Moment area method

a.)First Moment-Area Theorem

The angle between the tangents, denoted, is equal to the difference between  and 

First moment-area theorem: The angle  between the tangents to the deflection curve at two points A and B is equal to the area of the M/EI diagram between those points.

b.)Second Moment-Area Theorem

Second moment-area theorem: The tangential deviation  of point B from the tangent at point A is equal to the first moment of the area of the M/EI diagram between A and B, evaluated with respect to B.

The first moment of the area of the M/EI diagram can be obtained by taking the product of the area of the diagram and the distance  from point B to the centroid C of the area