Engineering Statics

F-4


Locate the centroid of the plane area shown.

The member can be described in terms of two standard shapes, 
but by subtraction, not addition.<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.<BR> 
Note that area 2 is to be subtracted, thus all values are assumed to be 
negative for the purposes of addition.
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.