1. viPaKeRKOgbgÁúM
Structural Analysis
GñkniBn§³ R.C. Hibbeler
ERbsMrYlCaexmrPasa³ etg qay
viTüasßanCatiBhubec©keTskm<úCa
mhaviTüal½ysMNg;sIuvil
qñaM 2010

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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>$> karviPaKFñwmtamviFIkmøaMg (Force method of analysis: Beams) ..................................342
!0>%> karviPaKeRKagtamviFIkmøaMg (Force method of analysis: Frames)..............................349
!0>^> karviPaK truss tamviFIkmøaMg (Force method of analysis: Trusses) ............................352
!0>&> eRKOgbgÁúMkMub:UsIut (Composite structures) ..................................................................355
!0>*> kMNt;sMKal;bEnßmelIkarviPaKtamviFIkmøaMg
(Additional remarks on the force method of analysis) ...........................................357
!0>(> eRKOgbgÁúMsIuemRTI (Symmetric structures) .................................................................359
!0>!0> ExST§iBlsMrab;FñwmminkMNt;edaysþaTic
(Influence lines for statically indeterminate beams) .............................................360
!0>!!> eKalkarN_mu‘yeyeRbsøÚsMrab;eRKag (Qualitative influence line for frames)............363
cMeNaT (Problems) ............................................................................................370
!!> karviPaKtamviFIbMlas;TI³ smIkar slope-deflection
Displacement method of analysis: Slope-deflection equations
!!>!> viFIsaRsþTUeTAkñúgkarviPaKtamviFIbMlas;TI
(Displacement method of analysis: General procedures).....................................................378
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7. Department of Civil Engineering NPIC
!!>@> smIkar slope-deflection (Slope-Deflection equation) .............................................380
!!>#> viPaKFñwm (Analysis of beams) ...................................................................................386
!!>$> 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