Explanation:

Lateral buckling is a phenomenon that occurs when a beam or column bends sideways under compressive loads. It is a critical issue in the design of steel structures, as it can lead to structural failure.

The moment of inertia of a beam is a measure of its resistance to bending. It depends on the shape of the cross-section and the distribution of the material. When a beam is subjected to compressive loads, its tendency to buckle sideways depends on the ratio of the moment of inertia about the bending axis to the moment of inertia about the minor axis.

The correct answer to the question is option 'B', i.e., the moment of inertia about the bending axis smaller than the other. This means that the beam has a cross-section that is more slender in the direction of the bending axis, which makes it more prone to lateral buckling.

Here are some key points to understand why lateral buckling occurs in beams with smaller moment of inertia about the bending axis:

- Compression flange: When a beam is subjected to compressive loads, the top and bottom flanges are in tension and compression, respectively. The compression flange is the one that is more prone to buckling, as it tends to bulge outwards under the compressive load.
- Slenderness ratio: The slenderness ratio is the ratio of the effective length of the beam to its radius of gyration. It is a measure of how slender the beam is in the direction of the bending axis. A beam with a smaller moment of inertia about the bending axis has a higher slenderness ratio, which makes it more prone to lateral buckling.
- Buckling modes: When a beam buckles laterally, it can do so in several modes, depending on the boundary conditions and the load distribution. The most common mode is the Euler buckling mode, which occurs when the beam buckles in a simple sinusoidal pattern. This mode depends on the slenderness ratio and the load distribution.

In conclusion, the problem of lateral buckling can arise in steel beams with smaller moment of inertia about the bending axis, which makes them more slender and prone to buckling. Engineers need to consider this issue when designing steel structures to ensure their safety and stability.

B