theory of structures problems solved by dk mamonai

7/23/2019 Theory of Structures Problems solved by Dk Mamonai

1/72

]bcfp{ fi Z}psj}spcz Zkp Mp'_s`nkp

5;JC:< > x U n l c

N' Zsuufp}z ? Zsuufp}z npc upfykmcm }f pczkz} }bc hfnmz']bcpc npc }bpcc }{ucz fi Zsuufp}z

>' Bkglc Zsuufp}? K} kz nh|n{z kg jhfja|kzc fp Ng}k$jhfja|kzc gf} bfpkfg}nh fp ycp}kjnh

0' Ikrcm Zsuufp}? Bfpkfg}nh fp Ycp}kjnh fp Jhfja|kzc

:' Jkpjshnp fp Pfhhcp Zsuufp}? Nh|n{z gfpdnh }f }bc zspinjc'

@' Hfnmz ?

Mcnm Hfnmz Hkyc Hfnmz

Sgkifpdk}{ Mkz}sp`cm Hfnm Dfykgl Hfnm

Sgkifpdh{ Ynp{kgl Hfnm \kgm Hfnm

Ufkg} Hfnm Zgf| Hfnm


2/72


5;JC:< 0 x U n l c

@cndz ?

"k+ Mc}cpdkgn}c @cnd fp Zkduh{ Zsuufp}cm @cnd?

"kk+ Jfg}kgsfsz @cnd ? Fgc fp dfpc zung kz znkm nz Jfg}kgsfsz @cnd'

"kkk+Jng}khcycp @cnd ? Kg Zkgmbk k} kz znkm nz JBNON.


3/72


5;JC:< : x U n l c

Upf`hcd?> ? Mc}cpdkgn}c Ifpdz

U

H

Ipcc @fm{ Mknlpnd U

Dn H

Pn Bn

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn U 4 5

Pn4 U

Dfdcg}(

!yc Jhfja|kzc D 4 5

Dn! Pn / H 45

Dn ! UH 4 5

Dn 4 $ UH


4/72


5;JC:< = x U n l c

Upf`hcd?0 ? Mc}cpdkgn}c Ifpdz

U4 25h`

H 4 >5

Ipcc @fm{ Mknlpnd U 4 25 h`

Dn H 4 >5

Pn Bn

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn U 4 5

Pn4 25 h`

Dfdcg}(

!yc Jhfja|kzc D 4 5

Dn! Pn / H 45

Dn ! UH 4 5

Dn 4 $ 255 h`$i} " Ng}k$jhfja|kzc +


5/72


5;JC:< 3 x U n l c

Upf`hcd?: ? Sgkifpdh{ mkz}sp`cm Hfnm

\ y&y

H

\H

Ipcc @fm{ Mknlpnd H&0 H&0

N J @

Dn H

Pn Bn

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn \H 4 5

Pn4 \H

Dfdcg}(

!yc Jhfja|kzc D 4 5 n} ufkg} J

Dn! Pn / H&0 45

Dn 4 $ " Pn / H & 0 +

Dn 4 $ " \H / H & 0+

Dn4 $ \ H0

& 0


6/72


5;JC:< 9 x U n l c

Upf`hcd?= ? Sgkifpdh{ mkz}sp`cm Hfnm

: aku&d

0d

9 aku

Ipcc @fm{ Mknlpnd >'3 >'3

N J @

Dn 0d

Pn Bn

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn \H 4 5

Pn4 9 Aku

Dfdcg}(


Dn! Pn / H&0 45

Dn4 $ \ H 0 & 0

Dn4 $ : "0+0

& 0

Dn4 $ 9 aku' d


7/72


5;JC:< < x U n l c

Upf`hcd?3? 95a : 95a

=

9 9 9

Ipcc @fm{ Mknlpnd 95a Ir 95a

I{

N J M 3:':5 @

Dn Bn P`

Pn 9 9 9

Ikpz} fi nhh jbnglkgl ]nglcg} kg}f Mclpcc

4 ]ng$> =&: 4 3:':5

Gf|( ikgmkgl R$[ jf$fpmkgn}cz fi }bc Kgjhkgcm Ifpjc

Ir4 I Jfz 4 95 Jfz 3:': 4 95 "5'3;+4 :9A 1 I{ 4 I Zkg 4 95 Zkg 3:': 4 95 "5'25>+4=2'>5A

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn Ir 4 5( Pn ! P` U $ I{ 4 5

Bn4Ir ( Pn ! P` $95 $=2 45

Bn4 :9 A( Pn ! P` 4 >52 $$$$$$$$$$$$$$$$$$$$$$$$$"k+


8/72


5;JC:< 2 x U n l c

Dfdcg}(

!yc Jhfja|kzc D 4 5 n} ufkg} N

95 / 9 ! I{ / >0 P` />2 4 5

95 / 9 ! =2 / >0 4 >2 P`

P` 4 30 A

Us}}kgl Ynhsc fi P` kg C~sn}kfg "k+

Pn ! P` 4 >52

Pn ! 03 4 >52

Pn 4 39 A


9/72


5;JC:< ; x U n l c

Upf`hcd?9?

>0 a >9a >9a : a & i}

0 A & i}

2 = = = = 9

Ipcc @fm{ Mknlpnd

>9 a >0 a >9 a >9 a ; a

N J M C I L @

Pn Bn P`

= = = = = = 0 0 0

Nz }bcpc kz Y'M'H 4 >&0 / 9 / : 4 ; a 1 R 4 H & : 4 9 & : 4 0

Ifp S'M'H 4 0/ 2 4 >9 A 1 R4 H & 0 4 2 & 0 4 =

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn >9a >0a >9a >9a ! P` ;a 4 5

Pn ! P` 4 9; $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


">9 / =+ ! ">0 / >0+ ! ">9 />9+ ! ">9 / 05+ $ "P` / 0=+ ! "; / 09+4 5

>5>2 0=P` 4 5

P` 4 =0'=> A


Pn ! P` 4 9; Pn ! =0'=> 4 9; Pn 4 09'9 A


10/72


5;JC:< >5 x U n l c

Upf`hcd * < Ufkg} Hfnm

=5 A 35A :5 A

:&=

N C J I M L B @

= 3 : : 2 : :

"UNP] > + \c Mkz}sp` }bkz Mknlpnd kg}f }|f N Ufkg} }f J Ufkg}

Ipcc @fm{ Mknlpnd =5 a

N C J

Bn Bj

= 3

Pn Pj

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn $ Bj 4 5( Pn =5 ! Pj 4 5

Bn4 Bj Pn ! Pj 4 =5 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


$ Pj / ;5 ! =5 /= 4 55 4 $; Pj ! >95

Pj 4 >2 A

Us}}kgl Ynhsc fi Pj kg C~sn}kfg "k+

Pn ! Pj 4 =5 Pn ! >2 =5 4 5 Pn 4 00 A


11/72


5;JC:< >> x U n l c

"Unp} 0+ 35a :0 A :5 A

J Bj I M L B @

: : = = : :

4 ]ng$>:&= :9'29

Ir 4 I Jfz 35 / Jfz :9'29 =5A

I{4 I Zkg 35 / Zkg :9'29 :5 A

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bj ! Ir 4 5( $ Pj I{ ! Pm :0 $:5 ! P` 4 5

Bj 4 $ =5 a P` ! Pm 4 >>5 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


$ Pj / >2 $ I{ / >3 ! Pm />0 :0/2 :5/0 4 5>0 Pm 4 >5;5

Pm 4 ;> A

Us}}kgl Ynhsc fi Pm kg C~sn}kfg "k+

P` ! Pm 4 >>5 P` ! ;> >>5 4 5 P` 4 >; A


12/72


5;JC:< >0 x U n l c

Upf`hcd * 2 ?

P a 9 a : a &i}

2 9 0

Ipcc @fm{ Mknlpnd =2a 9a

P a

Dn Pn Bn 2 2

2 9 0

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn $=2 :< $ 9 4 5

P` ! Pm 4 >=: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


Dn ! Pn />9 " =2 ! :< + / 2 $ 9 / 04 5

5 4 Dn ! >=: />9 >5;9 $ >0

Dn 4 $>>25 A' i}

Bcgjc }bc mkpcj}kfg fi Dfdcg} N zbfshm `c }nacg nz pcycpzcm'


13/72


5;JC:< >: x U n l c

Upf`hcd * ; ?

P A &i}

N @

05

Ipcc @fm{ Mknlpnd

P/05 a

Bn

9'99 9'99 9'99

Pn Pn

Ufkg} Hfnm 4 >&0 / :< / 05 2;5 a

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn 2;5 ! P` 4 5

Pn ! P` 4 2;5 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


2;5 / 9'99 $ P` / 05 4 5 05 P` 4 3;0


14/72


5;JC:< >= x U n l c

Upf`hcd * >5? Ikgm Sgagf|g Pcnj}kfgz

P a 2a

0'3 a&i} = a&i}

N J M @

= 2 9

Ipcc @fm{ Mknlpnd >5 a P a :0 a 2a

Pn N C J M @

Dn Bn

0 0 = = 9

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn >5 $ ::; a

Dfdcg}(


Dn ! Pn / >2 >5/ >9 :< / >=:0 / >5 4 5 5 4 Dn ! 0350 $>


15/72


5;JC:< >3 x U n l c

Upf`hcd * >>?

2 A P A 05 a

"5'0!P + A

=

2 3 3 ; 3

Ipcc @fm{ Mknlpnd?

2a "P !5'0 +A P A 05a

J N @

Pj P`

Bj Pn B`

=

2

; 3 ; 3

:0

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

B` 4 5( 2 >95 :< ! Pn 05 ! P` 4 5

Pn ! P` 4 >


16/72


5;JC:< >9 x U n l c

Upf`hcd * >0?

" >5! P&0+ A&i}

05

\c `pcna }bkz }pknglhc kg}f }|f unp}z

UNP] ? >

">5!P&0+ A Ipcc @fm{ Mknlpnd

">&0 / >5 / Q>5!P&0T +

N

Pn

Y'M'H 4 >& 0 / >5 / 3='3 Bn

4 0


17/72


5;JC:< >< x U n l c

Unp} 0?

" >&0 / >5 / Q>5!P&0T +

@

P`

:':: :':: :'::

Y' M'H 4 >&0 / >5 / 3='3

4 0


18/72


5;JC:< >2 x U n l c

Upf`hcd * >:?

>5 a 05 a P a

>&0

N @ C J I M

2 = 9 = 3 3 = 9

Mkz}sp`kgl kg}f : unp}z

Unp} > >5 a Ipcc @fm{ Mknlpnd >5 a

2 = 9

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn $ Bc 4 5( Pn $>5 ! P` ! Pc 4 5

Bn 4 0 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


>5 / 2 $ P` / >0 Pc / >2 4 5 $>0 P` 4 $ 0'>0 />2 P` 4 :'93 A

Us}}kgl Ynhsc fi Pn kg C~sn}kfg "k+

Pn ! P` 4 >0'>0 Pn ! :'93 >0'>0 4 5 P` 4 2'=< A


19/72


5;JC:< >; x U n l c

Unp} 0 ? Ipcc @fm{ Mklpnd?

05 a 05 a

= 3 3

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bc $ Bi 4 5( Pc ! $05 !Pj $Pi 4 5

Bc 4


20/72


21/72


5;JC:< 0> x U n l c

Upf`hcd * >=?

5'9 a & i} 0'= a &i}

>9

K} kz mkz}sp`cm hkac }bn}

>9

Ipcc @fm{ Mknlpnd?

>='= a

>='=

N @

Bn 2 3'::

Pn P`

;'9 a


22/72


5;JC:< 00 x U n l c

Ufkg} Hfnm fi S'M'H 4 >9 / 5'9 ;'9 a

Ufkg} Hfnm fi Y'M'H 4 >&0 / >9 / " 0'=5'9 + >='= a

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn $ ;'9 >='= ! P` 4 5

Pn ! P` 4 0= $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


;'9 / 2 ! >='= / >5'99 $ P` / >9 4 5 5 4 3 P` P` 4 >=':; A


Pn ! P` 4 0= Pn ! >=':; 0= 4 5 Pc 4 ;'9> A


23/72


5;JC:< 0: x U n l c

Upf`hcd * >3 ?

P A 055 h` &i}

>55 h`&i}

N J M

= = = 2

Zfhykgl }bkz c~sn}kfg `{ unp}z '

Unp} >?

J M

9 0 =

Zfhs}kfg?

@{ zfhykgl }bc n`fyc iklspc?

Ikpz} jfgycp} }bc S'M'H ngm Y'M'H kg}f zkglhc ufkg} hfnmz'

Ifp S'M'H 4 >0 / >55 4 >055 a Ifp Y'M'H 4 >&0 / >0 / >55 4 955 a

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pj $>055 955 ! Pm 4 5

Pn ! P` 4 >255 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

955 a

>055 a


24/72


5;JC:< 0= x U n l c

Dfdcg}(


>055 / 9 ! 955 / 2 Pm / >0 4 5 5 4 0 Pm Pm 4 >555 A


Pj ! Pm 4 >255 Pn ! >555 >255 4 5 Pc 4 255 A

Unp} 0? P a 255 a

= = =

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn $ 2; 255 ! P` 4 5

Pn ! P` 4 22; $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(


2; / = ! 255 / 2P` / >0 4 5 5 4 :39 ! 9=55 $>0 P` P` 4 39: A


Pn ! P` 4 22; Pn ! 39: 22; 4 5 Pc 4 :09 A


25/72


5;JC:< 03 x U n l c

Zbcnp Ifpjc ngm @cgmkgl Dfdcg}

Zbcnp Ifpjc ?

]bc Zbcnp ifpjc n} n jpfzz$ zcj}kfgnh fi n `cnd kz }bc sg`nhngjcm ycp}kjnh ifpjc }f }bc

}klb} fp hci} fi }bc zcj}kfg'

@cgmkgl Dfdcg}?

]bc `cgmkgl dfdcg} n} n jpfzz$zcj}kfg fi n `cnd kz }bc nhlc`pnkj zsd fi

}bc dfdcg}z fi }bc ifpjcz }f }bc pklb} fp hci} fi }bc zcj}kfg'

FP

Nhlc`pnkj zsd fi }bc jhfja|kzc ngm ng}k$jhfja|kzc dfdcg} kz jnhhcm @cgmkgl Dfdcg}'

Zbcnp Ifpjc ) @cgmkgl Dfdcg} Mknlpnd?

]bc zbcnp ifpjc ngm `cgmkgl dfdcg} |khh `c mkiicpcg} n} mkiicpcg} jpfzzzcj}kfgz mcucgmkgl sufg }bc

hfnmkgl fg }bc `cnd' ]bc ynpkn}kfg kg }bc }bcpc jng `c zbf|g lpnubkjnhh{ `{ uhf} }bc Z'I ngm @'D

mknlpnd'

Zbcnp Ifpjc Mknlpnd ifp Mkiicpcg} ]{ucz fi Hfnmkgl?

JNZC$K ?

Ifp ng{ jfgjcg}pn}cm & Ufkg} Hfnm zbcnp ifpjc kz z}pnklb} hkgc'

JNZC$KK ?

Ifp S'M'H }bc zbcnp ifpjc mknlpnd |khh `c kgjhkgcm hkgc' Fp ]pknglshnp Ifpd


26/72


5;JC:< 09 x U n l c

JNZC $ KKK ?

Ifp S'Y'H sgkifpd ynp{kgl hfnm 05 Jspyc |khh `c }bcpc kg k}z mknlpnd

05

ZKLG JFGYCPZKFG ?

Ng su|npm ifpjc }f }bc pklb} fi n zcj}kfg jfg}pk`s}cz }f n Ufzk}kyc Zbcnpkgl

ifpjc kg su|npm

H'B'Z

!YC $YC

P'B'Z

!YC $YC


27/72


5;JC:< 0< x U n l c

@cgmkgl Dfdcg} Mknlpnd ifp Mkiicpcg} Hfnmz

JNZC$KIfp Jfgjcg}pn}cm Ifpjc " Ufkg} Hfnm + }bc `cgmkgl dfdcg} mknlpnd |khh `c kgjhkgcm hkgc'

JNZC$KK

Ifp SMH }bc zbnuc fi @'D mknlpnd |khh `c unpn`fhkj n} 05

jspyc

05

JNZC$KKK

]bc zbnuc ifp Y'M'H fi @'D |khh `c n} :5 jspyc'

:5

ZKLG JFGYCPZKFG? N jhfja|kzc dfdcg} }f }bc pklb} fi }bcg zcj}kfg fp ng ng}kjhfja|kzcdfdcg} }f }bc hci} fi }bc zcj}kfg jfg}pk`s}cz }f ufzk}kyc `cgmkgl dfdcg}'

H'B'Z? P'B'Z ?

!YC $YC $YC !YC

Ufzk}kyc @cgmkgl Dfdcg} kz nhzf agf|g nz Bfllkgl @cgmkgl Dfdcg} ngm Gcln}kyc @'D kz nhzf

agf|g nz znllkgl @'D


28/72


5;JC:< 02 x U n l c

Upf`hcd ? >

0'3 a >'3 a 0 a

5'9 d 5'9 d 5'9 d

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( $ 0'3 ! Pn >'3 $ 0 4 5

Pn 4 9 a $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(

!yc Jhfja|kzc D 4 5 n} ufkg} @

Dn ! Pn / 5'>2 $ 0'3 / 5' >0>'3 / 5'9 4 5 5 4 Dn ! >5'2 :5'; Dn 4 $ 9'; A

Bcgjc }bc mkpcj}kfg fi dfdcg} |khh `c pcycpzcm }f |bkjb |c bnyc }nacg '


29/72


5;JC:< 0; x U n l c

Zbcnp ifpjc > 0 :

0'3a >'3 a 0 a

N Pn J M @

Bn

5'9 d 5'9 d 5'9 d

R>

R0

R:

Zcj}kfg " >$>+

Y> 4 Pn ! 9 } $$$$$$$$$$$ "k+

Ki 4 5 E N ! 9 }

Ki 4 5'9 E " N$J+ ! 9 }

Zcj}kfg " 0$0+

Y0 4 Pn0'3 90'3 ! :'3 } $$$$$$$$$$$ "kk+

Ki 4 5'9 E J ! :'3 }

Ki 4 >'0 E " N $M + ! :'3 }

Zcj}kfg " :$:+

Y: 4 Pn 0'3>'3 9 0'3>'3 ! 0 } $$$$$$$$$$$ "kkk+

Ki 4 >'0 E M ! 0 }

Ki 4 >'2 E " N $ @ + ! :'3 }


30/72


5;JC:< :5 x U n l c

@cgmkgl Dfdcg} ?

> 0 :

0'3 a >'3 a 0 a

Dn Pn

5'3 d 5' 9 d 5'9 d

R>

R0

R:

Zcj}kfg " >$>+

@'D> 4 Pn / >! Dn 9 > 9'; $$$$$$$$$$$ "k+

Ki > 4 5 E N 9 " 5+ 9'; $ 9'; }'d

Zcj}kfg " 0$0+

@'D0 4 Pn / 0 ! Dn0'3 / " 0 5'9+ 9 0 9;0'3" 0 5'9 + 9 0 9';0'3 0 >'3"kk+

Ki 0 4 5'9 E J 9 / 5'9 9';0'3 / 5'9 ! >'3 $ :': }d

Zcj}kfg " :$:+

@'D: 4 Pn / : ! Dn0'3 / " : 5'9+ >'3 " : >'0+ 9 : 9;0'3" : 5'9 +>'3 " : >'0 + $$$$$$$$$$$ "kkk+

Ki : 4 >'0 E M 9 / >'0 9; 0'3 " >'0 5'9 + >'3 " >'0 >'0 + $ >'0 }'d

Ki : 4 >'2 E @ 5 }'d


31/72


5;JC:< :> x U n l c

Zbcnp ngm @cgmkgl Dfdcg} Mknlpnd

0'3 a >'3 a 0 a

5'9 d 5'9 d 5'9 d

! 9 } ! :'3} ! 0'> }

$9'; }d $:': }d $>'0 }d


32/72


5;JC:< :0 x U n l c

Upf`hcd ? 0

\ h`&i}

N @

H

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn \H 4 5

Pn 4 \H $$$$$$$$$$$$$$$$$$$$$$$$$$$$$"k+

Dfdcg}(

!yc Jhfja|kzc D 4 5 n} ufkg} @

Dg ! \ / H&0 5 4 Dn ! \H0& 0 Dn 4 $ \H

0& 0 A


33/72


5;JC:< :: x U n l c

Ipcc @fm{ Mknlpnd fi Zbcnp ifpjc

N Pn @

Bn

H

R>

Zcj}kfg " >$>+

Y> 4 Pn $ \ \H $ \ $$$$$$$$$$$ "k+

Ki 4 5 E N \H \ "5+ ! \H

Ki 4 H E " @ + \H \ "H+ 5

@cgmkgl Dfdcg}

N Pn @

Dn

H

R>

@'D> 4 Dn ! Pn / \ / &0 Dn ! Pn / \0 &0 $$$$$$$$$$$ "k+

Ki > 4 5 E N Dn ! 5 $ \H0

& 0 }'d

Ki > 4H E @ $ \H0 & 0 ! \H0 \H0&0 5 }'d


34/72


5;JC:< := x U n l c


\ h`&i}

N @

H

!\H

5

5

$\H0

&0 05


35/72


5;JC:< :3 x U n l c

Upf`hcd ? :

N jng}khcycp `cnd N@ 0d hfgl jnpp{kgl n sgkifpd mkz}sp`cm hfnm fi 0'3 Ag&d fycp n hcgl}b fi >'9 d ipkg

ipcc bngm ' mpn| }bc Z'I ngm @'D mknlpnd ifp }bc `cnd'

0'3 Ag&d

N @

5'= d >'9 d

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn = 4 5

Pn 4 = AG

Dfdcg}(


Dn 4 Dn ! = / >'9 & 0 5 4 Dn ! ='2 Dn 4 $ ='2 AG ' d


36/72


5;JC:< :9 x U n l c

Ipcc @fm{ Mknlpnd fi Zbcnp ifpjc

> 0

= Ag

N

@

Pn Bn

5'= d 5'2 d 5'2 d

R>

R0

Zcj}kfg " >$>+

Y> 4 Pn = AG $$$$$$$$$$$ "k+

Ki 4 5 E N = AG

Zcj}kfg " 0$0+

Y0 4 Pn 0'3 /" 0 5'= + Pn 0'3 0 ! >

Ki 0 4 5'= E J = 0'3 " 5'=+ ! > = AG $$$$$$$$$$$ "kk+

Ki 0 4 0 E " @ + = 0'3 "0+ ! > 5 $$$$$$$$$$$ "kkk+


37/72


5;JC:< :< x U n l c

@cgmkgl Dfdcg}

> 0

= Ag

N @

Pn

5'= d 5'2 d 5'2 d

Dn

R>

Zcj}kfg " >$>+

@'D> 4 Dn ! > / Pn $$$$$$$$$$$ "k+

Ki > 4 5 E N Dn ! 5 $ ='2 }'d

Zcj}kfg " 0$0+

@'D0 4 Pn / 0 ! Dn0'3 / " 05'=+ q " 0 5'=+&0 t Dn ! Pn 0 $ >'03 " 0 5'= +

0

$ ='2 ! = 0 $ >'03" 0 $ 5'= +0

Ki 0 4 5'= E J $ ='2 ! >'9 $ 5 $ :'0 AG' d

Ki 0 4 0 d E @ 5 AG' d


38/72


5;JC:< :2 x U n l c


0'3 Ag&d

N @

5'= d >'9 d

!= Ag ! = Ag 5

$='25 ag'd $:'0 Ag'd 5

0f


39/72


5;JC:< :; x U n l c

Upf`hcd ? =

N jng}khcycp `cnd fi >'2 d kz hfnmcm nz zbf|g kg iklspc ' Mpn| }bc zbcnp ifpjc ngm `cgmkgl dfdcg}

mknlpnd'

0 Ag >'3 Ag > AG

0'3 Ag&d

N @ J M

5': d 5'9 d 5':d 5'9 d

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn 0 >'3 " 5'2 / 5'9 + $> 4 5

Pn 4 =';2 AG

Dfdcg}(


Dn 4 Dn ! 0 / 5': ! >'3 / 5'; ! 5'=2 / >'3

5 4 Dn ! 5'9 ! >':3 ! 5''2

Dn 4 $ ='=< AG ' d


40/72


5;JC:< =5 x U n l c

Ipcc @fm{ mknlpnd ngm Zbcnp Ifpjc

> 0 : =

0 ag >'3 ag 5'=2 Ag > Ag

N J M @

Pn Bn

5': d 5'9 d 5': d 5': d 5': d

R>

R0

R:

R=

Zcj}kfg " >$>+

Y> 4 Pn ! =';2 AG $$$$$$$$$$$ "k+ Ki > 4 5 E N !=';2 AG

Zcj}kfg " 0$0+

Y0 4 Pn 0 =';2 0 !0';2 AG Ki 0 4 5': E @ ! 0';2 AG

Zcj}kfg " :$:+

Y: 4 Pn 0>'3 =';2 :'3 >'=2 AG Ki : 4 5'; E J ! >'=2 AG

Zcj}kfg " =$=+

Y= 4 Pn 0 >'35'2" 0 >'0 + >'=2 $ 5'2 " 0 >'0 +

Ki = 4 >'0 E M ! >'=2 AG

Ki = 4 >'2 E C >'=2 5'2 " >'2 >'0 + > AG


41/72


5;JC:< => x U n l c

@cgmkgl Dfdcg}

> 0 : =

0 ag >'3 ag 5'=2 Ag > Ag

Dn

N @

Pn

5': d 5'9 d 5': d 5': d 5': d

R>

R0

R:

R=

Zcj}kfg " >$>+

@'D> 4 Pn / > ! Dn $$$$$$$$$$$ "k+

Ki > 4 5 E N Dn ! 5 $='=< Ag'd

Zcj}kfg " 0$0+

@'D0 4 Pn / 0 ! Dn 0 / " 0 5': +

=';2 0 ='= $ 0 0 ! 5'9

Ki 0 4 5': E @ =';2 " 5':+ $ ='= 0 " 5':+ ! 5'9 $ 0';< AG' d


42/72


5;JC:< =0 x U n l c

Zcj}kfg " :$:+

@'D: 4 Pn / : ! Dn 0 / " : 5': + >'3 ": 5'; +

$='=< ! =';2 : $ 0 : ! 5'9 >'3 : !>':3

>'=2 : 0'30

Ki : 4 5'; E J >'=2 " 5'; + $ 0'30 $ > '>22 AG' d

Zcj}kfg " =$=+

@'D= 4 Pn / = ! Dn 0 / " = 5': + >'3 "= 5'; + 5'2 "= >'0+ "= $>'0 & 0+

$='=< ! =';2 : $ 0 : ! 5'9 >'3 : !>':3 5'= "= >'0+0

$ 0'30 ! >'=2 = 5'= "= >'0+0

Ki = 4 >'0 E M $0'30 ! >'=2 ">'0 + 5'= " >'0 >'0 +0 $ 5''2 >'0 +0 5 AG' d


43/72


5;JC:< =: x U n l c


0 Ag >'3 Ag > AG

0'3 Ag&d

N @ J M

5': d 5'9 d 5':d 5'9 d

!=';2 ag !0';2 ag !>'=2 ag !>'=2 ag >ag

$ ='=< ag'd $0';< ag'd $>'>2 ag'd $ 5'


44/72


5;JC:< == x U n l c

Upf`hcd ? 3

N 3d hfgl jng}khcycp `pcnd jnppkcz n ufkg} hfnm fi P } n} }bc ipcc bngm ngm n SMH fi " >! 5'0 P + } &d

fycp n hcgl}b fi :d ipfd }bc ipcc cgm ' Mpn| }bc zbcnp ifpjc ngm `cgmkgl dfdcg} mknlpnd'

P }

>2'2 }

N @ J

0d : d

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn 39'= 2; 4 5

Pn 4 >=3'= }

Dfdcg}(


5 4 Dn ! 39'= / :'3 !2;/ 3

5 4 Dn ! >;


45/72


5;JC:< =3 x U n l c

Ipcc @fm{ mknlpnd ngm Zbcnp ifpjc

> 0

">!5'0 P +/: P }

N @ J

Pn Bn

0 d >'3 d >'3 d

R>

R0

ZBCNP IFPJC

Zcj}kfg " >$>+

Y> 4 Pn ! >=3'= } $$$$$$$$$$$ "k+ Ki > 4 5 E N !>=3'= }

Zcj}kfg " 0$0+

Y0 4 Pn >2'2 "0 $0 + >=3'= >2'2 "0 $0 +

Ki 0 4 0 E @ >=3'= >2'2 " 0 $ 0 + ! >=3'= }

Ki 0 4 3 E J >=3'= >2'2 " 3 $ 0 + ! 2; }


46/72


5;JC:< =9 x U n l c

@cgmkgl Dfdcg} ?

> 0

">!5'0 P +/: P }

Dn

N @ J

Pn

0 d >'3 d >'3 d

R>

R0

Zcj}kfg " >$>+

@'D> 4 Pn / > ! Dn >=3 > $ 90='= $$$$$$$$$$$ "k+

Ki > 4 5 E N Dn ! 5 $ 9=0'= }'d

Zcj}kfg " 0$0+

@'D0 4 Pn / 0 ! Dn ! >2'2 / " 0 0 + " 0 0 & 0 +

>=3'= 0 90='= $ ;'= " 0 ! 0+0

Ki 0 4 0 E @ >=3'= / 0 9=0'= ;'= " 0$ 0 +0 $ :3>'9 }' d

Ki 0 4 3 E J >=3'= / 3 9=0'= ;'= " 3$ 0 +0 5 }' d


47/72


5;JC:< =< x U n l c

Zbcnp ngm @cgmkgl Dfdcg} Mknlpnd?

P }

>2'2 }

N @ J

0d : d

!>=3'= } !>=3'=} 2;}

5

$9=0'= }d 05

$:3>'9 }d


48/72


5;JC:< =2 x U n l c

Upf`hcd ? 9

N jng}khcycp `cnd fi >35 jd zung jnppkcz n hfnm fi 0} n} 95 jd ipfd }bc ikrcm cgm ( n hfnm fi >} n} }bc

ipcc cgm ngm n hfnm fi = }fg SMH fycp 95 jd ipfd 0 }fg hfnm }f|npmz }bc ipcc cgm ' Mpn| Z'I ngm @(D

mknlpnd

0 } > }

9 } &d

N @ J

5'9 d 5'9 d 5': d

Hfnm kg}cgzk}{ 4 Hfnm & Hcgl}b 4 = & 5'99 4 9 }&d

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn 0 "=+ $ > 4 5

Pn 4 < }

Dfdcg}(


5 4 Dn ! 0 / 5'99 ! = / 5';; ! > / >'3

5 4 Dn ! >':: ! :';; ! >'3

Dn 4 $ 9':: } ' d


49/72


5;JC:< =; x U n l c

Ipcc @fm{ mknlpnd ngm Zbcnp ifpjc

> 0

0 }

= } > }

N @ J

Pn Bn

5'9 d 5': d 5': d 5': d

R>

R0

Zcj}kfg " >$>+

Y> 4 Pn ! < } $$$$$$$$$$$ "k+ Ki > 4 5 E N ! < }

Zcj}kfg " 0$0+

Y0 4 Pn 9 " 0 5'99 + Ki 0 4 5'99 E @ ! < }

Zcj}kfg " :$:+

Y: 4 Pn 9 "0 5'99 + $ 0 }

Ki : 4 >':: E J ! > }

Ki : 4 >'3 E M ! > }


50/72


5;JC:< 35 x U n l c

@cgmkgl Dfdcg} ?

> 0

0 }

Dn = } > }

N @ J M

Pn

5'9 d 5': d 5': d 5': d

R>

R0

Zcj}kfg " >$>+

@'D> 4 Pn / > ! Dn $$$$$$$$$$$ "k+

Ki > 4 5 E N Dn ! 5 $ 9':: }'d

Zcj}kfg " 0$0+

@'D0 4 Pn / 0 ! Dn0 / " 0 5'9 + 9 / " 0 5'9 + " 0 5'9 +&0 < 0 9':: 0 "0 5'9 + : "0 $ 5'9 +

0

Ki 0 4 5'99 E J < / 5'99 9':: $ 0'>9 }' d

Zcj}kfg " :$:+

@'D: 4 Pn / : ! Dn0 / " : 5'9 + = / " : 5';+ < : 9':: 0 ": $ 5'9 + = ": 5'; +

Ki : 4 5'; E M < / 5'; 9': 0 " 5'; 5'9 + 5 $ 5'9 } ' d

Ki : 4 >'3 E @ < / >'3 9': 0 " >'3 5'9 + = " >'3 $ 5+ 5 } ' d


51/72


5;JC:< 3> x U n l c

@cgmkgl Dfdcg} ngm Zbcnp Mknlpnd

0 } > }

9 } &d

N @ J

5'9 d 5'9 d 5': d

! } >}

$9':> }'d $0>'9 }'d 05 $5'9 }'d 5


52/72


5;JC:< 30 x U n l c

]PSZZCZ


53/72


5;JC:< 3: x U n l c

Upf`hcd > ?

05 a >3 a

@ M

95f

955

95f

95f

N 3 3 J 3 3 C

>5 >5

Pn P`

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn 05 >3 ! Pc 4 5

Pn ! Pc 4 :3 $$$$$$$$$$$$$$$$$$$$$$ "k+

Dfdcg}(


5 4 05 / 3 ! >3 / >3 05 Pc 4 5

5 4 :03 05 Pc

Pc 4 >9' 03 a Pn 4 >2'


54/72


5;JC:< 3= x U n l c

@

N 95f J

Ofkg} N ? Pn 4 >2'5'20

C~sn}kfg "k+ |khh `c I nj 4 $ >5'20 " J +

05 a

@ M

N J

Ofkg} @ ?

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

I n` r I `m ! I j` r 4 5( I n` { 05 I j` { 4 5

>5'20 ! I j` r $ I `m $$$$$$$$$$$$$$$$$$$$$$$$"kk+ >2''03

I j` { 4 I j` Zkg 955 I j` 4 >'== " J + ( I j` r 4 I j` Jfz 95

5 I j`r 4 $ 5'

C~sn}kfg "kk + |khh `c >5'20 I `m5' I `m 4 $ >5'20 " J +


55/72


5;JC:< 33 x U n l c

@ M

J

Ofkg} J ? N 95f 95

fC

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

I `j r I nj $ I jm r $ I jc 4 5( $ I `j { $ I jm { 4 5

Ijc ! I jm r 4 $>5'> $$$$$$$$$$$$$$$$$$$$$$$$"kkk+ $>'03 I jm { 4 5 I jm { 4 $ >'03

I jm { 4 I jm Zkg 955 I jm 4 >'=: " ] + ( I j` r 4 I j` Jfz 95

5 I j` r 4 $5'

C~sn}kfg "kkk + |khh `c I jc 5' 4 $ >5'> I jc 4 $ ;':3 A

@ M

J

C

Ofkg} M ?

C~skhk`pksd(

!yc Ir 4 5(

I `m I jm r $ I mc r 4 5(

Imc r 4 $ ;':2'


56/72


5;JC:< 39 x U n l c

Upf`hcd * 0 ? 0 a

:a I : a

L C

J M

N :5f

95f

95f

95f

95f

:5f

@

: : :

Pn P`

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn 4 5( Pn : 0 : ! P` 4 5

Pn ! P` 4 2 $$$$$$$$$$$$$$$$$$$$$$ "k+

@{ nuuh{kgl Zkgc Hn|

Zkg 95 & NL 4 Zkg ;5 & : NL 4 : Zkg 95 NL 4 0'3;

Jfz :5 4 NJ & NL NJ 4 0'3;

Zkg 95 & : 4 Zkg 95 & JI JI 4 :

Jfz 95 4 JM & : JM 4 >'3

Dfdcg}(


5 4 : / NJ ! 0 / " : ! JM + ! : / " 9 ! M@ + P` / ;

5 4 02'=9 ; P`

P` 4 ='0< a Pn 4 = a


57/72


5;JC:< 3< x U n l c

L

N 95f J

Pn

Ofkg} N ?

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

$ I nl r ! I nj 4 5( Pn $ I nl { 4 5

I nl r 4 I nj $$$$$$$$$$$$$$$$$$$$$$$$"k+ I nl { 4 = a

I nl { 4 I nl Zkg 955 I nl 4 2 a " J + ( I nl r 4 I nl Jfz 95

5 I nlr 4 9';0 a

C~sn}kfg "k + |khh `c I nj 4 I nl r I nj 4 9';0 a " ] +

:a

I

L

N J

Bcpc ki |c zfhyc k} mkpcj}h{ k} |khh `c dfpc mkiicpcg} ifp sz }f lc} }bc nzzsdcz `cnjsnzc 0sgagf|g |khh jfdc kg cnjb c~sn}kfg fi c~skhk`pksd'

Zf |c pf}n}c k} nz


58/72


5;JC:< 32 x U n l c

{

:5 a

:55

N I r

L

C

Ofkg} L ?

Ir4 I Jfz 95 : Jfz 95 >'3 ( I{ 4 I Zkg 95 : Zkg 95 0'9

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

I nl ! I li I r 4 5( I lj $ I{ 4 5

I li 4 9'3 G " J + I lj 4 0'9 " J +

Gf}c mcgf}cz }

ynhscz |bkjb npc

nhpcnm{ agf|g }f


59/72


60/72


5;JC:< 95 x U n l c

Dc}bfm fi Zcj}kfgz

Upcykfszh{ |c bnyc z}smkcm dc}bfmz fi ofkg}z ifp ngnh{zkz fi }pszzcz

Kg }bkz dc}bfmz |c jng mkpcj}h{ ngnh{zkz n }pszz ifpjc |k}bfs} jnhjshn}kgl ipfd kgk}knh ufkg} '

Bcpc jfgmk}kfg fi dfdcg} kz szcm pn}bcp }bng jfgmk}kfg fi z}n}kz}kjz " crjcu} kg crjcu}kfgnh jnzcz +

Gccm }f js} n zcj}kfg |bcpc dnrkdsd sgagf|g dcd`cpz ifpjc `cjfdcz cpf fp jng `c gclhcj}cm'

UPFJCMSPC

Js} n zcj}kfg

Mpn| n ipcc `fm{ mknlpnd

Nzzsdc jfdupczzkfg ngm }cgzkfg

Nuuh{ jf$uhngcp nuuhkjn}kfgz fi ifpjcz ngm c~sn}kfg fi dfdcg} }f mc}cpdkgc dcd`cpz ifpjc


61/72


5;JC:< 9> x U n l c

Upf`hcd ? > M

d 4>&:

@ I

d4:&0

N >0 J >0 C >0 L >0 B

Pn >055 >055 >055 Pb

!yc I{ 4 5 Pn ! Pb >055 $>055>055 4 5 Pn ! Pb 4 :955$$$$ " k +

]nakgl dfdc} n} N'

Dn 4 5 >055 />0 ! >055 / 0= ! >055 / :9 $ Pb / =2 4 5 =2 Pb 4 29=55 Pb 4 >255 h`

M Pn 4 >255 h`

@

Pn4>255 J >055 C

]nac }bc ufkg} |bcpc dnrkdsd sgagf|gz jng `c gclhcj}cm'

]nakgl dfdcg} n} @' >255 / >0 I jc / 2 4 5 I jc 4 00Ijc / >0 ! >255 / 0= 4 5 I `c r4 0=55 h`z

I `c r 4 I`c / Jfz ::'9; I `c 4 022='=: " J +


62/72


5;JC:< 90 x U n l c

Upf`hcd * 0?

Pc~skpcm gccmcm ifpjcz

Pjc 4 6 ( P`m4 6 ( Pjm4 6 ( P li4 6

Ifp Ijc ( |c }nac dfdcg} n} M'

I jc / 05 ! Pn / =5 05 / 05 4 5

05 Ijc 4$ $:5 / =5 ! =55

Ijc 4 =5 a " J + fp Ijc 4 =5 a " ] +

Ifp I`m }nakgl dfdcg} n} J'

I`m / 05 ! :5 / 05 4 5

I`m 4 $ :5 " ] + fp :5 " J +

Ifp Ijm |c }nac dfdcg} n} @'

Ijm { / 05 ! Ijc / 05 ! :5 / 05 4 5 05 Ijm { 4 055 Ijm { 4 >5 a " J+

Ijm { 4 I jm / Zkg =3 >5 4 Ijm / Zkg =3 Ijm 4 >='>= a


63/72


64/72


5;JC:< 9= x U n l c

NPJBCZ


65/72


5;JC:< 93 x U n l c

Upf`hcd > ? : bkglc unpn`fhkj npjb fi 05 i} ngm z}ngmnpmkc fi 3 jnpkgl n jfgjcg}pn}c hfnm fi 05 akuz n}

9 ipfd }bc hci} zkmc zsuufp}' Mpn| }bc `cgmkgl dfdcg} mknlpnd ifp }bc npjb( ufzk}kfg ngm dnlgk}smc

fi dnrkdsd `cgmkgl dfdcg} ifp }bc npjb nhzf ikgm }bc ynhsc fi }bc pcnj}kfg ifpjcz

J

05 akuz

{j43

N @

05 i}

MN]N?

[j 4 3

U 4 05 akuz

H 4 05

@'D 4 6

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn $ B` 4 5( Yn ! Y` 4 05 $$$$$$ " k +

Bn 4 B`


05/ 9Y` / 05 4 5 Y` 4 9 akuz us}}kgl }bkz ynhsc kg c~"k+ Yn 4 >= akuz

P'B'Z


Y` / >5 ! B` / 3 4 5 B`4 >0 akuz nz B`4Bn ( Zf ( Bn 4 >0 akuz

PCZSH]NG]

Pn 4 Bn0

! Yn0

>2'== akuz

P`4 B`0

! Y`0

>:'= akuz


66/72


5;JC:< 99 x U n l c

@'D dnr " !yc +

Szkgl Ifpdshn

[ 4 = [j " H + & H0

[ 4 = / 3/ 9 " 05 9 + & "05+0

[ 4 = '0 z'i}

Yn / 9 Bn / [ 4 >= / 9>0 / ='0 ::' 9 a'i}

@'D dnr " $yc +

B` / [Y` / $$$$$$$$$$$$$$$ "kkk+

Szkgl Ifpdshn

[ 4 = [j " H + & H0

[ 4 = / 3 / " 05 + & H0

[ 4 $ 0

& 05$$$$"ky+ us}}kgl [ ynhsc kg c~sn}kfg "kkk+

>0 / " 0

& 05+9 /

>0 >0 0&059

9 >0 0&05

Mkiicpcg}kn}kgl |'p'}

4 3 u us}}kgl }bkz ynhsc kg c~ "ky+ [ 4 $ >3


67/72


5;JC:< 9< x U n l c

Upf`hcd 0 ? : bkglc unpn`fhkj npjb fi 05 d ngm z}ngmnpmkc fi = d jnpkgl n jfgjcg}pn}c S'M'H fi

0 }fg&d ipfd }bc hci} zkmc zsuufp} fycp }bc hcgl}b fi 2 d ' Mpn| }bc `cgmkgl dfdcg} mknlpnd ifp }bc

npjb( ufzk}kfg ngm dnlgk}smc fi dnrkdsd `cgmkgl dfdcg} ifp }bc npjb nhzf ikgm }bc ynhsc fi }bc

pcnj}kfg ifpjcz

J

N 2d @

MN]N? 05 d

[j 4 = d

U 4 0 }f & d

H 4 05 d

@'D 4 6

C~skhk`pksd(

!yc Ir 4 5( !yc I{ 4 5

Bn $ B` 4 5( Yn ! Y` 4 >9 $$$$$$ " k +

Bn 4 B`


>9 / =Y` / 05 4 5 Y` 4 :'0 } us}}kgl }bkz ynhsc kg c~"k+ Yn 4 >0'2 }

P'B'Z


Yn / >9 ! Bn / =>9 / 9 4 5 B`4 2 } nz B`4Bn ( Zf ( Bn 4 2 }

PCZSH]NG]

Pn 4 Bn0

! Yn0

>3'5;= }

P`4 B`0

! Y`0

2'9> }


68/72


5;JC:< 92 x U n l c

@'D dnr " !yc +

Yn / Bn / [0 / / &0 $$$$$$$$ "y+

Szkgl Ifpdshn

[ 4 = [j " H + & H0

[ 4 = / = / " 05 + & "05+0

[ 4 5'2 5'5= 0

Us}}kgl Ynhsc fi [ kg c~ " y+

@'D4 >0'2 / 2 / " 5'2 5'5= 0

+ $ 0

@'D 4 >0'2 9'= ! 5':0 0

0

@'D 4 9'= 5'92 0

$$$$ " yk+

Mkiicpcg}kn}kgl |'p'}'

5 4 9'=" 5'92 + " 0 +

4 ='< d ipfd hci} bngm zkmc zsuufp}

Us}}kgl ynhsc fi kg c~ " yk +

@'D 4 9'= / ='


69/72


70/72


5;JC:<


71/72


72/72


Upf`hcd 0 ? N jnz} kpfg : d kg hcgl}b |bcg bkglcm n} `f}b cgmz bnz n jpk}kjnh ukjahkgl hfnm fiU akhflpnd

|bcg }bc jfhsdg kz ikrcm n} `f}b }bc cgmz k}z jpk}kjnh hfnm pkzcz }f U ! :5(555 akhflpnd ' ki pn}kf fi

cr}cpgnh mkndc}cp kz >'03 ngm C kz c~snh }f > / >5 9 ' Mc}cpdkgc }bc cr}cpgnh ngm kg}cpgnh mkndc}cp fi

jfhsdg'

H 4 :555 jd ( mf&mk 4 >'03 mf 4 >'03 mk

Hfnm |bcg `f}b cgmz npc bkglcm ? U al

Hfnm |bcg `f}b cgmz npc ikrcm ? U ! :5(555

C 4 > / >59

Szkgl Cshcpz }bcfpcd |bcg `f}b cgmz npc bkglcm H 4 h

U 4 0

C K & H0

$$$$$$$$$$$$$$$$$$$$$$$$$$ " k +

Ikgmkgl kg}cpkn " k+ 4 k 4 & 9= " mf0 mk0 + Us}}kgl ynhsc fi mf

k4 & 9= " >'03 mk +0

$ " mk +0

k4 & 9= " 5'03 mk + = $$$$$$$$$$$$$$$$$$$$$$$$$$$$$ "kk+

us}}kgl ynhsc fi k kg c~sn}kfg "k+

U 4 0 C K & H 0 U 4 0C " & " 5'03 mk + = + & 9= / H 0 U 4 : "5'03 mk+ = $$$$$$$$$$$$$$$$$$$$$$$$$$ "kkk+

Szkgl Cshcpz }bcfpcd |bcg `f}b cgmz npc ikrcm' H 4 h & 0 :555 & 0 >355 jd

U ! :5( 555 4 = 0 C K & H 0

Us}}kgl ynhsc fi k

U ! :5 ( 555 4 = 0C q & " 5'03 mk + = t & 9= / H 0 : " mk + =

U ! :5(555 4 :

" mk +=

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ "ky+

Us}}kgl ynhsc fi U ipfd c~ "kkk+ kg}f c~ " ky+

:

"5 03 mk+=

! :5 555 4 :

" mk +=

theory of structures problems solved by dk mamonai

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