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If three members are pin connected at their ends they form a
triangular truss that will be rigid, Fig. 1-72. Attaching two more
members and connecting these members to a new joint D forms a
larger truss, Fig. 1-73. This procedure can be repeated as many times
as desired to form an even larger truss. If a truss can be constructed by
expanding the basic triangular truss in this way, it is called a simple
truss.

32 Method of Joints

In order to analyze or design a truss, it is necessary to determine
the force in each of its members. One way to do this is to use the
method of joints. This method is based on the fact that if the entire
truss is in equilibrium, then each of its joints is also in equilibrium.
Therefore, if the free-body diagram of each joint is drawn, the force
equilibrium equations can then be used to obtain the member forces
acting on each joint. Since the members of a plane truss are straight
two-force members lying in a single plane, each joint is subjected to a
force system that is coplanar and concurrent. As a result, only
Σ
Σ F = 0 and F = 0 need to be satisfied for equilibrium.
y
x
For example, consider the pin at joint B of the truss in Fig. 1-
74,a. Three forces act on the pin, namely, the 500 N force and the
forces exerted by members BA and BC. The free-body diagram of the
pin is shown in Fig. 1-74,b. Here, F is “pulling” on the pin, which
BA
means that member BA is in tension; whereas F is “pushing” on the
BC
pin, and consequently member BC is in compression. These effects are
clearly demonstrated by isolating the joint with small segments of the
member connected to the pin, Fig. 1-74,c. The pushing or pulling on
these small segments indicates the effect of the member being either
in compression or tension.
When using the method of joints, always start at a joint having at
least one known force and at most two unknown forces, as in Fig. 1-
74,b. In this way, application of FΣ x = 0 and FΣ y = 0 yields two

algebraic equations which can be solved for the two unknowns. When
applying these equations, the correct sense of an unknown member
force can be determined using one of two possible methods.

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