A column supports the fourth-floor framing via four mutually perpendicular beams framing into it. If the reduced level of the third-floor slab at the column is 205.350 m and the undersides (soffits) of those beams are at 208.350 m, 208.450 m, 208.500 m, and 208.550 m, what is the supported (unbraced) length of the column?

Introduction / Context:
In frame analysis and column design, the supported (unbraced) length is measured between points where lateral support is provided—typically at floor or beam levels. For a column at the intersection of several beams, the lowest beam soffit defines the top bracing level for that storey, controlling the unbraced segment length.

Given Data / Assumptions:

• Third-floor slab level (at column): RL = 205.350 m.
• Beam soffit RLs at the next floor: 208.350 m, 208.450 m, 208.500 m, 208.550 m.
• Beams are mutually perpendicular and frame into the column, providing lateral restraint at their soffits.

Concept / Approach:

The unbraced length is from the lower bracing level (floor below) to the first bracing level above—i.e., the lowest soffit among the incoming beams. Using the lowest soffit is conservative and reflects the actual first restraint encountered along the column height.

Step-by-Step Solution:

Verification / Alternative check:

Even if higher beams brace later, the earliest bracing (lowest soffit) governs the segment length, which is the correct basis for slenderness and effective length evaluation.

Why Other Options Are Wrong:

• 3.100 m, 3.150 m, 3.200 m: Use higher soffits, overestimating unbraced length.
• 2.950 m: Not consistent with given levels; arithmetic mismatch.

Common Pitfalls:

• Measuring to beam centerline instead of soffit where restraint actually begins.
• Ignoring that different beams may sit at different soffit elevations.

Final Answer:

3.000 m