PREFACE ........................................................ ix
HISTORICAL OVERVIEW
I Introduction ................................................ 1
II Units and Conventions ....................................... 1
III Elasticity .................................................. 3
IV Structures .................................................. 4
V Yielding .................................................... 5
VI Concluding Remarks .......................................... 6
References ...................................................... 6
CHAPTER 1 PROPERTIES OF AREAS
1.1 Centroid and Moments of Area ............................... 7
1.2 Parallel and Perpendicular Axes ............................ 8
1.3 Principal Second Moments of Area .......................... 15
1.4 Graphical Solution to Iu and Iv ........................... 21
1.5 Matrix Method ............................................. 24
Exercises ...................................................... 27
CHAPTER 2 STATIC EQUILIBRIUM
2.1 Co-Planar, Concurrent Forces .............................. 31
2.2 Co-Planar, Non-Concurrent Forces .......................... 34
2.3 The Free-Body Diagram ..................................... 40
2.4 Bar Forces in Plane Frames ................................ 43
2.5 Forces and Moments in Beams ............................... 47
Exercises ...................................................... 53
CHAPTER 3 BASIC STRESS AND STRAIN
3.1 Direct Stress and Strain .................................. 61
3.2 Shear Stress and Strain ................................... 66
3.3 Compound Bars ............................................. 75
3.4 Temperature Effects ....................................... 83
3.5 Combined Mechanical and Thermal Effects ................... 87
Exercises ...................................................... 91
CHAPTER 4 LINEAR ELASTICITY
4.1 Elastic Constants ......................................... 97
4.2 Analysis of Pure Shear ................................... 114
4.3 Relationships Between Elastic Constants .................. 117
4.4 Extended Hooke's Law ..................................... 120
4.5 Thin-Walled Pressure Vessels ............................. 123
4.6 Thick-Walled Cylinder .................................... 130
4.7 Thick-Walled Sphere ...................................... 139
Exercises ..................................................... 145
CHAPTER 5 BENDING AND SHEAR IN BEAMS
5.1 Direct Stress in Bending ................................. 149
5.2 Combined Bending and Direct Stress ....................... 154
5.3 Bending of Composite Beams ............................... 160
5.4 Shear Stress Due to Shear Force .......................... 171
5.5 Shear Flow in Thin-Walled Sections ....................... 177
References .................................................... 187
Exercises ..................................................... 187
CHAPTER 6 SLOPE AND DEFLECTION OF BEAMS
6.1 Differential Equation of Flexure ......................... 195
6.2 Mohr's Theorems .......................................... 199
6.3 Telescopic Cantilever .................................... 215
6.4 Macaulay's Method ........................................ 223
6.5 Superposition Principle .................................. 228
Exercises ..................................................... 237
CHAPTER 7 THEORIES OF TORSION
7.1 Torsion of Circular Bars ................................. 243
7.2 Torsion of Thin Strips ................................... 253
7.3 Bredt-Batho Torsion Theory ............................... 263
Exercises ..................................................... 280
CHAPTER 8 BUCKLING OF STRUTS
8.1 Euler Buckling Theory .................................... 287
8.2 Imperfect Euler Struts ................................... 291
8.3 Empirical Buckling Formulae .............................. 306
8.4 Inelastic Buckling of Struts ............................. 318
Exercises ..................................................... 323
CHAPTER 9 BUCKLING OF PLATES AND TUBES
9.1 Buckling Modes ........................................... 329
9.2 Unsupported Plate Under Axial Compression ................ 330
9.3 Supported Plate Under Axial Compression .................. 332
9.4 Inelastic Buckling of Plates Under Axial Compression ..... 336
9.5 Post-Buckling of Plates Under Axial Compression .......... 340
9.6 Plate Under Biaxial Compression .......................... 342
9.7 Plate Under In-Plane Shear ............................... 344
9.8 Tension Field Beam ....................................... 347
9.9 Secondary Buckling of Plate Elements ..................... 353
9.10 Torsional Buckling of Thin Circular Tubes ................ 365
9.11 Torsional and Shear Buckling of Non-Circular Tubes ....... 368
References .................................................... 370
Exercises ..................................................... 371
CHAPTER 10 ENERGY METHODS
10.1 Internal Energy and External Work ....................... 373
10.2 Strain Energy Expressions ............................... 376
10.3 Application to Springs .................................. 388
10.4 Impact Loading .......................................... 406
10.5 Castigliano's Theorems .................................. 409
10.6 Stationary Potential Energy ............................. 423
Exercises .................................................... 427
CHAPTER 11 PLANE STRESS AND STRAIN
11.1 Plane Stress Analysis ................................... 433
11.2 Mohr's Circle ........................................... 444
11.3 Matrix Method ........................................... 448
11.4 Plane Strain Analyses ................................... 450
11.5 Wheatstone Bridge Theory ................................ 465
Exercises .................................................... 481
CHAPTER 12 YIELD, STRENGTH AND FAILURE CRITERIA
12.1 Yielding of Ductile Metals .............................. 487
12.2 Principal Biaxial Stress ................................ 501
12.3 Combined Axial and Shear Stresses ....................... 505
12.4 Failure Criteria for Brittle Solids ..................... 516
12.5 Failure Criteria for Fibrous Materials .................. 524
References ................................................... 534
Exercises .................................................... 534
CHAPTER 13 FINITE ELEMENTS
13.1 Stiffness Matrix ........................................ 543
13.2 Energy Methods .......................................... 544
13.3 Bar Element Under Axial Stress .......................... 548
13.4 Plane Frame ............................................. 553
13.5 Torsion Element ......................................... 560
13.6 Beam Element ............................................ 564
13.7 Plane Triangular Element ................................ 580
Exercises .................................................... 593
INDEX ........................................................ 599
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