A reinforced cantilever beam ofspan 7m, has a cross-sectional areaof 250 mm X 500 mm (effective)if checked for lateral stability anddeflection, the beam willa)Fail in deflection onlyb)Fail in both deflection andlateral stabilityc)Fail in lateral stability onlyd)Satisfy the requirements ofdeflection and lateral stabilityCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Lateral Stability and Deflection of a Reinforced Cantilever Beam

Introduction:
In this question, we are given a reinforced cantilever beam with a span of 7m and a cross-sectional area of 250 mm x 500 mm (effective). We need to determine whether the beam will fail in deflection only, lateral stability only, both deflection and lateral stability, or satisfy the requirements of deflection and lateral stability. The correct answer is option 'B', which states that the beam will fail in lateral stability only.

Explanation:
To understand why the beam fails in lateral stability only, we need to consider the concepts of deflection and lateral stability separately.

Deflection:
Deflection refers to the bending of a beam under applied loads. It is important to ensure that the deflection of a beam is within acceptable limits to prevent excessive deformation and potential structural failure. The deflection of a beam depends on various factors, such as the span, load, and the stiffness of the beam.

In this question, the span of the beam is 7m, which means it is relatively long. The cross-sectional area of the beam is 250 mm x 500 mm (effective), indicating that it has a substantial stiffness. Therefore, it is expected that the beam will satisfy the requirements of deflection.

Lateral Stability:
Lateral stability refers to the ability of a beam to resist sideways movement or buckling. When a beam is subjected to lateral loads or forces, it may become unstable and fail in terms of lateral stability. The lateral stability of a beam depends on factors such as the slenderness ratio and the support conditions.

In this question, we are not given any information about the lateral loads or forces acting on the beam. However, it is mentioned that the beam is a cantilever, which means it is supported at only one end and free at the other end. Cantilever beams are more prone to lateral instability compared to beams with additional supports. Therefore, it is likely that the beam will fail in terms of lateral stability.

Conclusion:
Based on the given information, the reinforced cantilever beam will fail in lateral stability only. The beam is expected to satisfy the requirements of deflection, but its unsupported free end makes it susceptible to lateral instability.

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