## 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.

$M = ( \, \Sigma M \, )_L = ( \, \Sigma M \, )_R$

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

$y = kx^n$

where n is the degree of power of x.

## 708 Centroid and area of spandrel by integration

Problem 708
Compute the area of the spandrel in Fig. P-708 bounded by the x-axis, the line x = b, and the curve y = kxn where n ≥ 0. What is the location of its centroid from the line x = b? Determine also the y coordinate of the centroid.