1. T.Chhay
Appendix A. karKNna nigkarviPaKedaylkçN³)aøsÞic
Plastic Analysis and Design
A >1> esckþIepþIm Introduction
eyIg)anENnaMBIKMniténkar)ak;eday)aøsÞic (plastic collapse) enAkñúgEpñk 5>2/ “ kugRtaMg
Bt; nigm:Um:g)aøsÞic” . kar)ak;rbs;eRKOgbgÁúMnwgekIteLIgenAeBlbnÞúkbegáItsnøak;)aøsÞicRKb;RKan;edIm,I
;
begáItCa mechanism EdlnwgeFVIeGaymanPaBdabedayminmankarekIneLIgbnÞúk. enAkñúgFñwmEdl
kMNt;edaysþaTic eKRtUvkarEtsnøak;)aøsÞicmYyEtb:ueNÑaH. dUcbgðajenAkñúgrUbTI A>1 snøak;nwgekIt
manenAkEnøgNaEdlmanm:Um:g;Gtibrma ¬krNIenHKWenAkNþalElVg¦. enAeBlEdlm:Um:g;Bt;mantMél
FMRKb;RKan;edIm,IeFVIeGaymuxkat;TaMgmUl yield/ enaHvaminGacTb;nwgkarekIneLIgrbs;m:Um:g;EfmeTot/
ehIysnøak;)aøsÞick¾RtUv)anbegáIteLIg. snøak;)aøsÞicenHRsedogKñanwgsnøak;FmμtaEdr EtxusRtg;fa
snøak;)aøsÞicmanlT§PaBTb;nwgm:m:g;xøH EdldUcKñay:agxøaMgnwg rusty hinge.
U
460 Appendix A

2. NPIC
lT§PaBm:Um:g;)aøsÞic (plastic moment capacity) EdlsMKal;eday M p Cam:Um:g;Bt;EdlekIt
manenARtg;snøak;)aøsÞic. vamantMélesμInwgm:Um:g;Tb;xagkñúgEdlekItBIkarEbgEckkugRtaMgEdlbgðaj
enAkñúgrUbTI A>1 c EtmanTisedApÞúyKña. eKGackMNt;m:Um:g;)aøsÞicenAeBlEdleKsÁal; yield stress
nigrUbragmuxkat; dUcbgðajenAkñúgrUbTI A>2. RbsinebIkarEbgEckkugRtaMgenAkñúglkçxNÐ)aøsÞiceBj
RtUv)anCMnYsedaykMlaMgsmmUlsþaTicBIrEdlmantMéldUcKña nigTisedApÞúyKña enaHvanwgbegáIt couple.
GaMgtg;sIueténkMlaMgnImYy²esμInwgplKuNrvag yield stress nigBak;kNþalRkLaépÞmuxkat;srub.
m:Um:g;EdlbegáIteday couple xagkñúgenHKW
A
M p = Fy a = Fy Z x
2
Edl A CaRkLaépÞmuxkat;srub/ a CacMgayrvagTIRbCMuTMgn;énRkLaépÞBak;kNþalBIr nig Z x Cam:U
Dulmuxkat;)aøsÞic. emKuNsuvtßiPaBcenøaHsßanPaB yielding dMbUg nigsßanPaB)aøsÞiceBjRtUv)ansM
EdgenAkñúgm:UDulmuxkat;. BIrUbTI A>1 b eKGacsresrm:Um:g;EdlbegáIt yield dMbUg
M p Fy Z x Z x
M y = Fy S x nig = =
M y F S
y x xS
pleFobenHCatMélefrsMrab;rUbragmuxkat;EdlsÁal; nigRtUv)aneKehAfa emKuNrUbrag. sMrab;Fñwm
EdlKNnaeday allowable stress theory vaCargVas;én reserve capacity ehIymantMélmFüm 1.12
sMrab; W-shapes.
enAkñúgFñwm b¤eRKagsþaTicminkMNt; eKRtUvkarsnøak;)aøsÞiceRcInCagmYyedIm,IbegáIt collapse
mechanism. snøak;TaMgenHnwgRtUv)anbegáIttamlMdab;lMeday eTaHbICaeKmincaM)ac;dwgBIlMdab;k¾eday.
eKnwgBicarNakarviPaKrcnasm<n§½sþaTicminkMNt;eRkayBIkarBiPakSatMrUvkarrbs; Specification.
461 Appendix A

3. T.Chhay
A>2> AISC Requirements
AISC Specification GnuBaØatieGayeRbI plastic analysis and design enAeBl eRKOg
bgÁúMenArkSaPaBlMnwgTaMg local nigTaMgmUl Rtg;cMnuc plastic collapse. edaysareKtMrUveGayFñwm
b¤eRKagrgnUvPaBdabFMenAeBlEdlsnøak;)aøsÞicRtUv)anbegáIt eKRtUvkar lateral bracing CaBiess.
edIm,IkarBar local buckling, AISC B5.2 TamTarfaGgát;man compact cross-sectional
shape Edl λ ≤ λ p sMrab;TaMgRTnug nigsøab. sMrab;Ggát; I-shaped shape dUcCa W nig S-shapes
pleFobTTwgelIkMras;EdlkMNt;BI Table B5.2 KW
bf 65 bf 170
≤ (US) ≤ (IS)
2t f Fy 2t f Fy
nig h
tw
≤
640
Fy
(US)
h 1680
tw
≤
Fy
(IS)
edIm,IkarBar lateral buckling, AISC F1.2d kMNt; unbraced length Gtibrma Lb Rtg;
TItaMgsnøak;)aøsÞicCa L pd EdlsMrab; I-shaped member
3600 + 2200(M 1 / M 2 )
L pd = ry (US) (AISC Equation F1-17)
Fy
24820 + 15170(M 1 / M 2 )
L pd = ry (IS)
Fy
enAkñúgsmIkarenH M 1 Cam:Um:g;EdltUcCagenARtg;cugén unbraced length nig M 2 CamU:m:g;EdlFMCag.
pleFob M 1 / M 2 KwviC¢manenAeBlEdl M 1 nig M 2 Bt;Ggát;eGaymankMeNagDub nigmantMél
GviC¢manenAeBlEdlvabegáItkMeNageTal.
sMrab; compact shape Edlman lateral bracing RKb;RKan; eKGacyk M n esμInwg M p sMrab;
eRbIenAkñúg plastic analysis. b:uEnþ AISC F1.2d kMNt;faenAkñúgtMbn;EdlekItmansnøak;)aøsÞiccug
eRkay nigenAkñúgtMbn;EdlminEk,rsnøak;)aøsÞic eKRtUveRbIviFIFmμtaedIm,IkMNt; M n .
AISC Specification provision epSgeTotEdlTak;Tgnwg plastic analysis and design
mandUcxageRkam.
A5.1 Plastic analysis RtUv)anGnuBaØatsMrab;Et Fy ≤ 65ksi .
C2.2 kMlaMgtamG½kSEdlbegáItedaybnÞúkTMnajemKuN nigbnÞúktamTisedkemKuNminRtUvFM
Cag 0.75φc Ag Fy .
462 Appendix A

4. NPIC
E1.2 sMrab;ssr slenderness parameter λc minRtUvFMCag 1.5K Edl K CaemKuNRbEvg
RbsiT§PaB.
A >3> karviPaK Analysis
RbsinebIvaGacman collapse mechanism eRcInCamYy dUcCaFñwmCab;EdlbgðajenAkñúgrUbTI A>3
eKGacrk)annUv collapse mechanism EdlRtwmRtUv ehIyviPaKCamYynwgCMnYyénRTwsþIeKalcMnYnbIrbs;
plaxtic analysis EdleGayenATIenHedayKμankarRsaybBa¢ak;.
!> Lower-bound theorem (static theorem): RbsinebIeKGacrk)annUvkarEbgEck
m:Um:g;d¾mansuvtßiPaB ¬Edlm:Um:g;mYytUcCag b¤esμInwg M p RKb;kEnøg¦ ehIyvaGacTTYl
bnÞúkedaysþaTic ¬lMnwgRtUv)anbMeBj¦ bnÞab;mkbnÞúkEdlRtUvKñaRtUvtUcCag b¤esμI
collapse load.
@> Upper-bound theorem (kinetic theorem): bnÞúkEdlRtUvnwg mechanism snμt;RtUvEtFM
Cag b¤esμInwg collapse load. Cavi)ak RbsinebIeKGegát mechanism EdlGacmanTaMg
Gs; mechanism mYyNaEdlRtUvkarbnÞúktUcCageKCa mechanism EdlRtwmRtUv.
#> Uniqueness theorem: RbsineKmankarEbgEckm:Um:g;EdlGacTTYlyk)anedaysþaTic
nigmansuvtßiPaB EdlenAkñúgenaH snøak;)aøsÞicRKb;RKan;begáIt collapse mechanism enaH
463 Appendix A

5. T.Chhay
bnÞúkEdlRtUvKñaCa collapse load EdlRbsinebI mechanism bMeBjTaMg upper-boud
theorem nig lower-bound theorem vaCa mechanism EdlRtwmRtUv.
karviPaKEdlQrelI lower-bound theorem RtUv)aneKehAfa equilibrium method ehIyRtUv)an
bgðajenAkñúg]TahrN_ A>1.
]TahrN_ A>1³ rkbnÞúkcugeRkay (ultimate load) sMrab;FñwmEdlbgðajenAkñúgrUbTI A>4a eday
equilibrium method rbs; plastic analysis. snμt;eKeRbI continuous lateral support nig EdlRb
ePT A36 .
dMeNaHRsay³ Edk A36 muxkat; W 30 × 99 Ca comapact shape ehIyCamYynwg continuous lateral
support, tMrUvkar lateral bracing KWRKb;RKan; dUcenHeKGacTTYlyk plastic analysis.
dMNak;karénkardak;bnÞúkelIFñwm BI working load eTAdl; collapse load
RtUv)anKUsbBa¢ak;enAkñúgrUbTI A>4a-d. enAeBl working load muneBl yielding ekIteLIgRKb;TIkEnøg
karEbgEckm:Um:g;Bt;RtUv)anbgðajenAkñúgrUbTI A>4a CamYynwgm:Um:g;GtibrmaEdlekItmanRtg;TMrbgáb;.
enAeBlEdlbnÞúkekIneLIgbnþicmþg² yielding cab;epþImekItmanRtg;TMr enAeBlEdlm:Um:g;Bt;eTAdl;
M y = Fy S x . enAeBlEdlbnÞúkekIneLIgkan;EtFM vanwgekItmansnøak;)aøsÞickñúgeBldMNalKñaenA
Rtg;cugnImYy² enAeBlEdl M p = Fy Z x . enARtg;kMrwténkardak;bnÞúkenH eRKOgbgÁúMenAmanesßrPaB
464 Appendix A

6. NPIC
enAeLIy FñwmRtUv)anERbkøayeTACasþaTickMNt;edaykarekItmansnøak;)aøsÞicBIr. Mechanism nwgekIt
anEtenAeBlEdlekItmansnøak;)aøsÞicTIbI. vaGacekItmanenAeBlEdlm:Um:g;viC¢manGtibrmamantMél
M p . edayGaRs½ynwg uniqueness theorem/ bnÞúkEdlRtUvKñaCa collapse load BIeRBaHkarEbgEck
m:Um:g;KWsuvtßiPaB ehIyGacTTYlyk)anedaysþaTic.
enARKb;tMNak;kalénkardak;bnÞúk plbUkénéldac;xaténm:Um:g;viC¢man nigm:Um:g;GviC¢manGti-
brmaKW wL2 / 8 . enAeBl collapse, plbUkenHkøayeTACa
16M p
M p + M p = wu L2 b¤
1
wu =
8 L2
eKRtUvEteRbobeFobbnÞúkemKuNCamYynwgersIusþg;emKuN dUcenHeKeRcIneRbI φb M p Cag M p enAkñúg
smIkarBIxagedIm. b:uEnþedIm,IrkSanimitþsBaØaeGaymanlkçN³samBaØ eyIgeRbI M p enARKb;]TahrN_
TaMgGs;rhUtdl;CMhancugeRkayeTIbeyIgCMnYs φb M p eTAkñúgsmIkar. lT§plEdlRtwmRtUv
sMrab;]TahrN_enHKW
16φb M p
wu =
L2
sMrab; W 30 × 99
36(312 )
M p = Fy Z x = = 936 ft − kips
12
ehIy φb M p = 0.9(936) = 842.4 ft − kips
eKk¾GacTTYltMélrbs; φb M p edaypÞal;BI Load Factor Design Selection Table enAkñúg Part 4 of
the Manual.
16(842.4 )
cemøIy³ w u =
(30)2
= 15.0kips / ft
]TahrN_ A>2³RbsinebIFñwmenAkñúg]TahrN_ A>1 minman continuous lateral support cUrkMNt;TItaMg
EdlRtUvBRgwg.
dMeNaHRsay³ snøak;)aøsÞicenAxagcugekIteLIgkñúgeBldMNalKña ehIymuneBlsnøak;enAkNþalElVg
ekIteLIg. dUcenHeKKYrEtRtYtBinitü unbraced length GtibrmaedayeFobeTAnwgcug ¬snøak;cugeRkay
EdlekIteLIgmintMrUvkar bracing sMrab; plastic analysis eT¦.
465 Appendix A

7. T.Chhay
edayeFobnwgsnøak;enAcugxageqVg snμt;facMnucBRgwgKWenAkNþalElVg. kñúgkrNIenH M 1 =
M 2 = M p dUcenHFñwmmankMeNagDub ¬m:Um:g;TaMgBIrmansBaØadUcKña¦ dUcenH M 1 / M 2 = +1 BI AISC
Equation F1-17, unbraced length GtibrmaKW
3600 + 2200(M 1 / M 2 ) 3600 + 2200(1.0)
L pd = ry = (2.10) = 338.3in. = 28.2 ft
Fy 36
cMNaMfa FñwmenHesÞIrEtRKb;RKan;edayminRtUvkar lateral bracing.
CamYynwg lateral mYyTl;enAkNþalElVg
L p = 15 ft < 28.2 ft (OK)
Unbraced length EdlRtUvBicarNarYmKWrYbbBa©ÚlTaMgsnøak;enAkNþalElVg. vaminmantMbn;Edlmin
enACab;nwgsnøak;)aøsÞiceT dUcenHvaminRtUvkarkarKNna design strength eT.
cemøIy³ eRbI lateral brace mYyenAkNþalElVg.
Mechanism method KWQrelI upper-bound theoremnigRtUvakrGegátRKb; collapse
mechanism EdlGacekItman. Collapse mechanism NaEdlRtUvkarbnÞúktUcCageKnwglub eyIy
bnÞúkEdlRtUvKñaCa collapse laod. eKRtUvGnuvtþeKalkarN_rbs; virtual work sMrab;viPaK
mechanism nImYy². Mechanism snμt;RtUvrgnUv virtual displacement RsbeTAtamclnaEdl
GacekItmanrbs; mechanism ehIyeKeGaykmμnþxageRkA nigkmμnþxagkñúgesμIKña. bnÞab;mkeKGacrk
TMnak;TMngrvagbnÞúk niglT§PaBTb;m:Um:g;)aøsÞic M p . bec©keTsenHRtUv)anbgðajenAkñúg]TahrN_
A>3 nig A>4.
]TahrN_ A>3³ FñwmCab;EdlRtUv)anbgðajenAkñúgrUbTI A>5 man compact cross section Edlman
design strength φb M p = 1040 ft − kips . eRbI mechanism method edIm,Irk collapse load Pu .
snμt; continuous lateral support.
dMeNaHRsay³ eKman failure mechanism sMrab;FñwmenHBIry:ag. dUcEdlbgðajenAkñúgrUbTI A>5
vamanlkçN³RsedogKñaEdlkMNat;Ggát;nImYy²rgnUv rigid-body motion. edIm,IGegát mechanism
enAkñúgElVg AB dak; vitual rotation θ Rtg; A. karvilEdlRtUvKñaenARtg;snøak;)aøsÞicRtUv)anbgðaj
enAkñúgrUbTI A>5b ehIybMlas;TItamTisQrébnÞúkKW 10θ . BIeKalkarN_rbs; virtual work
kmμnþxageRkA = kmμnþxagkñúg
466 Appendix A

8. NPIC
P(10θ ) = M p (2θ ) + M pθ
¬vaminmankmμnþxagkñúgenARtg; A eT eRBaHvaminmansnøak;)aøsÞic¦
collapse load KW
3M p
Pu =
10
Mechanism sMrab;ElVg AB manlkçN³xusKñabnþic³ RKb;snøak;TaMgbICasnøak;)aøsÞic.
Virtual work xagkñúg nig virtual work xageRkAkñúgkrNIKW
2 Pu (15θ ) = M pθ + M p (2θ ) + M pθ
enaH Pu = 15 M p
2
lT§PaBTIBIrenHRtUvkarbnÞúktUcCag dUcenHvaCa mechanism EdlRtwmRtUv. Collapse load Edlnwg
TTYl)anedayeRbI φb M p CMnYseGay M p
cemøIy³ Pu =
2
15
φb M p = (1040) = 139kips
2
15
467 Appendix A

9. T.Chhay
]TahrN_ A>4³ kMNt; collapse load P sMrab; rigid frame EdlbgðajenAkñúgrUbTI A>6. Ggát;
u
nImYy²rbs;eRKagKW W 21×147 Edlman Fy = 50ksi . snμt; lateral support Cab;.
dMeNaHRsay³ W 21×147 Ca compact shape sMrab; F y = 50ksi nigman lateral support Cab; dUc
enHvabMeBjlkçxNÐkñúgkareRbIR)as; plastic analysis.
dUcbgðajenAkñúgrUbTI A>6 eKman failure mode cMnYnbIsMrab;eRKagenH³ Fñwm mechanism enA
kñúgGgát; BC / sway mechanism nigmYyeTotCabnSMén mechanism BIrdMbUg. eyIgcab;epþImkarviPaK
mechanism nImYy²edaydak; virtual rotation θ enARtg;snøak;mYy ehIysresrsmIkarCaGnuKmn_
eTAnwgmMuenH.
468 Appendix A

10. NPIC
Virtual displacement rbs;Fñwm mechanism RtUv)anbgðajenAkñúgrUbTI A>6 b. BIsmPaBén
kmμnþxageRkA nigkmμnþxagkñúg
⎛5 ⎞ ⎛2 ⎞
Pu (10θ ) = M pθ + M p ⎜ θ ⎟ + M p ⎜ θ ⎟
⎝3 ⎠ ⎝3 ⎠
EdleKeRbI M p CMnYseGay φb M p . edaHRsayrk Pu
Pu = 0.3333M p
RbsinebIeKminKit axial strain enAkñúgGgát; BC / sway mechanism nwgxUcRTg;RTaydUcbgðaj
enAkñúgrUbTI A>6 c CamYynwgbMlas;TItamTisedkdUcKñaRtg; B nig C . Cavi)ak muMrgVilénRKb;snøak;
TaMgGs;KWlkçN³RsedogKña³
Pu (15θ ) = M p (4θ ) b¤ Pu = 0.2667 M p
BIrUbTI A>6d/ eKalkarN_én virtual work sMrab; combined mechanism eGay
⎛5 ⎞ ⎛2 ⎞
Pu (15θ ) + Pu (10θ ) = M pθ + M p ⎜ θ ⎟ + M p ⎜ θ + θ ⎟ + M pθ
⎝3 ⎠ ⎝3 ⎠
Pu = 0.2133M p ¬lub¦
cemøIy³ Collapse load sMrab;eRKagKW Pu = 0.2133φb M p = 0.2133(1400) = 299kips
cMNaMfa vamancMnucdUcKñaxøHrvagviFIénkarviPaKTaMgBIr. eTaHbICa equilibrium method
minRtUvkarBicarNaRKb; mechanism k¾eday k¾vaRtUvkareGayeyIgdwgBI mechanism enAeBlEdlkar
EbgEcgm:Um:g;snμt;RsbeTAnwg mechanism mYy. viFITaMgBIrRtUvkarkarsnμt; failure mechanism b:uEnþ
enAkñúg equilibrium method eKRtUvRtYtBinitükarsnμt;nImYy²sMrab;suvtßiPaB nigkarEbgEckm:Um:g;Edl
GacTTYlyk)anedaysþaTic ehIyvaminRtUvkarkarGegátRKb; mechanism eT.
A >4> karKNnamuxkat; Design
dMeNIrkarénkarKNnaKWRsedogKñanwgkarviPaKEdr EtvaxusKñaRtg;faGBaØtiEdlRtUvrkCalT§
PaBm:Umg;)aøsÞicEdlRtUvkar M p . eKsÁal; collapse load EdlTTYl)anBIkarKuN service load nwgem
KuNbnÞúk.
]TahrN_ A>4³ FñwmCab;bIElVgdUcbgðajenAkñúgrUbTI A>7 RtUvRTnUv gravity service load. bnÞúknI-
mYy²pSMeLIgedaybnÞúkefr 25% nigbnÞúkGefr 75% . eKeRbI cover plate enAkñúgElVg BC nig CD
469 Appendix A

11. T.Chhay
edIm,ITTYl)an moment strength dUcEdl)anbgðaj. snμt; continuous lateral support nigeRCIs
erIsrUbragEdksMrab;RbePT A36 .
dMeNaHRsay³ Collapse load EdlTTYl)anedaykarKuN service load edayemKuNbnÞúksmRsb.
sMrab; service load 45kips
Pu = 1.2(0.25 × 45) + 1.60(0.75 × 45) = 67.5kips
sMrab; service load 75kips
Pu = 1.2(0.25 × 75) + 1.60(0.75 × 75) = 85.5kips
eKRtUvGegát bIEdlman mechanism mYyenAelIElVgmYy. rUbTI A>7 c-e bgðajBI
mechanism
mechanism nImYy²eRkayBIrgnUv virtual displacement. enAeBlEdlsnøak;)aøsÞicekIteLIgenARtg;
470 Appendix A

12. NPIC
TMrEdlGgát;nImYy²minmanersIusþg;esμIKña vanwgekIteLIgenAeBlEdlm:Um:g;Bt;esμInwglT§PaBm:Um:g;)aøsÞic
rbs;Ggát;EdlexSayCag.
sMrab;ElVg AB
kmμnþxageRkA = kmμnþxagkñúg
67.5(5θ ) = M p (2θ + θ ) b¤ M p = 112.5 ft − kips
sMrab;ElVg BC
85.5(10θ ) = M pθ + 2M p (2θ ) + M pθ
5
3
b¤ M p = 128.2 ft − kips
sMrab;ElVg CD
85.5(10θ ) = M p (θ + 2θ + θ )
5
3
b¤ M p = 128.2 ft − kips
Upper-bound theorem RtUv)anbkRsaydUcxageRkam³ tMélénm:Um:g;)aøsÞicEdlRtUvKñanwg mechanism
Edlsnμt;KWtUcCag b¤esμInwgm:Um:g;)aøsÞicsMrab; collapse load. dUcenH mechanism EdlTamTarlT§PaB
m:Um:g;FMCageKCa mechanism EdlRtwmRtUv. Mechanism TaMgBIrcugeRkaymantMél M p dUcKña ehIy
GacnwgekIteLIgkñúgeBldMNalKña. CaTUeTAersIusþg;EdlRtUvkarCa design strength EdlRtUvkar dUc
enH
φb M p = 128.2 ft − kips
BI Load Factor Design Selection Table, rUbragEdlRsalCageKKW W 16 × 31 Edlman design
strength θ b M p = 146 ft − kips
sakl,g W 16 × 31 ehIyRtYtBinitükMlaMgkat; ¬eyagtamrUbTI A>8¦
sMrab;ElVg AB
∑ M B = V A (10 ) − 67.5(5) + 128.2 = 0
V A = 20.93kips
VB = 20.93 − 67.5 = −46.57 kips
sMrab;ElVg BC
⎛5⎞
∑ M B = − M p + 85.5(10) + ⎜ ⎟ M p − VC (20) = 0
⎝3⎠
85.5(10) + (2 / 3)M p 855 + (2 / 3)(128.2)
VC = = = 47.02kips
20 20
VB = 85.5 − 47.02 = 38.48kips
471 Appendix A

13. T.Chhay
sMrab;ElVg CD
∑ M C = − M p + M p + 85.5(10) − VD (20) = 0
5 5
3 3
VD = 42.75kips = VC
dUcenH kMlaMgkat;TTwgGtibrma VC KW)anmkBIElVg BC b¤esμIKña 47.02kips .
BItaragbnÞúkBRgayesμIemKuNenAkñúg Part 4 of the Manual, shear design strength rbs;
W 16 × 31 KW
φvVn = 84.9kips > 47.02kips (OK)
cemøIy³ eRbI W 16 × 31 .
A >5> karsnñidæan Conclusion Remark
karviPaKén mechanism EdlrgbnÞúkBRgaybgðajBIPaBsμúKsμajbEnßmeTotEdlmin)anerob
rab;enATIenH. bBaðaCak;EsþgenAkñúg plastic analysis or design rYmbBa©ÚlnUvkardak;bnÞúkEbbenH
y:agCak;Esþg. elIsBIenH eKKYrGegátGnþrGMeBIénT§iBlrbs;kMlaMgtamG½kS nigm:Um:g;Bt;sMrab;Ggát;
EdlrgTaMgkMlaMgtamG½kS nigm:Um:g;Bt; dUcenA rigid frame enAkñúg]TahrN_ A>4 .
cMeBaHviFIviPaKEdlmanlkçN³TUeTAdUcCa equilibrium method manniyayy:aglMGitenAkñúg
the plastic methods of structural analysis (Neal, 1977). ehIyvamanrUbmnþEdlman
lkçN³sμúKsμajsMrab; mechanism method eTotpg. CamYynwgviFIenH EdleKsÁal;faCa method of
inequalities eKGackMNt; mechanism EdlRtwmRtUveday linear programming technique eday
pÞal;. eKGaceRbI plastic design FmμtasMrab;KNnaeRKOgbgÁúMPaKeRcIn b:uEnþCaTUeTA mechanism
method EdlbgðajenAkñúg]bsm<½n§enHKWRKb;RKan;ehIy.
472 Appendix A