Deflection of beam by direct integration method is a technique used to calculate the deflection of a beam caused by a load applied to it. The method uses the integration of the moment-curvature equation of the beam, which is derived from the theory of elasticity. The method is used for both statically determinate and statically indeterminate beams. The method is especially useful in cases where the load and the beam geometry cannot be assumed to be constant, such as in the case of a cantilever beam.

## How Does The Deflection of Beam By Direct Integration Method Work?

The method of calculating the deflection of a beam using direct integration is based on the equations of equilibrium in the theory of elasticity. The equations of equilibrium state that the sum of all forces and moments acting on the beam must be equal to zero. The moment-curvature equation of the beam is used to calculate the curvature of the beam due to the load applied. The curvature is then integrated to obtain the deflection of the beam. This method is also known as the direct integration method.

## Advantages of Direct Integration Method

The direct integration method is a simple technique to calculate the deflection of a beam. It requires only a few parameters such as the beam geometry and the loading applied to it. The method is also relatively accurate and can be used for both statically determinate and statically indeterminate beams. Furthermore, the method is useful for cases where the load and the beam geometry cannot be assumed to be constant, such as in the case of a cantilever beam.

## Disadvantages of Direct Integration Method

The direct integration method is not suitable for cases where the beam geometry or the loading applied to it are highly complex. The method also requires a certain amount of time to calculate the deflection of the beam. Furthermore, the method is not suitable for cases where the deflection needs to be calculated accurately due to the presence of higher order terms in the equation of equilibrium.

## Conclusion

The direct integration method is an effective technique to calculate the deflection of a beam caused by a load applied to it. The method is simple and relatively accurate and can be used for both statically determinate and statically indeterminate beams. However, the method is not suitable for cases where the beam geometry or the loading applied to it are highly complex. Furthermore, the method is not suitable for cases where the deflection needs to be calculated accurately due to the presence of higher order terms in the equation of equilibrium.