Khmer Structural Analysis - Teng Chhay

8/9/2019 Khmer Structural Analysis - Teng Chhay

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viPaKeRKOgbgÁ

Structural Analysis

GñkniBn³ R.C. Hibbeler

bkERbeday³ etg q y

viTüasßanCatiBhubec©keTskm


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GarmÖkfa

edaysarnisi StvisVkrsMNg;sIuvilTaMgGs;minGaceKcputBIcMeNHdwgelImuxviC¢ad¾sMxan;enH)an

dUcenHva)anCMrujTwkcitþrbs;́ )aTeGaybkERbesovePAenHeLIg. ´)aT)andwgfanisi StTaMgGs;EdlmancMeNHdwgPasabreTskñ úgkMritkMNt;NamYyenaH BitCaBi)akkñ úgkarsikSaRsavRCavedayxø ÜnÉgdUcenH ́ )aTBitCasgÇwmfaesovePAmYyk,alenHnwgGacCYysMrYldl;karsikSaRsavRCavrbs;GñksikSa)an.

´)aTBitCa)anBüayamy:agGs;smtßPaBedIm,IeFV IeGaykarbkERbenHmanlkçN³eBleljb:uEnþeTaHCay:agenHkþI ´)aTenAEtTTYlsÁal;fa kareRbIBakübec©keTsCaPasaEx μrmYycMnYnenAkñ úgesov

ePAenHBitCaminGaceKcputBIPaBqÁg b¤minGacTTYlyk)anBIGñksikSa. edaymUlehtuenH BaküGg;-eKøsRtUv)aneRbI nigbgðajedayecosminput. dUcenH ral;mtiriHKn;TaMgGs;nwgRtUv)anTTYlykmkBicarNaedIm,IeFV IkarEksMrYl.

müa:gvijeTot edim,IeGaykarsikSa nigkaryl; ;dwgrbs;GñksikSaTaMgGs;elImuxviC¢aenHmanlkçN³TUlMTUlay nigc,as;las; ´)aTsUmENnaMeGayGñksikSaTaMgGs;KYrGanc,ab;edImCaPasaGg;eKøsEdlniBn§eday R.C. Hibbeler.


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Department of Civil Engineering NPIC

mati ka

T.Chhay-i

matika

Contents

> RbePTrcnasm!> esckþ Iepþ Im (Introduction)…………………………………………………………….....1 !>@> cMNat;fñak;eRKOgbgÁú M (Classification of structures)……………………….....……….….2!>#> bnÞ úk (Loads) ………………………………………………………………..……...….6 !>$> karsikSaKNnaeRKOgbgÁú M (Structural design)…………………………………………..19

cMeNaT (Problems)………………………………………… ....………………….20

@> viPaKrcnasm!> m: UEDleRKOgbgÁú M (Idealized structures) ..........................................................................24 @>@> eKalkarN_tRmYtpl (Principle of superposition) .......................................................34 @>#> smIkarlMnwg (Equations of equilibrium) .....................................................................35 @>$> PaBkMNt; nigsßiPaB (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 kñ úgbøg; (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 kñ úglMh (space trusses) ......................................................................................91


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBhubec©keTskm bnÞkxagkñgEdlekItmanenAkñgGgát;eRKOgbgÁ

(Internal loading developed in structural members)

$>!> bnÞ úkxagkñ úgenARtg;cMNucCak;lak; (Internal loading at a specified point) ................... 109 $>@> GnuKmn_kmøaMgkat; nigGnuKmn_m: Um:g; (Shear and moment function) ............................. 113 $>#> düaRkamkmøaMgkat; nigdüaRkamm:Um:g;sRmab;Fñwm

(Shear and moment diagram for a beam) .................................................................. 117 $>$> düaRkamkmøaMgkat; nigdüaRkamm: Um:g;sRmab;eRKag

(Shear and moment diagram for a frame) ................................................................. 128 $>%> karsg;düaRkamm: Um:g;Bt;edayeRbIviFItRmYtpl

(Moment diagrams constructed by the method of superposition) ........................... 132 cMeNaT (Problems)............................................................................................... 137

%> kab nigeRKOgbgÁekagbBaÄr (Cables and arches)

%>!> kab (cable)................................................................................................................ 148 %>@> kabrgbnÞúkcMcMNuc (Cable subjected to concentrated loads) ..................................... 148 %>#> kabrgbnÞúkBRgayes μ I (Cable subjected to a uniform distributed load)..................... 150

%>$> eRKOgbgÁ ú MekagbBaÄr (Arches) .................................................................................... 156 %>%> eRKOgbgÁú MekagbBaÄrsnøak;bI (Three-hinged arch)....................................................... 157

cMeNaT (Problems)............................................................................................... 163

^> ExS\T§BlsRmab;rcnasm!> ExS\T§ iBl (Influence lines) ....................................................................................... 168

^>@> ExS\T§ iBlsRmab;Fñ wm (Influence line for beams) ....................................................... 175 ^>#> eKalkarN_mu‘yeyeRbsøÚ (qualitative influence lines)................................................ 178 ^>$> ExS\T§ iBlsRmab;r:tRTkRmal (Influence lines for floor Girders) .............................. 185 ^>%> ExS\Ti §BlsRmab; trusses (Influence lines for trusses) .............................................. 188 ^>^> \T§iBlGtibrmaenARtg;cMNucmYyEdlbNþalBIes‘rIénbnÞ úkcMcMNuc


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(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

&> viPaKeRKOgbgÁminkMNt;edaysþaTicedayviFIRbEhl

(Approximate analysis of statically indeterminate structures)

&>!> beRmIbRmas;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 nigExSekageGLasÞ ic

(Deflection diagram and the elastic curve)..................................................................242 *>@> RTwsþ IFñwmeGLasÞic (Elastic-curve theory) ...................................................................246 *>#> viFIGaMgetRkalDub (The double integration method)..................................................248 *>$> RTwsþIbTRkLaépÞm: Um:g; (Moment-area theorems) ........................................................254 *>%> viFIFñ wmnimitþ (Conjugate-beam method) ......................................................................267

cMeNaT (Problems) ...............................................................................................276

(> PaBdabedayeRbvFfamBl

(Deflection Using Energy method)

(>!> km μnþxageRkA nigfamBlbERmbRmYlrageFob (External work and strain energy) ........281 (>@> eKalkarN_rbs;km μnþ nigfamBl (Principle of work and energy) ..............................284 (>#> eKalkarN_rbs;km μnþnimitþ (Principle of virtual work)................................................285 (>$> viFIkm μnþnimitþsRmab; Trusses (Method of virtual work: trusses) ................................288


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBhubec©keTskm%> viFIkm μnþnimitþsRmab;Fñ wm nigeRKag (Method of virtual work: beams and frames) ........ 294 (>^> famBlbERmbRmYlrageFobnimitþEdlbNþalBIbnÞúktamG½kS kmøaMgkat; kmøaMgrmYl nigsItuNðPaB

(Virtual strain energy caused by axial load, shear, torsion and Temperature) ........ 306

(>&> RTwsþIbTrbs;kasÞ IKøIy:aNU (Castigliano’s theorem)...................................................... 312 (>*> RTwsþIbTrbs;kasÞ IKø Iy:aNUsRmab; trusses (Castigliano’s theorem for trusses) ............ 314 (>(> RTwsþIbTrbs;kasÞ IKøIy:aNUsRmab;Fñ wm nigeRKag

(Castigliano’s theorem for beams and frames) ......................................................... 319

cMeNaT (Problems)............................................................................................ 326

0> viPaKeRKOgbgÁminkMNt;edaysþaTictamviFIkmøaMg

Analysis of statically indeterminate structures by the force method

!0>!> rcnasm@> viFIsaRsþTUeTAkñúgkarviPaKedayviFIkmøaMg

(Force method of analysis: general procedure)...................................................... 337 !0>#> RTwsþ IbMlas;TIersI uRbUkrbs;m:akSEvl c,ab;ebFI

Maxwell’s theorem of reciprocal displacement; Betti’s law ................................ 341 !0>$> karviPaKFñ wmtamviFIkmøaMg (Force method of analysis: Beams).................................. 342 !0>%> karviPaKeRKagtamviFIkmøaMg (Force method of analysis: Frames) ............................. 349

!0>^> karviPaKtruss

tamviFIkmøaMg(Force method of analysis: Trusses)............................ 352

!0>&> eRKOgbgÁú MkM ub: UsI ut (Composite structures).................................................................. 355!0>*> kMNt;sMKal;bEnßmelIkarviPaKtamviFIkmøaMg

(Additional remarks on the force method of analysis)........................................... 357

!0>(> eRKOgbgÁ ú MsIuemRTI (Symmetric structures) ................................................................. 359 !0>!0> ExS\T§ iBlsRmab;Fñ wmminkMNt;edaysþaTic

(Influence lines for statically indeterminate beams) ............................................ 360 !0>!!> eKalkarN_mu ‘yeyeRbsøÚsRmab;eRKag (Qualitative influence line for frames)......... 363

cMeNaT (Problems)............................................................................................ 370

> karviPaKtamviFIbMlas;TI³ smIkar slope-deflection

Displacement method of analysis: Slope-deflection equations

!!>!> viFIsaRsþTUeTAkñ úgkarviPaKtamviFIbMlas;TI(Displacement method of analysis: General procedures) ....................................... 378


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!!>@> smIkar slope-deflection (Slope-Deflection equation) .............................................380!!>#> viPaKFñ wm (Analysis of beams) ...................................................................................386 !!>$> viPaKeRKagEdlmineyal (Analysis of Frame: No sidesway)....................................395

!!>%> viPaKeRKagEdleyal (Analysis of frames: Sidesway) .............................................400 cMeNaT (Problems) ...............................................................................................410

@> karviPaKtamviFIbMlas;TI³ karEbgEckm:m:g;

Displacement method of analysis: Moment distribution

!@>!> eKalkarN_TUeTA nigniymn½y (General principles and definitions)...........................415 !@>@> karEbgEckm: Um:g;sRmab;Fñ wm (Moment distribution for beams)..................................418

!@>#> karEktRmUvemKuNkRmaj (Stiffness-factor modification) ........................................426 !@>$> karEbgEckm: Um:g;sRmab;eRKagmineyal

(Moment distribution for frames: No sidesway) ....................................................431 !@>%> karEbgEckm: Um:g;sRmab;eRKagEdleyal

(Moment distribution for frames: Sidesway)..........................................................432 cMeNaT (Problems) ...............................................................................................441

#> Fñm nigeRKagEdlmanGgát;Edlmanmuxkat;ERbRbYl

Beams and frames having nonprismatic members

!#>!> PaBdabrbs;Ggát;Edlmanmuxkat;ERbRbYl (Deflection of nonprismatic members)....445 !#>@> lkçN³énkardak;bnÞ úkrbs;Ggát;Edlmanmuxkat;ERbRbYledayeRbIviFIFñ wmnimitþ

(Loading properties of nonprismatic members using the conjugate-beam method) .447

!#>#> lkçN³énbnÞ úkrbs;Ggát;Edlmanmuxkat;ERbRbYlEdlmanpSayenAkñúgRBwtþ ib½Rtbec©keTs(Loading properties of nonprismatic members Available from publications) .......452

!#>$> karEbgEckm: Um:g;sRmab;eRKOgbgÁ úMEdlmanGgát;Edlmanmuxkat;ERbRbYl(Moment distribution for structures having nonprismatic members).....................455

!#>%> smIkar slope-deflection sRmab;Ggát; Edlmanmuxkat;ERbRbYl(Slope-deflection equation for nonprismatic members) .........................................459

cMeNaT (Problems) ............................................................................................461

$> karviPaK truss edayeRbIviFIPaBrwgRkaj

(Truss analysis using the stiffness method)


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBhubec©keTskm!> eKalkarN_mUldæanénviFIPaBrwgRkaj (Fundamentals of the stiffness method).......... 464 !$>@> m:aRTIsPaBrwgRkajrbs;Ggát; (Member stiffness matrix) ......................................... 466 !$>#> m:aRTIsbMElgénbMlas;TI nigkmøaMg

(Displacement and force transformation matrices) ................................................ 468

!$>$> m:aRTIsPaBrwgRkajrbs;Ggát;kñ úgkUGredaenskl(Member global stiffness matrix)........................................................................... 471

!$>%> ma:RTIsPaBrwgRkajsRmab; truss (Truss stiffness matrix)......................................... 472 !$>^> karGnuvtþénviFIPaBrwgRkajsRmab;karviPaK truss

(Application of the stiffness method for truss analysis) ........................................ 477 !$>&> kUGredaenrbs; node (Nodal coordinates) ................................................................ 487 !$>*> Trusses EdlmanbERmbRmYlsItuNðaPaB nigkMhusénplitkm μ

(Truss having thermal changes and fabrication errors).......................................... 491 !$>(> karviPaK truss kñ úglMh (Space-truss analysis).......................................................... 496 cMeNaT (Problems)............................................................................................ 498

%> karviPaKFñmedayeRbIviFIPaBrwgRkaj

(Beam analysis using the stiffness method)

!%>!> kMNt;cMNaMbzm (preliminary remarks) .................................................................... 501

!%>@> m:aRTIsPaBrwgRkajsRmab;Ggát;Fñ wm(Beam-member stiffness matrix)...................... 503

!%>#> m:aRTIsPaBrwgRkajsRmab;eRKOgbgÁ úMFñwm (Beam-structure stiffness matrix)............... 505 !%>$> karGnuvtþénviFIPaBrwgRkajsRmab;karviPaKFñ wm

(Application of the stiffness method for beam analysis) ....................................... 506 cMeNaT (Problems)............................................................................................... 518

^> karviPaKeRKagkñgbøg;edayeRbIviFIPaBrwgRkaj

(Plane frame analysis using the stiffness method)

!^>!> m:aRTIsPaBrwgRkajrbs;Ggát;eRKag (Frame-member stiffness matrix)...................... 521 !^>@> m:aRTIsbMElgénbMlas;TI nigm:aRTIsbMElgénkmøaMg

(Displacement and force transformation matrices) ................................................. 522 !^>#> m:aRTIsPaBrwgRkajsRmab;Ggát;eRKagkñ úgkUGredaenskl

(Frame-member global stiffness matrix)................................................................ 524

!^>$> karGnuvtþénviFIPaBrwgRkajsRmab;karviPaKeRKag


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(Application of the stiffness method for frame analysis) .....................................525 cMeNaT (Problems) ..................................................................................................535

A. m:aRTIssRmab;karviPaKeRKOgbgÁ

(Matrix algebra for structural Analysis)

A>!> niymn½y nigRbePTm:aRTIs (basic definitions and types of matrices)........................538 A>@> RbmaNviFIma:RTIs (matrix operation)........................................................................539 A>#> edETmINg; (Determinants) .......................................................................................543 A>$> cRmas;rbs;m:aRTIs (Inverse of a matrix) ..................................................................545 A>%> viFI Gauss sRmab;KNnaRbB½n§smIkar

(The Gauss method for solving simultaneous equation) .........................................547

cMeNaT (Problems) ...............................................................................................549

cemø IysRmab;cMeNaTeRCIserIs (Answers to selected problems) ..........................550


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RbePTrcnasm RbePTrcnasm esckþepþm (Introduction)

rcnasm


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RbePTrcnasm


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm


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RbePTrcnasm


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm#> bnÞk (Load)

enAeBlEdleKkMNt;TMhMrbs;eRKOgbgÁú MrYcehIy eKcaM)ac;kMNt;bnÞ úkEdleRKOgbnÞ úkRtUvRT. CaerOy² eKRtUveFV IkareRCIserIsbnÞúkeRcInRbePTEdleKrMBwgfavanwgeFV IGMeBImkelIeRKOgbgÁ ú MedIm,IeFV IkarsikSaKNna. ]TahrN_ eRKOgbgÁú MGKarx


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RbePTrcnasm


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RbePTrcnasm= O.K. dUcenH ) ) kN mmkN F F 9.630.45/42.1 22 == dUcenH bnÞ úkGefrsrubEdlRTedayssrCan;pÞal;dIKW

kN kN kN F F F F R 0.1079.631.43 =+=+= cemø Iy

bnÞks


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cMeNaT

T.Chhay -21

cMeNaT

!>!> kRmalrbs;XøaMgEdlpÞ úkTMnijRsal²RtUv)aneFIVeLIgedayebtugkRmas; mm150 .RbsinebIkRmalmanbeNþay m3 nigTTw wg m4.2 cUrkMNt;kmøaMgpÁÜbEdlbgáeLIgedaybnÞ úkefr nigEdlbgáeLIgedaybnÞ úkGefr.

!>@> CBa¢aMgGKarmYyeFVIBI\dæTMhM mm200 . enAépÞmçagrbs;CBa¢aMgeFV IBIr)areQITMhM ×mm50

mm100 nigmanbUkEtelIépÞCBa¢aMgmçag. Rbsin

ebICBa¢aMgenHmankm#> kRmalCan;TIBIréneragcRkTm¶n;RsalmYyRtUv)ansagsg;BIebtugGarem:kRmas; mm100 nigbEnßmBIelIeday cinder fill kRmas; mm75 dUcbgðajkñ úgrUb. RbsinebIBidansRmab;Can;TImYypSM BI metal lath nigbnÞHmñagsila cUrkMNt;bnÞúkefrkñ úgmYy ÉktþaépÞrbs;kRmal.

!>$> kRmalEdlmanRbehagxagkñ úgmYlRtUv)aneFV IBIebtugsuT§. kMNt;Tm¶n;rbs;kRmalenH.RbehagnImYy²manGgát;p©it mm100

!>%> kRmalxNÐénfñak;eronmYyeFI VBIebtugsuT§

Tm¶n;RsalEdlmankRmas;mm125

. RbsinebIkRmalenH manbeNþay m8 nigTTwg m6 cUrkMNt;kmøaMgpÁÜb EdlbgáeLIgedaybnÞúkefr nigbnÞ úkGefr.

!>^> Fñ wmGkSr T cak;Rsab;manmuxkat;dUcbgðajkñ úgrUb. kMNt;Tm¶n;rbs;vakñ úgmYyÉktþa RbsinebI

vaRtUv)anplitBIebtugGarem: nigmaneRbIEdkBRgwgTMhM mm20 .

!>&> kRmalCan;TIBIrbs;eragcRkTm¶n;RsalmYyRtUv)ansagsg;BIkRmalebtugkRmas; mm125 nigmanbEnßm cider fill dUcbgðajkñ úgrUb. RbsinebIBidansRmab;Can;TImYypSMBI metal lath nig


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm*> FñwmGkSa T EdleRbIsRmab;XøaMgpÞ úkTMnijF¶n;² RtUv)ansagsg;BIebtugEdlmanTm¶n;maD

3/6.19 mkN . kMNt;bnÞ úkefrkñ úgmYyÉktþaRbEvg

rbs;Fñ wmedayminKitTm¶n;rbs;EdkBRgwg nigbnÞ úk

GefrEdlmanGMeBIenABIxagelIFñwmkñ úgmYyÉktþaRbEvg.

!>(> Fñ wmRTdMbUlEdleFV IBI asphalt shingle nigkþabnÞHeQI (wood sheathing board). RbsinebIbnÞHkþamankRmas; mm38 nigmanTm¶n;maD

2/86.7 mkN ehIydMbUlmanmM u o30 cUrkMNt;

bnÞ úkefrrbs;dMbUlkñúgmYyÉktþaépÞ EdlRtUv)anRTkñ úgTis x nigkñ úgTis y rbs;édrENg (purlin).

!>!0> salaEdlmankm!!> GKarkariyal½ykm!@> sNæaKarkm!#> kMNt;kmøaMgpÁÜbEdlmanGMeBIenAelIépÞénsøaksBaØaEdlRTeday truss Edlsß itenAEk,r Los Angeles, California enAelITIvalrabes μ I.


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cMeNaT

T.Chhay -23

søaksBaØaenHmanTTwg m6 nigkm!$> søaksBaØamYysß itenATIvalrabes μ IénMinnesota. cUrkMNt;kmøaMgpÁ Übrbs;xül;EdlmanGMeBIelIépÞrbs;va. eRbIemKuNsMxan;

87.0= I .

!>!%> xül;bk;eTAelIRCugbiTCitrbs;ksidæanEdlmanTItaMgenAelITIvalrabes

μ

Ién Oklahoma.kMNt;sm xül;bk;eTAelIRCugbiTCitrbs;ksidæanEdlmanTItaMgenAelITIvalrabes μ Ién Oklahoma.kMNt;sm


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm karviPaKrcnasm m:EDleRKOgbgÁ

(Idealized structure)

Cak;Esþg eKminGacviPaKeRKOgbgÁ ú M)ansuRkiteT edaysareKRtUveFVIkar)a:n;RbmaNbnÞ úk nigPaBFn;rbs;smÖar³. elIsBIenH eKRtUveFVIkarsn μt;BITItaMgEdlbnÞ úkRtUveFVIGMeBIr. dUcenH vaCakarsMxan;Nas; EdlvisVkrRtUvGPivDÆsmtßPaBkñ úgkarbegáItm:UEDleRKOgbgÁú M. enAkñ úgkfaxNÐ enHeyIgnwgENnaMBIbec©keTsCamUldæanEdlcaM)ac;sRmab;kargarenH.

tMNTRm (Support Connection): Ggát;eRKOgbgÁú MRtUv)antamP¢ab;KñatamviFIeRcIn edayGaRs½yeTAelIectnarbs;visVkr. tMNsamBaØbIRbePTEdleKsÁal;PaKeRcInKW tMNsnøak; (pin connection)/

TRmkl; (roller support) nigtMNbgáb; (fixed joint). Pin-connection joint nig roller support GnuBaØat[Ggát;vil)an Et fixed joint minGnuBaØat[Ggát;vileT ehIyCaTUeTAkareFVI fixed joint TamTartémøx


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karviPaKrcnasm


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karviPaKrcnasm


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karviPaKrcnasm L L eKKitkRmalxNÐCakRmalxNÐmYyTis. épÞrgsm


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karviPaKrcnasm#> smIkarlMnwg (Equation of equilibrium)

enAkñ úgsþaTic)anEcgfa eRKOgbgÁú M b¤Ggát;mYyéneRKOgbgÁ ú MmanlMnwg enAeBlNaEdlvaGacrkSalMnwgénkmøaMg niglMnwgénm:Um:g;. CaTUeTA eKRtUvbMeBjnUvlMnwgénsmIkarkmøaMg nigsmIkarm: Um:g;tam

G½kSTaMgbI mann½yfa³0=∑ xF 0=∑ yF 0=∑ zF 0=∑ x M 0=∑ y M 0=∑ z M (2-1)

b:uEnþ PaKeRcIneRKOgbgÁ úMeRcInRTcMENkbnÞ úkEdlsß itenAkñ úgbøg;eTal ehIyedaysarEtbnÞ úkk¾sßitenAkñ úgbøg;enaH smIkartRmUvkarxagelIkat;bnßymkRtwm

0=∑ xF 0=∑ yF 0=∑ O M (2-2) enATIenH xF ∑ nig yF ∑ CaplbUkBiCKNiténbgÁ ú MkmøaMgtamG½kS x nigtamG½kS y erogKña EdlmanGMeBI

mkelIeRKOgbgÁ úM b¤Ggát;mYyrbs;eRKOgbgÁ úM ehIy O M ∑ CaplbUkBiCKNiténm:Um:g;énkmøaMgCM uvijG½kSEdlEkgnwgbøg; y x − ¬G½kS z ¦ ehIykat;tamcMNuc O .

enARKb;eBlEdleKGnuvtþsmIkarTaMgenH dMbUgeKcaM)ac;RtUvKUrdüaRkamGgÁesrI (free bodydiagram) rbs;eRKOgbgÁ úM b¤rbs;Ggát;. edIm,IKUrdüaRkamGgÁesrI eKRtUvpþac;Ggát;ecjBIKña nigecjBITRm.kmøaMgxageRkA kmøaMgkñ úg b¤kmøaMgRbtikm μRtUvbgðajenAelIGgát;Edl)anpþac;ecj. tamry³enH eKGackMNt;kmøaMgRbtikm μenARtg;TRmedayeRbItarag 2-1. ehIyeyIgRtUvcaMpgEdrfa enAelIdüaRkamGgÁ esrI kmøaMgkñ úgénGgát;BIrEdlP¢ab;KñamanTMhMdUcKña EtmanTispÞ úyKña.

RbsinebIeKcg;kMNt;kmøaMgkñúgenARtg;cMNucCak;lak;enAkñ úgGgát; eKRtUveRbIviFImuxkat; (methodof section). viFIenHtRmUv[kat;Ggát;tamTisEkgeTAnwgG½kSrbs;Ggát;Rtg;cMNucEdleKRtUvkarkMNt; kmøaMgkñúg. eKRtUvKUrdüaRkamGgÁesrIénkMNat;Ggát;nImYy²Edl)ankat; rYckMNt;kmøaMgkñúgedayGnuvtþ smIkarlMnwgeTAelIkMNat;Ggát;enaH. CaTUeTA kmøaMgkñ úgEdlmanGMeBIenAelImuxkat;rbs;Ggát;Edlkat; rYmmankmøaMgEkg (normal force) N / kmøaMgkat; (shear force) V nigm: Um:g;Bt; (bending moment)


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm$> PaBkMNt; nigsrPaB (Determinacy and stability)

muxnwgcab;epþ ImviPaKkmøaMgrbs;eRKOgbgÁú M eKcaM)ac;kMNt;nUvPaBkMNt; nigsß irPaBrbs;eRKOgbgÁ úM.

PaBkMNt;

(determinacy): smIkarlMnwgpþl;nUvlkçxNÐcaM)ac; nigRKb;RKan;sRmab;lMnwg. enAeBlEdlRKb;kmøaMgTaMgGs;enAkñúgeRKOgbgÁ úMGackMNt;edayeRbIsmIkarlMnwgxagelI enaHeKehAeRKOgbgÁú M enaHCa eRKOgbgÁú MkMNt;edaysþaTic (statically determinate structure). sRmab;eRKOgbgÁ úMEdlmancMnYnkmøaMgCaGBaØateRcInCagcMnYnsmIkarEdlGacman eK[eQ μaHvafa eRKOgbgÁ úMminkMNt;edaysþaTic(statically indeterminate structure). tamc,ab;TUeTA eKGackMNt;faeRKOgbgÁ úMmYyCaeRKOgbgÁ ú MkMNt;edaysþaTic b¤k¾eRKOgbgÁ úMminkMNt;edaysþaTicedayKUrdüaRkamGgÁesrIénGgát;TaMgGs;rbs;va b¤épñkén

Ggát;EdleRCIserIs ehIybnÞab;mkeRbobeFobcMnYnGBaØatsrubEdlCakmøaMg nigm: Um:g;CamYynwgcMnYnsrubénsmIkarlMnwgEdlGacman*. sRmab;eRKOgbgÁú Mkñ úgbøg; eKmansmIkarlMnwgbIsRmab;Ggát;nImYy²dUcenHRb sinebIeKmanGgát;srubcMnYn n ehIykmøaMgRbtikm μ nigm: Um:g;Rbtikm μcMnYn r enaHeyIg)an

nr 3= / kMNt;edaysþaTicnr 3> / minkMNt;edaysþaTic (2-3)

CaebIvaCaeRKOgbgÁ ú MminkMNt;edaysþaTicenaHeKRtUvkarsmIkarbEnßmedIm,IedaHRsayrkRbtikm μEdlCaGBaØatedayP¢ab;TMnak;TMngrvagbnÞ úkGnuvtþ

n_ nigRbtikm μ

eTAnwgbMlas;TI b¤mM urgV ilenARtg;cMNucepSgKñaenAelIRKOgbgÁú M. smIkarTaMgenHCasmIkarRtUvKña (compatibility equation) ehIyvaRtUvmancMnYnes μ InwgdWeRkénPaBminkMNt;rbs;eRKOgbgÁ ú M.smIkar compatibility Tak;TgnwglkçN³FrNImaRt niglkçN³rUbrbs;eRKOgbgÁ ú M ehIyeyIgnwgelIk

* karKUrdüaRkamGgÁesrImincaM)ac;CaTUeTAeT edaysareKGacrab;cMnUnGBaØat ehIyeFV IkareRbobeFobCamYynwgcMnUnsmIkarlMnwg)an.


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karviPaKrcnasm3³ cat;cMNat;fñak;rbs;Fñ wmnImYy²EdlbgðajenAkñ úgrUbTI 2-18 a rhUtdl; 2-18 d CaeRKOgbgÁ úMkMNt;edaysþaTic b¤eRKOgbgÁú MminkMNt;edaysþaTic. eKsn μt;faeKsÁal;kmøaMgEdlGnuvtþminelIFñ wm ehIyvaGacmanGMeBIenARKb;TItaMgTaMgGs;rbs;Fñ wm.

dMeNaHRsay³

eKRtUvpþac;Fñ wmpSM (compound beam) enAkñ úgrUbTI 2-18 c nig 2-18 d EdlpSMeLIgGgát;EdltP¢ab;KñaedaytMNsnøak;ecjBIKña. cMNaMfa enAkñúgkrNITaMgenH kmøaMgRbtikm μEdlCaGBaØatEdlmanGMeBIenAcenøaH Ggát;nImYy²RtUv)anbgðajCaKU EtmanTispÞ úyKña. düaRkamGgÁesrIRtUv)anbgðaj. edayGnuvtþ

nr 3= b¤ nr 3> lT§plénkarcat;cMNat;fñak;RtUv)anbgðaj.

]TahrN_ 2>4³ cat;cMNat;fñak;rbs;eRKOgbgÁ ú MEdltP¢ab;edaytMNsnøak;EdlbgðajenAkñúgrUbTI 2-19a rhUtdl; 2-19 d CaeRKOgbgÁ ú MkMNt;edaysþaTic b¤CaeRKOgbgÁ ú MminkMNt;edaysþaTic. RbsinebIvaCaeRKOgbgÁ úMminkMNt;edaysþaTic cUrR)ab;BIcMnYnéndWeRkénPaBminkMNt;. eRKOgbgÁ ú MrgnUvbnÞúkxageRkAEdl


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm lT§plénkarcat;cMNat;fñak;RtUv)anbgðaj.

]TahrN_ 2>5³ cat;cMNat;fñak;rbs;eRKagEdlbgðajenAkñúgrUbTI 2-20a

nig2-20d

CaeRKOgbgÁ ú MkMNt;edaysþaTic b¤CaeRKOgbgÁ ú MminkMNt;edaysþaTic. RbsinebIvaCa eRKOgbgÁ ú MminkMNt;edaysþaTiccUrR)ab;BIcMnYnéndWeRkénPaBminkMNt;. eRKOgbgÁ ú MrgnUvbnÞ úkxageRkAEdl eKsn μt;sÁal; ehIyvamanGMeBIenARKb;TItaMgTaMgGs;rbs;eRKOgbgÁú M.

dMeNaHRsay³

karkMNt;sß irPaB nigPaBkMNt;rbs;eRKOgbgÁ ú MeRKagmindUcKñanwgkarkMNt;sRmab;Fñ wm nigeRKOgbgÁú MEdlt


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karviPaKrcnasm6³ cUrcat;cMNat;fñak;rbs;eRKOgbgÁ úMnImYy²enAkñúgrUbTI 2-24a rhUtdl;2-24e CaeRKOgbgÁú Mmansß irPaB b¤K μansß irPaB. eRKOgbgÁú MrgnUvbnÞ úkxageRkANamYyEdleyIgsn μt;vasÁal;.

dMeNaHRsay³ eRKOgbgÁ úMRtUv)ancat;cMNat;fñak;dUcbgðajkñ úgrUb.


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karviPaKrcnasm%> karGnuvtþénsmIkarlMnwg (Application of the equation of equilibrium)

eBlxøH Ggát;rbs;eRKOgbgÁú MRtUv)antP¢ab;KñaedaytMNEdleKsn μt;faCatMNsnøak;. eRKagGKarnig truss CaRbePTeRKOgbgÁú MEdlCaerOy²sagsg;edayeRbItMNEbbenH. kñúgkrNIeRKOgbgÁú Mkñ úgbøg; EdltP¢ab;edaysnøak;mankarTb;RtwmRtUv nigminmanTRmelIs b¤Ggát;elIsedIm,IkarBarkardYlrlM enaHeKGackmøaMgEdlmanGMeBIenARtg;tMN nigenARtg;TRmedayGnuvtþsmIkarlMnwgTaMgbI ¬ 0=∑ xF /

0=∑ yF / 0=∑ O M ¦ eTAelIGgát;nImYy². enAeBlEdleKTTYl)ankmøaMgenARtg;tMN eKGacsikSaKNnaTMhMrbs;Ggát; kartP¢ab; nigTRmedayEp¥kelI design code specification.

edIm,IbgðajBIviFIénkarviPaKkmøaMg BicarNaeRKagEdlmanGgát;bIdUcbgðajenAkñúgrUbTI 2-25a

EdlrgnUvbnÞ úk 1P nig 2P . düaRkamGgÁesrIrbs;Ggát;nImYy²RtUv)anbgðajenAkñúgrUbTI 2-25 b. Casrub eKmanGBaØatTaMgGs; 9 ehIyeKmansmIkarlMnwgTaMgGs; 9 EdlGgát;nImYy²mansmIkarlMnwg 3 dUcenHeRKOgbgÁ ú MenHCaeRKOgbgÁ ú MkMNt;edaysþaTic. sRmab;dMeNaHRsayCak;Esþg ¬eBlxøHmanlkçN³gayRsYl¦ eKGacBicarNaeRKagCaEpñk b¤k¾eRKagTaMgmUl enAeBlEdlGnuvtþsmIkarxøHénsmIkarTaMg9 enH. Ca]TahrN_ düaRkamGgÁesrIéneRKagTaMgmUlRtUv)anbgðajenAkñúgrUbTI 2-25c. eKGackMNt; kmøaMgRbtikm μTaMgbI x A / y A nig xC enAelIRbB½n§eRKOgbgÁ ú MEdltP¢ab;edaytMNsnøak;rwgmaMenH bnÞab;

mk viPaKGgát;BIrkñ úgcMeNamGgát;TaMgGs;enAkñ úgrUbTI 2-25 b

edIm,ITTYl)anGBaØat6

epSgeTot.elIsBIenH eKGacRtYtBinitücMeLIyCaEpñkedayGnuvtþsmIkarlMnwgTaMgbIeTAelIGgát;TIbIEdlenAsl;.Casegçb eKGacedaHRsaybBaðaenHedaysresrsmIkarlMnwgy:ageRcInNas;cMnYn 9 edayeRbIdüaRkamGgÁesrIénGgát;nImYy² nig ¬b¤¦bnSMénGgát;EdltP¢ab;. smIkareRkABIsmIkarTaMg 9 xagelIRtUv)aneRbIedIm,IRtYtBinitülT§pl.


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karviPaKrcnasm10³ FñwmpSMenAkñúgrUbTI 2-30 a RtUv)anbgáb;enARtg;cMNuc A . kMNt;kmøaMgRbtikm μ

enARtg; A / B nigC . sn μt;fa B CatMNsnøak; ehIy C CaTRmkl;.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm11³ eRKOgbgÁú MEdlbgðajenAkñúgrUbRTkRmal nigBüÜrTUk. m:UEDleRKOgbgÁú MEdlbgðajenAkñ úgrUbenHRtUv)anbgðajenAkñúgrUbTI 2-31a

EdleyIgsn μ

t;fa A CaTRmkl; ehIy B CaTRmsnøak;. edayeRbIkUdkñ úgtMbn; (local code) bnÞ úkkRmalEdl sn μt;RtUv)aneTAelIrtKW mkN /6 .xül;Gnuvtþ kmøaMgpÁÜbtamTisedk kN 4 dUcbgðaj ehIym:as;rbs;TUkEdlBüÜreTAnwgrtKW Mg23 . TIRbCMu Tm¶n;rbs; m:as;TUksß itenARtg;G . kMNt;kmøaMgRbtikm μenARtg;TRm.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm1>

eKeRbIeRKagmYy[RTkRmaleQI ¬minbgðaj¦ EdlvargbnÞ úkBRgayes μ I 2/5.6 mkN .

KUrbgðajBIbnÞ úkEdlmanGMeBIenAelIGgát; BG nig ABCD . yk mb 3= / ma 5.1= .

2>2> kRmaldMbUlénGKarEdlmankMBs;mYyCan; rgnUvbnÞúkefr nigbnÞúkGefr 2/6 mkN . RbsinebIrnUtmanKMlatBIKña m2.1 ehIyrtmanKMlat

m5.7 BIKña cUrkMNt;bnÞ úkBRgayEdleFV IGMeBIelI rnUt DF nigbnÞ úkEdleFV IGMeBIelIrtenARtg;cMNuc A

/ B

/C

/

D

nig E

.

2>3> eKeRbIeRKagEdkedIm,IRTkRmalebtugGarem:Tm¶n;RsalkRmas; mm100 EdlRTbnÞ úkBRgayes μ I 2/25 mkN .

bgðajbnÞúkEdlmanGMeBIelIGgát; BE nig FD .yk mb 3= / ma 4.2= . CM nYy³ emIltarag 1-

3.

2>4> edaHRsaycMeNaT 2-3/ CamYynwg =b m6.3 / ma 2.1= .

2>5>

eKeRbIeRKageQIedIm,IRTkRmaleQI. bgðajbnÞ úkEdlmanGMeBIelIGgát; BG nig ABCD . yk

mb 3= / ma 5.1= . CMnYy³ emIltarag 1-4.

2>6> edaHRsaycMeNaT 2-5/ CamYynwg =b m4.2 / ma 4.2= .

2>7>

edaHRsaycMeNaT 2-5/ CamYynwg =b

m5.4 / ma 3= . 2>8>

cat;cMNat;fñak;éneRKOgbgÁ úMnImYy²CaeRKOgbgÁ ú MkMNt;edaysþaTic eRKOgbgÁ ú MminkMNt;edaysþaTic eRKOgbgÁ úMmansß irPaB b¤eRKOgbgÁ úMK μansi ßrPaB.RbsinebICaeRKOgbgÁú MminkMNt;edaysþaTic


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cMeNaT

T.Chhay -53

cUrkMNt;BIdWeRkénPaBminkMNt;.

2>9> cat;cMNat;fñak;éneRKOgbgÁ ú MnImYy²CaeRKOgbgÁú MkMNt;edaysþaTic eRKOgbgÁú MminkMNt;edaysþaTic b¤eRKOgbgÁú MK μansß irPaB. RbsinebICaeRKOgbgÁú MminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;.

2>10>

cat;cMNat;fñak;éneRKOgbgÁú MnImYy²CaeRKOgbgÁ ú MkMNt;edaysþaTic eRKOgbgÁ úMminkMNt; edaysþaTic b¤eRKOgbgÁ ú MK μansß irPaB. RbsinebICaeRKOg bgÁ ú MminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;.

2>11> cat;cMNat;fñak;éneRKOgbgÁ ú MnImYy²CaeRKOgbgÁ ú MkMNt;edaysþaTic eRKOgbgÁú MminkMNt;edaysþaTic b¤eRKOgbgÁ úMK μansßirPaB. RbsinebICaeRKOgbgÁ úMminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm12> cat;cMNat;fñak;éneRKOgbgÁú MnImYy²CaeRKOgbgÁú MkMNt;edaysþaTic eRKOgbgÁ ú MminkMNt; edaysþaTic b¤eRKOgbgÁ ú MK μansß irPaB. RbsinebICaeRKOgbgÁú MminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;. TRm nigsnøak;RtUv)ansn μt;dUcbgðaj.

2>13>

cat;cMNat;fñak;éneRKOgbgÁ ú MnImYy²CaeRKOgbgÁú MkMNt;edaysþaTic eRKOgbgÁ ú MminkMNt;

edaysþaTic b¤eRKOgbgÁ úMK μansß irPaB. RbsinebICaeRKOgbgÁ úMminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;. TRm nigtMNTaMgGs;RtUv)ansn μt;

dUcbgðaj.

2>14>

cat;cMNat;fñak;éneRKOgbgÁ ú MnImYy²CaeRKOgbgÁú MkMNt;edaysþaTic eRKOgbgÁú MminkMNt; edaysþaTic b¤eRKOgbgÁ úMK μansß irPaB. RbsinebICaeRKOgbgÁ úMminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;. tMNTaMgGs;CatMNrwg b¤tMNbgáb;.


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cMeNaT

T.Chhay -55

2>15>

cUrkMNt;BIdWeRkénPaBminkMNt;rbs;eRKOgbgÁ úMminkMNt;edaysþaTic. tMNTaMgGs;CatMNrwg b¤tMNbgáb;.

2>16>

cat;cMNat;fñak;éneRKOgbgÁú MnImYy²CaeRKOgbgÁ ú MkMNt;edaysþaTic eRKOgbgÁú MminkMNt;edaysþaTic b¤eRKOgbgÁ úMK μansßirPaB. RbsinebICaeRKOgbgÁ ú MminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaBminkMNt;. TRm nigtMNTaMgGs;RtUv)ansn

μ

t; dUcbgðaj.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm17> kMNt;kmøaMgRbtikm μenAelIFñ wm. eKsn μt; TRmenARtg; B CaTRmkl; nigminKitBIkRmas;rbs;Fñ wm.

2>18> kMNt;kmøaMgRbtikm μenARtg;TRm A nig B .sn μt; A CaTRmkl; nig B CaTRmsnøak;.

2>19>

kMNt;kmøaMgRbtikm μenAelIFñwm.

2>20>

kMNt;kmøaMgRbtikm μenAelIFñ wm.

2>21>

kMNt;kmøaMgRbtikm μenAelIFñ wm.

2>22> kMNt;kmøaMgRbtikm μ

enARtg;TRm A

nig B

.kRmal CD / DE / EF nig FG bBa¢ÚnbnÞ úkrbs;va eTAelIrttamTRmkl;.sn μt; A CaTRmkl; nig B CaTRmsnøak;.

2>23>

KNnakmøaMgRbtikm μenARtg;TRm A nig B énFñ wmpSM. enARtg;C CatMNsnøak;.


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cMeNaT

T.Chhay -57

2>24>

eKeRbIRKwHeCIgtagedIm,IRTbnÞ ú kN 50 . kM-Nt;GaMgtg;sI uet 1w nig 2w énbnÞ úkBRgayEdlmanGMeBIenAelI)atrbs;RKWHedIm,I[manlMnwg.


enAelIFñ wm.

2>26>

KNnakmøaMgRbtikm μ

enARtg;TRmrelag C nigenARtg;TRmsnøak; A . sn μt; B CatMNbgáb; .

2>27> KNnakmøaMgRbtikm μenARtg;TRmrelag A nigenARtg;TRmsnøak; B . tMNC CatMNbgáb; .

2>28> eKeRbIeCIgtagkugs‘ ul (cantileverfooting) edIm,IRTCBa¢aMgenAEk,rcugEKmrbs;RKwH A dUcenH vaeFV I[mansm


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm29> kMNt;kmøaMgRbtikm μenARtg;TRm A nig B rbs; truss. bnÞ úkBRgayRtUv)anbgáeLIgedaysarxül;.

2>30> dgsÞ Úc jib crane

mantMNsnøak;enARtg; A nigmanTRm smooth collar enARtg; B .kMNt;bMlas;TI x énbnÞ úk kN 5.22 dUcenHvaeFV I[mankmøaMgRbtikm μGtibrma nigGb,brma. KNnakmøaMgRbtikm μenAkñ úgkrNInImYy². sn μt;eKecalTm¶n;rbs;dgsÞúc. eKtRmUv[ m xm 32.1 ≤≤ .

2>31> kMNt;kmøaMgRbtikm μenARtg;TRm A nig B éneRKag. sn μt;fa A CaTRmkl;.

2>32> kMNt;kmøaMgRbtikm μenARtg;TRm A nig B

rbs; truss

. bnÞ úkBRgayRtUv)anbgáeLIgedaysarxül;.

2>33>

kMNt;bgÁ ú MkmøaMgRbtikm μedk nigQrenARtg;TRm A nig B . tMNenARtg;C nig D CatMNbgáb; .

2>34> kMNt;kmøaMgRbtikm μenARtg;TRm A / B nig E . sn μt; B CaTRmkl;.


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cMeNaT

T.Chhay -59

2>35>

kMNt;kmøaMgRbtikm μenARtg;TRm A / B /C nig D .

2>36>

kMNt;kmøaMgRbtikm μenRtg;TRmsRmab;Fñ wmpSM.eKmansnøak;enARtg; A / E nig F .

2>37>

sMNg;s38>

kMNt;kmøaMgRbtikm μenARtg;TRm A / C nig D .

2>39> kMNt;kmøaMgRbtikm μenARtg; A nigC .sn μt;fa A CaTRmkl; B CatMNbgáb; nigC Ca

tMNsnøak;.

2>40> kMNt;kmøaMgRbtikm μenARtg; A / B . sn μt; B CaTRmkl; ¬TRmrGil¦ C CatMNrwg.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm41> kMNt;kmøaMgRbtikm μenARtg;TRm A nig B .

2>42>

eRKags43> kMNt;bgÁ úMkmøaMgRbtikm μ

edk nigQrenARtg; A / B nigC . sn μt;eKP¢ab;eRKagedaytMNsnøak;enARtg;cMNucTaMgenH ehIy D nig E CatMNrwg.

2>44>

kMNt;kmøaMgRbtikm μenARtg;TRm A nig B .tMNC nig D CatMNrwg.

2>45>

kMNt;bgÁ ú MkmøaMgRbtikm μedk nigQrenARtg;TRm A nig B .


enARtg;TRm A nig D .sn μt;fa A CaTRmbgáb; ehIy B / C nig D Casnøak;.

2>47> kMNt;kmøaMgRbtikm μenARtg;TRm A nig C .eRKagRtUv)antP¢ab;edaytMNsnøak;enARtg; A / B nigC ehIytMNTaMgBIrCaTRmrwg.


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cMeNaT

T.Chhay -61

2>48>

kMNt;kmøaMgRbtikm μenARtg;tMN A / B nigC . sn μt;tMNnImYy²CatMNsnøak; ehIytMN B CatMNrwg.

2>49>

kMNt;bgÁú MkmøaMgRbtikm μenARtg;tMN A nigC én gable frame. sn μt;fa A / B nigC CatMNsnøak;. eKdak;bnÞ úkenARtg;cMNuc D / E / F nigG EkgeTAnwgG½kSrbs;rtnImYy².

2>50>

kMNt;bgÁ úMkmøaMgRbtikm μedk nigQrenARtg;TRm A / B nigC . sn μt;faeRKagRtUv)antP¢ab; edaytMNsnøak;enARtg; A / B / D / E nig F ÉC CaTRmbgáb;.

KMerag³

pøÚvrfePø IgRtUv)anRTedayeRKagebtug

Garem:. sn μ

t;rtTRmsmBaØBIrRTEdk rail nigkRmalpø ÚvrfePø IgEdlmanTm¶n; mkN /5.7 nigRTbnÞ úkrbs;rfePø Ig mkN /100 ¬rUbxageRkam¦.rt nImYy²manRbEvg mkN /100 . GnuvtþbnÞúkTaMgenHeTAelIeRKags


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm karviPaK truss kMNt;edaysþaTic

Analysis of Statically Determinate Trusses

enAkñ úgCM BUkenH eyIgnw gerobrab; BI vi FI sRmab; vi PaK truss kM Nt; edaysþaTickM Nt;edayeRbI vi FItMN

ni gviFI muxkat; . b: uEnþ dM bUgeyI gnwgBN’ naBI PaBkM Nt; nigsßi rPaBrbs; truss

. bnÞab; mkeyI gnwgBicarNakarvi PaK truss kñ úgbøg;bI TRmg; KW³ truss samBaØ/ truss pSM ni g truss saM júaM . cugeRkay eyI gnw gBi carNa

karvi PaK truss kñ úglM h.

#> > RbePTTUeTArbs truss (Common Types of Analysis)Truss CaeRKOgbgÁú MEdlpSMeLIgedayGgát;Evg²

EdltP¢ab;KñaenAxagcugrbs;va. Ggát;EdleRbICaTUeTA

edIm,IeFV I truss rYmmanr)areQI r)arEdk EdkEkg b¤EdkGkSr C. CaFm μta tMNRtUv)anbegá IteLIg edayb‘ ULúgb¤edaykarpSarcugGgát;eTAnwgbnÞHEdkFm μta EdleKehAfa gusset plate dUcbgðajenAkñ úg rUbTI 3-1 b¤edayP¢ab;Ggát;eTAnwgGgát;edayb‘ ULúg b¤edayknøas;. Truss kñ úgbøg; sß itenAkñúgbøg;eTal ehIyeKeRcIneRbIvaedIm,I RTdMbUl b¤eRbIvaCas


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truss kMNt;edaysþaTic

T.Chhay -63

ebtugGarem: b¤RTedayCBa¢aMg\dæ. edIm,IrkSa bent [rwg nigmanlT§PaBTb;Tl;nwgkmøaMgxül;tamTisedk eBlxøHeKRtUveRbIkar knee brace enARtg;ssrEdlCaTRm. KMlatrvag bent eK[eQ μaHfa bay.sRmab;lkçN³esdækic© eKykKMlat bay RbEhl m6.4 sRmab; bent EdlmanElVg m18 ehIyRbEhl m1.6 sRmab;ElVg m30 . CaerOy² eKP¢ab; bay edayGgát;BRgwgGgát;RTUgedIm,IrkSaPaBrwgmaM rbs;eRKagsMNg;.

eKeRCIserIs Truss EdleRbIedIm,IRTdM MbUledayEp¥kelIRbEvgElVg CRmal nigsmÖar³sRmab;dMeLIgdMbUl. RbePT truss EdleKniymeRbIRtUv)anbgðajenAkñúgrUbTI 3-3. CaFm μtaeKGaceRbI scissor truss¬rUbTI 3-3a) sRmab;ElVgxøIEdlRtUvkarlMhFM. Howe nig Pratt truss ¬rUbTI 3-3 b nig 3-3c¦RtUv)an


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm>.

Truss s


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T.Chhay -65

Parker truss ¬rUbTI 3-5d ¦ edIm,IsnSMsMécsmÖar³. eKGacsagsg; Warren truss EdlmanGgát;bBaÄrtamTRmg; Parker truss sRmab;ElVgrhUtdl; m90 . eKGacTTYl)anlkçN³esdækic©x


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm RKb;bnÞúkTaMgGs;RtUvGnuvtþenARtg;tMN. enAkñúgsßanPaBPaKeRcIn dUcCasRmab;s@> karcat;cMNat;fñak;rbs; truss kñgbøg; (Classification of Coplanar Trusses) munnwgcab;epþ ImviPaKrkkmøaMgrbs; truss/ eKcaM)ac;RtUvcat;cMNat;fñak;rbs; truss Ca truss

samBaØ truss pSM b¤ truss saMjúaM bnÞab;mkeTotkMNt;rkPaBkMNt; nigsß irPaBrbs;va.

Truss

samBaØ

(Simple truss):

edIm,IkarkardYlrlM rcnasm


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T.Chhay -69

PaBkMNt; (Determinacy): sRmab;karviPaK truss TaMgGs; eKRtUvdwgcMnYnsrubrbs;GBaØatedayrYmbBa©ÚlTaMgkmøaMgenAkñúgGgát;rbs; truss EdlmancMnYn b nigcMnYnkmøaMgRbtikm μxageRkAsrub r . edaysarGgát; truss suT§EtCaGgát;Rtg;rgkmøaMgtamG½kSEdlsßitenAkñúgbøg;EtmYy enaHRbB½n§kmøaMgEdleFV I GMeBIenARtg;tMNnImYy²KWenAkñ úgbøg; nigRbsBVKña. dUcenH smIkarlMnwgsRmab;karrmYl b¤sRmab;m: Um:g; RtUv)anbMeBjedaysV½yRbvtþenARtg;tMN ¬b¤snøak;¦ ehIyvacaM)ac;RtUvbMeBjsmIkarlMnwg 0=∑ xF nig 0=∑ yF edIm,IFanalMnwgkmøaMg b¤Fanakarcl½t. dUcenH eKGacsrsrsmIkarlMnwgEtBIrsRmab; tMNnImYy² ehIyRbsinebIeKmantMNcMnYn j enaHcMnYnsmIkarEdlGacmansRmab;dMeNaHRsayKW 2j.edayeRbobeFobcMnYnGBaØatsrub (b+r) CamYynwgcMnYnsrubrbs;smIkarEdlGacsresr)an dUcenHeKGackMNt;PaBkMNt;sRmab; truss TaMgGs;. eyIgman

jr b 2=+ kMNt;edaysþaTic jr b 2>+ minkMNt;edaysþaTic (3.1)

dWeRkénPaBminkMNt;RtUv)ankMNt;edayplsgéncMnYn ( ) jr b 2−+ .

sßrPaB (Stability): RbsinebI b + r < 2j enaH truss nwgminmansß irPaB ehIyvanwgdYlrlM edaysarvaminmancMnYnr)arRKb;RKan;edIm,I b¤kmøaMgRbtikm μRKb;RKan;edIm,ITb;tMNTaMgGs;min[cl½t)an.

ehIytruss

k¾GacGsßirPaBeTaHbIvaCaeRKOgbgÁ úMkMNt;edaysþaTic b¤minkMNt;edaysþaTick¾eday.sRmab;krNIsßirPaB eKRtUvkMNt;edaykarGegát b¤edaykarviPaKkmøaMg.

sßrPaBxageRkA (External stability): dUckarerobrab;enAkñ úgkfaxNÐ 2-4 eRKOgbgÁú M b¤ trussEdlGsß irPaBxageRkARbsinebIkmøaMgRbtikm μTaMgGs;rbs;vaRbsBVKña b¤RsbKña. ]TahrN_ truss BIrenAkñ úgrUbTI 3-13 Ca truss Gsß irPaBxageRkA edaysarRbtikm μTRmmanExSskm μRbsBVKña b¤RsbKña.


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T.Chhay -71

RbsinebI truss Ca truss saMjúaM eKminGacniyayfavamansß irPaBedaykarGegáteT. ]Ta-hrN_ eyIgGaceXIjBIkarviPaKEdlmanerobrab;enAkñúgkfaxNÐ 3-7 fa truss saMjúaMenAkñúgrUbTI 3-17K μansßirPaB b¤manTRmg;eRKaHfñak;RbsinebI d = d’. RbsinebI 'd d ≠ enaHvanwgmansßirPaB.

eyIgGackMNt;BIsß irPaBrbs; truss RKb;TRmg;eday[kMuBüÚT½redaHRsayRbB½n§smIkar 2j EdlsresrsRmab;RKb;tMNTaMgGs;rbs; truss. RbsinebIeyIgminGacTTYllT§pl enaHmann½yfa truss enaHK μansß irPaB b¤manTRmg;eRKaHfñak;.

RbsinebIeKminGacRbtþibtþ ikarviPaKtamkM uBüÚT½r eKGaceRbIviFIEdlmanerobrab;BIelIkmunedIm,I RtYtBinitüsßirPaBrbs; truss. Cakarsegçb RbsinebI truss manr)arcMnYn b/ kmøaMgRbtikm μ r nigtMNcMnYn j enaHRbsinebI

jr b 2


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm+ b¤ 1819 > . dUcenHvaCa truss minkMNt;edaysþaTic 1 dWeRk. tamkarGegátvaCa truss mansß irPaBxag

kñ úg.

rUbTI 3-18 c³ Truss enHmansß irPaBxageRkA. eday 9=b / 3=r / 6= j enaH jr b 2=+ b¤ 1212 = . dUcenHvaCa truss kMNt;edaysþaTic. tamkarGegátvaCa truss mansß irPaBxagkñ úg.

rUbTI 3-18 d ³ Truss enHmansßirPaBxageRkA. eday 12=b / 3=r / 8= j enaH jr b 2


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T.Chhay -73

#>#> viFItMN (The method of Joint)

RbsinebI truss sßitenAkñ úgsßanPaBmanlMnwg enaHtMNrbs;vanImYy²k¾sß itkñ úgsßanPaBlMnwgEdr.dUcenH viFItMNpSMRtUv)anbegáIteLIgedaybMeBjnUvlkçxNÐlMnwg 0=∑ xF nig 0=∑ yF sRmab;kmøaMgEdlmanGMeBIenAelIsnøak;Rtg;tMNnImYy²rbs; truss.

enAeBleRbIviFItMN eKcaM)ac;RtUvKUrdüaRkamrbs;tMNnImYy²munnwgGnuvtþsmIkarlMnwg. rMlwkfaExSskm μénkmøaMgrbs;Ggát;nImYy²EdleFV IGMeBIenAelItMNRtUvykecjBIragFrNImaRtrbs; truss, edaysarkmøaMgenAkñ úgGgát;rt;tamG½kSrbs;Ggát;. ]TahrN_ eKmantMN B én truss enAkñ úgrUbTI 3-19 a.BIdüaRkamGgÁesrI ¬rUbTI 3-19 b¦ GBaØatCaTMhMrbs;kmøaMgenAkñ úgGgát; BA nig BC . dUcbgðajenAkñ úgrUb BAF TajtMN EdlbgðajfaGgát; BA rgkarTaj cMENkÉ BC F rujtMN Cavi)akGgát; BC rgkarsgát;. \T§ iBlenHbgðajy:agc,as;edayeRbIviFImuxkat; nigdak;[tMNenAdac;edayELkBIKñaCamYy

nwgkMNat;Ggát;d¾xø IEdlP¢ab;eTAnwgtMNenaH ¬rUbTI 3-19 c¦. cMNaMfa karruj nigkarTajenAelIkMNat; Ggát;d¾xø IbgðajBI\T§iBlénGgát;Edlrgkarsgát; b¤karTaj.

enARKb;krNITaMgGs; karviPaKtMNKUrcab;epþ ImenARtg;tMNNaEdlmankmøaMgEdlsÁal;y:agticbMputmYy nigkmøaMgEdlGacGBaØaty:ageRcInbMputBIr dUcbgðajenAkñ úgrUbTI 3-19 b. tamviFIenH karGnuvtþsmIkar 0=∑ xF nig 0=∑ yF pþl;nUvsmIkarBiCKNitcMnYnBIrEdlGac[eyIgedaHRsayrk)ankmøaMgEdlCaGBaØatcMnYnBIr. enAeBlGnuvtþsmIkarTaMgenH eKGackMNt;TisedARtwmRtUvrbs;GBaØatEdlCakmøaMgedayeRbIviFIBIr.

!> sn μt;kmøaMgrbs;Ggát;EdlCaGBaØatEdleFV IGMeBIenAelIdüaRkamGgÁesrIrbs;tMNCakmøaMgTaj.RbsinebIvaEbbnwgEmn enaHdMeNaHRsayCatémøelxénsmIkarlMnwgnwg[CatémøviC¢man sRmab;


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm enAkñ úgkrNICaeRcIn eKGackMNt;TisedAd¾RtwmRtUvrbs;kmøaMgenAkñ úgGgát;EdlCaGBaØatedaykarGegát. ]TahrN_ BC F enAkñúgrUbTI 3-19 b RtUvEtrujtMN ¬sgát;¦ edaysarbgÁ úMkmøaMgedkrbs;va o BC F 45sin RtUvTUTat;CamYynwgkmøaMgGnuvtþn_ kN 500 ¬ 0=∑ xF ¦. dUcKña BAF CakmøaMgTaj edaysarvaTUTat;CamYynwgbgÁ ú MkmøaMgbBaÄr o BC F 45cos ¬ 0=∑ yF ¦. enAkñ úgkrNIEdls μ úKs μajCagenH eKGacsn μt;TisedAénkmøaMgkñ úgrbs;Ggát;EdlCaGBaØat bnÞab;mkeRkayBI GnuvtþsmIkarlMnwg eKGacEkERbTisedAEdlsn μt;eTAtamlT§plCaelxEdlTTYl)an. cemø IyviC¢manbgðajfaTisedAEdlsn μt;KWRtwmRtUv cMENkÉcemø IyGviC¢manbgðajfaeKRtUvRtLb;Tis

edAEdlbgðajenAelIdüaRkamGgÁesrI. enHCaviFIEdleyIgnwgeRbIenAkñ úg]TahrN_xageRkam.

dMeNIrkarkñgkarviPaK (Procedure for analysis)

CMhanxageRkamenHpþl;nUvmeFüa)aysRmab;karviPaK truss edayeRbIviFItMN. sg;düaRkamGgÁesrIéntMNEdlmankmøaMgEdlsÁal;y:agticmYy nigGBaØatEdlCakmøaMgy:ag

eRcInBIr. ¬RbsinebItMNenHenARtg;TRmNamYy eKcaM)ac;RtUvKNnaRbtikm μenARtg;TRmeday

eRbIdüaRkamGgÁesrIrbs; truss TaMgmUl¦. eRbIviFImYykñ úgcMeNamviFITaMgBIrEdlBiBN’naxagelIsRmab;sn μt;TisedArbs;GBaØatEdlCakmøaMg.

eKRtUvkMNt;G½kS x nigG½kS y y:agNaedIm,IgayRsYledaHRsaybgÁ úMkmøaMgtamG½kS x nigtamG½kS y enAelIdüaRkamGgÁesrI. GnuvtþsmIkarlMnwgBIr 0=∑ xF nig 0=∑ yF edIm,IkMNt;kmøaMgkñ úgrbs;Ggát;EdlCaGBaØat ehIyepÞ ógpÞat;TisedAsn μt;rbs;va.

bnþkarviPaKtMNdéTeTot EteKcaM)ac;RtUveRCIserIstMNNaEdlmanGBaØaty:ageRcInBIr nigman

kmøaMgEdlsÁal;y:agticmYy.

eKeRbIkmøaMgenAkñúgGgát;BIkarviPaKtMNRtg;cugmçagrbs;Ggát;BIelIkmunedIm,IviPaKkmøaMgEdlmanGMeBIenAelItMNenAcugmçageTotrbs;va. eKRtUvcgcaMfa Ggát;rgkarsgát;rujtMN ehIyGgát;rgkarTajTajtMN.


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T.Chhay -75

]TahrN_ 3 2³ kMNt;kmøaMgkñúgénGgát;nImYy²rbs; truss dMbUldUcbgðajenAkñ úgrUbTI 3-20a.bgðajfaGgát;rgkarTaj b¤sgát;. eK[kmøaMgRbtikm μenARtg;tMN.

dMeNaHRsay³

eKcaM)ac;kMNt;kmøaMgenAkñ úgGgát;EtcMnYnBak;kNþalEtb: ueNÑaH edaysartruss enHman lkçN³sIuemRTITaMgbnÞ úk nigragFrNImaRt. tMN A / rUbTI3-20 b/ eyIgGaccab;epþImkarviPaKenARtg;tMN A . ehtuGV I?düaRkamGgÁesrIRtUv)anbgðajenAkñ úgrUbTI 3-20b.

0=∑↑+ yF / 030sin4 =− o AGF ( )C kN F AG 8=

0=∑→+

xF / 030cos8 =− o ABF ( )T kN F AB 93.6=

tMN G / rUbTI 3-20c/ enAkñ úgkrNIenH cMNaMBIrebobkMNt;Tisrbs;G½kS x nig y edIm,IeCosvagRbB½n§smIkar+ 0=∑ yF 030cos3 =− oGBF ( )C kN F GB 60.2= + 0=∑ xF / 030sin38 =−− GF o F

( )C kN F GF 50.6= tMN B / rUbTI 3-20d /

0=∑↑+ yF

/060sin60.260sin =− oo BF F

( )T kN F BF 60.2= 0=∑→

+

xF / 093.660cos6.260cos60.2 =−++ oo BC F ( )T kN F BC 33.4=


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T.Chhay -77

#>$> Ggát;kmøaMgsUnü (Zero-Force Members)

eKGacsRmYlkargarviPaK truss EdleRbIviFItMN RbsinebIeKGackMNt;CaCMhandMbUgral;Ggát;TaMgLayNaEdlminrgkmøaMg. Ggát;kmøaMgsUnüTaMgGs;enHmansar³sMxan;sRmab;sß irPaBrbs; truss kñ úgGMLúgeBlsagsg; nigpþl;CaTRmRbsinebIbnÞ úkGnuvtþn_RtUv)anpøas;bþ Úr. CaTUeTA eKGackMNt;Ggát;kmøaMgsUnürbs; truss edaykarGegáttMN ehIyvaekItmanBIrkrNI.

krNITI1³ BicarNa truss enAkñ úgrUbTI 3-22a. Ggát;BIrEkgKñaenARtg;tMNC ehIyminmanbnÞ úkxageRkAenARtg;tMNenaH. düaRkamGgÁesrIéntMNC ¬rUbTI 3-22 b¦ bgðajfakmøaMgenAkñúgGgát;nImYy²es μ IsUnüedIm,IrkSalMnwg. elIsBIenH dUcenAkñ úgkrNItMN A ¬rUbTI 3-22c¦ vaBitCaRtwmRtUvedayminxVl;BImM u ¬Gacniyayfaθ ¦rvagGgát;EdlpÁ úMKña.

krNITI2³ Ggát;kmøaMgsUnük¾ekItmanenARtg;tMNEdlmanlkçN³FrNImaRtdUctMN D enAkñ úgrUbTI 3-

23a. enATIenH minmankmøaMgxageRkAeFV IGMeBIelItMN dUcenHplbUkkmøaMgtamTis y ¬rUbTI 3-23 b¦EdlEkgeTAnwgGgát;BIrrt;elIbnÞat;EtmYy TamTar[ 0= DF F . edayeRbIlT§plenH FC k¾CaGgát;kmøaMgsUnü dUcbgðajedaykarviPaKkmøaMgéntMN F ¬rUbTI 3-23c¦.

Casegçb RbsinebIGgát;BIrEdlminsßitenAelIbnÞat;EtmYybegá ItCatMN truss ehIyminmanrgGMeBIbnÞúkxageRkA b¤kmøaMgRbtikm μTRm enaHGgát;TaMgBIrenaHCaGgát;kmøaMgsUnü ¬krNITI1¦. ehIy


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T.Chhay -79

#>%> viFImuxkat; (The method of Section)

RbsinebIeKcg;kMNt;EtkmøaMgenAkñ úgGgát;xøH CaTUeTAviFImuxkat;pþl;nUvmeFüa)aykñ úgkarTTYl)ankmøaMgTaMgenaHedaypÞal;. viFImuxkat;CaviFIekIteLIgedaykarkat; truss enaHCaBIrcMENk. RbsinebI truss TaMgmUlsß itenAkñ úgsßanPaBlMnwg enaHEpñkTaMgBIreRkayeBlEdlkat;k¾sßitenAkñ úgsßanPaBlMnwgEdr ehIyCalT§pl eKRtUvGnuvtþsmIkarlMnwgcMnYnbIeTAelIEpñkNamYyén truss Edlkat;rYc edIm,I kMNt;rkkmøaMgrbs;Ggát;enARtg;muxkat;enaH.

enAeBlEdleKeRbIviFImuxkat;edIm,IKNnakmøaMgenAkñ úgrbs;Ggát; eKRtUveFV IkarseRmcBIrebobkat; truss enaH. edaysareKGacGnuvtþEtsmIkarlMnwgbIEdlÉkraCüBIKña¬ 0=∑ xF / 0=∑ yF nig O M ∑

0= ¦eTAelIEpñkrbs; truss Edlkat;rYc CaTUeTAeKRtUveRCIserIsmuxkat;NaEdlminmankmøaMgkñ úgrbs;Ggát;EdlCaGBaØtelIsBIbI. ]TahrN_ cUrBicarNa truss enAkñ úgrUbTI 3-25a. RbsinebIeKRtUvkar

kMNt;kmøaMgenAkñúgGgát; GC karkat;tammuxkat; aa KWsaksmbMput. düaRkamGgÁesrIrbs;EpñkTaMgBIrRtUv)anbgðajenAkñ úgrUbTI 3-25 b nig 3-25c. cMNaMfa ExSskm μénkmøaMgnImYy²enAkñ úgGgát;Edlkat;RtUv)ankMNt;BIlkçN³FrNImaRtrbs; truss edaysarkmøaMgenAkñ úgGgát;sßitenAelIG½kSrbs;Ggát;.ehIykmøaMgEdlmanGMeBIenAcugmçagrbs;Ggát; truss mantémøes μ IKña EtmanTispÞ úyKñanwgkmøaMgEdlmanGMeBIenAelIcugmçageTotrbs;Ggát;dEdlenaH ¬c,ab;TIbIrbs;jÚtun¦. dUckarbgðaj eKsn μt;[Ggát; BC nigGC rgkarTaj ÉGgát;GF rgkar sgát;.

eKGacTTYlkmøaMgkñ úgrbs;Ggát;EdlCaGBaØat BC F / GC F nig GF F edayGnuvtþsmIkarlMnwgbI eTAelIdüaRkamGgÁesrIenAkñ úgrUbTI 3-25 b. b:uEnþ RbsinebIeKBicarNadüaRkamGgÁesrIenAkñ úgrUbTI 3-


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T.Chhay -81

KUrdüaRkamGgÁesrIénEpñkrbs; truss Edlkat;rYcEdlmankmøaMgmYycMnYnmanGMeBIelIva.

eRbIviFImYykñ úgcMeNamviFITaMgBIrEdlerobrab;xagelIedIm,IedATisedArbs;kmøaMgEdlCaGBaØat.

smIkarlMnwg (Equations of equilibrium)

eKKYreFV IplbUkm: Um:g;enARtg;cMNucNaEdlsß itenARtg;TIRbCM uénExSskm μrbs;kmøaMgEdlCaGBaØat

cMnYnBIr tamviFIenHeKGackMNt;kmøaMgEdlCaGBaØatTIbIedaypÞal;BIrsmIkarenH.

RbsinebIkmøaMgEdlCaGBaØatBIrRsbKña eKRtUveFV IplbUkkmøaMgtamTisEdlEkgeTAnwgkmøaMgTaMgBIrenaHedIm,ITTYl)ankmøaMgEdlCa GBaØatTIbIedaypÞal;.

]TahrN_ 3 5³ kMNt;kmøaMgenAkñúgGgát; CF nigGC rbs; truss dMbUlEdlbgðajenAkñ úgrUbTI 3-

26a. bgðajfaGgát;rgkmøaMgTaj b¤kmøaMgsgát;.Rbtikm μTRmRtUv)aneK[.

dMeNaHRsay³

Ggát;CF düaRkamGgÁesrI³ eKGacTTYlkmøaMgenAkñ úgrbs;Ggát; CF edayBicarNamuxkat;aa enAkñ úgrUbTI 3-26a. düaRkam

GgÁesrIénEpñkxagsþaMrbs;muxkat;enHRtUv)an bgðajenAkñ úgrUbTI 3-26 b.smIkarlMnwg³ eKGacTTYl)andMeNaHRsayedaypÞal; sRmab; CF F edayGnuvtþ 0=∑ E M . ehtuGV I? edIm,IgayRsYlyl; eyIgnwgrMkil CF F eTAcMNuc C ¬eKalkarN_énPaBGacbBa¢ Ún)an¦ rUbTI 3-26 b. dUcenH

0=∑+ E M ( ) ( ) 031.250.1430sin =+− o

CF F ( )C kN F CF 73.1=

Ggát;GC düaRkamGgÁesrI³ eKGacTTYlkmøaMgenAkñ úgrbs;Ggát; GC edayBicarNamuxkat;bb enAkñ úgrUbTI 3-26a. muxkat;kat;Ggát;cMnYnbYn b: uEnþkmøaMgenAkñ úgGgát; GC RtUv)anKNnarYc.düaRkamGgÁesrIénEpñkxageqVgrbs;muxkat;enHRtUv)anbgðaj


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T.Chhay -83

( )C kN F GD 80.1= ]TahrN_ 3 7³ kMNt;kmøaMgkñ úgrbs;Ggát; BC nig MC rbs; K-truss EdlbgðajenAkñ úgrUbTI 3-28 a.bgðajfaGgát;rgkarTaj b¤rgkarsgát;. eK[kmøaMgRbtikm μTRm.

dMeNaHRsay³

düaRkamGgÁesrI³ eTaHbICamuxkat;aa EdlbgðajenAkñúgrUbTI 3-28 a

kat;4Ggát;k¾edayk¾eKmanlT§PaBedaHRsayrkkmøaMgenAkñ úgGgát; BC edayeRbImuxkat;enH. düaRkamGgÁesrIénEpñkxageqVgrbs; truss RtUv)anbgðajenAkñúgrUbTI 3-28 b.smIkarlMnwg³ kareFV IplbUkm: Um:g;Rtg;cMNuc L GaceCosvagGBaØatbI dUcenH

0=∑+ L M ( ) ( ) 065.45.14 =+− BC F ( )T kN F BC 9.10=

düaRkamGgÁesrI³ eKGacTTYl)ankmøaMgenAkñúg MC edayminpÞal;edaydMbUgeyIgRtUvKNnakmøaMgenAkñ úg MB BIsmIkarkmøaMgbBaÄrenARtg;tMN B ¬rUbTI 3-28 c¦enaHeyIgTTYl)an ( )T kN F MB 6= .bnÞab;mkBIdüaRkamGgÁesrIenAkñúgrUbTI 3-28 b eyIg)an

0=∑↑+ yF 0665.14 =−+− MLF

( )T kN F ML 5.14=

edayeRbIlT§plTaMgenHdüaRkamGgÁesrIéntMN M

RtUv)anbgðajenAkñ úgrUbTI 3-28 d .smIkarlMnwg³

0=∑→+

xF 013

3

13

3=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎟

⎠

⎞⎜⎜⎝

⎛ MK MC F F

0=∑↑+ yF 013

2

13

265.14 =⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎟

⎠

⎞⎜⎜⎝

⎛ −− MK MC F F


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T.Chhay -85

viFItMN. bnÞab;mk eyIgGnuvtþkmøaMgEdlrk)aneTAelItMNrbs; truss rg ehIybnÞab;mkedayeRbIviFI tMN eyIgGackMNt;kmøaMgkñ úgrbs; truss rg ¬emIl]TahrN_ 3-10¦.

]TahrN_ 3 8³ bgðajBIrebobviPaK truss pSMEdlbgðajenAkñ úgrUbTI 3-29 a. eK[kmøaMgRbtikm μenARtg;tMN.

dMeNaHRsay³ vaCa truss pSMRbePTTI1 edaysar truss samBaØ ACH nig CEG RtUv)antP¢ab;edaytMNenARtg;tMNC nigr)ar HG .

muxkat; aa enAkñ úgrUbTI 3-29 a kat;Rtg;r)ar HG nigGgát; BIrepSgeTotEdlmankmøaMgCaGBaØat. düaRkamGgÁesrIsRmab;Epñktruss xageqVgEdlbgðajenAkñ úgrUbTI 3-29 b.

eKkMNt;kmøaMgenAkñ úgGgát; HG

dUcxageRkam³0=∑+ C M ( ) ( ) 060sin42445 =++− o HGF ( )C kN F HG 46.3=

eyIgGacbnþkarkMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss samBaØ edayeRbIviFItMN. Ca]TahrN_ düaRkamGgÁesrIrbs; truss ACH RtUv)anbgðajenAkñúgrUbTI 3-29 c. eKGacviPaKtMNrbs; trusstamlMdab;lMedaydUcxageRkam³

tMN A ³ kMNt;kmøaMgkñ úg AB nig AI .tMN H ³ kMNt;kmøaMgkñ úg HI nig HJ .tMN I ³ kMNt;kmøaMgkñúg IJ nig IB .tMN B ³ kMNt;kmøaMgkñ úg BC nig BJ .tMN J ³ kMNt;kmøaMgkñ úg JC .


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T.Chhay -87

]TahrN_ 3 10³ bgðajBIrebobviPaK truss pSMsI uemRTIEdlbgðajenAkñúgrUbTI 3-31a. eK[kmøaMgRbtikm μenARtg;TRm.

dMeNaHRsay³

eKcat;cMNat;fñak; truss xagelICa truss pSMRbePTTI3 Edlman truss AGEF nig truss CHED Catruss rg ehIy truss ABCD Ca truss em.

edayyk truss rgTaMgBIrecj ¬rUbTI 3-31 b¦ eKRtUvdak;CMnYsRbtikm μrbs;vaEdlmçag²es μ Inwg kN 5.1 enARtg;tMNsnøak; A nigtMN E ehIyenARtg;tMN E nigtMNC . eKGackMNt; kmøaMgRbtikm

μ

rbs; truss rgTaMgBIrenH)an edaysarGnuvtþsmIkarlMnwgeTAelI truss nImYYy².Truss emCamYynwgkardak;bnÞ úk kN 5.1 RtUv)anbgðajenAkñúgrUbTI 3-31c. eKGackMNt;kmøaMgenAkñ úgGgát;nImYy²BIviFItMN. Ca]TahrN_ sRmab;tMN A düaRkamGgÁesrIRtUv)anbgðajenAkñúgrUbTI 3-31d .eyIgman

0=∑↑+ yF 045sin45sin5.162.4 =−− o

AE o

F

( )C kN F AE 03.5= 0=∑→

+

xF 045cos03.545cos5.1 =+− ABoo F ( )T kN F AB 50.2=

edaydwgfa ( )C kN F AE 03.5= eyIgGacGnuvtþkmøaMgEdlCatémøelxenHeTAelI truss rg AGEF enAkñ úgrUbTI 3-31 b ehIybnÞab;mkbnþkarviPaKkmøaMgenAkñúgGgát;rbs; truss enHedayviFItMN.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm&>

TrusssaMjúaM

(Complex Trusses)

eKGackMNt;kmøaMgxagkñ úgGgát;rbs; truss saMjúaMedayeRbIviFItMN b:uEnþeKRtUvkarsresrsmIkarlMnwgBIrsRmab;RKb;tMNEdlmancMnYn j rbs; truss ehIybnÞab;mkedaHRsaysMnMuRbB½n§smIkarcMnYn j2 1.viFIenHBitCaBi)aksRmab;karKNnaedayéd CaBiesssRmab;krNI truss FM². dUcenH viFIEdlmanlkçN³pÞal;sRmab;viPaK truss saMjúaMKWviFICMnYsGgát; (method of substitute members) ehIyviFI wenHRtUv)anykmkerobrab;enATIenH.

dMeNIrkarkñgkarviPaK

(Procedure for analysis) eyagtam truss enAkñ úgrUbTI 3-32a, xageRkamCaCMhancaM)ac;edIm,IedaHRsayrkkmøaMgkñúg

rbs;Ggát;edayeRbIviFICMnYsGgát;.

kareFV[vaeTACa truss samBaØsßrPaB. kMNt;kmøaMgRbtikm μenARtg;TRm nigcab;epþ ImviPaKkmøaMgkñúg

rbs;Ggát;edayeRbIviFItMN. eKRtUvCMnYsedayGgát;nimitþcMnYnmYy enARtg;tMNNaEdlmanGBaØatEdlCakmøaMgcMnYnbI. kareFVIEbbenH KWeKeFVI[ truss køayCa truss samBaØsß irPaB.

Ca]TahrN_ enAkñúgrUbTI 3-32a eyIgsegÁteXIjfatMNnImYy²mankmøaMgkñ úgrbs;Ggát;CaGBaØatcMnYnbImanGMeBIelIva. dUcenH eyIgnwgykGgát; AD ecj ehIyCMnYsvaedayGgát;nimitþ EC ¬rUbTI

1 eKGaceRbIviFIenHedaymanCMnYyBIkM uBüÚT½rEdlnwgmanbgðajenAkñ úgCMBUkTI14.


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T.Chhay -89

3-32 b¦. eKGacviPaK truss enaHedayviFItMNsRmab;bnÞ úkTaMgBIrRbePTdUcxageRkam.kmøaMgxageRkAenAelI truss samBaØ³ dak;bnÞúkCak;EsþgenAelI truss samBaØ bnÞab;mkkMNt;kmøaMg iS ' enAkñ úgGgát; i . enAkñ úgrUbTI 3-32 b/ kñ úgkrNIEdleKkMNt;kmøaMgRbtikm μrYc eKGaccab;epþImkar viPaKtruss Rtg;tMN AD edIm,IkMNt;kmøaMgenAkñ úgGgát; AB nig AF bnÞab;mkviPaKtMN F edIm,IkM MNt;kmøaMgenAkñ úgGgát; FE nig FC bnÞab;mkeTotviPaKtMN D edIm,IkMNt;kmøaMgenAkñúgGgát; DE nig DC ¬Ggát; TaMgBIrenHCaGgát;EdlmankmøaMgsUnü¦ ehIybnÞab;mkeTot viPaKtMN E edIm,IkMNt;kmøaMgrbs;Ggát; EB nig EC ehIycugeRkay viPaKtMN B edIm,IkMNt;kmøaMgenAkñ úgGgát; BC .ykkmøaMgxageRkAecjBI truss samBa³ BicarNa truss samBaØEdlminmankmøaMgxageRkA. dak;bnÞ úkmYyÉktþaenARtg;tMNTaMgBIrEdleyIg)anykGgát;ecj edaybnÞ úkÉktþaenaHmanTisedApÞ úyKña. RbsinebIbnÞ úkÉktþaenHbegá ItkmøaMg iS enAkñúgGgát; truss TI i enaHedaysmamaRt kmøaMgEdlCaGBaØat x enA

kñ úgGgát;EdlykecjnwgeFVI[Ggát;TI i rgkmøaMg i xs .BIrUbTI 3-32c/ bnÞ úkÉktþanwgminbegá It[mankmøaMgRbtikm μenARtg;TRm A nigTRm C enA

eBlEdlGnuvtþsmIkarlMnwgeTAelI truss TaMgmUl. eKGackMNt;kmøaMg is edayviPaKtMNtamlMdab;lM edaydUcelIkmun eBalKWcab;epþImBItMN A bnÞab;mktMN F / tMN D / tMN E nigcugeRkaytMN B .eFVtRmYtpl (superposition)³ RbsinebIeKpÁ Üb\T§ iBlrbs;bnÞ úkTaMgBIrxagelI kmøaMgenAkñ úgGgát;TI i rbs; truss nwgkøayCa³

iii xsS S += ' (1)

sRmab;kmøaMgenAkñúgGgát;nimitþ EC enAkñ úgrUbTI 3-32 b KW EC EC EC xsS S += ' . edaysar enAkñúgtruss Cak;EsþgminmanGgát;nimitþenH dUcenHeyIgRtUveRCIserIstémørbs; x EbbNaEdlvanwgeFV I[Ggát; nimitþCaGgát;kmøaMgsUnü. dUcenH

0' =+ EC EC xsS (2) b¤ EC EC sS x /'−= . enAeBlEdlkMNt;témørbs; x rYcehIy enaHeKGackMNt;kmøaMgenAkñ úgGgát;rbs; truss saMjúaMBIsmIkar (1).

]TahrN_ 3 11³ kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss saMjúaMEdlbgðajenAkñ úgrUbTI 3-33a.sn μt;tMN B / F nig D sß itenAelIbnÞat;edk. bgðajnUvsßanPaBrgkmøaMgrbs;Ggát;nImYy².

dMeNaHRsay³

eFV[ truss køayCa truss samBaØmansßrPaB. edaykarGegát tMNnImYy²mankmøaMgEdlCaGBaØatcMnYnbI . eKGacGnuvtþviFItMNedayédRbsinebIeKykGgát;CF yk ehIyCMnYsGgát; DB vij


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T.Chhay -91

#>*> Truss kñglMh (Space Trusses)

Truss kñ úglMhpSMeLIgedayGgát;EdltP¢ab;KñaenARtg;cugrbs;edIm,Ibegá ItCarcnasm


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T.Chhay -93


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T.Chhay -95

krNITI2³ RbsinebIGgát;BIrkñ úgcMeNamGgát;epSgeTotEdltP¢ab;KñaenARtg;tMNmYyCaGgát;kmøaMgsUnüenaHGgát;EdlenAsl;BIrepSgeTotk¾CaGgát;kmøaMgsUnüEdr kñ úgkrNIEdlBYkvaminsß itenAelIbnÞat;EtmYy. sßanPaBEbbenHRtUv)anbgðajenAkñ úgrUbTI 3-37 EdleKdwgfaGgát; A nigC CaGgát;kmøaMgsUnü.edaysar DF sß itenAelIG½kS y enaHkarGnuvtþén 0=∑ xF b¤ zF ∑ TamTar[bgÁú MkmøaMgtamG½kS x b¤ G½kS z rbs; BF RtUvEtes

μ

IsUnü. dUcenH 0= BF . ehIy 0= DF edaysar 0=∑ yF .

enAeBleFV IkarviPaK truss kñ úglMheKRtUvykcitþTukdak;CamYynwgkrNITaMgBIrEdlerobrab;xagelI edaysarkardwgBIGgát;kmøaMgsUnüsRmYldl;karviPaK truss kñ úglMhy:ageRcIn.

dMeNIrkarkñgkarviPaK

(Procedure for analysis)

eKGaceRbIviFItMN b¤viFImixkat;edIm,IviPaKkmøaMgkñ úgEdlekItmanenAkñúgGgát;rbs;truss

kñúglMh.viFImuxkat;³ RbsinebIeKRtUvkarkMNt;kmøaMgkñ úgrbs;Ggát;xøH eKGaceRbIviFImuxkat;. enAeBleKkat; truss CaBIrcMENk enaHRbB½n§kmøaMgEdleFVIGMeBIenAlIcMENkén truss nImYy²RtUvEtbMeBjsmIkarlMnwg6KW

0=∑ xF / 0=∑ yF / 0=∑ zF / 0=∑ x M / 0=∑ y M nig 0=∑ z M . edaykareRCIserIsmuxkat; nigG½kSd¾RtwmRtUvsRmab;eFV IplbUkkmøaMg nigm: Um:g; enaHeKGackMNt;kmøaMgkñúgrbs;Ggát;EdlCaGBaØatedaypÞal; edayeRbIlMnwgsmIkarEtmYy. sRmab;krNIEbbenH eyIgRtUvcaMfam: Um:g;énkmøaMgRtg; cMNucmYyes μ IsUnü RbsinebIkmøaMgRsbeTAnwgG½kSEdlcMNucenaHsß itenA.

viFItMN³ CaTUeTA vIFIEdlsaksmbMputsRmab;karkMNt;kmøaMgenAkñúgGgát;TaMgGs;rbs; truss KWviFItMN.enAeBleKeRbIviFItMN eKcaM)ac;RtUvedaHRsaysmIkarlMnwgbI 0=∑ xF / 0=∑ yF nig 0=∑ zF sRmab; tMNnImYy². edaysarkarKUrdüaRkamGgÁesrI nigkarGnuvtþsmIkarlMnwgmanlkçN³gayRsYlenaHkar Gnuvtþrbs;vamanlkçN³zitezr.


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T.Chhay -97

0=∑ yF 06

44 =⎟

⎠

⎞⎜⎝

⎛ +− BE F ( )T kN F BE 6=

0=∑ xF 06

262 =⎟

⎠

⎞⎜⎝

⎛ −− BC F 0= BC F

0=∑ zF 06

46 =⎟

⎠

⎞⎜⎝

⎛ − BAF ( )C kN F BA 4=

tMN

A³ edayeRbIlT§plén ( )C kN F BA 4= . düaRkamGgÁesrIrbs;tMN A RtUv)anbgðajenAkñúgrUbTI 3-38 d . eyIgman

0=∑ zF 045sin44 =+− o AC F 0= AC F

0=∑ yF 045

2=+⎟⎟

⎠

⎞⎜⎜⎝

⎛ − AE F ( )C kN F AE 47.4=

0=∑ xF 05

147.42 =⎟⎟

⎠

⎞⎜⎜⎝

⎛ ++− ADF 0= ADF

tMN

D³ edaykarGegát Ggát;enARtg;tMN D ¬rUbTI 3-38 a¦ rgbnÞ úksUnüedaysarkarteRmobrbs;Ggát;manlkçN³RsedogKñanwgkrNITaMgBIrEdlmanbgðajenAkñ úgrUbTI 3-36nig 3-37. ehIyBIrUbTI 3-38 e

0=∑ xF 0= DE F 0=∑ zF 0= DC F

tMN

C ³ edaykarGegátdüaRkamGgÁesrIénrUbTI 3-38 f 0=CE F

]TahrN_ 3 13³ kMNt;Ggát;kmøaMgsUnürbs; truss EdlbgðajenAkñ úgrUbTI 3-39 a. TRmGnuvtþbgÁ úM kmøaMgRbtikm μmkelI truss dUcbgðajenAkñúgrUb.


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cMeNaT

T.Chhay -99

cMeNaT

3>1> cat;cMNat;fñak; truss xageRkamCa trussmansß irPaB K μansßirPaB kMNt;edaysþaTic min

kMNt;edaysþaTic. RbsinebIminkMNt;bgðajBIdWeRkrbs;va. Ggát;TaMgGs;RtUv)antP¢ab;edaysnøak;enAxagcugrbs;va.

3>2> cat;cMNat;fñak; truss xageRkamCa truss kMNt;edaysþaTic minkMNt;edaysþaTic b¤K μan

sß irPaB. RbsinebIminkMNt; cUrbgðajdWeRkrbs; va.

3>3> cat;cMNat;fñak; truss xageRkamCa truss

kMNt;edaysþaTic minkMNt;edaysþaTic b¤K μ

ansß irPaB. RbsinebIminkMNt; cUrbgðajdWeRkrbs; va.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm4> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss.bgðajsPaBrgkmøaMgrbs;Ggát;.

3>5> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss.bgðajsPaBrgkmøaMgrbs;Ggát;. yk kN P 8= .

3>6> Truss EdlbgðajRtUv)aneRbIedIm,IRTkRmal deck . bnÞúkBRgayenAelIkRmalKW mkN /30 . bnÞ úkenHRtUv)anepÞrBIkRmaleTA

Fñ wmEdlQrenAelItMNxagelIrbs; truss.kMNt;kmøaMgkñúgGgát;nImYy²rbs; truss ehIybgðajBIsPaBkmøaMg EdlGgát;rg. sn μt;Ggát;

TaMgGs;RtUv)antP¢ab; edaytMNsnøak;.

3>7> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss.

bgðajsPaBrgkmøaMgrbs;Ggát;.

3>8> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; truss.bgðajsPaBrgkmøaMgrbs;Ggát;. sn

μ

t;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.

3>9> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs;dMbUltruss. bgðajsPaBrgkmøaMgrbs;Ggát;. sn μt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.


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cMeNaT

T.Chhay -101

3>10> Howe truss rgbnÞúkdUcbgðajkñúgrUbxageRkam. kMNt;kmøaMgenAkñúgGgát; GF / CD nigGC . bgðajsPaBrgkmøaMgrbs;Ggát;.

3>11> kMNt;kmøaMgenAkñ úgGgát; GH / BC nig BG rbs; Howe truss xagelI. bgðajsPaBrg

kmøaMgrbs;Ggát;.3>12> kMNt;kmøaMgenAkñúgGgát;nImYy²rbs; dMbUl truss. bgðajsPaBrgkmøaMgrbs;Ggát;.

3>13> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs;dMbUl truss. bgðajsPaBrgkmøaMgrbs;Ggát;.sn μt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.

3>14> kMNt;kmøaMgenAkñúgGgát; GH / BC nig BG rbs; truss s15> kMNt;kmøaMgenAkñ úgGgát;nImYy²rbs; dMbUl truss. bgðajsPaBrgkmøaMgrbs;Ggát;.

3>16> edaHRsaycMeNaT 3>15> eLIgvijedaysn μt;famanEtbnÞúk kN 15 b:ueNÑaHEdleFVIGMeBIelItMN I .


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm17> kMNt;kmøaMgenAkñúgGgát; GF / FC nigCD rbs; truss kugs‘ul. bgðajsPaBrgkmøaMgrbs;Ggát;. sn μt;Ggát;TaMgGs;tP¢ab;Kñaeday

snøak;.

3>18> kMNt;kmøaMgenAkñ úgGgát; KJ / CD nigCJ rbs; truss. bgðajsPaBrgkmøaMgrbs; Ggát;.

3>19> kMNt;kmøaMgenAkñ úgGgát; JI / JD nig

DE rbs; truss xagelI. bgðajsPaBrgkmøaMgrbs;Ggát;.3>20> kMNt;kmøaMgenAkñ úgGgát;rbs; truss edayeRbItYbnÞ úk P ehIybgðajsPaBrgkmøaMgrbs; Ggát;.

3>21> Ggát; AB nig BC GacRTRTg;kmøaMgsgát;Gtibrma kN 4 ehIyGgát; AD / DC nig BD GacRTRTg;kmøaMgTajGtibrma kN 5.7 . Rbsin

ebI ma 3=

kMNt;bnÞ úkFMbMputrbs; P Edl truss GacRT)an. ¬rUbkñ úgcMeNaT 3>20¦3>22> Ggát; AB nig BC GacRTRTg;kmøaMgsgát;Gtibrma kN 4 ehIyGgát; AD / DC nig BD GacRTRTg;kmøaMgTajGtibrma kN 10 . RbsinebI ma 8.1= kMNt;bnÞ úkFMbMputrbs; P Edltruss GacRT)an. ¬rUbkñ úgcMeNaT 3>20¦

3>23> eKeRbI truss Ggát;bIedIm,IRTbnÞúk P .kMNt;mM u θ edIm,IkMu[kmøaMgTajGtibrma nigkmøaMgsgát;GtibrmaFMCag P25.1 nig P8.0 erogKña.

3>24> kMNt;kmøaMgenAkñúgGgát; GF / FB nig BC rbs; Fink truss. bgðajsPaBrgkmøaMgrbs;Ggát;.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm31> kMNt;kmøaMgenAkñúgGgát; IH / AH nig BC rbs; truss. bgðajBIsPaBrgkmøaMgrbs;Ggát;.

3>32> kMNt;kmøaMgenAkñúgGgát;nImYy². bgðajBIsPaBrgkmøaMgrbs;Ggát;.

3>33> kMNt;kmøaMgenAkñ úgGgát;nImYy². bgðajBIsPaBrgkmøaMgrbs;Ggát;.

3>34> kMNt;kmøaMgenAkñ úgGgát;TaMgGs;rbs; truss saMjúaM. bgðajBIsPaBrgkmøaMgrbs;Ggát;.CMnYy ³ CMnYsGgát; JE edayGgát;Edldak;enA

cenøaH K nig F .

3>35> kMNt;kmøaMgenAkñ úgGgát;TaMgGs;rbs; truss saMjúaM. bgðajBIsPaBrgkmøaMgrbs;Ggát;.sn μt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.

3>36> kMNt;kmøaMgenAkñ úgGgát; JI / DI nig DE rbs; Pratt truss . bgðajBIsPaBrgkmøaMgrbs;Ggát;. sn μt;Ggát;TaMgGs;tP¢ab;Kñaeday

snøak;.


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cMeNaT

T.Chhay -105

3>37> eRKag truss mYyrgbnÞ úkdUcbgðaj.kMNt;kmøaMgenAkñ úgGgát; JI / JD nig ID .bgðajBIsPaBrgkmøaMgrbs;Ggát;.

3>38> kMNt;kmøaMgenAkñ úgGgát; HI / ED nig EI enAkñúg truss éncMeNaT 3>37. bgðajBIsPaBrgkmøaMgrbs;Ggát;.3>39> kMNt;kmøaMgenAkñ úgGgát; EF / EP nig LK én truss s40> kMNt;kmøaMgenAkñ úgGgát; HG / BG nig BC rbs; truss. bgðajBIsPaBrgkmøaMgrbs;

Ggát;.

3>41> kMNt;kmøaMgenAkñúgGgát; BG / HG nig BC rbs; truss nigbgðajBIsPaBrgkmøaMgrbs; Ggát;.

3>42> eKeRbI Warren truss edIm,IRTdMbUlGKar]sSahkm μ. Turss enHRTedayTRmsamBaØ enAelICBa¢aMg\dæenARtg; A nig G dUcenHmanEtkmøaMgRbtikm μtamTisQrb:ueNÑaHekItmanenARtg;TRmTaMgenH. kMNt;kmøaMgenAkñ úgGgát; LC /CD nig KD . bgðajBIsPaBrgkmøaMgrbs;Ggát;.sn μt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.

3>43> kMNt;kmøaMgenAkñ úgGgát; KJ / NJ / ND nig CD én K-truss . bgðajBIsPaBrgkmøaMgrbs;Ggát;.


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mhaviTüal½ ysM Ng; sI uvil viTüasßanCatiBh ubec©keTskm44> kMNt;kmøaMgenAkñúgGgát; IH / CD nig LH én K-truss . bgðajBIsPaBrg kmøaMgrbs; Ggát;. CM nYy³ kat; truss Rtg;Ggát; IH / IL /

LC nig CD edIm,Irk IH nig CD sn μ

t;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.

3>45> kMNt;kmøaMgenAkñúgGgát;TaMgGs;rbs;

truss saMjúaM. bgðajBIsPaBrgkmøaMgrbs;Ggát;.CM nYy³ CMnYsGgát; AD edayGgát;enAcenøaH E nigC .

3>46> kMNt;kmøaMgenAkñúgGgát;TaMgGs;rbs; truss saMjúaM. bgðajBIsPaBrgkmøaMgrbs;Ggát;.CM nYy³ CMnYsGgát; JE edayGgát;enAcenøaH K

nig F .

3>47> kMNt;kmøaMgenAkñúgGgát;nImYy² nigbgðajBIsPaBrgkmøaMgrbs;Ggát;.

3>48> kMNt;kmøaMgRb

Documents

Khmer Structural Analysis - Teng Chhay