Steel design – Effective length for lateral–torsional buckling For a simply supported steel beam whose ends are restrained against torsion, and whose compression flange at the supports is only partially restrained against lateral bending, the effective buckling length L is taken as:

Introduction / Context:
Lateral–torsional buckling of steel beams depends on how well the compression flange and the member are restrained at the supports. Design codes tabulate an “effective length” factor to convert the actual span into an equivalent buckling length used for capacity checks.

Given Data / Assumptions:

• Beam is simply supported for vertical bending actions.
• Ends are restrained against torsion (warping/twist prevented).
• Compression flange at supports is only partially restrained against lateral movement.
• We need the effective length expressed as a fraction of physical span.

Concept / Approach:
Effective length factors reduce from 1.0 as end restraints improve. With torsion restraint present but only partial lateral restraint of the compression flange, tabulated factors are typically about 0.85 of span, reflecting improved stability compared with an unrestrained flange.

Step-by-Step Solution:

Verification / Alternative check:
Design handbooks and summary tables of end-restraint cases consistently show factors near 0.85 for the stated condition, higher than fully restrained (≈0.7–0.75) and lower than unrestrained (1.0).

Why Other Options Are Wrong:
L = span assumes no beneficial restraint. 0.70–0.75 correspond to stronger flange restraint. 1.25 × span implies adverse conditions (not applicable here).

Common Pitfalls:
Confusing flexural effective length (for column buckling) with lateral–torsional buckling effective length; ignoring flange bracing at intermediate points.

Final Answer:
L = 0.85 × span