In stress analysis, principal planes are defined as those material planes on which which type(s) of stress act at a point under a general state of stress?

Introduction / Context:
Principal stresses and principal planes simplify a complex, combined stress state into a convenient set of orthogonal directions with no shear. Recognizing what happens on principal planes is foundational for Mohr’s circle, failure theories, and fatigue assessments.

Given Data / Assumptions:

• A general 2D or 3D stress state exists at a material point.
• We consider rotations of the reference axes to find extremal normal stresses.

Concept / Approach:
Principal planes are oriented such that the shear stress on them is zero. On these planes, only normal stresses act, and those normal stresses are the principal stresses (maximum or minimum among all orientations). This follows from the transformation equations or Mohr’s circle, where principal stresses lie at points where the shear ordinate is zero.

Step-by-Step Solution:
1) Write the plane stress transformation formulas or use Mohr’s circle.2) The condition for principal planes is τ = 0.3) At these orientations, the normal stresses equal σ_1 and σ_2 (or σ_3 in 3D).4) Conclude: principal planes carry normal stresses only and no tangential (shear) stress.

Verification / Alternative check:
In Mohr’s circle, principal stresses lie at the intersections with the σ-axis, where τ = 0 by construction, confirming the absence of shear on principal planes.

Why Other Options Are Wrong:

• Tangential only: contradicts the definition; shear vanishes on principal planes.
• Normal plus tangential: also incorrect; shear is zero by definition.
• None of these: invalid because the correct definition is known.

Common Pitfalls:

• Confusing principal planes (τ = 0) with planes of maximum shear (τ = τ_max).
• Assuming principal directions align with geometry without checking stress resultants.

Final Answer:
normal stresses only.