Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.
Theorems of Area-Moment Method
The change in slope between the tangents drawn to the elastic curve at any two points A and B is equal to the product of 1/EI multiplied by the area of the moment diagram between these two points.
The deviation of any point B relative to the 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 1/EI multiplied by the moment of an area about B of that part of the moment diagram between points A and B.
- The deviation at any point is positive if the point lies above the tangent, negative if the point is below the tangent.
- Measured from left tangent, if θ is counterclockwise, the change of slope is positive, negative if θ is clockwise.