General Information Assistant Lecturer: Asmaa Ab. Mustafa Email : asmaa.abdulmajeed@ishik.edu.iq Department : Civil Engineering Course Title : Engineering Mechanics I Code : Credit : 2 Office Hour : Monday 15:00 16:00 or by appointment Website : http://www.sul.ishik.edu.iq/asmaa-abdulmajeed/ Grade : 1 st Year : 2017-2018 1 Required Textbook : *Engineering Mechanics-Statics by R.C.-Hibbeler, 12 th Edition Additional Reference : *Engineering Mechanics-Statics by Meriam & Kraige, 7 th Edition 2 1
Evaluation Criteria : Weekly Quizzes : 10% Assignments : 10% Bonus Quizzes : 5% Project : 5% Mid-term Exam : 30% Final Exam : 40% Assignments : Approximately (10) homework assignments will be given during the term. These assignments are very important. Their purpose is to promote your understanding of the course material, and to provide needed practice with example problems that are too lengthy to discuss in class. It is your responsibility to complete each homework assignment within one week of distribution. 3 Weekly Quizzes : Except for the week corresponding to the midterm, weekly quizzes will be given once per week, during the first fifteen minutes of lecture. In the Quiz, you will be expected to solve one of the questions from the previous week s subject (possibly with slight alterations in the numbers). The weekly quizzes will be completely closed book although calculators will be allowed. Midterms and Exam : One midterms will be scheduled in addition to the final examination. Midterm and the final exam will be closed book. You will also be allowed to use a non-communicating calculator. Prerequisites : Mathematics and Physics 4 2
Class Attendance and Absences : Students are strongly encouraged to attend class since some course material may only appear in lectures. Students that miss class are responsible for obtaining class notes from a classmate. Also students whom their absent percentage pass 20% will fail in that course automatically. Conduct : Students are expected to arrive at lectures on time, and to conduct themselves during class in a professional and respectful manner that is not disruptive to others. Please put your cell phone in silent mode before coming to class, quiz or exam. Course Format : There will be daily lectures. Your active participation is essential in making the class a success. Read the material before class and come equipped with questions. 5 Manner Guideline in this Lecture Course Be reasonable and act politely. Turn off your mobile phone. If you have urgent calls to make or answer, kindly leave the room. No food. Only water and candy are allowed. No noisy chat and all other activities that can distract the lecture should be avoided. Do not disturb your classmates. 6 3
Mechanics? Mechanics A branch of physical science which deals with ( the states of rest or motion of ) bodies under action of forces Statics -Equilibrium -Selected Topics Dynamics Statics: Equilibrium of bodies (no accelerated motion) under action of Forces Dynamics: Motion of bodies Kinematics -Particles -Rigid Bodies Kinetics -Particles - Rigid Bodies 7 Engineering Mechanics Statics Equilibrium Analysis of particles and bodies. Dynamics Accelerated motion of particles and bodies Kinematics and Kinetics. Theory of Vibration 8 4
Static Analysis Dynamic Analysis Force and Equilibrium Kinematics of a Particle Force System Resultants Structural Analysis Internal forces Friction Centroid and Moments of Inertia Virtual Work and Stability Kinetics: Force and Acceleration Work and Energy Impulse and Momentum (Impact) Planar Kinematics and Kinetics 3-D Kinematics and Kinetics Vibrations 9 Contents of Engineering Mechanics Static Chapter -1- General Principles Chapter -2- Force Vectors Chapter -3- Equilibrium of a Particle Chapter -4- Force System Resultants Chapter -5- Equilibrium of a Rigid Body Chapter -6- Structural Analysis Chapter -7- Internal Forces Chapter -8- Friction Chapter -9- Center of Gravity and Centroid Chapter -10- Moments of Inertia Chapter -11- Virtual Work 10 5
Chapter -1- General Principles 11 Chapter -1- General Principles 1.1 Mechanics 1.2 Fundamental Concepts 1.3 Units of Measurement 1.4 The International Systems of Units 1.5 General Procedure for Analysis 12 6
1.1 Mechanics Mechanics is the physical science which deals with the effects of forces on objects. No other subject plays a greater role in engineering analysis than mechanics. Statics Dynamics Mech. of Materials Fluid Mechanics Vibration Fracture Mechanics Etc. Mechanics Structures Automotives Robotics Spacecrafts MEMs Etc. 13 Mechanics : Generally are subdivided in to three branches: 1- Rigid-body Mechanics 2- Deformable-body Mechanics 3- Fluid Mechanics In this course we will study rigid-body mechanics since it is a basic requirement for the study of the mechanics of deformable bodies and the mechanics of fluids. Furthermore rigid-body mechanics is essential for the design and analysis of many types of structural members, mechanical components or electrical devices encountered in engineering. 14 7
Rigid-body mechanics is divided into two areas: statics and dynamics. Statics deals with the equilibrium of bodies, that is those that are either at rest or move with a constant velocity. Whereas dynamics is concerned with the accelerated motion of bodies. We can consider statics as a special case of dynamics, in which the acceleration is zero. 15 1.2 Fundamental Concepts Before we begin our study of engineering mechanics, it is important to understand the meaning of certain fundamental concepts and principles. Basic Quantities; The following four quantities are used throughout mechanics. length. meter [m] time. second [s] mass. gram [g] force. newton [N] 16 8
Space : Collection of points whose relative positions can be described using a coordinate system Length : Is used to locate the position of a point in space and thereby describe the size of a physical system. Time : Although the principles of statics are time independent. This quantity plays an important role in the study of dynamics. Mass : Is a measure of a quantity of matter. Force : 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 pushing on a wall. A force is completely characterized by its magnitude, direction, and point of application. 17 Particle : Has a mass, but it size can be neglected. A rigid body can be considered as a combination of a large number of Particles. Concentrated Force : a concentrated force is a representation of loading as a single point force. This is justified if the load is applied to an area which is small compared to the overall size of the body 18 9
Particle: Rigid body: Body of negligible dimensions Body with negligible deformations Non-rigid body: Body which can deform Before considering whether the body can be assumed rigid-body or not, you need to estimate the relevant force first. In Statics, bodies are considered rigid unless stated otherwise. 19 Newton s Three Laws of Motion First law equilibrium if F = 0 then v = const. Second law accelerated motion F = m a Third law action = reaction F AB = - F BA F AB F BA 20 10
Newton's Law of Gravitational Attraction: Shortly after formulating his three laws of motion. Newton postulated a law governing the gravitational attraction between any two particles. Stated mathematically. Where; F: Force of gravitational between the two particles. G: Universal constant of gravitation, according to experimental evidence. m1, m2: Mass of each of the two particles. r: Distance between the two particles. 21 Weight : Refers to the gravitational attraction of the earth on a body or quantity of mass. The weight of a particle having a mass is stated mathematically. g = 9.81 m/s² = 32.2 ft/ s² *Therefore, a body of mass 1 kg has a weight of 9.81 N, a 2 kg body weights 19.62 N, and so on. 22 11
1. SI units: 1.3 Units of Measurement The international System of units. Abbreviated SI is a modern version which has received worldwide recognition. The SI system defines length in meters (m), time in seconds (s), and mass in kilograms (kg). In the SI system the unit of force, the Newton is a derived unit. Thus, 1 Newton (N) is equal to a force required to give 1 kilogram of mass and acceleration of 1 m /s². 1 N = (1 kg)(1 m/ s²) 23 2. US customary: In the U.S. Customary system of units (FPS) length. Is measured in feet (ft), time in seconds (s), and force in pounds (lb). The unit of mass, called a slug. Thus, 1 slug is equal to the amount of matter accelerated at 1 ft/s² when acted upon by a force of 1 Ib. 1 slug = 1 lb s 2 /ft = m 24 12
SI system basic units meters [m] seconds [s] kilogram [kg] derived unit Newton [N = kg m /s 2 ] FPS system basic units derived unit feet [ft] seconds [s] pounds [lb] slug [slug = lb s 2 /ft] 25 Conversion from one System of Units to Another: 1 ft = 0.3048 m 1 lb = 4.448 N 1 slug = 1 lb s² /ft = 14.59 kg 1 ft = 12 in 1 mile = 5280 ft 1 kp kilo pound = 1000 lb 1 ton = 2000 lb 26 13
27 Prefixes: When a numerical quantity is either very Large or very small, the units used to define its size may be modified by using a prefix. Some of the prefixes used in the SI system are shown in Table 1.3. Each represents a multiple or submultiples of a unit which, if applied successively, moves the decimal point of a numerical quantity to every third place. For example, 4000000N=4000kN (kilonewton) =4MN (mega-newton), or 0.005m=5mm (milli meter). 28 14
SCALARS AND VECTORS We use two kinds of quantities in mechanics-scalars and vectors. Scalar quantities are those with which only a magnitude is associated. Examples of scalar quantities are time, volume, density, speed, energy. Scalars: associated with Magnitude alone - mass, density, volume, time, energy, 29 PRINCIPLES OF MECHANICS Some principles that governs the world of Mechanics: 1. Newton s First Law discussed 2. Newton s Second Law discussed 3. Newton s Third Law discussed 4. Newton s Law of Gravitation discussed 5. The Parallelogram Law 6. The Principle of Transmissibility 30 15
The Parallelogram Law The two vectors V 1 and V 2, treated as free vectors, can be replaced by their equivalent V, which is the diagonal of the parallelogram formed by V 1 and V 2 as its two sides. V 2 V2 V V V 2 V 1 V 1 V 1 V V V 1 2 (generally V V V ) 1 2 31 The Principle of Transmissibility F? = F If we concerns only about the external resultant effects on rigid body. We can slide the force along its line of action. (force can be considered as sliding vector) A force may be applied at any point on its given line of action without altering the resultant effects external to the rigid body on which it acts. 32 16
concurrent forces Summation of Force F 1 2 2 F F F 1 non-concurrent F 2 if there are sliding vectors F F 1 F 2 2 F 1 F 1 33 Exercise 1.1: 34 17
Exercise 1.2: 35 Exercise 1.3: 36 18
37 Homework 1: Determines the mass in kilograms of an object that has a weight of: (a) 20 mn (b) 150 kn (c) 60 MN 38 19
References: 1. Engineering Mechanics -Statics, Twelfth Edition, R. C. Hibbeler, 2009. 2. Engineering Mechanics-Statics by Meriam & Kraige, 7th Edition. 3. Dr. Daniel C. Deckler,, The University of Akron, Wayne College. 4. Lecture Notes and Exercises on Statics, by Dr. Abdulwahab Amrani 39 20