MOMENT AREA METHOD OF STRUCTURAL ANALYSIS:
Theorem – I
The change in slope between tangents drawn to the elastic curve at any two points A and B is equal to the product of and the area of the moment diagrams between those two points (figure 1(a)).
Theorem – II
The deviation of any point B relative to a tangent drawn to the elastic curve at any other point A, in a direction perpendicular to the original position of the beam, is equal to the product of and the moment of area about B of that part of the moment diagram between points A and B (figure 1(b)).
This method is useful for finding slope and deflection at a specified position.
(Area of Bending Moment diagram between A and C)
(moment of area of the BMD between A and C about C)