Different Methods:

The following methods are utilized to determine the slopes & deflections:

(a) Double Integration Method

It is most appropriate when concentrated or Udl over entire length is working on the beam.

 (b) Macaulay's Method

This method is most conveniently utilized when a concentrated load is working on a beam at some of point other than mid-point.

 (c) Moment Area Method

This is conveniently utilized when the area of BMD might be easily determined and beam cross-section changes after certain length.

 (d) Conjugate Beam Method

This is most appropriate for beams along varying moment of inertia.

(e) Strain Energy Method

(f)  Virtual Work Method

(g) Unit Load Method