Reinforced concrete flexure — over-reinforced section: For an over-reinforced RC beam, is the depth of the actual neutral axis equal to the critical neutral axis depth?

Introduction:
Neutral axis depth governs strain compatibility and failure mode in RC beams. Over-reinforcement leads to compression-controlled behavior rather than tension steel yielding first.

Given Data / Assumptions:

• Rectangular RC section under flexure.
• Definitions: critical neutral axis depth x_c separates tension-controlled from compression-controlled behavior.

Concept / Approach:
In an over-reinforced beam, the actual neutral axis lies deeper (nearer to the compression face) than the critical depth. This leads to crushing of concrete before yielding of tension steel, which is brittle and undesirable per modern codes.

Step-by-Step Solution:

Verification / Alternative check:
Strain diagrams for over-reinforced sections show higher compression block depth before steel yield, confirming a larger NA depth than x_c.

Why Other Options Are Wrong:

• True / equal: Contradicts the definition of over-reinforced behavior.
• “Actual less than critical”: That corresponds to under-reinforced sections.
• Insufficient data: Standard definitions are enough to conclude.

Common Pitfalls:
Confusing under- vs over-reinforced; thinking NA position is fixed regardless of reinforcement amount.

Final Answer: