Strength of Materials and Structures

Strength of Materials and Structures: An Introduction to the Mechanics of Solids and Structures provides an introduction to the application of basic ideas in solid and structural mechanics to engineering problems.This book begins with a simple discussion of stresses and strains in materials, structural components, and forms they take in tension, compression, and shear. The general properties of stress and strain and its application to a wide range of problems are also described, including shells, beams, and shafts. This text likewise considers an introduction to the important principle of virtual work and its two special forms-leading to strain energy and complementary energy. The last chapters are devoted to buckling, vibrations, and impact stresses.This publication is a good reference for engineering undergraduates who are in their first or second years.

PrefacePrincipal NotationNote on SI Units1 Tension and Compression: Direct Stresses 1.1 Introduction 1.2 Stretching of a Steel Wire 1.3 Tensile and Compressive Stresses 1.4 Tensile and Compressive Strains 1.5 Stress-Strain Curves for Brittle Materials 1.6 Ductile Materials 1.7 Proof Stresses 1.8 Working Stresses 1.9 Load Factors 1.10 Lateral Strains Due to Direct Stresses 1.11 Strength Properties of Some Engineering Materials 1.12 Weight and Stiffness Economy of Materials 1.13 Strain Energy and Work Done in the Tensile Test 1.14 Initial Stresses 1.15 Composite Bars in Tension or Compression 1.16 Temperature Stresses 1.17 Temperature stresses in Composite Bars 1.18 Circular Ring Under Radial Pressure 1.19 Creep of Materials Under Sustained Stresses 1.20 Fatigue Under Repeated Stresses2 Pin-Jointed Frames 2.1 Introduction 2.2 Statically Determinate Pin-Jointed Frames 2.3 Displacements of Statically Determinate Frames 2.4 Frames with Non-Linear Members 2.5 Statically Indeterminate Problems3 Shearing Stresses 3.1 Introduction 3.2 Measurement of Shearing Stress 3.3 Complementary Shearing Stresses 3.4 Shearing Strain 3.5 Strain Energy Due to Shearing Actions4 Joints and Connections 4.1 Importance of Connections 4.2 Modes of Failure of Simple and Riveted Joints 4.3 Efficiency of a Connection 4.4 Group-Bolted and -Riveted Joints 4.5 Eccentric Loading of Bolted and Riveted Connections 4.6 Welded Connections 4.7 Welded Connections Under Bending Actions5 Analysis of Stress and Strain 5.1 Introduction 5.2 Shearing Stresses in a Tensile Test-Specimen 5.3 Strain Figures in Mild Steel; Lüder's Lines 5.4 Failure of Materials in Compression 5.5 General Two-Dimensional Stress System 5.6 Stresses on an Inclined Plane 5.7 Values of the Principal Stresses 5.8 Maximum Shearing Stress 5.9 Mohr's Circle of Stress 5.10 Strains in an Inclined Direction 5.11 Mohr's Circle of Strain 5.12 Elastic Stress-Strain Relations 5.13 Principal Stresses and Strains 5.14 Relation Between E, G, and v 5.15 Strain 'Rosettes' 5.16 Strain Energy for a Two-Dimensional Stress System 5.17 Three-Dimensional Stress Systems 5.18 Volumetric Strain in a Material Under Hydrostatic Pressure 5.19 Strain Energy of Distortion 5.20 Yielding of Ductile Materials Under Combined Stresses 5.21 Elastic Breakdown and Failure of Brittle Materials6 Thin Shells Under Internal Pressure 6.1 Thin Cylindrical Shell of Circular Cross-Section 6.2 Thin Spherical Shell 6.3 Cylindrical Shell with Hemispherical Ends7 Bending Moments and Shearing Forces 7.1 Introduction 7.2 Concentrated and Distributed Loads 7.3 Relation Between the Intensity of Loading, the Shearing Force, and Bending Moment in a Straight Beam 7.4 Sign Conventions for Bending Moments and Shearing Forces 7.5 Cantilevers 7.6 Cantilever with Non-Uniformly Distributed Load 7.7 Simply-Supported Beams 7.8 Simply-Supported Beam Carrying a Uniformly Distributed Load and End Couples 7.9 Points of Inflection 7.10 Simply-Supported Beam with a Uniformly Distributed Load Over Part of the Span 7.11 Simply-Supported Beam with Non-Uniformly Distributed Load 7.12 A Graphical Method of Drawing Bending Moment Diagrams 7.13 Plane Curved Beams 7.14 More General Case of Bending of a Curved Bar8 Bending Moments and Shearing Forces Due to Slowly Moving Loads 8.1 Introduction 8.2 A Single Concentrated Load Traversing a Beam 8.3 Uniformly Distributed Load of Sufficient Length to Cover the Whole Span 8.4 Two Concentrated Loads Traversing a Beam 8.5 Several Concentrated Loads 8.6 Influence Lines of Bending Moment and Shearing Force9 Longitudinal Stresses in Beams 9.1 Introduction 9.2 Pure Bending of a Rectangular Beam 9.3 Bending of a Beam About a Principal Axis 9.4 Beams Having Two Axes of Symmetry in the Cross-Section 9.5 Beams Having Only One Axis of Symmetry 9.6 More General Case of Pure Bending 9.7 Elastic Section Modulus 9.8 Longitudinal Stresses while Shearing Forces are Present 9.9 Calculation of the Principal Second Moments of Area 9.10 Compound Beams 9.11 Elastic Strain Energy of Bending 9.12 Change of Cross-Section in Pure Bending10 Shearing Stresses in Beams 10.1 Introduction 10.2 Shearing Stresses in a Beam of Narrow Rectangular Cross-Section 10.3 Beam of Any Cross-Section Having One Axis of Symmetry 10.4 Shearing Stresses in an I-Beam 10.5 Shearing Stresses in Compound Beams 10.6 Principal Stresses in Beams 10.7 Superimposed Beams 10.8 Shearing Stresses in a Channel Section; Shear Centre11 Beams of Two Materials 11.1 Introduction 11.2 Transformed Sections 11.3 Timber Beam with Reinforcing Steel Flange Plates 11.4 Ordinary Reinforced Concrete12 Bending Stresses and Direct Stresses Combined 12.1 Introduction 12.2 Combined Bending and Thrust of a Stocky Strut 12.3 Eccentric Thrust 12.4 Pre-Stressed Concrete Beams13 Deflections of Beams 13.1 Introduction 13.2 Elastic Bending of Straight Beams 13.3 Simply-Supported Beam Carrying a Uniformly distributed Load 13.4 Cantilever with a Concentrated Load 13.5 Cantilever with Uniformly Distributed Load 13.6 Propped Cantilever with Distributed Load 13.7 Simply-Supported Beam Carrying a Concentrated Lateral Load 13.8 Use of Step-Functions 13.9 Simply-Supported Beam with Distributed Load Over a Portion of the Span 13.10 Simply-Supported Beam with a Couple Applied at an Intermediate Point 13.11 Beam with End Couples and Distributed Load 13.12 Beams with Non-Uniformly Distributed Load 13.13 Cantilever with Irregular Loading 13.14 Beams of Varying Section 13.15 Non-Uniformly Distributed Load and Terminal Couples; the Method of 'Moment-Areas' 13.16 Use of Fourier Series 13.17 The Funicular Analogue of Beam Deflections 13.18 Deflections of Beams Due to Shear14 Built-In and Continuous Beams 14.1 Introduction 14.2 Built-In Beam with a Single Concentrated Load 14.3 Fixed-End Moments for Other Loading Conditions 14.4 Disadvantages of Built-In Beams 14.5 Effect of Sinking of Supports 14.6 Continuous Beams 14.7 Slope-Deflection Equations for a Single Beam 14.8 The Three-Moment Equation15 Plastic Bending of Mild-Steel Beams 15.1 Introduction 15.2 Beam of Rectangular Cross-Section 15.3 Elastic-Plastic Bending of a Rectangular Mild-Steel Beam 15.4 Fully-Plastic Moment of an I-Section; Shape Factor 15.5 More General Case of Plastic Bending 15.6 Comparison of Elastic and Plastic Section Moduli 15.7 Regions of Plasticity in a Simply-Supported Beam 15.8 Plastic Collapse of a Built-In Beam16 Torsion of Circular Shafts and Thin-Walled Tubes 16.1 Introduction 16.2 Torsion of a Thin Circular Tube 16.3 Torsion of Solid Circular Shafts 16.4 Torsion of a Hollow Circular Shaft 16.5 Principal Stresses in a Twisted Shaft 16.6 Torsion Combined with Thrust or Tension 16.7 Strain Energy of Elastic Torsion 16.8 Plastic Torsion of a Circular Shaft 16.9 Torsion of Thin Tubes of Non-Circular Cross-Section 16.10 Torsion of a Flat Rectangular Strip 16.11 Torsion of Thin-Walled Open Sections17 The Principle of Virtual Work and Its Applications 17.1 Introduction 17.2 The Principle of Virtual Work 17.3 The Displacements of a Pin-Jointed Frame 17.4 Statically Indeterminate Pin-Jointed Frames 17.5 Temperature Stresses in Redundant Frames 17.6 Deflections of Beams 17.7 Statically Indeterminate Beam Problems 17.8 Plastic Bending of Mild-Steel Beams 17.9 Reciprocal Characteristics of Linear-Elastic Systems18 Strain Energy and Complementary Energy 18.1 Properties of the Strain Energy Function 18.2 Complementary Energy 18.3 Statically Determinate Frame Carrying Two Equal and Opposite External Forces 18.4 Solution of Statically Indeterminate Frames Using Complementary Energy 18.5 Initial Lack of Fit of Members of the Frame 18.6 Complementary Energy in Problems of Bending19 Springs 19.1 General Properties of Springs 19.2 Coiled Springs 19.3 Geometry of Helical Springs 19.4 Close-Coiled Helical Spring: Axial Pull 19.5 Close-Coiled Helical Spring: Axial Couple 19.6 Open-Coiled Helical Spring: Axial Force 19.7 Open-Coiled Helical Spring: Axial Couple 19.8 Plane Spiral Springs 19.9 Close-Coiled Conical Spiral Spring 19.10 Approximate Theory of Leaf Springs20 Elastic Buckling of Columns and Beams 20.1 Introduction 20.2 Flexural Buckling of a Pin-Ended Strut 20.3 Pin-Ended Strut with Eccentric End Thrusts 20.4 Initially Curved Pin-Ended Strut 20.5 Design of Pin-Ended Struts 20.6 Strut with Uniformly Distributed Lateral Loading 20.7 Buckling of a Strut with Built-In Ends 20.8 Buckling of a Strut with One End Fixed, and the Other End Free 20.9 Buckling of a Strut with One End Pinned, and the Other End Fixed 20.10 Flexural Buckling of Struts with Other Cross-Sectional Forms 20.11 Torsional Buckling of a Cruciform Strut 20.12 Modes of Buckling of a Cruciform Strut 20.13 Lateral Buckling of a Narrow Beam21 Vibrations of Beams 21.1 Introduction 21.2 Free Vibrations of a Mass on a Beam 21.3 Free Vibrations of a Beam with Distributed Mass 21.4 Forced Vibrations of a Beam Carrying a Single Mass 21.5 Damped Free Oscillations of a Beam 21.6 Damped Forced Oscillations of a Beam 21.7 Vibrations of a Beam with End Thrust22 Impact Stresses in Rods 22.1 Introduction 22.2 Velocity of Propagation of Stress in a Straight Rod 22.3 Constant Stress Applied at One End of the Rod 22.4 Reflection of the Stress Wave at the Ends of a rod 22.5 Longitudinal Impact of Rods 22.6 Rod Struck by a Moving MassAnswers to ProblemsIndex