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

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