Neutral axis orientation in pure bending:\nFor a transverse section of a prismatic beam, the neutral axis passes through the centroid. What is its orientation relative to the plane in which the beam bends?

Introduction / Context:
Neutral axis (NA) is a fundamental concept in beam bending. It is the line in the cross-section where bending stress changes sign and is zero. Correctly identifying its location and orientation is essential for stress analysis and section design.

Given Data / Assumptions:

• Prismatic beam under pure or predominant bending.
• Linear elastic material; plane sections remain plane.
• NA passes through the centroid of the section for homogeneous, isotropic beams.

Concept / Approach:
In pure bending about, say, the z-axis (causing curvature in the x–z plane), the bending stress varies linearly with distance from the NA, and the NA is oriented perpendicular to the plane of bending. Thus, if bending occurs in a vertical plane, the NA is horizontal across the section and vice versa.

Step-by-Step Solution:

Verification / Alternative check:
From flexure formula, σ = M*y/I for bending about the horizontal centroidal axis. The line y = 0 (through the centroid) carries zero stress and is perpendicular to the plane of bending, confirming the rule.

Why Other Options Are Wrong:

• “In the same plane” misinterprets NA orientation; NA lies in the cross-section, not along the curvature plane.
• Fixed vertical or horizontal answers depend on which plane the beam bends in, so only the perpendicular statement is generally correct.

Common Pitfalls:
Confusing the neutral axis with the neutral surface; assuming a fixed direction regardless of the bending plane; ignoring composite-section effects that shift NA location (but orientation rule still holds relative to bending plane).

Final Answer:
at right angle to the plane in which the beam bends