Lateral–torsional buckling in steel beams The problem of lateral buckling can arise only in those beams where the compression flange is not adequately restrained against lateral movement and twist during bending. Which statement best reflects this condition?

Introduction / Context:
Lateral–torsional buckling (LTB) is a stability limit state in flexural members. It occurs when a beam bent about its strong axis deflects laterally and twists because the compression flange is insufficiently restrained. This question probes the correct qualitative condition that leads to LTB.

Given Data / Assumptions:

• Steel beam in bending about its strong axis.
• Compression flange may or may not be laterally braced.
• No special warping restraints unless stated.

Concept / Approach:
LTB is governed by restraint of the compression flange and torsional stiffness (J, Cw), not by a simple comparison of the two principal second moments of area alone. A fully restrained (continuously braced) compression flange prevents LTB. Merely stating that one moment of inertia is larger or smaller does not establish the presence of lateral restraint, so such statements do not by themselves cause or prevent LTB.

Step-by-Step Solution:
1) Identify the key trigger: unbraced compression flange → risk of combined lateral deflection and twist.2) Recognize that inertia magnitudes (I_major vs I_minor) influence susceptibility, but are not the definitive condition.3) Note that a fully supported compression flange eliminates LTB (hence option c is not a trigger condition).4) Therefore, none of the statements (a–c) correctly isolate the true cause; choose “None of the above”.

Verification / Alternative check:
Design codes compute LTB capacity using unbraced length between lateral restraints, section properties (I_y, J, Cw), and loading position. The decisive parameter is bracing of the compression flange.

Why Other Options Are Wrong:
Option (a) and (b): Comparing principal inertias does not define LTB onset; both are true for many beams with or without LTB. Option (c): A fully supported compression flange prevents, rather than causes, LTB.

Common Pitfalls:
Assuming large I_major alone prevents LTB; ignoring load height relative to shear center; overlooking intermittent lateral bracing effectiveness.

Final Answer:
None of the above