Download CHAPTER ONE

Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Engineering Mechanics/1st Stage
Syllabus:
I-Statics
1- Basic concepts
2- Resultant of force system
3- Equilibrium
4- Friction
5- Centroid and center of gravity
6- Second moment area or moment of inertia
II-Dynamic
1- Kinematics-Absolute motion
2- Kinematics-Relative motion
3- Kinetics-force, mass and acceleration
Textbook
1- Engineering Mechanics A. Higdon.
2- Engineering Mechanics, statics and dynamic R.C Hibbeler.
References
1- Engineering Mechanics F.L Singer.
2- Mechanics of Engineering F.P Bear.
Chapter One: Basic Concepts
Mechanics:- is the branch of physical science which considers the
motion of bodies, with rest being consider a special case of motion.
Engineering mechanics:- is essentially a study of the external effects
of a system of forces acting on a rigid body.
The mechanics of rigid bodies subdivided into:
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
I-Statics
When the force system acting on a body is balanced, the system has
no external effects on the body. The body is in equilibrium and the
problem is one of statics.
I-Dynamics
When the force system has a resultant different from zero, the body
will be accelerated and the problem is one of dynamics scalar and
vector quantities.
Scalar:
Physical quantities which has only magnitude (mass, volume, time,
area,….)
Vector:
Physical quantities which has both magnitude and direction (force,
velocity, displacement,.….)
Force on a Particle:
Force: the action of one body on another body which changes or tends
to change the motion of the body acted on.
Characteristics of a Force:
Which describe its external on a rigid body:
B
1-Magnitude
200 N
2-Direction
3-Line (point) of action
Action point A
Principle of Transmissibility:
The external effect of a force on a
2
rigid body is independent of
Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
the point application of the force along its line of action.
Force System:
when several forces act in given situation they are called a system of
forces or a force system.
Force System
A: Coplanar force system (in B: Non-coplanar force system (in
plane)
space)
A:
1- Concurrent:
2- Parallel:
F1-F2,
F1-F6,
F4-F6,
F1-F3
F4-F5
3- Non-concurrent, non-parallel (general):
F1-F3-F7
B:
1- Concurrent:
2- Parallel:
F1-F2-F3
F3-F4-F5
3- Non-concurrent, non-parallel (general):
Y-axis
F2-F6-F7
F2
F1
F3
F7
F6
F5
F4
Z-axis
3
X-axis
Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Chapter Two: Resultant of force system
Resultant:
Simplest force system which have same external effect of the original
system.
1-Resultant of concurrent coplanar force system
2-Resultant of parallel coplanar force system
3-Resultant of general coplanar force system
Chapter Three: Equilibrium
Equilibrium:
A situation or condition of body when a system of forces acting on
it has no resultant (i.e resultant = 0)
Free Body Diagram (F.B.D):
A sketch of a body, a portion of a body completely isolated or free
from all other bodies, showing the forces exerted by all other
bodies on the one being considered.
1- Earth:
Always a vertical force equal to the weight and passing through the
center of gravity of the body.
c.g
body
Earth
W
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
2- Flexible Cord, Rope, Cable Strand:
Always a single force (tension) along the cable.
T
Φ
Body
Φ
Body
3- Smooth Surface:
Always a single force perpendicular to the smooth surface
Body
Body
Φ
Φ
N
4- Roller or Ball:
Always a force perpendicular to the surface on which roller or ball can
move
Body
Body
Body
R
5- Smooth Pin:
A force through the pin at unknown angle usually shows as two
independent components.
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Body
RX
Body
Ry
6- Fixed Support:
R
A force at the cut section at an unknown angle, usually shown as two
perpendicular components and a couple.
RX
Body
Body
M
Ry
Chapter Four: Friction
When a body slides or tends to slides on another body, the force
tangent to the contact surface which resists the motion or the tendency
toward motion of one body relative to the others is defined as friction.
Friction: due to:
- irregularities of the surface.
- molecular attraction.
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Theory of Friction: (Static and Kinetic Friction)
Friction
Force (F)
Equilibriu
m
motion
a
b
a
Relative velocity
between contact surface
b
Applied Load
(P)
The static frictional force is always the minimum force required to
maintain equilibrium or prevent motion.
When one body moves relative to another body, the resisting force
between the bodies tangent to the contact surface is called kinetic
friction.
Note:
The frictional force between two bodies always opposes the relative
motion of the bodies or the tendency to move.
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Coefficient of Friction:
The frictional force between two bodies always opposes the relative
motion of the bodies or the tendency to move.
Coefficient of Static Friction 
The ratio of the magnitude of the maximum frictional force (F'), to the
magnitude of the normal force (N), between the two surfaces.

F'
N
A
A
P
P
W
W
F
'
N
F.B.D
-The coefficient of friction is an experimentally determined contact
which depends on the materials from which the contacting bodies are
made and on the condition of the contact surfaces.
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
Angle of Friction:
A
A
A
P
P=0
P
W
W
W
R=N
Φ
F
'
R
N
N
- If no applied load (P=0), the resultant R reduces to the normal
force N (R=N).
- Which increasing the applied load from zero to a certain value,
the force R will have a horizontal component F and, thus, will
form a certain angle with the vertical.
- If the applied force is increased until motion becomes
impending, the angle between R and vertical
grows and
reaches a maximum value is called the angle of friction.
Types of Problem Involving Frictional Forces:
We must know whether the magnitude of the friction is equal to or
less than the limiting or maximum friction (F'=  .N).
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
It is usually desirable to classify problems involving frictional forces
according to the available data to:
1-impending motion is not assured from the statement of the problem.
2-impending or relative motion is specified at all contact surfaces
where there are frictional forces.
3-impending motion is known to exist, but either the type of
impending movement (slipping or tipping) is not specified, or the
surface or surfaces where motion impends are not specified.
Chapter Five: Centroid and Center of Gravity
- A body consists of a number of particles each of which has a
weight or force of attraction directed toward the center of the
earth. The resultant of this parallel system of gravitational
forces in space is the weight of the body.
- The resultant weight passes through one point in the body, or
the body extended, for all orientations of the body, and this
point is defined as the center of gravity or center of mass of the
body.
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
The resultant weight of the plate can be determined by considering the
plate to be made up of an infinite number of small elements each
having a weight given by:
dW    t  d A
Where:
dW = weight of an element
 = specific weight
t = thickness of the plate
d A = area of the element (surface area in XY-plate)
The total weight of the plate is:
W    t  dA
W   dW
The coordinates of a point of the line of action of the resultant weight
can be determined by the principle of moments:
dM X  d w  y    t  d A  y
M X   dM X     t  y  d A
dM Y  d w  x    t  d A  x
M Y   dM Y     t  x  d A
M x    t  y  dA
y 

W
   t  dA
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Engineering Mechanics/1st Stage……...…..…. Dr. Fatimah H. N. Al Mamoori
x 
My
W
 t  x d


 t d
A
A
- The center of gravity of the body is one a line parallel to the Zaxis through the point (x', y').
When t and Ɣ are constant, z' can be obtained by symmetry. If either t
or Ɣ is a variable, the plate can be rotated so that either the x-axis or
the y-axis is vertical. Then the principal of moments.
given:
z   d

z' 
 d
v
v
when dv is equal to (dA ×dt)
- Since the center of gravity of a body id defined as appoint, three
coordinates are necessary to indicate completely its position.
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