Minimum area of tension reinforcement in an RC beam — constant K in Ast,min = K * b * d / fy

Difficulty: Medium

Correct Answer: 0.85

Explanation:


Introduction:
The minimum steel area in flexural members prevents sudden tension-cracking and ensures post-cracking stiffness. In beams, codes express Ast,min with a constant K multiplied by section dimensions and divided by steel yield strength.



Given Data / Assumptions:

  • RC beam under bending.
  • Formula form: Ast,min = K * b * d / fy.
  • b = width, d = effective depth, fy = yield strength of steel.


Concept / Approach:
Unlike slabs (often governed by a percentage of gross area), beams use a K-based expression. The constant K encapsulates empirical calibration so that beams have sufficient distributed reinforcement to control crack widths and maintain ductility.



Step-by-Step Solution:
1) Recall the prescribed K for beams in code tables.2) The value widely specified is K = 0.85.3) Therefore Ast,min = 0.85 * b * d / fy.


Verification / Alternative check:
For typical beam sizes and Fe 415 steel, this formula yields steel percentages consistent with serviceability crack control requirements.



Why Other Options Are Wrong:
Values 0.95, 0.90, and 0.80 do not match the standard beam constant and would either increase or reduce minimum steel beyond code intent.



Common Pitfalls:
Mixing slab and beam minimum steel rules; using overall depth instead of effective depth; forgetting that Ast,min must also satisfy bar spacing and cover constraints.



Final Answer:
0.85

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