Columns – definition of the load that just maintains a small lateral deflection The maximum axial load that is just sufficient to keep a column in a slightly deflected configuration (neutral equilibrium) is called:

Introduction / Context:
Column stability is governed by the concept of Euler buckling. At a certain load level, a perfectly straight column theoretically has neutral equilibrium: any infinitesimal lateral deflection will persist without additional load. This load is central to design and is commonly derived from Euler’s formula for ideal columns.

Given Data / Assumptions:

• Axially loaded, prismatic column.
• Small initial lateral deflection or imperfection may exist in practice.
• Elastic behavior within the proportional limit.

Concept / Approach:
The load that just maintains a small lateral deflection (neither grows nor vanishes in the ideal mathematical sense) is the critical load. In many texts it is also termed the Euler buckling load. “Crippling load” is sometimes used loosely for failure load but typically implies inelastic crushing or local instability rather than ideal elastic buckling.

Step-by-Step Solution:
Recognize the neutral equilibrium condition → Euler concept.Name associated with this threshold → critical load.Differentiate from ultimate crushing (material failure) and from allowable load (service design).

Verification / Alternative check:
For an ideal pinned–pinned column: P_cr = (π^2 * E * I) / L^2. At P = P_cr, infinitesimal lateral deflection solutions exist without extra load, representing the “just sufficient” definition.

Why Other Options Are Wrong:

• Buckling load: often used synonymously with critical load, but to avoid ambiguity with “crippling,” the precise textbook term is critical load.
• Crippling/ultimate crushing: refer to material or local failures, not neutral equilibrium buckling onset.
• Allowable load: includes safety factors and is below critical load.

Common Pitfalls:
Assuming “crippling” equals “critical.” In design, “crippling” may indicate failure beyond elastic stability, whereas critical load is the elastic buckling threshold.

Final Answer:
Critical load