Solved: Determine the location y of the centroid C for a

Step 1 of 4

We need to Find  of the beam. The beam is symmetric about the y-axis.

Step  2 of 4

Since the beam is symmetric about y-axis we can look only at the part of the beam right of the y-axis. Also we can make this beam as a superposition of bid rectangle with sides 6 in. and 4 in. with positive area and two smaller parts with negative area. One of those parts is square with sides 1 in. while other one is a rectangle with sides 3 in. and 1 in. . We  marked them with red numbers in the picture below.

We need to find centroids of each part and since they are all rectangles we know their centroid is in their middle. We  marked centroid of each part with red dot in the picture below.

Step  3 of 4

In the table below everything we need to find