Deflection of a beam with varying cross section is a phenomenon in which the shape of the beam is changed due to the difference of its cross section. As the name suggests, when the cross section of a beam varies, the deflection of the beam will also vary. This phenomenon is usually found in the structures of beams and columns which are subjected to different kinds of loads. The load can be static, dynamic or a combination of both. When the beam or column is subjected to the load, the forces acting on the beam will cause it to bend or deflect. The amount of deflection depends on the type and magnitude of the load, the size and shape of the beam, and the material used in the beam.

## The Effect of Cross Section on Beam Deflection

The cross section of a beam can significantly influence the amount of deflection that it experiences. The cross section of a beam determines how much of the load is absorbed by the beam and how much of it is transferred to other parts of the structure. This can affect the total amount of deflection that the beam experiences. If the cross section of the beam is too large, then it will absorb more of the load and lead to a greater amount of deflection. On the other hand, if the cross section of the beam is too small, then it will absorb less of the load and lead to a smaller amount of deflection.

## Methods of Calculating Deflection of a Beam With Varying Cross Section

The deflection of a beam with varying cross section can be calculated using a variety of methods. The most common method is the application of the Euler-Bernoulli equation, which calculates the deflection of a beam as a function of its cross sectional area and the applied load. Another method is the application of the Timoshenko beam theory, which takes into account the shear deformation of the beam. Other methods such as the finite element method and the energy method are also used to calculate the deflection of a beam with varying cross section.

## Factors That Affect Beam Deflection With Varying Cross Section

The amount of deflection experienced by a beam with varying cross section is affected by several factors. The size and shape of the cross section, the type of load applied, and the material used for the beam are some of the most important factors. The magnitude of the load, the stiffness of the beam, and the mass of the beam also play a role in determining the amount of deflection. In addition, other factors such as the temperature and humidity of the environment can also affect the amount of deflection.

## Types of Deflection

The deflection of a beam with varying cross section can be classified into two types – static and dynamic. Static deflection is the deflection that occurs when the beam is subjected to a static load. This type of deflection is usually smaller than dynamic deflection. Dynamic deflection, on the other hand, occurs when the beam is subjected to a dynamic load. This type of deflection is usually bigger than static deflection.

## Methods of Reducing Beam Deflection With Varying Cross Section

The amount of deflection experienced by a beam with varying cross section can be reduced by several methods. One method is to use stiffer materials for the beam. This will reduce the amount of deflection that the beam experiences. Another method is to use different shapes for the cross section of the beam. This will help to reduce the amount of deflection that the beam experiences. Finally, adding additional supports or bracing can also help to reduce the amount of deflection that the beam experiences.

## Conclusion

The deflection of a beam with varying cross section is a phenomenon that is affected by several factors. The size and shape of the cross section, the type and magnitude of the load, and the material used for the beam are some of the most important factors. In addition, other factors such as the temperature and humidity of the environment can also affect the amount of deflection. The amount of deflection can be reduced by using stiffer materials for the beam, using different shapes for the cross section of the beam, and adding additional supports or bracing.