1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted