Design of RC Members Under Flexure

 

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V^BJGGIAL@Z B

YMG

CKG^AJCL JBLJ^GYG A L Z Y A Y W Y G

HBW^LCE bo tmg

CK G^ A J CL J BLJ ^ GYG

ALZYAYWYG

0966 ZGJBLI N B W EG _ C ^ I

I G Y^ B A Y

K A JM A @ C L

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K C ^ JM - C V ^ A E 31:0

Igsa`l b o ^galobrjgi Jbljrgtg Kgkngrs Wligr Oegxurg b r

Jbknalgi Oegxurg cli Iargjt Jbkprgssabl N Q JMC^EGZ s

PMAYLGQt

KGKNG^ CKG^AJCL JBLJ^GYG A L Z Y A Y W Y G

as tmg purpbsg bo tmas pcpgr tb su``gst c jbkpegtg rgvasabl bo tmg kgtmbi bo igsa`lal` rgalobrjgi jbljrgtg kgkngrs sunhgjtgi tb nglial` cli tb prgsglt c rctablce kgtmbi obr tmg prbpbrtablal` bo crjm rans, rgjtcl`uecr jbeukls uligr gjjgltraj ebci, cli rgjtcl`uecr ngcks. Ymas kgtmbi kcy ng gxtgligi tb jbvgr tmg igsa`l bo Y ngcks, rbuli jbeukls cli cly btmgr obrk bo jbljrgtg kgkngrs. Zakpeg obrkuecs crg `avgl wmajm prgiajt tmg uetakctg strgl`tm watm rgkcrdcneg cjjurcjy ncsgi bl tmg jyealigr strgl`tm bo tmg jbljrgtg cli tmg yagei pbalt bo tmg stgge aligpgliglt bo tmg rctab bo tmgar kbiuea bo gecstajaty. t as ngeagvgi tmct tmgsg gquctabls waee `rgctey sakpeaoy tmg wbrd bo tmg igsa`lgr cli rgsuet al tmg kbrg gooajaglt cli gjblbkajce usg bo rgalobrjgi jbljrgtg. Ymg su``gstabls crg altgligi tb pecjg strujturce jbljrgtg igsa`l bl c sbeai prcjtajce obulictabl wmajm as lbw hustaoagi ny tmg civcljg al jblstrujtabl prcjtajgs, tmg cvcaecnaeaty bo ngttgr kctgraces, cli tmg alobrkctabl `calgi ny c `rgct ckbult bo rgsgcrjm wbrd. Ymg prgsglt kgtmbi bo igsa`lal` kgkngrs uligr nglial` cli jbknalgi nglial` cli iargjt strgss as ulsctasocjtbry obr sgvgrce rgcsbls. Ymg usuce obrkuecs ncsgi bl cssukptabl bo c jrcjdgi sgjtabl sgjtabl cli strca`mt ealg vcractabl bo strgss crg ocr orbk jbrrgjt nbtm uligr wbrdal` ebcis wmgl tmg jbljrgtg as lbt kctgraceey jrcjdgi cli uligr uetakctg ebcis wmgl tmg strgss al tmg jbljrgtg as lbt gvgl cpprbxakctgey prbpbrtablce t b tmg iastcljg orbk tmg lgutrce cxas. Ymgy t

Ogn. 33, 31:0. tmg Alstatutg ^gjgavgi nyGl`alggr tJblsuetal` Kaewcudgg.

9=:)

 

9=9

Kcr.-Cpr. 31:0

HbW^LCE BO YMG CKG^AJCL J b L J ^ G Y G ALZYAYWYG

ib lbt `avg c `bbi aliajctabl bo tmg jbliatabls uligr wbrdal` ebcis cli jcllbt ng usgi tb prgiajt tmg uetakctg strgl`tm watm cly ig`rgg bo cjjurcjy. Ymgy ib lbt prbpgrey rgjb`lazg tmg strgl`tm bo tmg jbljrgtg al jbkprgssabl cli prbvaig c kujm ma`mgr ocjtbr bo scogty c`calst ocaeurg bo tmg jbljrgtg tmcl bo tmg stgge. 5>  ?< Ymct kcy mcvg nggl hustaoagi iural` tmg gcrey icys bo rgalobrjgi jbljrgtg bl tmg `rbulis bo ulrgeacnaeaty nut at as jgrtcaley lbt hustaoa hustaoagi gi tbicy . Vrbpgr ey ncecljgi igsa`l waee pgrkat tmg usg bo c jblsaigrcney ma`mgr pgrjglt c`g bo tglsaeg stgge watm c jblsgquglt rgiujtabl al tmg sazg cli wga`mt bo kgkngrs. Ymg usuce oegxurg obrkuecs crg jbkpeajctgi ny tmg usg bo tmg vceug bo l wmajm as quatg ulprgiajtcneg uligr ma`m ebcis cli cjtuceey mcs eatteg googjt bl tmg uetakctg strgl`tm bo tmg ngck. > 1 36 Ymg googjtavg vceug bo l as waigey iaoogrglt obr igci cli eavg ebcis. A l tmg jcsg bo crjm rans tmg igci cli eavg ebci strgssgs jcllbt ng  

 

<

l

cli ciigi tb`gtmgr jbkputgi sgpcrctgey watm iaoogrglt vceugs bo ngjcusg igci ebci kcy prbiuj prbiujgg jbkprgssabl bley wmaeg wmaeg tmg eavg ebci kbkglt ceblg wbuei rgquarg cssukptabl bo c jrcjdgi sgjtabl. Ymg jcejuectabl al tmas jcsg wbuei ng vgry jbkpeajctgi watm twb vceugs bo l Ymg prgsglt kgtmbi kcdgs lb prgiajtabl bo tmg ebcial` wmajm waee jcusg jrcjdal` cli ibgs lbt `avg cjjurctg jbltrbe bvgr tmg ocjtbrs bo scogty uligr igci ebcis cli eavg ebcis. Ymg kgtmbi mgrg prbpbsgi obr tmg igsa`l bo kgkngrs uligr ngli al` cli iargjt strgss pcrtajue crey ob obrr crjmgs crjmgs as iargjt cli sakpeg. Oarst cl clceysas bo tglsaeg strgss al tmg crjm ran smbuei ng kcig cssukal` tmg jratajce jbknalctabl bo eavg cli igci ebcis tb`gtmgr watm tgkpgrcturg smraldc`g cli pecstaj oebw ebw googjts. googjts. Ymas jcl ngst ng iblg ny usal` tmg jbkpegtg trclsobrkgi sgjtabl watmbut jrcjds. Ymg googjtavg vceugs bo l obr igci cli eavg ebcis jcl ng prgiajtgi

watm suooajaglt cjjurcjy obr tmas purpbsg c t ceebwcneg wbrdal` strgssgs cli tmg igci cli eavg ebci strgssgs obr jbrrgspblial` vceug= bo l jcl ng jbkputgi sgpcrctgey cli ciigi tb`gtmgr. Ymg tglsaeg strgss al tmg jbljrgtg sb igtgrkalgi smbuei lbt gxjggi tmg kbiueus bo rupturg bo tmg jbljrgtg al cl ulrgalobrjgi ngck al brigr tmct tmg crjm ran smcee lbt ng jrcjdgi al sgrvajg. Ymg jbkprgssavg strgss obr tmas jbliatabl as rgectavgey ulakpbrtclt ngjcusg tmg strgl`tm bo tmg ran waee ng jbltrbeegi ny cl uetakctg strgl`tm jcejuectabl. A l crjm rans wmbsg jgltgr ealgs obeebw tmg igci ebci prgssurg ealgs tmg tglsaeg strgss jcl gcsaey ng dgpt sbkgwmct ngebw tmg kbiueus A l tmg ra`ai orckg typg bo crjm at kcy ng pbssaneg tb bo rupturg.

 

^galobrjgi ^galo brjgi

bljrgt bljrgtgg Kgkngrs Wligr Oegxurg

9=7

pgrkat tmg tglsaeg strgss obr tmg gxtrgkg jcsg tb sea`mtey gxjggi tmg >=-icy kbiueus bo rupturg watmbut altrbiujal` bnhgjtablcneg jrcjd

al`4 br ao tmg jratajce jbknalctabl bo ebcis aljeuigs bley c pbrtabl bo tmg ouee eavg ebci, tmg jcejuectgi tglsaeg strgss jcl prbncney ng dgpt ngebw tmg kbiueus bo rupturg watmbut iaooajuety. Ymas kgtmbi bo igsa`l wbuei mcvg tmg civcltc`g bo iargjtal` cttgltabl tb tmg tglsaeg strgssgs cli wbuei gljburc`g tmg usg bo jbljrgtg watm ma`mgr tglsaeg strgl`tm. Ymas jcejuectabl usal` tmg ouee strgl`tm bo tmg uljrcjdgi sgjtabl

ka`mt rg uet al tmg usg bo tbb eatteg rgalobrjal` stgge cli prbvaig c l alcigquctg ocjtbr bo scogty ulegss cl ciiatablce jcejuectabl as kcig bo tmg uetakctg strgl`tm bo tmg ran. Ngjcusg bo tmg ecr`g strcals

bjjurral` ngobrg ocaeurg, tmg googjts bo tgkpgrcturg jmcl`g, smrald c`g, cli pecstaj oebw mcvg lb prcjtajce googjt bl tmg uetakctg t as tmgrgobrg prbpbsgi tmct tmgsg googjts ng lg` strgl`tm. t c 9e egjtgi cli tmct tmg uetakctg strgl`tm bo tmg kgkngr ng jbkputgi ny c lgw typg bo obrkuec ncsgi bl tmg uetakctg strgl`tm bo tmg jbl jrgtg, cli bl tmg yagei pbalt strgl`tm bo tmg stgge. t mcs nggl pbaltgi but rgjgltey n y sgvgrce a l v g s t a ` t b r s e 5 ~ e t b )

tm c t wmaeg tmg strgss vcractabl al tmg jbljrgtg as cpprbxakctgey ealgcr uligr vgry ea`mt ebcis, cli pcrcnbeaj uligr altgrkgiactg ebcis, cs tmg uetakctg ebci as cpprbcjmgi at cssukgs c smcpg cnbut cs smbwl

al Oa`.

3

Ymg strgss aljrgcsgs vgry rcpaiey lgcr tmg lgutrce cxas cli as lgcrey

ulaobrk obr tmg `rgctgr pcrt bo tmg igptm bo tmg jbkprgssabl sgjtabl, prbncney igjrgcsal` sea`mtey tbwcri tmg gi`g bo tmg ngck. Zcea`gr5 36 < rgpbrts tmg uetakctg strcal al tmg jbljrgtg c t tmg butgr gi`g bo tmg ngck tb ng orbk .66: tb .660 wmaeg tmg eakat rgcjmgi n y jbljrgtg prasks c t ocaeurg wcs .66> tb .669. Ymg usuce pcrcnbeaj obrkuecs mcvg nggl ncsgi bl tmg tmgbry tm c t tmg strgss vcractabl al tmg ngck

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OA@ 3 - Z Y ^ G Z Z - Z Y ^ C A L JW^_G OB^ V ^AZ K CLI OB^ NG C K CY WEYAKCYG EBCI

 

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HBW^L

E B O YMG

K G ^ A J L J B L J ^ G Y G ALZYAYWYG

Kcr.-Cpr. 31:0

obeebwgi tmg smcpg bo tmg oarst pcrt bo tmg strgss-strcal jurvg obr tmg jbljrgtg jyealigr up tb tmg pbalt bo kcxakuk ebci. Ymas as gvaig ltey jblsaigrcney al grrbr ngjcusg bo tmg `rgctgr uetakctg strcals cli tmg iaoogrglt ngmcvabr bo tmg jbljrgtg al tmg ngck. Bl tmas cjjbult, tmg wratgr qugstabls tmg vceug bo cly rgoalgkglts bo ngck tmgbry ncsgi bl cl cttgkpt tb gstakctg tmg uetakctg strgssgs al c ngck ny jbkpcrasbl watm tmg strgss-strcal jurvg obr tmg jyealigr br btmgr stclicris. A t as tmgrgobrg prbpbsgi tmct c rgjtcl`uecr nebjd bo ulaobrk strgss cs aliajctgi ny tmg ibttgi ealgs bl Oa`. 3 ng usgi tb rgprgsglt wmct gvgr strgss kcy gxast al tmg jbljrgtg. Pmctgvgr a t cjtuceey as, a t kust mcvg cl cvgrc`g altglsaty, oj cli cl googjtavg igptm, c. Ymg rgsuetclt as cssukgi c t tmg kaiieg bo tmg rgjtcl`eg. Wligr uetakctg ebci, Mbbdg s Ecw cli tmg tmgbry bo gecstajaty mcvg lb sa`laoajcljg cs ocr cs tmg altgrlce strgssgs crg jbljgrlgi. Ymg kctgraces crg kbrg lgcrey al c pecstaj stctg nut tmg akpgrogjt cli vcracneg cjtabl bo tb tmg tmgbry bo pecstajaty jbljrgtg kcdgsLbc ourtmgr ra`ai sbeutabl cjjbrial` akprcjtajce. tmgbrgtajce hustaoajctabl bo tmg cssukptabl c rgjtcl`uecr jbkprgssavg strgss nebjd as lgjgsscry ao tmg obrkuecs igravgi tmgrgorbk cjjurctgey prgiajt tmg uetakctg strgl`tm bo tmg kgkngr. Ymas tmgy cppgcr t b ib. Ymas cssukptabl bo ulaobrk jbkprgssavg strgss bl tmg jbljrgtg al c ngck mcs nggl su``gstgi ny @gncugr cli ny Jbpgg nut tmgar obrkuecs ib lbt cppgcr gltargey sctasocjtbry ngjcusg bo tmgar btmgr cssukptabls. Zaljg tmg igvgebpkglt bo tmg obeebwal` trgctkglt iasjussabls ls ny tmg wratgr, vbl Gkpgr`k°5 1e cli Zcea`gr HB)4 al gxjgeeglt iasjussab bo tmas sunhgjt mcvg rgjbkkgligi tmg usg bo sakpeaoagi uetakctg Ymgar obrkuecs crg strgl`tm obrkuecs obr ngcks aligpgliglt bo l

sbkgwmct egss sakpeg cli ib lbt cppgcr tb jmgjd tmg rgsuets bo Ckgr ajcl ngck tgsts quatg cs wgee cs tmbsg prgsgltgi mgrgal. ZAKVEG OEG]W^G

Ymg cssukgi rgectabls obr c rgjtcl`uecr ngck uligr sakpeg oegxurg

crg smbwl al Oa`. >. A t as cssukgi tmct al cl uligr-rgalobrjgi ngck, tmct as, blg wmajm waee ocae al tmg tglsaeg stgge, tmg jbljrgtg waee jrcjd cs tmg stgge strgtjmgs cli tmg igptm bo tmg ngck al jbkprgssabl c waee ng rgiujgi ultae tmg jbljrgtg ulat strgss rgcjmgs tmg uetakctg br c

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Co

no al wmajm, C

on o

Gq. ( ) ;

crgc bo tglsaeg stgge

;

pbalt strgss al stgge ; yagei waitm bo ngck ;

uetakctg strgl`tm bo jbljrgtg

 

9=0

^galobrjgi Jbljrgtg Kgkngrs Wligr Oegxurg

Orb. > Ymas igtgrkalgs tmg egvgr crk bo tmg stgge rgalobrjgkglt saljg c

j ;

>

waee ng cssukgi tmct tmg uetakctg jbkprgssavg strgl`tm bo tmg jbljrgtg al tmg ngck as gquce tb =7 pgr jglt bo tmg jyealigr strgl`tm At

al brigr tb ng jblsastglt watm tmg rgsuets bo tgsts bl jbljgltrajceey ebcigi jbeukls cli tb mcvg c trgctkglt wmajm jcl ng cppeagi t b tmg ouee rcl`g bo jcsgs orbk sakpeg oegxurg tb iargjt ebci. Ymg vceugs bo c cli j crg igravgi cs obeebws obr cly pcrtajuecr nglial` kbkglt8 i-

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orbk wmajm c ;

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Ymgsg gxprgssabls crg aligpgliglt bo tmg crgc bo stgge cli tmg vceug bo G • . Gj Ymg rgquargi stgge crgc as sakpey, C,; -

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Zaljg tmg cssukgi jbkprgssavg strgss iastranutabl mcs lb gxcjt tmgbrgtajce ncsas, tmg eakatal` vceug bo tmg igptm bo jbkprgssabl c obr gquce jbljrgtgA ocli stgge strgl`tms al oegxurg kust ng igtgrkalgi gxpgrakgltceey. tmg ngck mcs c t egcst suooajaglt stgge tb oueey

 

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YGZYZ ^GVB^YGI NQ ZECYG^ CLI EQZG

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=3=,666

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Kcxakuk Kbkglt al ens.)

_ceug bo orbk Gq

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6

Cjtuce Kcxakuk Kbkglt Iavaigi ny Kcxakuk Kbkglt cs avgl ny

cxakuk

i

Kukglt

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orbk Gq

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:1?,666

3.76=*

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3.76*

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=33,666

3.660

3.73

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8 88

b.737

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6.10:

3. 76

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=

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6.779

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3.63:

3. 79

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6.9=3

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3.??6.666

6.177

3.9?

6.17

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3.76

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3,>96,666

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6. 77:

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3

79:,bbb

7.:?

6.?06*

0.1

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>166

A

:36,666

9.30

6.06=*

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.67?

3

36

9 .3

=.6

~ 6 : 6

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:=36

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A

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A 3.9:6.666 >.>76.666

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3,>>6,666

A

3.637

3.7?

3.6:

90=,666

3.3:7*

3.??*

3.3:*

>??,666

3.3??*

3.?1*

3.39*

3.9=

3.66

3.77

3.6:

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6.77>

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3.63?

301,666

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6.70?

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303,666

3.69?

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Cvgrc`g

A

3 . 6 6 ; . 6 > 9 3 3 . 7 3 ; . 6 > = / 3 . 6 6 ; .6>9

*Ymgsg vceugs lbt aljeuigi al cvgrc`g.

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^galobrjgi Jbljrgtg Kgkngrs Wligr Oegxurg

9=1

igvgebp tmg strgl`tm bo tmg jbljrgtg, ciiatablce stgge ibgs lbt kctg raceey aljrgcsg tmg strgl`tm bo tmg ngck. Ymg eakatal` vceug bo c cs jbkputgi orbk tgsts rgpbrtgi ny Zectgr cli Eysg5 >e as `avgl al Ycneg 3. Ymg vceug b o o cssukgi al Gq. :) as =7 pgr jglt bo tmg jbrrgspblial` jyealigr strgl`tm bo, o ; 6 =7 oj .

Geakalctal` obur `rbups bo tgsts wmajm cppgcr tb ng grrctaj, tmg

cvgrc`g vceug boRR RR as 6.7:0. 6.7:0. i

Ymas as ali gpg lig lt bo p i, cli o,.

Ymg oegxurce strgl`tm bo c oueey rgalobrjgi rgjtcl`uecr ngck watm tglsaeg stgge bley as tmgl, orbk Gq. >).

K

br

K

i•

i 6.>?=7 i) 6.7:0 i n h 6.:1: n i > o

; 6.:1: h ;

+° '

Gq. ?)

al wmajm o as =7 pgr jglt bo tmg jbkprgssavg strgl`tm bo stclicri jyealigrs, h / Jbeukl 3 bo Ycneg 3 `avgs tmg kcxakuk kbkglt obr tmg tgst ngcks cs prgiajtgi ny Gq. ?). t kcy ng lbtgi tmct tmg pgrjgltc`g bo grrbr as prcjtajceey tmg sckg obr Gq. ?) cs obr tmg pcrc nbeaj obrkuec `avgl ny Zectgr cli Eysg usal` tmg kgcsurgi vceug bo l K

Oa`. : smbws tmg vceug bo

ni >h /

`avgl ny tmg :? ngcks tgstgi

ny Zectgr cli Eysg cli ny :: ngcks tgstgi ny Mukpmrgy533 e wmajm mci jyealigr strgl`tms ngtwggl 3666 cli >766 p.s.a. Ymg Mukpmrgy ngcks watm ma`mgr strgl`tm jbljrgtg wgrg lbt aljeuigi ngjcusg a t cppgcrs tmct tmgrg wcs lbt suooajaglt rgalobrjgkglt t b oueey igvgebp sujm ma`mgr jbljrgtg strgl`tm gvgl tmbu`m tmgy kcy mcvg nggl rg pbrtgi pbr tgi cs jbkprgssabl ocaeurgs. Zbkg jblousabl lb ibunt gxasts ngjcusg a t as iaooajuet tb iaoogrgltactg ngtwggl prakcry stgge br jbl jrgtg ocaeurg ulegss tmg ckbult bo stgge as jblsaigrcney ngebw tmg

jratajce pgrjgltc`g rgquargi tb igvgebp tmg ouee ouee jbljrgtg str gl`t m. C sea`mt strgtjmal` bo tmg stgge kcy rgiujg tmg jbljrgtg jbkprgssabl crgc cli jcusg wmct ebbds eadg c jbljrgtg ocaeurg al cl uligr-rgal obrjgi ngck. Ymg vceug bo

~

smbwl ny Oa`. : as ulcoogjtgi ny tmg jbljrgtg

ni >h

strgl`tm ngtwggl :666 cli ?666 p.s.a. cetmbu`m a t rasgs cnbut 76 pgr jglt obr wgcdgr jbljrgtgs orbk :666 tb 3666 p.s.a. Patm tmg prgsglt kgtmbis cli kctgraces, a t as lbt prbncneg tmct kujm strujturce jbl-

 

916

Kcr.-Cpr. 31:0

HBW^LCE BO YMG CKG^AJCL JBLJ^GYG ALZYAYWYG

6.0

e t 3 @t4.b Z u vg8 (.6 bj. C .j . A. A ~ X p 6.?

Yttsos

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Ac g r blg E5 s g g As (.C ur3. b / ~ j .A. .1:6 pt. 76) 766 br :666 p.s.a., cli ao at as usgi, c `rgctgr ocjtbr bo scogty as lbt alcpprbpractg. Ymgrgobrg a t cppgcrs tmct c vceug bo 6.::: obr

K

ni > j

3

jcl ng usgi `glgrceey.

Obr ngcks watm egss stgge tmcl rgquargi tb igvgebp tmg ouee jbk prgssavg strgl`tm tmg ceebwcneg nglial` kbkglt as `avgl n y tmg

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(0)

Ymg jratajce pgrjgltc`g bo stgge rgquargi tb igvgebp tmg ouee jbkprgssavg strgl`tm bo tmg jbljrgtg as8

h/ ° . . . . . . . . . . . . . . . . . . . Gq (=) o Ycneg > smbws tmg rgsuets bo tmg cppeajctabl bo Gq. 7) tb 0> ngcks bo tmg sgrags tgstgi ny Mukpmrgy5•< gxjgpt ngcks 9=1-916-913 wmgrg Gq. ?) jbltrbes bl cjjbult bo tmg ebw strgl`tm jbljrgtg. Ymg cvgrc`g p. ; 6.97?

 

8

^galobrjgi Jbljrgtg Kgkngrs Wligr Oegxurg

913

rctab bo cjtuce kcxakuk kbkglt tb tmct `avgl ny tmg obrkuecs as 3.603 t b 3 cli, geakalctal` tmg ebw strgl`tm jaligr jbljrgtg ngcks, tmg rctab as 36?.>9 tb 3. Jecssaoagi cjjbrial` tb c`g, tmg rctab as 3.67> tb 3 c t 9 wggds cli 3.61 tb 3 c t 7> wggds. Cjjbrial` tb pgrjgltc`g bo stgge, at as 333.0 obr p ; 6.6691, 367.99 obr p ; 6.661=, cli 369.6> obr p 6.631?. Ymgrg cppgcrs tb ng lb jbrrgectabl ngtwggl kbiueus bo gecstajaty bo tmg jbljrgtg cli tmg cjjurcjy bo tmg obrkuec. Ymg vceug bo tmg stgge egvgr crk, RjR orbk Gq. 9) as `avgl al Ycn Ycneg eg >

i

obr jbkpcrasbl watm tmg stclicri vceug, h Ymg vceug `avgl ny Gq. 9) as `rgctgr cli cppgcrs tb ng kbrg sctasocjtbry tmcl h ny tmg usuce

kgtmbi. 7) ?) cli 0) cppgcr tb jmgjd tmg rgsuets bo wgee jbl trbeegi tgsts watmal tmg eakats bo tmg vcracnaeaty bo tmg kctgraces. Ymgy cppgcr tb ng cs cjjurctg cs cly trgctkglt wmajm jcl ng ig vasgi orbk alobrkctabl cvcaecneg cetmbu`m kbrg jbkpegtg tgsts kcy kcdg pbssaneg c sea`mt akprbvgkglt al tmg gkparajce jblstclt. Gquctabls

Ymg googjt bo tmgsg obrkuecs as smbwl al Oa`. 9 ncsgi bl :666 p.s.a. jbljrgtg jyealigr strgl`tm cli 76,666 p.s.a. stgge yagei pbalt watm c ocjtbr bo scogty bo >048e obr nbtm jbljrgtg cli stgge.. Ymg ceebwcneg

vceug bo K

as pebttgi c`calst tmg pgrjgltc`g bo stgge cli jbkpcrgi

watm tmg vceug ny tmg usuce obrkuec watm o ; 3>66 p.s.a., h ; >6,666 p.s.a. cli l ; 36. Ymg lgw obrkuecs rcasg tmg jratajce pgrjgltc`g bo stgge orbk 6.633: tb 6.6>0: cli tmg ceebwcneg

K

>

orbk 310.7 tb

966. Obr uligr-rgalobrjgi ngcks, tmgy `avg c ma`mgr vceug bo tmg stgge egvgr crk cli c jebsgr cpprbxakctabl tb tmg trug stgge strgssgs. kcy ng lbtgi tmct tmg sckg kgtmbi jcl ng cppeagi tb Y ngcks ao at as igtgrkalgi orbk tgsts wmct tmg eakatal` googjtavg prbpbrtabls smbuei ng. Ymg wratgr mcs lbt cs ygt kcig cly gxckalctabl bo tgst t

ictc nut tmgrg crg prbncney glbu`m bl rgjbri tb aliajctg mbw waigey tmg ulaobrk jbkprgssavg strgss al tmg jbljrgtg jcl ng cssukgi tb

ng iastranutgi.

NG C KZ ^GAL O B ^JGI OB ^ JB KV^G ZZA B L

tmgrg as stgge al tmg jbkprgssabl saig bo tmg ngck cs al tmg jcsg bo c sykkgtrajceey rgalobrjgi crjm ran, tmg jbkprgssabl stgge waee ng strgssgi up tb ats gecstaj eakat a tmg ngck ocaes al jbkprgssabl. o a t ocaes al tmg tglsaeg stgge, tmg prgsgljg bo tmg jbkprgssavg stgge wa waee ee mcvg jbkpcrctavgey eatteg googjt bl ats uetakctg strgl`tm A l tmg ecttgr o

 

YCNEG >----jBKVC^AZBL BO JCEJWECYGI CLI CJYWCE WEYAKCYG ZY^GL@YM BO NGCKZ

YGZYGI NQ MWKVM^GQ CLI EBZZG

Ztgge

Jbljrgtg

Ngck Lukngrs

C``rg`ctg

C`g wggds

3?>-3?:-3?9 3=?-3=0-3== >:0->:=->:1 303-30>-30: 317-31?-310

rclatg

7>

7>

>:9->:7-->:?

>77-->7?->70 >0:-->09->07

:>3-:>>-:>: >9?->90->9=

9 9 9 7>

akgstblg

9 9 9 7>

Jyealigr Ztrgl`tm (ens. pgr sq. al.)

:>93

>=60 :37=

77=1 76=? 9170

>6=0

>?66 >0>7 96?1

C

(sq. al.) .:1: .0=7 3.703 .:1:

. 0=7

3.703

.:1: .0=7 3.703 .:1:

Qagei

(al.) 36 36

1)9

36

36

1)9

36 36

1)9

36

p

Vbalt (ens. pgr

.91 .1 = 3.1? .91 .1= 3.1?

9>,916 9:,69: 93,=70 9>,70: 9>,:>6 93,=00

.91 .1= 3.1? .91

93,?7: 96,010 :=,6:0 93,66:

'-5 6

Kcx. Kbkglt Cjtuce al.ens.)

j

-

Kcx. Kbkglt Jcejuectgi

O r b k G q (7) al.ens.)

sq. al.)

300,666

:>3,666 91>,666 31:,?66 :96,666 79:,666

3?9,666

>13,666 903,666

3=:,666

.1?>3 .1337 .=:76 .10= .17> .=17 .19>7 .1617 .=37 .106=

3?6,766

Kcxakuk

KIkglt Cjtuce Iavaigi ny Jcejuectgi

760,666 3?:,766 :31,666

3.36: 3.69: .106 3.3=: 3.6??

797,666 379,666 >=1,666 973,666 370,666

.11? 3.6?9 3.66? 3.699 3.3?7

:60,766

< t5

6

e

3.3

3.3

88e

z8

6 6

7>

>=>->=:-->=9 ::S--::3-::> :::-::9-::7 :70-:7=-:71

7>

@rcvge

967--96?-960

:9>-:9:-:99 :??-:?0-:?= 939-937-93? 930-93=-931 993-99>-99: 9=1-916-913 9>?-9>0-9>= 976-973-97> 91=-911-766

9 9 9 7>

7> 7>

9

Jaligrs

9

9

7> 7> 7>

9:?6 9>:6

. 0=7 3.703

:993

.:1:

::0? 73=? 7>9> 79?0

3.703 .:1:

93,93: :0,?0:

36

.91 .1= 3.1? .91 .1= 3.1?

9:,990 9>,?66 :=,?:: 99,396 96,360 :=,?9:

.91

:0,:70 93,306 :0,==0 :=,:9: 93,36: :=,690

36

1)9

36 36

. 0=7

3.703

3?>1 3777 3?9: >199 >?31 >0?:

.1= 3.1?

1)9

. 0=7

:996

36

1)9

36

.:1:

. 0=7

. 1=

36 1)9

3.703 .:1: .0=7 3.703

3.1? .91 .1= 3.1?

36 36

1)9

:30,666 7:>,666

.1973 .=16

9=0,666

:60,666

3.6:: 3.61>

3?1,666

.1?:7 .1>=7 .=70 .1079 .1771 .13>6

3?9,666 :36,666 9=>,666 3?1,666 :66,666 73>,666

3.6:6 3.6:7 3.697 3.6>> 3.3=? 3. 6- 6

.1::0 .=907

3:=,666 >0:,666 :0?,666* 397,666 >1:,666 97=,666

3.3=> 3.6:6 3.603 3.3== 3.699 3.6?9

:>3,666

769,666 30:,666 :7?,666 7::,666 3?:,>66

>=3,666 96:,666

. 0:37

30>,?66 :6?,666

.1?>9 .1616 .=>0

9==,666

Cvgrc`g

*Igtgrkalgi ny Jbljrgtg Ztrgl`tm, Gq. (?)

3. 603 ; 67

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jcsg, tmg jbkprgssavg stgge jcl staee ng oa`e rgi c t ats gecstaj eakat ao a t jbkgs watmal tmg jbkprgssabl zblg cli tmg egvgr crk bo tmg tglsaeg stgge jcl ng jbkputgi bl tmct ncsas. Patm jbkprgssavg stgge, tmg uetakctg strgl`tm al jbkprgssabl as jbkputgi ny ciial` tmg kbkglt bo tmg stgge jbkprgssavg strgss t b tmct bo tmg jbljrg jbljrgtg tg strgss jbkputgi ngobrg. ngobrg. Yma s jbliatabl as as smbwl al Oa`.

7

OA@. 7

Ymg uetakctg jbkprgssavg kbkglt waee ng K,

;

6.::: ni >oj'

Gq. (1)

i' C , o ,

Ymg uetakctg tglsaeg kbkglt waee ng K, ; C.h,

jcno,

cno

+ i C ,o, ; + C ,o,

]

Gq. (36)

C,o,

 

919

H b W ^ L C E BO YMG CKG^AJCL J b L J ^ G Y G A L Z Y A Y W Y G

Kcr.-Cpr. 31:0

al wmajm tmg vceug bo j as bntcalgi orbk Gquctabl

9)

usal`

K - i C h.) al pecjg bo K , cli x as tmg iastcljg orbk tmg jgltgr bo tglsaeg stgge tb tmg jgltgr bo `rcvaty bo tmg jbkprgssavg strgssgs al tmg ngck. Ce Cesb sb lbtg lbt g tmct oj ; 6.=7o jb Gquctabls 1) cli 36) mcvg cesb nggl jmgjdgi c`calst tgsts watm sctasocjtbry rgsuets prbvaigi tmg ocaeurg as lbt tmrbu`m smgcr br nbli. Ymg rgsuets bo tgsts bo ngcks watm jbkprgssavg stgge kcig ny Ncjm cli @rco c t Ztutt`crt cli rgpbrtgi ny vbl Gkpgr`gr 5 • pc`g >>7 <

crg bo altgrgst ngjcusg tmgy smbw tmg icl`gr bo nbli ocaeur ocaeurg. g. Ymg ouee yagei pbalt strgss bo :7666 p.s.a. wcs igvgebpgi al >6 kk. rbuli ncrs nut tmg ngcks watm ncrs bo stgge watm c ?6,666 en. yagei pbalt ocaegi al nbli ngobrg tmg ouee strgl`tm wcs igvgebpgi. igvgeb pgi. @eclva @eclvaeeg5 eeg53> < civasgs c`calst jbultal` bl tmg jbkprgssabl rgalobrjgkglt nut mas tgsts wgrg kcig bl vgry skcee ngcks wmajm gvaigltey ocaegi al smgcr ngobrg tmg ouee kbkglt wcs igvgebpgi. Mg scys, A l tmg sakpeg ngcks, sgrabus jrcjdal` igvgebpgi tbwcris tmg gli bo tmg tgsts, cli a t as pbssaneg tmct tmg ma`mgr smgcr strgssgs al tmg jbltalubus ngcks watm jbkprgssabl rgalobrjgkglt kcy mcvg nggl tmg rgcsbl obr tmg ebw kbkglt jcrragi bvgr tmg jgltrce suppbrt. O E G ] W ^ G CLI I A^GJY EBCI

Ymg jcsg bo nglial` cli iargjt strgss jcl ng trgctgi al tmg sckg kcllgr cs nglial` ceblg. Ymg strgl`tm bo tmg jbkprgssavg saig waee ng tmg sckg cs ngobrg cli tmg stgge tglsabl waee ng rgiujgi ny tmg ckbult bo tmg iargjt jbkprgssabl, V, cs smbwl al Oa`. ?.

g

OA@. ? Ymg uetakctg jbkprgssavg kbkglt as `avgl n y Gq. 1) K,

;

g

;

+ i C ,H,

6.:::ni>o ,

 

917

^galobrjgi bljrgtg Kgkngrs Wligr Oegxurg

Ymg uet akctg tglsaeg tglsaeg kbkglt as K,

; Vg ;

C.h,

Gq

RxR

x

33} °

Pmgl tmgrg as lb stgge bl tmg jbkprgssavg saig Gq ucta uc tabl bl 33) 33) ngjbkgs K, ; Vg ; C.h,

Gq

RjR

j

3

3>)

R

g

cli tmg vceug bo j jcl ng bntcalgi orbk tmg obrkuec j ;

Ti + g

al wmajm y ; CH, noj

;

i

+ g)•- 9ig + >Qg[ ........................Gq 3:}

CH.

6.=7 nh' j

Pmgl tmgrg as stgge bl tmg jbkprgssabl saig nut tmg ebci as lbt suooajaglt tb igvgebp tmg oue oueee jbkprgssav jbkprgssavgg strgl str gl`tm `tm bo nbt m tmg stgge cli jbljrgtg, tmg rgquargi tglsaeg stgge crgc jcl ngst ng jbkputgi ny jblsaigral` tmg googjt bo tmg jbkprgssabl stgge cli jbljrgtg sgpc rctgey. Oarst jbkputg tmg crgc bo tglsaeg stgge rgquargi t b igvgebp tmg kbkglt (i C'. .) bo tmg jbkprgssavg strgss watm tmg obrkuec8 C,

; C',

8

)

Gq

39}

Ymgl igiujt tmg kbkglt (i C',o.) orbk tmg gxtgrlce kbkglt, Vg, cli jbkputg tmg ciiatablce crgc bo tglsaeg stgge rgquargi tb ncecljg tmg jbkprgssabl strgss al tmg jbljrgtg usal` Gq. 3>). Pmgl tmg gjjgltrajaty as skcee jbkpcrgi watm i, tmg uetakctg

strgl`tm bo tmg kgkngr jcl ng jbkputgi cs twajg tmg strgl`tm bo tmg wgcdgr saig bo tmg sgjtabl orbk tmg obrkuec sg sggg Oa`. Oa`. 0)8

t i

OA@. 0

 

91?

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V ; >C ,o,

+ 3.0n

Kcr.-Cpr. 31:0 Gq. (37)

i-g) o j

wmajm ngjbkgs obr c jbljgltraj ebci bl c sykkgtrajce kgkngr8 ;

>C ,o,

+ 6.=7nto • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gq.

(3?)

Ymg vceug bo g obr wmajm tmg Gquctabl (1) cli (37) waee `avg gquce vceugs bo as `avgl n y Gquctabl (30) cli obr skceegr gjjgltrajatags, Gquctabl (37) smbuei ng usgi. g

;

~

i +Q +

i

+

. . . . . . . . . . . . . . . . . Gq. (30)

Q )> -6 .0 = ? i > - > Q i [

al wmajm C ,o, . 6.=7no j

Ymg obrkuecs obr uetakctg strgl`tm bo kgkngrs uligr oegxurg cli iargjt ebci mcvg nggl vgraoagi ny jbkpcrasbl watm tmg rgsuets bo tgsts bl 9? jbeukls kcig ny Ncjm cli @rco 5   = Ymg rctab bo cjtuce uetakctg ebci tb jcejuectgi uetakctg strgl`tm as `avgl al Ycneg : wmajm smbws cl cvgrc`g grrbr bo tmrgg pgr jglt obr tmg sgrags. Ymg jbeukls wgrg cnbut = ot. : al. ebl` cli 3? al. squcrg cli wgrg ebcigi watm gjjgltrajatags vcryal` orbk zgrb tb cnbut > al. Ymg cvgrc`g :6 gk. jung strgl`tm bo tmg jbljrgtg wcs >>7 d`. pgr sq. gk. cli <

YCNEG :- JB K V C ^A Z B L BO JCEJWECYGI CLI CJYWCE WEYAKCYG EBCIZ OB^ JBEWKLZ YGZYGI WLIG^ GJJGLY^AJ EBCIZ NQ NCJM CLI @^CO

(Zgg Jbeukl

Hbu^L

E

Ckgr. Jbljrgtg Alst. Vrbjggial`s _be. >?, p. ??3. Cprae, 31:6.)

Gjjgltrajaty

Jcejuectgi Wetakctg Ebci

Obrkuec Lb.

Ebci-D`.

Cjtuce Wetakctg

Ebci-D`.

Cjtuce Ebci Iavaigi ny Jcejuectgi Ebci

Yypg A

6

3? 3> 3> 3>

>03,666 19,666 70,666 >1,666

>=6,::: 1:,666 ?6,::: >1,1?0

3.6:7 .116 3.670 3.63?

6

3? 37 1

39 39

::3,?66 31?,366 3>=,666 ?1,=66 :>,=66

::=,::: >6>,766 3>9,666 ?1,?66 :>,:76

3.6>3 3.6:> .1?= .11= .1=?

39 39

:01,366 >9:,=66 376,666 36?,766 7?,666

969,066 >>7,666 370,766 367,666 7:,766

3.6?0 .1>:* 3.676 .1=0 .177

>06,966 3:7,>66

>0?,3?0 3:?,666

3.6>6 3.667

.76 .07 3.>7

Yypg AA

Yypg A A A

.>7 .76 .07 3.>7

3> 3>

6

3?

.>7 .76 .07 3.>7

Vecal Jbeukls

3> 3>

37 1 3?

6

.>7

37

Cvgrc`g Cvgrc`g Grrbr

*Cvgrc`g bo twb tgsts bley, 6.==> cli 6.1?7.

3. 660

• 6:3

 

^galobrjg ^galo brjgi i

910

bljrg bljrgtg tg Kgkngrs Wligr Oegxurg

tmg jyealigr strgl`tm wcs tcdgl cs

>>7 br 311 d`. pgr sq. gk. 3.3:

Ymg

yagei pbalt bo tmg stgge cvgrc`gi :00: d`. pgr sq. gk. obr Yypgs A cli A A cli :70> obr Yypg AAA. Ymg kcxakuk vcractabl al tmg strgl`tm bo tmg jungs wcs cnbut

³1Q> pgr jglt. Ymg grrbrs smbwl n y tmg uetakctg strgl`tm obrkuecs crg wgee watmal tmg eakats bo tmg vcracnaeaty bo tmg kctgraces cli a t wbuei cppgcr tmct tmg usg bo kbrg gecnbrctg obrkuecs as lbt wcrrcltgi. Obr skcee gjjgltrajatags, Gquctabl 7 c`rggs watm tgst rgsuets kujm ngttgr tmcl tmg usuce obrkuec ncsgi bl strca`mt ealg strgss vcractabl.

Zujm c`rggkglt as kbrg akpbrtclt tmcl tmgbrgtajce vgraoajctabl nut at jcl ng suppbrtgi bl tmg ncsas bo cjtuce strgss vcractabl. t as ourtmgr suppbrtgi ny tmg rgsuets bo tgsts bl twb pecal jbljrgtg prasks rgpbrtgi ny Zectgr cli Eysg 5  • pc`g =71< Ymg = x = x 3> al. prasks wgrg ebcigi watm g ;

t

cli tmg uetakctg ebci cvgrc`gi 377,7>6

ens. Ymg jyealigr strgl`tm bo tmg jbljrgtg wcs 96?6 p.s.a. `avgs V

;

= 3.0 ] = ] Z

] 96?6

;

Gq.

37)

390,666 ens.

b r cnbut 19.? pgr jglt bo tmg cjtuce ebci. Ymg obrg`bal` gquctabls prgiajt tmg ultakctg strgl`tm bo c kgkngr nut jcllbt ng usgi tb jbkputg tmg cjtuce strgssgs ngebw tmg uetakctg. Ngal` ncsgi bl =7 pgr jglt bo tmg jyealigr strgl`tm tmgy

crg jblsastglt watm tmg rgsuets bo tgsts bo jbeukls uligr jbljgltraj ebci. t as mbpgi tmct tmgy waee prbvaig c sctasocjtbry kgtmbi wmajm as lbw ecjdal` obr tmg igsa`l bo kgkngrs bo gecstaj orckgs cli crjmgs cotgr tmg gxtgrlce kbkglts mcvg nggl igtgrkalgi n y tmg tmgbry bo gecstajaty. Ymgy aliajctg tmct c ma`mgr pgrjgltc`g bo tglsaeg stgge kcy ng usgi tmcl as lbw `glgrce prcjtajg watmbut bvgrstrgssal` tmg jbljrgtg cli tmgy waee pgrkat ea`mtgr kgkngrs wmgrg nbli cli smgcr jcl ng prbpgrey tcdgl jcrg bo. as ourtmgr prbpbsgi tmct tmg igci ebci kbkglts cli tmrusts ng kuetapeagi ny c suatcneg ocjtbr bo scogty cli ciigi tb tmg eavg ebci kbkglts cli tmrusts kuetapeagi ny c l cpprbpractg ocjtbr, prbncney ecr`gr tmcl tmct usgi obr igci ebci, gquctal` tmg tbtce tb tmg uetakctg .strgl`tm `avgl n y tmg gquctabls. Ymg ocjtbrs bo scogty jbuei cesb ng t

 

91=

HBW^LCE BO YMG CKG^AJCL JBLJ^GYG ALZYAYWYG

Kcr.-Cpr. 31:0

altrbiujgi n y usal` rgiujgi vceugs bo tmg strgssgs a at prbvgs igsar t kcy ng tmct tmg uetakctg strgl`tm obrkuecs ceblg waee ng cneg. suooajaglt obr brialcry nuaeial` igsa`l watmbut tmg lgjgssaty obr kcdal` cly jcejuectabl bo tmg tglsaeg strgssgs uligr wbrdal` ebcis. C tmbrbu`m stuiy smbuei ng kcig tb igtgrkalg wmct ocjtbrs bo scogty smbuei ng usgi obr iaoogrglt typgs bo strujturgs. ^GOG^GLJGZ (') Oalce ^gpbrt bo tmg Zpgjace Jbkkattgg bl Jbljrgtg cli ^galobrjgi Jbljrgtg Crjmgs, Yrclscjtabls Ck. Zbj. bo Javae Gl`alggrs, 31:7, p. 39>0. ( >) Jbkprgssavg Ztrgl`tm bo Jbljrgtg al Oegxurg, Zectgr cli Eysg, Hbu^LCE Ck. Jbljrgtg Alst., Hulg 31:6, Vrbjggial`s _be. >?, p. =:3. ( : ) ^galobrjgi Jbljrgtg Jbeukl Alvgsta`ctabl, Ygltctavg Oalce ^gpbrt bo Jbk kattgg 367, O. G. ^ajmcrt, Jmcarkcl, Hbu^LCE Ckgr. Jbljrgtg Alst., Ogn. 31::, Vrbjggial`s _be. >1, p. >07. ('') Jblsaigrctabls sur eg Jecjue gt ec Zgjuratg igs Vagjgs Oegjmags, ny ^ Jbpgg, Vuneajctabls bo tmg Altgrlctablce Cssbjactabl obr Nrai`g cli Ztrujturce Gl`alggral`, _be. :, p. 31. (') Ztrgl`tm bo Jbljrgtg Ngcks, ny ^ajmcri E. Mukpmrgy cli Ebuas M. Ebssg, Ygjmlbeb`ar Vcpgrs bo tmg Nurgcu bo Ztclicris. (•) Oegxurce ^gsastcljg bo Zmceebw Jbljrgtg N gcks, ny J. N. KjJueebu`m, Gl`alggral` Lgw-^gjbri _be. 337, p. 96?. vbl Gkpgr`gr, _b _be. e. 3 :ri giatabl, p. >96. ( 0 ) Mclinujm our Gasgl ngtbl ncu, ( =)Iasjussabl ny @gbr`g M. Igee, Hbu^LCE Ckgr. Jbljrgtg Alst., Cpr. 31:6, Vrbjggial`s _be. >?, p. ??3. ny Oratz v. Gkpgr`gr, Ngtbl uli Gasgl Bjt. 31:?, p. :>9. ( 1 ) Igr Ngawgrt l, ( 36 ) Nrujmzustcli uli Zajmgrmgat ak Gasglngtblncedgl, ny ^uibeo Zcea`gr, Ngtbl uli Gasgl Bjt. 31:?, p. :30. ( ) Jbkprgssavg Ztrgl`tm bo Jbljrgtg al Oegxurg, ny Zectgr cli Xapprbit, Vrbjggial`s Ckgr. Jbljrgtg Alst., 31>6, p. 3>6. >) Ymg ^giastranutabl bo Kbkglts al ^galobrjgi Jbljrgtg Ngcks cli Orckgs, ny P. M. @eclvaeeg cli O. @. Ymbkcs, HbW^LCE Alstatutabl bo Javae Gl`alggrs, .Yulg 31:?, p. >13. Iasjussabl bo tmg obrg`bal` pcpgr waee ng wgejbkg a

rgjgavgi al tra

peajctg ny tmg Zgjrgtcry bo tmg Alstatutg ny ulg 3 31:0. Obr sujm iasjussabl cs kcy igvgebp rgcigrs crg rgogrrgi tb c Zuppegkglt tb ng assugi watm tmg Hbu^LCE obr Zgpt.-Bjt. 31:0.