APPLIED MECHANICS NOTES OF PURBANCHAL UNIVERSITY 2ND SEM

APPLIED MECHANICS



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Chapter I Static
1.1 Mass, strength and weight 1
1.2 Equilibrium Forces: Triangle of Forces 3
1.3 Resulting and Balanced: Parallelogram of Forces 4
1.4 Resolution of forces 4
1.5 Polygon of forces 5
1.6 Moment of a Force 6
1,7 Couple 6
1.8 Principle of Moments 6
1.9 Resolution of a force into a force and a couple 7
1.10 General conditions of equilibrium 8
1.11 Free body diagram 9
1.12 Contact Forces; supports and connections 10
Chapter 2 Frames
2.1 Forces in the frames 22
2.2 Wind loads on farms 24
2.3 Analytical methods: method of sections: method of resolution 31
Chapter 3 Friction
3.1 Friction on a rough inclined plane 38
3.2 The angle of friction and the total reaction 42
3.3 Application of the angle of friction to the movement on the inclined plane 43
3,4 holds 45
3.5 Filling or sliding 49
3.6 The problem of the scale 51
3.7 Other remarks on friction and lubrication 53
3.8 The square threaded screw 55
3.9 Revision of a screw 58
3.10 Tribology 63 \\ nvi Table of Contents
Chapter
4 Speed ​​and Acceleration
4.1
Average speed 64
4.2 Constant speed 64
4.3 Variable speed 64
4.4 Speed ​​66
4.5 Movement in
a straight line 66
4.6 Summary of formulas for uniform acceleration 67
4.7 Body in free fall 68
4.8 Relative speed; speed chart 69
4.9 Angular velocity of
a line 73
4.10 Movement
a body in
a plane 73
4.11 Triangle of convenience for
a rigid link. Application to the mechanisms 75
Chapter
5 Inertia and change of motion
5.1 The laws of Newton's movement 81
5.2 Inertia and mass 81
5.3 Strength 82
5.4 Weight 83
5.5 The equation of motion 84
5.6 Mass units and force 85
5.7 Inertia force 86
5.8 Active and active forces 87
5.9 Variable Forces 88
5.10 Tensile strength 88
5.11 Tensile force 91
5.12 Driving Couple on
a vehicle 94
5.13 Maximum tensile force possible 95
5.14 Application of inertial force to connected bodies 98
5.15 Single hoist 100
Chapter
6 Movement in
a circle
6.1 Centripetal acceleration 103
6.2 Centripetal force 104
6.3 Rotational inertia force 105
6.4 Centrifugal force 105
6.5 Dynamic instability 107
6.6 Rounding off the vehicle
a curve 109
6.7 Superelevation of lanes: Elimination of lateral thrust 109
6.8 Comfort of passengers
- the pendular car 113
6.9 Reversal of vehicles 115
Chapter
7 Balancing
7.1 Static equilibrium
- two masses in
a plane 119
7.2 dynamic equilibrium
- two ~ omen in
a plane 119
7.3 Rotor balancing method 120
7.4 Static equilibrium
- several masses in a plane 121
7.5 Dynamic balance of several masses in a plane 122
Content vii
7.6 Dynamic forces at the bearings 125
7.7 Balancing the car wheels 127
Chapter
8 Periodic movement
8.1 Periodic movement 130
8.2 Simple harmonic motion 130
8.3 Simple harmonic motion derived from
a circular motion 131
8.4 Periodic 134
8.5 Frequency 134
8.6 Amplitude 135
8.7 Dynamics of simple harmonic motion 138
8.8 The mass and the spring 139
8.9 Simple pendulum 145
8.10 Remuneration 147
8.11 Periodic movement of
a conical clock 150
Chapter
9 Rotational dynamics
9.1 Angular acceleration 154
9.2 Chart of angular velocity and time 155
9.3 Using the w-t chart 156
9.4 Dynamics of
a rotating particle 159
9.5 Dynamics of
a rotating body 161
9.6 Inertia torque 162
9.7 Accelerated shaft with bearing friction 162
9.8 The tree resting 162
9.9 Units 163
9.10 Values ​​of
I for single rotors 163
9.11 The hoist 167
Appendix to Chapter 9; Gravitation: Satellites 170
Chapter 10 Work, Energy and Power
10.1Work done by
a force of 180
10.2 Work performed in special cases 181
10.3 Work performed by
a couple 182
10.4 Springs 183
10.5 Energy 186
10.6 Cine Energy: Work-Energy Equation 187
10.7 Potential energy 188
10.8 Units of Energy 189
10.9 De-energizing energy 191
10.10 Conservation of energy 194
10.11 Cylindrical rotation energy 195
10.12 Total kinetic energy of
a wheel bearing 196
10.13 Power 200
10.14 Power developed by
a couple 201
10.15 Efficiency 201
10.16 Power to drive
a vehicle 204
10.17 Function of
a flywheel 207 \\ nviii Table of Contents
Chapter 11 Impulse and Momentum
Il.l Linear Moment: pulse 212
11.2 Pulse and motion units 213
11.3 Force varying with time 214
11.4 Retention of Linear Pulse 216
11.5 Impulsive Forces 217 11.6 Note on the Use of Quantities of Motion and Energy 217
11.7 Explosions 217 11.8 CoIlision of two bodies 221
11.9 Perfectly elastic body collision 222
II.IO Non-elastic collisions 224
II.II Collision of elastically partial bodies 229
11.12 Angular momentum and impulse 232
Chapter 12 Aircraft and Rockets
12.1 Propulsion of reaction 235
12.2 Response aircraft 235
12.3 Notes on aircraft speeds 236
12.4 Thrust of a jet 236
12.5 Compressible and incompressible flow 237
12.6 Mass flow rate 238
12.7 International Standard Atmosphere (ISA) 239
12.8 Power developed by a turbo player 239
12.9 Powered Aircraft by a Pilot 243
12.10 Notes on lift and drag forces on an aircraft 247
12.II Forces on an aircraft in flight 249
12.12 Removal and landing 253
12.13 Banking an aircraft 256
12.14 Helicopters 258
12.15 Rocket Propulsion: Shooted 262
12.16 Forces on a rocket in flight 265
Chapter 13 Stress and Direct Stress
13.1 Stress 273 13.2 Strain 274 13.3 Relation between stress and deformation: Young's elasticity modulus 274 13.4 Composite bars 277 '13 .5 Thermal tension 281 13.6 Sign convention 282 13.7 Effects of thermal deformation 283 13.8 Poisson's ratio: lateral deformation 287 13.9 Degradation energy: resilience 289 13.10 Application of deformation energy to shocks and loads applied suddenly 292 13.11 hoops in a cylinder 295
13.12 Axial stress in a cylinder 296
13.13 Tangential stress in a spherical field 297
Summary ix
13.14 Effects of joints on stresses in thin shells 298
13.15 Rotating ring 301
Chapter 14 Mechanical Properties of Materials
14.1 Metals and alloys 305
14.2 Black soft steel in tension 306
14.3 Constraint-strain curve 310
14.4 Elasticity module 310
14.5 Specific elasticity module 312
14.6 Black soft steel in compression: malleability 313
14.7 Shiny mild steel 313
14.8 Ductile metals 314
14.9 Evidence Stress 314
14.10 Fragile materials 315
14.11 Resilience and endurance 316
14.12 Mechanical properties of metals 316
14.13 Fatigue 319
14.14 Creep 320
14.15 Hardness 321
14.16 Polymers and plastics 323
14.17 Fibers 324
14.18 Strengthening fibers: composite materials 324
14.19 Non-destructive testing 325
Chapter 15 Shear and Twist
15.1 Shear stress 327
15.2 Riveted seals 327
15.3 Shear strain 331
15.4 Relationship between shear stress and shear deformation: rigidity modulus 332
15.5 Torsion of a thin tube 332
15.6 Torsion of solid trees 334
15.7 Torsion of hollow trees 335
15.8 Rigidity and strength 336
15.9 Power and torque 337
Chapter 16 Shear force and bending moment
16.1 Shear force 341
16.2 Shear force diagram 341
16.3 Bending moment 342
16.4 Diagram of bending moments 344
16.5 Calculating Beam Reactions 345
16.6 Uniformly distributed charges 351
16.7 Combined Loading 353
16.8 Condition for maximum bending moment 357
Chapter 17 Bending beams
17.1 Pure Bending of an Elastic Beam 362 \\ nx Content
17.2 Relationship between curvature and distortion 363
17.3 Position of the neutral axis 365
17.4 Moment of resistance 366
17.5
I of rectangular and circular sections 368
17.6 Strength of
a beam in flexion 372
17.7 Calculation of
I for complex sections 373
17.8 Module of section 378
Chapter 18 Combined bending and direct stress
18.1 Principle of superposition 380
18.2 Combined bending and direct stress
a loaded column 380
18.3 Other Safety Considerations: Limited Design 388
Chapter 19 Fluid at rest
19.1 Fluid 389
19,2 Pressure 389
19.3 Transmission of fluid pressure 390
19.4 Density; relative density; specific weight; specific gravity 391
19.5 Pressure in
a liquid owing to its own weight 392
19.6 Pressure measurement 393
19.7 Measuring manometric pressure 394
19.8 Measuring differences in pressure 395
19.9 Total push on
a vertical flat surface 396
19.10 Pressure Center 396
19.11 Inclined surface 403
19.12 Pressure center for inclined surface 404
Chapter 20 Fluid in motion
20.1 Pressure energy 407
20.2 Potential energy 408
20.3 Cine power 409
20.4 Exchange of pressure and kinetic energy 409
20.5 Bernoulli Equation (Energy Conservation) 410
20.6 Pipe flow: continuity equation 410
20.7 Bit 411
20.8 Variation of pressure in the head
a hose 411
20.9 The flow of true fluids 415
20.10 Viscosity 415
20.11 Low speed rate 415
20.12 Start of turbulence 416
20.13 Loss of pressure in a turbulent flow 417
20.14 Swirl Formation 417
20.15 Energy from
a loss of fluid and pressure 418
20.16 Pipe Flow Measurement: 420 Venturi Meter
20.17 Load factor for
a Venturi 421 meter
20.18 Loading by
a small hole 423
20.19 Coefficient of discharge for
a small hole 424
Contents xi
20.20 Coefficient of accuracy 424
20.21 Vena contracta: contraction coefficient 424
20.22 Relation between the coefficients 425
20.23 Power of
a 425 jet
20.24 Experimental determination of orifice coefficients 427
20.25 Impact of the jets. Rotodynamic machines 429
Chapter 21 Experimental Errors and Data Adjustment
21.1 Experience 431
21.2 Error and discrepancy 431
21.3 Classification of errors
432
21.4 Justifiable accuracy
434
21.5 Possible errors
434
21.6 Propagation of error or error
435
21.7 Region of uncertainty 435
21.8 Value accepted 435
21.9 Error Derived from the Sum of Two Quantities 435
21.10 Graphic methods 437
21.11 The graph in a straight line 438
21.12 Equation
a straight line 439
21.13 Equations that can be reduced to
a straight line 441
21.14 Choice of axes

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