Strength of Materials and Structures

Preface

Principal Notation

Note on SI Units


1 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 Stresses


2 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 Problems


3 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 Actions


4 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 Actions


5 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 Materials


6 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 Ends


7 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 Bar


8 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 Force


9 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 Bending


10 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 Centre


11 Beams of Two Materials


11.1 Introduction


11.2 Transformed Sections


11.3 Timber Beam with Reinforcing Steel Flange Plates


11.4 Ordinary Reinforced Concrete


12 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 Beams


13 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 Shear


14 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 Equation


15 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 Beam


16 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 Sections


17 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 Systems


18 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 Bending


19 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 Springs


20 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 Beam


21 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 Thrust


22 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 Mass

Answers to Problems

Index