l-08 introduction to bridge engineering (coloured)
TRANSCRIPT
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
E`ltur` - >2
Jftrimultjif ti Drjmh`
@fhjf``rjfh
Dy; rig Mr. Qajsar Aej
Ljvje @fhjf``rjfh M`parto`ft
P@] ^`sbawar
www.mrqajsaraej.lio
1
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
]ipjls
Jftrimultjif
Drjmh` Liopif`fts
]yp`s ig Drjmh`s
Eiams gir Drjmh` M`sjhf
Afaeysjs & M`sjhf ig \jopey \uppirt`m TL \ead Drjmh`s
M`sjhf \t ps gir \jopey \uppirt`m TL \ead Drjmh`
@xaope`
Gaoius Drjmh`s jf tb` Xirem
4
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Jftrimultjif
Drjmh` js a strultur` bavjfh af ip`fjfh fit e`ss
tbaf 7>>> oo tbat giros part ig a bjhbway ir iv`r,
ir ufm r wbjlb tb` bjhbway pass`s.
\trultur`s 5 7>>> oo h`f`raeey laee m luev`rts.
<
Luev`rtDrjmh`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Jftrimultjif
Drjmh` js tb` c`y `e`o`ft jf a ]rafspirtatjif
\yst`o;
Jt liftries tb` lapaljty ig tb` syst o.
Jt js tb` bjhb`st list p`r oje` ig tb` syst o.
Jg tb` drjmh` gajes, tb` syst o gajes.
=
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh` Liopif`fts
A drjmh` lifsjsts ig sup`r strultur` afm sudstrultur`.
0
\up`r strultur`; \trulturae parts ig tb` drjmh` wbjlb privjm`s tb` birjziftae spaf.
\ud strultur`; \trulturae parts ig tb` drjmh` wbjlb suppirts tb` birjziftae spaf.
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
7
^j`r
^j`r Lap Mjapbrahos
^je` Lap
Hjrm`r
M`lc
^je`s
Drjmh` Liopif`fts
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s laf d` leassjgj m allirmjfh ti;
Oat rjaes (liflr`t , st` e ir wiim `tl),
Psah` (p`m`strjaf, bjhbway, ir rajeriam),
\paf (sbirt, o`mjuo, ir eifh),
\trulturae giro (seads, hjrm`r, truss, arlb, susp`fsjif, ir
lade`-stay`m).
8
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Jt js biw`v`r sujtade` ti leassjgy drjmh`s allirmjfh ti
tb` eilatjif ig tb` oajf strulturae `e o`fts r`eatjv` ti
tb` surgal` if wbjlb tb` us`r trav`es;
Oajf strultur` D`eiw tb` m`lc ejf ,
Oajf strultur Adiv` tb` m`lc ejf`, ir
Oajf strultur` Lijfljmjfh wjtb tb` m`lc ejf .
2
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` D`eiw M`lc ejf`
Arlb`m, ]russ-Arlb`m Drjmh`s, Oasifry Arlb, Liflr`t`
Arlb, tb` \t``e-]russ Arlb, afm tb` \t``e M`lc ]russ.
:
Oasifry Arlb \t``e M`lc ]russ Drjmh`Oasifry Arlb
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` D`eiw M`lc ejf`
1>
Liflr`t` Arlb
\t``e ]russ Arlb
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` D`eiw M`lc ejf`
Xjtb arlb sbap`, hravjty eiams ar` trafsojtt`m ti tb`
suppirts prjoarjey dy axjae liopr ssjv` girl`s.
At tb` suppirts, ditb v`rtjlae afm birjziftae r`altjifs oust
d` r`sjst m.
11
Arlb
Axjae girl` Axjae girl`
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` D`eiw M`lc ejf`
\aej ft g`atur`s ig Arlb ]yp` Drjmh`
]b` arlb giro js jft`fm`m ti r`mul` d`fmjfh oio`fts jf tb`
sup`rstrultur`.
]b` oist sujtade sjt` gir tbjs giro ig strultur js a vaee`y, wjtb
tb` arlb giufmatjif eilat`m if mry rilc seip`s.
]b` lifv`ftjifae lurv`m arlb rjd oay bav` bjhb gadrjlatjif afm
`r`ltjif lists, aetbiuhb tb`s` oay d` liftriee`m dy scjee`m
eadir.
]b` leassjl arlb giro t`fms ti gavir liflr t` as a lifstrultjif
oat`rjae.
14
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` D`eiw M`lc ejf`
\aej ft g`atur`s ig Arlb ]yp` Drjmh`
]b` arlb rjd js usuaeey sbap`m ti tac` m`am eiam wjtbiut
d`fmjfh oio`fts. ]bjs eiam js tb`f laee m tb` giro eiam.
Jg tb` giro eiam js earh`, tb` ejv` eiam d`lio`s `ss`ftjaeey a
soaee mjsturdafl` appej`m ti a liopr`ss`m o`od`r.
1<
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
1=
\usp`fsjif; M`lc js suppirt`m dy twi oajf lade`s tbriuhb
s`lifmary lade`s (bafh`rs).
]yp`s ig Drjmh`s
Oajf \trultur` Adiv` M`lc ejf`
\usp`fsjif, Lade \tay`m, afm ]briuhb-]russ drjmh`s ar
jfleum`m jf tbjs lat hiry.
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
10
Lade`-stay`m; M`lc js suppirt`m dy tiw`r mjr`ltey tbriuhb lade`s.
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
17
]briuhb Drjmh`s
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
\aej ft g`atur`s ig \usp`fsjif Drjmh`s
]b` ge`xjde` lade`s ig a susp`fsjif drjmh` js sbap`m afm
suppirt`m ti trafsg`r tb` oakir eiams ti tb` tiw`rs afm
aflbirah`s dy mjr lt t`fsjif.
]b` m`lc js bufh grio tb` lade dy bafh`rs lifstrult`m ig bjhb
str`fhtb wjr` rip`s jf t`fsjif.
]bjs us` ig bjhb str`fhtb st``e jf t`fsjif e`ams ti af
`lifiojlae strultur`.
18
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
\aej ft g`atur`s ig \usp`fsjif Drjmh`s
]b` oajf lade js stjgg`f`m `jtb r dy a pajr ig stjg g fjfh truss`s
ir dy a syst o ig hjrm rs at m`lc e`v`e.
]bjs stjgg`fjfh syst`o s`rv`s ti;
a) Liftrie a`rimyfaojl oiv`o fts,
d) Ejojt eilae afhe lbafh`s jf tb` m`lc.
12
\tjgg`fjfh
truss`s
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
\aej ft g`atur`s ig Lade` \tay`m drjmh`s
As liopar`m wjtb susp`fsjif drjmh`s, tb` lade`s ar` strajhbt
ratb`r tbaf lurv`m. As a r`suet, tb` stjggf`ss js hr`at`r.
A`rimyfaojls jfstadjejty bas fit giufm ti d` a pride`o jf sulb
strultur`s.
1:
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Adiv` M`lc ejf`
\aej ft g`atur`s ig ]briuhb Drjmh`s
A drjmh` truss bas twi oajf strulturae amvaftah`s;
1. ]b` prjoary o`od r girl`s ar axjae eiams3
4. ]b` ip f w`d syst o p rojts tb` us` ig a hr at r iv raee m`ptb
(mu` ti e`ss r m`am eiam) tbaf gir af `qujvae`ft siejm w`d hjrm`r.
Ditb tb s` galtirs e`am ti `lifioy jf oat`rjae afm a r`mul`m
m`am w jhbt.
]b` jflr`as`m m`ptb aesi e`ams ti r`mul`m m ge ltjif.
@lifiojlae gir o`mjuo spafs, a`stb`tjlaeey pe`asjfh.
4>
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`
Hjrm`r drjmh`s ig aee typ`s ar` jfleum`m jf tbjs lat`hiry.
@xaope`s ar ;
\ead (siejm afm vijm`m),
]-d`ao,
J-d`ao,
Xjm`-geafh` d`ao,
Liflr t` dix hjrm`r,
\t``e dix,
\t``e peat` hjrm`r.
41
Liflr`t` Dix Hjrm`r Drjmh`
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`
44
Dix Hjrm`r Drjmh`
Hjrm`r Drjmh` Pfm`r Lifstrultjif
]yp`s ig Drjmh`s
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`
4<
]yp`s ig Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Eiams gir Drjmh` M`sjhf
4=
Eiams ti d` lifsjm`r`m jf drjmh` m`sjhf laf d` mjvjm`m
jfti twi driam lat`hirj s;
^`roaf`ft eiams,
]rafsj`ft eiams.
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Eiams gir Drjmh` M`sjhf
^`roaf`ft Eiams \`eg w`jhbt ig hjrm rs afm m`lc, w`arjfh surgal , lurds afm
parap ts afm rajejfhs, utjejtj`s afm euojfarj s afm pr ssur`s
grio `artb r`tajfo`fts.
]wi jopirtaft m`am eiams ar`;
ML; M`am eiam ig strulturae liopif`fts afm fif strulturae
attalbo`fts.
MX; M`am eiam ig w arjfh surgal`.
40
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
^`roaf`ft Eiams
Oat rjae ^rip`rtj s gir ^av`o`ft
μdjtuo`f ? 440> ch/o< ? 44.1 cF/o< (1=> ed/ g <)
μliflr`t` ? 4=>> ch/o< ? 4<.7 cF/o< (10> ed/ g <)
Eiam galtirs gir ^av`o`ft M`am Eiams
]b` oaxjouo eiam galtir gir ML ? 1.40
]b` oaxjouo eiam galtir gir MX ? 1.0
47
Eiams gir Drjmh` M`sjhf
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
48
Eiams gir Drjmh` M`sjhf
]rafsj`ft Eiams Hravjty (Ejv`) eiams mu` ti v`bjluear, rajeway afm p`m`strjaf
traggjl.
]b` autioidje` js if` ig tb` oist liooif v`bjluear ejv`
eiam if oist drjmh`s3 jt js tb` trulc tbat laus`s tb` lrjtjlae
eiam `gg`lts.
Eat`rae eiams mu` ti wat`r, wjfm, `artbquac` afm sbjp
lieejsjifs `tl.
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
42
Eiams gir Drjmh` M`sjhf
]rafsj`ft Eiams
Gieeiwjfh `gg`lts laus`m dy Ejv` eiam ar` aesi v`ry
jopirtaft afm oust d` lifsjm`r m jf tb` m`sjhf ig a drjmh .
Jopalt (myfaojl `gg`lts),
Dracjfh girl`s,
L`ftrjguhae girl`s (jg pr`s`ft) afm
]b` `gg lts ig itb`r trulcs sjouetaf`iusey pr`s`ft.
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams ]b` AA\B]I m`sjhf eiams oim e lifsjsts ig tbr`` mjstjfltey
mjgg r`ft eiams;
M`sjhf ]rulc,
M`sjhf ]afm`o,
M`sjhf Eaf .
4:
Eiams gir Drjmh` M`sjhf
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams
M`sjhf ]rulc
^r`vjiusey B\4> was us`m as M`sjhf trulc. ]b` B m`fit`s
bjhbway afm \ m`fit`s \`oj traltir afm 4> js tb` w`jhbt ig
traltir jf tifs (P\L ufjts).
]b` f`w v`bjle liodjfatjif as m`slrjd`m jf AA\B]I (1::=)
ETGM Drjmh` sp`ljgjlatjifs ar` m`sjhfat`m as BE-:< gir
Bjhbway Eiamjfh all`pt`m jf 1::<.
<>
Eiams gir Drjmh` M`sjhf
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams
<1
BE-:< ]rulc Eiam
1=0 cF
(<4 cjps)
(1=.0 tifs)
1=0 cF
(<4 cjps)
(1=.0 tifs)
<0 cF
(2 cjps)
(<.0 tifs)
=.< o ti :.> o
(1= gt ti <> gt)
=.< o
(1= gt)
Eiams gir Drjmh` M`sjhf
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams
M`sjhf ]afm`o
<4
11> cF
(4= cjps)
(11 tifs)
11> cF
(4= cjps)
(11 tifs)
1.4 o
(= gt)
Eiams gir Drjmh` M`sjhf
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams M`sjhf Eaf` Eiam
]b` AA\B]I m`sjhf eaf` eiamjfh js ejc` a laravaf ig trulcs.
Jt js :.< cF/o afm js assuo`m ti illupy a r hjif ig <.> o (1> gt).
Jt js appej`m as <.1 cF/o4 ir >.>7= c/gt4 (7= ed/gt4) igpr`ssur` tia wjmtb ig <.> o ir 1> gt
iv r tb``ftjr e`fhtbig drjmh`gir G@O.
<<
<.> o (1> gt)Drjmh`
:.< cF/o
(>.7= cjp/ gt)
Eiams gir Drjmh` M`sjhf
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
W`bjluear M`sjhf Eiams
Jf suooary tbr`` m`sjhf eiams sbiuem d` lifsjm`r`m; tb`
m`sjhf trulc, m`sjhf tafm`o, afm tb` m`sjhf eaf .
]b`s` eiams ar` sup`rjopis`m dy twi ways ti yj`em tb` ejv`
eiam `gg`lts, wbjlb ar liodjf`m wjtb tb` itb r eiam `gg`lts.
]b` twi ways ig sup rpisjtjif ar ; ]rulc + eaf ,
]afm`o + eaf ,
<=
Eiams gir Drjmh` M`sjhf
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Eiam Oimjgj`r A galtir alliuftjfh gir multjejty, r`mufmafly afm tb`
ip`ratjifae jopirtafl` ig tb` drjmh`.
Jt js tac`f as 1.>0 gir sjopey suppirt`m drjmh`s afm js
appej`m if aer`amy galtir m vaeu`s ig d`fmjfh oio`fts.
<0
Eiams gir Drjmh` M`sjhf
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s
<7
\jopey \uppirt`m TL \ead Drjmh`
]bjs typ` ig drjmh` lifsjst ig ifey sead (wjtbiut afy itb`r suppirtjfh
o`od r sulb as hjrm`rs).
]bjs giro ig drjmh js wjm ey us`m wb`f tb` drjmh` lriss s a ojfir riam ir
soaee rjv r.
Jf sulb las`s, tb` spaf js r eatjv ey soaee afm ouetjpe` spafs ar jfg`asjde`
ir/afm uff`l`ssary.
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
<8
Afaeysjs afm M`sjhf ig \jopey
\uppirt`m TL \ead Drjmh`s
@ @ @ @@
Afaeysjs ig \ead Drjmh`
\ead drjmh`s laf d` afaeyz m as <M, 4M afm 1M oim es.
Jg jt js ti d` afaeyz`m as 1M oim`e (ejf` afaeysjs), tb drjmh` wjmtb wjee d`
mjvjm`m jfti varjius strjps ig sp`ljgjl wjmtb (@). ]b`s` strjps ar` laee`m
m`sjhf eaf`s.
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
<2
Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s
Oio`ft Idtajf`m grio 1M afaeysjs
O/@ O/@ O/@ O/@O/@
• M`sjhf eaf` wjmtbs laf d` laelueat`m usjfh quatjifs hjv`f if f`xt sejm`
Afaeysjs ig \ead Drjmh`
]b` m`sjhf eaf`s ar` tb`f
trafsgiro`m ti ejf` `e`o`fts (1M
oim e) gir ejf` afaeysjs. ]b` oio`ft
ar` laelueat`m grio ejf` afaeysjs.
]b s` oio`fts (O) ar tb`f mjvjm m
dy tb` m`sjhf eaf` wjmtb (@) ti h`t
oio`ft p r giit (O/@) gir tb` sead.
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
<:
X
X1
\
Afaeysjs afm M`sjhf ig \jopey
\uppirt`m TL \ead Drjmh`s
M`sjhf Eaf`s M`sjhf Eaf` Xjmtb
Gir sjfhe` eaf` eiam`m;
@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1)
E1 ? Oimjgj m spaf e`fhtb ? Ojfjouo ig (\) afm 7> gt
X1 ? Oimjgj`m `mh` ti `mh` wjmtb ? Ojfjouo ig (Iv`raee wjmtb ig
drjmh , X1) ir <> gt
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
=>
X
X1
\
Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s
M`sjhf Eaf`s
M`sjhf Eaf` Xjmtb
Gir ouetjeaf` eiam`m;
@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE
E1 ? \ao` as sjfhe eaf eiam m las` ? Ojfjouo ig (\) afm 7> gt
X1 ? Ojfjouo ig (iv raee wjmtb ig drjmh , X1) ir 7> gt
FE ? Fi. ig m`sjhf eaf s? JF] (X/14)
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Ouetjpe` ^r`s`fl` Galtir Ouetjpe` pr s`fl` galtirs oimjgy tb` v`bjluear ejv` eiams gir tb` pridadjejty
tbat v`bjluear ejv` eiams illur tih tb`r jf a gueey eiam`m stat`.
]b`s` galtirs sbiuem d` appej`m d gir` afaeysjs ir m`sjhf ifey wb`f mijfh
tbr``-mjo fsjifae oim`ejfh, wircjfh wjtb sudstrultur s.
A galtir ig 1.4 js aesi us`m jf tb` ejf` afaeysjs ig `mh` strjp ig a sead drjmh`.
=1
Afaeysjs afm M`sjhf ig \jopey
\uppirt`m TL \ead Drjmh`s
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
=4
\
Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s
Ojfjouo \ead M`ptb gir \ead Drjmh`
Ojfjouo m`ptb gir T.L.L \eads (b);
b? 1.4(\ + 1>)/<> (wb`r` ‒\‚ js jf gt.)
Xb`r \ ? spaf ig drjmh` (l/l ig d`arjfh).
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
M`sjhf \t`ps gir \jopey \uppirt`m TL
\ead Drjmh`
\t`p >1; \jz`s
Ojfjouo m`ptb gir T.L.L \eads;
M ptb, b (gt) ? 1.4(\ + 1>)/<>
Xb`r \ ? spaf ig drjmh .
\t`p >4; Eiams
M t`rojf` eiam ML, XML ? bμliflr`t`
M t`rojf` eiam MX, XMX ? bμw`arjfh surgal`
\t`p ><; Afaeysjs
M t`rojf` sead oio`fts mu` ti m`am eiams;
OML ? XML\4/2
OMX ? XMX\4/2
=<
\
M`am Eiams
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p ><; Afaeysjs (Liftjfu`m)
M t`rojf` sead oio`fts mu` ti ejv` eiams;
1. Oio`ft mu` BE-:< ]rulc eiam, O]rulc
(Oax. oio`ft mu ti trulc eiam laf d` idtajf m dy pealjfh tb ojmme` axe` at ojm spaf ig
tb drjmh` afm r ar axe` eiam at mjstafl` ig 1= gt grio tb ojmme` axe` eiam)
==
<4 cjps<4 cjps2 cjps
1= gt1= gt
\/4
M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p ><; Afaeysjs (Liftjfu`m)
M t`rojf` sead oio`fts mu` ti ejv` eiams;
4. Oio`ft mu` ]afm`o Eiam, O]afm`o
(Oax. oio`ft mu` ti tafm`o eiam laf d` idtajf`m dy pealjfh tb twi eiams at mjstafl` ig
4 gt grio tb` ojm spaf)
=0
4= cjps4= cjps
4 gt4 gt
\/4
M`sjhf \t`ps gir \jopey \uppirt`m TL
\ead Drjmh`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p ><; Afaeysjs (Liftjfu`m)
M t`rojf` sead oio`fts mu` ti ejv` eiams;
<. Oio`ft mu` m`sjhf eaf` eiam, OEaf`
OEaf` ? >.7= \4/2
]ac` hr at`r oio`ft vaeu` aoifh O]afm`o afm O]rulc afm ouetjpey jt dy
jopalt galtir ig 1.<< afm tb`f amm jt wjtb OEaf`
]b`r gir , OEE+JO ? 1.<<(O]afm`o IT O]rulc) + OEaf`
Lifv`rt OEE+JO ti oio`ft/gt, Mjvjm` OEE+JO dy ―@‟ m`sjhf eaf wjmtb.
=7
>.7= cjp/gt
\
M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p ><; Afaeysjs (Liftjfu`m)
Gir Jft`rjir \trjp, \jfhe` Eaf` Eiam`m, ―@‟ js hjv`f dy;
@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1) (1)
Gir Jft rjir \trjp, Ouetjeaf` eiam`m, ―@‟ js hjv`f dy;
@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE (4)
Gjfaeey, M`sjhf Eaf` Xjmtb @, js tb` soaee`st vaeu` ig (1) & (4)
M`t rojf` Ou gir jft rjir strjp;
Ou (jft`rjirstrjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO _ (p`r giit)
=8
M`sjhf \t`ps gir \jopey \uppirt`m TL
\ead Drjmh`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p ><; Afaeysjs (Liftjfu`m)
Gir @mh` \trjp, ―@‟ js hjv`f dy;
@ ? Darrj`r wjmtb at das` + 1 gt + (1/4) strjp wjmtb ≭ Guee strjp wjmtb ir 7
gt (wbjlb`v`r js e`ss)
D`laus` tb` `mh` strjp wjmtb js ejojt`m ti 7‴ , if`-eaf` eiam`m
(wb``e ejf` ? ¿ eaf` eiam) wjtb a ouetjpe` pr s fl` galtir, o ig 1.4
wjee d` lrjtjlae. B`fl` `mh` strjp oio`ft p r giit wjmtb js `quae ti;
OEE+JO (@mh` strjp) p`r giit ? ¿ Ø (OEE+JO) Ø 1.4/@
M`t rojf` Ou gir @mh` \trjp;
Ou (jft`rjir strjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO _ (p`r giit)
=2
M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\t`p >=; M`sjhfa) M`sjhf gir Jft`rjir \trjp (laelueat` As usjfh Jft rjir \trjp Oio`ft)
d) Mjstrjdutjif r`jfgirl`o`ft gir jft`rjir strjp (dittio trafsv`rs`
r`jfgirl`o`ft) {A0.1=.=.1};
Atrafsv`rs` ? (1>>/∛\ ir 0> %) ig As (wbjlb v`r js e`ss, Dut Jt sbiuem fit d` e`ss
tbaf As(\brjfcah`)
Astojo (sbrjfcah`)? >.>>12Ah
l) M`sjhf gir @mh` \trjp (Laelueat` As usjfh @mh \trjp Oio`ft)
m) Mjstrjdutjif T`jfgirl`o`ft gir @mh` \trjp ( \ao` ^ril`mur` as Adiv`)
`) \brjfcah` afm t`op`ratur` r`jfgirl`o`ft jf tip gal` ig sead (eifh afmtrafsv`rs` ditb); Gir hram` 7> st` e,
• Ast ? >.>>12Ah
=:
M`sjhf \t`ps gir \jopey \uppirt`m TL
\ead Drjmh`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
T`jfgirl`o`ft M`taje jf \ead Drjmh`;
As, Oajf r`jfgirl`o`ft
(ti d` m`sjhf`m)
]rafsv`rs` Dittio r`jfgirl`o`ft
(e`ast ig 1>>/∛\ % ir 0> %) ig As
As p`r sbrjfcah` afm
t`op ratur r`jfgirl`o`ft
r`qujr`o`fts
M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`
A
A‴
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
T`jfgirl`o`ft M`taje jf \ead Drjmh`;
Drjmh` T`jfgirl`o`ft Afjoatjif
01
M`sjhf \t`ps gir \jopey \uppirt`m TL
\ead Drjmh`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
M`sjhf ^ride o; M`sjhf ig
sjopey suppirt m sead drjmh`
gir BE-:< ejv` eiam.
\paf e`fhtb ig <0 gt l`ftr` ti
l`ftr` ig d`arjfhs.
Tiamway wjmtb js == gt lurd ti
lurd.
Aeeiw gir a gutur` w`arjfh
surgal` ig < jflb tbjlc
djtuojfius iv`reay.
Ps` g l‴ ? =>>> psj afm g y ? 7>
csj.
04
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi 1; \jz`s.
\paf e`fhtb ig drjmh` (\) ? <0 gt l/l
Le ar riamway wjmtb (X) ? == gt (lurd ti lurd)
Gir a lurd wjmtb ig 10 jflb`s, titae wjmtb ig tb` drjmh` (X1) ?
== + (4 Ø 10/14) ? =7.0 gt
Ojfjouo tbjlcf`ss ig drjmh` sead js hjv`f dy girouea;
bojf ? 1.4(\ + 1>)/<> ? 1.4 (<0 + 1>)/<> ? 1.2 gt ? 41.7‼ ≂ 44‼
0<
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif;
\t`p Fi 4; Eiams.
\ead eiam (wML) ? bμlifl
? (44/14) Ø >.10 ? >.480 csg
X`arjfh surgal` eiam (wMX) ? bμw`arjfh surgal`
? (</14) Ø >.1= ? >.><0 csg
0=
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi <; Afaeysjs.
M`am eiam oio`fts;
\ead oio`fts (OML) ? wML\4/2
? >.480 Ø (<04)/2 ? =4 gt-cjp/gt
X`arjfh surgal` oio`ft (OMX) ? wMX\4/2
? >.><0 Ø <04/2 ? 0.< gt-cjp/gt
00
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
07
@xaope`
\ieutjif;
\t`p Fi <; Afaeysjs.
Ejv` eiam oio`fts;
]rulc Eiam oio`fts;
O]rulc ? <0> gt-cjp
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi <; Afaeysjs.
Ejv` eiam oio`fts;
]afm`o oio`ft;
Otafm`o ? <84 gt-cjp
Eaf` oio`ft;
Oeaf` ? 7=> Ø <04/2 ? :2>>> gt-ed ? :2 gt-cjp
08
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
02
\ieutjif;
\t`p Fi <; Afaeysjs.
Ejv` eiam oio`fts;
Otafm`o 6 Otrulc, tb`r gir w` wjee us` Otafm`o
OEE+JO (Jfleumjfh jopalt) ? 1.<<Otafm`o + Oeaf`
? 1.<< Ø <84 + :2 ? 0:< gt-cjp
]i lifv`rt OEE+JO ti oio`ft/gt, Mjvjm` OEE+JO dy ―@‟ m`sjhf eaf` wjmtb.
]b` AA\B]I lim` r`lioo`fms s`parat` laelueatjif ig @ afm r suetjfh
d`fmjfh oio`ft ―O‟ gir af jft`rjir afm `mh` strjps ig a TL sead drjmh`.
B`fl` f`xt sejm`s mjsluss`s jft rjir afm `mh strjps s`parat`ey.
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi <; Afaeysjs.
M`sjhf Eaf` wjmtb ―@‟ gir jft rjir strjp;
Gir sjfhe` eaf` eiam`m;
@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1)
E1 ? Oimjgj`m spaf e`fhtb ? Ojfjouo ig (\ ? <0 gt) afm 7> gt ? <0 gt
X1 ? Oimjgj`m `mh` ti `mh` wjmtb ? Ojfjouo ig (X1 ? =7.0 gt) ir <>
gt ? <> gt
]b`r gir , @ ? 1>.>> + 0.>∛ (<0 Ø <>.>>) ? 184 jf ? 1=.< gt
0:
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
7>
\ieutjif;
\t`p Fi <; Afaeysjs.
M`sjhf Eaf` wjmtb ―@‟ gir jft rjir strjp;
Gir ouetjeaf` eiam`m;
@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE
E1 ? <0 gt
X1 ? Ojfjouo ig (X1 ? =7.0 gt) ir 7> gt ? =7.0 gt
FE ? Fi. ig m`sjhf eaf`s.? JF] (X/14) ?JF] (==/14) ? <
@ ? 2= + 1.== ∛ (<0 Ø =7.0) ≭ =7.0/<
? 1=4 jflb ir 11.2= gt ≭ 10.0
]b`r`gir`, @ ? 11.2= gt (E`ast ig aee)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi <; Afaeysjs.
Jft rjir \trjp Oio`ft (p`r giit)
OEE +JO (Jft rjir strjp) p r giit ? 0:</11.2= ? 0> gt-cjp/gt
Fiw,
Ou (jft`rjirstrjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO (p r giit)_
Ou (jft rjirstrjp) ? 1.>0 (1.40 Ø =4 + 1.0 Ø 0.<< + 1.80 Ø 0>)
Ou (jft`rjirstrjp) ? 100.< gt-cjp/gt ? 127<.7 jf-cjp/gt
71
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif;
\t`p Fi <; Afaeysjs.
M`sjhf eaf` wjmtb gir `mh` strjp; Allirmjfh ti AA\B]I ETGM
lim` A=.7.4.1.=,
@ ? Darrj`r wjmtb at das` + 1 gt + (1/4) strjp wjmtb ≭ Guee strjp wjmtb
ir 7 gt (wbjlb`v r js e`ss)
@ ? 1.40 gt + 1 gt + (1/4) Ø 11.2= ≭ 11.2= gt ir 7gt
@ ? 2.18 gt 6 7 gt
]b`r`gir @ ? 7 gt
74
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi <; Afaeysjs.
@mh` \trjp Oio`ft (p`r giit);
D`laus` tb` `mh` strjp wjmtb js ejojt`m ti 7‴ , if`-eaf` eiam`m
(wb``e ejf` ? ¿ eaf` eiam) wjtb a ouetjpe` pr`s fl` galtir, o ig
1.4 wjee d` lrjtjlae. B`fl` `mh` strjp oio`ft p`r giit wjmtb js
`quae ti (T`g r`fl ; lbapt`r =, Darc r afm ^ulc tt) ;
OEE+JO (@mh` strjp) p r giit ? ¿ Ø (0:<) Ø 1.4/7 ? 0:.< gt-cjp/gt
Ou (`mh` strjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO (p r giit)_
Ou (`mh` strjp) ? 1.>0 (1.40 Ø =4 + 1.0 Ø 0.<< + 1.80 Ø 0:.<)
Ou (`mh strjp) ? 184.=2 gt-cjp/gt ? 4>7:.8: jf-cjp/gt
7<
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
7=
\ieutjif;
\t`p Fi =; M`sjhf.
(a) M`sjhf gir Jft`rjir strjp;
Jft`rjir strjp oio`ft (Ou) ? 100.< gt-cjp/gt ? 127<.7 jf-cjp/gt
@gg`ltjv` m`ptb ig drjmh` sead (m) ? b “ liv`r “ ¿ Ø Mja ig dar
us`m
Psjfh #2 dar, `gg`ltjv` m`ptb js dittio liv`r gir sead js tac`f
`quae ti 1‼.
m ? 44 “ 1 “ ¿ Ø 1 ? 4>.0 jflb
Asojf ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4
As ? Ou/{Χg y (m “ a/4)}
Agt`r trjaes, As ? 1.2> jf4,(#2 N 0 jflb`s l/l)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
70
\ieutjif; \t`p Fi =; M`sjhf.
(d) Mjstrjdutjif r`jfgirl`o`ft gir jft`rjir strjp (dittio
trafsv`rs` r`jfgirl`o`ft) {A0.1=.=.1};
]b` aoiuft ig dittio trafsv`rs` r jfgirl`o`ft oay d` tac f as
a p`rl`ftah` ig tb` oajf r`jfgirl`o`ft r`qujr`m gir pisjtjv`
oio`ft as gieeiws dut fit e`ss tbaf \brjfcah` r jfgirl`o`ft;
Atrafsv`rs` ? (1>>/∛\ ir 0> %) ig As (wbjlb`v`r js e`ss)
1>>/∛E ? 1>>/∛<0 ? 17.: % 5 0> %
]b r`gir , Atrafsv`rs` ? >.17: Ø 1.2> ? >.<>= jf4
Astojo (sbrjfcah`)? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N
2 jflb`s l/l)
@xaope`
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif;
\t`p Fi =; M`sjhf.
(d) Mjstrjdutjif r jfgirl`o`ft gir jft`rjir strjp (dittio trafsv`rs`
r`jfgirl`o`ft) {A0.1=.=.1};
Oaxjouo spaljfh gir t`op`ratur st e r`jfgirl`o`ft jf if` way
sead allirmjfh ti ALJ 8.14.4.4 js ojfjouo ig;
<bg ?< Ø 44 ? 77‼
12‼
]b`r gir #0 N 2 jflb`s l/l js IC.
77
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
78
\ieutjif; \t`p Fi =; M`sjhf.
(l) M`sjhf gir @mh` strjp;
@mh` strjp oio`ft (Ou) ? 184.=2 gt-cjp/gt ? 4>7:.8: jf-cjp/gt
@gg`ltjv` m`ptb ig drjmh` sead (m) ? b “ liv`r “ ¿ Ø Mja ig dar us`m
Psjfh #2 dar, `gg`ltjv` m`ptb js dittio liv`r gir sead js tac`f`quae ti 1‼.
m ? 44 “ 1 “ ¿ Ø 1 ? 4>.0 jflb
Asojf ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4
As ? Ou/{Χg y (m “ a/4)}3 Agt`r trjaes As ? 4.>1= jf4, (#2 N =.8jflb`s)
Gjfaeey us` #2 N = jflb`s l/l ditb gir jft`rjir as w`ee as `mh`strjps
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
72
\ieutjif;
\t`p Fi =; M`sjhf.
(m) Mjstrjdutjif r jfgirl`o`ft gir `mh` strjp;
Atrafsv`rs` ? >.17: Ø 4.>1= ? >.<= jf4
Astojo (sbrjfcah`)? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N
2 jflb`s l/l)
Oaxjouo spaljfh gir t`op`ratur` st e r jfgirl`o`ft jf if` way
sead allirmjfh ti ALJ 8.14.4.4 js ojfjouo ig;
<bg ? < Ø 44 ? 77‼
12‼
Ps` #0 N 2 jflb`s l/l as dittio trafsv`rs r`jfgirl`o`ft
`v`rywb`r`.
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif; \t`p Fi =; M`sjhf.
( ) \brjfcah` afm t`op`ratur r jfgirl`o`ft jf tip gal` ig sead
(eifh afm trafsv`rs` ditb); Gir hram` 7> st e,
Ast ? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N 2 jflb`s l/l)
Gjfaeey us` #0 N 2 jflb`s l/l.
Gjfae T`lioo`fmatjif;
Oajf st``e (dittio) ? #2 N =‼ l/l gir jft rjir as w`ee as `xt rjir.
]rafsv rs` dittio r jfgirl`o`ft ? #0 N 2‼ l/l tbriuhbiut.
]ip st e (eifh afm trafsv rs ) ? #0 N 2‼ l/l.
7:
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
@xaope`
\ieutjif;
\t`p Fi 0; Mragtjfh
8>
(Oajf r`jfgirl`o`ft)
(Dittio trafsv`rs` r`jfgirl`o`ft)
(\brjfcah` r`jfgirl`o`ft)
(\brjfcah` r`jfgirl`o`ft)
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\io` Gaoius Drjmh`s
Eifh`st Drjmh`
Mafyafh “Cufsbaf Hrafm Drjmh` jf Lbjfa (17=2>> o)
81
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\io` Gaoius Drjmh`s
Eifh`st \paf
Acasbj Cajcyŏ Drjmh , Kapaf (1::1 o)
84
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
\io` Gaoius Drjmh`s
Bjhb`st Drjmh`
\j Mu Tjv r Drjmh` (=84 o bjhb)
8<
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Eafsmiwf` Drjmh`, \uccur
8=
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Kaosbiri Drjmh`, Kaosbiri
80
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Attilc Drjmh`, Attilc
87
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Oaejr Drjmh`, Caralbj
Eifh`st Drjmh` jf ^acjstaf (0>>> o)
88
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Lbjfjit Tajeway Drjmh`
Lifstrult m jf 1288.
82
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
Drjmh`s jf ^acjstaf
Drjmh` if O4 Oitirway
If` ig tb` bjhb`st jf Asja.
8:
^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
T`g`r`fl`s
M`sjhf ig Bjhbway Drjmh`s dy Tjlbarm O. Darc r.
ALJ <12
2>
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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ
M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar
]B@ @FM
21