Principal Stresses and Strains MCQ with answer and solution

Concept

Principal planes carry only normal stress, and the shear stress on them is zero.

Formula

tan 2θ_p = 2τ_xy / (σ_x - σ_y)

Step-by-step solution

1. A principal plane is defined as a plane with zero shear stress. 2. The normal stress on it is a principal stress (maximum or minimum). 3. So on the plane of maximum principal stress, shear stress is zero.

Explanation

By definition, principal planes have no shear stress. Only normal stress acts on them. Maximum shear stress acts on planes at 45° to the principal planes.

Why the other options are wrong

B: Maximum shear acts on planes at 45° to the principal planes. C: Zero is the exact value, not just a minimum in magnitude. D: Shear does not change sign there; it is simply zero.

Shortcut

Principal plane means zero shear.

Common mistake

Confusing the principal plane with the plane of maximum shear stress.