Question

When the two principal stresses are equal and are alike, the resultant stress on any plane is

• A. Equal to the principal stress
• B. Zero
• C. One-half of the principal stress
• D. One-third of the principal stress

Hint:

If \[ \boxed{\sigma_1=\sigma_2,} \] Mohr's circle reduces to a point and the stress on every plane is equal to the principal stress.

Answer 1

The Correct Option is A

Step 1: Recall the condition of equal principal stresses. Let \[ \sigma_1=\sigma_2=\sigma. \] When the principal stresses are equal, the state of stress is hydrostatic (or isotropic).

Step 2: Determine the stress on any plane. Since the normal stress is the same in every direction and the shear stress is zero, \[ \sigma_n=\sigma, \qquad \tau=0. \] Hence, the resultant stress on every plane is simply \[ \boxed{\sigma.} \] Therefore, \[ \boxed{(A)} \] is the correct answer.