Moment Diagrams by Parts
The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagrams by parts and to calculate the moment of such diagrams about a specified axis.
- The bending moment caused by all forces to the left or to the right of any section is equal to the respective algebraic sum of the bending moments at that section caused by each load acting separately.
- The moment of a load about a specified axis is always defined by the equation of a spandrel
where n is the degree of power of x.
The graph of the above equation is as shown below
and the area and location of centroid are defined as follows.
A = area of moment diagram
Mx = moment about a section of distance x
barred x = location of centoid
Degree = degree power of the moment diagram
|Couple or Moment Load
|Uniformly Distributed Load
|Uniformly Varying Load