Euler's column theory — identify the foundational assumptions: Which of the following are assumed in Euler's elastic buckling theory for slender columns?

Introduction:
Euler's theory predicts the critical load for ideal slender columns. Knowing its assumptions clarifies when the formula Pcr = π^2EI/Le^2 applies.

Given Data / Assumptions:

• Ideal geometry: straight column, prismatic section.
• Axial load through centroid with negligible initial curvature.
• Linear elasticity up to buckling.

Concept / Approach:
The theory presumes elastic behavior and buckling as the governing limit state, valid for high slenderness ratios where inelastic yielding is not reached before instability.

Step-by-Step Solution:

Verification / Alternative check:
Columns with low slenderness do not satisfy Euler's assumptions; inelastic or empirical formulas (e.g., Rankine-Gordon) are then used, confirming the boundary of applicability.

Why Other Options Are Wrong:

• “Load acts with large eccentricity”: That violates the central-loading assumption in the classical derivation.

Common Pitfalls:
Applying Euler's formula to stocky columns; ignoring end conditions when computing effective length Le; assuming plasticity while using elastic theory.

Final Answer: