Structural and Stress Analysis, Second Edition

Front Matter......Page 1
Table of Contents......Page 3
1.1 Function of a Structure......Page 13
1.3 Structural Systems......Page 14
1.3.2 Trusses......Page 15
1.3.3 Moment Frames......Page 16
1.3.5 Cables......Page 17
1.3.6 Shear and Core Walls......Page 18
1.4 Support Systems......Page 20
1.5 Statically Determinate and Indeterminate Structures......Page 22
1.6 Analysis and Design......Page 23
1.7 Structural and Load Idealization......Page 24
1.8 Structural Elements......Page 26
1.9.1 Steel......Page 27
1.9.3 Timber......Page 28
1.9.4 Masonry......Page 29
1.9.7 Composite Materials......Page 30
1.10 The Use of Computers......Page 31
2.1 Force......Page 32
2.1.1 Parallelogram of Forces......Page 34
2.1.2 The Resultant of a System of Concurrent Forces......Page 36
2.1.3 Equilibrant of a System of Concurrent Forces......Page 37
2.1.4 The Resultant of a System of Non-Concurrent Forces......Page 39
2.2 Moment of a Force......Page 40
2.2.2 Equivalent Force Systems......Page 42
2.3 The Resultant of a System of Parallel Forces......Page 43
2.4 Equilibrium of Force Systems......Page 45
2.5 Calculation of Support Reactions......Page 46
Problems......Page 50
3.1.1 Axial Load......Page 54
3.1.2 Shear Load......Page 55
3.1.4 Torsion......Page 56
3.2 Notation and Sign Convention......Page 58
3.3 Normal Force......Page 59
3.4 Shear Force and Bending Moment......Page 63
3.5 Load, Shear Force and Bending Moment Relationships......Page 75
3.6 Torsion......Page 82
3.7 Principle of Superposition......Page 85
Problems......Page 86
4.1 Types of Truss......Page 93
4.2 Assumptions in Truss Analysis......Page 94
4.3 Idealization of a Truss......Page 96
4.4 Statical Determinacy......Page 97
4.5 Resistance of a Truss to Shear Force and Bending Moment......Page 100
4.6 Method of Joints......Page 103
4.7 Method of Sections......Page 107
4.8 Method of Tension Coefficients......Page 109
4.9 Graphical Method of Solution......Page 112
4.10 Compound Trusses......Page 115
4.11 Space Trusses......Page 116
4.12 A Computer-Based Approach......Page 120
Problems......Page 121
5.1 Lightweight Cables Carrying Concentrated Loads......Page 126
5.2.1 Governing Equation for Deflected Shape......Page 131
5.2.2 Cable under its Own Weight......Page 133
5.2.3 Cable Subjected to a Uniform Horizontally Distributed Load......Page 135
5.2.4 Suspension Bridges......Page 139
Problems......Page 142
6.1 The Linear Arch......Page 145
6.2.1 Support Reactions - Supports on Same Horizontal Level......Page 148
6.2.2 Support Reactions - Supports on Different Levels......Page 151
6.3 A Three-Pinned Parabolic Arch Carrying a Uniform Horizontally Distributed Load......Page 154
6.4 Bending Moment Diagram for a Three-Pinned Arch......Page 155
Problems......Page 158
7.1 Direct Stress in Tension and Compression......Page 162
7.2 Shear Stress in Shear and Torsion......Page 165
7.3 Complementary Shear Stress......Page 166
7.5 Shear Strain......Page 167
7.7.1 Hooke's Law and Young's Modulus......Page 168
7.7.3 Volume or Bulk Modulus......Page 169
7.8 Poisson Effect......Page 171
7.9 Relationships between the Elastic Constants......Page 172
7.10 Strain Energy in Simple Tension or Compression......Page 176
7.10.1 Deflection of a Simple Truss......Page 179
7.10.2 Composite Structural Members......Page 181
7.10.3 Thermal Effects......Page 183
7.10.4 Initial Stresses and Prestressing......Page 187
7.11 Plane Stress......Page 191
7.12 Plane Strain......Page 194
Problems......Page 195
8.1.1 Ductility......Page 200
8.2 Testing of Engineering Materials......Page 201
8.2.1 Tensile Tests......Page 202
8.2.3 Bending Tests......Page 203
8.2.4 Shear Tests......Page 205
8.2.5 Hardness Tests......Page 206
8.2.6 Impact Tests......Page 207
8.3.1 Low Carbon Steel (Mild Steel)......Page 208
8.3.2 Aluminium......Page 210
8.3.3 Brittle Materials......Page 211
8.3.4 Composites......Page 213
8.5 Creep and Relaxation......Page 214
8.6 Fatigue......Page 215
8.7 Design Methods......Page 217
Problems......Page 219
9. Bending of Beams......Page 221
9.1 Symmetrical Bending......Page 222
9.1.2 Direct Stress Distribution......Page 223
9.1.3 Elastic Section Modulus......Page 226
9.2 Combined Bending and Axial Load......Page 231
9.2.1 Core of a Rectangular Section......Page 234
9.2.2 Core of a Circular Section......Page 235
9.3 Anticlastic Bending......Page 237
9.5 Unsymmetrical Bending......Page 238
9.5.2 Sign Conventions and Notation......Page 239
9.5.3 Direct Stress Distribution......Page 240
9.5.4 Position of the Neutral Axis......Page 242
9.6.2 Theorem of Perpendicular Axes......Page 243
9.6.3 Second Moments of Area of Standard Sections......Page 244
9.6.4 Product Second Moment of Area......Page 246
9.6.5 Approximations for Thin-Walled Sections......Page 249
9.6.6 Second Moments of Area of Inclined and Curved Thin-Walled Sections......Page 252
9.7 Principal Axes and Principal Second Moments of Area......Page 253
9.8 Effect of Shear Forces on the Theory of Bending......Page 255
Problems......Page 256
10. Shear of Beams......Page 262
10.1 Shear Stress Distribution in a Beam of Unsymmetrical Section......Page 263
10.2 Shear Stress Distribution in Symmetrical Sections......Page 265
10.3 Strain Energy Due to Shear......Page 271
10.4 Shear Stress Distribution in Thin-Walled Open Section Beams......Page 272
10.4.1 Shear Centre......Page 275
10.5 Shear Stress Distribution in Thin-Walled Closed Section Beams......Page 278
10.5.1 Shear Centre......Page 281
Problems......Page 285
11.1 Torsion of Solid and Hollow Circular Section Bars......Page 291
11.1.1 Torsion of a Circular Section Hollow Bar......Page 294
11.1.2 Statically Indeterminate Circular Section Bars under Torsion......Page 295
11.3 Plastic Torsion of Circular Section Bars......Page 298
11.4 Torsion of a Thin-Walled Closed Section Beam......Page 300
11.5 Torsion of Solid Section Beams......Page 303
11.6 Warping of Cross Sections under Torsion......Page 307
Problems......Page 308
12.1 Steel-Reinforced Timber Beams......Page 312
12.2.1 Elastic Theory......Page 317
12.2.2 Ultimate Load Theory......Page 324
12.3 Steel and Concrete Beams......Page 330
Problems......Page 333
13.1 Differential Equation of Symmetrical Bending......Page 335
13.2 Singularity Functions......Page 348
13.3 Moment-Area Method for Symmetrical Bending......Page 355
13.4 Deflections Due to Unsymmetrical Bending......Page 362
13.5 Deflection Due to Shear......Page 365
13.6 Statically Indeterminate Beams......Page 368
13.6.1 Method of Superposition......Page 369
13.6.2 Built-in or Fixed-End Beams......Page 371
13.6.3 Fixed Beam with a Sinking Support......Page 376
Problems......Page 377
14.1 Representation of Stress at a Point......Page 385
14.2 Determination of Stresses on Inclined Planes......Page 386
14.2.1 Biaxial Stress System......Page 388
14.2.2 General Two-Dimensional Case......Page 390
14.3 Principal Stresses......Page 393
14.4 Mohr's Circle of Stress......Page 396
14.5 Stress Trajectories......Page 399
14.6 Determination of Strains on Inclined Planes......Page 400
14.7 Principal Strains......Page 402
14.8 Mohr's Circle of Strain......Page 403
14.9 Experimental Measurement of Surface Strains and Stresses......Page 405
14.10 Theories of Elastic Failure......Page 409
14.10.1.1 Maximum Shear Stress Theory......Page 410
14.10.1.2 Shear Strain Energy Theory......Page 411
14.10.1.4 Yield Loci......Page 415
14.10.2 Brittle Materials......Page 419
14.10.2.1 Maximum Normal Stress Theory......Page 420
Problems......Page 422
15. Virtual Work and Energy Methods......Page 427
15.1 Work......Page 428
15.2.1 Principle of Virtual Work for a Particle......Page 429
15.2.2 Principle of Virtual Work for a Rigid Body......Page 431
15.2.4 Work Done by Internal Force Systems......Page 434
15.2.4.1 Axial Force......Page 435
15.2.4.2 Shear Force......Page 436
15.2.4.3 Bending Moment......Page 437
15.2.4.4 Torsion......Page 438
15.2.5 Virtual Work Due to External Force Systems......Page 439
15.2.7 Applications of the Principle of Virtual Work......Page 441
15.3.1 Strain Energy and Complementary Energy......Page 449
15.3.2 The Principle of the Stationary Value of the Total Complementary Energy......Page 453
15.3.3 Temperature Effects......Page 460
15.3.4 Potential Energy......Page 462
15.3.5 The Principle of the Stationary Value of the Total Potential Energy......Page 463
15.4 Reciprocal Theorems......Page 466
15.4.1 Theorem of Reciprocal Displacements......Page 467
15.4.2 Theorem of Reciprocal Work......Page 471
Problems......Page 472
16. Analysis of Statically Indeterminate Structures......Page 479
16.1 Flexibility and Stiffness Methods......Page 480
16.2 Degree of Statical Indeterminacy......Page 481
16.2.1 Rings......Page 482
16.2.2 The Entire Structure......Page 483
16.2.4 Degree of Statical Indeterminacy......Page 484
16.2.5 Trusses......Page 486
16.3 Kinematic Indeterminacy......Page 487
16.4 Statically Indeterminate Beams......Page 490
16.5 Statically Indeterminate Trusses......Page 498
16.5.1 Self-Straining Trusses......Page 503
16.6 Braced Beams......Page 505
16.7 Portal Frames......Page 508
16.8 Two-Pinned Arches......Page 511
16.8.1 Secant Assumption......Page 514
16.8.2 Tied Arches......Page 517
16.9 Slope-Deflection Method......Page 518
16.10.1 Principle......Page 526
16.10.2 Fixed-End Moments......Page 527
16.10.3 Stiffness Coefficient......Page 528
16.10.5 Stiffness Coefficients and Carry over Factors......Page 529
16.10.5.1 Case 1: A Fixed, B Simply Supported, Moment M_BA Applied at B......Page 530
16.10.5.3 Case 3: A and B Simply Supported, Equal Moments M_BA and -M_AB Applied at B and A......Page 531
16.10.6 Continuous Beams......Page 532
16.10.7 Portal Frames......Page 538
Problems......Page 549
17. Matrix Methods of Analysis......Page 560
17.1 Axially Loaded Members......Page 561
17.2 Stiffness Matrix for a Uniform Beam......Page 573
17.3 Finite Element Method for Continuum Structures......Page 579
17.3.1 Stiffness Matrix for a Beam-Element......Page 581
17.3.2 Stiffness Matrix for a Triangular Finite Element......Page 585
17.3.3 Stiffness Matrix for a Quadrilateral Element......Page 592
Problems......Page 597
18.1.1 The Uniqueness Theorem......Page 604
18.2 Plastic Analysis of Beams......Page 605
18.2.1 Plastic Bending of Beams Having a Singly Symmetrical Cross Section......Page 606
18.2.2 Shape Factor......Page 608
18.2.3 Moment-Curvature Relationships......Page 612
18.2.4 Plastic Hinges......Page 614
18.2.5 Plastic Analysis of Beams......Page 615
18.2.6 Plastic Design of Beams......Page 622
18.2.7 Effect of Axial Load on Plastic Moment......Page 623
18.3 Plastic Analysis of Frames......Page 625
18.3.1 Beam Mechanism......Page 626
18.3.3 Combined Mechanism......Page 627
Problems......Page 632
19.1.1 Yield Lines......Page 637
19.1.3 Internal Virtual Work Due to an Ultimate Moment......Page 639
19.1.4 Virtual Work Due to an Applied Load......Page 640
19.2 Discussion......Page 648
Problems......Page 649
20.1 Influence Lines for Beams in Contact with the Load......Page 652
20.2 Mueller-Breslau Principle......Page 659
20.3.1 Concentrated Loads......Page 662
20.3.1.2 Maximum Bending Moment at K......Page 663
20.3.2 Distributed Loads......Page 667
20.3.2.1 Maximum Shear Force at K......Page 668
20.3.2.2 Maximum Bending Moment at K......Page 669
20.3.2.4 Maximum Bending Moment at K......Page 670
20.3.3 Diagram of Maximum Shear Force......Page 671
20.3.4 Reversal of Shear Force......Page 672
20.3.5 Determination of the Point of Maximum Bending Moment in a Beam......Page 674
20.4 Influence Lines for Beams Not in Contact with the Load......Page 677
20.5 Forces in the Members of a Truss......Page 680
20.5.1 Counterbracing......Page 683
20.6 Influence Lines for Continuous Beams......Page 685
Problems......Page 691
21. Structural Instability......Page 696
21.1 Euler Theory for Slender Columns......Page 697
21.1.1 Buckling Load for a Pin-Ended Column......Page 698
21.1.2 Buckling Load for a Column with Fixed Ends......Page 700
21.1.3 Buckling Load for a Column with One End Fixed and One End Free......Page 701
21.1.4 Buckling of a Column with One End Fixed and the other Pinned......Page 702
21.2 Limitations of the Euler Theory......Page 705
21.3.1 Rankine Theory......Page 706
21.3.2 Initially Curved Column......Page 707
21.4 Effect of Cross Section on the Buckling of Columns......Page 711
21.5 Stability of Beams under Transverse and Axial Loads......Page 712
21.6 Energy Method for the Calculation of Buckling Loads in Columns (Rayleigh-Ritz Method)......Page 716
Problems......Page 721
BookmarkTitle:......Page 725
Appendix B: Bending of Beams......Page 727
B......Page 729
C......Page 731
D......Page 734
E......Page 735
F......Page 736
I......Page 737
L......Page 738
M......Page 739
N......Page 740
P......Page 741
S......Page 744
T......Page 750
V......Page 753
Y......Page 754