Lateral–torsional buckling effective length for a cantilever beam For a cantilever of span L that is continuous at the support, unrestrained against torsion at the support, and free at the other end, what is the effective lateral–torsional buckling length l used in design?

Introduction / Context:
Lateral–torsional buckling (LTB) limits the bending capacity of beams whose compression flange is not adequately restrained. The “effective length” models boundary conditions for lateral displacement and twist, converting them into a single buckling length factor multiplied by the actual span.

Given Data / Assumptions:

• Cantilever beam of span L.
• Support is continuous but unrestrained against torsion (no torsional restraint at the fixed end).
• Free end is unrestrained (typical cantilever tip).
• We seek the LTB effective length l for design checks.

Concept / Approach:
Effective length for buckling problems reflects end conditions. The most flexible condition (one end free) increases the effective length compared to simply supported cases. For classical exam problems, a cantilever with a free tip and inadequate torsional restraint at the support is commonly taken with an LTB effective length of about 2L, capturing its greater susceptibility to instability.

Step-by-Step Solution:

Verification / Alternative check:
Compare with a simply supported beam (l ≈ L in many textbook tables). A cantilever is more slender effectively because one end is free, so an increased factor such as 2L is used in traditional design tables for teaching.

Why Other Options Are Wrong:
l = L understates the buckling length for a free-end case; 0.5L is for a much stiffer condition; 3L, 3.5L are excessively conservative for the stated assumption set.

Common Pitfalls:
Confusing column Euler effective-length factors with beam LTB factors; assuming any “fixed” support provides torsional restraint even when the problem explicitly denies it.

Final Answer:
l = 2L