Principal planes and shear — property of the plane of maximum principal stress Along a principal plane that carries the maximum principal normal stress at a point in a stressed body, which statement is true?

Introduction / Context:
Stress at a point can be represented by normal and shear components on various planes passing through that point. Principal planes are special orientations where the shear stress component is zero and the normal stress reaches an extreme (maximum or minimum). Recognizing this property is vital for failure analysis and Mohr’s circle interpretation.

Given Data / Assumptions:

• General 2D or 3D stress state at a point.
• Principal directions exist (symmetric Cauchy stress tensor).
• Standard sign conventions for stresses.

Concept / Approach:

On a principal plane, the traction vector is collinear with the plane’s normal; hence the shear component vanishes. The principal stresses σ1, σ2, σ3 are purely normal components acting on their respective principal planes. The maximum principal stress is the largest of these normal components, and on that plane there is no shear by definition.

Step-by-Step Solution:

Verification / Alternative check:

Mohr’s circle: principal planes correspond to the intersection points of the circle with the horizontal axis (τ = 0), confirming no shear on those planes, including the one at σ_max.

Why Other Options Are Wrong:

• “Maximum/minimum shear acts” contradicts principal-plane definition.
• “None of these” is incorrect since a definitive property applies.

Common Pitfalls:

• Confusing planes of maximum shear (located 45° from principal planes in 2D) with principal planes themselves.

Final Answer:

No shear stress acts on that plane.