Slenderness limits: For a compression member carrying dead load plus superimposed load (no significant dynamic effects), what is the maximum permissible slenderness ratio (effective length / least radius of gyration) according to common steel design practice?

Introduction / Context:
Compression members must satisfy slenderness limits to control buckling risk and ensure service performance. Different categories of loading (e.g., dead + superimposed, wind/earthquake, members carrying stress reversals) may have distinct permissible limits in design standards.

Given Data / Assumptions:

• Member is primarily in compression under dead load plus superimposed load.
• No special conditions like solely wind bracing or temporary erection members.
• Slenderness ratio kL/r is to be checked against a maximum limit.

Concept / Approach:

Typical steel design provisions (working-stress tradition and echoed in guidance tables) restrict slenderness for always-in-compression members to about 180. Tighter or looser limits may apply for tension-only members, wind-only struts, or secondary bracing, but for gravity-loaded compression members, 180 is the widely cited maximum.

Step-by-Step Solution:

Verification / Alternative check:

Design handbooks list 180 for compression members in buildings under steady gravity actions, with other categories (e.g., members under wind only) sometimes permitted higher limits (such as 250 or more), which are not applicable here.

Why Other Options Are Wrong:

• 200–350: typically associated with exceptional cases (e.g., wind-only bracing, secondary/temporary members) and not recommended for gravity-carrying columns.

Common Pitfalls:

• Applying wind-bracing limits to main gravity columns.
• Using r about the wrong principal axis (minimum r must be used).

Final Answer:

180.