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resultant force. For all practical purposes these lines of action will be
concurrent at a single point G, which is called the center of gravity of
the body.
Composite Bodies. A composite body consists of a series of
connected “simpler” shaped bodies, which may be rectangular,
triangular, semicircular, etc. Such a body can often be sectioned or
divided into its composite parts and, provided the weight and location
of the center of gravity of each of these parts are known, we can then
eliminate the need for integration to determine the center of gravity for
the entire body. Formulas analogous to Eqs. 1-54 result; however,
rather than account for an infinite number of differential weights, we
have instead a finite number of weights. Therefore,

zW
xW
Σɶ Σɶ yW Σɶ
x = , y = , z = , 1-67
Σ W Σ W Σ W
here ,,x yz represent the coordinates of the center of gravity G of the
composite body; ,,x yz ɶ represent the coordinates of the center of
ɶɶ
gravity of each composite part of the body; WΣ is the sum of the
weights of all the composite parts of the body, or simply the total
weight of the body.
To determine the mass-center coordinates for a composite body
we substitute m instead W
Σɶ Σɶ ym Σɶ zm
xm
x = , y = , z = . 1-68
Σ m Σ m Σ m
When the body has a constant density or specific weight, the
center of gravity coincides with the centroid of the body. The centroid
for composite lines, areas, and volumes can be found using relations
analogous to Eqs. 1-67; however, the W’s are replaced by L’s, A’s, and
V’s, respectively. Centroids for common shapes of lines, areas, shells,
and volumes that often make up a composite body are given in the
table on the appendices. Note, that if the composite body includes the
“holes” then the parts are taken as negative.

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