Mechanics of Solids - SS. Bhaivikatti
Preface
Mechanics of Solids is an important course for all engineering students by which they develop analytical skill. In this course, laws of mechanics are applied to parts of bodies and skill is developed to get solution to engineering problems maintaining continuity of the parts.
The author has clearly explained theories involved and illustrated them by solving a number of engineering problems. Neat diagrams are drawn and solutions are given without skipping any step. SI units and standard notations as suggested by Indian Standard Code are used throughout. The author has made this book to suit the latest syllabus of Gujarat Technical University.
Author hopes, the students and teachers of Gujarat Technical University will receive this book whole-heartedly as most of the earlier books of the author have been received by the students and teachers all over India.
The suggestions and corrections, if any, are most welcome. The author acknowledges the efforts of M/s. New Age International Publish- ers in bringing out this book in nice form. He also acknowledges the opportunity given by AICTE for associating him with B.U.B. Engineering College, Hubli.
Contents:
1 INTRODUCTION TO MECHANICS OF SOLIDS 1–14
1.1 Basic Terminologies in Mechanics ......... 2
1.2 Units ......................................................... 5
1.3 Scalar and Vector Quantities ................ 6
1.4 Composition and Resolution of Vectors ........ 6
Important Formulae .............................................. 13
Theory Questions .................................................. 14
Problems for Exercise ........................................... 14
2 FUNDAMENTALS OF STATICS 15–64
2.1 Principles of Statics .................................................................................. 152.2 System of Forces ....................................................................................... 182.3 Moment of a Force ................................................................................. 182.4 Varignon’s Theorem ................................................................................ 192.5 Couple ........................................................................................................ 222.6 Transfer of a Force to Parallel Position .............................................. 232.7 Composition of Concurrent Coplanar Forces......................................... 232.8 Equilibriant of a Force System .................................................................. 282.9 Composition of Coplanar Non-concurrent Force System ........................ 282.10 X and Y Intercepts of Resultant ............................................................... 292.11 Types of Forces on a Body ...................................................................... 382.12 Free Body Diagram ............................................................................... 402.13 Equilibrium of Bodies .......................................................................... 402.14 Equilibrium of Concurrent Force Systems ............................................ 412.15 Equilibrium of Connected Bodies ........................................................... 472.16 Equilibrium of Non-concurrent Force Systems ................................... 53Important Formulae .......................................................................................... 57Theory Questions .................................................................................................58Problems for Exercise ......................................................................................... 59
3 TRUSSES 65–93
3.1 Perfect, Deficient and Redundant Trusses ................................................ 65
3.2 Assumptions ............................................................................................... 66
3.3 Nature of Forces in Members ............................................................................. 67
3.4 Methods of Analysis ................................................................................... 68
3.5 Method of Joints ................................................................................................. 68
3.6 Method of Section ............................................................................................... 81
Important Formula .................................................................................................... 87
Theory Questions ........................................................................................................ 87
Problems for Exercise ................................................................................................. 88
4 DISTRIBUTED FORCES, CENTRE OF GRAVITY AND MOMENT 94–160 OF INERTIA
4.1 Determination of Areas and Volumes ..................................................................... 94
4.2 Centre of Gravity and Centroids ...................................................................... 99
4.3 Centroid of a Line ................................................................................................... 100
4.4 First Moment of Area and Centroid .............................................................. 104
4.5 Second Moments of Plane Area ................................................................................ 119
4.6 Moment of Inertia from First Principles ........................................................122
4.7 Moment of Inertia of Composite Sections ........................................................... 129
4.8 Theorems of Pappus-Guldinus .................................................................... 142
4.9 Centre of Gravity of Solids ....................................................................................... 146
Important formulae .................................................................................................. 151
Theory Questions ...................................................................................................... 152
Problems for Exercise ............................................................................................... 152
5 FRICTION 161–190
5.1 Coefficient of Friction ............................................................................................... 161
5.2 Laws of Friction ....................................................................................................... 162
5.3 Angle of Friction, Angle of Repose and Cone of Friction ....................................162
5.4 Problems on Blocks Resting on Horizontal and Inclined Planes ........................ 164
5.5 Application to Wedge Problems ..........................................................................174
5.6 Application to Ladder Problems ........................................................................177
5.7 Belt Friction ........................................................................................................180
Important Formulae ................................................................................................. 187
Theory Questions ...................................................................................................... 187
Problems for Exercise ............................................................................................... 187
6 SIMPLE MACHINES 191–227
6.1 Definitions .......................................................................................................... 191
6.2 Practical Machines ...................................................................................... 192
6.3 Law of Machine ................................................................................................ 194
6.4 Variation of Mechanical Advantage ............................................................ 195
6.5 Variation of Efficiency .......................................................................................195
6.6 Reversibility of a Machine ....................................................................199
6.7 Lever Arm .......................................................................................................200
6.8 Pulleys ............................................................................................................ 201
6.9 Wheel and Axle ............................................................................................. 205
6.10 Wheel and Differential Axle .................................................................. 205
6.11 Weston Differential Pulley Block ............................................................... 206
6.12 Inclined Plane .............................................................................................. 208
6.13 Screw Jack................................................................................................. 213
6.14 Differential Screw Jack ................................................................................ 218
6.15 Winch Crabs ................................................................................................ 219
Important Formulae ................................................................................................. 223
Theory Questions ...................................................................................................... 224
Problems for Exercise ............................................................................................... 225
7 PHYSICAL AND MECHANICAL PROPERTIES OF 228–233 STRUCTURAL MATERIALS
7.1 Physical Properties ................................................................................................... 228
7.2 Mechanical Properties .............................................................................................. 229
Theory Questions ...................................................................................................... 233
8 SIMPLE STRESSES AND STRAINS 234–282
8.1 Meaning of Stress ..................................................................................................... 234
8.2 Unit of Stress ........................................................................................................... 236
8.3 Axial Stress .............................................................................................................. 236
8.4 Strain ...............................................................................................................237
8.5 Stress-Strain Relation .............................................................................................. 238
8.6 Nominal Stress and True Stress .............................................................................. 241
8.7 Factor of Safety......................................................................................................... 242
8.8 Hooke’s Law ............................................................................................................. 242
8.9 Extension/Shortening of a Bar ................................................................................. 243
8.10 Bars with Cross-sections Varying in Steps .............................................................. 246
8.11 Bars with Continuously Varying Cross-sections ...................................................... 248
8.12 Shear Stress ...................................................................................................... 253
8.13 Simple Shear ..............................................................................................253
8.14 Poisson’s Ratio .......................................................................................................... 255
8.15 Volumetric Strain ..................................................................................................... 255
8.16 Elastic Constants ........................................................................................ 256
8.17 Relationship between Modulus of Elasticity and Modulus of Rigidity ..................... 257
8.18 Relationship between Modulus of Elasticity and Bulk Modulus .............................. 258
8.19 Composite/Compound Bars ....................................................................................... 264
8.20 Thermal Stresses .............................................................................................. 269
8.21 Thermal Stresses in Compound Bars....................................................................... 274
8.22 Hoop Stresses .............................................................................................. 277
Important Formulae ................................................................................................. 278
Theory Questions ...................................................................................................... 279
Problems for Exercise ............................................................................................... 280
9 BEAMS 283–312
9.1 Introduction .............................................................................................................. 283
9.2 Types of Supports ..................................................................................................... 283
9.3 Types of Beams ......................................................................................................... 284
9.4 Types of Loading ....................................................................................................... 285
9.5 Reactions from Supports of Beams ........................................................................... 286
9.6 Shear Force and Bending Moment ........................................................................... 291
9.7 Sign Convention ....................................................................................................... 293
9.8 Relationship between Load Intensity, Shear Force and Bending Moment .............. 293
9.9 Shear Force and Bending Moment Diagrams .......................................................... 294
9.10 SFD and BMD for a few Standard Cases ................................................................. 295
9.11 Short-cut Procedure ...................................................................................... 307
Important Formulae ................................................................................................. 310
Theory Questions ...................................................................................................... 310
Problems for Exercise ............................................................................................... 310
10 STRESSES IN BEAMS 313–345
10.1 Assumptions ........................................................................................................... 314
10.2 Bending Equation ................................................................................................... 314
10.3 Locating Neutral Axis ............................................................................................ 316
10.4 Moment Carrying Capacity of a Section ................................................................. 317
10.5 Section Moduli of Standard Sections ...................................................................... 318
10.6 Proportioning Sections ............................................................................................ 329
10.7 Shear Stress Distribution ....................................................................................... 330
10.8 Shear Stresses in Built-up Sections ....................................................................... 338
Important Formulae ................................................................................................. 342
Theory Questions ...................................................................................................... 343
Problems for Exercise ............................................................................................... 343
11 PRINCIPAL STRESSES AND STRAINS 346–373
11.1 Stresses on Inclined Planes .................................................................................... 346
11.2 Principal Stresses and Planes ................................................................................ 348
11.3 Principal Stresses in Beams .................................................................................... 360
11.4 Principal Strains ................................................................................................ 365
11.5 Measurement of Strain ............................................................................................. 368
Important Formulae ................................................................................................. 371
Theory Questions ...................................................................................................... 372
Problems for Exercise ............................................................................................... 372
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