Question

What is the value of the maximum shear stress in a rock, for which the state of stress is given by the following Mohr circle?

• A. 20 MPa
• B. 40 MPa
• C. 50 MPa
• D. 60 MPa

Hint:

The maximum shear stress corresponds to the radius of the Mohr's circle and is calculated as half the difference between the maximum and minimum principal stresses.

Answer 1

The Correct Option is A

To determine the maximum shear stress from the Mohr circle, we can use the following relation: \[ \tau_{{max}} = \frac{\sigma_1 - \sigma_3}{2} \] Where:
\( \sigma_1 = 50 \, {MPa} \) (major principal stress),
\( \sigma_3 = 10 \, {MPa} \) (minor principal stress).
Step 1: Apply the formula
Substituting the values into the formula for maximum shear stress: \[ \tau_{{max}} = \frac{50 \, {MPa} - 10 \, {MPa}}{2} = \frac{40 \, {MPa}}{2} = 20 \, {MPa} \] Step 2: Conclusion
The maximum shear stress is \( 20 \, {MPa} \).