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F and F create zero moment about C. Likewise, F can be
BC
BC
GC
directly obtained by summing moments about G. Finally, F can be
GC
found directly from a force summation in the vertical direction since
F and F have no vertical components. This ability to determine
BC
GF
directly the force in a particular truss member is one of the main
advantages of using the method of sections.
As in the method of joints, there are two ways in which we can
determine the correct sense of an unknown member force:
• The correct sense of an unknown member force can in many
cases be determined “by inspection.” For example, F is a tensile
BC
force as represented in Fig. 1-76,b since moment equilibrium about G
requires that F create a moment opposite to that of the 1000 N
BC
force. Also, F is tensile since its vertical component must balance
GC
the 1000 N force which acts downward. In more complicated cases,
the sense of an unknown member force may be assumed. If the
solution yields a negative scalar, it indicates that the force’s sense is
opposite to that shown on the free-body diagram.
• Always assume that the unknown member forces at the cut
section are tensile forces, i.e., “pulling” on the member. By doing this,
the numerical solution of the equilibrium equations will yield positive
scalars for members in tension and negative scalars for members in
compression.

VIII WEIGHT AND THE CENTER OF GRAVITY

When a body is within a gravitational field (for example,
attraction of the earth), then each of its particles have a specified
weights. Such a system of forces can be reduced to a single resultant
force acting through a specified point. We refer to this force resultant
as the weight W of the body and to the location of its point of
application as the center of gravity. If the body is uniform or made
from the same material, the center of gravity will be located at the
body’s geometric center or centroid. This chapter treats the
determination of the point in a body through which the resultant
gravitational force acts, and discusses the associated geometric
properties of lines, areas, and volumes.

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