Introduction / Context:
Aside from strength and stability checks (like buckling), columns and frames must satisfy serviceability limits on lateral deflection (sway) to ensure functionality, comfort, and to protect non-structural components. Many design guides and exam syllabi use simple span-based ratios as permissible lateral deflection limits when detailed drift checks are not performed.
Given Data / Assumptions:
- Column of actual length L is subjected to lateral forces (e.g., wind or seismic service-level loads).
- We seek a commonly used order-of-magnitude limit for maximum lateral deflection at the top.
- Detailed code-specific drift limits can vary by material, occupancy, and load case; here a typical exam value is intended.
Concept / Approach:
Deflection limits help control cracking, prevent damage to finishes, and maintain occupant comfort. For many building systems, lateral drift limits around L/500 at service loads are widely cited as a target value in educational and exam contexts. This sits between looser (L/300) and tighter (L/600) criteria sometimes adopted in special cases.
Step-by-Step Solution:
Identify that we need a serviceability drift ratio, not a strength check.Recall typical textbook/exam guidance: permissible sway ≈ L/500 for columns/frames at service conditions.Select L/500 as the acceptable upper bound in this context.
Verification / Alternative check:
Cross-check with common practice: many references present drift limits between 0.002 to 0.0033 times the height (i.e., H/500 to H/300) depending on usage; educational questions often adopt the stricter L/500 value.
Why Other Options Are Wrong:
L/200 and L/300: generally too large a sway for serviceability in typical buildings.L/400: sometimes used, but the question expects the more conservative educational standard.L/600: stricter than commonly required; acceptable but not the typical exam key.
Common Pitfalls:
Confusing ultimate drift limits with serviceability limits.Ignoring that code-specific values may differ; here a standard exam convention is used.
Final Answer:
L/500
Discussion & Comments