Rectangular Components
When adding more than two forces, it is easier to find the components of each force along specified
axes, add these components algebraically, and then form the resultant, rather than form the resultant of
the forces by successive application of the parallelogram law.
Any force can be resolved into its rectangular components Fx and Fy, which lie along the x and y axes,
respectively.
Magnitude
F = √ F2x + F2y
F
Fy = F sin 
Direction


Fx = F cos 
(First Quadrant)
or
 = tan –1
Fy
Fx
(See Below)
First Quadrant:  = 
Second Quadrant:  = 180 - 
Third Quadrant:  = 180 + 
Fourth Quadrant:  = 360 -  or  = -
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Resultants by Rectangular Components
Using rectangular components, obtained by resolving forces in the system, the resultant can be obtained.
The resultant force, just like any other force, can be thought of as being able to be resolved into x and y
components Rx and Ry.
The magnitude of the components Rx and Ry is simply the sum of the x and y components of the forces
in the system.
Magnitude
Rx =  Fx
R = √ R2x + R2y
Ry =  Fy
Direction
 = tan –1
Ry
Rx
 is determined by which Quadrant the Resultant lies in:
Quadrant I
=
Quadrant II
 = 180 - 
Quadrant III
 = 180 + 
Quadrant IV
 = 360 -  or  = -
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Example 1: Four forces act on bolt A as shown. Determine the resultant of the forces on the bolt.
Solution.
Force (kN)
Direction ()
Fx = F cos  (kN)
Fy = F sin  (kN)
 Fx =
 Fy =
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Example 2: Using the method of rectangular components, find the resultant of the following concurrent
forces.
Solution.
Note: All angles measured CCW from the +x axis
Force (lb)
Direction ()
Fx = F cos  (lb)
Fy = F sin  (lb)
 Fx =
 Fy =
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Example 3: Three plates are connected using welds with concurrent forces applied as shown. Calculate
the resultant of the forces.
Solution.
Force (lb)
Direction ()
Fx = F cos  (lb)
Fy = F sin  (lb)
 Fx =
 Fy =
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