Slenderness ratio basics: The slenderness ratio λ of a column is defined as L_e / r. Under what condition would the slenderness ratio be zero?

Introduction / Context:
Slenderness ratio λ = L_e / r is a key geometric parameter in column stability. It influences the buckling capacity and the applicability of Euler or inelastic buckling curves.

Given Data / Assumptions:

• L_e is the effective length accounting for end restraints.
• r is the radius of gyration about the buckling axis.

Concept / Approach:
By definition, λ approaches zero only if the numerator L_e → 0, since r is positive for any real cross-section. Physically, L_e = 0 is a limiting conceptual case (e.g., an element of zero effective length), not realized in practice but useful to understand the mathematics.

Step-by-Step Solution:

Verification / Alternative check:
Other conditions (e.g., L_e = r) give λ = 1, not zero; making supports “continuous” reduces L_e but not to zero in real structures.

Why Other Options Are Wrong:
L_e = r yields λ = 1; “continuously supported” reduces but does not nullify L_e; “between points of zero moment” defines buckling curve but not λ = 0; r = 0 is non-physical for a finite cross-section.

Common Pitfalls:
Confusing “very small slenderness” with “zero”; neglecting direction-specific r and end-restraint factors in effective length calculation.

Final Answer:
When the effective length is zero (L_e = 0)