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

 

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.
 

θAB=1EI(AreaAB)

 

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.
 

tB/A=1EI(AreaAB)ˉXB

 

and
 

tA/B=1EI(AreaAB)ˉXA

 

Rules of Sign

area-moment-rules-of-sign.jpg

 

  1. The deviation at any point is positive if the point lies above the tangent, negative if the point is below the tangent.
  2. Measured from left tangent, if θ is counterclockwise, the change of slope is positive, negative if θ is clockwise.