Serviceability limit for filler joists: For filler joists supporting a structural concrete slab, the ratio of span L to the depth d (measured from the underside of the joist to the top of the structural concrete) should not exceed which limiting value?

Introduction / Context:Limiting span-to-depth ratios provide a quick serviceability check to control deflection and vibration in joist-and-slab floor systems. For traditional steel filler joists with a concrete topping, commonly used empirical limits help ensure satisfactory stiffness without detailed deflection calculations for preliminary design.

Given Data / Assumptions:

• Filler joists are simply supported or lightly continuous with a concrete slab.
• Depth d is measured from the underside of the joist to the top of structural concrete (i.e., composite overall depth for serviceability).
• Standard occupancy loading and normal deflection criteria are implied.

Concept / Approach:Span-to-depth limits are calibrated so that the elastic deflection under typical service loads remains within acceptable fractions of span (such as L/325 to L/360 for floors). For filler joists with slab, a frequently used quick limit is L/d ≤ 45. This balances economy (shallower sections) with serviceability (acceptable deflection).

Step-by-Step Solution:Identify member type: filler joist with concrete slab.Apply the empirical serviceability limit L/d ≤ 45.Compare with the listed options and select 45.

Verification / Alternative check:Detailed elastic deflection y_max can be estimated using y_max = 5 * w * L^4 / (384 * E * I) for uniform loading or y_max = W * L^3 / (48 * E * I) for point loads. Back-calculations typically align with L/d limits near 45 for common spans and loads.

Why Other Options Are Wrong:

• 60: often too flexible for floor comfort and finishes.
• 35, 25, 20: overly conservative for typical filler-joist floors, inflating steel tonnage.

Common Pitfalls:

• Using beam limits for composite members without recognizing the slab contribution.
• Ignoring continuity or partition loads that can alter deflection behavior.

Final Answer:45