Rectangular Beam Deflection

The deflection of any rectangular beam SS is a crucial factor that engineers and designers consider when designing structures and machines. The deflection refers to the amount of bending or deformation that occurs in a beam when subjected to an external load. The following are the four options provided in the question and their explanations:

A. Directly proportional to its weight

The weight of a beam is an external force that influences the deflection. However, it is not directly proportional to the deflection. The weight affects the stress and strain of the beam, which ultimately determines the deflection.

B. Inversely proportional to its width

The width of a beam is one of the factors that determine its moment of inertia, which is a measure of its resistance to bending. A wider beam has a higher moment of inertia, which means it is less likely to bend or deflect. Therefore, the deflection is inversely proportional to the width.

C. Inversely proportional to the cube of its depth

The depth of a beam is another factor that determines its moment of inertia. A deeper beam has a higher moment of inertia, which means it is less likely to deflect. However, the deflection is not inversely proportional to the depth. It is inversely proportional to the fourth power of the depth.

D. Directly proportional to the cube of its length

The length of a beam is a significant factor that influences its deflection. The longer the beam, the more it will bend or deflect. The deflection is directly proportional to the cube of the length. Therefore, if the length of the beam doubles, the deflection will increase by a factor of eight.

Conclusion

In conclusion, the deflection of a rectangular beam is influenced by various factors such as weight, width, depth, and length. However, the most significant factors are the width and depth, which determine the beam's moment of inertia. The deflection is inversely proportional to the width and the fourth power of the depth. On the other hand, the deflection is directly proportional to the cube of the length.