Transcript Resultant of concurrent coplanar forces

Mr. Alok Damare
Prof. Civil Engg. Dept.
INTRODUCTION

Engineering mechanics is that branch of
science which deals with deals with the system
of forces, effect produced by these forces on
rigid object.

Mechanics can be divided into two main
branches – Statics and Dynamics.
Statics
Statics is that branch of Engineering
mechanics, which deals with the study of system
of forces and effect produced by these forces on
rigid bodies, which are at rest and remains at
rest.
Dynamics
Dynamics is that branch of Engineering
mechanics, which deals with the study of system of
forces and motion produced by these forces on rigid
bodies.

There are two sub division of Dynamics
Kinematics
Kinematics is the study of motion of
a body without considering the effect
of its mass and forces acting on it.
Kinetics
Kinetics deals with the
problems which requires determination
of the effect of forces on the motion of
the body.
Body
A portion of matter which occupies a finite space. A body is made of atoms
and molecules arranged in complex but continues manner.
Rigid Body
A body which dose not change
its size and shape when
subjected to external load .
• In some case the
deformation is negligible and
assume that it is rigid.
Deformable
Body
A body which change its size
and shape when subjected to
external load
Actually solid bodies are never rigid, they deform under the action of applied forces.
In those cases where this deformations negligible compared to the size of the body,
the body may be considered to be rigid.
PARTICLE
Portion of matter having smallest size or its
dimensions. A body whose dimensions are negligible as
compared to distance travelled by it during motion may also
be treated as particle
For example, while studying the motion of sun and earth, they
are considered as particles since their dimensions are small
when compared with the distance between them.
Force
It is that agent which causes or tends to cause, changes or
tends to change the state of rest or of motion of a mass.
A force is fully defined only when the following four
characteristics are known:
(i) Magnitude
(ii) Direction
(iii) Point of application
(iv) Sense.
characteristics of the force 10 kN are :
(i)
(ii)
(iii)
(iv)
Magnitude = 10 kN
Direction = at an inclination of 60° to the x-axis
Point of application = at point A shown
Sense = towards point A
10kN
60°
A
Effect of force on Particle
Scalars and Vectors
A quantity is said to be a ‘scalar 'if it is completely defined by
its magnitude alone.
Example: Length, Area, and Time.
A quantity is said to be a ‘vector 'if it is completely defined
only when its magnitude and direction are specified .
Example : Force, Velocity, and Acceleration.
Principle of Transmissibility
It is stated as follows : ‘The external effect of a force on a rigid body is
the same for all points of application along its line of action’.
For example, consider the above figure. The motion of the block will be
the same if a force of magnitude P is applied as a push at A or as a pull
at B.
P
A
P
P
B
O
P
The same is true when the force is applied at a point O.
RESULTANT OF COPLANAR FORCES
It is defined as that single force which can replace
a set of forces, in a force system, and cause the same
external effect.
Resultant of two forces acting at a point
Parallelogram law of forces point
‘If two forces acting at a point are represented in magnitude and direction by the
two adjacent sides of a parallelogram, then the resultant of these two forces is
represented in magnitude and direction by the diagonal of the parallelogram
passing through the same point.
Triangle law of forces
‘If two forces acting at a point can be represented both in magnitude
and direction, by the two sides of a triangle taken in tip to tail order,
the third side of the triangle represents both in magnitude and
direction the resultant force F, the sense of the same is defined by
its tail at the tail of the first force and its tip at the tip of the second
force’.
Component of a force

Component of a force, in simple terms, is the effect of a force in a
certain direction. A force can be split into infinite number of components
along infinite directions.

Usually, a force is split into two mutually perpendicular components,
one along the x-direction and the other along y-direction (generally
horizontal and vertical, respectively).

Such components that are mutually perpendicular are called
Rectangular Components’.

The process of obtaining the components of a force is called
‘Resolution of a force’.
Component of a force
Consider a force F making an angle θ with
x-axis.
 Then the resolved part of the force F along
x-axis is given by
H = F cosθ
 The resolved part of the force F along y
axis is given by
V = F sinθ

Oblique component of a force
Let F1and F2be the oblique components of a
force F. The components F1and F2can be
found using the ‘triangle law of
forces’.βαFF1F2The resolved part of the force
F along OM and ON can obtained by using the
equation of a triangle. βαFF1F2MON
 F1/ Sin β= F2 / Sin α= F / Sin(180 -α-β)

A force that can replace a set of forces, in a force system,and cause the same
‘external effect’ is called the Resultant
Coplanar Non-concurrent Force System
This is the force system in which lines of
action of individual forces lie in the same plane but
act at different points of applications.

Parallel Force System –Lines of action of
individual forces are parallel to each other.

Non-Parallel Force System –Lines of action
of the forces are not parallel to each other.
MOMENT OF A FORCE
Moment is the tendency of a force to make a
rigid body to rotate about an axis.

The applied force can also
tend to rotate the body
about an axis in addition to
motion. This rotational
tendency is known as
moment.

This is a vector quantity
having both magnitude and
direction.
MOMENT OF A FORCE
Moment Axis: This is the axis about which rotational
tendency is determined. It is perpendicular to the plane
comprising moment arm and line of action of the force
(axis 0-0in the figure).


Moment Center: This is the
position of axis on co-planar
system. (A).
Moment Arm: Perpendicular
distance from the line of action of
the force to moment center.
Distance AB = d.
Sense of moment:


The sense is obtained by ‘Right
Hand Thumb rule. ‘If the fingers
of the right hand are curled in the
direction of rotational tendency of
the body, the extended thumb
represents the sense of moment
vector.
For the purpose of additions, the
moment direction may be
considered by using a suitable
sign convention such as + ve for
counterclockwise and – ve for
clockwise rotations or vice-versa.