Definition – Principal stress Is the direct normal stress acting across a principal plane known as the principal stress?

Introduction / Context:Principal stresses and planes are fundamental in failure analysis and stress transformation. On a principal plane, the shear stress is zero and the normal stress attains an extremum value.

Given Data / Assumptions:

• Plane stress or 3D stress state in a linear elastic continuum.
• Principal planes are mutually orthogonal.

Concept / Approach:By definition, a principal plane has zero shear stress. The corresponding normal stress on that plane is a principal stress (maximum, middle, or minimum depending on order).

Step-by-Step Clarification:Find planes where τ = 0 via Mohr’s circle or eigenvalue problem.The normal stresses on these planes are σ1, σ2 (and σ3 in 3D).Therefore the direct normal stress across a principal plane is indeed the principal stress.

Verification / Alternative check:Eigenvectors of the stress tensor give principal directions; eigenvalues are principal stresses—purely normal, no shear.

Why Other Options Are Wrong:Presence of shear contradicts the definition; restriction to uniaxial or ductile materials is unnecessary.

Common Pitfalls:Confusing maximum principal stress with Von Mises equivalent stress; mixing plane of maximum shear with principal plane.

Final Answer:Yes