Problem 13.1

Please plot the correct sigma values and read the result off of the graph. Hand in the plots of the Mohr circle and where the normal and shear stress are located. Do not print out this page.

Things to Rememeber

• \(\sigma_2\) is perpendicular to \(\sigma_1\) and \(\sigma_3\)
• Angles are defined from from \(\sigma_1\) towards \(\sigma_3\)
• Angles on the Mohr diagram are double those in the real world.

Problem 13.2

Use the equations $$\sigma_n = \frac{\sigma_1 + \sigma_3}{2} + \frac{\sigma_1 - \sigma_3}{2}\cos 2\theta$$ $$\sigma_s = \frac{\sigma_1 - \sigma_3}{2} \sin 2\theta$$

You can check your work by looking at the angles

Problem 13.3

Problem 13.4

1. Plot the experiments.
2. Draw the failure envelope.
3. Meausure the slope of the line or angle of internal friction, \(\phi\).
4. Convert \(\phi\) to the columb coefficient, \(\mu\).
5. Finally, determine the angle of fracture plane with: $$\theta = 45^\circ + \frac{\phi}{2}$$