Force Force System Laws of forces

1. Engineering Mechanics
and
Strength of Materials
Complete Concept With Practice Set
By:-
Ashish
Mishra

2. Syllabus for SSC-JE
Equilibrium of Forces, Law of motion, Friction, Concepts of stress and
strain, Elastic limit and elastic constants, Bending moments and shear
force diagram, Stress in composite bars, Torsion of circular shafts,
Bucking of columns – Euler’s and Rankin’s theories, Thin walled pressure
vessels.
Force Systems : Concentrated and distributed force systems, Co-
planer force systems, Equivalent force systems, Equations of
equilibrium, Two-dimensional force systems, Centre of gravity,
Statically determinate force systems, Shear force and bending
moment diagrams for statically determinate beams, Plane truss and
its analysis. Simple stress and strain, One dimensional thermal stress,
Elastic constants, Stress due to bending and torsion. Kinematics of
particle, Co-planer motion, Velocity and acceleration motion on
curved path. Kinetics of particle, System of particles and rigid bodies,
D'Alembert's principle, Kinetics of rigid bodies in plane motion.
Principal stresses and Principal planes, Total and Distortion strain energies,
Theories of failure, Fatigue and Creep, Buckling of columns, stress in thick and
thin cylinders.

3. Force
Force:- Force is defined as an external cause that
changes or tends to change the state of the body once
applied, if the body is in motion it comes to rest and if at
rest then will come to motion. It can also cause a change
in the direction, shape, size, etc of the body. Example:
Pushing or pulling a door by applying force.
Force is a vector quantity which means it has both
magnitudes as well as direction. According to Newton's
second law, force is stated as the “product of mass and
acceleration of a body”.
What are the Effects of Force?
Force acting on the body may affect the shape of the body
or will accelerate or decelerate the body, or it will give
motion to the static body or it will stop the motion of the
dynamic body.

4. Force
Types of Forces:
There are two types of forces:
1. Contact forces:- Contact force is a force which is
applied by actually touching the body.
Examples: Tension Force, Spring Force , Normal Force,
Air resistance Force, Frictional Force , Force of Gravity ,
Applied Force
2. Non- contact forces:- It is the force that acts without
any physical contact between the bodies. There are three
types of Non-Contact Force. These are:
Gravitational Force
Electrostatic Force
Magnetic Force

5. Force
Unit of Force:
Unit of force is Newton (N). A Newton is a force
required to give a mass of 1 kilogram (1 kg) an
acceleration of 1 meter per second squared (1 m/s²). SI
unit of mass is kilogram (kg) and acceleration is meter
per second squared (m/sec²) hence it is written as kg
m/sec² which is denoted by Newton.

6. Force
How force is a vector quantity?
Force has both direction and magnitude and obeys the vector law of
addition. Hence, it is a vector.
Characteristics of Vectors
The characteristics of the vectors are as follows:
Vectors possess magnitude as well as the direction
Either the magnitude or direction change or both change
It does not obey the ordinary law of algebra
Examples of vectors
Few examples of vector quantities are,
Displacement, Acceleration, Force, Momentum, Weight, Velocity

7. Force
A Force has following basic characteristics
i) Magnitude
ii) Direction
iii) Point of application
iv) Line of action

8. Force System
When a mechanics problem or system has more than one force acting,
it is known as a ‘force system’ or ‘system of force’.

9. Force System
Coplanar forces- Coplanar forces means the forces in a plane. Or a
system in which all the forces lie in the same plane, it is known as
coplanar force system.
Coplanar Collinear forces - Collinear forces are those forces which
have a common line of action, i.e. the line of action of the forces lie
along a single straight line either they are push or pull in nature.
Examples: two people standing at the opposite ends of a rope and
pulling on it.

10. Force System
Coplanar Parallel forces- Parallel forces are those forces
which are in the same plane but never intersect by each other
and they may be same or opposite in direction..
Coplanar Concurrent Forces- Concurrent forces are those
forces which are acting at a same point and at a same plane,
also they may be pull or push in nature.

11. Force System
Non-coplanar forces-Non-coplanar forces are those forces
which are not acting from a same plane.
Non coplanar non- concurrent forces- Non- Coplanar non-
concurrent forces are those forces which are not acting at a
same point and not at a same plane, also they may be pull or
push in nature.

12. Force System
Non-coplanar concurrent forces- Non- Coplanar concurrent
forces are those forces which are acting at a same point but not
from a same plane, also they may be pull or push in nature.
Non-coplanar parallel forces- Non-coplanar Parallel forces are
those forces which are not in the same plane and never
intersect by each other, they may be same or opposite in
direction.

13. Equivalent Force System
If a force acting on a body is represented (or replaced) by another
force or a force-moment system (at a different point on the body)
such that the resulting rigid-body effects (i.e., translation and
rotation) remain unchanged, the two systems are said to
be statically equivalent.
When a number of forces and couple moments are acting on a
body, it is easier to understand their overall effect on the body if
they are combined into a single force and couple moment having
the same external effect The two force and couple systems are
called equivalent systems since they have the same external effect
on the body

14. Equations Of Equilibrium
A body is subjected to a system of forces that lie in the x-y
plane. When in equilibrium, the net force and net moment
acting on the body are zero .This 2-D condition can be
represented by the three scalar equations:
∑F x = 0, ∑F y = 0, ∑ Mo = 0
Where point O is any arbitrary point.

15. Equations Of Equilibrium
As stated earlier, when a body is in equilibrium, the
net force and the net moment equal zero, i.e.
∑F = 0, ∑ M = 0
These two vector equations can be written as six
scalar equations of equilibrium. These are.
∑F x = 0, ∑F y = 0, ∑ Fz = 0
∑ Mx = 0, ∑ My = 0, ∑ Mz = 0,
6 equations for 3D equilibrium
##The moment equations can be determined about
any point. Usually, choosing the point where the
maximum number of unknown forces are present
simplifies the solution.

16. Equations Of Equilibrium
.

17. Free Body Diagram
.
To study the equilibrium of a body, it is imagined that the supports are
replaced by the reaction exerted on body. A diagram of an isolated body
which show only the reactions acting on the body is called a free body
diagram (F.B.D
A Free Body Diagram is a visual representation of force and object
interactions. Individual objects or members are isolated from their
environment or system, illustrating all external forces acting upon them.
A body may consist of more than one element and supports. Each
element or support can be isolated from the rest of the system by
incorporating the net effect of the remaining system through a set of
forces. This diagram of the isolated element or a portion of the body
along with the net effects of the system on it is called a ‘free-body
diagram’. Free-body diagrams are useful in solving the forces and
deformations of the system

18. Laws of Forces
Law of Parallelogram of Forces.
The law of parallelogram of forces is used to determine the resultant*
of two forces acting at a point in a plane.
It states, “If two forces, acting at a point be represented in magnitude
and direction by the two adjacent sides of a parallelogram, then their
resultant is represented in magnitude and direction by the diagonal of
the parallelogram passing through that point.”

19. Laws of Forces
Law of Parallelogram of Forces.
Let,
P,Q = Forces whose resultant is needed to be found out.
θ= Angle that the resultant forces makes with one of the forces
α= Angle between the forces P and Q
Direction ( θ ):

20. Laws of Forces
Law of Parallelogram of Forces.
Special cases:-
i) Resultant R is max when two forces collinear and are
in the same direction.
(ii) Resultant R is min when two forces collinear but acting
in the opposite direction.
That is α = 1800 => Rmin = P- Q
(iii) If a = 900, that is when the forces act at right angle,
then
R = P2 + Q2
(iv) If the two forces are equal that is, when
P = Q =>R = 2P.cos(θ/2)

21. Laws of Forces
Triangle Law of Forces
If two forces acting at a point are represented in magnitude and
direction by the two adjacent sides of a triangle taken in order, then the
closing side of the triangle taken in the reversed order represents the
resultant of the forces in magnitude and direction.

22. Laws of Forces
Polygon Law of Forces
It states that “if more than two forces acting simultaneously on a
particle, be represented in magnitude and direction by the sides
of a polygon, taken in order, their resultant may be ,represented
in magnitude and direction by the side closing of the polygon,
taken in opposite order”.
A, B, C, D, E are five forces.2. R
is the resultant forces i.e. the
closing side of the polygon taken
in opposite order.

23. Laws of Forces
Lames theorem
“If three coplanar forces acting on a point in a body keep it in equilibrium,
then each force is proportional to the sine of the angle between the other two
forces.”
From geometry of parallelogram oadb, we find
bd = P and ad = Q ∠bod = (180 – α) and ∠bdo = ∠aod = ∠(180 – β)

24. Laws of Forces
Transmissibility Of A Force
The principle of transmissibility of forces states that when a force acts upon a
body, its effect is the same whatever point in its line of action is taken as the
point of the application provided that the point is connected with the rest of the
body in the same invariable manner

25. Laws of Forces
Principle Of Resolved Parts
The principle of resolved parts states : “The sum of the resolved parts
of two forces acting at a point in any given direction is equal to the
resolved parts of their resultant in that direction
Mutually perpendicular components.
Let the force P to be resolved is represented in magnitude and direction by oc
in Fig. 2.11. Let Px is the component of force P in the direction oa making an
angle α with the direction oc of the force. Complete the rectangle oacb. Then
the other component Py at right angle to Px will be represented by ob which is
also equal to ac.
From the right-angled triangle oac
Px = oa = P cos α Py = ac = P sin α.

26. Thank You