According to reinforced concrete design practice (IS 456 context), the minimum area of tension reinforcement required in a beam must be greater than which expression?

Introduction / Context:
Minimum tension steel in beams is provided to ensure ductility, crack control, and to prevent sudden failure after concrete cracking. Codes specify a formula linking minimum steel to beam dimensions and steel strength so that a small but necessary reinforcement area is always present, even when flexural demand is low.

Given Data / Assumptions:

• Beam breadth b and effective depth d are design dimensions.
• fy is the characteristic yield strength of the reinforcement.
• We seek the standard minimum tension steel requirement.

Concept / Approach:

A common code expression for beams is Ast,min ≥ 0.85 * b * d / fy. This ensures the reinforcement percentage decreases with stronger steel (higher fy) yet maintains a floor for post-cracking capacity. The expression has proper dimensions of area and scales with section size.

Step-by-Step Solution:

Verification / Alternative check:

Design examples across textbooks use this expression for various grades of steel, producing typical minimum percentages around 0.2% to 0.3% of the concrete area for common fy values.

Why Other Options Are Wrong:

• 0.87 fy/bd: Inverse dimensions (stress divided by area) and not an area.
• 0.04 bd or 0.4 bd/y: Arbitrary/incorrect forms not tied to fy; may be unconservative or excessive.
• 0.12 bd/fck: Relates to concrete strength rather than steel yield; not the standard minimum steel formula.

Common Pitfalls:

• Forgetting to compare provided Ast with both minimum and maximum limits.
• Using gross depth instead of effective depth d.

Final Answer:

0.85 bd/fy