__INTRODUCTION__

- Whenever a structure got affected from any external sources, then there may be a chance of having deflection in the structures.
- The external sources mentioned above may be anything such as loading applied (axial force, shear force, bending moment, torsion), self weight, change in temperature (increase/decrease),fabrication or misfits errors, support settlements, etc.
- The calculations of these deflections in the structures are very important to know.
- The deflections of structures must be within permissible limit as per design to prevent cracking or even failure of structure. So, it is very much necessary to calculate deflection at all critical points of the structure so that the structure should be designed as such deflection in structure remains within the permissible limit as per the design.
- The calculation of deflection is also very much necessary in case of analysis of indeterminate structures, where deflection is required to write compatibility equation.

# __TYPES OF DEFLECTION METHOD__

*Double integration method**Method of superposition**Moment area method**Conjugate beam method**Castigliano's method**Method of virtual work/ unit load method*

*DOUBLE INTEGRATION METHOD*

- This method is also sometimes known as Macaulay's method/Singularity function method/ Discontinuity function method.
- This method of finding deflection is very much used in case of beams.
- This method is only used for finding deflection for bending.
- This method gives the equation of deflected elastic curve of whole beam at once.
- This method can't be applied directly for the structures having some kind of discontinuity in the elastic deflected curve. By discontinuity we mean to say presence of any hinge or slider.
- This method can also be not applied directly for the non-prismatic beams.
- This deflection method is best for the case when deflection or slope is required to be found at too many points.

*METHOD OF SUPERPOSITION*

- In this method of finding deflection, deflection at any point on the structure can be calculated by summing up the effects of each load acting on the structure one by one.
- This method of superposition is only helpful in the case if deflection/slope at any point is already known for the given applied loading. And so, the limitation of this method is that this method can only be used for standard types of loading or supports present in the beams.

*MOMENT AREA METHOD*

- This method of finding deflection is only used to find bending deflections.
- This method is generally used to find deflection for beams subjected to a series of concentrated loads and for non-prismatic beams.
- This method can't be applied directly for the structures having some kind of discontinuity as hinge or slider.

*CONJUGATE BEAM METHOD*

- This method of finding deflection is only used to find bending deflections.
- This method is generally used to find deflection for beams subjected to a series of concentrated loads and for non-prismatic beams.
- This method of finding deflection can be even applied directly for the structures having any discontinuity like hinge or slider.

## *CASTIGLIANO'S METHOD*

- This method of finding deflection can be used for all types of external loading.
- This method of finding deflection can also be applied for ant discontinuity case or even in non-prismatic case.
- The limitation of the castigliano method is that it can't be applied for support settlement case(can be applied for support settlement in case of self restraining structure) and in temperature change case.

*METHOD OF VIRTUAL WORK/ UNIT LOAD METHOD*

- This method of finding deflection can be applied for all types of external loadings.
- This method of finding deflection can also be applied for ant discontinuity case or even in non-prismatic case.
- This method can also be applied for support settlement case or in case of temperature change also.