Flat slab column head (capital) sizing guideline: For a flat slab supported on columns, the diameter of the column head (capital) is generally taken as which fraction of the slab span length (rule-of-thumb)?

Introduction / Context:
In flat slab construction, a column head (capital) or drop panel is often provided to reduce punching shear and to enhance negative moment capacity over columns. Preliminary sizing rules help during conceptual design before detailed analysis.

Given Data / Assumptions:

• Flat slab (beamless) system with columns and possible capitals.
• Preliminary sizing question seeking a proportion to span length.

Concept / Approach:
A typical rule-of-thumb sets the capital diameter on the order of one-quarter of the span length to effectively spread the load path and reduce punching shear stress around column perimeters. Exact sizes are later refined by punching shear checks and moment distribution requirements.

Step-by-Step Solution:
Identify target: provide a capital large enough to reduce shear stresses.Adopt preliminary proportion: D_cap ≈ 0.25 × span.Select the corresponding option.

Verification / Alternative check:
Many design aids suggest 0.2–0.3 of span as a starting point, later adjusted after performing punching shear and serviceability checks. This aligns well with 0.25 of span.

Why Other Options Are Wrong:

• Proportions to column diameter or fixed 4–5 cm increases are too small to influence punching shear effectively in most practical spans.
• “None of these” is unnecessary because a standard preliminary ratio exists.

Common Pitfalls:
Relying solely on thumb rules without verifying punching shear; forgetting the role of drop panels vs. column capitals; overlooking edge/corner column differences that may need larger capitals.

Final Answer:
0.25 times the span length