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 موضوع: كتاب Engineering Mechanics  Statics  Fifteenth Edition السبت 12 نوفمبر 2022, 1:22 am  

أخواني في الله أحضرت لكم كتاب Engineering Mechanics  Statics Fifteenth Edition in SI Units R. C. Hibbeler Si Conversion by Jun Hwa Lee
و المحتوى كما يلي :
Contents 1 General Principles 25 Chapter Objectives 25 1.1 Mechanics 25 1.2 Fundamental Concepts 26 1.3 The International System of Units 29 1.4 Numerical Calculations 32 1.5 General Procedure for Analysis 34 2 Force Vectors 39 Chapter Objectives 39 2.1 Scalars and Vectors 39 2.2 Vector Operations 40 2.3 Vector Addition of Forces 42 2.4 Addition of a System of Coplanar Forces 54 2.5 Cartesian Vectors 65 2.6 Addition of Cartesian Vectors 68 2.7 Position Vectors 76 2.8 Force Vector Directed Along a Line 78 2.9 Dot Product 8618 contents 3 Equilibrium of a Particle 103 Chapter Objectives 103 3.1 Condition for the Equilibrium of a Particle 103 3.2 The FreeBody Diagram 104 3.3 Coplanar Force Systems 107 3.4 ThreeDimensional Force Systems 120 4 Force System Resultants 135 Chapter Objectives 135 4.1 Moment of a Force—Scalar Formulation 135 4.2 Principle of Moments 137 4.3 Cross Product 145 4.4 Moment of a Force—Vector Formulation 148 4.5 Moment of a Force about a Specified Axis 158 4.6 Moment of a Couple 167 4.7 Simplification of a Force and Couple System 179 4.8 Further Simplification of a Force and Couple System 190 4.9 Reduction of a Simple Distributed Loading 202contents 19 5 Equilibrium of a Rigid Body 217 Chapter Objectives 217 5.1 Conditions for RigidBody Equilibrium 217 5.2 FreeBody Diagrams 219 5.3 Equations of Equilibrium 230 5.4 Two and ThreeForce Members 240 5.5 FreeBody Diagrams 253 5.6 Equations of Equilibrium 258 5.7 Constraints and Statical Determinacy 259 6 Structural Analysis 279 Chapter Objectives 279 6.1 Simple Trusses 279 6.2 The Method of Joints 282 6.3 ZeroForce Members 288 6.4 The Method of Sections 296 6.5 Space Trusses 306 6.6 Frames and Machines 31020 contents 7 Internal Forces 347 Chapter Objectives 347 7.1 Internal Loadings 347 7.2 Shear and Moment Equations and Diagrams 363 7.3 Relations among Distributed Load, Shear, and Moment 372 7.4 Cables 383 8 Friction 403 Chapter Objectives 403 8.1 Characteristics of Dry Friction 403 8.2 Problems Involving Dry Friction 408 8.3 Wedges 430 8.4 Frictional Forces on Screws 432 8.5 Frictional Forces on Flat Belts 439 8.6 Frictional Forces on Collar Bearings, Pivot Bearings, and Disks 447 8.7 Frictional Forces on Journal Bearings 450 8.8 Rolling Resistance 452contents 21 9 Center of Gravity and Centroid 465 Chapter Objectives 465 9.1 Center of Gravity, Center of Mass, and the Centroid of a Body 465 9.2 Composite Bodies 488 9.3 Theorems of Pappus and Guldinus 502 9.4 Resultant of a General Distributed Loading 511 9.5 Fluid Pressure 512 10 Moments of Inertia 529 Chapter Objectives 529 10.1 Definition of Moments of Inertia for Areas 529 10.2 ParallelAxis Theorem for an Area 530 10.3 Radius of Gyration of an Area 531 10.4 Moments of Inertia for Composite Areas 540 10.5 Product of Inertia for an Area 548 10.6 Moments of Inertia for an Area about Inclined Axes 552 10.7 Mohr’s Circle for Moments of Inertia 555 10.8 Mass Moment of Inertia 56322 contents 11 Virtual Work 581 Chapter Objectives 581 11.1 Definition of Work 581 11.2 Principle of Virtual Work 583 11.3 Principle of Virtual Work for a System of Connected Rigid Bodies 585 11.4 Conservative Forces 597 11.5 Potential Energy 598 11.6 PotentialEnergy Criterion for Equilibrium 600 11.7 Stability of Equilibrium Configuration 601 Appendix A. Mathematical Review and Formulations 616 Fundamental Problem Solutions and Answers 620 Review Problem Answers 637 Selected Answers 640 Index Index A Acceleration, dynamics and, 25 Active force, 105 Angles, 56, 66–67, 86–88, 90, 98–99, 405–407, 432, 616–617 Cartesian force vectors, 66–67 coordinate direction, 66, 98–99 dot product used for, 86–88, 90, 99 dry friction and, 405–407, 432 formed between intersecting lines, 90 horizontal (u), 67 impending motion and, 405, 407 kinetic friction (uk), 406–407 lead, 432 mathematical review of, 616–617 projection, parallel and perpendicular, 87 Pythagorean’s theorem and, 56, 87, 617 resultant forces from, 56 screws, 432 static friction (us), 405, 407 vectors and, 56, 66–67, 86–88, 90, 98–99 vertical (f), 67 Applied force (P), 404–407, 430–431, 459–460 Area (A), 468, 470, 474–476, 502–505, 523–524, 530–535, 540–542, 548–557, 576–577 axial symmetry and rotation, 502–505, 524, 548–551, 577 centroid (C) of an, 468, 470, 474–476, 502–505, 523–524, 576 centroidal axis of, 530–531 composite bodies (shapes), 503, 524, 540–542, 576–577 inclined axis, about, 552–554 integration for, 468, 474–476, 523, 529–530 Mohr’s circle for, 555–557 moments of inertia (I) for, 530–535, 540–542, 548–557, 576–577 Pappus and Guldinus, theorems of, 502–505, 524 parallelaxis theorem for, 530–532, 540, 549, 576 plane, volume generated revolution of, 503 polar moment of inertia, 530–531 principal moments of inertia, 553–554, 577 procedures for analysis of, 470, 532, 540 product of inertia for, 548–551, 553, 576 radius of gyration of, 531 surface of revolution, 502, 504–505, 524 transformation equations for, 552, 577 volume of revolution, 503–505, 524 Associative law, 146 Axes, 158–162, 202, 212, 529–535, 540–542, 548–557, 563–570, 576–577 area moments of inertia for, 529–535, 548–554, 576 centroidal axis of, 530–531, 576 composite bodies, 540–542, 568–570, 576–577 distributed load reduction, 202 inclined, area about, 552–554 line of action for, 158–160, 212 mass moments of inertia for, 563–570, 577 Mohr’s circle for, 555–557 moment of a force about specified, 158–162, 212 moments of inertia (I), 529–535, 540–542, 552–557, 563–570, 576–577 parallelaxis theorem for, 530–532, 540, 549, 567, 576 principal, 553–557, 577 procedures for analysis of, 532, 556, 564 product of inertia and, 548–551, 553, 576 radius of gyration for, 531, 568 resultant forces and, 158–162, 202, 212 righthand rule for, 158–160 scalar analysis, 158, 212 transformation equations for, 552 vector analysis, 159–162, 212 Axial loads, friction analysis of, 447–449 Axial revolution, 502–505, 524 Axial symmetry, 502–505, 524–525 axial revolution and, 502–505, 525 centroid (C) and, 502–505, 524 composite bodies, 503 Pappus and Guldinus, theorems of, 502–505, 525 rotation and, 502–505, 525 surface area and, 502, 504–505, 525 volume and, 503–505, 525 Axis of symmetry, 469, 488–489, 524, 548–551, 553, 576 area (A) of, 548–551 centroid (C) and, 469, 488–489, 524, 576 parallelaxis theorem for, 549, 576 principal axes, 553 product of inertia, 548–551, 553, 576 B Ball and socket connections, 253–254, 256 Base units, 29, 31 Beams, 347–382, 398–400 bending moments (M) and, 348–349, 373–377, 398 cantilevered, 347–348, 363 centroid (C), 348 couple moment (M) and, 374 distributed loads and, 372–377, 400 force equilibrium, 372–373 freebody diagrams, 347–349, 398 internal forces, 347–382, 398–400 internal loads of, 347–354, 372–377 method of sections for, 347–354, 364 moments, 348–349, 372–377, 398 normal force (N) and, 348–349, 398 procedures for analysis of, 349, 364654 Index Beams (Continued) resultant loadings, 348, 398 shear and moment diagrams, 363–366, 372–377, 399–400 shear force (V) and, 348–349, 372–377, 398 sign convention for, 349, 399 simply supported, 363 torsional (twisting) moment, 348, 398 Bearings, 253–257, 447–451, 461 axial loads, 447–449 collar, 447–449, 461 freebody diagrams, 253–257 frictional analysis of, 447–451, 461 journal, 254–256, 450–451, 461 lateral loads, 450–451 pivot, 447–449, 461 rigidbody support reactions, 253–257 thrust, 255, 256 Belts (flat), frictional analysis of, 439–441, 460 Bending moment diagrams, 363–366. See also Shear and moment diagrams Bending moments (M), 348–349, 373–377, 398–400 distributed loads and, 373–377, 400 internal forces and, 348–349, 372–377, 398, 400 method of sections for, 348–349 shear (V) and, 373 shear and moment diagrams, 372–377, 399–400 Body at rest (zero), 218 By inspection, determination of forces, 282, 288–289 C Cables, 104, 109, 131, 220, 221, 254, 383–397, 400 concentrated loads, 383–385, 400 connections, 220, 221 continuous, 131 distributed loads, 386–389, 400 equilibrium of, 104, 109, 131 flexibility of, 383 freebody diagram for, 104, 109, 131, 220, 254 inextensible, 383 internal forces of, 109, 383–397, 400 sagging, 383 support reactions, 220, 254 weight of as force, 390–393, 400 Calculations, engineering importance of, 32–33 Cantilevered beam, 347–348, 363 Cartesian coordinate system, 55–58, 65–70, 76–81, 86, 98–99, 145–152, 211 addition of vectors, 55–58, 68 concurrent force resultants, 55, 65–70, 99 coordinate direction angles, 66–67, 98–99 coplanar force resultants, 55–58 cross product for, 145–147 direction and, 66–68, 98–99, 145, 148 dot product in, 86, 99 force vector directed across a line, 78–81 horizontal angles (u), 67 magnitude of, 55, 66–68, 98, 145, 148 moment of a force, calculations by, 148–152, 211 position vectors (r), 76–77, 79–80, 99 rectangular components, 55–58, 65–70, 98 righthand rule, 65, 145–146, 148 sign convention for, 146 threedimensional systems, 65–70 twodimensional systems, 55–58 unit vectors, 55, 65–66, 78, 98 vector formulation, 146–152, 211 vector representation, 65–66, 98–99 vertical angles (f), 67 Cartesian vector notation, 55 Center of gravity (G), 29, 222, 464–527 center of mass (Cm) and, 467, 524 centroid (C) as, 222, 464–527 composite bodies, 488–492, 525 constant density and, 488 coplanar forces, 222 freebody diagrams of, 222 location of, 465–466, 469–478, 524 Newton’s law of gravitational attraction and, 29 procedure for analysis of, 470, 489 rigidbody equilibrium and, 222 specific weight and, 488 weight (W) and, 29, 222, 465–466, 488, 524 Center of mass (Cm), 467, 470, 478, 523 Center of pressure (P), 513, 525 Centroid (C), 203, 222, 348, 464–527 area in x–y plane, 468, 470, 474–476, 523 axis of symmetry, 469, 488–489, 523 axial symmetry, 502–505, 523–524 beam crosssection location, 348 center of gravity (G) as, 222, 464–527 center of mass (Cm) of a body, 467, 470, 478, 523 composite bodies, 488–492, 524 composite shapes, 503 coplanar forces, 222 distributed loads and, 511–518, 525 distributed loads, 203 flat surfaces, 511 fluid pressure and, 512–518, 525 freebody diagrams for, 222 integration for determination of, 467–478, 523 line in xy plane, 468–473, 523 line of action for, 203, 513, 520, 525 location of, 203, 467–478, 523Index 655 mass of a body (Cm), 467, 469, 478 method of sections and, 348 Pappus and Guldinus, theorems of, 502–505, 524 plates, 511–518 procedure for analysis of, 470, 489 Pythagorean’s theorem for, 469 resultant forces and, 203, 348, 511–518, 525 rigidbody equilibrium and, 222 rotation of an axis, 502–505, 524 surface area and, 502, 504–505, 524 volume, of a, 467, 470, 503–505, 524 Centroidal axis, 530–531, 576 Coefficient of kinetic friction (μk), 406–407 Coefficient of rolling resistance, 452–453 Coefficient of static friction (μs), 405, 407, 447–448 Collar bearings, frictional analysis of, 447–449, 461 Collinear couple moment, 192 Collinear vectors, 41, 97 Commutative law, 41, 86, 146 Component vectors of a force, 40, 42–48, 97 Composite bodies, 488–492, 503, 524, 540–542, 568–570, 576–577 area (A) of, 503, 540–542, 576 axial symmetry and, 488–489, 503 center of gravity (G), 488–492, 524 centroid (C) of, 488–492, 503, 524 constant density and, 488 mass moments of inertia, 568–570, 577 moments of inertia (I), 540–542, 568–570, 576 procedure for analysis of, 489, 540 theorem of Pappus and Guldinus for parts of, 503 specific weight and, 488 weight (W) and, 488, 524 Compressive forces (C), 280–283, 296–297 method of joints and, 282–283 method of sections and, 296–297 truss members, 280–281 Concentrated force, 27 Concentrated loads, 372–373, 383–385, 399–400 cables subjected to, 383–385, 400 distributed loads, 372–373 sagging from, 383 shear and moment discontinuities from, 373, 399 Concurrent forces, 40, 55, 65–70, 105, 120–124, 131, 190–192, 240–241, 260 addition of vectors, 40, 65–70 Cartesian coordinate system for, 55, 65–70 constraints and, 260 equilibrium of, 108, 120–124, 131, 260 equivalent systems of, 190–192 freebody diagrams, 108, 120–124, 131 force and couple systems, simplification of, 190–192 lines of action for, 190 procedure for analysis of, 192 resultant couple moment, 190 statical determinacy and, 260 threedimensional systems, 65–70, 120–124, 190–192 threeforce members, 240–241 twodimensional coplanar resultants, 55 Connections, freebody diagrams of, 219–221. See also Joints; Support reactions Conservative forces, 597–598 friction as nonconservative, 598 spring force, 597 virtual work (U) and, 597–598 weight, 597 Constant density, center of gravity (G) and, 488 Constraints, 259–267, 276 improper, 260–261, 276 procedure of analysis of, 262 redundant, 259 statical determinacy and, 259–267, 276 support reactions and, 259–267 rigidbody equilibrium and, 259–267, 276 Continuous cables, 131 Coordinate direction angles, 66–67, 98–99 Coordinates, 65–70, 76–80, 98–99, 585–590, 600, 612. See also Cartesian coordinate system Cartesian, 65–70, 76–77, 79–80, 98–99 frictionless systems, 600 position, 76–77, 79–80, 585–590, 600, 612 potential energy and, 600 righthand rule for, 65 vector representation, 65–70, 76–78 virtual work for rigidbody connections, 585–590, 600, 612 x, y, z positions, 65–66, 76, 98–99 Coplanar distributed loads, 202–206 Coplanar forces, 54–59, 98, 107–111, 131, 179–184, 190–196, 202–206, 218–252, 275–276 addition of systems of, 54–59, 107 Cartesian vector notation, 55 center of gravity, 222 centroid (geometric center), 222 couple moments of, 179–184, 190–196 direct solution for unknowns, 230–239, 276 direction of, 54–55, 107 distributed load reduction, 202–206 equations of equilibrium, 107, 131, 230–239, 275 equilibrium of, 107–111, 131, 218–252, 275–276 equivalent systems of, 179–184, 190–196 freebody diagrams, 107–111, 219–228, 275 idealized models of, 222–223 internal forces and, 222656 Index Coplanar forces (Continued) lines of action, 179, 190–196 magnitude of, 55, 56, 107 particles subjected to, 107–111, 131 procedure for analysis of, 108, 181, 192, 224, 231 rectangular components, 54–59, 98 resultant couple moment, 190 resultants, 55–59, 179–184, 190–196, 202–206 rigid bodies, 218–252, 275–276 scalar notation, 54, 55 support reactions, 219–221, 275 system components, 54–59 systems, simplification of, 179–184, 190–196 twoand threeforce members, 240–241 vectors for, 54–59, 98 weight and, 222 Cosine functions, 617 Cosine law, 42, 44, 97 Cosines, direction of, 66–67 Coulomb friction, 403. See also Dry friction Couple, 167 Couple moments (M0), 167–172, 179–184, 190–196, 212–213, 217–219, 374, 582–583 collinear, 192 concurrent force system simplification, 190–192, 213 coplanar force system simplification, 179–184, 190–196, 212–213 distributed loading, 179–184, 190–196, 212–213, 374 equivalent couples, 168 equivalent systems, 179–184, 190–196, 212–213 force systems and, 167–172, 217–218 free vectors, 167 internal forces and, 374 parallel force system simplification, 191–192, 213 procedure for analysis of, 181, 192 resultants, 168–169, 190–196 righthand rule for, 167 rigid bodies, equilibrium of, 217–218 rotation of, 219, 582–583 scalar formulation of, 167 shear and moment diagrams, 374 shear load (V) relationships, 374 support reactions and, 219 systems, simplification of, 179–184, 190–196, 212–213 threedimensional systems, 179–184, 190–196, 213 translation of, 219, 582 vector formulation of, 167–172 virtual work of, 583 work of, 582 wrench, reduction of forces to, 192, 213 Cross product, 145–147 Cartesian vector formulation, 146–147 direction for, 145 laws of operation, 146 magnitude for, 145 righthand rule for, 145–146 vector multiplication using, 145–147 Curved plates, fluid pressure and, 514 Cylinders, rolling resistance of, 452–453 D Deformation, rolling resistance and, 452, 461 Derivatives, 618 Derived units, 29–31 Dimensional homogeneity, 32 Direct solution for unknowns, 230–239, 276 Direction, 39, 55–56, 66–68, 76–78, 87–90, 97–99, 105, 107, 136, 145, 148, 158–160, 167, 211, 219, 407, 409, 430, 432–434, 460 axis, moment of a force about, 158–160 Cartesian coordinate vectors, 66–68, 76–78, 98 Cartesian vector notation, 55 coordinate direction angles, 66–67, 98 coplanar force systems, 55–56, 107 cross product and, 145 dot product applications, 87–90 equilibrium and, 105, 107, 219 force vector along a line, 78 freebody diagrams, 105, 107, 219 frictional forces, 407, 409, 430, 432–434, 460 horizontal angle u, 56 impending motion and, 432–434, 460 line of action, 39–40, 78, 99, 148, 158–160 moment of a couple, 167 moment of a force (MO), 136, 148, 158–160, 211 position vectors, 76–77, 99 righthand rule for, 65, 145, 148, 158–160, 167, 211 screws, impending motion of, 432–434, 460 threedimensional systems, 66–68 translation, 219 vector sense of, 39, 55–56, 97 vertical angle f, 56 Direction cosines, 66–67 Disks, 447–449, 461, 564, 566, 577 frictional analysis of, 447–449, 461 mass moments of inertia, 564, 566, 577 Displacement (d), 583–590, 600, 612 frictionless systems, 600 potential energy and, 600 principle of virtual work and, 583–590, 612Index 657 procedure for analysis of, 586 rigid bodies, connected systems of, 585–590 virtual work (U) and, 583–590, 600, 612 virtual work equations for, 583–584, 586 Distributed loads, 202–206, 213, 372–377, 386–389, 399–400, 511–518, 525 axis (single) loading, 202 beams subjected to, 372–377, 399–400 bending moment (M) relationships, 372–377, 400 cables subjected to, 386–389, 400 center of pressure (P), 512, 525 centroid (C) of, 203, 213, 511–518, 525 concentrated loads and, 372–373, 399–400 coplanar, 202, 213 couple moment (M0) relationships, 374 fluid pressure from, 512–518, 525 force equilibrium, 372–374 force system resultants, 202–206, 213 incompressible fluids, 512 internal forces, 372–377, 386–389, 399–400 linearly, 513, 525 line of action of, 203, 213 loading curve for, 203, 213 magnitude and, 202, 511, 525 reduction of forces, 202–206, 213 resultant forces of, 202–206, 213, 511, 525 shear and moment diagrams, 372–377, 399–400 shear force (V) relationships, 372–377, 400 uniform, 372, 525 Distributive law, 86, 146, 150 Dot notation, 31 Dot product, 86–90, 99, 159 angles between intersecting lines, 87, 99 applications of, 87–90 Cartesian vector formulation, 86, 99 laws of operation, 86 moment about a specified axis, 159 projections, parallel and perpendicular, 87–88, 99 unit vectors and, 86–87, 99 vector angles and direction from, 86–90, 99 Dry friction, 403–463 angles (u) of, 405–406 applied force (P) and, 404–407, 459–461 bearings, analysis of, 447–451, 461 belts (flat), analysis of, 439–441, 460 collar and pivot bearings, analysis of, 447–449, 461 characteristics of, 403–407, 459 coefficients of (μ), 405–407, 459 direction of force, 407, 409 disks, analysis of, 447–449, 461 equations for friction versus equilibrium, 409–416 equilibrium and, 404–405, 409 frictional force, 404–407, 450 impending motion, 405, 408–416, 432–434, 459–460 journal bearings, analysis of, 450–451, 461 kinetic force (Fk), 406–407, 459 motion and, 405–416, 432–434, 447–453 problems involving, 408–416 procedure for analysis of, 411 rolling resistance and, 452–453, 461 screws, forces on, 432–434, 460 sliding and, 406–416, 459 slipping and, 405, 407–409, 459 static force (Fs), 405, 407, 459 theory of, 404 tipping effect, balance of, 404, 459 wedges and, 430–431, 460 Dynamics, study of, 24–26 E Elastic potential energy (Ve), 598 Engineering notation, 32 Equations of equilibrium, 103, 107–108, 120–124, 218, 230–239, 258, 275–276, 409–416 alternative sets for, 230–231 body at rest (zero), 218 coplanar force systems, 107–108, 230–239, 275–276 direct solution, 230–239, 276 direction and, 107 frictional equations and, 409–416 magnitude and, 107 particles, 103, 107–108, 120–124 procedure for analysis using, 108, 120, 231, 411 rigid bodies, 218, 230–239, 275–276 scalar form, 258, 275–276 threedimensional force systems, 120–124, 258, 276 twoand threeforce members, 240–241 vector form, 258, 276 Equilibrium, 25, 102–133, 216–277, 372–373, 404–405, 409, 600–606, 613 concurrent forces, 105, 120–124, 131, 260 conditions for, 103, 217–218, 230 constraints, 259–267 coplanar force systems, 107–111, 131, 218–252, 275–276 direction and, 105, 107, 219 distributed load relationships, 372–373 freebody diagrams, 104–111, 120–124, 219–228, 253–257, 275–276 friction and, 404–405, 409 frictionless systems, 600658 Index Equilibrium (Continued) idealized models for, 222–223 impending motion and, 409 improper constraints and, 260–261, 276 neutral, 601–602, 613 one (single) degreeoffreedom system, 602–603 particles, 102–133 potentialenergy (V) criterion for, 600, 613 procedures for analysis of, 108, 120, 224, 231, 262, 603 redundant constraints and, 259 rigid bodies, 216–277 shear and moment diagrams, 372–373 stability of systems, 260–261, 276, 601–606, 613 stable, 601–603, 613 statical determinacy and, 259–267, 276 statics and, 25 support reactions, 219–221, 253–257, 259–267, 275–276 threedimensional force systems, 120–124, 131, 253–267, 276 tipping effect, balance of, 404, 459 twoand threeforce members, 240–241 twodimensional force systems, 107–111, 131 unstable, 602–603, 613 virtual work (U) and, 600–606, 613 zero condition, 103, 107, 131, 218 Equivalent couples, 168 Equivalent systems, 179–184, 190–196 concurrent force systems, 190–192 coplanar force systems, 179–184, 190–196 external effects of, 179 force and couple moment simplification, 179–184, 190–196 lines of action of, 179, 190–196 parallel force systems, 191–192 principle of transmissibility for, 179 procedures for analysis, 181, 192 system of force and couple moments, 180 threedimensional systems, 179–184, 190–196 wrench, reduction to, 192 Exponential notation, 31 External effects for equivalent systems, 179 External forces, 217, 283, 296 F Fixed supports, 219, 221, 255 Flat belts, frictional analysis of, 439–441, 460 Flat plates, 511, 513, 515–516, 525 constant width, 513 distributed loads on, 511, 525 fluid pressure and, 513, 515–516, 525 variable width, 515 Floor beams, truss analysis and, 280 Fluid pressure, 512–518, 525 acceleration due to gravity (g), 513 center of pressure (P), 513 centroid (C), 512–518, 525 curved plate of constant width, 514 flat plate of constant width, 513 flat plate of variable width, 515 incompressible fluids, 512 line of action, 513 Pascal’s law, 512 plates, 512–518, 525 resultant forces and, 512–518, 525 Force, 25–29, 38–215, 217–218, 222, 240–241, 279–305, 310–341, 346–463, 511–518, 525, 581–583, 585–590, 597–598 active, 105 addition of vectors, 40–48, 54–59, 68–70 applied (P), 404–407, 430–431, 459–460 axis, about a specified, 158–162, 202, 212 basic quantity of mechanics, 26 beams, 347–382, 398–399 bending moments (M) and, 348–349, 372–377, 398, 400 by inspection, 282, 288–289 cables, 104, 109, 383–397, 400 Cartesian vector notation for, 55, 76–81, 149 components of, 42–48, 54–59, 97 compressive (C), 280–283, 296–297 concentrated, 27, 372–373, 383–385, 399–400 concurrent, 40, 55, 65–70, 99, 190–192, 260 conservative, 597–598 coplanar, 54–59, 98, 107–111, 131, 179–184, 190–196, 202–206, 213 couple moments and, 167–172, 179–184, 190–196, 212–213, 217–218 cross product, 145–147 directed along a line, 78–81 displacements from, 585–590 distributed loads, 202–206, 213, 372–377, 386–389, 400, 511–518 dot product, 86–90, 99 equilibrium and, 102–133, 217–218, 240–241, 372–373 equivalent systems, reduction to, 179–184, 190–196 external, 217, 283, 296 fluid pressure, 512–518, 525 frames, 310–325 freebody diagrams, 104–111, 120–124, 131, 222, 310–341, 347–349 friction as, 402–463, 598 frictional, 404–407, 459 gravitational, 29 idealized models for, 222–223 internal, 222, 296–298, 346–401Index 659 kinetic frictional (Fk), 406–407, 459 line of action, 39–40, 78, 99, 148–149, 158–160, 179, 190–196, 203, 212 machines, 310–325 mechanics of, 25 method of joints and, 282–290 method of sections for, 296–301, 347–354, 364 moment (M) of, 135–139, 148–152, 158–162, 167–172, 179–184, 190–199, 211–212, 348–349, 398, 400 motion and, 405–407 multiforce members, 310 Newton’s laws, 28–29 nonconservative, 598 normal (N), 104, 348–349, 398, 404–406 parallel systems, 191–192 parallelogram law for, 40, 42–44, 97 particles subjected to, 102–133 position vectors and, 76–77, 79–80, 99 principle of moments, 137–139, 150 principle of transmissibility, 148, 179 procedures for analysis of, 44, 105, 108, 181, 192, 231, 316, 349 pulleys, 104, 110 reactive, 105 rectangular components, 54–70, 98–99 resultant, 40, 42–48, 55–59, 97, 99, 134–215, 348–349, 511–518, 525 rigid bodies, equilibrium of, 217–218, 222–223 scalar notation for, 54, 55 scalar formulation, 39, 40, 86, 97, 135–136, 158, 167, 211 shear (V), 348–349, 372–377, 398, 400 simplification of systems, 179–184, 190–196, 213 smooth surface contact, 104 spring (Fs), 104, 597 springs, 104, 111 static frictional (Fs), 405, 407, 459 structural analysis and, 279–305, 310–341, 347–354 structural members, 240–241, 279–290, 296–301, 347–382 systems of, 54–59, 134–215 tensile (T), 280–283, 296–297, 439–441 threedimensional systems, 65–70, 76–80, 120–124, 131, 179–184, 190–196, 212 trusses, 279–305, 342–343 twoand threeforce members, 240–241 unbalanced, 28 units of, 30–31 unknown, 282–287, 296–301 vector formulation, 38–133, 145–152, 159–162, 167–172, 211 virtual work (U) and, 581–583, 585–590, 597–598 weight, 29, 222, 390–393, 400, 597 work (W) of, 581–583 wrench, reduction to, 192 Frames, 310–325, 343 freebody diagrams for, 310–316, 343 multiforce members of, 310, 343 procedure for analysis of, 316 structural analysis of, 310–325, 343 Freebody diagrams, 104–116, 120–124, 131, 219–228, 230–239, 253–257, 259–267, 275–276, 296–301, 310–316, 342–343, 347–354, 398, 585–590 beams, 347–354, 398 cables, 104, 109 center of gravity, 222 centroid (geometric center), 222, 348, 398 concurrent forces, 120–124 coplanar force systems, 107–111, 131, 219–228, 230–239, 275–276 constraints, 259–267, 276 direction and, 105, 107, 219 equilibrium and, 104–116, 120–124, 131, 219–228, 230–239, 253–257, 259–267, 275–276 external forces and, 296–297 frames, 310–316, 343 idealized models of, 222–223 internal forces and, 222, 296–297, 347–354, 398 machines, 310–316, 343 method of sections using, 296–301, 347–354 particle equilibrium, 104–106 procedures for analysis using, 105, 108, 120, 224, 231, 262, 298, 316 pulleys, 104, 110 rigid bodies, 219–228, 230–239, 253–257, 259–267, 275–276 smooth surface contact, 104 springs, 104, 111 statical determinacy and, 259–267, 276 structural analysis using, 296–301, 310–316, 342–343 support reactions, 219–221, 253–257, 259–267, 275–276 threedimensional systems, 120–124, 131, 253–257, 276 trusses, 296–301 virtual work, 585–590 weight and, 222 Free vector, 167, 224 Friction (F), 402–463, 598 angles (u) of, 405–406 applied force (P), 404–407, 430–431, 459–460 axial loads and, 447–449 bearings, analysis of, 447–451, 461 belts (flat), forces on, 439–441, 460 characteristics of, 403–407, 459 coefficients of (μ), 405–407, 447–448, 459 collar bearings, analysis of, 447–449, 461 Coulomb, 403660 Index Friction (F) (Continued) disks, analysis of, 447–449, 461 dry, 403–463 equations for friction and equilibrium, 409–416 equilibrium and, 404–405, 409 impending motion, 405, 408–416, 432–434, 459–460 journal bearings, analysis of, 450–451, 461 kinetic force (Fk), 406–407, 459 lateral loads and, 450–451 nonconservative force, as a, 598 point of contact, 403–409, 452–453, 459 pivot bearings, analysis of, 447–449, 461 procedure for analysis of, 411 rolling resistance and, 452–453, 461 screws, forces of, 432–434, 460 shaft rotation and, 447–451, 461 sliding and, 406–416, 459 slipping and, 405, 407–409, 459 static force (Fs), 405, 407, 459 virtual work (U) and, 598 wedges and, 430–431, 460 Frictional circle, 450 Frictional force, 404–407, 459 Frictionless systems, 600 G Geometric center, 203, 222, 348. See also Centroid (C) Gravitational attraction, Newton’s law of, 29 Gravitational potential energy (Vg), 598 Gravity, see Center of gravity (G) Gusset plate, 280–281 H Hinge connections, 221, 253, 255–256 Hyperbolic functions, 618 I Idealizations (models) for mechanics, 27, 222–223 Impending motion, 405, 408–416, 432–434, 459–460 all points of contact, 408 angle of static friction for, 405 coefficient of static friction (μs) for, 405, 459 downward, 433, 460 dry friction problems due to, 408–416 equilibrium and frictional equations for, 409–416 friction and, 405, 408–416, 432–434, 459–460 no apparent, 408 points of contact, 405, 408–409 procedure for analysis of, 411 screws and, 432–434, 460 slipping, verge of, 405 tipping and, 409 upward, 432–433, 460 Inclined axes, moment of inertia for area about, 552–554 Incompressible fluids, 512 Inertia, see Moments of inertia Integrals, 529, 619 Integration, 467–478, 511, 515, 525, 529–535, 563, 576–577 area (A), centroid of, 468, 474–476, 529–535 center of mass (Cm), determination of using, 467, 478 centroid (C), determination of using, 467–478, 511, 515, 525, 576 distributed loads, 511, 515, 525 fluid pressure distribution from, 515, 525 line, centroid of, 468–469, 471–473 mass moments of inertia, determination of using, 563, 577 moments of inertia, determination of using, 529–535, 576 parallelaxis theorem, 530–531, 576 procedure for analysis using, 470, 532 resultant forces determined by, 511, 515 volume (V), centroid of, 467, 477 volume elements for, 563 Internal forces, 222, 296–297, 346–401 beams subjected to, 347–382, 398–399 bending moments (M) and, 348–349, 372–377, 398, 400 cables subjected to, 383–397, 400 compressive (C), 296 concentrated loads, 372–373, 383–385, 399–400 couple moment (M0) and, 374 distributed loads, 372–377, 386–390, 399–400 force equilibrium, 372–373 freebody diagrams, 222, 296–297, 347–354, 398 method of sections and, 296–297, 347–354, 364 moments (M) and, 348–349, 372–377, 398–400 normal force (N) and, 348–349, 398 procedures for analysis of, 349, 364 resultant loadings, 348–349, 398 rigidbody equilibrium and, 222 shear and moment diagrams, 363–366, 372–377, 399–400 shear force (V) and, 348–349, 372–377, 398, 400 sign convention for, 349, 399 structural members with, 296–297, 347–354, 398 tensile (T), 296 torsional (twisting) moment, 348, 398 weight, 390–393, 400 International System (SI) of units, 29–31 J Joints, 279–282, 290. See also Method of joints equilibrium of, 282–283 loadings at, 280–281 pin connections, 280–281 procedure for analysis of, 283 truss analysis and, 279–290 unknown forces, 282–287Index 661 zeroforce members, 288–290 Joules (J), unit of, 582 Journal bearings, 254–256, 450–451, 461 freebody diagrams, 254–256 frictional analysis of, 450–451, 461 support reactions, 254–256 K Kinetic frictional force (Fk), 406–407, 459 L Lateral loads, friction analysis of, 450–451 Lead of a screw, 432 Lead angle, 432 Length, 26, 30–31, 468–473, 523 basic quantity of mechanics, 26 centroid (C) of lines, 468–473, 523 integration for, 468–469, 471–473, 523 procedure for analysis of, 470 Pythagorean theorem for, 469 units of, 30–31 Line of action, 39–40, 78, 99, 148–149, 158–160, 179, 190–196, 212, 511, 513, 525 centroid (C) location from, 203, 511 collinear vectors, 40 distributed loads, 511, 513, 525 fluid pressure and, 513 force and couple system simplification, 179, 190–196 force vector directed along, 78, 99 moment forcevector formulation, 148–149 moment of a force about an axis, 158–160, 212 perpendicular to force resultants, 190–196 principle of transmissibility, 148, 179 resultant force, 203, 511 vector representation of, 39–40, 78, 99, 159–160 Linear elastic behavior, 104 Linear load distribution, 513, 525 Lines, centroid (C) of, 468–473. See also Length integration for, 468–469, 471–473 procedure for analysis of, 470 Loading curve, 203, 213 Loads, 202–206, 279–281, 347–354, 372–377, 383–400, 447–451, 511–518, 525. See also Distributed loads axial, 447–449 beams, 347–354, 372–377, 398–399 cables, 383–397, 400 concentrated, 372–373, 383–385, 399–400 distributed, 202–206, 372–377, 386–389, 399–400, 511–518 fluid pressure, 512–518 friction (F) and, 447–451 internal, 347–354 lateral, 450–451 linear distribution of, 513, 525 moment (M) relations with, 373–377, 400 plates, 511–518, 525 resultant forces, 202–206, 511–518 reduction of distributed, 202–206 shaft rotation and, 447–451 shear (V), 372–377, 398, 400 single axis representation, 202 structural analysis and, 279–281 threedimensional, 348, 398 truss joints, 279–281 uniform, 525 units of, 202 weight, 390–393, 400 M Machines, 310–325, 343 freebody diagrams for, 310–316, 343 multiforce members of, 310, 343 vector formulation, 38–133, 145–152, 159–162, 167–172, 211 procedure for analysis of, 316 structural analysis of, 310–325, 343 Magnitude, 39, 42–48, 54–56, 66–67, 105, 107, 131, 136, 145, 148, 167, 202–203, 211, 511, 525 Cartesian vectors, 55, 66–68 coplanar force systems, 54–56, 107 constant, 131 couple moments, 167 cross product and, 145 distributed load reduction and, 202–203, 511, 525 equilibrium and, 105, 107 force components, 42, 44, 54–56, 105 freebody diagrams, 105, 107 integration for, 511, 525 moments and, 136, 145, 148, 211 Pythagorean theorem for, 56 resultant forces, 42, 44, 202–203, 511, 525 righthand rule for, 148 sine and cosine laws for, 42, 44 vector force addition and, 42, 44–48 vector representation of, 39, 42, 44, 54–56, 66 units of, 136 Mass, 26, 30, 467, 470, 478, 523 basic quantity of mechanics, 26 center of (Cm), 467, 470, 478, 523 integration of, 467, 478, 523 units of, 30 Mass moments of inertia, 563–570, 577 axis systems, 563–570, 577 composite bodies, 568–570, 577 disk elements, 564, 566, 577662 Index Mass moments of inertia (Continued) integration for, 563, 577 parallelaxis theorem for, 567 procedure for analysis of, 564 Pythagorean theorem for, 567 radius of gyration for, 568 shell elements, 564–565, 577 volume elements for integration, 563 Mathematical expressions, 616–619 Mechanics, study of, 25 Members, 240–241, 279–290, 296–301, 310–325, 343, 347–354, 398. See also Beams compressive force (C), 280–282, 296–297 equilibrium of forces, 240–241 frame analysis, 310–325, 343 internal loads(forces) in, 296, 347–354, 398 joint connections, 279–290 machine analysis, 310–325, 343 method of sections for, 296–301 multiforce, 310, 343 pin connections, 280–281 procedure for analysis of, 349 tensile force (T), 280–281 threeforce, 240–241 truss analysis, 279–290, 296–301 twoforce, 240–241 unknown forces, 282–287, 296–301 zeroforce, 288–290 Method of joints, 282–290, 306–307, 342 compressive forces, 282–283 procedures for analysis using, 283, 306 space truss analysis, 306–307 structural analysis using, 282–290, 306–307, 342 tensile forces, 282–283 truss analysis, 282–290, 306–307, 342 unknown forces, 282–287 zeroforce members for, 288–290 Method of sections, 296–301, 306, 342, 347–354, 364 beam analysis using, 347–354, 364 compressive forces (C), 296–297 external forces and, 296–297 internal forces and, 296–297, 347–354 freebody diagrams for, 296–301, 347–354 procedures for analysis using, 298, 306, 349 shear and moment diagrams from, 364 space truss analysis, 306 structural analysis using, 296–301, 306, 342, 347–354 tensile forces (T), 296–297 truss analysis, 296–301, 306, 342 unknown member forces, 296–301 Models (idealizations), 27, 222–223 Mohr’s circle, 555–557 Moment arm (perpendicular distance), 135–137, 158, 212 Moment axis, 136, 148, 158–162, 212 direction and, 136, 148 force about a, 158–162, 212 forcevector formulation and, 148 righthand rule for, 136, 148, 158–160 scalar analysis of, 158 vector analysis of, 159–162 Moments (M), 134–215, 348–349, 372–377, 398, 400. See also Couple moments bending (M), 348–349, 372–377, 398, 400 concentrated load discontinuities, 373 couple (M0), 167–172, 179–184, 190–196, 212–213, 374 cross product for, 145–147 direction and, 136, 145, 148, 211 distributed loads and, 202–206, 213, 372–377, 400 equivalent systems, reduction to, 179–184, 190–196 force, of, 134–215 forcevector formulation, 148–152 free vector, 167 internal forces and, 348–349, 372–377, 398, 400 magnitude and, 136, 145, 148, 211 normal force (N) and, 348–349 parallel force systems, 191–192 perpendicular to force resultants, 190–196 principle of moments, 137–139, 150, 211 principle of transmissibility, 148, 179 procedures for analysis of, 181, 192 righthand rule for, 136–137 resultant forces and, 136, 149, 168–169, 202–206 scalar formulation of, 135–136, 158, 167, 211 shear loads (V) and, 348–349, 372–377, 400 sign convention for, 136, 146 system simplification of, 179–184, 190–196, 212–213 torque, 136 torsional (twisting), 348, 398 Varignon’s theorem, 137–139 vector formulation of, 148–152, 159–162, 167–172, 211 wrench, reduction of force and couple to, 192 Moments of inertia (I), 529–579 algebraic sum of, 540 area (A), 530–535, 540–542, 548–554, 576 axis of symmetry, 548–551, 563–570, 596 axis systems, 529–535, 540–542, 563–570 composite bodies, 540–542, 568–570, 576–577 disk elements, 564, 566 inclined axis, area about, 552–554 integrals, 529 integration and, 529–535 mass, 563–570, 577Index 663 Mohr’s circle for, 555–557 parallelaxis theorem for, 530–532, 540, 549, 567, 576 polar, 530–531 principle, 553–554, 556, 577 procedures for analysis of, 532, 540, 556, 564 product of inertia and, 548–551, 555–556, 576 radius of gyration for, 531, 568 shell elements, 564–565, 577 transformation equations for, 552–553, 577 Motion, 28, 405–416, 430–434, 439–441, 447–453, 459–461. See also Revolution; Shaft rotation bearings, 447–451, 461 belt drives, 439–441, 460 coefficients of friction (μ) and, 405–407, 452–453, 459 downward, 433, 460 equilibrium and frictional equations for, 409–416 friction and, 405–416, 430–434, 439–441, 447–453, 459–461 impending, 405, 408–416, 432–434, 459–460 kinetic frictional force (Fk), 406–407, 459 Newton’s laws of, 28 points of contact, 405–409 procedure for analysis of, 411 rolling resistance and, 452–453, 461 screws and, 432–434, 460 selflocking mechanisms, 430, 433 shaft rotation, 447–451, 461 sliding, 406–416, 459 slipping (impending), 405, 408–409, 459 static frictional force (Fs), 405, 407, 459 upward, 432–433, 460 verge of sliding, 405 wedges, 430–431, 460 Movement, virtual, 583 Multiforce members, 310. See also Frames; Machines N Neutral equilibrium, 601–602 Newton, unit of, 30 Newton’s laws, 26, 28–29 dynamics and, 26 gravitational attraction, 29 motion, 28 Nonconservative force, friction as a, 598 Normal force (N), 348–349, 398, 404–406 dry friction and, 404–406 equilibrium and, 404 impending motion and, 405–406 internal forces as, 348–349, 398 method of sections for, 348–349, 398 Numerical calculations, importance of, 32–33 P Pappus and Guldinus, theorems of, 502–505, 524 axial revolution and symmetry, 502–505, 524 centroid (C) and, 502–505, 524 composite shapes, 503 surface area and, 502, 504–505, 524 volume and, 503–505, 524 Parallelaxis theorem, 530–532, 540, 549, 567, 576 area (A) and, 530–532, 540, 549, 576 centroidal axis for, 530–532, 576 composite parts, 540 mass moments of inertia determined by, 567 moments of inertia determined by, 530–532, 540, 567, 576 product of inertia determined by, 549, 576 Parallel force systems, 191–192, 240 equilibrium of, 240, 260–261 improper constraints, 260–261 reactive, 260–261 threeforce members, 240 simplification of, 191–192 Parallelogram law, 40, 42–44, 97 Particles, 27–29, 102–133 coplanar force systems, 107–111, 131 defined, 27 equations of equilibrium, 103, 107–108, 120–124 equilibrium of, 102–133 freebody diagrams, 104–106 gravitational attraction, 29 idealized model of, 27 Newton’s laws applied to, 28–29 nonaccelerating reference of motion, 28 procedures for analysis of, 105, 120 threedimensional force systems, 120–124, 131 twodimensional force systems, 107–111, 131 zero condition, 103, 131 Pascal’s law, 512 Perpendicular distance (moment arm), 135–137, 158, 212 Pin connections, 219–221, 223, 253, 255–256, 280–281 concurrent forces of, 280–281 coplanar systems, 219–221, 223 freebody diagrams of, 219–221, 253, 255–256 threedimensional systems, 253, 255–256 truss member analysis, 280–281 Pivot bearings, frictional analysis of, 447–449 Planar truss, 279 Plates, 511–518, 525 flat of constant width, 513 distributed loads on, 511, 525 centroid (C), 511–518, 525 curved of constant width, 514664 Index Plates (Continued) flat of constant width, 513 flat of variable width, 515 fluid pressure and, 512–518, 525 linear distribution on, 513, 525 resultant forces acting on, 511–518, 525 Point of contact, 403–409, 452–453, 459 friction and, 403–409, 452–453, 459 impending motion (slipping), 405, 408–409 kinetic friction and, 406–407 motion (sliding), 406–407 rolling resistance and, 452–453 static friction and, 405, 407 Polar moments of inertia, 530–531 Position coordinates, 585–590, 600, 612 Position vectors (r), 76–77, 79–80, 99 Cartesian vector form, 76–77, 79–80, 99 headtotail addition, 76–77 x, y, z coordinates, 76, 99 Potential energy (V), 598–606, 613 elastic (Ve), 598 equilibrium, criterion for, 600, 613 equilibrium configurations, 601–606 frictionless systems, 600 gravitational (Vg), 598 position coordinates for, 600 potential function equations, 599 procedure for analysis of, 603 single (one) degreeoffreedom systems, 599, 602–603 stability of systems and, 601–606, 613 virtual work (V) and, 598–606, 613 Powerseries expansions, 618 Pressure, see Fluid pressure Principal axes, 553–557, 576 Mohr’s circle for, 555–557 principal moment of inertia and, 553–557 procedure for analysis of, 556 product of inertia for, 553, 576 Principle moments of inertia, 553–554, 556, 577 Mohr’s circle for, 555–557 principal axes, 553–554, 556, 577 procedure for analysis of, 556 transformation equations for, 553, 577 Principle of moments, 137–139, 150, 211 Principle of transmissibility, 148, 179 Principle of virtual work, 581, 583–590, 612 Product of inertia, 548–551, 553, 555–556, 576 axis of symmetry for, 548–551 centroid for, 549, 576 Mohr’s circle and, 555–556 parallelaxis theorem for, 549, 576 procedure for analysis of, 556 principal axes and, 553 Procedure for analysis, 34–36 Projections, parallel and perpendicular, 87–88, 99, 159 Pulleys, freebody diagram of, 104, 110, 131 Purlins, 279 Pythagorean theorem, 56, 87, 469, 567, 617 Q Quadratic formula, 618 R Radius of gyration, 531, 568 Reactive force, 105, 260–261 Rectangular components, 54–70, 98–99 coplanar force systems, 54–59, 98–99 force vectors of, 54–70, 98–99 resultant force, 55–56, 98 Resultant forces, 40, 42–48, 55–59, 65–71, 97–98, 134–215, 348–349, 398, 511–518, 525 axis, moment of force about, 158–162, 202, 212 beams, 348–349 Cartesian vector components, 65–70 Cartesian vector notation for, 55 centroid (C) and, 203, 348, 511–518, 525 concurrent forces, 55, 65–70, 99, 190–192 coplanar forces, 55–56, 98, 179–184, 190–196 couple moments, 167–172, 179–184, 190–196, 213 cross product for, 146–147 direction of, 146, 211 distributed loads, 511–518, 525 fluid pressure and, 512–518, 525 force components and, 40, 42–44, 97 force system, 55–59, 99, 134–215 integration for, 511, 525 internal forces, 348–289, 398 lines of action, 158–160, 179, 190–196, 203, 511, 513 magnitude of, 146, 202, 211, 511, 525 method of sections for, 348–349 moments of a force, 135–139, 149, 158–162, 211, 348–349 parallel force systems, 191–192 parallelogram law for, 40, 42–44, 97 perpendicular to moments, 190–196 plates, 511–518, 525 principle of moments, 137–139, 211 procedure for analysis of, 44, 192 reduction of distributed loads, 202–206, 213 scalar formulation of, 135–136, 158, 167, 211 scalar notation for, 55 system reduction for, 179–184, 190–196, 213 vector addition for, 40–44, 55–59 vector formulation of, 42–48, 97, 148–152, 167–172, 211–212 vector subtraction for, 41 wrench, reduction to, 192, 213Index 665 Revolution, 502–505, 524 axial symmetry and, 502–505 centroid (C) and, 502–505, 524 composite shapes, 503 Pappus and Guldinus, theorems of, 502–505, 524 plane area, 503 surface area, 502, 504–505, 524 volume from, 503–505, 524 Righthand rule, 65, 136–137, 145–146, 148, 158–160, 167 axis, moment of a force about, 158–160 cross product direction, 145–146 forcevector formulation, 146, 148 moment of a couple, 167 moment of a force, 136–137, 158–160 threedimensional coordinate systems, 65 Rigid bodies, 25, 27, 216–277, 585–590, 600–606, 612 center of gravity, 222 centroid (geometric center), 222 conditions for, 217–218 connected systems of, 585–590, 612 constraints of, 259–267 coplanar force systems, 218–252, 275–276 defined, 27 displacement (d) and, 585–590, 600, 612 equations of equilibrium for, 218, 230–239, 275–276 equilibrium of, 216–277, 600–606 external forces and, 217 force and couple systems acting on, 217–218 freebody diagrams, 219–228, 253–257, 259–267, 275–276 frictionless systems, 600 idealized models of, 27, 222–223 internal forces and, 222 improper constraints for, 260–261, 276 mechanics, study of, 25 position coordinates for, 585–590, 600, 612 potential energy and, 600–606 procedures for analysis of, 224, 231, 262, 586, 603 redundant constraints for, 259 statical determinacy and, 259–267, 276 support reactions, 219–221, 253–257, 259–267, 275–276 threedimensional systems, 253–267, 276 twoand threeforce members, 240–241 uniform, 222 virtual work (V) for, 585–590, 600–606, 612 weight and, 222 Rocker connections, 220, 221 Roller connections, 219–220, 223, 254, 256 Rolling resistance, frictional forces and, 452–453, 461 Roof truss, 279–280, 342 Rotation, 219, 447–448, 450, 461, 582–583. See also Revolution; Shaft rotation Rounding off numbers, 33 S Scalar notation, 54, 55 Scalar product, 86 Scalar triple product, 159 Scalars, 39, 40, 54, 86, 107, 135–136, 158, 167, 211, 258, 275–276, 582 axis, moment of force about, 158 couple moments, formulation by, 167 division of vectors by, 40 dot product and, 86 equations of equilibrium, 258, 275–276 magnitude of, 39 moment of a force, formulation by, 135–136, 158, 211 multiplication of vectors by, 40, 86 negative, 54, 107 torque, 135 vectors and, 39, 40, 86 work of a couple moment, 582 Screws, frictional forces on, 432–434, 460 Selflocking mechanisms, 430, 433 Sense of direction, 39 Shaft rotation, 447–451, 461 axial loads, 447–449 collar and pivot bearings, 447–449, 460 disks, 447–449, 460 frictional analysis of, 447–451, 460 frictional circle, 450 journal bearings, 450–451, 460 lateral loads, 450–451 Shear and moment diagrams, 363–366, 372–377, 399–400 beam analysis using, 363–366, 372–377, 399 couple moment (M0) and, 374 discontinuities in, 373 distributed load relations and, 372–377, 400 internal forces and, 363–366, 372–377, 399–400 method of sections for, 364 moment (M) relations in, 373–377, 399–400 procedure for analysis of, 364 shear force (V) relations in, 372–377, 399–400 Shear force (V), 348–349, 372–377, 398–400 beams, 348–349, 372–377, 398 bending moments (M) and, 348–349, 372–377, 398, 400 concentrated load discontinuities, 373 couple moment (M0) and, 374 distributed load relations, 372–377, 400 internal forces, 348–349, 372–377, 398–400 method of sections for, 348–349 shear and moment diagrams, 372–377, 399–400 Shell elements, mass moments of inertia, 564–565, 577 Significant figures, 32–33 Simple trusses, 279–281, 342 Simply supported beam, 363 Sine functions, 617666 Index Sine law, 42, 44, 97 Single degreeoffreedom systems, 599, 602–603 Sliding, 405–416, 459–460 friction and, 405–416 kinetic frictional force (Fk), 406–407, 459 motion of, 406–416 problems involving, 408–416 verge of, 405 Sliding vector, 148, 179, 224 Slipping, 405, 407–416, 459 friction and, 405, 407–416, 459 impending motion of, 405, 408–409, 459 points of contact, 405, 408–409 problems involving, 408–416 static frictional force (Fs), 405, 407, 459 Smooth surface contact (support), 104, 254 Solving problems, procedure for, 34–36 Space trusses, structural analysis of, 306–307, 343 Specific weight, center of gravity (G) and, 488 Spring constant (k), 104 Spring force (Fs), virtual work and, 597 Springs, freebody diagram of, 104, 111, 131 Stable equilibrium, 601–603, 613 Stability of a system, 260–261, 276, 601–606, 613. See also Equilibrium equilibrium configurations for, 601–606, 613 freebody diagrams for, 260–261, 276 improper constraints and, 260–261 neutral equilibrium, 601–602, 613 one (single) degreeoffreedom system, 602–603 potential energy and, 601–606 procedure for analysis of, 603 reactive parallel forces, 260–261 rigidbody equilibrium and, 260–261, 276 stable equilibrium, 601–603, 613 statical determinacy and, 260–261, 276 unstable equilibrium, 601–603, 613 virtual work and, 601–606, 613 Static frictional force (Fs), 405, 407, 459 Statical determinacy, 259–267, 276 equilibrium and, 259–267 procedure for analysis of, 262 improper constraints and, 260–261 indeterminacy, 259, 276 redundant constraints and, 259 rigidbody equilibrium and, 259–267, 276 stability and, 260–261, 276 Statically indeterminate bodies, 259, 276 Statics, 24–37 basic quantities, 26 concentrated force, 27 equilibrium and, 25 force, 26–30 gravitational attraction, 29 historical development of, 26 idealizations, 27 length, 26, 29–31 mass, 26, 29–31 mechanics study of, 24–25 motion, 28 Newton’s laws, 28–29 numerical calculations for, 32–33 particles, 27 procedure for analysis of, 34–36 rigid bodies, 27 study of, 24–37 time, 26, 30 units of measurement, 29–31 weight, 29 Stiffness factor (k), 104 Stringers, 280 Structural analysis, 278–345, 347–382 beams, 347–382 compressive forces (C), 280–283, 296–297 frames, 310–325, 343 freebody diagrams, 296–301, 310–316, 342–343 internal forces and, 296–297, 347–382 machines, 310–325, 343 method of joints, 282–290, 306–307, 342 method of sections, 296–301, 306, 342, 347–354, 364 multiforce members, 310, 343 procedures for analysis of, 283, 298, 306, 316, 349, 364 shear and moment diagrams for, 363–366 space trusses, 306–307, 343 tensile forces (T), 280–283, 296–297 trusses, 279–309, 342–343 unknown forces, 282–287, 296–301 zeroforce members, 288–290 Structural members, see Members Support reactions, 219–221, 223, 253–257, 259–267, 275–276 coplanar force systems, 219–221, 223, 275 freebody diagrams, 219–221, 223, 253–257, 259–267, 275–276 improper constraints, 260–261 procedure for analysis of, 262 redundant constraints, 259 rigidbody equilibrium and, 219–221, 223, 253–257, 259–267 statical determinacy and, 259–267, 276 threedimensional force systems, 253–257, 259–267, 276 Surface area, centroid (C) and, 502, 504–505, 524 Symmetry, see Axial symmetry; Axis of symmetryIndex 667 System simplification, 179–184, 190–196 concurrent force system, 190–192 coplanar force systems, 179–184, 190–196 equivalent system, reduction to, 179–184, 190–196 lines of action and, 179, 190–196 parallel force systems, 191–192 procedures for analysis, 181, 192 reduction to a wrench, 192 system of force and couple moments, 180 threedimensional systems, 179–184, 190–196 T Tangent functions, 617 Tensile forces (T), 280–283, 296–297, 439–441 flat belts, 439–441 method of joints and, 282–283 method of sections and, 296–297 truss members, 280–281, 296–297 Tetrahedron form, 306 Thread of a screw, 432 Threedimensional systems, 65–70, 76–81, 86–90, 98–99, 120–124, 131, 179–184, 190–196, 253–267, 276. See also Concurrent forces addition of vectors, 68 Cartesian coordinate system for, 65–70, 98–99 Cartesian unit vectors, 65–66, 78, 98–99 Cartesian vector representation, 65–66 concurrent forces, 65–70, 99, 120–124, 131, 190–192, 276 constraints for, 259–267, 276 coordinate direction angles, 66–67, 98–99 direction angles for, 66–67 dot product for, 86–90, 99 equations of equilibrium, 120, 258, 276 equilibrium of, 120–124, 131, 253–267, 276 equivalent systems, 179–184, 190–196 force and couple moment system simplification, 179–184, 190–196 force vectors, 65–70, 78–81, 99 freebody diagrams, 120–124, 253–257, 276 magnitude of, 66 parallel system simplification, 191–192 particles, 120–124, 131 position vectors, 76–77, 79–80, 99 procedure for analysis of, 120 reactive parallel forces, 261 rectangular components, 65–70, 98–99 resultants, 65–70 righthand rule, 65 rigid bodies, 253–267, 276 statical determinacy and, 259–267, 276 support reactions for, 253–257, 259–267, 276 x, y, z position coordinates, 65–66, 76, 98–99 Threeforce member equilibrium, 240–241 Thrust bearing connections, 255, 256 Time, 26, 30 basic quantity of mechanics, 26 units of, 30 Tipping effect, balance of, 404, 459 Torque, 135. See also Moments (M) Torsional (twisting) moment, 348, 398 Transformation equations, moments of inertia (I) and, 552–553, 577 Translation, 219, 582 Trapezoid, distributed loading of, 206 Triangle rule, 41, 97 Triangular truss, 281 Trigonometric identities, 618 Trusses, 279–309, 342–343 assumptions for design, 280–281, 306 bridges, 279–280 compressive force (C) and, 280–283, 296–297 floor beams, 280 gusset plate for, 280–281 joints, 279–290 method of joints, 282–290, 306–307, 342 method of sections, 296–301, 306, 342 planar, 279 procedures for analysis of, 283, 298, 306 purlins, 279 roof, 279–280, 342 simple, 279–281, 342 space trusses, 306–307, 343 stringers, 280 structural analysis for, 279–309, 342–343 tensile force (T) and, 280–283, 296–297 triangular, 281 zeroforce members, 288–290 Twodimensional systems, 54–59, 98, 107–111, 218–252. See also Coplanar forces Cartesian unit vectors, 55, 98 coplanar force vectors, 54–59, 98 freebody diagrams for, 107–111 particle equilibrium, 107–111 procedure for analysis of, 108, 224, 231 rigidbody equilibrium, 218–252 scalar notation for, 54 Twoforce member equilibrium, 240–241 U Unbalanced force, 28 Uniform distributed load, 372, 525 Uniform rigid bodies, 222668 Index Unit vector (u), 55–56, 65–66, 78, 86–87, 98–99. See also Cartesian coordinates Cartesian vectors, 55–56, 65–66, 78, 98 dot product and, 86–87, 99 threedimensional, 65–66, 78, 98–99 force components, 55–56 force vectors, 78, 99 Units of measurement, 29–31 base, 29, 31 derived, 29–31 International System (SI) of, 30–31 prefixes, 30 rules for use, 31 Unknown member forces, 282–287, 296–301 Unstable equilibrium, 601–603, 613 V Varignon’s theorem, 137–139 Vectors, 38–101, 145–152, 159–162, 167–172, 211, 258, 276 addition of, 40–48, 54–59, 68–70 addition of forces, 42–48, 54–59 axis, moment of a force about, 159–162 Cartesian coordinate system, 55–58, 65–70, 76–81, 98, 145–152, 211 Cartesian notation for, 55 components of a force, 40, 42–48, 97 concurrent forces, 40, 55, 65–70, 99 coplanar force systems, 54–59 cross product method of multiplication, 145–147 collinear, 41, 97 couple moments, formulation by, 167–172 direction and, 39, 55–56, 66–68, 145, 148 division by scalars, 40, 97 dot product, 86–90, 99, 169 equations of equilibrium, 258, 276 force directed along a line
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