CHAPTER I. PRINCIPLE OF STATICS
CHAPTER OBJECTIVES
1.Explain the fundamental principle related to Statics of Rigid
Bodies.
2.Understand the concepts of force systems.
3.Discuss the introduction of
free-body diagram
4. Identify the difference between the vector and scalar quantities.
5.Discuss the parallelogram and triangular law
6.Review the unit of measurement.
STATICS OF RIGID BODIES The study of bodies is in
equilibrium. This means there are no unbalanced forces on
the body, thus the body is at rest or moving at a uniform
velocity.
DYNAMICS OF RIGID BODIES is the branch of mechanics which
deals with the study of bodies in motion.
1.1 FUNDAMENTAL CONCEPTS & DEFINITION f
1.2. FORCE SYSTEM
ENGINEERING MECHANICS IS the branch of science which
describes and predicts the condition of rest or motion of
bodies under the action of forces.
FORCE may be defined as the action of one body on
another body that affects the state of motion or rest of
body. In late 17th century , sir Isaac Newton summarized
the effect effects of force in three basic laws.
MECHANICS CAN BE DIVIDED INTO THREE BRANCHES:
1. RIGID-BODIES MECHANICS
2. DEFORMABLE-RIGID BODIES
3. FLUID MECHANICS
Mechanics of Rigid Bodies: This course deals solely with
the mechanics of rigid bodies. A rigid body is a body
which does not deform under the influence of forces.
.RIGID- BODIES MECHANICS DEALS WITH
1. STATICS
2. DYNAMICS
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 FIRST LAW: Any body at rest will remain at
rest and any body in motion will move
uniformly in a straight line, unless acted
upon by the force.( EQUILIBRIUM)
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Force A on B
F2
Force of B on A
F1
A
B
V
b. Action-reaction
F3
a. Equilibrium
 SECOND LAW: The time rate of change of momentum
is equal to the force producing it, and the
change takes place in the direction in which
the force is acting.
F=mxa
Ground resistance on a building
a
F
b. Accelerated Motion
 THIRD LAW: For every force of action, there is
a reaction that is equal in magnitude, opposite
in direction and has the same line of action.
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For example, if a building with a weight W is placed on the
ground, we can say that the building is exerting a downward force
of W on the ground. However, for the building to remain stable on
the resisting ground surface without sinking completely, the
ground must resist with an upward force of equal magnitude. If
the ground resisted with a force less than W, where R < W, the
building would settle. On the other hand, if the ground exerted
an upward force greater than W (R > W), the building would rise
(levitate).
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CHARACTERISTICS OF A FORCE
A force is characterized by its (a) magnitude, (b)
direction, (c) point of application/position of its line
of action
a) Point of Application: Defines the point where the
force is applied.
b) Magnitude: Refers to the quantity of force, a
numerical measure of the intensity.
c) Direction can be defined by:
1. Line of action refresents an infinite straight line
along which the force is acting.
Rope pulling on an eyebolt
Notes:
 The sense and direction can be either written
as (down and to the right, up and to the left)
 It can be also expressed in terms of 360 deg.(
i,e. 112 degrees, 273 degrees,87.5 degrees). In
the later case, one begins with zero and
increases clockwise with the direction of the
arrow head until 360 is reached.
TENSION AND COMPRESSION FORCE
a. Tension Force: may be described as the pulling
force transmitted through a rope, string or wire
b. Compression force: is the action or state of being
squished down or pressed down.
a. Force in Tension
b. Force in Compression
2. SENSE OF A FORCE: specifies direction (positive or
negative) in which the force moves along the line of
action. Graphically, the sense can be represented by
an arrowhead.
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2. Coplanar- All forces acting in the same plane.
RIGID BODIES
In Statics, we deal with a body of matter which
undergoes no deformation.
(a) Original, unloaded box. (b) Rigid body (example: stone) (c) Deformable body (example: foam).
Forces in a buttress system
Types of forces
Force systems are often identified by the type or
types of system on which they act.
1. Collinear- All forces acting along the same
straight line
3. Coplanar, Parallel- all forces are parallel and
act in the same plane.
A beam supported by a series of columns
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4. Coplanar ,Concurrent- all forces intersects at a
common point and lie in the same plane
6. Non-coplanar, concurrent-all forces intersects at
a common point but do not all lie in the same
plane.
Loads applied to a roof truss.
5. Non-coplanar, parallel- all forces are parallel
to each other, but not all lie in the same plane.
One component of a three-dimensional space frame
7. Non-coplanar,non-concurrent
skewed
- all forces are
Column loads in a concrete building.
Array of forces acting simultaneously
on a house.
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INTERNAL AND EXTERNAL FORCE
EXTERNAL FORCE-the external effect of a force tends to
change the state of motion of a body.
- are the forces that
emanate from the outside the system
- are those which are
applied to the element such as beam or column.
INTERNAL FORCE- the internal effect of a force is to
produce stress and deformation in the body on which the
forces acts.
If we remove the nail and examine the forces acting on it,
we discover frictional forces that develop on the embedded
surface of the nail to resist the withdrawal force F
Withdrawal force on a nail.
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Treating the nail as the body under consideration, we can
then say that forces F and S are external forces. They are
being applied outside the boundaries of the nail. External
forces represent the action of other bodies on the rigid
body. Let’s consider just a portion of the nail and examine
the forces acting on it. In the frictional force S plus
the force R (the resistance generated by the nail internally)
resist the applied force F. This internal force R is responsible for keeping the nail from pulling apart.
1.3.Introduction to Free-Body Diagrams
One of the most important concepts in mechanics is
that of the free-body diagram. A sketch of the isolated
body which shows only forces acting upon the body is
defined as a free-body diagram. The forces acting on the
free body diagram are the action forces, also called the
applied forces. The reaction forces are those exerted by
the free body upon other bodies. The free body may
consist of an entire assembled structure or an isolated
part of it.
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Vector Quantity has both magnitude and direction.
Example: Displacement, velocity, acceleration
i1.5.Parallelogram Law and Triangle Law
Parallelogram Law
The resultant of two forces is the diagonal of the
parallelogram formed on the vectors of these forces.
Two vectors can be added to give a resultant; this
resultant in turn can be added to a third vector
i1.4.Scalar and Vector Quantities Introduction
Scalar Quantity has only magnitude, but no direction.
Example: Length, mass, volume, pressure
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Triangle Law
If two forces are represented by their free vectors
placed tip to tail, their resultant vector is the third
side of the triangle, the direction of the resultant
being from the tail of the first vector to the tip of the
last vector.
standard unit of length is defined, one can then use it to
define distances and geometric properties of a body as
multiples of this unit.
2. Mass is a measure of a quantity of matter that is used to
compare the action of one body with that of another. This
properly manifests itself as a gravitational attraction
between two bodies and provides a measure of the resistance
of matter to a change in velocity.
3. Time is conceived as a succession of events. Although the
principles of statics are time independent, this quantity
plays and important role in the study of dynamics.
4. Force . In general time is considered as a "push" or
"pull " exerted by one body on another. This interaction
can occur when there is direct contact between the bodies,
such as a person
We will work with two units in Statics:
1.6. UnitS Of Measurement
Units are arbitrary names we give to the physical
quantities.
Four
fundamental Physical quantities
1. Length is used to locate the position of a point in space
and thereby describe the size of the physical system. Once a
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1. International System (S.I)
The International System of Units, abbreaviated SI
after the French “Systѐme International d’ Unitѐs” is a
modern version of the metric system which has received
worldwide recognition. As shown in Table 1-1, the SI
system defines length in meters(m), time in seconds(s),
and mass in kilograms (kg). The unit of force, called
(N), is derived from F=ma. Thus, 1 newton is equal to a
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force required to give 1 kilogram of mass an acceleration
of 1m/s2(N=kg. m/s2).
𝑚=
𝑊
𝑔
(𝑔 =
32.2𝑓𝑡
)
𝑠2
If the weight of a body located at the “standard
location” is to be determined in Newton’s, then W=mg must
be applied. Here measurements give g=9.80665 m/s2,
however, for calculations, the value of g=9.81 m/s2 will
be used. Thus,
W=mg
1 slug
32.2 lb
(g=9.81 m/s2)
1 kg
Table 1.1. System Of Units
NAME
9.81 N
2.U.S. Costumary (USCS)/ English System
In the U.S. customary system of units (FPS) length is
measured in feet(ft), time in seconds(s), and force in
pounds(lb), in table 1-1.The unit of mass , called a
slug, is derived from F=ma.Hence, 1 slug is equal to the
amount of matter accelerated at 1 ft/s2 when acted upon
by a force of 1 lb(slug=lb.s2/ft).Therefore, if the
measurements are made at the “standard location”,where
g=32.2 ft/s2, thus
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Internationa
l System Of
units(SI)
U.S.
Customary
FPS
MASS
FORCE
Meter(m)
LENGTH
Second(s)
TIME
Kiligram(kg)
Newton(N)
(kg.m)/S2
Foot(ft)
Second(s)
Slug
(lb.s2)/ft
Pound
(lb)
Table 1.2. Common Conversion Factors
Quantity
Force
Mass
Length
Unit of
Measurement (FPS)
Lb
Slug
ft
Unit of
measurement(SI)
4.448 N
14.59Kg
0.3048m
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Example1.1: Convert the quantities 300 lb and 52 slug/ft 3 to
appropriate SI Units.
EXERCISE 1:
PROBLEM 1. Determine the weight in N of a cylinder whose
mass is 1400 kg. Convert the mass of the cylinder to
slugs and then determine its weight in pounds.
Solution
Using table 1.1. , 1 lb=4.448 N
4.448 𝑁
300 lb.s = 300lb (
1 𝑙𝑏
)
= 1334.5 N= 1.33 KN
ans.
Since Slug = 14.59 kg and 1 ft =0.3048 m, then
52𝑠𝑙𝑢𝑔
52 slug/ ft3 =(
𝑓𝑡3
14.59𝑘𝑔
1 𝑓𝑡
)(( 1 𝑠𝑙𝑢𝑔 ) (0.3048)
= 26.8(103) Kg/m3
3
ans.
PROBLEM#2.Convert each of the following to three
significant figures: (a)20 lb.ft to N.m, (b) 450 lb/ft3
to KN/m3, and (c)15 ft/h to mm/s.
Problem#3. The density (mass/volume)of aluminum is 5.26
slug/ft3. Determine its density in SI units. Use an
appropriate prefix.
Proble#4. Water has a density of 1.84 slug/ft3. What is
the density expressed in SI units?Express the answer to
three significant figures.
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References:
Portrait of Newton at 46 by Godfrey Kneller,1689,
https://en.wikipedia.org/wiki/File:GodfreyKnellerIsaacNewton-1689.jpg
Barry Onouye, Kevin Kane, C 2012, Statics and
Strength of Materials for Architecture and Building
Construction 4th edition, Pearson Education, Inc.,
Prentice Hall, One Lake Street ,Upper Saddle River,
New Jersey 07458
R. C. HIBBELER,C 2013, Engineering Mechanics Statics 13th
edition, Pearson Education, Inc. Pearson Prentice Hall
Upper Saddle River, New Jersey 07458
Singer,Ferdinand L,C 1954,Engineering Mechanics, 2nd
edition,Harper & Row, New York, Evanston & London
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