2. 2
STRENGTH OF MATERIALS
and
STRUCTURAL ANALYSIS
(Formerly Elementary Structural Analysis)
Ashok K. Jain
Ph.D. (Michigan), F.I.E.
Professor of Civil Engineering
Indian Institute of Technology Roorkee
Roorkee
Second Edition 2008
Nem Chand & Bros., Roorkee 247 667, India
3. 3
Contents
1. INTRODUCTION 1 - 18
1.1 Introduction 1
1.2 Need of Analysis 2
1.3 Idealization of the Solid 3
1.4 Techniques of Idealization of Civil Engineering Structures 4
1.5 Loads on Structures 12
1.6 Basic Tools of Analysis 13
1.7 Principle of Superposition 17
1.8 Factor of Safety 17
References 18
2. PROPERTIES OF MATERIALS 19 - 30
2.1 Introduction 19
2.2 Stress – Strain Diagram 20
2.3 Hooke’s Law 22
2.4 Idealized Stress – Strain Relations 25
2.5 Compressive Strength 26
2.6 Shear Strength 26
2.7 Fatigue Strength 26
2.8 Impact Strength 27
2.9 Poisson’s Ratio 28
2.10 Composite Materials 28
Problems 30
3. PROPERTIES OF SECTIONS 32 - 45
3.1 Importance of Section Property 32
3.2 Area of the Section and Moment of Areas 33
3.3 Finding the Neutral Axis 34
3.4 Finding the Moment of Inertia 36
3.5 Principal Axes and Principal Moment of Inertia 40
Problems 45
4. AXIAL STRESS AND DEFORMATIONS IN BARS 46 - 76
4.1 Introduction 46
4.2 Axial Deformation 46
4.3 St. Venant’s Principle 48
4.4 Illustrative Examples 48
4.5 Statically Indeterminate Problems 55
4. 4
4.6 Thermal Strains and Deformations 65
Problems 72
vii
viii
5. SHEAR STRESS IN RIVETS AND WELDS 77 - 92
5.1 Introduction 77
5.2 Riveted Connections 77
5.3 Types of Joints 78
5.4 Transmission of Forces through Rivets 79
5.5 Failure of a Riveted Connection 80
5.6 Welded Connections 85
5.7 Design of Butt Weld 87
5.8 Design of Fillet weld 87
Problems 91
6. CONCEPT OF STRESSES 93 - 122
6.1 Definition of Stress 93
6.2 Stress Components 94
6.3 Stresses on Oblique Planes 96
6.4 Principal Stresses 97
6.5 Maximum and Minimum Shear Stresses 99
6.6 State of Pure Shear 100
6.7 The Mohr’s Circle 101
6.8 Illustrative Examples 103
6.9 Stress Transformation in 3-D 113
Problems 120
7. CONCEPT OF STRAINS 123 - 148
7.1 Introduction 123
7.2 Generalized Hooke’s Law for Isotropic Materials 123
7.3 Strains in 2-D 126
Plane Stress Problems
Plane Strain Problems
7.4 Transformation of Strain in 2-D 128
7.5 Principal Strains and Maximum Shearing Strain 130
7.6 Mohr’s Circle for Plane Strain 130
7.7 Strain Rosettes 131
7.8 Illustrative Examples 133
7.9 Strain Transformation in 3-D 136
7.10 Volumetric Strains and Bulk Modulus 138
7.11 Relation Between the Elastic Constants 140
Problems 146
8. THIN AND THICK PRESSURE VESSELS 149 - 168
8.1 Introduction 149
5. 5
8.2 Thin Cylindrical Pressure Vessel 149
8.3 Thick Walled Cylindrical Pressure Vessel 151
8.4 Thin Spherical Pressure Vessel 154
8.5 Illustrative Examples 155
Problems 167
ix
9. TORSION IN SHAFTS 169 - 188
9.1 Introduction 169
9.2 St. Venant’s Torsion 169
9.3 Torsion Formula 170
9.4 Angle of Twist 171
9.5 Membrane Analogy 172
9.6 Illustrative Examples 174
9.7 Close Coiled Helical Springs 185
Problems 188
10. FAILURE THEORIES AND FATIGUE 189 - 207
10.1 Introduction 189
10.2 Maximum Normal Stress Theory 189
10.3 Maximum Strain Theory (St. Venant Theory) 190
10.4 Maximum Shear Stress Theory 192
10.5 Energy of Distortion Theory (Von-Mises Yield Criteria) 193
10.6 Octahedral Shear Stress Theory 195
10.7 Fatigue 196
10.8 S-N Curve 199
10.9 Effect of Mean Stress on Endurance Limit 200
10.10 Illustrative Examples 201
11. PLANE TRUSSES 208 - 248
11.1 Introduction 208
11.2 Arrangement of Members of a Truss 209
11.3 Conventional Types of Roof and Bridge Trusses 210
11.4 Stability and Determinacy 211
11.5 Free Body Diagrams 215
11.6 Notation and Sign Convention 216
11.7 Analysis of Trusses 218
11.8 Illustrative Examples 219
11.9 Equations of Condition 235
11.10 Zero Load Test 236
11.11 Classification of Trusses 239
11.12 Illustrative Examples 240
Problems 244
12. BENDING MOMENT AND SHEAR FORCE – BEAMS 249 - 293
12.1 Introduction 249
12.2 Definitions and Sign Convention 249
12.3 Static Determinacy 251
12.4 Equations of Conditions 251
6. 6
12.5 Stability of Structures 251
12.6 Computation of Axial Force, Shear Force and Bending Moment 253
12.7 Relationship between Load, Shear and Moment 254
12.8 Properties of Shear Force and Bending Moment Diagrams 256
12.9 Illustrative Examples 256
Problems 289
x
13. BENDING MOMENT, SHEAR FORCE AND THRUST –
PLANE FRAMES 294 - 319
13.1 Introduction 294
13.2 Stability and Determinacy 294
13.3 Sign Convention 295
13.4 Illustrative Examples 297
Problems 317
14. STRESSES IN BEAMS 320 - 363
14.1 Introduction 320
14.2 Bending Stresses – Theory of Simple Bending 320
14.3 Assumptions and Limitations in the Flexure Formula 324
14.4 Illustrative Examples 325
14.5 Shear Stresses 341
14.6 Shear Stresses in Common Beams 343
14.7 Illustrative Examples 345
Problems 359
15. COLUMNS AND STRUTS 364 - 396
15.1 Introduction 364
15.2 Euler’s Theory 364
15.3 Strength of a Perfect Column 373
15.4 Eccentric Loading of Columns 375
15.5 Elastic design 376
Rankine Gordon Formula
Straight Line Formula
Johnson’s Parabolic Formula
AISC Parabolic Formula (1989)
Perry Robertson Formula
Secant Formula
Merchant Rankine Formula
Multiple Curves for Steel Columns
15.6 Illustrative Examples 383
Problems 395
16. COMBINED AXIAL AND BENDING STRESSES 397 - 416
16.1 Introduction 397
16.2 Combined Stresses in Beams 397
16.3 Combined Stresses in Columns 401
16.4 Combined Stresses in Walls 410
Problems 414
7. 7
17. UNSYMMETRICAL BENDING AND SHEAR CENTER 417 - 448
17.1 Introduction 417
17.2 Assumptions 418
17.3 Stress at Any Point in a Short Column 419
xi
17.4 Illustrative Examples 420
17.5 Shear in Thin Walled Sections 429
17.6 Locating Shear Center 431
17.7 Shear Flow in Rectangular Section 434
17.8 Illustrative Examples 436
Problems 446
18. DEFLECTION OF BEAMS 449 - 510
18.1 Introduction 449
18.2 Direct Integration Method 450
18.3 Illustrative Examples 452
18.4 The Moment Area Method 468
18.5 Basic Properties of Parabolic Curves 470
18.6 Illustrative Examples 471
18.7 Elastic Load Method 480
18.8 Conjugate Method 482
18.9 Illustrative Examples 485
18.10 Principle of Virtual Work for Rigid Bodies 490
18.11 Unit Load Method 493
18.12 Illustrative Examples 495
18.13 Other Useful Theorems 503
Betti’s Law of Reciprocal Deflections
Maxwell’s Law of Reciprocal Deflections
Castigliano’s Theorems
Problems 507
19. DEFLECTION OF FRAMES 511 - 523
19.1 Introduction 511
19.2 Moment Area Method 511
19.3 Unit Load Method 514
Problems 519
20. DEFLECTION OF TRUSSES 524 - 541
20.1 Introduction 524
20.2 Virtual Work Method 524
20.3 Illustrative Examples 526
20.4 Williot Diagram 533
20.5 Williot Mohr Diagram 535
Problems 538
21. ARCHES 542 - 555
8. 8
21.1 Introduction 542
21.2 Arch vs. Beam 544
21.3 Three Hinged Arch 545
21.4 Illustrative Examples 546
Problems 554
xii
22. INFLUENCE LINES 556 - 602
22.1 Introduction 556
22.2 Moving Loads 556
22.3 Influence Lines 563
22.4 Influence Lines for Beams 564
22.5 Influence Lines for Girders with Floor Beams 576
22.6 Muller – Breslau Principle 580
22.7 Influence Lines for Trusses 583
22.8 Counters in Bridge Trusses 591
22.9 Influence Lines for Arches 592
Problems 599
23. CABLES 603 - 631
23.1 Introduction 603
23.2 Static Determinacy and Stability 604
23.3 General Equation of a Cable 605
23.4 Length of Cable 612
23.5 Graphical Analysis 613
23.6 Deformations of a Parabolic Cable 617
23.7 Illustrative Examples 619
Problems 630
24. SPACE TRUSSES 632 - 644
24.1 Introduction 632
24.2 Analysis of Space Trusses 633
24.3 Illustrative Examples 635
Problems 642
25. APPROXIMATE ANALYSIS OF STATICALLY
INDETERMINATE STRUCTURES 645 - 661
25.1 Introduction 645
25.2 Number of Assumptions Required 645
25.3 Portal Frames 646
25.4 Mill Buildings 647
25.5 Lateral Bracing for Bridges 648
25.6 Building Frames for Vertical Loads 648
25.7 Analysis for Lateral Loads 651
Problems 659
INDEX 662
