A 24-hour load test is performed on a flexural member. If l is the effective span in metres and D is the overall depth in mm, acceptance requires the measured maximum deflection (in mm) to be less than which expression?

Introduction / Context:
Load testing verifies in-situ stiffness and serviceability of flexural members. Beyond general span/ratio limits, some acceptance clauses relate permissible deflection to both span and section depth, recognizing that deeper sections deflect less under the same span and load pattern.

Given Data / Assumptions:

• Effective span l (metres) and overall depth D (mm) are given.
• We seek the acceptance criterion expressed directly in millimetres of deflection.
• 24-hour maintained load test is considered (serviceability verification).

Concept / Approach:

An empirical acceptance expression ties allowable deflection to span squared divided by depth times a constant. This reflects classic elastic beam behavior (deflection ∝ l^2/EI for uniform loads) and introduces D in the denominator as a proxy for I.

Step-by-Step Solution:

Verification / Alternative check:

While simple span/250 rules exist, the l^2/(DK) form better captures the influence of section depth. Residual deflection recovery criteria may also be checked (e.g., recovery fraction after unloading), but the question asks only the deflection bound.

Why Other Options Are Wrong:

• l/250, l/360: Span-ratio limits not expressed with D; also dimensional inconsistency unless l is in mm.
• l^2/(D6000): More permissive (larger deflection) than the typical acceptance, not conservative.
• 0.003*l: Generic limit; does not reflect depth influence and unit handling is ambiguous.

Common Pitfalls:

• Forgetting unit consistency (l in m and D in mm) leads to wrong magnitudes.
• Confusing total maximum deflection with residual deflection after unloading.

Final Answer:

l^2 / (D * 9000)