Preface viii Introduction x PART I STATICS Chapter 1 Resultant force and moment 1 1.1 Horizontal and vertical forces 1 1 .2 Components of a force 2 1 .3 Resultant of concurrent forces: Analytical solution 4 1 .4 Resultant of concurrent forces: Computer solution 5 1.5 Resultant of concurrent forces: Graphical solution 5 1.6 Moment of a force (M) 7 1 . 7 Resultant of parallel forces: Analytical solution 9 1.8 Resultant of parallel forces: Graphical solution 10 1.9 Resultant of forces (general case): Analytical solution 13 1.10 Resultant of forces (general case): Computer solution 15 1.11 Resultant of forces (general case): Graphical solution 17Problems 17Chapter 2 Equilibrium of forces 21 2.1 Systems of forces 21 2.2 Conditions for equilibrium 22 2.3 Equilibrant force 24 2.4 Equilibrant moment 262.5 The three force system 27 2.6 Members, joints and supports 30 2. 7 Determination of unknown forces 32Problems 39Chapter 3 Loads and support reactions 47 3.1 Types of load 48 3.2 Types of support 50 3.3 Cantilever beam reactions: Analytical solution 50 3.4 Cantilever beam reactions: Computer solution 53 3.5 Cantilever beam reactions: Graphical solution 54 3.6 Simply supported beams 54 3. 7 Simply supported beam reactions: Analytical solution 563.8 Simply supported beam reactions: Computer solution 57 3.9 Simply supported beam reactions: Graphical solution 58 3.10 Link or cable supported structures 59 3.11 Statically indeterminate beams 62Problems 63 iii
Chapter 4 Chapter 5 Forces in frame members 69 4.1 General principles 69 4.2 Method of joints: Analytical solution 73 4.3 Method of joints: Computer solution 78 4.4 Method of joints: Graphical solution 794.5 Combined force polygon 83 4.6 Method of sections 87 Problems 91 Shear force, bending moment and torque distribution diagrams 98 5.1 Shear force at any section 98 5.2 Bending moment at any section 995.3 Shear force and bending moment: Concentrated loads 100 5.4 Shear force and bending moment diagrams: Concentrated loads on a simply supported beam 100 5.5 Relationship between shear force and bending moment 104 5.6 Shear force and bending moment: Uniformly distributed loads 105 5.7 Shear force and bending moment diagrams: Uniformly distributed loads on a simply supported beam 106 5.8 Shear force and bending moment diagrams: Cantilever beam 110 5.9 Turning moment or torque (r) 113 5.10 Torque distribution diagrams 114 5.11 Combined shear force, bending moment and torque distribution diagrams 117 Problems 119 Chapter 6 Friction 126 6.1 Review of friction 126 6.2 Friction on the inclined plane 129 6.3 Wedges 133 6.4 Screw threads 139 6.5 Forces on a square screw thread 141 6.6 Efficiency of a screw thread 145 6.7 Forces on a vee screw thread 146 6.8 Band friction 147 6.9 Band brakes 149 6.10 Flat belt drives 153 6.11 Vee belt drives 155 6.12 Disc or collar friction 155 Problems 158
PART II DYNAMICS Chapter 7 Kinematics of motion 169 7 .1 Displacement (s) 169 7.2 Velocity (v) 170 iv
7 .3 Acceleration (a) 170 7 .4 Sign convention for displacemeI)t, velocity and acceleration 172 7 .5 Changes in velocity and acceleration 173 7 .6 Equations for common modes of motion 177 7. 7 Vector addition of motion 1797 .8 Relative motion 181 7 .9 Rotational motion 184 7. 10 Centripetal acceleration 1877 .11 Coriolis acceleration 188Problems 192Chapter 8 Dynamics of motion 196 8.1 Accelerating force 196 8.2 Inertia force 197 8.3 Acceleration on the inclined plane 202 8.4 Centrifugal force (Fe) 204 8.5 Rotation on the inclined plane 207 8.6 Accelerating torque and inertia torque: Point mass 210 8. 7 Rotating non-point mass and mass moment of inertia 2128.8 Calculation of the mass moment of inertia 213 8.9 Systems of connected masses: Translation 218 8.10 Systems of connected masses: Translation and rotation 2 22 Problems 225 Chapter 9 Momentum, energy and power 235 9.1 Momentum 235 9.2 Principle of momentum conservation 237 9.3 Mechanical energy 240 9.4 Work and power 241 9.5 Principle of energy conservation 245 9.6 Mechanical machines and efficiency 252 Problems 256 Chapter 10 Mechanical vibration 262 10.1 Definition of terms 263 10.2 Simple harmonic motion 263 10.3 Vibrating spring-mass system 268 10.4 Simple pendulum 271 10.5 Forced vibration 273 10.6 Resonance 275 Problems 279 Chapter 11 Balance and reaction of rotating masses 283 11 . 1 Static and dynamic balance 283 11 .2 Coplanar balance: Single mass 285 11.3 Coplanar balance: Multiple masses 286 11.4 Bearing reactions for coplanar masses 289 11.5 Balance of non-coplanar masses 292 11.6 Bearing reactions for non-coplanar masses 296 Problems 301
PART Ill STRENGTH OF MATERIALS Chapter 12 Stress and strain 307 12.1 Stress (j) 30712.2 Strain ( t) 31112.3 Relationship between stress and strain 31212.4 Non-uniform stress distributions 31512.5 Pressure stress 31812.6 Thermal stress 32012.7 Rotational stress 32212.8 Series bars: Axial stress 32512.9 Parallel bars: Axial stress 328Problems 330 Chapter 13 Strain energy and dynamic loads 337 13.1 Strain energy ( U) 337 13.2 Series and parallel bars 34013.3 Resilience 34113.4 The energy method 343 13.5 Suddenly applied loads 34513.6 Impact or dynamic loads 34713.7 Axial stress due to dynamic loads 34813.8 Axial stress due to suddenly stopped loads 351Problems 353Chapter 14 Centroid and second moment of area 356 14.1 Centroid ( C) 356 14.2 Location of the centroid: Analytical method 357 14.3 Centroid location for common shapes 359 14.4 Second moment of area ([) 361 14.5 Parallel axis theorem 363 14.6 Radius of gyration (k) 365 14. 7 Comparison of mass and area concepts 36614.8 Standard properties of sections 367 14.9 Computer solution 36814.10 Polar moment of inertia (J) 370 Problems 372 Chapter 15 Bending and shear in beams and shafts 375 15.1 Bending of beams 375 vi 15.2 Axial bending stress in beams 376 15.3 Curvature and bending moment 38015.4 Shear stress in beams 38215.5 Derivation of the shear stress formula 38315.6 Distribution of shear stress over a section 38715.7 Shear stress in fabricated beams 38815.8 Shafts in torsion 39015.9 Torsion in shafts with varying torque 394Problems 397
Chapter 16 Combined stress 402 16.1 Combined bending and axial stress 402 16.2 Combined pressure and axial stress 405 16.3 Combined bending and torsion 407 16.4 Stress on an inclined plane 413 16.5 Combined stress (general case) 415 16.6 Maximum stress 417 16. 7 Computer solution 42116.8 Graphical solution 42116.9 Combined bending and shear in beams 423Problems 426Chapter 17 Beam deflection 433 17 .1 Double integration method: Theory 434 17 .2 Macaulay's method (outline) 437 17 .3 Cantilever beam: Concentrated loads 437 17 .4 Cantilever beam: Distributed load 439 17.5 Cantilever beam: Combined loads 442 17 .6 Simply supported beam: Concentrated loads 444 17. 7 Simply supported beam: Distributed load 44717 .8 Simply supported beam: Combined loads 44817 .9 Computer solution 450Problems 451Chapter 18 Columns 456 18.1 Effective length of a column (L.) 456 18.2 Slenderness ratio 458 18.3 Slender column buckling 461 18.4 Thick column buckling 463 18.5 Limiting slenderness ratio 464 18.6 Column selection: General procedure 468 18. 7 Computer solution 470Problems 470Appendix 1 Principal symbols 474 Appendix 2 Principal formulas 477 Appendix 3 Computer programs 483 Index 541
