Engineering Statics

F-2


Locate the centroid of the plane area shown.

The member is divided into two more convenient shapes.<BR> 
Each shape is numbered for identification.
We create a table listing the area of each shape, the x coordinate of 
the centroid for each shape, and the y coordinate of the centroid for 
each shape.<BR> 
We then multiply the centroid distances by the area for intermediate values.<BR> 
These values are then added together at the bottom of the table along 
with the area.
We enter in all values for the first shape, 
and do a few calculations to get x(bar)A and y(bar)A.
We perform the same steps for the second shape...
These intermediate values are then added together at the bottom of the 
table along with the area.<BR> 
(Notice that some of the values can get very large.)
The x coordinate of the centroid is determined by dividing the sum of 
the products of the x coordinates and the areas by the total area.<BR> 
This gives us the x coordinate of the centroid for the entire shape.
Similarly, we perform the same steps to determine the y coordinate of the 
centroid for the entire shape.