Area-Moment Method | Beam Deflections
Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.
![Deviation and Slope of Beam by Area-Moment Method](/sites/default/files/images/deviation-and-slope-by-area-moment.jpg)
Theorems of Area-Moment Method
Theorem I
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.
Theorem II
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.
and
![area-moment-rules-of-sign.jpg](/sites/default/files/reviewer-strength/06-beam-deflections/area-moment-rules-of-sign.jpg)
- 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.
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