1. The document discusses methods for analyzing systems of coplanar and non-coplanar concurrent and non-concurrent forces in 2D and 3D. 2. It describes laws of mechanics including Newton's laws of motion and gravitation, and laws of parallelogram of forces. 3. Methods are presented for determining the resultant and direction of equivalent forces, or solving for unknown forces, in equilibrium problems involving concurrent and non-concurrent force systems. Examples of solving for the resultant of systems of forces are shown.

1. 1
T.PARAMESH
Department of Mechanical
engineering

4.  Magnitude
 Direction
 Point of application
 Nature

6.  Resolution of force
 The process of replacing a single force into
number of components, without changing its
effect on the body is called Resolution of
force

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Systemof
Forces
Coplanar
2D
Concurrent Non-
concurrent
Parallel General
Non-
coplanar
3D
Concurrent
Non-
concurrent
Parallel General

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10. Method of approach to solve CONCURRENT and NON CONCURRENT FORCE Systems
Problem
2-D
Concurrent
NotEquilibrium
(Resultant)
1.ParallelogramLaw
2. Trianglelaw
3. Polygonlaw
4.Methodof
projections
Equilibrium
(Unknowns)
Fx=0
Fy=0
Non-concurrent
NotEquilibrium
(Resultant)
1.Choose a reference
Point
2.Shift all the forces
to apoint
3.Find the resultant
force and couple at
thatpoint
4.Reduce the force-
couple system to a
single force
Equilibrium
(Unknowns)
ΣFx=0
ΣFy=0
ΣMz=0
3-D
Concurrent
Notequilibrium
(Resultant)
--- --- --- -- R
= F1+F2+F3
Equilibrium
(Unknowns)
--- ---
R = 0
--- --- -- --
F1+F2+F3,,= 0
ΣFx=0
ΣFy=0
ΣFz=0,
NonConcurrent
NotEquilibrium
(Resultant)
--- -- -- --
R=F1+F2+F3….
--- --- --- ---
M = M1+M2+M3....
--- ---
OPͯr R =M
Equilibrium
(Unknowns)
--- ---
R = 0
--- ---
M = 0
10
ΣFx=0 , ΣMx=0
ΣFy=0, ΣMy=0
ΣFz=0, ΣMz=0

11. Method of approach to solve Coplanar (2D) problems
Problem
2-D
Concurrent
NotEquilibrium
(Resultant)
1. ParallelogramLaw
2. Trianglelaw
3. Polygon law
4. Method ofprojections
Equilibrium
(Unknowns)
F =0x
Fy=0
Non-concurrent
NotEquilibrium
(Resultant)
1.Choose a referencePoint
2. Shift all the forces to apoint
3.Find the resultant forceand
couple at that point
4.Reduce theforce-couple
system to a singleforce
Equilibrium
(Unknowns)
ΣFx=0
ΣFy=0
ΣMz=0
11

12.  Laws of mechanics
Newton’s first law of motion
Newton’s second law of motion
Newton’s third law of motion
Newton’s law of gravitation
Laws of parallelogram of force

15. Determine the resultant of the following figure

16. Determine the resultant of the following figure

17. Determine the resultant of the following figure
Problem – 2D- Concurrent - Resultant
17

18. R  199.12
14.32
R 199.6N
5
Force Mag x comp y comp
F1 150 150cos30 150Sin30
F2
80 80sin 20 80Cos20
F3
110 0 110
F4
100 100cos15 100sin1
F x
199.1 F y
14.3
2 2
 F X
  FY
R Resultant is
199.1N
tan  
14.3 N
  4.1
Direction is
8
Problemsolution

19. Determine the resultant of the following figure
Problem – 2D- Non Concurrent - Resultant
11

20. Moment of force
 The rotational effect produced by force is
known as Moment of force
Couple
 Two non collinear parallel forces of equal
magnitude but acting in opposite direction
from couple

21. FBD
 FBD is a sketch of the body showing all active
and reactive forces that acts on it after
removing all supports with consideration of
geometrical angles and distance.
Lamis theorem
 If a body is an equilibrium under the action of
three forces each force is proportional to the
sine of the angle between the other two
forces

22. Determine the resultant of the following figure

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