SMTS II Theory of Structures [CONTAINING 28 CIIAPTKRS] STRENGTH OF MATERIALS AND THEORY OF STRUCTURES (VOLUME II) By PUNMIA Dr. B.C. B.E. (Hons.), M.E. (Hons.)* Ph.D. FORMERLY PROFESSOR AND HEAD, DEPARTMENTOFCrViLENGINEERING, & DEAN, FACULTYOFENGINEERING J.N.V. UNIVERSITY, JODKPUR * ASHOK KUMAR JAIN CONSULTING ENGINEER ARIHANTCONSULTANTS, BOMBAY * ARUN KUMAR JAIN ASSISTANT PROFESSOR OF CIVIL ENGINEERING M.B.M. ENGINEERING COLLEGE, JOD-HPUR IN SI UNITS NINTH EDITION (Thoroughly Revised and Enlarged) LTD LAXMI PUBLICATIONS PVT. NEW DELHI . : 'ithiisbedby AXMIPUBLICATIONS (P)LTD /19,Ansari Road,Daryaganj, JewDelhi - 110002. / 326 23 68 'hones : \ 326 23 70 Preface to the Third Edition 327 67 99 I In this volume, the author has attempted to present more "axes 011-325 25 72 advanced topics in strength ofmaterials and mechanics ofstructures 011-326 22 79 in a rigorous and coherent manner. Both volumes I and II cover the entire course for degree, diploma and AMIE examinations in H,7sd-diAar.iTMbaounttdioalr,aslJaaSttlraenedth.aTr.CNiatgyar{,PhMoandera:s018{1P-h2o2ne1:207424)-4344726) cbthoeinastmassiunbasjnedcfto.furraVmcoehsla,uptmaeserswIeIlolnhaassmoobvneiensntgatdilcioavalidldsyeidonndienttseotartmfiiconaualrltyepadbreettsae.mrsmP.ianrPatatrteI -2-453.1stFloor,RamkotePostOffice,Hyderabad(Phone:040-4750247) II dealswithstaticallyindeterminatestructures and contains ten chap- EMAIL [email protected] ters, including a chapter on deflection of perfect frames. Part III WEBSI:TE wvw.LaxmiPub!icatioiis.com contains five chapters on advanced topics on strength of materials. : Thesechapters are mostly useful formechanical engineeringstudents. FirstEdition July. 1965 Pan IV has three chapters on miscellaneous topics., including one Second Edition : Oct., I%7 on elementary theory of elasticity. The contents of the book are TFhoiurrdthEdEidtiitoinon : JJaann.., 11997714 sodesignedthat thebookisequallyusefultocivilaswellasmechanical FifthEdition :: May, 197S and electrical engineering students. SixthEdition : June, 1982 Thebookiswrittenentirelyinmetricunits.Eachtopicintroduced NSEiiengvthethnhtEhEddiEitdtiiiotoninon::: JJAaapnnr..i.,l.11991S899692 ilsartgehornouumgbhelry doefscnruimbeerd,icathleetxhaemoprlyesisarriegoirnoculsuldyeddetvoeliolpleuds,traatneditas Reprint Oct., 1993 application. General statements ofimportantprinciplesand methods RRReeeppprrriiinnnttt : OAAcpptrr.ii,ll,,11399999S%5 anruembaelrmosotf prionbvalreimasblyagriev-eanvailbayblepraatctitchaelenidllucsftreataicohns.chapAterl,artgoe Reprint : Jan..2000 enable the student to test his reading at different stages of his Reprint Oct.,2000 studies. : ©1971,1989,1992 B.C. PUNMIA The author is highly thankful to Prof. S.C. Goyal and Shri ©1992 ASHOKKUMARJAIN,ARUN KUMARJAIN O.P. Kalani for their permission to reproduce some chapters and examples from the book 'Strength of Materials and Theory of ISBN : 81—7008—138—6 StructuresVol. TPwrittenbytheauthorin theircollaboration. Thanks are also due to the senate of the London University and to the AllRightsReservedhytheAuthors. Secretary of the Institution of Structural Engineers, London, for Thisbook, orpansthereof, maynothereproducedinanyform ortranslated their kind permission to reproduce their examination questions. The withoutthewrittenpermissionojtheAuthors. London University is in no way responsible for the accuracy of the C—3631/00 answers. In preparing this text, the author has freely consulted many excellent books on the subject and the help is grateniiy Price: Rs. 210.00 Only. acknowledged. MEMRAOFFSETPRESS Every effort was made to eliminate errors in the book, but Printed at : should the reader discover some, the author would appreciate 1979.Ganj MeerKhan,New.Delhi.Phones 3268574 (vi) (Wi) having these brought to his attention. Suggestions from the readers for improvement in the book will be most gratefully acknowledged. Preface to the Ninth Edition Jodhpur, PUNMIA In the Ninth Edition, the book has been completely rewritten. January 17, 1971 B.C. The book has been divided into four sections. Section I, containing five chapters, is on 'Moving Loads*. Section 2 on 'Statically Indeter- Preface to the Fourth Edition minate* Structures', contain eleven chapters. Section three is devoted-^ In the fourth edition, the subject matter of the book has to 'Advanced Topics in Strength of Materials' and has six chapters. been updated. An appendix, containing questions from the AMIE Lastly, section 4 has six chapters on 'Miscellaneous Topics*. Thus section B examinations in "Theory of Structures", has been added. in the Ninth Edition of the book, which has 28 chapters, five new 'chapters have been added. The author is thankful to Shri J.N. Shrivastava for his valuable sug- gestions for improvements in the book. In each chapter, the subject matter has been rearranged and new articles have been added. Many new advanced problems have Jodhpur, January 1, 1974 B.C. PUNMIA been added which will be useful for competitive examinations. Jodhpur B.C, PUNMIA Preface to the Sixth Edition Mahaveer Jayaniee ASHOK KUMAR JAIN In the Sixth Edition, the subject matter has been revised and 15-4-92 ARUN KUMAR JAIN updated. A large number of Examples in SI «nits have been added at the end of the book. Jodhpur, PUNMIA 15th June, 1982 B.C. Preface to the Seventh*fidition In the Seventh Edition, the entire book has been rewritten using SI units. The old diagrams have been replaced by new onesr Jodhpur PUNMIA Deepawaii B.C. 18.11.85. Preface to the Eighth Edition In the Eighth Edition, the subject matter has been revised and updated. A new chapter on Building Frames has been added at the end of the book. Jodhpur 1st Sept, 1988 B.C PUNMIA Contents PART MOVING LOADS I : I. ROLLING LOADS 3.53 1.1 Introduction ... 3 1.2. Single Concentrated Load 4 ... 1.3 Uniformly Distributed Load Longer than the Span of the Girder 7 ... 1.4. Uniformly Distributed Load Shorter than the Span of the Girder ... 10 1.5. Two Point Loads with a Fixed Distance Between them ... 15 1.6. Several Point Loads : Max. B.M. ... 37 1.7. Several Point Loads : Max. S.F. ... 40 1.8. Equivalent Uniformly Distributed Load 46 ... 1.9. Combined Dead and Moving Load S.F. Diagrams 43 ... 2. INFLUENCE LINES 54-78 2.1. Definitions 54 ... 2.2. Influence Line for Shear Force ... 55 2.3. Influence Line for Bending Moment 58 ... 2.4. Load Position for Max. S.F. at a Section 59 ... - 25."Load Position for Max. B.M. at a Section ... 60 3. INFLUENCE LINES FOR GIRDERS WITH FLOOR BEAMS 79-88 3.1. Introduction ... ijg 3.Z Influence Line of S.F. for Girder with Floor Beams 80 ... 33. Load Positions for Max. S.F. 82 ... 3.4. Influence line of B.M. for Girder with Floor Beams 84 ... 3.5. Load Positions for Max. B.M. . ... 85 4. LNFLUENCE LINES FOR STRESSES IN FRAMES 89-114 4.1 Pratt Truss with Parallel Chords 89 ... 4.2. Pratt Truss with Inclined Chords .„ 91 4.3. Warren Truss with Inclined Chords 94 ... 4.4. K-Truss .„ 95 45. Baltimore Truss with sub-ties : Through Type ... 99 w (xi) 4.6. Hultimore Truss with sub-ties 8.5. Fixed Beams — 182 : Deck Type ... 103 SLOPE DEFLECTION METHOD 200-244 9. THE44..M87..U:LPBeaLTnlEhntrsRiyom-louvBrgaeRhniETatSryuLposerAsUPweitPttihRtIsNTurCbu-IssPtsrLuEwtisth sub-ties 11.5.....-111501260 999...123... ICFnoutnnrtdoiadnmuuecotniutosanlB:eEaqSumigasntiaoCnnodsnveFnrtaimoens without ».-.•. 222000152 Joint Translation 5.1. Introduction ... U5 9.4. Portal Frames with Side Sway - 219 5.2. The Muller-Breslau Principle .„ 115 MOMENT DISTRIBUTION METHOD 245-327 10. 55..34.. PInrfolpupeendceCLainntielsevfeorrs Statically Determinate Beams .„.. 112136 1100..1Z. IFnutnrdoadmuectnitoanl:PrSoipgonsiCtoinonvseftion -~ 224457 5.5. Continuous Beam : Influence Line for B.M. ... 127 103. The Moment Distribution Method ... 252 5.6. Continuous Beam : Influence Line for S.F. ... 129 10.4. Sinking of Supports - 263 5.7. Influence Line for Horizontal Reaction ... 130 10.5. Continuous Beam on Elastic Props ... 265 5.8. Fixed Beams ... .146 10.6. Portal Frames with ho Side Ssway ... 265 PART 10.7. Portal Frames with Side Sway ... 288 STATICALLY INDEIITERMINATE 10.8. Portal Frames with Inclined Members ... 310 COLUMN ANALOGY METHOD 328-365 STRUCTURES 11. 11.1. The Column Analogy •• 328 STATICALLY INDETERMINATE BEAMS AND 11.2. ABpepalmicsation of the Analogy for Fixed % - 331 FRAMES 155-167 U3. Properties of a Symmetrical Analogous 6.1. Introduction „. 155 Column »• 332 6.2. Types of Supports : Reaction Components ... 156 11.4. Portal Frames - 343 6.3. External Redundancy ... 157 11.5. Generalised Column Flexure Formula ... 344 6.4. Staticajiy Indeterminate Beams „ 158 11.6. Portal Frame with Hinged Legs - 346 6.5. Degree of Redundancy of Articulated METHOD OF STRAIN ENERGY 366-400 12. Structures _. 159 12.1. General Principles - 366 TIIEb6..76G..EFDMNreeEagtmrhReeoAsedLsofoMfEReATndHaulOnydsDiasncy of Rigid Jointed 16*„_.-111766*24 11122Z..423... SCFDiatersrfstaltiiegnclTtihEiaoennnoeo'rrsogefymFiBrisnetaLmTihneebaoyrreCEamlsatsitgilciaSnoy'sstem --•• 333666679 (Method of Consistent Deformation) 7.1. Introduction „ 168 12^.5. SMeicnoinmduTmheSotrraeinm Energy and Castigliano's •• ^2 7.2. Statically Indeterminate Beams and Frames „. 168 1Z6. Analysis of Statically Indeterminate Beams 73. Maxwell's Law of Reciprocal Deflection „ 174 and Portal Frames by Minimum Strain 7.4. Generalised Maxwell's Theorem : Betti's Reciprocal Energy - 385 Theorem _ 175 DEFLECTION OF PERFECT FRAMES 401-441 THE THREE MOMENT EQUATION METHOD 179-199 l'j. 13.1- General ... 401 8.1. Clapeyron's Theorem of Hire; Moments _ 179 13.2. The Unit Load Method ... 402 8.2. EI Constant .* General Loading ... 181 13.3. Joint Deflection if Linear Deformation 8.3. EI Constant : No settlement ... 181 of all the Members are known ... 404 8.4. EI Constant : U.D.L. on both Spans 181 13:4. Deflection by Castigliano's First Theorem ... 424 (xii) (xiii) 13.5. Maxwell's Reciprocal Theorem Applied to Frames 429 PART III 136 Granhica! Method ... *tj£ ADVANCED TOPICS IN STRENGTH OF MATERIALS i\mLUVnUAPiI tKAMiU> 442-494 14.1. Degree of Redundancy ™ 442 BENDING OF CURVED BARS 607-643 14.2. Application of Castigliano's Theorem 17. - 607 of Minimum Strain Energy 443 17.1. Introduction 14.3. Maxwells Method 462 17.2. Bars with Large Initial Curvature - 609 i1h4..j4.. StrieisjsuienscudueouctsoseEsrrsoureiniuLejncxgitehrnsi ...... 469 1177.34.. ADJetteenramtiinvaetiEoxnpreosfsiFoanctfoorrm/ for Various •-» 661134 Load and Error in I.enel.h AT) Sections 14.6. Externally Indeterminate Frames *¥!(* 17.5. BinentdhiengPloafneCuorfveSdymBmaertrbyy Forces Acting - 624 ^AULiEo AINU svSrlLNMvJPf BsvlD\«fco 495...-544H5j 17.6. Stresses in Hooks - 625 17.7. Stresses in Rings Subjected to 15.1. Introduction „ 495 Concentrated Load - 631 15.2. Equilibrium of Light Cable : General 17.8. Stresses in Simple Cham Link 637 v^iiojc incorcm — 496 STRESSES DUE TO ROTATION 644-666 i1j3-.j4.. Aufnliciin]o]fuijuyaclwAeisaucci vsotc .«.. 459072 18. 18.1. Rotating Ring or Wheel Rim - 644 1i5j..5o.. TieimirpcecraxtiumrgecuStoruesuseensinign Suiursupcernsion Cabie „™. 550132 1188.32.. RDoitsactiwnigthDiCsecntral Hole •--• 666455703 1u5.i8. GT-iiipwwr.uudmieunr&emlriaail1g1uiclro^p oO^itulri*iv*co«n*2i*ui«igiIInIijTiLrmWuvnsJi fP-XfIiXnIwKrCtU ... 534 111888..346... SPDoeilrsimcdisosDfiibsUlceniSfpoeremdSotfrenagtSholid Disc •» 665547 - 659 18.7. Rotating Cylinder 54(i-<iw>4 18A Hollow Cylinder - 661 io.i. introauction _. 546 - 664 iioo.jz.. ununueyars aitnceocre(rianeoreucai /\rcn} « 55447S 19. VIBI&R9A.TISoOlNidSCAylNiDndeCrRITICAL SPEEDS 667-702 16.4. Three Hinged Arch - 549 19.1. Introduction ~ 667 16.5. Moving Loads on Three Hinged Arches 563 19.2. Linear Vibrations : Simple Harmonic - 667 (6.6. Two Hinged Arch - 571 Motion - 669 16.7. TfworoKHinged Parabolic Arch : Expression ™ 573 1199.34.. LTornagnistvuedrisnealViVbirbartaitoinosn - 674 16.8. fTowroHHinged Circular Arch : Expression ™ 575 19.5. TLroaandsevdersBeeaVimbroatrioSnhsaftof a Uniformly - 676 io.y. Moving Loaos on two rnngea Arches 580 19.6. Transverse Vibrations of a Beam or Shaft with 1166..1101.. TReeamcpteiroantuLroecuesffefcotrs Two. Hinged Arch ...... 558914 19.7. SCreivteircaall oProinWthirLloiandgsSpeed of Shafts -- 667888 - 691 16.12. Fixed Arch _ 593 19.8. Torsional Vibrations 16.13. Three Hinged Spandril Braced Arch 597 20. FLAT CIRCULAR PLATES 703-718 ... - 703 20.1. Introduction 20.2. Symmetrically Loaded Circular Plate - 703 203. Circular Plate Freely Supported at its ^ Circumference — 7 (xiv) (xv) 20.4. CSiurpcpuolrartedPlaatte iwtsithCirCceuntmrfaelrenHcoele : Freely 7j3 PART IV 20.5. Circular Plate Clamped at its MISCELLANEOUS TOPICS Circumference 714 21. ASYMMETRICAL BENDING 7191756 23. WELDED JOINTS 788-809 21.1. Introduction 7i9 23.1. General ... 733 21.2. Centroidai Principal Axes of a Section 720 23.Z Types of Welds ... 789 21.3. Graphical Method for Locating Principal 233. Strength of Welds • ... 792 Axes 722 23.4. Fillet Welds of Unsymmetrical Sections, 21.4. Moments of Inertia Referred to any set of Arially Loaded. ... 798 Rectangular Axes 725 23.5. Welded Joint Subjected to Bending 21.5. Bending Stresses in Beam Subjected to Moment goo Unsymmetrical Bending " 730 23.6. Welded Joint Subjected to Torsion S02 ... 21.6. Resolution of Bending Moment into Two 24. METHOD OF TENSION COEFFICIENTS 810-820 Components along Principal Axes 730 24.1. Introduction g|rj 21.7. Resolution of B.M. into any Two 2211..98.. .GLRroeaccpathtaiincoganullaoMrfeNtAexhueotsdraTl:hrMAooxiumsgehnttahle EClelrifptsreoid ... 7773334]3 25. SP22A44C..32E.. FATnReanAlsyMisoEinsSCoofefPflicaineentFsrames 821.....-. 8g831i62o 21.10. The Z-Poiygon "* 25.1. Introduction 821 ?43 ... 21.11. Deflection of Beam Under Unsymmetrical 25.2. Method of Tension Coefficients Applied Bending ^ ?4? to Space Frames ... 822 22. ELEMENTARY THEORY OF ELASTICITY 757-786 25.3. Illustrative Examples ... 824 22.1. State of Stress at a Point : Stress tensor _ 75? 26. PLASTIC THEORY 837-882 22.2. Equilibrium Equations 26.1. Introduction _ 837 759 223. Strain Components : Strain Tensor 75j 26.2. The Ductility of Steel ... 838 22.4. Compatibility Equations 26.3. Ultimate Load Carrying Capacity of 762 22.5. Bounda^ Condition Equations **" 7^4 . Members Carrying Axial Forces ... 839 22.6. Generalised Hooke's Law : Homogeneity ^ 26.4. Plastic Bending of Beams ... 847 and Lsotropy 26.5. Evaluation of Fully Plastic Moment 849 ... 22.7. Two Dimensional Problems 767 26.6. Plastic Hinge 353 22-8. Compatibility Equations in Two 26.7. Load Factor ... 355 Dimensional Case 76g 26.8. Method of Limit Analysis : Basic 22.9. Stress Function "* 770 Theorems ... 856 22.10. Equilibrium Equations in Polar 26.9. Determination of Collapse Load for Some Coordinates Standard Cases of Beams 859 ... 22.11. Compatibility Equations and Stress Function 26.10. Portal Frames 874 in Polar Coordinates 773 27. BUILDING FRAMES 883-930 22.1Z Solution of Two Dimensional Problems by 27.1. Introduction g83 Polynomials Tn 27.2. Substitute Frame g84 22.13. Bending of a Cantilever Loaded at the 27.3. Analysis for Vertical Loads . 887 ... ...783 27.4. Methods of Computing B.M. 890 ... 27.5. Analysis of Frames Subjected to (xvi) 27.6. Portal Method - 904 27.7. Cantilever Method - 906 27.8. Factor Method - 915 METHOD 931-974 28, KAMI'S SECTION 1 931 28.1. Introduction --* 28.2. Continuous Beams and Frames without MOVING LOADS --932 Joint Translation 28.3 Symmetrical Frames » 953 28.4 Frames with Side Sway - 956 INDEX 975 • Chapter ROLLING LOADS 1. FOR BEAMS INFLUENCE LINES t FOR GIRDERS WITH FLOOR X INFLUENCE LINES BEAMS FOR FRAMES INFLUENCE LINES 4. THE MULLER BRESLAU PRINCIPLE 5.