Mechanics of Solids and Structures, Second Edition

by Fenner; Roger T.

• ISBN13: 9781439858141
• ISBN10: 1439858144
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-06-12
• Publisher: CRC Press

Summary

Mechanics of Solids emphasizes the development of analysis techniques from basic principles for a broad range of practical problems, including simple structures, pressure vessels, beams and shafts. Increased use of personal computers has revolutionized the way in which engineering problems are being solved and this is reflected in the way subjects such as mechanics of solids are taught. A unique feature of this book is the integration of numerical and computer techniques and programs for carrying out analyses, facilitating design, and solving the problems found at the end of each chapter. However, the underlying theory and traditional manual solution methods cannot be ignored and are presented prior to the introduction of computer techniques All programs featured in the book are in FORTRAN 77-the language most widely used by engineers and most portable between computers. All of the programs are suitable for PCs, minicomputers, or mainframes and are available on disk. Another important feature of this book is its use of both traditional and SI units. Many examples through the text are worked in both sets of units. The data and results for every example are also shown in both types of units. Mechanics of Solids is intended for use in a first course in mechanics of solids offered to undergraduates. An Instructor's Manual containing solutions to every problem in the book is available.

Table of Contents

List of Symbols	p. xiii
List of Computer Programs	p. xv
Preface (to the second edition)	p. xvii
Preface (to the first edition)	p. xix
Introduction	p. 1
Modeling of engineering systems	p. 2
Review of statics	p. 4
Some definitions and concepts	p. 4
Laws of motion	p. 5
Free body diagrams	p. 6
Conditions of equilibrium	p. 8
Examples	p. 9
Concepts of stress and strain	p. 17
Definition of stress	p. 17
Normal and shear stresses	p. 19
Stress concentrations	p. 24
Allowable stresses	p. 26
Definitions of strain	p. 28
Influence of material properties	p. 30
Principles of mechanics of solids	p. 33
Use of numerical methods and computers	p. 35
Problems	p. 36
Statically Determinate Systems	p. 45
Pin-jointed structures	p. 45
Equilibrium analysis of plane pin-jointed structures	p. 49
Method of sections for plane pin-jointed structures	p. 61
A computer program for plane pin-jointed structures	p. 62
Analysis of space frames	p. 72
Uniformly loaded thin shells	p. 73
Pressurized thin-walled cylinder	p. 73
Pressurized thin-walled sphere	p. 81
Thin rotating ring or cylinder	p. 84
Flexible cables	p. 86
Simplified analysis for cables with small dip	p. 86
Problems	p. 96
Relationships between Stress and Strain	p. 103
Hydrostatic stress and volumetric strain	p. 103
Elastic stress-strain equations	p. 106
Normal loading	p. 106
Shear loading	p. 112
Hydrostatic loading	p. 112
Relationships between the elastic constants	p. 113
Thermal strains	p. 116
Other stress-strain relationships	p. 120
Deformations of statically determinate systems	p. 122
Pin-jointed structures	p. 122
Pressurized thin-walled cylinder	p. 126
Pressurized thin-walled sphere	p. 131
Problems	p. 135
Statically Indeterminate Systems	p. 139
Pin-jointed structures	p. 139
Finite element analysis	p. 140
Computer program	p. 149
Practical applications	p. 152
Design of pin-jointed structures	p. 163
Other statically indeterminate systems	p. 164
Example problems	p. 164
Liquid-filled thin-walled vessels	p. 173
Resisted thermal expansion	p. 176
Problems	p. 183
Bending of Beams: Moments, Forces, and Stresses	p. 193
Some practical examples of beams	p. 193
Types of supports for beams	p. 195
Types of loads on beams	p. 199
Shear forces and bending moments in beams	p. 202
Definition of shear force and bending moment	p. 202
Relationships between distributed lateral force, shear force, and bending moment	p. 213
Computer method for shear force and bending moment distributions	p. 231
Stresses due to bending	p. 247
Normal stresses due to bending	p. 247
Shear stresses due to bending	p. 256
Beams of various cross sections	p. 262
Unsymmetrical bending	p. 271
Reinforcement of beams	p. 274
Composite beams	p. 278
Bending of initially curved beams	p. 288
Combined bending and axial loads	p. 290
Problems	p. 296
Bending of Beams: Deflections	p. 309
Relationship between curvature and bending moment	p. 310
Deflection of statically determinate beams	p. 313
Solutions for some simple cases	p. 313
Use of step functions	p. 323
Solution by superposition	p. 336
Beams of varying cross section	p. 338
Deflection of statically indeterminate beams	p. 341
Computer method for beam deflections	p. 351
Finite element analysis	p. 351
Computer program	p. 359
Practical applications	p. 363
Problems	p. 372
Torsion	p. 379
Torsion of shafts	p. 380
Torsion of thin-walled cylinders	p. 380
Torsion of solid circular shafts	p. 384
Torsion of hollow circular shafts	p. 390
Nonuniform circular shafts	p. 393
Shafts of noncircular cross section	p. 397
Statically determinate torsion problems	p. 397
Statically indeterminate torsion problems	p. 403
Combined bending and torsion	p. 410
Problems	p. 413
Instability and the Buckling of Struts and Columns	p. 421
Stable, neutral, and unstable equilibrium	p. 423
Buckling of pin-ended struts	p. 428
The perfect pin-ended strut	p. 428
Eccentrically loaded struts	p. 432
Initially curved struts	p. 437
Effects of lateral loading	p. 439
Struts and columns with other end conditions	p. 442
Column with ends fixed and free	p. 443
Column with both ends fixed	p. 445
Column with ends fixed and pinned	p. 447
More general cases of column buckling	p. 450
Failure of real struts and columns	p. 453
Problems	p. 458
Transformations of Stress and Strain	p. 465
Transformation of stress	p. 467
Notation for stresses	p. 467
Plane stress	p. 470
Principal stresses and maximum shear stresses	p. 476
Mohr's circle for plane stress	p. 482
Principal stresses and maximum shear stresses in a three-dimensional state of stress	p. 485
Transformation of strain	p. 489
Notation for strains	p. 489
Plane strain	p. 491
Principal strains and maximum shear strains	p. 496
Relationship between Young's modulus and shear modulus	p. 497
Mohr's circle for plane strain	p. 499
Use of strain gages	p. 500
Computer method for stresses and strains at a point	p. 506
Yield and fracture criteria	p. 508
Yield criteria for ductile materials	p. 509
Failure criteria for brittle materials	p. 514
Examples	p. 516
Problems	p. 521
Equilibrium and Compatibility Equations: Beams and Thick-Walled Cylinders	p. 529
Stress equilibrium equations	p. 529
Equilibrium equations in Cartesian coordinates	p. 529
Equilibrium equation in polar coordinates for axial symmetry	p. 531
Strain compatibility equations	p. 533
Definitions of strains in terms of displacements	p. 534
Compatibility equation in Cartesian coordinates	p. 537
Compatibility equation in polar coordinates for axial symmetry	p. 538
Application to beam bending	p. 538
Pure bending	p. 538
Cantilever with a concentrated end force	p. 543
Simply supported beam with a distributed force	p. 549
Application to thick-walled-cylinders and disks	p. 554
Internally pressurized thick-walled cylinder	p. 555
Compound cylinders	p. 562
Rotating disks	p. 572
Problems	p. 577
Energy Methods of Structural Mechanics	p. 583
Introduction	p. 583
Concepts of work and energy	p. 584
Strain energy and complementary strain energy	p. 588
Virtual work and complementary virtual work	p. 598
Preliminary comments	p. 598
Internal and external virtual work	p. 599
Variational operator and fundamental lemma	p. 604
The principle of virtual displacements and its special cases	p. 607
The principle of virtual displacements	p. 607
The principle of minimum total potential energy	p. 609
Castigliano's Theorem I	p. 612
The principle of virtual forces and its special cases	p. 620
The principle of complementary virtual work	p. 620
The principle of minimum complementary energy and Castigliano's Theorem II	p. 622
Problems	p. 632
Appendices	p. 637
Properties of Materials	p. 637
Density, elastic, and thermal-properties	p. 637
Strength properties	p. 639
Conversion factors between SI metric and US customary units	p. 640
Moments of Area	p. 640
First moment of area	p. 640
Second moment of area	p. 645
Parallel axis theorem	p. 646
Perpendicular axis theorem	p. 648
Properties of some simple shapes	p. 649
Deflections and Slopes for Some Common Cases of the Bending of Beams	p. 649
Cantilevers	p. 651
Simply supported beams	p. 652
Built-in beams	p. 653
Answers to Even-Numbered Problems	p. 655
Index	p. 665
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