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joint and no external load or support reaction is applied to the joint,
the two members must be zero-force members. The load on the truss in
Fig. 1-75,a is therefore supported by only five members as shown in
Fig. 1-75,c.

34 Method of Sections

When we need to find the force in only a few members of a
truss, we can analyze the truss using the method of sections. It is based
on the principle that if the truss is in equilibrium then any segment of
the truss is also in equilibrium. For example, consider the two truss
members. If the forces within the members are to be determined, then
an imaginary section, indicated by the blue line, can be used to cut
each member into two parts and thereby “expose” each internal force
as “external” to the free-body diagrams shown on the right. Clearly, it
can be seen that equilibrium requires that the member in tension (T)
be subjected to a “pull,” whereas the member in compression (C) is
subjected to a “push.”
The method of sections can also be used to “cut” or section the
members of an entire truss. If the section passes through the truss and
the free-body diagram of either of its two parts is drawn, we can then
apply the equations of equilibrium to that part to determine the
member forces at the “cut section.” Since only three independent
Σ
0 Σ
Σ
equilibrium equations ( F = , F = 0, M = ) can be applied to
0
x
O
y
the free-body diagram of any segment, then we should try to select a
section that, in general, passes through not more than three members
in which the forces are unknown. For example, consider the truss in
Fig. 1-76,a. If the forces in members BC, GC, and GF are to be
determined, then section aa would be appropriate. The free-body
diagrams of the two segments are shown in Figs. 1-76,b and 1-76c.
Note that the line of action of each member force is specified from the
geometry of the truss, since the force in a member is along its axis.
Also, the member forces acting on one part of the truss are equal but
opposite to those acting on the other part – Newton’s third law.
Members BC and GC are assumed to be in tension since they are
subjected to a “pull,” whereas GF in compression since it is subjected
to a “push.”

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