Buckling analysis terminology: The “equivalent length” of a column is defined as the length of a hinged–hinged column of the same material and section that has the same Euler crippling load as the given column with its end conditions. Is this definition correct?

Introduction / Context:
In column buckling, end restraints change the effective buckling length and thus the critical load. Using an equivalent length allows all end conditions to be treated with a single Euler formula by adjusting the effective column length.

Given Data / Assumptions:

• Elastic buckling per Euler theory.
• Same cross-section and material for real and equivalent columns.
• End conditions captured via an effective length factor K.

Concept / Approach:
Euler's critical load: P_cr = pi^2 * E * I / (L_e)^2, where L_e = K * l. The equivalent (effective) length L_e is defined so a hypothetical hinged–hinged column of length L_e buckles at the same load as the actual column with given end fixity.

Step-by-Step Solution:

Verification / Alternative check:
Mode shapes for different end conditions show different effective half-wavelengths; the K factors are derived from boundary-condition solutions of the buckling differential equation.

Why Other Options Are Wrong:
Restriction to short or long columns is incorrect; the definition is general within Euler's elastic range (slender columns).

Common Pitfalls:
Confusing actual length with effective length; misapplying K, leading to large errors in P_cr.

Final Answer:

True