Engineering Mechanics: Statics

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 12
a. What is engineering mechanics?......Page 14
b. Problem formulation and the accuracy of solutions......Page 15
a. Scope of Newtonian mechanics......Page 16
d. Units and dimensions......Page 17
e. Mass, force, and weight......Page 18
g. Law of gravitation......Page 19
1.3 Fundamental Properties of Vectors......Page 23
a. Rectangular components and direction cosines......Page 31
c. Relative position vectors......Page 33
d. How to write a vector in rectangular form......Page 34
a. Dot (scalar) product......Page 40
b. Cross (vector) product......Page 42
c. Scalar triple product......Page 44
2.2 Equivalence of Vectors......Page 50
2.3 Force......Page 51
2.4 Reduction of Concurrent Force Systems......Page 52
b. Geometric interpretation......Page 62
d. Vector and scalar methods......Page 64
2.6 Moment of a Force about an Axis......Page 73
a. Definition......Page 74
b. Geometric interpretation......Page 75
c. Vector and scalar methods......Page 77
b. Moment of a couple about a point......Page 86
d. Notation and terminology......Page 88
e. The addition and resolution of couples......Page 89
2.8 Changing the Line of Action of a Force......Page 99
3.2 Reduction of a Force System to a Force and a Couple......Page 110
3.3 Definition of Resultant......Page 118
a. General coplanar force system......Page 119
b. Concurrent, coplanar force system......Page 120
c. Parallel, coplanar force system......Page 121
3.5 Resultants of Three-Dimensional Systems......Page 129
b. Parallel, three-dimensional force system......Page 130
c. General three-dimensional force system: The wrench......Page 131
a. Surface loads......Page 141
b. Line loads......Page 143
c. Computation of resultants......Page 144
4.1 Introduction......Page 156
4.3 Free-Body Diagram of a Body......Page 157
4.4 Coplanar Equilibrium Equations......Page 166
4.5 Writing and Solving Equilibrium Equations......Page 168
4.6 Equilibrium Analysis for Single-Body Problems......Page 179
4.7 Free-Body Diagrams Involving Internal Reactions......Page 192
4.8 Equilibrium Analysis of Composite Bodies......Page 203
4.9 Special Cases: Two-Force and Three-Force Bodies......Page 213
4.10 Description of a Truss......Page 227
4.11 Method of Joints......Page 228
4.12 Method of Sections......Page 237
5.1 Introduction......Page 250
5.3 Free-Body Diagrams......Page 251
a. General case......Page 262
b. Concurrent force system......Page 263
c. Parallel force system......Page 264
5.5 Improper Constraints......Page 265
5.6 Writing and Solving Equilibrium Equations......Page 266
5.7 Equilibrium Analysis......Page 276
*6.1 Introduction......Page 294
*6.2 Internal Force Systems......Page 295
*6.3 Analysis of Internal Forces......Page 304
*6.4 Area Method for Drawing V- and M-Diagrams......Page 316
*6.5 Cables under Distributed Loads......Page 331
*6.6 Cables under Concentrated Loads......Page 343
7.1 Introduction......Page 354
a. Static case......Page 355
d. Further discussion of Coulomb friction......Page 356
e. Limitations......Page 357
7.3 Problem Classification and Analysis......Page 358
7.4 Impending Tipping......Page 374
a. Angle of friction......Page 382
b. Wedges......Page 384
c. Square-threaded screws......Page 385
*7.6 Ropes and Flat Belts......Page 392
*7.7 Disk Friction......Page 399
*7.8 Rolling Resistance......Page 404
a. Definitions......Page 414
b. Integration techniques......Page 416
c. Composite shapes......Page 418
8.3 Centroids of Curved Surfaces, Volumes, and Space Curves......Page 432
8.4 Theorems of Pappus-Guldinus......Page 451
8.5 Center of Gravity and Center of Mass......Page 455
a. Center of gravity......Page 456
c. Composite bodies......Page 457
a. General case......Page 463
b. Normal loads on flat surfaces......Page 464
c. Line loads......Page 465
d. Uniform pressure on curved surfaces......Page 466
e. Fluid pressure......Page 467
9.1 Introduction......Page 484
a. Moment of inertia of area......Page 485
c. Parallel-axis theorems......Page 486
e. Integration techniques......Page 488
f. Method of composite areas......Page 489
a. Definition......Page 505
b. Parallel-axis theorem......Page 506
a. Transformation equations for moments and products of inertia......Page 513
b. Principal moments of inertia......Page 514
*9.5 Mohr’s Circle for Moments and Products of Inertia......Page 521
a. Construction of Mohr’s circle......Page 522
b. Properties of Mohr’s circle......Page 523
c. Verification of Mohr’s circle......Page 524
*10.1 Introduction......Page 536
b. Virtual motion of a rigid body......Page 537
a. Virtual work of a force......Page 538
b. Virtual work of a couple......Page 539
c. Virtual work performed on a rigid body......Page 540
a. Principle of virtual work......Page 541
c. Implementation of the method of virtual work......Page 542
*10.5 Instant Center of Rotation......Page 552
a. Potential energy......Page 561
d. Stationary potential energy and stability......Page 562
A.1 Introduction......Page 572
A.3 Simpson’s Rule......Page 573
B.2 Newton’s Method......Page 576
B.3 Secant Method......Page 577
Appendix C: Densities of Common Materials......Page 580
Answers to Even-Numbered Problems......Page 582
Index......Page 589