A.
FORCES AND STATICS
Force
Concurrent Forces
Colinear Forces
Unit Gizmos
Resolution
of Forces
Cantilever
Simple
Truss
Bridge
Tower
B. SECTION PROPERTIES
Section
Properties
C. TRUSS ANALYSIS
Truss
Analysis
D. BEAM ANALYSIS
Beam
Analysis
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In
a concurrent force system, all forces pass through a common point. In the
previous case involving the application of two forces to a body, it was
necessary for them to be colinear, opposite in direction, and equal in
magnitude for the body to be in equilibrium. If three forces are applied
to a body, as shown in the figure, they must pass through a common point
(O), or else the condition, SMo
= 0, will not be satisfied and the body will rotate because of unbalanced
moment. Moreover, the magnitudes of the forces must be such that
the force equilibrium equations,
SFx
= 0, SFy=
0, are satisfied.
 Concurrent
Forces
It is fairly
easy to see the reasoning for the first condition. Consider the two forces,
F1
and F2,
intersecting at point O in the figure. The sum of moments of these two
forces about point 0 is obviously equal to zero because they both pass
through 0. If F3
does not pass through 0, on the other hand, it will have some nonzero moment
about that point. Since this nonzero moment will cause the body to rotate,
the body will not be in equilibrium.
Therefore,
not only do three nonparallel forces applied to a body have to be concurrent
for the body to be in an equilibrium state, but their magnitudes and directions
must be such that the force equilibrium con-ditions are satisfied (SFx
= SFy
= 0). Notice that there is no need for the moment equilibrium equation
in this case since it is automatically satisfied.
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