Effect of over-reinforcing a singly reinforced concrete beam: By how much (approximately) can the moment of resistance be increased beyond the balanced condition?

Introduction / Context:
In working-stress-era beam design, a “balanced” section is one where concrete reaches its permissible compressive stress simultaneously as steel reaches its permissible tensile stress. Adding more tensile steel (over-reinforcing) without altering dimensions does not proportionally increase the moment capacity because the limiting concrete stress controls. This question checks the typical upper bound often cited in basic texts.

Given Data / Assumptions:

• Singly reinforced rectangular section under bending.
• Working stress method assumptions and permissible stresses.
• Concrete compression is governing at balanced or over-reinforced states.

Concept / Approach:

Beyond the balanced level, additional tension steel carries little extra moment because the compression block of concrete governs the capacity. Textbooks commonly note that over-reinforcement may raise the moment of resistance modestly, typically not exceeding about 25% over the balanced value, after which increasing depth or making the beam doubly reinforced is more effective.

Step-by-Step Solution:

Verification / Alternative check:

Comparison of M values from basic rectangular stress block relations confirms diminishing returns of adding tensile steel without increasing depth or adding compression steel.

Why Other Options Are Wrong:

10–20% are conservative but do not reflect the common upper bound; 40% is too high for the stated assumptions.

Common Pitfalls:

Pursuing heavy tension reinforcement to gain moment instead of increasing depth; ignoring ductility and failure mode concerns with over-reinforced sections.

Final Answer:

25%