Moment Diagram 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 diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

Basic Principles

  1. 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.
     
    M=(ΣM)L=(ΣM)R

     

  2. The moment of a load about a specified axis is always defined by the equation of a spandrel
     
    y=kxn

    where n is the degree of power of x.

 

The graph of the above equation is as shown below
 

Area and Centroid of General Spandrel

 

and the area and location of centroid are defined as follows.
 

A=1n+1bh

 

XG=1n+2b

 

Cantilever Loadings
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
cantilever-moment-load.jpgA=CL

Mx=C

ˉx=12L

Degree: zero

Concentrated Load
cantilever-concentrated-load.jpgA=12PL2

Mx=Px

ˉx=13L

Degree: first

Uniformly Distributed Load
cantilever-uniform-load.jpgA=16woL3

Mx=12wox2

ˉx=14L

Degree: second

Uniformly Varying Load
cantilever-triangular-load.jpgA=124woL3

Mx=wo6Lx2

x=15L

Degree: third

 

Saan po galing yung L sa Mx=−[wox2]/6L under Uniformly Varying Load?

Pagkaintindi ko po sa moment is
Mx = -1/2 * (wo) * x * (1/3)x = −[wox2]/6

In reply to by Bhong

Mali po ang equation mo. Palitan mo ng y ang wo sa inyong equation, then i-express mo ang y in terms of x and wo, magawa mo yan by ratio and proportion. Sa equation na nakapost na Mx=wo6Lx2, try mo palitan ang x ng L and it will make sense, mapapalabas mo kasi ang Mmax.