Moment area theorem

 The moment area theorem is based on the following two theorems:

Theorem 1:

  The change in slope of the tangent of elastic curve between two points in straight member is equal to the area under M/EI diagram between two points.

 Theorem 2:

  The deflection at any point in a beam in the direction perpendicular to its original tangent to the elastic curve at another point is given by the moment of M/EI diagram about the point where deflection is required.