In reinforced concrete design practice, serviceability deflection control is often checked using span-to-depth ratios. If the ratio of the clear span (L) to the overall depth (D) does not exceed 10, for which type of beam will the stiffness ordinarily be considered satisfactory?

Introduction / Context:
In structural engineering, controlling deflection (serviceability) is as important as ensuring flexural and shear safety (strength). A common preliminary check uses the span-to-overall-depth ratio (L/D). Different beam types demand different stiffness levels due to their boundary conditions. This question examines which beam configuration achieves satisfactory stiffness when L/D ≤ 10.

Given Data / Assumptions:

• Ratio in question: L/D ≤ 10.
• Beam types: simply supported, continuous, and cantilever.
• Ordinary reinforced concrete, normal serviceability expectations, typical finishes.

Concept / Approach:
Cantilevers deflect the most for the same span and depth because one end is free. Therefore, cantilevers require smaller L/D (i.e., greater depth) to satisfy deflection limits. Typical starting rules of thumb use the lowest L/D for cantilevers, a larger L/D for simply supported beams, and the largest L/D for continuous beams. Hence, an L/D as small as 10 indicates a configuration aligned with cantilever stiffness needs.

Step-by-Step Solution:
Recognize that cantilevers are the most flexible for a given depth.Lower L/D means higher relative stiffness.An L/D of 10 is consistent with cantilever preliminary sizing for acceptable deflection.

Verification / Alternative check:
Preliminary proportioning guides usually recommend L/D of about 7–10 for cantilevers, approximately 20 for simply supported beams, and around 26 for continuous beams. Therefore, L/D ≤ 10 best matches a cantilever beam to keep deflections in check.

Why Other Options Are Wrong:

• Simply supported beam: typically acceptable at much higher L/D (around 20); 10 is overly conservative.
• Continuous beam: even higher permissible L/D due to continuity.
• None of these: incorrect because a cantilever fits.

Common Pitfalls:
Confusing ultimate strength with serviceability, and assuming one L/D fits all boundary conditions. Also, mixing overall depth with effective depth during preliminary checks can mislead sizing.

Final Answer:
Cantilever beam.