Statics of Rigid Bodies
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
1.2 Statics of Particles
1.3 Force Vectors
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
WHAT IS MECHANICS?
Mechanics can be defined as that science which describes and predicts the conditions of
rest or motion of bodies under the action of forces. It is divided into three parts: 1) mechanics of
rigid bodies, 2) mechanics of deformable bodies, and 3) mechanics of fluids.
The mechanics of rigid bodies is subdivided into statics and dynamics, the former dealing
with bodies at rest, the latter with bodies in motion. In this part of the study of mechanics, bodies
are assumed to be perfectly rigid.
Mechanics is a physical science, since it deals with the study of physical phenomena. It s
the foundation of most engineering sciences and is an essential prerequisite to their study.
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
Review Topics:
A. Units and Dimensions
B. Conversion of Units
C. Mathematics: Algebra, Trigonometry,
Geometry, Calculus, etc.
D. Physics: Vectors, Mass, Force, and
Weight
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
➢ Units and Dimensions
The standards of measurement are called units. The term dimension refers to the
type of measurement, regardless of the units used. For example, kilogram and
m/s are units, whereas mass and length/time are dimensions. Throughout this
text we use SI system (from Système internationale d’unités).
The base dimensions in the SI system are mass [M], length [L], and time [T], and
the base units are kilogram (kg), meter (m), and second (s). All other dimensions
or units are combinations of the base quantities. For example, the dimension of
velocity is [L/T ], the units being ft/s, m/s, and so on.
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
➢ Conversion of Units
A convenient method for converting a measurement from one set of units to another is to
multiply the measurement by appropriate conversion factors. For example, to convert 360
km/h into m/s, we proceed as follows:
where the multipliers 1.0 h/3600 s and 1000 m/1.0 km are conversion factors. Because 1.0
h = 3600 s and 1000 m= 1.0 km, we see that each conversion factor is dimensionless and of
magnitude 1. Therefore, a measurement is unchanged when it is multiplied by conversion
factors—only its units are altered. Note that it is permissible to cancel units during the
conversion as if they were algebraic quantities.
Conversion factors applicable to mechanics are listed inside the front cover of the book.
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
A. Conversion of Units
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Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
➢ Conversion of Units
ES10c_archi_sc_pCloribel
Chapter 1 Fundamental Concepts
1.1 Introduction to Statics
➢ Mass, force, and weight
If a force F acts on a particle of mass m, Newton’s second law states that:
where a is the acceleration vector of the particle.
The derived unit of force in the SI system is a newton (N), defined as the force that
accelerates a 1.0-kg mass at the rate of 1.0 m/s2.
Weight is the force of gravitation acting on a body. Denoting gravitational acceleration
(free-fall acceleration of the body) by g, the weight W of a body of mass m is given by
Newton’s second law as:
where g = 9.81 m/s2 is the acceleration due to gravity in Earth.
Chapter 1 Fundamental Concepts
1.2 Statics of Particles
Objectives:
1) To study the effect of forces acting on particles
2) To learn how to replace two or more forces acting on a given particle by a single
force having the same effect as the original forces
The use of the word “particle” does not imply that our study will be limited to
that of small corpuscles. What it means is that the size and shape of the bodies under
consideration will not significantly affect the solution of the problems treated in this
chapter and that all the forces acting on a given body will be assumed to be applied at the
same point.
The first part of the chapter 2 is devoted to the study of forces contained in a
single plane, and the second part to the analysis of forces in three-dimensional space.
Chapter 1 Fundamental Concepts
1.3 Force Vectors Scalars and Vectors
Many physical quantities in engineering mechanics are measured
using either scalars or vectors.
Scalar. A scalar is any positive or negative physical quantity that
can be completely specified by its magnitude. Examples of scalar
quantities include length, mass, and time.
Vector. A vector is any physical quantity that requires both a
magnitude and a direction for its complete description. Examples
of vectors encountered in statics are force, position, and moment.
A vector is shown graphically by an arrow. The length of the arrow
represents the magnitude of the vector, and the angle θ between
the vector and a fixed axis defines the direction of its line of
action. The head or tip of the arrow indicates the sense of
direction of the vector, Fig. 2–1.
In print, vector quantities are represented by boldface letters such as A, and the magnitude of a vector is
italicized, A. For handwritten work, it is often convenient to denote a vector quantity by simply drawing an
arrow above it, A
Chapter 1 Fundamental Concepts
1.3 Force Vectors Vector Operations
Multiplication and Division of a Vector by a Scalar. If a
vector is multiplied by a positive scalar, its magnitude is
increased by that amount. Multiplying by a negative
scalar will also change the directional sense of the vector.
Graphic examples of these operations are shown in the
figure:
A x 2
A x (-1)
A ÷ -2
Chapter 1 Fundamental Concepts
1.3 Force Vectors Vector Operations
Vector Addition. When adding two vectors together it is important to account for both their
magnitudes and their directions. To do this we must use the parallelogram law of addition. To
illustrate, the two component vectors A and B in Fig. 2–3a are added to form a resultant vector R = A +
B using the following procedure:
1. First join the tails of the components at a point to make them concurrent, Fig. 2–3b.
2. From the head of B, draw a line parallel to A. Draw another line from the head of A that is parallel
to B. These two lines intersect at point P to form the adjacent sides of a parallelogram.
3. The diagonal of this parallelogram that extends to P forms R, which then represents the resultant
vector R = A + B, Fig. 2–3c.
Chapter 1 Fundamental Concepts
1.3 Force Vectors Vector Operations
Vector Addition. We can also add B to A, Fig. 2–4a, using the triangle rule, which is a special case of
the parallelogram law, whereby vector B is added to vector A in a “head-to-tail” fashion, i.e., by
connecting the head of A to the tail of B, Fig. 2–4b. The resultant R extends from the tail of A to the
head of B. In a similar manner, R can also be obtained by adding A to B, Fig. 2–4c. By comparison, it is
seen that vector addition is commutative; in other words, the vectors can be added in either order, i.e.,
R = A + B = B + A.
Chapter 1 Fundamental Concepts
1.3 Force Vectors Vector Operations
Vector Subtraction. The resultant of the difference between two vectors A and B of the same type may
be expressed as:
This vector sum is shown graphically in Fig. 2–6. Subtraction is therefore defined as a special case of
addition, so the rules of vector addition also apply to vector subtraction.
Statics of Rigid Bodies
Chapter 2 Force systems
2.1 Forces in a Plane (Two Dimensional)
2.2 Resultant of Concurrent Forces
2.3 Equilibrium of a Particles in a Plane
2.4 Forces in Space (Three Dimensional)
2.5 Resultant of Forces in Space
2.6 Equilibrium of a Particle in Space
Force systems
Forces in a Plane Magnitude
Point of Application
A Force represents the action of one
body on another and is generally
characterized by its point of application, θ = 30˚
its magnitude and its direction.
Concurrent forces, however, have the Direction
same point of application.
Point of Application
Force systems
Resultant of Concurrent Forces
Two or more forces acting on a particle may be replaced by a single force,
called their resultant through:
1) Parallelogram Law;
2) Triangle Law; and
3) Resolution of a force into components.
Chapter 2 Force systems
2.1 Forces in a Plane (Two Dimensional)
Sample Problem #1
Two forces are applied at point B of beam AB. Determine
graphically the magnitude of their resultant using the
parallelogram law and triangle law R
α= 100˚
B= 3KN A= 2KN
A= 2KN
R R
θ= 80˚ θ= 80˚
θ= 80˚
Solving resultant R using Cosine law: a B
B= 3KN c2 = a2 + b2 - 2abcosθ
c
α= 100˚ C
R2 = A2 + B2 - 2ABcosθ
b A
parallelogram law triangle rule 𝑅 = 22 + 32 − 2 2 3 cos 80°
𝑹 = 𝟑. 𝟑𝟎𝟒 𝑲𝑵
