COURSE:COURSE: CE 201 (STATICS)CE 201 (STATICS)

LECTURE NO.:LECTURE NO.: 0101

FACULTY:FACULTY: DR. SHAMSHAD AHMADDR. SHAMSHAD AHMAD

DEPARTMENT:DEPARTMENT: CIVIL ENGINEERINGCIVIL ENGINEERING

UNIVERSITY:UNIVERSITY: KING FAHD UNIVERSITY OF PETROLEUM KING FAHD UNIVERSITY OF PETROLEUM & MINERALS, DHAHRAN, SAUDI ARABIA& MINERALS, DHAHRAN, SAUDI ARABIA

TEXT BOOK:TEXT BOOK: ENGINEERING MECHANICSENGINEERING MECHANICS--STATICS STATICS by R.C. HIBBELER, PRENTICE HALLby R.C. HIBBELER, PRENTICE HALL

LECTURE NO. 1LECTURE NO. 1INTRODUCTION, SCALARS & VECTORSINTRODUCTION, SCALARS & VECTORS

Objectives:Objectives:►► To explain the To explain the basic definitions basic definitions of engineering of engineering

mechanicsmechanics►► To define To define scalars and vectorsscalars and vectors►► To explain To explain vector operationsvector operations, such as:, such as:

Multiplication and division of a vector by a Multiplication and division of a vector by a scalarscalarVector additionVector additionVector subtractionVector subtractionResolution of vectorResolution of vector

DefinitionsDefinitions::

Mechanics: It is the branch of physics dealing with state of bodies under the influence of forces.

Statics: It is the branch of mechanics dealing with rigid bodies at rest or those moving at a constant velocity.

Dynamics: It is the branch of mechanics dealing with rigid bodies at motion (acceleration).

PHYSICS

MECHANICS

DEFORMABLEBODIES

RIGIDBODIES

FLUIDS

STATICS(CE 201)

DYNAMICS(ME 201)

SCALARS AND VECTORS SCALARS AND VECTORS Scalar QuantitiesScalar Quantities

•• A scalarA scalar is a quantity that is a quantity that has only magnitudehas only magnitude, either , either positive or negative.positive or negative.

•• For example, For example, mass, volume, and lengthmass, volume, and length are the scalar are the scalar quantities often used in statics.quantities often used in statics.

•• Scalars are indicated by letters in italic type, such as Scalars are indicated by letters in italic type, such as the scalar the scalar ‘‘AA’’..

SCALARS AND VECTORS SCALARS AND VECTORS Vector QuantitiesVector Quantities

•• A vectorA vector is a quantity that is a quantity that has has both a magnitude and a both a magnitude and a direction.direction.

•• For example, For example, position, force, and momentposition, force, and moment are the are the vector quantities frequently encountered in statics.vector quantities frequently encountered in statics.

•• Vectors are Vectors are indicated by bold lettersindicated by bold letters, such as the , such as the vector vector ‘‘AA’’ oror

•• The The magnitude of a vector is always a positive magnitude of a vector is always a positive quantityquantity and is symbolized in italic type, and is symbolized in italic type, written as or written as or AA

A

A vector is A vector is represented graphically by an arrowrepresented graphically by an arrow, , which is used to define itswhich is used to define its

►► magnitude magnitude ((by the by the lengthlength of the arrowof the arrow))►► directiondirection ((by the by the angleangle between a reference axis and between a reference axis and

the arrowthe arrow’’s line of actions line of action))►► sensesense ((by the by the arrowheadarrowhead))

For For exampleexample, the vector shown below has, the vector shown below has• A magnitude = 4 units• A direction = 20°, measured counterclockwise

from the horizontal axis• A sense which is upward and to the right• Point O is called tail of the vector

• Point P is called tip or head of the vector

SCALARS AND VECTORS Vector Quantities----contd.

VECTOR OPERATIONS VECTOR OPERATIONS Multiplication and Division of a Vector by a ScalarMultiplication and Division of a Vector by a Scalar

•• The product of a vector The product of a vector AA and a scalar and a scalar aa = = a a AA

•• Magnitude of the product vector = Magnitude of the product vector = ||a a A|A|

•• Sense of the product vector Sense of the product vector a a AA will be the same will be the same if if aa is positiveis positive

•• Sense of the product vector Sense of the product vector a a AA will be opposite will be opposite if if aa is negativeis negative

VECTOR OPERATIONS VECTOR OPERATIONS Multiplication and Division of a Vector by a ScalarMultiplication and Division of a Vector by a Scalar------

Graphic examples of multiplication and division of a Graphic examples of multiplication and division of a vector vector AA are shown in the following Figures:are shown in the following Figures:

Two vectors Two vectors AA and and B B may be added to form a resultant may be added to form a resultant vector vector

RR = = AA + + BBusing the following methods:using the following methods:►► Parallelogram lawParallelogram law►► Triangle constructionTriangle construction

Two given vectors

VECTOR OPERATIONSVector Addition

or

VECTOR OPERATIONSVECTOR OPERATIONSVector SubtractionVector Subtraction

Vectors Vectors AA and and BB may be subtracted to form a resultant may be subtracted to form a resultant vector vector

RR′′ = = AA –– BB = = AA + (+ (–– BB))using the following methods:using the following methods:►►Parallelogram lawParallelogram law►►Triangle constructionTriangle construction

Triangularconstruction

Two givenvectors

Parallelogramlaw

VECTOR OPERATIONSVECTOR OPERATIONSResolution of VectorResolution of Vector

A vector may be resolved into two components having known A vector may be resolved into two components having known lines of action by using the parallelogram law.lines of action by using the parallelogram law.

For example, a vector For example, a vector RR may be resolved into two vectors may be resolved into two vectors AAand and BB along the lines a and b, using the parallelogram law, as along the lines a and b, using the parallelogram law, as

shown below:shown below:

Multiple Choice Problems

1. The material properties of a body may be neglected by

(a) Particle idealization

(b) Rigid body idealization

(c) Concentrated force idealization

(d) None of the above

Multiple Choice Problems

2. According to the Particle idealization of a body,---------- may be neglected

(a) area over which the load is applied

(b) geometry of the body

(c) material properties of the body

(d) None of the above

Multiple Choice Problems

3. Multiplication of a vector by a scalar will never change the vector’s

(a) magnitude

(b) sense

(c) direction