Concurrent Forces
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.