Principal planes – definition check Planes in a stressed body that carry no shear stress are known as principal planes. State whether this is true or false.

Introduction / Context:
Principal stresses and principal planes are central to failure theories and stress analysis. Identifying planes with zero shear simplifies complex stress states and enables use of criteria like maximum normal stress or von Mises.

Given Data / Assumptions:

• Continuum, small deformations.
• At a given point, a triad of mutually orthogonal principal planes exists.
• Material behavior not restricted to ductile or brittle for the definition.

Concept / Approach:
For any 2D or 3D stress state, there are orientations where the stress tensor becomes diagonal (no shear components). Those orientations define principal planes, and the normal stresses on them are the principal stresses.

Step-by-Step Reasoning:
Resolve stresses on an arbitrary plane using transformation equations.Set shear stress on that plane to zero and solve for the plane angle(s).Solutions correspond to principal directions; the associated planes are principal planes with zero shear.

Verification / Alternative check:
Mohr’s circle: principal planes occur at points where the circle crosses the σ-axis; at these points, shear τ = 0 by construction.

Why Other Options Are Wrong:
The statement is general and not limited to specific materials, torsion, or Poisson’s ratio conditions.

Common Pitfalls:
Confusing maximum shear planes with principal planes; assuming principal planes always align with geometric axes (not true for unsymmetrical loading).

Final Answer:
True