T-beam effective flange width calculation (IS-style rule of thumb): Given a slab thickness = 10 cm, web (rib) width bw = 30 cm, web (beam) overall depth = 50 cm, centre-to-centre spacing of beams = 3 m, and effective span = 6 m. Determine the effective flange width of the T-beam. Use beff = min( bw + lo/6 + 6Df , centre-to-centre spacing , actual available slab width ).

Introduction / Context:
In T-beams formed by a slab monolithically cast over a web, the effective flange width beff models the portion of slab that participates in compression. Codes provide empirical limits based on span, slab thickness, and beam spacing.

Given Data / Assumptions:

• Df (slab thickness) = 10 cm.
• bw (web width) = 30 cm.
• Centre-to-centre spacing of beams s = 300 cm.
• Effective span lo = 600 cm.
• Use beff = min( bw + lo/6 + 6Df , s , available slab width ).

Concept / Approach:
The term lo/6 approximates the span influence; 6Df captures the flange thickness influence; bw accounts for the web. However, the effective width cannot exceed the physical spacing or the actual available slab width, ensuring no overlap with adjacent T-beams.

Step-by-Step Solution:
Compute lo/6 = 600 / 6 = 100 cm.Compute 6Df = 6 * 10 = 60 cm.Trial beff1 = bw + lo/6 + 6Df = 30 + 100 + 60 = 190 cm.Check spacing limit: s = 300 cm → beff ≤ 300 cm. So beff = min(190, 300) = 190 cm.

Verification / Alternative check:
Beff is comfortably below spacing; no need to curtail further. The value is consistent with typical code heuristics for moderate spans and thin slabs.

Why Other Options Are Wrong:

• 150 cm / 100 cm: Underestimates effective participation, leading to conservative but incorrect design capacity.
• 220 cm / 300 cm: Exceeds the empirical bound from lo/6 + 6Df + bw without justification.

Common Pitfalls:
Using overall depth instead of slab thickness in the 6Df term; forgetting the spacing cap; confusing effective span with clear span.

Final Answer:
190 cm