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Machine Design Databook PDF

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Copyrighted Material MACHINE DESIGN DATABOOK K. Lingaiah, Ph.D. Bangalore University Professor Emeritus Adichunchanagiri Institute of Technology Second Edition l\1cGraw-Hill New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyrighted Material Copyrighted Material M 1.j:}pdt.fl§IQll •. l11/Ti,i .M Copyright 0 2003, 1994 by The McGraw-Hin C'°mpanies. Die. All cigh13 reserved. Exce.pt as pennitted wtder U1e United St3tes Copyright Act of 1976. no part of this publication m3y be reproduced or distnlmted in any form or by any means. or stored in a data- base or l'etJ~ev.U iy1;.1.e1n, \vir.hout the prio1· \VTitr.e.n peimi~ion of the publisher. ISBN: 97S-0--07-150<>49-4 MAID: 0-07-150049-9 The material in Un• <Book also appea·rs in Ute print vmiou of this tiUe: ISBN: 978-0-07-136707-3, JvllilD: 0-07-136707-1. ~~ll tJadensarkJ> a~ tra..kn1arks of tht irr~J>t'ctiv~ Q\vne~. Rallier llw,u put. 3 lndc:1nark syn1l>ol -af\cI o~ry occurri:uce of a trodtaria-rked n3.me1 \\1t3 use names in an editorl3l fashion only. and t\> tho benetitofthe trademark 0 \\1ler. "\Vith no intention ofinfc1ngetnent of the cradcmack. \\'11ere such designations appear in this book. they have been printed \Vith initial caps. f\.1cGr3\\'· Rill eBooks are a-....'3Hablc at special quantity discounts lO me. as prcmimns and saJcs prv1notions, or for use in corporate training progf3ms. ·ro contact a rcprcscnL'ltivc please "isit the Cont'lct Us page a.t w''"v.mhprofcssivnal.con1. Infut1nation conuined in this \\'Otk has bttn obtained by The McOm,v-flill Co1npanies.. Inc. (''~·lcOru\v-lllll") fro1n sources believed co be reliable. HO\vever. neither McOta\v-HiH not its authors guarantee the nc.<:1.lr'dC}' or co1npleteness of any info11nalion published hie.rein, nnd neilhet f\.fc0raw-Hil1 nor its aut110ts s.hall l>e 1·espons-ible for any enX>rs, onlissions, OI' darooges mising out of use oft11is inform..tiou. Thi& '"''k is published wid1 the understsnding that McGraw-Hill and its awh<>rs are supplying infoallarion but are not at.tcnrpting to render eng:iJletring or other- professionl\J Ut"\~~ s. lf such scivices att rtqui~d rhe :JSSisc3ncc. of an Appropriate professional should l>c sought. TBRMS OF tJSB This is a copydgbtcd \\'Otk and The Mc.Graw·Bill Cornpanies. Inc. ('~tcGro\v .. ffiU') and its licensors n-set'-<e all rights in and to the '"'Ork. Use of this '"'Ork is subject to these tenns. Except as pernlltted wider the Copyright.Act of 1976 and the right to store and retrieve ono copy of tltc "\Vork. you ni::.ty not decompile, disassetublc. reverse engineer. reproduce. rnodif)'. create derivative V.'Otks based upotL ttan:smit, distribut.e. dissen1inar.e. sell, j)Ublish or sublice-nse dte work 01· :my pal't of it "~tho1n 'f\.1cGraw·RilPs p1·ior consent. You 1nay use cJ1e \Vork for your ov.'Tl nonc.ontnle.rciaJ and personal use~ any at.her we of c.he \\.Yll"k is strictly prohibited. \'0111· 1ight to use dte work ID3)' bl! temlinar.ed if you fail to cotnply \vith these tenns. THB WORK JS PR0\·1DED .,AS IS." McGRAW-HILL AND ITS LlCBNSORS MAKE NO GUARANTEES OR WARRANTLES AS TO THE ACCURACY. ADEQUACY OR COMPLETENESS OF OR RESUUS TO BE OBTAINED FROM USING THE WORK. INCLUDING A}.'Y rNFORM.l\flON THAT CAN Bil ACCESSED THROUGH TUil WORK VIA llYPERLINK OR OTHERWISE. AND EXPRESSLY DISCJ..AJM ANY WARRANTY. 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Tilis limitation of liability sl1a1J apply to any claim or cause \Vha1.s.oever \vhether such c1aim or 03use a.rises in contract. lort or otherwise. Copyrighted Material Copyrighted Material CONTENTS Preface xv Ackuowledgments xix 1 Pro1>erties of Engineering lVlaterials 1.1 S)~nbols I.I Suffixes l.2 Abbreviations 1.2 Hardness l.7 Wood 1.1 1 References 1.81 Bibliography Ui2 2 Static Stresses in !Vfachine Elements 2.1 Symbols 2.L Simple Stress and Strain 2.3 Srresses 2.4 Pure Shear 2.6 Biaxial Stresses 2.6 Biaxial Stresses Combined with Shear 2.7 Mohr's Circle 2.8 T ria.xi al Stress 2.8 Mohr's Circle 2.9 S!ress-S(rain Relations 2.10 Statistically Iudetenniuate Members 2.11 Thermal S(ress and Strain 2.12 Compo11nd Bars 2.13 Equivalent or Combined Modulus of Elas'.icity of Compound Bars 2.14 Power 2.14 Torsion 2.15 Bending 2.16 Eccentric Loading 2.17 Column Formulas 2.17 Hertz Contact Stress 2.20 Design of Machine Elements and Structures Made of Composite 2.23 Filament Reinforced Structures 2.25 Filament Binder Composite 2.27 Filament-Overlay Composite 2.29 Formula' and Darn. for Various Cross Sections of Machine Rlemen~5 230 Refe.rences 2.49 Bibliography 2.49 iii Copyrighted Material Copyrighted Material iv Contents- 3 Dynamic Stresses in l\ilacbinc Elements 3.1 Symbols 3.1 Inertia Force J.3 Energy Met11od 3.3 fmpact Stresses 3.4 Bcudjng Stress in Beams due to Cmpact 3.6 Torsion of Beam/llar due to Impact 3.7 Longitudinal Stre>>·Wave iu Elastic Media 3.8 Longitudinal Impact on a Long Bar 3.8 Torsional Impact 011 a Bar 3.10 Illertia in Collision of Elastic Bodies 3.12 Resilience 3.12 References 3.16 Oibliography 3.16 4 Stress Concentration and Stress Intensity in J\'Iachine l\1embers 4.1 Symbols 4.1 Reduction or Mitigation of Stress Concentrations 4.19 Stress Intensity Factor or Fracture Toughness Factor 4.25 References 4.33 5 Design of l\il achine Elements for Strength 5.1 Symhols 5.1 Slatjc Loads 5.3 Index of Sensitivity S.4 Surface Condit.ion 5.4 Safety Fac:.or S.5 T heories of Frulure 5.10 Cyclic Loads 5.10 Stress-Stress and Stress-Load Relations S.12 The Combined Stresses 5.16 Combined Stresses in Terms of Loads 5.17 Creep 5.18 Reliability S.19 References 5.25 6 Cains 6.1 Symbols 6.1 Radius of Curvature. of Disk Cam with Roller Follower 6.2 Radius of Curvature of Disk Cam with Flat-Faced Follower 6.3 PressUl'e Angle 6.4 Radial Cam-T ranslating Roller-Follower-Force Analysis 6.6 Side Thrust 6.7 Basic Spiral Contour Cam 6.7 Basic Spiial Conrour Ca.m Constants 6.8 Her12. Contact Stresses 6.8 References 6.15 Copyrighted Material Copyrighted Material Contents ,. 7 Pipes, Tubes, and Cylinders 7.1 Symbols 7.1 Long Thin Tubes with lu!e.rnal Pressure 7.2 Engines aud Pressure Cylinders 7.9 Openings in Cylindrical Drums 7.9 Tbin Tubes 1\-iLh E.xtcrnal Pressure 7.10 Sl1ort Tubes with External Pressures 7. l l Lame's Equations for Thick Cylinders 7.12 Deformation of a Thick Cylinder 7.13 Compo11nd Cyijnders 7.14 Thermal S:resses in Long Hollow Cylinders 7.14 Clavarino's Equation for Closed Cylinders 7.16 Dirnie·s Equations for Open Cylinders 7.16 Oarlow's Equation ?.Ii References 7.20 8 Design of Pressure Vessels, Plates, and Shells 8.1 Symbols 8.1 Plates 8.7 Shells (Unfired Pressure Vessel) 8.11 Fonned Heads under Pressure o n Concave Side 8.23 Formed Heads under Pressure o n Convex- Side 8.27 Unstayed Flat Heads and Covers 8.31 Stayed F lat and Braced Pla(es or Surfaces 8.35 Openings and Reinforcem~ut 8.37 Ligamenr.s 8.60 Bolted Plange Connect.ions 8.61 Integral-Type F langes and L-00se-Type Flanges with a Hub 8.67 Loose-Type Flanges without Hub and Loose-Type F langes with Hub Which (he Designer Chooses to Calculate 8.67 References 8.71 9 Design of Power Boilers 9.1 Symbols 9.l Boiler Tubes and Pipes 9.2 Dished Head.• 9.7 Unstayed F lat Heads and Covers 9.& Combustion Chamber and Furnaces 9.9 T he Maxim1011 Allowable Pressure for Special Furnaces Having Walls Reinforced by Ribs, Rings, and Corrngations 9.14 Final Ratios 9.19 Refe.rences 9.26 10 Rotating Disks and Cylinders 10.l Symbols 10.l Disk of Uniform Strength Rotating at w rad/ s 10.l Solid Disk Rotating at w rad/s 10.I Hollow Disk Rotating at w rad/ s 10.2 Solid Cylinder Rotating at w rad /s 10.3 Copyrighted Material Copyrighted Material vi Contents- Hollow Cylinder Rotating al w rad/ s I0.3 Solid Thin Ut1iform Disk Ro'.ating at w rad/ sunder Exrerual Pressure Po I0.4 Hollow Cylinder of Unifonu T hickness Rotating at w rad is. Subject to Internal (p;) and External (;oJ Pressures 10.5 Rotating Thick Disk a11d Cylinder wilh Unifom1 Thickness Subject to Thermal Stresses 10.6 Rotating L-Ong Hollow Cylinder with Uniform Thickness Rotating at w rad/s Subject to T hermal Stress 10.7 Deflection or a Rotating Disk of Uniform Thickness in Radial Direction with a Ce11trnl Circular Cutout 10.7 Refe.rences I 0.9 11 l\1etal Fits, Tolerances, and Surface Texture Symbols Suffixes Press and Shrink Fi:s lnterfereuce Fits Tolerances and Allowances References 12 Design of \Velded Joints Symbols Fillet Weld Butt Weld T ransverse Fillet Weld Parallel Fillet Weld Length of Weld Eccentricity in a Fillet Weld Eccentric Loads S:resses .Fatigue Strength Design Stre..<s of Welds T he St re.nglh Aiialysis of a Typical Weld Joint Subjected to Eccentric Loading Combined Force Due to P, , P,. and .P, at Point Q General Refe.re11ces Bibliography 13 Riveted Joints Symbols Pressure \ 7 essels Pitches Margin Cover Plaies Strength Analy~is of Typical Riveted Joint Efficiency of the RiveLed Joint. T he Length of the Shank of Rivet Copyrighted Material 11.1 I I.I I I.I I l.2 11.4 I 1.6 11.33 12.l 12.1 12.2 12.2 12.3 12.3 12.4 12.4 12.5 12.5 12.6 12.7 12.7 12.10 12.11 12.11 12.11 13.1 13.1 13.2 13.2 13.6 13.6 13.8 U.9 13.9 14 15 Structural Joint Riveted Bracker References Bibliography Design of Shafts Symbols Suffixes Solid Shafts Hollow Shafts Copyrighted Material Comparison Bet.ween Diamerers of Solid and Hollow Shafts of Same Lengrlt Stiffness Rigidity Effect of Keyways The Buckling Factor Shafts Subjected to Various Stresses GeneJ'al Refere11ces Bibliography Flywheels Symbols Kinetic Energy Flywheel Effect or Polar Moment of Inertia Stres.<es in Rim Stresses in Anns Rim Dimensions Arms References 16 Packings and Seals Symbols Elastic Packing Friction Metallic Gaskets Self-Scaling Packing Paclcingless Seals S:raight-01!. Sealings V-Ring Packing Bolt Loads in Gasket Joint According to ASilfE Boil~,. a1Jd PreJSure Vessd Lode Flange Design Dolt Load W References 17 Keys, Pins, Cotters, and Joints Symbols Suffixes Round or Pin Keys Copyrighted Material 13.IO 13.IO 13.11 13. l l 14.l 14.l 14.2 14.2 14.5 14.9 14.IO 14.IO 14.IO 14.10 14.10 14.16 14.17 14.17 15.1 15.I 15.2 15.3 15.3 15.4 15.4 15.5 15.5 16.l 16.l 16.2 16.2 16.2 16.3 16.4 16.4 16.5 16.6 16.7 16.34 17.l 17.1 17.2 17.2 Contents vii vil i Cont~nts Strength of Keys Taper Key Friction of Feather Keys Splines Indian Standard Pins Colter References Copyrighted Material 17.2 17.4 17.7 17.10 t 7.16 17.20 17.24 17.26 18 Threaded Fasteners and Screws for Power Trans1nission 18.1 Symbols S11ffixes Screws Tension Bolled Joint under Exte.rnal L-0ad Preloaded Bolt Gasket .Joints Preloaded Bolts 1111der Dynamic Loading Loading General References 19 Couplings, Clutches, and Brakes Symbols Suffixes 19.1 Couplings Common Flange Co11pling Marine Type of Flange Coupling Pulley Flange Coupling Pin or Busl1 Type Flexible Coupling Oldham Coupling Muff or Sleeve Co11pling Fairbairn's Lap-Box Coupling Split Muff Coupling Slip Couplhtg Sellers' Cone Coupling Hydraulic Couplings 19.2 O utches Positive Clutd1es Frictjoo Clutches Disk Clmches Dimensions of Disks Design of a Typical Clutch Operati11g Lever BxpandJng-R.ing Outches Rim Clutd1es Centrifugal Clutch Overrunning Clutches 1.9.3 llrakes Energy EqlJations Brake Formulas Copyrighted Material 18.1 18.3 l&.3 l&.5 18.6 L8.7 l&.7 18.13 18.20 18.76 19.l 19.L 19.4 19.4 19.4 19.7 19.9 19.1 1 19.12 19.14 19.15 19.15 19.16 19.17 19.17 19.19 19 19 19.20 19.21 19.22 19 23 19.24 19.24 19.25 19.27 19.29 19.29 19.31 Cone Brakes Considering the Lever Disk Drakes Internal Expanding-Rim Brake External Contracting-Rim Brake Heating of Brakes Reiereuces Copyrighted Material 19.34 19.34 19.35 19.35 19 37 19.38 19.42 20 Springs 20. l Symbols 20.I Suffixes 20 .2 Leaf Springs 20.2 Laminated Spring 20.4 Laminated Springs with Initial Curvature 20.5 Disk Springs (Belleville Springs) 20.6 lleLlcal Springs 20.9 Spring Sea le 20.10 Resilience 20.10 Rectangular Section Springs 20.10 Square Sectjon Spring 20. 13 Selection of Maltrials and Stresses for Springs 20.14 Design of Helical Compression Springs 20.15 $(ability of Helical Springs 20.21 Repeated Loading 20.22 Concentric Spr in g.~ 20.24 Vibration of Helical Springs 20.24 S:ress Wave Propagation in Cylindrical Springs under Impact Load 20.26 Helical E.xtension Springs 20.27 Conical Springs 20.28 1\oumetallic Springs 20.29 Torsio11 Springs 20.29 References 20.33 Bibliography 20.33 21. Flexible l\tlacbine Elements 21.1 Symbols Suffixes Belts Belt Lengths and Contact Angles for Open and Crossed Belts Pulleys Indian Standard Specification V-Belt Minimum Allowances for Adjustment of Centers for Two Transmission Pulleys Initial Tension Syncb.ronous Belt Drive Analysis c:onveyor Short. Center Urive Ropes Copyrighted Material 21.l 21.4 21.4 21.14 21.16 21.17 21.22 21.35 21.35 21.35 21.43 21.44 21.45 Cont.cnts ix X Contents Hoisting Tackle Drums Copyrighted Material Iloldiug Capacity of Wire Rope Reels Wire Rope Construction Chains Check for Actual Safety Factor Reierences 22 J\1echaoical Vibrations 21 .46 21.49 21.50 21 .50 21.50 21.&3 21.100 22.l S)~ubols 22.l Simple Harmonic Motion 22.2 Energy 22.4 Logarithmic Decrement 22.7 Equivalent Spring Consr.antS 22.7 Unbala11ce due to Rotating Mass 22.10 Whipping of Rotating Shaft 22.12 Excitatfon of a System by Motion of Support 22.12 Instrument for Vibration Measuring 22.13 Isolation of Vibration 22.13 Undamped Two-Degree-ol~Freedom System \\~tit.out Ex:erual Force 22.15 Dynamic Vibration Absorber 22.15 Torsional Vibrating Systems 22.16 References 22.25 23 Design of Bearings and Tribology 23.l 23.1 Slicling Contact Bearings 23.1 Symbols 21.1 Sllear Stress 23.5 Viscosity 23.5 Hagen-Poiseuille Law 23.12 Vertical Shaft Rotating in a Guide Dearing 23.13 Dearing Pressure 23.17 Idealized Journal Bearing 23.21 Influence of Misalignment of Shaft in Bearing 23.33 Power Loss 23.34 Partial Journal Bearing 23.37 Influence of End Leakage 23.38 Friction in a Full Journal Bearing with End Leakage from B''<lring 23.45 Oil Flow through Journal Bearing 23.47 T hermal Equilibrium of Journal Bearing 23.49 Bearing Cap 23.55 External Pressurized Bearing or Hydros:atic Bearing: Journal Bearing 23.56 Idealized Slider Bearing 23.59 Design of Vertical, Pivot, and Collar Bearing 23.61 Plain Thrust Dearing 23.64 Oil Fihn T hickness 23.66 Coeffi.(,~ent of Fri(.iion 23.67 Hydrosrar.ic Bearing: Step-Bearing 23.67 Spnerical Ilea rings 23. 75 ~ 23.M Copyrighted Material 23.2 Rolling Contact Be.arings Symbols Rolling Elements Beariugs Speed Gear-Tooth Load Static Loadiug Copyrighted Material Basic Static Load R.atillg as per Indian Standards Thnist Bearings Catalogue Information from FAG for the Selection of Bearing Dynamic Load Rating of Bearings Life Basic Dynamic Load Rating as per FAG Catalogue Life Adj1L~ tment Factors Basic Dynamic Load Rating of Bearings as per Indian Standards Thrust Bearings The Equivalen: Dynamic Load for Angular Contact Ball Bearings The Bquivalne~ Dynamic Load for Tapered Roller Boariug's Dimensions, Basic Load Rating Capacity, Fatigue Load Limit, and Maximum PennL'5ible Speed of Rolling Contact Bearings Needle Bearing Load Capacity Pressure Hertz-Con:act Pressure Selection of Fi: for Bearings 23.3 Friction and Wear Symbols Frictjon Wear and Abra<ion General Refe.rences Bibliography 24 l\1iscellaneous l\1lachine Elements 24 .. 1 Crankshafts S}1nbols Suffixes Force Analysis Side Crank llollow Crankpin Dimension of Crankshaft Main Bearing Proportions of Crankshafts Center era n.k Equivalen L Shafts Empirical Proporuons 24.2 Cun·ed Beam Symbols Suffixes General Approximate Empirical Equation for Curved Beams S~resses in Rings Deffection Copyrighted Material 23.77 23.77 23.&0 23.80 23.82 23.&4 23.&4 23.86 23.&8 23.90 23.90 23.90 23.101 23.!05 23.!08 23.117 23.119 23.119 23.120 23.120 23.121 23.150 23.154 23.154 23.156 23.158 23.167 23.173 23.174 24.l 24.1 24.l 24.2 24.2 24.3 24.4 24.5 24.6 24.7 24.9 24.9 24.12 24.12 24.12 24.13 24.15 24.15 24.16 Cont.cnts xi xii Conl•n1S Link Cra11e Hook of Circular Section 24.3 Connecting and Coupling Rod Symbols Design of Connecting Rod Design of Small and Big Ends Design of Bolts for Big-End Cap Design of Coupling Rod 24.4 Piston and Piston Rings S)~ubols Steam Engine Pistons Copyrighted Material Proportions for Preliminary Layout for Plate Pistons S;res.<es Pisrnos for lnremal-Comb1L5rion Engines Commonly Used Empirical Formulas in the Design of Trnnk Pistons for Automotive-Type Engines 24.5 Design of Speed Reduction Gears and Variable-Speed Dri•cs Symbols Planetary Reduction Gears Conditions of Proper Assembly of Planetary Gear Transmission Wave-Type Reduction Gears Variable-Speed Drives Dissipation of Hear in Reduction Gear Drives Minimum and Total Weight Equation for Gear Systems 24.6 Fl'ic.tion Gearin~ S)~ubols Spur Fricrfon Gears Bevel Friction Gears Disk Friction Gears Bearing Loads of Frictio11 Gearing 24. 7 Mecl1anics of Vehicles Symbols Suffixes Calculation of Power Transmission Gearbox Hydraulic Coupling Hydro<l~rnmic Torque Converter Tractive Effort Curves for Cars, Trucks, and Ciry Buses 24.8 lntetmitteot-Motion Mechanisms S~ubols Pawl and Ratchet 24.9 Geneva Mechanism Symbols External Geneva Wheel Displacement Velocity Acceleration Snock or Jerk Torque Acting on ShaftS of Geoeva Wheel and Driver Instantaneous Power Copyrighted Material 24.16 24.16 24.19 24. 19 24.20 24.22 24.22 24.24 24.26 24.26 24.27 24.28 24.28 2430 24.30 24.47 24.47 24.50 24.51 24.52 24.52 24.54 24.56 24.58 24.58 24.58 24.60 24.62 24.65 24.67 24.67 24.68 24.68 24.70 24.73 24.74 24.75 24.79 24.79 24 79 24.82 24.82 24.&3 24.&4 24.84 24.85 24.86 24.87 24.87 Copyrighted Material Contents xiii Forces at the Point of Contact 24.89 Iitternal Gene.va Wheel 24.89 24.10 Uni<ersal Joint 24.91 Symbols 24.91 Single Universal Joint 24.91 Double Universal Joint 24.92 24.11 Unsynunetric.al Bending and Tor.sion of Nondrmlar Cross-Section Machine Elemeuts 24.97 Symbols 24.97 Shear Center 24.98 Unsymmetrical Bending 24.98 Torsion 24.9& Narrow R ectartgnlar Cros.5 Sect.ion.< 24.99 Composire Sections 24.!03 Hollow Thi11-Walled Tubes 24.104 Bending Stresses Caused by Torsion 24.105 Transverse L-Oad o n Deam of Channel Section not through Shear Center 24.106 References 24.116 25 Elements of l\1;1cltinc Tool Design 25.1 Symbols 25.1 25.1 Metal Cutting Tool Design 25.4 Forces ou a Single-Poin: Metal Cutting Tool 25.4 Merchant's Circle for 0..tting Forces for a Single-Point Metal Cutting Tool 25.5 Power 25.8 Speeillc Power or Unit Power Cou:mmption 25.8 Tool Design 25.9 Tool Signature~ 25.9 Tool Life 25.10 25.2 Machine Tools 25.15 Lathe Turning 25.17 DrilLing Machine 25.19 Taps and Tapping 25.25 Broachii1g Machine 25.2& Milling M achines 25.31 References 25.103 26 Retaining Rings and Circlips 26.1 Symbols 26.1 Retaining Rings and Circlips: 26.2 References 26.13 27 Applied Elasticity 27.l Symbols 27.1 Stress ar a Point. 27.3 Equations of Equilibrium 27.6 Transformation of Stress 27.6 Copyrighted Material xiv Cont"'1ts Principal Stresses S(rain Copyrighted Material T hree-Dimensional Stress-Strain System Biaxial Stress-Strain System Shear Strains Strain and Displaceme11t Boundary Conditions Compatibility General Hooke's Law A.iry's Stress Function Cylindrical CoordinaLes SysLem Strain Components Airy's Stress Function in Polar Coordinates Solution of £lastici1.y Problems Using A.iry's Stress Punction Application of Stress Function S(ress Distribution in a Flat Plate with Holes or Cutouts under Different Types of Loads Rotating Solid Disk with Unifonn T ltickness Rotating Disk -.ilh a Central Qrcular Hole of Unifonu Thickness Rotating Disk of Variable Thickness l\eutral Holes (Mansfield Theory) Complex Variable Method Applied to Elasticity Strain Combinations Plane Strain Boundary Conditions Force and Couple Resultant.s around the Boundary Generalized Plane Stress Conditions along a Stress-free Boundary Sol111ion fo,•olving Circular Boundaries Applicat:ion of Conformal Transformation Muskhelishvili's Direct Medtod Torsio11 T orsio11 of Circular Shafi of Variable Diameter Plates Index Copyrighted Material 27.& 27.10 27.10 27. 11 27.11 27.12 27.15 27.15 27.16 27.21 27.22 27.23 27.24 27.25 27.27 27.28 27.32 27.33 27.35 27.36 27.39 27.40 27.41 27.41 27.42 27.42 27.43 27.43 27.44 27.52 27.59 27.68 27.70 T. l

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