the range of values of [tex]\tau_{xy}[/tex] for which the maximum tensile stress is equal to or less than 60 MPa.

    Given in the provided figure:
    [tex]\sigma_x[/tex] = -120 MPa
    [tex]\sigma_y[/tex] = -60 MPa

    2. Relevant equations

    [tex]\sigma_{ave} = \frac{\sigma_x + \sigma_y}{2}[/tex]

    [tex]R = \tau_{max} = \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}[/tex]

    [tex]\sigma_{max,min} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}[/tex]

    [tex] \tan{2\theta_p} = \frac{2\tau_{xy}}{\sigma_x - \sigma_y}[/tex]

    3. The attempt at a solution

    I have drawn a representation of Mohr's Circle using the provided data. I am confused with the statment saying "tensile stress" when the provided stresses are in compression. They represent the shear stress in the positive direction. I am also unclear about how to approch this beyond my Mohr's circle figure.

    I'm not sure if this is correct but I tried this:

    [tex]\sigma_{max} = \frac{\sigma_x + \sigma_y}{2} + \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}[/tex]

    Solve for [tex]\tau_{xy}[/tex] and inputing known values:

    [tex]\tau_{xy} = \pm[/tex]59.9 MPa
    Last edited: Apr 19, 2007
  2. jcsd
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