Question

Slenderness ratio, of a axial compression of the member, is the ratio of effective length (le) to the of the member

• A. Least radius of gyration
• B. Least lateral dimension
• C. Average lateral dimension
• D. None of these

Answer 1

Answer:

A. Least radius of gyration

• The slenderness ratio is a fundamental parameter in structural engineering used to assess the stability of compression members like columns. It is defined as the ratio of the effective length (le) of a member to its least radius of gyration (r).

• Mathematically: Slenderness ratio (λ) = le/r

• Where:

  • le = effective length of the member (depends on end conditions and support restraints)

  • r = least radius of gyration of the cross-section

• The radius of gyration is a geometric property that represents how the cross-sectional area is distributed around the centroidal axis. For any cross-section, there are two radii of gyration - one about each principal axis. The "least" radius of gyration is the smaller of these two values, as it represents the axis about which the member is most likely to buckle.

• The slenderness ratio is crucial in determining:

  1. The buckling behavior of compression members

  2. Whether a member will fail by crushing or buckling

  3. The design capacity of columns and struts

• A higher slenderness ratio indicates a more slender member that is more prone to buckling failure, while a lower ratio suggests a stockier member that may fail by material crushing rather than instability.