Proportional Limit. Yield.Point. Ultimate Strength CHAPTER I. STREBB AND STRAIN

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1 ART --CHAPTER I STREBB AND STRAIN 1 Introduction 2 Types of Loading 3 Stresses Due to Central Loads 4 Stresses on Oblique Section 5 Strains Due to Central Loads 6 Stress-strain Cu~e Proportional Limit YieldPoint Ultimate Strength Elastic Limit Yield Strength Modulus of Elasticity 7 Properties of Structural Materials 8 Statically Indeterminate Axial-Loaded Members 9 Working Stress 10 Thermal Stresses 11 Types or Phenomena of Failure and the Maximum Utilizable Strength of a Material PAQE 12 Stresses in Thin-wailed Cylinders and Spheres Riveted Joints Types of Riveted Joints Definitions Modes of Failure Stresses in Riveted Joints Assumptions Conditions Affecting Strength of Riveted Joints Allowable Stress Welded Joints 'Torsional Load Twisting Moment and Resisting Moment Defined 21 The Torsion Formula 22 Justification for Assumption of Stress Distribution 23 Twisting Moment in Terms of Horsepower and Speed 24 Angle of Twist of Cylindrical Shaft 25 Shaft Couplings 26 Stress Beyond Propol-tional Limit Modulus of Rupture 27 Longitudinal Shearipg Stress in Torsional Member 28 Diagonal Tensile (and Compressive) Stress in Torsional Member 72 vii

2 ART PAGE 29 Preliminary Conaideratione Vertical Shear, Resisting Shear, Bending Moment, and Resisting Moment The Flexure Formula Section of Maximum Bendina - Moment Shear and Moment Diagrams Relation between Shear and Moment Overhanging Beams' Bending Moments Determined Graphically Economical Sections of Beams Shearing Stress in a Beam ' Stress Beyond Proportional Limit Modulus of Rupture Maximum Moment Due to Moving Loads Aaaumptions and Limitations Involved in the Flexure Formula 116! 42 Introduction Elastic Curve Equation Deflection of Simple Beam, Uniform Load Deflection of Simple Beam, Concentrated Load at Mid-span Deflection of Cantilever Beam, Uniform Load Deflection of Overhanging Beam, Uniform Load Deflection of Simple Beam, Concentrated Load Not at Mid-span General Expression for Maximum Deflection Deflection of Beam Due to Shear Introduction Beam Fixed at One End, Supported at Other End; Uniform Load Beam Fixed at Both Ends; Uniform Load Beam Fixed at Both Ends; Concentrated Load at Mid-Span Beam Fixed at One End, Supported at Other End, Concentrated Load at Mid-span Com~arison with Simde Beams Continuous Beams Theorem of Three Momenta Solution of a Typical Problem Values of Momenta and Shears Advantages and Disadvantages of Continuous Beams Theorem of Three Moments for Concentrated Loads 158 CHAPTER VII COMBINED AXIAL AND BENDING LOADS ECCENTRIC LOADS 62 Introduction 160 a A Beam Subjected to an Axial End Load 160

3 CONTENTS 64 Eccentric Longitudinal Load in Plane of Symmetry Eccentric Loads on Riveted Connections Helical Spring 172 CHAPTER VIII COMPREB~ION MEMEIERB COLUMNB 67 Introduction Distinguishing Features of Column Action Slendernessbtio Two Limiting Caaea of Compression Members t Euler's Column Formula Graphical Representation of Formulas for Ideal Columns Effect of Endconditions Methods of Obtaining Formulas for Columns Having Intermediate Slenderness Ratids Gordon-Rankine Formula Significance of Assumption that Column Composed of Component PartsActsmaUnit Straight-line Formula Straight-line Formula for Fixed-ended Columns Straight-line Formula for High*arbon and Alloy-ateel Columns Eccentrically Loeded Columns The Parabolic Formula Equivalent Eccentricity Secant Formula 211 CHAPTER IX RELATION BET-EN STRE~BEB AT A POINT ON DIF~RENT PLANEB PA~~ING THROUGH TEE POINT THEORIE~ OF FAILURP) 85 Maximum Normal Stress Occurs on Plane of Zero Shearing Stress 8 83 Introduction Maximum Shearing Streas in Terms of Principal Stresses 219 Ellipse of Stress Shearing Stresses Combined with One Normal Stress Diagonal Tensile Stress in a Beam Strain Due to Principal Stresses Expression for Ee Theories of Failure of Elastic Action and Their Application 236 CHAPTER X REPEATED LOADS FATIGUE OF METAL^ 90 Introduction EndursnceLimit Lo&ed Stress and Fatigue Failure Values of Endurance Limits with Completely Reversed Stress Working Stregs Based on Endurance Limit Stress Concentration Factor Method of Calculating Localized Stress EfFect of Range of Stress Corrosion-Fatigue 263

4 ART CHAPTER XI IYPA~ AND ENERGY LOADS PAGE 98 Introduction Calculation of Energy Delivered to Resisting Member Stress in Bar Due to Axial Energy Load Comparison of Effects of Static and Energy Loads Special Cases of Axial Energy Loads Working Stress and Working Value of Energy Stresses in Beams Due to Energy Loads EfIect of Form on Energy Resistance of Beams Special Caws of Energy Loads and Beams Torsional Energy Loads Reduction in Energy Load Due to Inertia of Resisting Member 288 PART 11 SPECIAL TOPICS CHAFTER XII DEFLE~ION OF STATICALLY DETERMINATE (MOMENT-AREA METHOD) BEAMS 109 Introduction 292 Slopedeviation Method 110 Theorems of the Slope-Deviation Method Simple Beam; Concentrated Load at Mid-Span Cantilever Beam; Concentrated Load at End Simple Beam; Load Distributed Uniformly Cantilever Beam; Load Distributed Uniformly 298 Conjugatebeam Method 115 Conjugate Beam Defined Simple Beam; Concentrated Load at Mid-span Cantilever Beam; Concentrated Load at End Simple Beam; Load Distributed Uniformly Cantilever Beam; Load Distributed Uniformly Simple Beam; Concentrated Load at Any Point Simple Beam; Cross-Section Not Constant 305 CHAPTER XIII STATICALLY INDETERMINATE BEAMS (MOMENT-AREA METHOD) 122 Introduction 307 Slope-dariation Method 123 Beam Fixed at Both Ends; Load Concentrated at Mid-span Beam Fixed at Both Ends; Load Uniformly Distributed Beam Fixed at One End; Supported at Other End; Load Concentrated at Mid-span Beam Fixed at one End, Supported at Other End; Load Uniformly Distributed Continuous Beam; Theorem of Three Moments 310

5 CONTENTS xi Conjugate-b earn Method PAGE 128 Beam Fixed at Both Ends Load Distributed Uniformly Beam Fixed at Both Ends; Load Concentrated at Mid-span Beam Fixed at One End Supported at Other End; Load Uniformly Distributed Continuous Beam; Theorem of Three Moments 315 CHAPTER XIV LIMITATION OF THE FLEXURE FORMULA FOR SEC~IONS HAVING ONLY ONE AXIS OF SYMMETRY 132 Bending Axis and Shear Center Defined The Shear Center and the Flexure Formula Approximate Location of the Shear Center for a Channel Section Shear Center for Certain Other Sections Having One Axis of Symmetry 323 CHAPTER XV UNSYMMETRICAL BENDING 136 Introduction Stress in Beam Subjected to Unsymmetrical Loading Change in Slope of Neutral Axis and Increase in Streas in Rolled Sections Due to a Very Small Inclination of Plane of Loads to a CHAPTER XVI CURVED FLEXURAL MEMBERS 142 Unit-Stress at Any Point in a Curved Beam The Winkler-Bach Formula 140 Introduction Essentiai Difference between Straight, Beams andcwed Beams Correction Factors for Use in the Straight-Beam Formula 341 CHAPTER XVII FLAT PLATES 146 Stress in Square Plate 144 Introduction Stress in Circular Plate Stress in Rectangular Plate 349 CHAPTER XVIII THICK-WALLED CYLIP~DERS 148 The Problem Defined Lamb's Solution Maximum Shearing Stress MaKimurn Strain and Maximum Value of Ee 362 CHAPTER XIX TORSIONAL RESISTANCE OF BARS HAVING NON-CIRCULAR CROSS-BECTIONS 152 Introduction Torsion of Bar Having a Rectangular Cross-section 367

6 ' CONTENTS CEIAPTER XX COMPOBITE BEAMS REINFORCED CONCRETEI BEUS 164 Composite (Two-material) Beam Timber Beam Reinforced by Steel Plates Reinforoed Concrete Beams Streas in Steel and in Concrete Tee Beams Beams Reinforced in Both Tension and Compression Shearing Stress BondStressmd Anchorage DiagonalTension Reinforcement for Diagonal Tension 387 APPENDIX I PROPERTIES OF AN AREA 1 FIRBT MO~NTB m~ CENTROFB OF AREM 164 Definitions Centroids Found by Integration Centroids of Composite Areas SECOND Momm OR Momm OF INERTIA OF rn AREA 167 Moment of Inertia of an Area Defined Polar Moment of Inertia Radius of Gyration Parallel Axis Theorem Momenta of Inertia Found by Integration Momenta of Inertia of Composite Areas Approximate Method P ~o~ucr oa INERTIA 174 Product of Inertia Defined Parallel Axis Theorem for Product's of Inertia Relation between Momenta of Inertia and Products of Inertia with Respect to TWO Sets of Rectangular Axes through the Same Point in the Area Principal Axea Graphical Solution VALWEB OF Z FOR USE IN CURVED-BEAM FORMULA 179 Values of Z by Integration 416 APPENDIX I1 TABLES OF PROPERTIES OF MATERIALS 180 Uee of Tablee 419 APPENDIX I11 PROPERTIES OF ROLLED STEEL SECTIONS 429 INDIUX 433