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this classic text continues to provide the same high quality material seen in previous editions. The text is extensively rewritten with updated prose for content clarity, superb new problems in new application areas, outstanding instruction on drawing free body diagrams, and new electronic supplements to assist readers. Furthermore, this edition offers more Webbased problem solving to practice solving problems, with immediate feedback; computational mechanics booklets offer flexibility in introducing
2/13/2013 1 00. Introduction HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 0.01 Introduction Chapter 00 – Introduction - Name of course: ENGINEERING MECHANICS - STATICS - Number of Credits: 3 - Level: 1 st , 2 nd year student - Time allocation • Lecture: 4 hrs/week • Assignment: 4 hrs/week - Course Description Analysis of systems of bodies considering the fundamental concepts of statics, including vectors, two-dimensional and three-dimensional force systems, equilibrium, friction, centroids, and moments of inertia HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 0.02 Introduction - Overall Educational Objectives/Learning Outcomes At the end of the course a successful student should be able to • utilize standard engineering approaches to model mechanical systems • utilize a variety of techniques to analyze rigid-body equilibrium problems, select an appropriate technique for a particular analysis, and evaluate the quality of results - Student responsibility • Student is expected that you will spend at least 8 hours/week studying this course (4 lecture + 4 assignment) • University regulations indicate that if students attend less than 80% of scheduled classes they may be refused final assessment HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 0.03 Introduction - Course Assessment Policy • One midterm exam: 30% • One comprehensive final exam: 50% • In-class quizzes, class participation and learning attitude: 20% - Textbooks R.C. Hibbeler, Engineering Mechanics-Statics and Dynamics, 12Ed., Prentice Hall, 2010 - Grade scale: 100 - Course Outline General Principles - Force Vectors - Equilibrium of a Particle - Force System Resultants - Equilibrium of a Rigid Body - Structural Analysis - Internal Forces - Friction - Center of Gravity and Centroid - Moments of Inertia - Virtual Work HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 0.04 Introduction 2/13/2013 1 01. General Principles HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.01 General Principles Chapter Objectives • To provide an introduction to the basic quantities and idealizations of mechanics • To give a statement of Newton’s Laws of Motion and Gravitation • To review the principles for applying the SI system of units • To examine the standard procedures for performing numerical calculations • To present a general guide for solving problems HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.02 Force Vectors §1. Mechanics - Mechanics: the study how body react to the forces acting on them - Branches of mechanics • Statics deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity • Dynamics is concerned with the accelerated motion of bodies HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.03 General Principles §2. Fundamental Concepts - Basic Quantities • Length, : 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, : mass is a measure of a quantity of matter • Force, : considered as a push or pull exerted by one body on another A force is completely characterized by - magnitude - direction - point of application HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.04 General Principles §2. Fundamental Concepts - Idealizations • Particle: particle has a mass, but it size can be neglected • Rigid body: a rigid body can be considered as a combination of a large number of particles • Concentrated force: represents the effect of a loading which is assumed to act at a point on a body HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.05 General Principles Three forces act on the hook at . Since these forces all meet at a point, then for any force analysis, we can assume the hook to be represented as a particle Steel is a common engineering material that does not deform very much under load. We can consider this railroad wheel to be a rigid body acted upon by the concentrated force of the rail §2. Fundamental Concepts - Newton’s Laws of Motion • First Law A particle originally at rest, or moving in an straight line with constant velocity, will remain in this state provided the particle is not subjected to an unbalanced force • Second Law A particle acted upon by an unbalanced force experiences an acceleration that has the same direction as the force and a magnitude that is directly proportional to the force: • Third Law The mutual forces of action and reaction between two particles are equal, opposite and collinear HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.06 General Principles 2/13/2013 2 §2. Fundamental Concepts - Newton’s Law of Gravitational Attraction Gravitational attraction between any two particles : force of gravitational between the two particles, : universal constant of gravitation, From experiment: : mass of each of the two particles, : distance between the two particles, - Mass Mass is an absolute property of a body The mass provides a measure of the resistance of a body to a change in velocity, as defined by Newton's second law of motion HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.07 General Principles §2. Fundamental Concepts - Weigh Weight refers to the gravitational attraction of the earth on a body or quantity of mass The astronaut is weightless, for all practical purposes, since she is far removed from the gravitational field of the earth HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.08 General Principles §3. Units of Measurement - SI units: The International System of units abbreviated SI after the French “Système International d’Unités” - U.S. Customary (FPS) HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.09 General Principles §3. Units of Measurement - Conversion of Units HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.10 General Principles §4. Units of Measurement - Prefixes - Rules for Use: when performing calculations, represent the numbers in terms of their base or derived units by converting all prefixes to powers of . E.g. HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.11 General Principles §5. Numerical Calculations - Dimensional Homogeneity: dimensions have to be the same on both sides of the equal sign, (e.g. ) - Significant Figures: the number of significant figures contained in any number determines the accuracy of the number use an appropriate number of significant figures E.g. might have three (), four (), or five () significant figures. To avoid these ambiguities, rewrite - Rounding Off Numbers: be consistent when rounding off • greater than 5, round up: • smaller than 5, round down: • equal to 5 + the digit preceding the 5 is an even number: + the digit preceding the 5 is an odd number: HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.12 General Principles 2/13/2013 3 §6. General Procedure for Analysis Problem Solving Strategy - Interpret: read carefully and determine what is given and what is to be found/delivered. Ask if not clear. If necessary, make assumptions and indicate them - Plan: think about major steps (or road map) that you will take to solve a given problem. Think of alternative/creative solutions and choose the best one - Execute: carry out your steps. Use appropriate diagrams and equations. Estimate your answers, avoid simple calculation mistakes, Reflect on/revise your work HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.13 General Principles 2/13/2013 1 02. Force Vectors HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.01 Force Vectors Chapter Objectives • To show how to add forces and resolve them into components using the Parallelogram Law • To express force and position in Cartesian vector form and explain how to determine the vector’s magnitude and direction • To introduce the dot product in order to determine the angle between two vectors or the projection of one vector onto another HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.02 Force Vectors §1. Scalars and Vectors - Scalar: a scalar is any positive or negative physical quantity that can be completely specified by its magnitude Examples: length, mass, and time - Vector: a vector is any physical quantity that requires both a magnitude and a direction for its complete description Examples: force, position, and moment A vector is shown graphically by an arrow • the length of the arrow: the magnitude of the vector • the angle between the vector and a fixed axis: direction of its line of action • the head or tip of the arrow: the sense of direction of the vector - Notation: , HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.03 Force Vectors §2. Vector Operations - Multiplication and division of a vector by a scalar - Vector addition • Parallelogram law • Triangle rule HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.04 Force Vectors §2. Vector Operations - Vector subtraction • Parallelogram law • Triangle construction HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.05 Force Vectors §3. Vector Addition Forces - Experimental evidence has shown that a force is a vector quantity since it has a specified magnitude, direction, and sense and it adds according to the parallelogram law - Finding a resultant force The two component forces and acting on the pin can be added together to form the resultant force HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.06 Force Vectors 2/13/2013 2 §3. Vector Addition Forces - Finding the components of a force To resolve a force into two components in order to study its pulling or pushing effect in two specific directions HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.07 Force Vectors §3. Vector Addition Forces - Addition of several forces To resolve a force into two components in order to study its pulling or pushing effect in two specific directions HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.08 Force Vectors §3. Vector Addition Forces - Example 2.1 The screw eye is subjected to two forces, and . Determine the magnitude and direction of the resultant force Solution HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.09 Force Vectors §3. Vector Addition Forces - Example 2.2 Resolve the horizontal force into components acting along the and axes and determine the magnitudes of these components Solution HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.10 Force Vectors §3. Vector Addition Forces - Example 2.3 Determine the magnitude of the component force and the magnitude of the resultant force if is directed along the positive axis Solution HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.11 Force Vectors §3. Vector Addition Forces - Example 2.4 It is required that the resultant force acting on the eyebolt be directed along the positive axis and that have a minimum magnitude. Determine this magnitude, the angle , and the corresponding resultant force Solution Magnitude of is a minimum its line of action is perpendicular to the line of action of , that is, when and HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.12 Force Vectors 2/13/2013 3 Fundamental Problems - F2.1: Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the axis HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.13 Force Vectors Fundamental Problems - F2.2: Two forces act on the hook. Determine the magnitude of the resultant force HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.14 Force Vectors Fundamental Problems - F2.3: Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive axis HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.15 Force Vectors Fundamental Problems - F2.4: Resolve the force into components along the and axes, and determine the magnitude of each of these components HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.16 Force Vectors Fundamental Problems - F2.5: The force acts on the frame. Resolve this force into components acting along members and , and determine the magnitude of each component HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.17 Force Vectors Fundamental Problems - F2.6: If force is to have a component along the axis of , determine the magnitude of and the magnitude of its component along the axis HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.18 Force Vectors 2/13/2013 4 §4. Addition of a System of Coplanar Forces - Scalar Notation - Cartesian Vector Notation HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.19 Force Vectors §4. Addition of a System of Coplanar Forces - Coplanar Force Resultants HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.20 Force Vectors §4. Addition of a System of Coplanar Forces - Example 2.5 Determine the and components of and acting on the boom. Express each force as a Cartesian vector Solution HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.21 Force Vectors §4. Addition of a System of Coplanar Forces Scalar notation HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.22 Force Vectors §4. Addition of a System of Coplanar Forces Cartesian vector notation HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.23 Force Vectors §4. Addition of a System of Coplanar Forces - Example 2.6 The link is subjected to two forces and . Determine the magnitude and direction of the resultant force Solution 1 Scalar Notation : : HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.24 Force Vectors 2/13/2013 5 §4. Addition of a System of Coplanar Forces Solution 2 Cartesian vector notation ( ) HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.25 Force Vectors §4. Addition of a System of Coplanar Forces - Example 2.7 The end of the boom is subjected to three concurrent and coplanar forces. Determine the magnitude and direction of the resultant force Solution : : HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.26 Force Vectors Fundamental Problems - F2.7: Resolve each force acting on the post into its and components HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.27 Force Vectors Fundamental Problems - F2.8: Determine the magnitude and direction of the resultant force HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.28 Force Vectors Fundamental Problems - F2.9: Determine the magnitude of the resultant force acting on the corbel and its direction measured counterclockwise from the axis HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.29 Force Vectors Fundamental Problems - F2.10: If the resultant force acting on the bracket is to be directed along the positive axis, determine the magnitude of and its direction HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.30 Force Vectors 2/13/2013 6 Fundamental Problems - F2.11: If the magnitude of the resultant force acting on the bracket is to be directed along the axis, determine the magnitude of and its direction HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.31 Force Vectors Fundamental Problems - F2.12: Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive axis HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.32 Force Vectors §5. Cartesian Vectors - Right-Handed Coordinate System HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.33 Force Vectors §5. Cartesian Vectors - Rectangular Components of a Vector - Cartesian Unit Vectors , - Cartesian Vector Representation - Magnitude of a Cartesian Vector HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.34 Force Vectors §5. Cartesian Vectors - Direction of a Cartesian Vector: Unit vector Relation between the direction cosines and HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.35 Force Vectors §5. Cartesian Vectors - The direction of can be specified using two angles, and HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 2.36 Force Vectors [...]... Tan Tien HCM City Univ of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien 8 2/13/2013 Engineering Mechanics – Statics 2.49 Force Vectors Fundamental Problems - F2.16: Express the force as a Cartesian vector HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 2.51 Engineering Mechanics – Statics 2.50 Force Vectors Fundamental Problems - F2.17: Express... indicates its sense is the reverse of that shown on the free-body diagram HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics Engineering Mechanics – Statics HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics Nguyen Tan Tien 3.24 Equilibrium of a Particle §4 Three-Dimensional Force Systems - Example 3.6 The 10𝑘𝑔 lamp is... Faculty of Mechanical Engineering Engineering Mechanics – Statics Nguyen Tan Tien 4.57 Force System Resultants §7 Simplification of a Force and Couple System Summation 3 +→ 𝐹 𝑅𝑥 = 3𝑐𝑜𝑠300 + 5 5 = 5.598𝑘𝑁 𝑦 + ↑ 𝐹 𝑅 = −6.50𝑘𝑁 = 6.50𝑘𝑁 ↓ +↺ 𝑀 𝑅 𝑂 = 2.46𝑘𝑁𝑚 ↻ HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 𝐹 𝑅𝑥 2 + 𝐹𝑅 Engineering Mechanics – Statics 4.59 4.58... about a point provides a measure of the tendency for rotation (sometimes called a torque) 𝑀 = 𝐹𝑑 𝑀 = 𝐹𝑑 ′ = 𝐹𝑑𝑠𝑖𝑛𝜃 𝑀 = 𝐹𝑑 = 0 Engineering Mechanics – Statics 4.02 HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics Engineering Mechanics – Statics 4.05 Nguyen Tan Tien Force System Resultants §1 Moment of a Force – Scalar Formulation - Example 4.1 For each case... wires HCM City Univ of Technology, Faculty of Mechanical Engineering HCM City Univ of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien Nguyen Tan Tien 6 2/13/2013 Engineering Mechanics – Statics 4.01 Force System Resultants 04 Force System Resultants HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 4.03 Nguyen Tan Tien Force System Resultants §1... Faculty of Mechanical Engineering Engineering Mechanics – Statics 2.63 Nguyen Tan Tien Force Vectors HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 2.64 Fundamental Problems - F2.20: Determine the length of the rod and the position vector directed from 𝐴 to 𝐵 What is the angle 𝜃? HCM City Univ of Technology, Faculty of Mechanical Engineering Force Vectors... of Mechanical Engineering HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 4.51 Nguyen Tan Tien Force System Resultants Fundamental Problems - F4.21 Determine the magnitude of 𝐹 so that the resultant couple moment acting on the beam is 1.5𝑘𝑁𝑚 clockwise HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 4.53 Nguyen... HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 2.47 Nguyen Tan Tien Force Vectors Fundamental Problems - F2.14: Express the force as a Cartesian vector HCM City Univ of Technology, Faculty of Mechanical Engineering HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics 2.48 Nguyen Tan Tien Force Vectors Fundamental... Mechanical Engineering Engineering Mechanics – Statics ⟹ 𝐴 𝐵 = 𝐴 𝑥 𝐵𝑥 + 𝐴 𝑦 𝐵 𝑦 + 𝐴 𝑧 𝐵𝑧 2.71 Nguyen Tan Tien Force Vectors §9 Dot Product - Example 2.17 The frame is subjected to a horizontal force 𝐹 = 300𝑗 𝑁 Determine the magnitude of the components of this force parallel and perpendicular to member 𝐴𝐵 HCM City Univ of Technology, Faculty of Mechanical Engineering Engineering Mechanics – Statics Nguyen... Mechanical Engineering Nguyen Tan Tien HCM City Univ of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien 12 2/13/2013 Engineering Mechanics – Statics 2.73 Force Vectors §9 Dot Product - Example 2.18 The pipe is subjected to the force of 𝐹 = 80𝑁 Determine the angle 𝜃 between 𝐹 and the pipe segment 𝐵𝐴 and the projection of 𝐹 along this segment Solution Angle 𝜃 Engineering Mechanics – Statics . Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 0.01 Introduction Chapter 00 – Introduction - Name of course: ENGINEERING MECHANICS - STATICS - Number of Credits: 3 - Level:. attitude: 20% - Textbooks R.C. Hibbeler, Engineering Mechanics- Statics and Dynamics, 12Ed., Prentice Hall, 2010 - Grade scale: 100 - Course Outline General Principles - Force Vectors - Equilibrium. Mechanical Engineering Nguyen Tan Tien Engineering Mechanics – Statics 1.02 Force Vectors §1. Mechanics - Mechanics: the study how body react to the forces acting on them - Branches of mechanics