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  • 1. viPaKeRKOgbgÁúM Structural Analysis GñkniBn§³ R.C. Hibbeler ERbsMrYlCaexmrPasa³ etg qay viTüasßanCatiBhubec©keTskm<úCa mhaviTüal½ysMNg;sIuvil qñaM 2010
  • 2. GarmÖkfa edaysarnisiStvisVkrsMNg;sIuvilTaMgGs;minGaceKcputBIcMeNHdwgelImuxviC¢ad¾sMxan;enH)an dUcenHva)anCMrujTwkcitþrbs;´)aTeGaybkERbesovePAenHeLIg. ´)aT)andwgfanisiStTaMgGs;Edl mancMeNHdwgPasabreTskñúgkMritkMNt;NamYyenaH BitCaBi)akkñúgkarsikSaRsavRCavedayxøÜnÉg dUcenH ´)aTBitCasgÇwmfaesovePAmYyk,alenHnwgGacCYysMrYldl;karsikSaRsavRCavrbs;Gñk sikSa)an. ´)aTBitCa)anBüayamy:agGs;smtßPaBedIm,IeFVIeGaykarbkERbenHmanlkçN³eBlelj b:uEnþeTaHCay:agenHkþI ´)aTenAEtTTYlsÁal;fa kareRbIBakübec©keTsCaPasaExμrmYycMnYnenAkñúgesov ePAenHBitCaminGaceKcputBIPaBqÁg b¤minGacTTYlyk)anBIGñksikSa. edaymUlehtuenH BaküGg;- eKøsRtUv)aneRbI nigbgðajedayecosminput. dUcenH ral;mtiriHKn;TaMgGs;nwgRtUv)anTTYlykmk BicarNaedIm,IeFVIkarEksMrYl. müa:gvijeTot edim,IeGaykarsikSa nigkaryl;;dwgrbs;GñksikSaTaMgGs;elImuxviC¢aenHman lkçN³TUlMTUlay nigc,as;las; ´)aTsUmENnaMeGayGñksikSaTaMgGs;KYrGanc,ab;edImCaPasa Gg;eKøsEdlniBn§eday R.C. Hibbeler.
  • 3. Department of Civil Engineering NPIC matika Contents !> RbePTrcnasm<½n§ nigbnÞúk (Types of structures and loads) !>!> esckþIepþIm (Introduction)…………………………………………………………….....1 !>@> cMNat;fñak;eRKOgbgÁúM (Classification of structures)……………………….....……….….2 !>#> bnÞúk (Loads) ………………………………………………………………..……...….6 !>$> karsikSaKNnaeRKOgbgÁúM (Structural design)…………………………………………..19 cMeNaT (Problems)………………………………………… ....………………….20 @> viPaKrcnasm<½n§kMNt;edaysþaTic (Analysis of statically determinate structures) @>!> m:UEDleRKOgbgÁúM (Idealized structures) ..........................................................................24 @>@> eKalkarN_tMrYtpl (Principle of superposition)..........................................................34 @>#> smIkarlMnwg (Equations of equilibrium) .....................................................................35 @>$> PaBkMNt; nigesßrPaB (determinacy and stability) .......................................................36 @>%> karGnuvtþsmIkarlMnwg (Application of the equations of equilibrium) ..........................43 cMeNaT (Problems) .................................................................................................52 #> karviPaK trusses kMNt;edaysþaTic (Analysis of statically determinate trusses) #>!> RbePTrbs; trusses (Common types of trusses) ...........................................................62 #>@> cMNat;fñak;rbs; trusses kñúgbøg; (Classification of coplanar trusses) .............................66 #>#> viFItMN (the method of joints) .....................................................................................73 #>$> Ggát;kmøaMgsUnü (Zero-force members) ........................................................................77 #>%> viFImuxkat; (The method of section) .............................................................................79 #>^> Truss pSM (Compound trusses).....................................................................................84 #>&> Truss saMjúaM (Complex trusses) ..................................................................................88 #>*> Truss kñúglMh (space trusses)......................................................................................91 matika T.Chhay-i
  • 4. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa cMeNaT (Problems) .................................................................................................99 $> bnÞúkxagkñúgEdlekItmanenAkñúgGgát;eRKOgbgÁúM (Internal loading developed in structural members) $>!> bnÞúkxagkñúgenARtg;cMnucCak;lak; (Internal loading at a specified point)......................109 $>@> GnuKmn_kmøaMgkat; nigGnuKmn_m:Um:g; (Shear and moment function)..............................113 $>#> düaRkamkmøaMgkat; nigdüaRkamm:Um:g;sMrab;Fñwm (Shear and moment diagram for a beam) ..................................................................117 $>$> düaRkamkmøaMgkat; nigdüaRkamm:Um:g;sMrab;eRKag (Shear and moment diagram for a frame)..................................................................128 $>%> karsg;düaRkamm:Um:g;Bt;edayeRbIviFItMrYtpl (Moment diagrams constructed by the method of superposition)............................132 cMeNaT (Problems) ...............................................................................................137 %> kab nigeRKOgbgÁúMekagbBaÄr (Cables and arches) %>!> kab (cable) ................................................................................................................148 %>@> kabrgbnÞúkcMcMnuc (Cable subjected to concentrated loads)........................................148 %>#> kabrgbnÞúkBRgayesμI (Cable subjected to a uniform distributed load) .....................150 %>$> eRKOgbgÁúMekagbBaÄr (Arches).....................................................................................156 %>%> eRKOgbgÁúMekagbBaÄrsnøak;bI (Three-hinged arch) .......................................................157 cMeNaT (Problems) ...............................................................................................163 ^> ExST§iBlsMrab;rcnasm<½n§kMNt;edaysþaTic (Influence lines for statically determinate structures) ^>!> ExST§iBl (Influence lines)........................................................................................168 ^>@> ExST§iBlsMrab;Fñwm (Influence line for beams) ..........................................................175 ^>#> eKalkarN_mu‘yeyeRbsøÚ (qualitative influence lines) ................................................178 ^>$> ExST§iBlsMrab;r:tRTkMral (Influence lines for floor Girders)....................................185 ^>%> ExSTi§BlsMrab; trusses (Influence lines for trusses) .................................................188 ^>^> T§iBlGtibrmaenARtg;cMnucmYyEdlbNþalBIes‘rIénbnÞúkcMcMnuc Contents T.Chhay -ii
  • 5. Department of Civil Engineering NPIC (Maximum influence at a point due to a series of concentrated loads)....................192 ^>&> kmøaMgkat; nigm:Um:g;Gtibrmadac;xat (Absolute maximum shear and moment)............198 cMeNaT (Problems) ...............................................................................................203 &> viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl (Approximate analysis of statically indeterminate structures) &>!> bMerIbMras;énviFIRbhak;RbEhl (Use of approximate methods) ....................................214 &>@> Trusses......................................................................................................................215 &>#> kmøaMgbBaÄrenAelIeRKagsMNg; (Vertical loads on Building Frames)..........................218 &>$> Portal Frame nig Trusses ..........................................................................................221 &>%> bnÞúkxagmanGMeBIelIeRKagsMNg;³ Portal method (Lateral load on building frame: Portal method) .......................................................227 &>^> bnÞúkxagmanGMeBIelIeRKagsMNg;³ Cantilever method (Lateral load on building frame: Cantilever method)...............................................230 cMeNaT (Problems) ...............................................................................................236 *> PaBdab (deflection) *>!> düaRkamPaBdab nigExSekageGLasÞic (Deflection diagram and the elastic curve)..................................................................242 *>@> RTwsþIFñwmeGLasÞic (Elastic-curve theory) ...................................................................246 *>#> viFIGaMgetRkalDub (The double integration method)..................................................248 *>$> RTwsþIbTRkLaépÞm:Um:g; (Moment-area theorems) ........................................................254 *>%> viFIFñwmnimitþ (Conjugate-beam method) ......................................................................267 cMeNaT (Problems) ...............................................................................................276 (> PaBdabedayeRbIviFIfamBl (Deflection Using Energy method) (>!> kmμnþxageRkA nigfamBlbMErbMrYlrageFob (External work and strain energy) .............281 (>@> eKalkarN_rbs;kmμnþ nigfamBl (Principle of work and energy) ..............................284 (>#> eKalkarN_rbs;kmμnþnimitþ (Principle of virtual work) ................................................285 (>$> viFIkmμnþnimitþsMrab; Trusses (Method of virtual work: trusses) ...................................288 matika T.Chhay-iii
  • 6. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa (>%> viFIkmμnþnimitþsMrab;Fñwm nigeRKag (Method of virtual work: beams and frames) ...........294 (>^> famBlbMErbMrYlrageFobnimitþEdlbNþalBIbnÞúktamG½kS kmøaMgkat; kmøaMgrmYl nigsItuNðPaB (Virtual strain energy caused by axial load, shear, torsion and Temperature).........306 (>&> RTwsþIbTrbs;kasÞIKøIy:aNU (Castigliano’s theorem) ......................................................312 (>*> RTwsþIbTrbs;kasÞIKøIy:aNUsMrab; trusses (Castigliano’s theorem for trusses) ...............314 (>(> RTwsþIbTrbs;kasÞIKøIy:aNUsMrab;Fñwm nigeRKag (Castigliano’s theorem for beams and frames)..........................................................319 cMeNaT (Problems) ............................................................................................326 !0> viPaKeRKOgbgÁúMminkMNt;edaysþaTictamviFIkmøaMg Analysis of statically indeterminate structures by the force method !0>!> rcnasm<½n§minkMNt;edaysþaTic (Statically indeterminate structures) ........................334 !0>@> viFIsaRsþTUeTAkñúgkarviPaKedayviFIkmøaMg (Force method of analysis: general procedure) ......................................................337 !0>#> RTwsþIbMlas;TIersIuRbUkrbs;m:akSEvl c,ab;ebFI Maxwell’s theorem of reciprocal displacement; Betti’s law .................................341 !0>$> karviPaKFñwmtamviFIkmøaMg (Force method of analysis: Beams) ..................................342 !0>%> karviPaKeRKagtamviFIkmøaMg (Force method of analysis: Frames)..............................349 !0>^> karviPaK truss tamviFIkmøaMg (Force method of analysis: Trusses) ............................352 !0>&> eRKOgbgÁúMkMub:UsIut (Composite structures) ..................................................................355 !0>*> kMNt;sMKal;bEnßmelIkarviPaKtamviFIkmøaMg (Additional remarks on the force method of analysis) ...........................................357 !0>(> eRKOgbgÁúMsIuemRTI (Symmetric structures) .................................................................359 !0>!0> ExST§iBlsMrab;FñwmminkMNt;edaysþaTic (Influence lines for statically indeterminate beams) .............................................360 !0>!!> eKalkarN_mu‘yeyeRbsøÚsMrab;eRKag (Qualitative influence line for frames)............363 cMeNaT (Problems) ............................................................................................370 !!> karviPaKtamviFIbMlas;TI³ smIkar slope-deflection Displacement method of analysis: Slope-deflection equations !!>!> viFIsaRsþTUeTAkñúgkarviPaKtamviFIbMlas;TI (Displacement method of analysis: General procedures).....................................................378 Contents T.Chhay -iv
  • 7. Department of Civil Engineering NPIC !!>@> smIkar slope-deflection (Slope-Deflection equation) .............................................380 !!>#> viPaKFñwm (Analysis of beams) ...................................................................................386 !!>$> viPaKeRKagEdlmineyal (Analysis of Frame: No sidesway)....................................395 !!>%> viPaKeRKagEdleyal (Analysis of frames: Sidesway) .............................................400 cMeNaT (Problems) ...............................................................................................410 !@> karviPaKtamviFIbMlas;TI³ karEbgEckm:Um:g; Displacement method of analysis: Moment distribution !@>!> eKalkarN_TUeTA nigniymn½y (General principles and definitions)...........................415 !@>@> karEbgEckm:Um:g;sRmab;Fñwm (Moment distribution for beams)..................................418 !@>#> karEktRmUvemKuNkRmaj (Stiffness-factor modification) ........................................426 !@>$> karEbgEckm:Um:g;sMrab;eRKagmineyal (Moment distribution for frames: No sidesway) ....................................................431 !@>%> karEbgEckm:Um:g;sMrab;eRKagEdleyal (Moment distribution for frames: Sidesway)..........................................................432 cMeNaT (Problems)................................................................................................................ !#> Fñwm nigeRKagEdlmanGgát; nonprismatic Beams and frames having nonprismatic members !#>!> PaBdabrbs;Ggát; nonprismatic (Deflection of nonprismatic members) ........................ !#>@> lkçN³énkardak;bnÞúkrbs;Ggát; nonprismatic edayeRbIviFI conjugate-beam (Loading properties of nonprismatic members using the conjugate-beam method) .... !#>#> lkçN³énkardak;bnÞúkrbs;Ggát; nonprismatic EdlmanpSayenAkñúgRBWtþib½Rtbec©keTs (Loading properties of nonprismatic members Available from publications) ............. !#>$> karEbgEckm:Um:g;sMran;eRKOgbgÁúMEdlmanGgát; nonprismatic (Moment distribution for structures having nonprismatic members)........................... !#>%> smIkar slope-deflection sMrab;Ggát; nonprismatic (Slope-deflection equation for nonprismatic members) ............................................... cMeNaT (Problems) .................................................................................................. !$> karviPaK truss edayeRbIviFIPaBrwgRkaj (Truss analysis using the stiffness method) matika T.Chhay-v
  • 8. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa !$>!> eKalkarN_mUldæanénviFIPaBrwgRkaj (Fundamentals of the stiffness method)................. !$>@> m:aRTIsPaBrwgRkajrbs;Ggát; (Member stiffness matrix)................................................ !$>#> m:aRTIsbMElgénbMlas;TI nigkmøaMg (Displacement and force transformation matrices) ...................................................... !$>$> m:aRTIsPaBrwgRkajrbs;Ggát;kñúgkUGredaenskl (Member global stiffness matrix) ................................................................................. !$>%> ma:RTIsPaBrwgRkajsMrab; truss (Truss stiffness matrix) .................................................. !$>^> karGnuvtþénviFIPaBrwgRkajsMrab;karviPaK truss (Application of the stiffness method for truss analysis) ............................................... !$>&> kUGredaenrbs; node (Nodal coordinates)....................................................................... !$>*> Trusses EdlmanbMErbMrYlsItuNðaPaB nigkMhusénplitkmμ (Truss having thermal changes and fabrication errors) ................................................ !$>(> karviPaK truss kñúglMh (Space-truss analysis) ................................................................ cMeNaT (Problems) .................................................................................................. !%> karviPaKFñwmedayeRbIviFIPaBrwgRkaj (Beam analysis using the stiffness method) !%>!> kMNt;cMNaMbzm (preliminary remarks)........................................................................... !%>@> m:aRTIsPaBrwgRkajsMrab;Ggát;Fñwm (Beam-member stiffness matrix) ............................... !%>#> m:aRTIsPaBrwgRkajsMrab;eRKOgbgÁúMFñwm (Beam-structure stiffness matrix)........................ !%>$> karGnuvtþénviFIPaBrwgRkajsMrab;karviPaKFñwm (Application of the stiffness method for bema analysis).............................................. cMeNaT (Problems) ..................................................................................................... !^> karviPaKeRKagkñúgbøg;edayeRbIviFIPaBrwgRkaj (Plane frame analysis using the stiffness method) !^>!> m:aRTIsPaBrwgRkajrbs;Ggát;eRKag (Frame-member stiffness matrix)............................. !^>@> m:aRTIsbMElgénbMlas;TI nigkmøaMg (Displacement and force transformation matrices) ....................................................... !^>#> m:aRTIsPaBrwgRkajsMrab;Ggát;eRKagkñúgkUGredaenskl (Frame-member global stiffness matrix) ...................................................................... !^>$> karGnuvtþénviFIPaBrwgRkajsMrab;karviPaKeRKag Contents T.Chhay -vi
  • 9. Department of Civil Engineering NPIC cMeNaT (Problems) .................................................................................................. A. m:aRTIssMrab;karviPaKeRKOgbgÁúM (Matrix algebra for structural Analysis) A>!> niymn½y nigRbePTm:aRTIs (basic definitions and types of matrices) .............................. A>@> karKNnama:RTIs (matrix operation) ............................................................................... A>#> edETmINg; (Determinants) ............................................................................................. A>$> m:aRTIsRcas (Inverse of a matrix) .................................................................................. A>%> viFI Gauss sMrab;KNna simultaneous equation (The Gauss method for solving simultaneous equation) ............................................... cMeLIysMrab;cMeNaTeRCIserIs (Answers to selected problems) .................................. matika T.Chhay-vii

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