Flange width limitation for T-beams — the effective flange width should be restricted to which of the following (select the least governing limit)?

Introduction / Context:
In T-beams, part of the slab acts compositely with the beam web (rib) as the flange under compression. To avoid overestimating the contribution of slab concrete, design codes limit the effective flange width using practical geometric rules. Designers must select the least (most restrictive) of several limits to be safe.

Given Data / Assumptions:

• Monolithic slab-beam construction forming T-section under sagging moments.
• Effective span, spacing of adjacent beams, and slab thickness are known design parameters.
• Standard effective flange width rules apply.

Concept / Approach:

Effective flange width accounts for shear lag and non-uniform stress distribution. The beam cannot mobilize the entire slab width equally; thus, codes limit the assumed flange width by span-based and spacing-based limits as well as a local width tied to web breadth plus a multiple of slab thickness. The controlling value is the smallest among the specified limits.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Shear lag theory and test data underpin these limits; using the least value prevents unconservative flange participation assumptions.

Why Other Options Are Wrong:

Any single limit (A–C) alone may be unconservative; “Any of the above” (E) ignores the requirement to take the least.

Common Pitfalls (misconceptions, mistakes):

Adding limits instead of taking the minimum; confusing effective flange width with total slab width between beams.

Final Answer:

Least of the above