Question

Which one of the following represents deviatoric stress in a 2D stress Mohr Circle?

• A. Radius
• B. Center
• C. Pole
• D. Diameter

Hint:

- Center of Mohr circle = Mean stress (hydrostatic).
- Radius of Mohr circle = Deviatoric stress.
- Diameter = Differential stress.
- Pole = Used to find stress orientation, not stress magnitude.

Answer 1

The Correct Option is A

Step 1: Recall Mohr Circle construction.
In a 2D stress system, the Mohr circle is drawn using the maximum principal stress (\( \sigma_1 \)) and the minimum principal stress (\( \sigma_3 \)).
- The center of the circle is located at \( \frac{\sigma_1 + \sigma_3}{2} \), which represents the mean stress (or hydrostatic stress).
- The radius of the circle is \( \frac{\sigma_1 - \sigma_3}{2} \), which represents the deviatoric stress.
Step 2: Distinguishing stress components.
- Mean stress (hydrostatic) → Center of the circle.
- Deviatoric stress → Radius of the circle, since it shows the differential stress between the principal stresses.
- The diameter of the circle corresponds to \( \sigma_1 - \sigma_3 \), i.e., the total differential stress, not the deviatoric stress alone.
- The pole is a graphical construction point used to determine stress on any plane, but it does not represent deviatoric stress directly.
Step 3: Final Answer.
Thus, in Mohr circle analysis: \[ \text{Deviatoric stress} = \frac{\sigma_1 - \sigma_3}{2} = \text{Radius of the Mohr circle}. \] \[ \boxed{\text{Radius (Option A)}} \]