# Mechanics of Materials II - Mohr's Circle

1. Apr 19, 2007

### Double A

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

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

Given in the provided figure:
$$\sigma_x$$ = -120 MPa
$$\sigma_y$$ = -60 MPa

2. Relevant equations

$$\sigma_{ave} = \frac{\sigma_x + \sigma_y}{2}$$

$$R = \tau_{max} = \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}$$

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

$$\tan{2\theta_p} = \frac{2\tau_{xy}}{\sigma_x - \sigma_y}$$

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:

$$\sigma_{max} = \frac{\sigma_x + \sigma_y}{2} + \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}$$

Solve for $$\tau_{xy}$$ and inputing known values:

$$\tau_{xy} = \pm$$59.9 MPa

Last edited: Apr 19, 2007