Figure 9.3 is a beam cross section, unsymmetrical with respect to the horizontal axis (X-X in Figure 9.3c). Find the location of the horizontal centroidal axis for this shape.

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Accepted Answer

The usual process for this problem is to first divide the shape into units for which both the area and centroid of the unit are easily determined. The division chosen here is shown in Figure 9.3b, with two parts labeled 1 and 2.

The second step is to chose an arbitrary reference axis about which to sum statical moments and from which the centroid of the shape is readily measured. A convenient reference axis for this shape is one at either the top or bottom of the shape. With the bottom chosen, the distances from the centroids of the parts to this reference axis are as shown in Figure 9.3b.

The computation next proceeds to the determination of the unit areas and the unit statical moments. This work is summarized in Table 9.1, which shows the total area to be 80 in.² and the total statical moment to be 520 in.³. Dividing the moment by the area produces the value of 6.5 in., which is the distance from the reference axis to the centroid of the whole shape, as shown in Figure 9.3c.

TABLE 9.1 Summary of Computations for Centroid: Example 1
Part	Area (in.²)	y (in.)	A × y (in.³)
1	2 × 10 = 20	11	220
2	6 × 10 = 60	5	300
∑	80		520
[latex]y_x=520/80=6.5 \;in.[/latex]

Question 9.1: Figure 9.3 is a beam cross section, unsymmetrical with respe...

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