ELEMENTARY STATICS

By Z. MIVAY

CONTENTS 1 INTRODUCTION INTRODUCTION TO MECHANICS DEFINITIONS IDEALISATION IN MECHANICS RIGID BODY PARTICLE BASIC CONCEPTS FUNDAMENTAL PRINCIPLES NEWTON’S LAWS OF MOTION NEWTON’S LAW OF GRAVITATION PARALLELOGRAM LAW PRINCIPLE OF TRANSMISSIBILITY SYSTEM OF UNITS DIMENSIONAL ANALYSIS DIMENSIONAL HOMOGENEITY DIMENSIONS OF UNKNOWN VARIABLES METHODS OF SOLUTION VECTOR ALGEBRA SUMMARY 13 EXERCISES 13 COMPUTER PROGRAM ASSIGNMENT 2 STATICS OF PARTICLES — CONCURRENT FORCES IN PLANE 2 1 INTRODUCTION RESULTANT OF FORCES TRIANGLE LAW OF FORCES POLYGON LAW RESOLUTION AND COMPONENTS OF FORCE RESULTANT OF SEVERAL CONCURRENT FORCES EQUILIBRIUM OF A PARTICLE EQUILIBRANT EQUATIONS OF EQUILIBRIUM APPLICATION OF STATICS OF PARTICLES FREE BODY FREEBODY DIAGRAM EQUILIBRIUM OF A TWO-FORCE BODY EQUILIBRIUM OF A THREE-FORCE BODY LAMI’S THEOREM SUMMARY 34 EXERCISES 35 COMPUTER PROGRAM ASSIGNMENT 3 STATICS OF PARTICLES — CONCURRENT FORCES IN SPACE INTRODUCTION COMPONENTS OF FORCE IN SPACE EQUILIBRIUM OF A PARTICLE IN SPACE APPLICATION OF STATICS OF PARTICLE SUMMARY 49 EXERCISES 49 COMPUTER PROGRAM ASSIGNMENT 4 STATICS OF RIGID BODIES: NON-CONCURRENT FORCES IN PLANE MOMENT OF A FORCE ABOUT A POINT VARIGNON’S THEOREM MOMENT OF A COUPLE RESOLUTION OF A GIVEN FORCE INTO A FORCE AT O AND A COUPLE COPLANAR PARALLEL FORCE SYSTEM COPLANAR CONCURRENT FORCE SYSTEM COPLANAR NON-CONCURRENT FORCE SYSTEM REDUCTION OF FORCE COUPLE SYSTEM AT O TO A SINGLE FORCE RESULTANT OF COPLANAR NON-CONCURRENT SYSTEM EQUILIBRIUM OF RIGID BODIES APPLICATION OF STATICS OF RIGID BODIES TYPES OF SUPPORTS IN TWO DIMENSIONS BEAMS TYPES OF LOADS MULTI-FORCE MEMBERS REACTIONS OF PINJOINTED PLANE TRUSS SUMMARY 93 EXERCISES 95 COMPUTER PROGRAM ASSIGNMENT 5 STATICS OF RIGID BODIES: NON-CONCURRENT FORCES IN SPACE MOMENT OF FORCE ABOUT A POINT MOMENT OF FORCE ABOUT A GIVEN AXIS COUPLES IN SPACE RESOLUTION OF FORCE INTO FORCE AND COUPLE RESULTANT OF NON-CONCURRENT, NON-COPLANAR SYSTEM EQUILIBRIUM OF RIGID BODY IN THREE DIMENSIONS SUMMARY 120 EXERCISES 121 COMPUTER PROGRAM ASSIGNMENT 6 ANALYSIS OF PIN-JOINTED PLANE TRUSSES STRUCTURAL MODEL ASSUMPTIONS FREEBODY DIAGRAMS OF JOINT AND MEMBER TYPES OF TRUSSES METHOD OF JOINTS STEPS IN METHOD OF JOINTS METHOD OF SECTIONS STEPS IN METHOD OF SECTIONS ZERO-FORCE MEMBERS SUMMARY 157 EXERCISES 158 COMPUTER PROGRAM ASSIGNMENT 7 UNIFORM FLEXIBLE SUSPENSION CABLE CABLES AND LOADS CONCENTRATED LOADS UNIFORMLY DISTRIBUTED LOADS UNIFORMLY DISTRIBUTED LOAD PER UNIT HORIZONTAL DISTANCE UNIFORMLY DISTRIBUTED LOAD PER UNIT LENGTH ALONG THE CABLE ANCHOR CABLES SUMMARY 186 EXERCISES 187 COMPUTER PROGRAM ASSIGNMENT 8 FRICTION TYPES OF FRICTION 8 2 CHARACTERISTICS OF DRY FRICTION 8 3 LAWS OF FRICTION 8 4 ANGLE OF FRICTION 8 5 ANGLE OF REPOSE 8 6 CONE OF FRICTION 8 7 APPLICATIONS 8 7 1 BODY ON HORIZONTAL PLANE OR INCLINED PLANE SUBJECTED TO FORCES 8 7 2 TWO BODIES IN CONTACT 8 7 3 LADDER FRICTION 8 7 4 WEDGE FRICTION 8 7 5 SCREW FRICTION 8 7 6 BELT FRICTION 8 7 7 ROLLING RESISTANCE SUMMARY 223 EXERCISES 224 COMPUTER PROGRAM ASSIGNMENT 9 CENTROID AND CENTRE OF GRAVITY CENTROID OF AREA, LINE AND VOLUME AREA LINE VOLUME CENTROID OF A LINE CENTROID OF STRAIGHT LINE CENTROID OF CURVED LINE CENTROID OF SEMICIRCULAR ARC CENTROID OF A WIRE BENT IN A GIVEN SHAPE CENTROID OF AN AREA CENTROID OF A RECTANGLE CENTROID OF A RIGHT-ANGLED TRIANGLE CENTROID OF CIRCLE, QUADRANT AND SEMICIRCLE CENTROID OF A COMPOSITE AREA CENTROID AND AXIS OF SYMMETRY THEOREMS OF PAPPUS AND GULDINUS CENTROID OF A VOLUME CENTROID OF A RIGHT CIRCULAR CONE CENTROID OF A HEMISPHERE CENTRE OF GRAVITY CENTRE OF THE MASS DISTRIBUTED LOADS ON A STRUCTURAL MEMBER SUMMARY 263 EXERCISES 264 COMPUTER PROGRAM ASSIGNMENT 10 MOMENT OF INERTIA AND MASS MOMENT OF INERTIA SECOND MOMENT OF AREA RADIUS OF GYRATION PRODUCT OF AREA PARALLEL-AXIS THEOREM PERPENDICULAR-AXIS THEOREM MOMENT OF INERTIA OF PLANE AREA BY INTEGRATION RECTANGLE RIGHT-ANGLED TRIANGLE (WIDTH = B, DEPTH = H) CIRCLE SEMICIRCLE QUADRANT OF A CIRCLE TYPES OF STEEL SECTIONS MOMENT OF INERTIA OF COMPOSITE SECTION PRINCIPAL AXES AND PRINCIPAL MOMENTS OF INERTIA MASS MOMENT OF INERTIA MASS MOMENT OF INERTIA FOR THIN PLATES PARALLEL-AXIS THEOREM FOR MASSES MASS MOMENT OF INERTIA OF A THIN RECTANGULAR PLATE MASS MOMENT OF INERTIA OF A THIN CIRCULAR DISC MASS MOMENT OF INERTIA OF SOLIDS MASS MOMENT OF INERTIA OF A ROD MASS MOMENT OF INERTIA OF A SOLID CYLINDER MASS MOMENT OF INERTIA OF A PRISM MASS MOMENT OF INERTIA OF A SPHERE 10 6 10 MASS MOMENT OF INERTIA OF A CONE SUMMARY 332 EXERCISES 334 COMPUTER PROGRAM ASSIGNMENT 11 METHOD OF VIRTUAL WORK REAL WORK OF A FORCE PRINCIPLE OF VIRTUAL DISPLACEMENTS DEGREE OF FREEDOM PRINCIPLE OF VIRTUAL DISPLACEMENT FOR A PARTICLE PRINCIPLE OF VIRTUAL DISPLACEMENT OF A RIGID BODY APPLICATION OF PRINCIPLE OF VIRTUAL DISPLACEMENT TO LINKAGES 11 8 APPLICATION OF PRINCIPLE OF VIRTUAL WORK TO LIFTING MACHINES APPLICATION OF PRINCIPLE OF VIRTUAL WORK TO PULLEYS APPLICATION OF PRINCIPLE OF VIRTUAL WORK TO BEAMS APPLICATION OF PRINCIPLE OF VIRTUAL WORK TO LADDER PROBLEM APPLICATION OF PRINCIPLE OF VIRTUAL WORK TO TRUSSES METHOD OF MINIMUM POTENTIAL ENERGY SUMMARY 372 EXERCISES 373 COMPUTER PROGRAM ASSIGNMENT 12 KINEMATICS OF PARTICLES — RECTILINEAR MOTION RECTILINEAR MOTION MEASURED AND DERIVED QUANTITIES AS A FUNCTION OF TIME DETERMINATION OF MOTION OF A PARTICLE NUMERICAL INTEGRATION FREELY FALLING OBJECTS RELATIVE MOTION DEPENDENT RELATIVE MOTION SUMMARY 426 EXERCISES 429 COMPUTER PROGRAM ASSIGNMENT 13 KINEMATICS OF PARTICLES — CURVILINEAR MOTION RECTANGULAR COMPONENTS TWO-DIMENSIONAL MOTION WITH CONSTANT ACCELERATION PROJECTILE MOTION PROJECTION ON INCLINED PLANE UNIFORM CIRCULAR MOTION TANGENTIAL AND NORMAL ACCELERATION SIMPLE HARMONIC MOTION MOTION OF A PARTICLE IN POLAR COORDINATES — RADIAL AND TRANSVERSE COMPONENTS MOTION IN CYLINDRICAL COORDINATES MOTION OF PARTICLE IN SPHERICAL COORDINATES RELATIVE MOTION OF TWO PARTICLES SUMMARY 482 EXERCISES 485 COMPUTER PROGRAM ASSIGNMENT 14 KINETICS OF PARTICLES — NEWTON’S SECOND LAW NEWTON’S SECOND LAW OF MOTION REFERENCE FRAMES EQUATIONS OF MOTION D’ ALEMBERT’S PRINCIPLE ANALYSIS OF LIFT MOTION MOTION OF SEVERAL CONNECTED BODIES MOTION OF TWO BODIES CONNECTED BY A STRING LINEAR MOMENTUM ANGULAR MOMENTUM KEPLER’S LAWS OF PLANETARY MOTION MOTION UNDER A CENTRAL FORCE SUMMARY 537 EXERCISES 539 COMPUTER PROGRAM ASSIGNMENT 15 KINETICS OF PARTICLES—WORK AND ENERGY WORK DONE BY A FORCE WORK DONE BY A SPRING WORK OF THE GRAVITATIONAL FORCE POWER KINETIC ENERGY AND WORK-ENERGY PRINCIPLE APPLICATIONS OF WORK-ENERGY PRINCIPLE CONSERVATIVE FORCES AND POTENTIAL ENERGY CONSERVATIVE FORCE NON-CONSERVATIVE FORCE CONSERVATIVE SYSTEMS AND POTENTIAL FUNCTIONS CONSERVATION OF ENERGY ENERGY DIAGRAMS AND EQUILIBRIUM OF A SYSTEM SUMMARY 583 EXERCISES 585 COMPUTER PROGRAM ASSIGNMENT 16 KINETICS OF PARTICLES — IMPULSE AND MOMENTUM IMPULSE-MOMENTUM PRINCIPLE CONSERVATION OF TOTAL MOMENTUM OF PARTICLES APPLICATION OF PRINCIPLE OF IMPULSE AND MOMENTUM SUMMARY 612 EXERCISES 613 COMPUTER PROGRAM ASSIGNMENT 17 COLLISION OF ELASTIC BODIES DIRECT CENTRAL IMPACT IMPORTANT CASES OF ELASTIC IMPACT OBLIQUE CENTRAL IMPACT IMPACT AGAINST A FIXED PLANE PROBLEMS INVOLVING ENERGY AND MOMENTUM SUMMARY 645 EXERCISES 646 COMPUTER PROGRAM ASSIGNMENT 18 KINEMATICS OF RIGID BODIES TYPES OF RIGID BODY MOTION TRANSLATION ROTATION ABOUT A FIXED AXIS EQUATIONS DEFINING THE ROTATION OF A RIGID BODY ABOUT A FIXED AXIS GENERAL PLANE MOTION ABSOLUTE AND RELATIVE VELOCITY IN PLANE MOTION INSTANTANEOUS CENTRE OF ROTATION ABSOLUTE AND RELATIVE ACCELERATION IN A PLANE MOTION RELATIVE MOTION-ROTATING AXES SUMMARY 685 EXERCISES 687 COMPUTER PROGRAM ASSIGNMENT 19 KINETICS OF RIGID BODIES EQUATIONS OF TRANSLATIONAL MOTION EQUATIONS OF ROTATIONAL MOTION TYPES OF MOTION NEWTON’S LAW AND D’ ALEMBERT’S PRINCIPLE INERTIA FORCE AND INERTIA COUPLE CENTRE OF PERCUSSION CONSTRAINED MOTION NON-CENTROIDAL MOTION ENERGY METHODS WORK OF A FORCE ON A RIGID BODY WORK OF A MOMENT WORK OF A CONSTANT FORCE WORK OF A CONSTANT MOMENT KINETIC ENERGY OF A RIGID BODY ROTATION ABOUT ARBITRARY FIXED AXIS PRINCIPLE OF WORK AND ENERGY CONSERVATIONS OF ENERGY IMPULSE AND MOMENTUM OF A RIGID BODY LINEAR IMPULSE AND MOMENTUM ANGULAR IMPULSE AND MOMENTUM SYSTEM OF RIGID BODIES CONSERVATION OF ANGULAR MOMENTUM SUMMARY 723 EXERCISES 724 COMPUTER PROGRAM ASSIGNMENT 20 MECHANICAL VIBRATIONS SPRING MASS SYSTEM SIMPLE PENDULUM COMPARISON OF SIMPLE HARMONIC MOTION AND UNIFORM CIRCULAR MOTION ENERGY OF SIMPLE HARMONIC OSCILLATOR FREE VIBRATION OF RIGID BODIES WITHOUT DAMPING DAMPING FREE VIBRATIONS LOGARITHMIC DECREMENT FORCED VIBRATION WITHOUT DAMPING FORCED VIBRATION WITH DAMPING ROTATING UNBALANCE ANSWERS TO END-OF-CHAPTER EXERCISES COMPUTER ASSIGNMENT USING EXCEL PACKAGE OBJECTIVE TYPE QUESTIONS DO-YOU-KNOW ASSIGNMENT REFERENCES