(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Mechanics of Materials II - Mohr's Circle

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