Engineering Mechanics (Statics) Stage: First Year Haider Kadhem Sakban Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Thi-Qar University College of Engineering Department of Petroleum and Gas Engineering Course Number: PGE102: Engineering Mechanics (Statics) Instructor: Haider K. Sakban Credit hours: 3 Textbook: Hibbeler R. C., Engineering Mechanics, Statics , 14th ed, 2015 References: 1. M. E. Plesha, Engineering Mechanics Statics, 1st ed, 2010. 2. A. Bedford, Engineering Mechanics Statics, 5th ed, 2008. Course Contents: This course covers: principles of statics, Resultant of a force system, Equilibrium of a force system, Moment of a force, Friction, centroid and center of gravity, Moment of inertia, analysis of internal forces, Strain, Stress-Strain diagram, Hook’s law, Shearing deformation, Poisson’s Ratio, Volumetric strain, Thin walled cylinders, Thermal stress, Shear and bending moment in beam. Grading Policy: The final letter grade will be computed using the following criteria: • Homework/Quizzes 5% • Midterm Exam I 17.5% • Midterm Exam II 17.5% • Final Exam 60% 1 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Contents 1. Chapter One: Review and Fundamental concepts: ................................................................. 4 Fundamental concepts and units of measurement ............................................................ 5 General procedure for analysis ......................................................................................... 6 2. Chapter Two: Force vectors: ................................................................................................... 7 Vector Operations ............................................................................................................ 7 Rectangular Components :Two Dimensions .................................................................. 11 Rectangular Components: Three Dimensions ................................................................ 14 Moment of a force .......................................................................................................... 17 3. Chapter Three: Equilibrium for a Rigid Body ...................................................................... 20 Conditions for Rigid-Body Equilibrium ........................................................................ 20 Free-Body Diagrams ...................................................................................................... 22 4. Structural Analysis ................................................................................................................ 31 4................................................................................................................................................. 31 Analysis of trusses:......................................................................................................... 31 The Method of Joints .............................................................................................. 32 The Method of Sections .......................................................................................... 35 5. Chapter Five: Friction ........................................................................................................... 39 Theory of Dry Friction ................................................................................................... 39 Types of Friction Problems ............................................................................................ 42 .6 Chapter six: Center of Gravity and Centroid ........................................................................ 53 Center of Gravity:........................................................................................................... 53 Composite Bodies .......................................................................................................... 58 7. Chapter Seven: Moments of Inertia ...................................................................................... 62 2 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Moments of Inertia of an area ........................................................................................ 62 Parallel-Axis Theorem for an Area ................................................................................ 63 Radius of Gyration of an Area ....................................................................................... 63 Moments of Inertia for Composite Areas ....................................................................... 67 8. Chapter Eight: Kinematics of a Particle ................................................................................ 71 Rectilinear Kinematics. .................................................................................................. 72 Conservation of Energy .................................................................................................. 77 3 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year 1. Chapter One: Review and Fundamental concepts: Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces. In general, this subject can be subdivided into three branches: rigid-body mechanics, deformable-body mechanics, and fluid mechanics. In this semester 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. 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; however, statics deserves separate treatment in engineering education since many objects are designed with the intention that they remain in equilibrium. Scientific method: Recognize a question (unexplained fact) Make an educated guess (hypothesis) Make prediction about the consequences of the hypothesis Perform an experiment or make calculations Formulate a general rule 4 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Fundamental concepts and units of measurement The following four quantities are used throughout mechanics: 1. Length 2. Time 3. Mass 4. Force 5 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year General procedure for analysis Read the problem carefully and try to correlate the actual physical situation with the theory studied. Tabulate the problem data and draw to a large scale any necessary diagrams. Apply the relevant principles, generally in mathematical form. When writing any equations, be sure they are dimensionally homogeneous. Solve the necessary equations, and report the answer with no more than three significant figures. Study the answer with technical judgment and common sense to determine whether or not it seems reasonable. Example: Convert 2 km/h to m/s. How many ft /s is this? Solution: Since 1 km = 1000 m and 1 h = 3600 s, the factors of conversion are arranged in the following order, so that a cancellation of the units can be applied: 2 푘푚 2 푘푚 1000푚 1 ℎ 2000 푚 = ( ) ( ) = = 0.556 푚/푠 ℎ ℎ 푘푚 3600 푠 3600 푠 From Table 1–2, 1 ft = 0.3048 m. Thus, 푚 푚 1 푓푡 0.556 = 0.556 ( ) = 1.82 푓푡/ 푠 푠 푠 0.3048 m 6 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year 2. Chapter Two: Force vectors: 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. 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. Vector Operations Procedure for Analysis: 1. Redraw a half portion of the parallelogram to illustrate the triangular head-to-tail addition of the components. 2. From this triangle, the magnitude of the resultant force can be determined using the law of cosines, and its direction is determined from the law of sines. The magnitudes of two force components are determined from the law of sines. The formulas are: Cosine law: C = √A2 + B2 − 2AB cos (푐) Sine law: A B C = = 푠푛 푎 푠푛 푏 sin 푐 7 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Example: The screw eye in Figure below is subjected to two forces, F1 and F2. Determine the magnitude and direction of the resultant force. Solution: The two unknowns are The magnitude of FR and the angle θ (theta). Using the law of cosines: 2 2 0 퐹푅 = √(100) + (150) − 2(100)(150) cos 115 퐹푅 = √10000 + 22500 − 30000 (−0.4226) 퐹푅 = 212.6 Applying the law of sines to determine θ, 150 212.6 = sin θ sin 1150 150 (sin 1150) sin θ = 212.6 θ = 39.80 Thus, the direction Φ (phi) of FR, measured from the horizontal, is: Φ = 39.80 + 15 0 = 54.80 8 Eng. Mechanics (Statics) Instructor: Haider K. Sakban First Year Example: Resolve the horizontal 600-lb force in Figure (a) below into components acting along the u and v axes and determine the magnitudes of these components. Solution: The two unknowns are the magnitudes of Fu and Fv. Applying the law of sines, 퐹 600 푢 = sin 1200 sin 300 퐹푢 = 1039 lb 퐹 600 푣 = sin 300 sin 300 퐹푣 = 600 lb 9 Eng.