Chapter 2 (Loads On Structures) - Advanced Methods of Structural Analysis

 

8 Afbs  Ptru`turms 8.6 8.8 8.0 8.2 8.= 8.7 8.> 8.? 8.3 8.6<    

Ptru`turfa Pystmjs gkr Rrfdsjcttcdn Akfbs Bmfb Akfbs Acvm Akfbs @afsscgc`ftckd kg Hucabcdns gkr Mdvcrkdjmdtfa Akfbs ^cdb Akfbs Pdkw Akfbs Mfrtoqufem Akfbs Oybrkstftc` fdb Pkca \rmssurms Romrjfa fdb Ktomr Mggm`ts Akfb @kjhcdftckds Pujjfry \rkhamjs

Mfrtoqufem-Bfjfnmb Hucabcdn  Cdts Wcejfdcs/Pouttmrstk`e. Wcejfdcs/Pouttmrstk`e.`kj `kj

Rom khim`tcvm k f stru`turfa mdncdmmr cs tk bmscnd f stru`turm toft wcaa hm fham tk wctostfdb faa tom akfbs tk woc`o ct cs suhim`tmb wocam smrvcdn cts cdtmdbmb purpksm torkunokut cts cdtmdbmb acm spfd. Cd bmscndcdn f stru`turm, fd mdncdmmr just, tomrmkrm, `kdscbmr faa tom akfbs toft `fd rmfacstc`faay hm mxpm`tmb tk f`t kd tom stru`turm burcdn cts pafddmb acm spfd. Rom akfbs toft f`t kd `kjjkd `cvca mdncdmmrcdn stru`turms stru`turms `fd hm nrkupmb f``krbcdn tk tomcr dfturm fdb skur`m cdtk tormm `afssms9 (6) bmfb akfbs bum tk tom wmcnot k tom stru`turfa systmj ctsma fdb fdy ktomr jftmrcfa pmrjfdmdtay fttf`omb tk ct5 (8) acvm akfbs, woc`o frm jkvfham kr jkvcdn akfbs bum tk tom usm k tom stru`turm5 fdb (0) mdvcrkdjmdtfa akfbs, woc`o frm `fusmb hy mdvcrkdjmdtfa mm`ts, su`o fs wcdb, sdkw, fdb mfrtoqufems. Cd fbbctckd tk mstcjftcdn tom jfndctubms k tom bmscnd akfbs, fd mdncdmmr just fask `kdscbmr tom pksschcacty toft skjm k tomsm akfbs jcnot f`t scjuatfdmkusay kd tom stru`turm. Rom stru`turm cs cdfaay bmscndmb sk toft ct wcaa hm fham tk wctostfdb tom jkst udfvkrfham `kjhcdftckd k akfbs toft cs acemay tk k``ur cd cts acmtcjm. Rom jcdcjuj bmscnd akfbs fdb tom akfb `kjhcdftckds kr woc`o tom stru`turms just hm bmscndmb frm usufaay spm`ccmb cd hucabcdn `kbms. Rom dftckdfa `kbms prkvcbcdn nucbfd`m kd akfbs kr hucabcdns, hrcbnms, fdb ktomr stru`turms cd`aubm FP@M Ptfdbfrb Ptfdbfrb Jcdcjuj Bmscnd Akfbs Akfbs fdb Fssk`cftmb @rctmrcf  gkr Hucabcdns   fdb Ktomr Ptru`turms (FP@MyPMC >-67) U8Z,*  FFPORK FFPORK AXGB  Hrcbnm Bmscnd Ppm`cgc`ftckds Ppm`cgc`ftckds U6Z, Jfdufa gkr Xfcawfy Mdncdmmrcdn U8>Z, fdb  Cdtmrdftckdfa Hucabcdn Hucabcdn @kbm U67Z.

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Rom dujhmrs cd hrf`emts rmmr tk ctmjs acstmb cd tom hchacknrfpoy. hchacknrfpoy.

 

@OF\RMX 8 Afbs  Ptru`turms

Fatokuno tom akfb rmqucrmjmdts k jkst ak`fa hucabcdn `kbms frm nmdmrfaay hfsmb kd toksm k tom dftckdfa `kbms acstmb omrmcd, ak`fa `kbms jfy `kdtfcd fbbctckdfa prkvcsckds wfrrfdtmb hy su`o rmnckdfa `kdbctckds fs mfrtoqufems, tkrdfbkms, ourrc`fdms, omfvy sdkw, sdkw, fdb tom acem. Ak`fa hucabcdn `kbms frm usufaay amnfa bk`ujmdts mdf`tmb tk sfmnufrb puhac` wmafrm fdb sfmty, fdb tom mdncdmmr just hm`kjm tokrkunoay fjcacfr wcto tom hucabcdn `kbm kr tom frmf cd woc`o tom stru`turm cs tk hm hucat. Rom akfbs bms`rchmb cd tom `kbms frm usufaay hfsmb kd pfst mxpmrcmd`m fdb stuby fdb frm tom jcdcjuj kr woc`o tom vfrckus typms k stru`turms just hm bmscndmb. Okwmvmr, tom mdncdmmr just bm`cbm c tom stru`turm jcnot hm suh im`tmb tk fdy akfbs cd fbbctckd tk toksm `kdscbmrmb hy tom `kbm fdb, c sk, just bmscnd tom stru`turm tk rmscst tom fbbctckdfa akfbs. Xmjmjhmr toft tom mdncdmmr cs uatcjftmay rmspkdscham kr tom sfm bmscnd k tom stru`turm. Rom khim`tcvm k tocs `ofptmr cs tk bms`rchm tom typms k akfbs `kjjkday md`kudtmrmb cd tom bmscnd k stru`turms fdb tk cdtrkbu`m tom hfsc` `kd`mpts k akfb mstcjftckd. Hmkrm bcs`usscdn tom spm`cc` typms k akfbs, wm hmncd tocs `ofptmr wcto f hrcm bms`rcptckd k tom typc`fa stru`turfa systmjs usmb cd `kjjkd hucabcdns fdb hrcbnms kr trfdsjcttcdn akfbs tk tom nrkudb. Cd tocs crst sm`tckd, wm fask cdtrkbu`m tom `kd`mpts k akfb pfto fdb trchutfry frmf. Dmxt, wm bms`rchm bmfb akfbs fdb tomd bcs`uss acvm akfbs kr hucabcdns fdb hrcbnms, cd`aubcdn tom bydfjc` mm`t, kr tom cjpf`t, k acvm akfbs. ^m bms`rchm mdvcrkdjmdtfa akfbs, cd`aubcdn wcdb akfbs, sdkw akfbs, fdb mfrtoqufem akfbs. ^m ^m ncvm f hrcm bcs`ussckd k oybrkstftc` fdb skca prmssurms fdb tomrjfa mm`ts fdb `kd`aubm wcto f bcs`ussckd fhkut tom `kjhcdftckds k akfbs usmb kr bmscnd purpksms. Rom jftmrcfa prmsmdtmb omrmcd cs jfcday hfsmb kd tom  FP@M Ptfdbfrb    Jcdcjuj Bmscnd Akfbs fdb Fssk`cftmb @rctmrcf gkr Hucabcdns fdb Ktomr Ptru`turms (FP@MyPMC >-67), woc`o cs `kjjkday rmmrrmb tk fs tom  FP@M   fdb cs pmrofps tom jkst wcbmay usmb stfdbfrb cd prf`tc`m. Pcd`m > Ptfdbfrb  fdb tom cdtmdt omrm cs tk fjcacfrczm tom rmfbmr wcto tom nmdmrfa tkpc` k akfbs kd stru`turms, jfdy k tom bmtfcas ofvm dkt hmmd cd`aubmb. Dmmbamss tk sfy, tom `kjpamtm prkvcsckds k tom ak`fa hucabcdn `kbms kr tom FP@M > Ptfdbfrb † just hm kaakwmb cd bmscndcdn stru`turms.

8.6 Ptru`turfa Pystmjs gr Rrfsjtt Afbs Cd jkst `kjjkd hucabcdns, hrcbnms, fdb ktomr `cvca mdncdmmrcdn f`cactcms, twk kr jkrm k tom hfsc` stru`turfa typms bms`rchmb cd Pm`tckd 6.0 (m.n., hmfjs, `kaujds, safhs, trussms, mt`.) frm fssmjhamb tknmtomr tk krj f stru`turfa systmj toft `fd trfdsjct tom fppacmb akfbs tk tom nrkudb torkuno tom kudbftckd. Pu`o stru`turfa systmjs frm fask rmmrrmb tk fs  grfj cdn systmjs  kr  grfj  grfjmwkr mwkres es , fdb tom `kjpkdmdts k su`o fd fssmjhafnm frm `faamb stru`turfa jmjhmrs.

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@kpcms k tocs stfdbfrb jfy hm pur`ofsmb rkj tom Fjmrc`fd Pk`cmty k @cvca Mdncdmmrs, 6? eD

Rocs > eD eDyj  akfb cs udckrjay bcstrchutmb fakdn tom amdnto k tom hmfj, fs sokwd cd Gcn. 8.7(h). Rocs cnurm fask sokws tom rmf`tckds mxmrtmb hy tom suppkrtcdn ncrbmrs ft tom hmfj–s mdbs. Fs tom hmfj cs syjjmtrc`faay akfbmb, tom jfndctubms k tom rmf`tckds frm mqufa tk ofa k tom tktfa akfb f`tcdn kd tom hmfj9  X F

=

XH

=

6 8

(> eDyj)(3 j)

=

06.= 06 .= eD

Rom akfb kd tom cdtmrckr hmfj  MG  cs `kjputmb cd f scjcafr jfddmr. Grkj Gcn. 8.7(h), wm smm toft tom akfb trfdsjcttmb tk mf`o kdm-jmtmr amdnto k tom hmfj  MG  cs (0.= (0 .= eDyj 8 )( )(2 2 j) j)((6 j)

=

62 eD

Rocs akfb f`ts fs f udckrjay bcstrchutmb akfb k jfndctubm 62 eDyj fakdn j  fakdn tom hmfj–s amdnto. Rom rmf`tckds k tom cdtmrckr hmfj frm9  X M

=

XG 

=

6 8

(62 eDyj)(3 j)

=

70 eD eD  

Hm`fusm k tom syjjmtry k tom rfjcdn pafd fdb akfbcdn, tom rmjfcdcdn hmfjs fs tom hmfjs fdb  FH , rmspm`tcvmay.

@B fdb NO  frm   frm

suhim`tmb tk tom sfjm akfbs

 Fds.

Ncrbmrs.  Rom ncrbmr akfbs `fd hm `kdvmdcmdtay khtfcdmb hy fppaycdn tom hmfj rmf`tckds fs `kd`mdtrftmb `kd`mdtrft mb akfbs (cd rmvmrsm bcrm`tckds) ft tomcr `krrmspkdbcdn suppkrt (`kddm`tckd) pkcdts kd tom ncrbmr. Fs sokwd cd Gcn. 8.7(`), scd`m ncrbmr  FN  suppkrts mxtmrckr hmfjs  FH  fdb NO  ft  ft pkcdts  F fdb N , tom rmf`tckds (06.= eD) k eD)  k tom twk mxtmrckr hmfjs frm fppacmb ft tomsm pkcdts. Pcjcafray, tom rmf`tckds k twk cdtmrckr hmfjs (@B fdb  MG ) frm fppacmb ft pkcdts @  fdb  fdb  M , womrm tomsm cdtmrckr hmfjs frm suppkrtmb kd tom ncrbmr. Dktm toft tom suj k tom jfndctubms k faa kur `kd`mdtrftmb akfbs fppacmb tk tom ncrbmr mqufas cts trchutfry frmf (2 (2..= j 0 68 j)  juatcpacmb hy tom akkr akfb cdtmdscty (0.= eDy j8 ), toft cs (smm Gcn. 8.7(`))

06.= 06 .= eD 6 70 eD 6 70 eD 6 06 06.= .= eD = (0 (0.= .= eDy j8 )(2. )(2.= = j) j)((68 j) = 6? 6?3 3 eD `kdtcdumb 

 

Pm`t 8.8 Bmfb Afbs Afbs

Fs sokwd cd Gcn. 8.7(`), tom mdb rmf`tckds k tom ncrbmr frm 6  X F = XN = U8(06 U8(06.= .=)) 6 8( 8(70 70)Z )Z= 32. 32.= = eD 8 Hm`fusm k syjjmtry, tom akfb kd ncrbmr

 Fds.

cs tom sfjm fs kd ncrbmr  FN .

@kaujds.  Fs sokwd cd Gcn. 8.7(b), tom fxcfa akfb kd `kaujd  F cs khtfcdmb hy fppaycdn tom rmf`tckd  X F ( 32 32.= .= eD eD))  k ncrbmr  FN  kd tom `kaujd wcto cts bcrm`tckd rmvmrsmb. Rocs `kaujd fxcfa akfb `fd fask hm mvfauftmb hy juatcpaycdn tom trchutfry frmf (2.= j 0 7 j ) k `kaujd  F hy tom akkr akfb cdtmdscty (0.= eDy j8 ), toft cs (smm Gcn. 8.7(b))  

(0.= (0. = eDyj )(2 )(2.= .= j)( j)(7 7 j)

=

=

32.= 32 .= eD

Hm`fusm k syjjmtry, tom tormm rmjfcdcdn `kaujds frm suhim`tmb tk tom sfjm fxcfa `kjprmsscvm akfb fs `kaujd F.  Fds. Gcdfaay, tom suj k tom fxcfa akfbs `frrcmb hy faa kur `kaujds just hm mqufa tk tom prkbu`t k tom tktfa surf`m frmf k tom akkr tcjms tom akkr akfb cdtmdscty9  

2(32. 2(3 2.= = eD)

=

(0.= (0. = eDyj 8 )(3 j)( j)(68 68 j)

=

0>? 0> ? eD 

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Cd tom krmnkcdn mxfjpam, wm ofvm kday `kdscbmrmb mxtmrdfaay fppacmb akfbcdn hut dmnam`tmb tom sma-wmcnot k tom safh fdb tom ktomr jmjhmrs k tom akkr systmj. Cd tom dmxt sm`tckd, wm bcs`uss tom prk`mburm kr `kjputcdn tom wmcnot k tom stru`turfa systmj ctsma.

8.8 Bmfb Afbs

  RFhAM 8.6

]dcR ^McnORP kG @kdPRX]@Rckd JFRMXcFAP ]dct ^mcnot

Jftmrcfa Faujcduj Hrc`e @kd`rmtm, rmcdkr`mb Ptru`turfa stmma ^kkb

 

eDyj

8=.3 6?.? 80.7 >>.< 7.0

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 Bmfb akfbs frm nrfvcty akfbs k `kdstfdt jfndctubms fdb cxmb pksctckds toft f`t pmrjfdmdtay kd tom stru`turm. Pu`o akfbs `kdscst k tom wmcnots k tom stru`turfa systmj ctsma fdb k faa ktomr jftmrcfa fdb mqucpjmdt pmrjfdmdtay fttf`omb tk tom stru`turfa systmj. Gkr mxfjpam, tom bmfb akfbs kr f hucabcdn stru`turm cd`aubm tom wmcnots k rfjms, rfjcdn fdb hrf`cdn systmjs, akkrs, rkks, `mcacdns, wfaas, stfcrwfys, omftcdn fdb fcr-`kdbctckdcdn systmjs, paujhcdn, mam`trc`fa systmjs, fdb sk krto. Rom wmcnot k tom stru`turm cs dkt edkwd cd fbvfd`m k bmscnd fdb cs usu-

faay fssujmb hfsmb kdbmtmrjcdmb, pfst mxpmrcmd`m. Ftmrwmcnot Ftmr tom stru`turm ofs hmmd fdfayzmb fdb tom jmjhmr sczms tom f`tufa cs `kjputmb hy uscdn tom jmjhmr sczms fdb tom udct wmcnots k jftmrcfas. Rom f`tufa wmcnot cs tomd `kjpfrmb tk tom fssujmb wmcnot, fdb tom bmscnd cs rmvcsmb c dm`mssfry. Rom udct wmcnots k skjm `kjjkd `kdstru`tckd jftmrcfas frm ncvmd cd Rfham 8.6. Rom wmcnots k pmrjfdmdt smrvc`m mqucpjmdt, su`o fs omftcdn fdb fcr-`kdbctckdcdn systmjs, frm usufaay khtfcdmb rkj tom jfduf`turmr.

Mfjpam 8.8 Rom akkr systmj k f hucabcdn `kdscsts k f 68= jj toc`e rmcdkr`mb `kd`rmtm safh rmstcdn kd kur stmma akkr hmfjs, woc`o cd turd frm suppkrtmb hy twk stmma ncrbmrs, fs sokwd cd Gcn. 8.>(f). Rom `rkss-sm`tckdfa frmfs k tom akkr hmfjs fdb tom ncrbmrs frm 3,=