Steel design – deflection control: For a simply supported steel beam carrying a single concentrated load at midspan, the beam will be considered safe in deflection if the span-to-depth ratio (L/d) satisfies which of the following?

Introduction / Context:
Serviceability in steel beams is often controlled by deflection limits rather than strength. For a simply supported beam with a central point load, empirical span-to-depth limits are widely used to get a quick check on deflection without detailed calculations.

Given Data / Assumptions:

• Beam: simply supported.
• Loading: single concentrated load at midspan.
• Material: structural steel; elastic behavior assumed.
• Serviceability criterion: standard building practice limits for instantaneous deflection.

Concept / Approach:
Maximum elastic deflection for a central load is y_max = W * L^3 / (48 * E * I). For rectangular sections, I is proportional to d^4, so deflection varies strongly with depth. Traditional design guides give ready-reckoner limits on L/d to ensure y_max stays within permissible limits (commonly around L/325 to L/360 for floors). For a central point load, a conservative quick check is L/d less than about 19.

Step-by-Step Solution:
Identify beam condition: simply supported with central point load.Recall conservative rule: L/d must be below an approximate limiting value.For this loading, a common check is L/d < 19.Select option matching this requirement.

Verification / Alternative check:
Using y_max = W * L^3 / (48 * E * I) and target y_max ≈ L/325 to L/360 leads to depth estimates agreeing closely with an L/d limit near 19 for a single midspan load.

Why Other Options Are Wrong:

• < 24: too lenient for a central point load; may exceed target deflection.
• > 19 or > 24 or > 37: larger L/d means shallower beams and more deflection, not “safe.”

Common Pitfalls:

• Confusing limits for uniformly distributed load with those for point loads.
• Ignoring composite action or finishes that can change deflection behavior.

Final Answer:
< 19