Buckling of a cantilevered circular electric pole An electric pole of length L and constant diameter is erected in the ground and behaves as a cantilever. The effective length for buckling is:

Introduction / Context:
Effective length represents the distance between inflection points of the buckled shape. For column design, the effective length coefficient K depends on end restraints. A free-top, fixed-base electric pole approximates a classic cantilever boundary condition.

Given Data / Assumptions:

• Pole with one end fixed in ground, other end free.
• Uniform diameter and material along length.
• Euler buckling framework is applicable.

Concept / Approach:
For a cantilever, the buckling half-wavelength spans from a point of zero moment (free end) to a maximum moment at the fixed end. The effective length factor is K = 2.0, so LE = K * L.

Step-by-Step Solution:
1) Identify end conditions: fixed–free.2) Use K = 2.0 for cantilever.3) Compute effective length LE = 2.0 * L.4) Select 2.00 L as the correct value.

Verification / Alternative check:
Euler load P_cr = pi^2 * E * I / (K * L)^2; using K = 2 correctly predicts the lowest critical load for a cantilever.

Why Other Options Are Wrong:
0.80 L, 1.20 L, and 1.50 L correspond to other end conditions (e.g., fixed–fixed, fixed–pinned); they do not model a cantilevered pole.

Common Pitfalls:
Assuming partial fixity or soil flexibility without justification; for embedded poles, p–y effects may modify K, but the textbook answer for a cantilever is K = 2.0.

Final Answer:
2.00 L