Span-to-depth ratios for preliminary sizing of beams up to 10 m span Select the correct set of safe span/depth ratios for cantilever, simply supported, and continuous beams.
Correct Answer: Cantilever 7; Simply supported 20; Continuous 26
Introduction:Span/depth ratios help in preliminary sizing to meet deflection control before detailed analysis. For spans up to about 10 m, common guideline values exist for different support conditions.
Given Data / Assumptions:
- Ordinary reinforced concrete beams.
- Typical service loads and normal exposure.
- Preliminary sizing stage (to be refined later).
Concept / Approach:
Cantilevers deflect more for the same depth, so they require smaller span/depth ratios. Continuous beams are stiffer than simply supported and can use a larger ratio.
Step-by-Step Solution:
1) Recall guide values: cantilever ≈ 7, simply supported ≈ 20, continuous ≈ 26.2) Compare options with these targets.3) Choose the exact matching set.Verification / Alternative check:
Final designs should include modification factors for tension reinforcement percentage, compression steel, and flanged sections.
Why Other Options Are Wrong:
Other sets either over- or under-estimate stiffness for the given support system.
Common Pitfalls:
Treating these ratios as code limits rather than starting points; ignoring long-term creep and shrinkage effects.
Final Answer:
Cantilever 7; Simply supported 20; Continuous 26