Laterally unsupported cantilever – effective projecting length for lateral–torsional buckling A cantilever beam of length L is built-in at the support and is restrained against torsion at the free end. What effective projecting length l should be used for lateral–torsional buckling checks?

Introduction / Context:
Lateral–torsional buckling (LTB) depends on the unbraced length and boundary restraints. For cantilevers, restraining the free end against torsion (and sometimes warping) reduces the effective buckling length compared to a fully free tip.

Given Data / Assumptions:

• Cantilever length L, built-in at one end.
• Free end is restrained against torsion (lateral restraint present).
• LTB effective length factor required for design.

Concept / Approach:
Coefficient tables for LTB provide factors to convert the physical length into an effective length for buckling. With torsional restraint at the free end, the effective projecting length is reduced to about 0.70 L, reflecting improved stability compared to an unrestrained free tip (which would be ≈ L).

Step-by-Step Solution:
Identify boundary conditions → built-in at one end, torsion-restrained at the other.Adopt recommended factor for this case → l ≈ 0.70 L.

Verification / Alternative check:
Handbooks of stability coefficients list 0.7 L for cantilevers with torsional restraint at the tip, consistent with test data and theory.

Why Other Options Are Wrong:

• 0.75 L or 0.85 L: less beneficial than typical tabulated restraint effect for this condition.
• 0.50 L: too optimistic for a cantilever.
• L: corresponds to an unrestrained free end.

Common Pitfalls:
Assuming restraint at the tip without detailing an actual torsion/lateral brace; the factor is valid only if the restraint is truly provided.

Final Answer:
l = 0.70 L