- #1
Double A
- 31
- 0
Homework Statement
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
Homework 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]
The Attempt at a Solution
I have drawn a representation of Mohr's Circle using the provided data. I am confused with the statement 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: