1

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7002

REINFORCED CONCRETE

PRINCIPLES

DR. A. PISANTY

FACULTY OF CIVIL ENGINEERING

TECHNION

Published by Dr. A. Pisanty All Rights Reserved to Dr. A. Pisanty

ISBN 965-555-098-2

Fourth Edition March 2007

. "

. " " . "

2-890-555-569 NBSI 7002

1

. 1

1.1 ,

. , , , , , ,

. , ,

-" " , . , ,

. . ,

, , .

, (. )

. . , ( )

) , , , (5002

. , , , , , .

, ) ' ' ) . (',

. ( ,

, . , ( ) /

82 , ( ) .

.

2

[ 83] (698 " ) , [(. 73] ) .

[ 93]

.

, , .

. ,

) ( ,

" . " " " , , 03 , .

, ( [ )1] , , ,

) , (

, , , ,, . '

, , , .

, ,

. ,

.

2.1

1.2.1 1.1 ) .

. ( . .

.( ) .

, (. a1.1 )

. , ,

, . ,

, b1.1( ) .

.

1.1

, .

. ( ) )

(. c1.1 .

4 3 , 62 "

.

3

4

2.2.1

, . ' 021 .' 001

) (. 503 ( 6 ) ' 051

( ") (. 21)' , [ . 4 ]BEC [ 8 ]2CE

, [ 4 ]BEC [ 04][ 8 ]2CE

051 [ 4] [ 04][ 8] ( . )'

.' 051 ( ' 001 )

[ 4] [04 ][8] . 82 . 82 82

[ 8] [ 1] [ 4]

[.4] [ 04][ 8] [ 53]

' 051 7 ' 001 ( . ) 82

' 001 [ 53] ' 051 21.1 - 61.1 7

. 82 [ 53] " ,

. : , 61.1-21.1 , "

. , .

' 001 [ 53] [04 ][8] , 7

5

[ 1] . [4] :(' )

'

' 051 ) ( 82

06 05 04 03 52 02

7 ' 001

6.35 3.44 1.53 1.62 7.12 2.71

' 82

4.34 0.53 9.82 3.12 4.71 8.31

' 001 .2.1 ' 051

3.2.1 (. 5.2.1 )

. .

"." , , %59 , ( elitcarf %5 ) %5

. kcf

(. ) .

( ) , " "

. , , - .

.

7 ' 001 : ( 2.2.1 )

; ( ) )

6

' , ( . ,

. ( ) : 811 "

. 6002 . [14 ] (: 3 )

3 + kcf m,cf: 3 kcf nim,cf:

,

8 811 " . . 01

. , 1-602 NE "

( 3 ( ) )[24 ]1002 :

4 + kcf m,cf: 4 kcf nim,cf:

( 51 ) :

84.1 + kcf m,cf: 4 kcf nim,cf:

, aPM 4 . . NE 602 -1: 1002

4.2.1 ,

. ) 82

, ( . .

.

7

. 7 ( ) .,

. , 82

. ,

.

1' 664 (1 " )

.1 , , , )

(.

1' jcf / kcf

09 82 41 7 3 01.1 00.1 08.0 56.0 04.0 052 " 50.1 00.1 58.0 07.0 54.0 003 " 51.1 00.1 57.0 55.0 03.0 052 "

2' [ 6] 5891 2 traP 0118SB .

: ', 051

- 2'

kcf )aPM(

2 7

3

6

21

52 42 32 22 5.31 02 02

13 03 92 5.72 5.61 52 52

73 63 53 33 02 03 03

05 5.74 5.54 44 82 04 04

06 5.75 5.55 45 63 05 05

" .

5.2.1 . 3.2.1

, mcf

. 2.1 , , ,

2.1

. ( n) .

%59 kcf %5

. :

536.1 - mcf = kcf( 1.2.1)

. 536.1 . . 82

. ,

. .

, , .

8

9

. ,

( )

. 82

6.2.1 ,

.

. .

4.2.1 .

. . ,

, 3'

02

52 03

04

05

06 06 05 04 03 52 02 ' 001 aPM **664 " 06 05 04 03 52 02 ' 051 aPM 0118SB*

06 05 04 03 52 02 ' 051 aPM BEC 2CE 05 04 23 52 02 61 aPM BEC 2CE

0417 0075 0754 0753 0682 0032 isp 813 ICA 26 25 24 33 62 12 ' 002 aPM *5401 NID

1002 - 3 ' * [.8 ]2CE ' 051

' 051 ** .2.1.1

c/c 7.2.1

. . 3.1

. : ,

3.1

. %04-53 . .

. c cf . uc ucf ( ) .

" : c/c 4.1

( ) . c. .

ucf - . . , uc

. . . 2.2 c

. 3 uc , ,

01

4.1

4.1 3.1 . . ,

dellortnoc noitamrofed dellortnoc daol .

. -

) . (

,[04] [ 8] c/c 5.1 -

. : CE2 5.1 , uc

05 04 03 52 02 61 ( ) - 8.2 - 0.3 - 2.3 - 3.3 - 4.3 - 5.3 3-01 uc [8 ]CE2

- 5.3 - 5.3 - 5.3 - 5.3 - 5.3 - 5.33-01 uc [04 ]CE2

11

5.1

: 5.1

) (( 2.2.1a)1k2

fk2

+ cc=

c/0.220

= ( 2.2.1b)0.2200 )c2.2.1(

fk1.1Ec

mc

=

) (

=+ E9.5f8 mckc13 )d2.2.1(

. 6.1 5.1 4.1 3.1 .

". " 6.1 . ,

. ,

(. hcsuR )

.

21

6.1

= f00011052 ckccc) ( (3.2.1)

, " " 6.1 ,1 664

. c/c 04 ) ( 3.2.1)

- 5.3 ( . 2

: . c/c .

. " " . .

: ( 6.1 ) .

. .

. ( )

.

31

8.2.1 .

- c/c

.

7.1

:(7.1 ) 3 , , : . tE - suludom tnegnat . 1

gt = cd / cd = tE( 4.2.1)

: , '

. suludom tnegnat laitini . 2

. (. 0) ' . sE( suludom tnaces) . 3

' :

)5.2.1( 1gt = sE

c/c : ' ,

.c/c

41

51

" .

, kcf 4.0 , : .( )

[ 4 ]09.C.M BEC : , 82 icE:

3/1]01/) 8 + kcf( [ 401 51.2 = icE( 6.2.1)

: , ( ) icE 58.0 = cE( 7.2.1)

' , aPM kcf , [ 4] :( )[1] 4

[1] [4 ]BEC 4' 05 04 03 02 61 BEC -

93 63 43 03 5.82 3-01 icE 33 13 92 62 42 3-01 cE

7.13 03 82 52 8.32 664 " [ 4] : 4'

.' 051 664 " ( 8.2.1) [ 8 ]2CE

: 5' ( " [ )8 ]2CE 301 3/1) 8 + kcf ( 5.9 = mcE( 8.2.1)

[1] [04 ][8 ]CE2 5' 05 04 03 52 02 61 2CE -

73 53 23 5.03 92 5.72 [8] 3-01 mcE 73 53 33 13 03 92 [04]3-01 mcE

2.53 4.33 5.03 1.92 8.72 5.62 [1 ]664 " 664 " [04] [8] :

( )' 051 .[04]

61

:Ec01 -3 [ 1 ]664 " - 6' 06 05 04 03 52 02 51 7.13 03 2.82 2.62 52 8.32 5.22

2.53 4.33 4.13 1.92 8.72 5.62 2.52 / .( 001 )' 051 [ 1] :

j ( 9.2.1) 82

. 82 . .

2/1)kcf / jcf( cE = jcE( 9.2.1)

9.2.1 .

, .

. .

, : , . ( )

1.9.2.1 ,

. , ( ).

)a 8.1 )b8.1 ( " 0001

, , . " ( . " 519

, .

8.1

ktcf .mtcf

( ) 2.9.2.1

elisnet gnittilps) ( htgnerts .

( . b 9.1 ) a ( a 9.1 )h a . a

. ( b01.2.1) ( a01.2.1)

: ( a01.2.1)

ah2P

= ps( b01.2.1 )

a ps22P

=

. . : 4 62 " .ps,tcf

71

9.1

3.9.2.1

) . ' mm 001 + d3 d (

. d3 3/L ( 01.1 )

01.1

81

. , ( 11.2.1) lf

/ 01.1 (. )

( 11.2.1)

d6M

3tlu

= lf

: 4 62 " .lf,tcf .

01.2.1 ,

. , .

. , .

. mcf

ktcf - kcf . mtcf [ 8] [04 ][4]

[ 1 ]664 " , [4] [ 8] .

.

[.1 ]664 " : [ 04] [ 8]

3( 21.2.1)2

= f0.03f mtckcf0.7f ktcmtc

. kcf

=( 31.2.1)( 41.2.1) . ps,tcf

= f0.9f mtctc,ps

91

) (( 51.2.1)b0.7 ) (

0.7b

11.5h/001 mtctc,lf=+ ff1.5h/001

. bh lf,tcf:

02

[. 1 ]664 " 7' [4] [04] [8]

)' 001 .(2.2.1

aPM [ 1 ]664 " - 7' 811 "

060504035202

6.353.441.531.627.122.71 kcf( 051 ) 4.340.539.823.124.718.31 ( )

56.272.249.136.1 4.1 2.1 ktcf 87.342.377.233.2 0.227.1 mtcf

11.2.1

(. a11.1 )' 05 ' 002 051 :

[ 42 ]refpuK . . 4-3 ,

.

b11.1 .

. 2 1 , .

: . - .

. %52 %71 - . - .

.

. 03

( ) .

11.1

.

21.2.1 . 52.0 51.0

. , , "

, .

31.2.1 ( sc)

. : ,

, . , .

12

.

. . .

cA u / cA 2 = oh . oh " " ) u

(. . .

(. ) . ,

[04 ][8 ]2CE [ 4 ]BEC [ 93] ( )

[ 1] . [ 4] [ 8]

:[(8] ) sc . 006 = oh 051 oh

05.0- 3-01 06.0- 3-01 %05 82.0- 3-01 - 33.0 3-01 %08

41.2.1 ( )

mcf 4.0 c . .

.

22

rc(t)c= ( 61.2.1)

- )t( - rc, - c: , ,

, ) : , , ( ,

( ) (. 41.2.1 " ) "

, ( ) , : .

32

( ) . )t( . .

, [ 1 ]664 " , [ 4] [ 8]

. [:8] )t(

%08 %05 oh oh

006 051 05 006 051 05 9.2 2.3 6.3 7.3 6.4 5.5 1

0.2 3.2 6.2 6.2 1.3 9.3 7

5.1 7.1 9.1 0.2 5.2 0.3 82

2.1 4.1 5.1 6.1 0.2 4.2 09

0.1 0.1 1.1 2.1 5.1 8.1 563

21.1' . le 0 .

1z . 1zc 1z 2z le .

2z . 1rc - )2zc . 3z .le

3z (. . 3rc - . le

( ) . 2zc

21.1

51.2.1 ( C051 )

. 5-01 = t

.

3.1

1.3.1 .

, %55.0 - %02.0 .

.

42

52

.

) . (

( ) .

, .

) , , . . ( 0021

. : ,

, ( ) , , ) ,

(. .

. .

) , , (

, .

: 2 , 1 : 6644 "

4 , ( 937 ") 3 , ( 398 ") ) 5 ( 085 ")

(. . ( 6002 ) aPM 004 aPM 005 . aPM 005

(. )

( ) :

62

, (. ) . ( 4 )

: .( 398 ") 2 6644 " - .( 937 " )3 6644 " - . " - w (.085 " )4 6644 "

.085 " -

2.3.1,

. 6644 " , s/s

, a31.1 , 2 . , ( )

(4 )3 6644 " , , b31.1

s/s . tf

.31.1

31.1 a31.1

. . ( %2 )

) , b31.1 2 , ( yf , , .

.b31.1

72

. , tf ,

82

,tgA ks : tf . tf , ku u

.tf s/s ktf ( kyf )

, (ryf/rtf)k .

. 41.1 . .

, y - ( . gninedrah niarts)

41.1

. tf ( tgA ) u ( y u) , .

.

) yf / tf ( ) (

) (.

.

) 51.1 s/s : ( : ksf ( citsalp yltcefrep-citsale raenil)

51.1

" . u tgA c/c "

retemosnetxe . ( ) .

( %05 - %04) ( ks) u ,u .

.

8' ( 398) "

2/6644

( 937) " 3/6644

(085) " 4/6644

/

/

005 004 042 )ksf=( yf - 025 - 055 005 003tf

%7 %21 %02 ks %5.2 %6-5 %9-8 u

50.1 52.1 02.1k)ryf/rtf(

92

03

. 8' ( )

[ 4 ]09 .C.M BEC :( aPM 005 )9

[ 4] 9' B ssalc leetS epyt leetS

ytilitcud wol A ssalc leetS ytilitcud lamron

S ssalc leetS ytilitcud hgih

%0.6 %0.5 %5.2 tgA 51.1 80.1 50.1 k)yf/tf(

, S [ 4] B A

eht rof leetS 08001 NE . etercnoc fo tnemecrofnier

(: ) 01 NE08001 01'

A ssalC B ssalC C ssalC 005 005 054 yF

50.1 80.1 51.1 k)ryf/rtf( %5.2 %0.5 %8 tgA

tgA . C S

tgA k)ryf/rtf( . k)ryf/rtf( ( ) tgA ,

". k)ryf/rtf( ,

,

08001 NE [ 4] . .

s/s [ 04 ]CE2 51.1 41.1 . 61.1

. gninedrah niarts - . y . ktf ksf

. " " . ku . sE / ksf 51.1 , ,

, 41.1 61.1 .

() .

. " " (%02 ) ku 9.0 = du [ 04]

ku .

52-02 . 02 -

61.1

3.3.1

: .aPM 000,002 = sE . . 5-01 = t , C002+ - 02- , .

13

..3.0 = . ) .

. , , , , , (

. , , ( ytilibadlew) .

( ) . .

, , ( %42.0 - %22.0 ) .%25.0 %05.0 ( qeC)

4.3.1 .

, : . . )

. ( 71.1 . - 71.1

1.17

23

33

. , ,

. , .

) sc / sh = Rf Rf NE (. sc sh,

: , Rf 08001

' 04 11 ' 5.01 9 ' 5.8 5.6 ' 6 5 650.0 250.0 540.0 930.0 Rf

. Rf

, . 2

1.2.

( , )

. ,

( ) . " "

, , .

" "

.

. )

. ( .

. .

[( 1] ) ". " , . %001

. ) ". "

. (

1

" "" " .

.

1.1.2

( ) .

( ) .

.

. ,

.

, , . ( ) -

.

(. )

: ) .

. ( . ( c/c) .

. 1 .( ) .

.

2

c . :

/1 = c c( 1.1.2) .

. s 1.2 .

: , ( )

T C . T .

, ,

. ( ) ,

.

1.2

) : ( ) T C ( 2.2

uT uC .

.

, ( uc) /

3

2.2

a . ) x

(. uT

. BEC 01, 5)

. , (' ) uC uC . z - ( uT

. uT .

: . s c s/ksf sA z = uT z = M( 2.1.2)

( x b ) :

c/kcf bx z = uC z = M( 3.1.2) ( )

. , c

. s .

4

2.1.2 ( )

4691 .C.M BEC .

: . . 1

, ,

. " . 2

, , , ,

. , , . 3

. , , , )

(. ', .

( ) . .

. .

. a3.2

. L . R . mL mR

. - kR: ( ) kL kR %5 %59

%5 kL. %59

5

3.2

. kR kL . R L

, . .

kR kL .

kR kL . , , ,

.

6

: R ( b3.2 ) kR kL

.dR dL dR dL kL L kR R L

. .

, R L R .

. , L

( mR mL) .

. , . a4.2 .

2R 1R : 1R. . b4.2 . 2R.

, 1L 2L .

. 1L 1R

1L 1R ,2L 2R 2R 1L 1R : .

.2L .

(. , ) ( ) .

. dohtem citsilibaborpimes

7

4.2

, , . R L )

, (. .

, [ 4 ].C.M BEC , [6 ]0118 SB , [ 5 ]813 ICA

. [04][ 8 ]2CE , . 5791

8

) (.

2.2 , ,

) . (

, . ,

,

, . ( )

. .

. , : .

(. ) , , ICA BEC, .

: ( ) : 5-01

0001/1 001/1 .

, , , ,

(. )

, . .

9

. .

.( )

( , ) , 05 , 5 :

. " . 005 - 001 ( )

.

3.2

(. ) , ( ) , "

. , , , ,

) ,

(. . , ,

. .

)etatS timiL etamitlU( - 1.3.2 : .' , , . (. ) . . . . . . .

01

, ) , (.

)etatS timiL ytilibaecivreS( 2.3.2 : , ( ' , ) .

( ) , .

. . , ( )

. , ,

. . .

3.3.2 .

. .' ,

4.3.2

. :

)

(. )

, ,

11

(. .

, .' ,

. ,

. ,

4.2

.

1.4.2

.

)

(.

: ( kF ) ( sdaol daed ,tnenamrep ) kG , , , , ,

) , (.

( sdaol desopmi ,evil ,elbairav ) kQ :

kQ , , : ,

, , . .

21

. ,

- . , ,

.

( sdaol latnedicca ) kA ( )

. "

.

kG .

, , kQ .

. ' .

214 " , . :

, .

) , ,

, 314 " . '( : 414 " .

. , .

.

31

.

0.1 0 [ 1 ]1 664 " . .

2.4.2 - dF

.f f kF = dF ( 1.4.2)

: ,

.' , f

fqm

i

m1 FGQ d,xamnimkfgkm

==+

. 0.1 0 f ,

( .0) ( 0.1) ) 4.1 f

( . ) 2.1 6.1 ( 2.1 )

(. [.1] 4.1

3.4.2

. , ,

( ) .

( 2.4.2)

41

. ( 2.4.2) , ,

. .

( 1.2) [ 1] [ 7] [ 6], [5] . ( 2.2)

, ) . ( )

. ( ,

) . 5.2' ( L ) . 4 (

: , nim,dF xam,dF kq 6.1 + kg 4.1 = xamdF( 3.4.2) kg 2.1 = nimdF (4.4.2)

5.2

:( 4.4.2) ( 3.4.2) 4.1 = xam g f 2.1 = nim g f:

6.1 = xam q f 0 = nim q f: :

kq 0.1 + kg 0.1 = xamdF( 5.4.2) kg 0.1 = nimdF ( 6.4.2)

: 0.1 = xam g f 0.1 = nim g f:

51

0.1 = xam q f 0 = nim q f:

.

: .

. . .

. . , ,

. 0 0.1

5.2

1.5.2 , 1 kcf

" " . %59

.ktcf :62 "

". , , , [14 ] : - 811

, ( ' 03 , 02) .

. ' 051 ) "

62 " 811 "[ 1] 664 " ( ' 021 ' 001 , ' 001

[ )1] [ 4] [ 8] (.2.2.1 1.2.1

61

[ 1 ]664 " , :(' 001 )

3/2kcf 861.0 = ktcf( 1.5.2)

ksf %5 ( , . 1

: . , ( )398 " ( )2 6644 "

( )937 " ( )3 6644 " (. )085 " ( )4 6644 "

. , , .

. ( ) ,

, . , ,

, . . .

, . . , . :

. . , ( )

, . .

.

2.5.2.

71

. m . : . dR kR

m / kR = dR( 2.5.2)

. . 51.1 = s

f (. )

ks

: dsf s / ksf = dsf( 3.5.2)

. c . 0.2 = c [ 1]

kcf dcf , .1.2 c / kcf = dcf( 4.5.2)

2.2.1 , 1 , ' 051 ' 001

kcf ) ' (:( 4.5.2)

( c= 2) 1.2

06 05 04 03 52 02

(2.2.1 -' 1 ) 6.35 3.44 1.53 1.62 7.12 2.71

9.62 1.22 5.71 0.31 8.01 6.8 dcf

22.2 [ 6] . c 5.1 [ 4] [ 04 ][8 ]2CE .

.

81

[ 04] .578.1 , 58.0 [ 4] [ 8] 58.0 0.1

(. 0118SB )12.2 . 0.2 = c

. 0.1 m .

, . " . " (. )

: c / ktcf = dtcf = ktcf( 6.5.2)

.[(8] [ 04] ) 5.1 = c

6.2

) d ( ,

:dR dR d( 1.6.2)

dS

( q g kQ kG ) ( :s c ksf kcf

d S dR( 2.6.2): ( 2.6.2)

f

m :

dM dM( 3.6.2)

91

f. dM m/1. dM:

: ", dM m/1. f dM

.',

7.2 ( 91 )

. :

) ( ) . (.

) . (.

: " ) .

(. . .

, . (. ) ,

.' , , [ 8] [ 4]

(. 0 = nim,f 0.1 = xam,f)

. 0.1 s = c =: resF [ 1]

( ) :

kG = nim, resF mkQ + kG = xam,resF

02

1.7.2 .

- ) (.

. ,

. ( ) , : [ 1 ]664 "

l 052/l( : ' , ) .

. 005/l: .005/l ,

.005/l:

2.7.2

(. )

, ) (.

3.0 , , [1 ]664 " ) '

. (. ")' 1.0

[.1] (. ,

. .

. %02

12

3.7.2 ,

(. )

.

. , 0001-005 /H

.

8.2

. , [1] , . :

. . .

. . . . .

.

, , . ,

.' ,

) , (

.

fo ksir eht gniziminim" ) " [. 1] (. espalloc evissergorp

22

( ) )

, , (.

, ,

, 0.1 = f : ( 0.2 ) 3.1 = c: , ( 6.1 - 4.1 )

(.51.1 ) 0.1 = s

9.2

. n

, , (, %02 %01 )

. . ( ' , , )nyd,f

. '

" "7221 " . .

32

. 3

" " . .

. ,

) (.

) . (

1.3 . 2

dS .

: , dR dS dR , dS.

, ( ecnatsiser) dR .

" , " . , , "

1002 2002 , .

". " .

, .

. : ( dR)

( dS)

1

. .8

. .

, , . '

melborp eulav negie .

)

, ,

(.

( )

. d ( . )

2.3 91

" " , .

(. )

. , : kR kS

(. kR) , , (kS) ( 8 )

) (.

2

.

.91

3

. 4

1.4 , )

, ( , )

. ( , ,

. , ,

. .

, . .

. .

2.4,

. , ( )

, ( )

. )

. 1.4 ( . /

.

1

, a1.4 .

. b1.4 .

1.4

- . .

,c1.4 " "

(. 2.2 ) c/ c

. e1.4 d1.4 ( . 2.2 ) f1.4

.

. ,

2

- . 6

. , ( )

(. )

3.4

c/ c . .

. :

) , (

. , -

. ( %01 %5)

. : . . .

.

.

. c , 2.4

2.4 c . 5.3

.

04

3

, . ". " aPM06 ,

, (. )aPM 05 - ) -5.3 -2

(. " " " "

2.4

3.4 .

(. )

3.4

4

.

. : ( )

5.3-

. sE / ksf ,

. ,

4.4( )

. d h a4.4 d . dM

. sA . b4.4 - cA

(. ) , .

c . c4.4 c/ c . s

. 3.4 s/ s 2.4' , C

, T , cf . d4.4

. s .

z.T = z.C = dM - , .T = C ,

5

4.4

, ". " 3 ( ) ,

( ) . .

, 2.4' . . 2.4 c c

3.4' . . 2- , c

. ksf

sE/ksf , ( dsf) .sE/dsf

. ,

, , )

(.

6

. : . ,

.

. %5.3- = c ,

( . 5.4 ) sE/ ksf = s )

(. , : x

d3.5%f/E

3.5%x

kss+ xam

( 1.4) =

apM 004 = ksf - . d 4636.0 = x:

, dcf db 2515.0 5.4 . dcf db 05.0

, d 05.0 ~ xamx 8.0 " " 5.4 . dcf db 05.0 = xamC

5.4

, . 8.0

7

dcf ]8[ 2CE 58.0 =

.

, :( )

kc,ebuc2

c

kc,lyc0.071dbf dc,xam

f = M0.05db0.57d

( 2.4)

8.0 .5.1 = c ', 051 [ 8] [ 4]

[ 1] , 664 " "

xamx , 5.4 ,

.dcf - xamx 8.0 0.2 = c

]8[ 2CE , , : ]4[ 0991 .C.M BEC

0.2/ kcf = dcf : . d 4,0 = xamx

(3.4)kc

kc220.061bdf dc,xam

f == M0.04bd(d0.2d)

( ),[ 8] ( ) ,

6.4

2.4

( ) dcf d4.0 = xamx :

( 4.4)dc

2 = M0.23bdf dc,xam

.

8

, 5.3 = sx > x

sE/ksf . xam,dcM < dcM xam

6.4

" " 5.4

". " . 2.4 c / c " "

)

. , c/ c

lyc,kcf )

) - (. " " (.

. " " , ,

, , , b7.4 . 7.4 ( )

/ ( . 2.4

,7 6 )3.4 , ,

, s/ s

9

7.4

,

c7.4

. sE/ksf

[(. 1],

.

gninedrah niarts ( . 41.1 hcnarb

. / .

.

. 01 5 ,

, , "" , .02

"" "

)

.

. 8.4 .

. 2- 5.3- . -B' . - A' :

01

B A . . , :

8.4

, )

,

( 2 1)

( 3 )BA ( . 'A - A )-2 ,

) 4 . D - D (. , . 5.3- (

( 5 ) .2- ,

. ,

. .8.4

[1 ]664 " 6.4

1.6.4

11

3.4 . 4.4

)

, ( 0

,

) c/ kcf = ( dcf (

) ,

(.8.4 .

) , 4.4 , 4636.0 d

d5. .

04 ( )

.

) , , ( :9.4

9.4

cA

. - S .

0

(.2db = 0S )

21

" " cA

. 4.4 :

) . h . dM (.

. sA

- 'cA x .

z 'cA

, 8.0 " , .dcf

. cS ( . 2db 23.0 )x5.0 d( x b = cS )

: 0S 46.0 cS( 5.4)

d4.0 = xamx x xamx

0S 46.0 = xam,cS( 6.4)

2.6.4 a9.4

sd ,

. 'sA , 'sd , d

.sA dM

( ) 'cA . x . 'cA .

'cA . dcf 'cA = C: . dcf

.sA

As'

31

( . 9.4 )dM . z

cc

'cA :cS

= SA'z( 7.4) :M

dcf 'cA = dcM( 8.4)

dM .sA

: , cS

( 01.4)

: A

dc

z C = z :

dcf 0S 46.0 = dcf xam,cS = xam,dcM ( 9.4)

,

dcf cS = dcM = dM s ( ( 01.4) cS )z

( 11.4)

dszf s

Md = A:

dsf sA = T = dcf 'cA = C( 21.4)

: dM = dcM ( 31.4)

As' : 'sA

.dM

xam,dcM > dM. xam,dcM 'sA .

41

01.4

' xam,cS dM

:dM xam,dcM > dM , xam,dcM dM = dM( 41.4)

( 01.4 ) , dM - : .

dsf 'cA = C = dsf 1sA = 1T( 51.4) :

'dsf 'sA = dsf 2sA = 2T( 61.4) ,

. , ' dsf = dsf ( 61.4) :

dsf 'sA = dsf 2sA = 2T( 71.4) , 'sd 'sA

'sd . , sA .

- dsf 2sA = 2T .T .2T + 1T = T

2T z 1T 2T 1T :)'sd d(

)'sd d( dsf 2sA = dM ( 81.4) : "

51

( 91.4)

sds

d

nimds

dc,xams

(dd')fM

zfM

=+ A

( 91.4) nimz (.nimz z cS )xam,cS

' : , ,

. ' , )'sd-d , 'sd 'sA

.sA ( 01.4 tca'sA , 'sA

: , = d,tcastcadss MA'f(dd')( 02.4)

dM ( 02.4) tca, dM :- tca,dcM

dM = tca,dcM tca,dM( 12.4) , tca,dcM z , :cS z

dcf cS = tca,dcM( 22.4) , )'sd-d( z d59.0 z

. :

( 32.4)

tcads

dc,tcazf ss

M =+ AA'

'sA , . sA ,

. dM

61

: dsf tca,sA = dsf tca'sA + C( 42.4)

:, , dsf )'sA sA( = dcf 'cA = C( 52.4)

. tcaz tca 'cA : . d59.0 )'sd d(

tcaz dcf 'cA + )'sd d( dsf 'sA = dM( 62.4) )'sd d( d59.0 , tcaz,

: , ( 52.4) 'cA , xamz dcf 'cA + )'sd d( dsf 'sA = dM( ( 72.4)

, . ; . :

. . 8.4 ,

3.6.4

h - b . 2.6.4 - 1.6.4 (:11.4' ) d

2d b 05.0 = 0S( 82.4) 0S 46.0 2d b ) - 1 ( = ) x - d( x b = cS( 92.4)

04.0 = xam d/x = : . - dcM

= dcM dcf 2d b ) - 1 ( ( 03.4) : -

1/2

dc2

dc

bdf 112M

( 13.4) =

71

h b ( )dsf( ) dcf .dM - (. )'sd - sd -

1/2

dc2

d

bdf 112M

=

) (

( 23.4)

. d 4.0 ( 33.4)

ds

d10.5df s

= AM

) (

: d 4.0 > xam,dcM dM = dM ( 43.4)

: ( 53.4)

sds

ddd'f s

= A'M

:

( 63.4)

ds

dc,xam0.8df ss

M =+ AA'

( sA, 'sA) , ( h ,b ,sd ,'sd ,d )

: ( dcf , dsf) : 'sA

= dsdss MA'f(dd')( 73.4) :

+= sds CA'fT( 83.4)

+= dbfA'fAf dcsdssds : xam

dcsdss MMM0.23dbfA'f(dd') ( 93.4)2

=+=+ ddc,xamd

81

: xam < =+ dddc MMdbfz( 04.4)

d )5.0 1( = z d/'sd2 ( 04.4) .)'sd-d( = z d/'sd2 <

.'sA 'sA

()xam xam,sA : . (nim ) nim,sA

7.4 .

. , , .

.

. ,

.

) . (.7.91

1.7.4 . , ,

) (

. mtcf, -

. mtcf . ,

: "

91

hbfAfd6mtcs,nimks M1

2( 14.4) == r

nim 9.0 ~ h/d d b nim = nim,sA : ( 14.4)

( 24.4)

ks

2mtc

ks

mtcf nim

(h/d)0.02f61

f = f

. nim 1.4 , [1]

, hb nim . tb d tb

,

[ 1] . : ,

. %001 %05 . [ 6]

nim - 1.4 06 05 04 03 52 02

1.4 5.3 0.3 6.2 2.2 9.1 mtcf

apM 032 = ksf 6300.0 0300.0 6200.0 3200.0 9100.0 7100.0

apM 004 = ksf

1200.0 8100.0 5100.0 3100.0 1100.0 0100.0

apM 005 = ksf 6100.0 4100.0 2100.0 0100.0

: [ 1 ]664 " nim 2100.0 = nim - 5100.0 = nim - 6200.0 = nim -

02

2.7.4 .

( ) ( . )

. [ 5[ ]7[ ]6[ ]8[ ]4] . xam = 40.0

[ .1 ]664 " 40.0 = xam.

. ,

, [ 8[ ]7[ ]6[ ]5[ ]4] , . - 80.0

, , 40.0 .

.40.0

, .

.

.

) "( " ,

.

3.7.4 ,

. 'sA

12

. .

: [ 1 ]664 "

dsf xam

'0.510053 ( 52 02)

[ 1 ]664 " , . xam,dcM dM:

, : .

, .

8.4 ( )

, , x , . d 2/x d = z , , z

. 11.4 xamz z ) 6.4 4.4

, , ( " " , . ,

a11.4 . (. " )" 4.0 = xam = -

, , . d8.0 57.0d ( 3.4 " ) "

. (. b11.4 )

22

11.4

( )

.

" c c11.4( ) "

d4.0 , d31.0

" " )d79.0 , . d78.0. 511.1 ~ 78.0/79.0 , (d11.4 -

.%51 . 'sA

. )'sd d( ( dsf 'sA) .

, , .

- ( d09.0 ) d59.0 )'sd d( , , ,

(. d59.0 , d09.0 . 'sA d59.0 )'sd-d( d59.0 [ 1 ]664 "

9.4

32

1.9.4, ( )

)T( , ( ) . )(

( .21.4 ) ,

) (.

21.4

. )( , ,

, , . .

( ) .

fb: ( 31.4 ) 'sd sd, h, ft, wb,

)'sA( )sA( - . ,

. ( ) ,

( . )

42

31.4

.h/wb , ( 1.6.4 )

( :5.4) 0S 46.0 xam,cS( 5.4)

cS 0S , .

, , :

d4.0 = xamx (. 41.4 )

( .5.4) , d4.0 < xamx , , ,

, ( )

( .5.4 )

2.9.4 ,

: , , ,

52

, , .

. . 31.4

. . dcf , 0S,

, wb :

2 ( 34.4)=+ S(bb)t(d0.5t)0.5bd 0fwffw

M0.46Sf dc,xam0dc

: =( 44.4)

, xam,dcM ( 44.4) ( 44.4) ( 34.4) sA

. ,

. z d)5.0-1( )z ( d4.0 )

( :41.4 ) , fcS ( 54.4)

:sA = fcfff Sbt(d0.5t)( 54.4)

)xam,cS , 0S .( 0S 46.0 = xam,cS -( 5.4)

xamx: (. b41.4 ) xamx ( a41.4 ) ) ( )xamx x

(.'sA

62

41.4

: ( )ft xamx fcS xam,cS . 1

, , .h / fb

ft x xamx x dM xam,dcM dcf fcS dM . 2 x

.h / fb xamx , fcS xam,cS xam,dcM > dM . 3

.'sA h / fb , , ( h/ fb) "

. a41.4 'sA - dcf fcS x

'sA fcS > xam,cS xam,dcM > dM . 5 ( .b41.4 )ft > xamx ,

dcf

72

) . x . 0 x

(441.a ) x : ft < x

12

dc2

f

d

bdf112M

( 64.4) =

: . ft d = x: xam,cS )x 5.0 d( x fb = cS( 74.4)

( ft x) x, : sA . d ) 5.0 = 1 ( = z:

( 84.4)

ds

d(10.5)df s

= AM

ft xamx fcS < xam,cS xam,dcM > dM : sA

( 94.4)

xamds

dc,xam

ds'

s

ddc,xam(d0,5x)f s

M(dd)f

MM+ A

=

xam,dcM dM , 'sA, )'sd d( dsf 'sA = dM: ,

.dM - dM = dcM d/'sd2 < . dcM , dM 'sA

.

( 441.b ) x ft x

(. d/ ft < ( 64.4) )

82

)ft > x ( xam,dcM < dcM ) dcf fcS > dcM (.b41.4

, a51.4 , 51.4 (.c51.4 )wb ( b51.4 )wb fb :

51.4

sA ft )wb fb( :dfM

= dffwfdcf M(bb)tf(d0.5t)( 05.4) sA ( x wb)

: dwM

== Mbxfd0.5x(10.5)bdf dwwdcwww2dc ) (MMM dcdfdw

( 15.4)

: =+ ( 25.4)

) xam , xam xamx xam

(.. , xamx ft > x

:

92

( 35.4) =+= S(bb)t(d0.5t)bx(d0.5x)0.46S c,xamfwffwxamxam0

, ft < xamx ( 35.4) . xamx ( 35.4) - )fcS xam,cS , ft > xamx

( . ft xamx : xamx

] [ds

dcfwfw

'f ss

( 45.4) =++ AA(bb)tbxf

:

( 55.4)

wds

dw

fds

'df(10.5)df ss

M(d0.5t)f

M=++ AA

01.4 )

, ( .

, .

5 h 61.4 )2sA 1sA( )'3sA '2sA '1sA ( )

( . .

[ 1 ]1 664 " , .

) . )/ (

b/h (.

. b/h

03

s/ s, c/ c . 5.4 ,

. ' , .

61.4

. 0 ( ) ,

61.4 . 0 , . 1sA '1sA

. ) .

(

. , , .

13

'

1.4 002 ' 004

( . ) 02 . ' 006 . ' . mm 06 = sd

) (.

: mm 045 = d mm 06 = sd mm 006 = h: ,

mm 002 = bb mm 004 = tb : 0S - . mm 022

3mm 601 75.94 = 045 3/2 045 09 5.0 2 + 2045 022 5.0 = 0S 3mm 601 527.13 = 0S 46.0 = xam,cS:

: mNk 372 = mmN 6.8 601 527.13 = dcf xam,cS = xam,dcM

.sA

2.4 mm 003= b: . 02

aPM 6.8 = dcf . mm 035 = d mm 07 = sd mm 006 = h .aPM 053 = dsf

23

. : . .

?mNk 002 = dM

:

mNk 232 = mmN 701 91.32 = 6.8 2035 003 23.0 = dcf 2d b 23.0 = xam,dcM2

0.080.350.533651mm s: == A232

: mNk 002 = dM

0.330030358.6

1120020112

2

6

=

(10.50.33)0.350.531921mm s2 = == A002

3.4 ( 03 )

. 2 b d . mNk 051 = dM .mm 06 = sd

: apM 7.21 = dcf apM 053 = dsf mm 06 = sd 2 = b/d:

0.31 2d d 5.0 23.0 = xam,dcM: xam,dcM d .mm 084 = h mm 012 = b mm 024 ~ mm 414 = d

mNk 1.451 = 6-01 0.31 2024 012 23.0 = xam,dcM: 2:

0.80.240.536721mm s == A051.0

33

4.4 . 03 . mm 054/002

( . ) ( ) ( ) mm 04 = 'sd . mNk 002 = dM

.mm 06 = sd

:

( ) aPM 053 = dsf aPM 0.31 = dcf . mm002 = b mm 093 = d: . mNk 002 = dM( )aPM 002 = dsf

dM < mNk 5.621 = 6-01 0.31 2093 002 23.0 = xam,dcM mNk 5.37 = 5.621 002 = xam,dcM dM = dM

2(0.930.40)0.021501mm s

== A'37.5:

: 2

0.080.930.5300685118571mm s621.5

(0.930.40)0.53=+=+= A37.5

5.4 . 03 . mm 005/052

.mm 04 = 'sd mm 41 2 .mm 06 = sd ( . ) . mNk 022 = dM

: mm 052 = b aPM 0.31 = dcf( )aPM 053 = dsf( )aPM 002 = dsf:

43

.2mm 003 = 'sA . mm 044 = d mNk 0.42 = )40.0 44.0( 02.0 003 = )'sd d( dsf 'sA = dM

mNk 691 = 42 022 = dM - dM = dcM

0.0405204431.0

1126910112

2

6

=

=

: 2mm 6081 = sA 0.31 044 052 04.0 + 002 003 = 053 sA

6.4 01 2 03 . mm 004/002

07 = dM . (.) . mm 05 = 'sd = sd . mNk

: mm 053 = d aPM 0.31 = dcf mm 002 = b mm 004 = h:

.mNk 07 = dM( )aPM 002 = dsf ( )aPM 053 = dsf

53

mNk 4.9 = )50.0 53.0( 02.0 651 = )sd-d( dsf 'sA = dM mNk 6.06 = 4.9 0.07 = dM - dM = dcM

0.2200205331.0

11206.60112

2

6

=

0.92 ==>: = 053205

d2d

' s

: 'sA

0.5200205331.0

11207.00112

2

6

=

mNk 07 = dcM = dM =

2(10.50.52)0.530.53356mm s

== A07

'

7.4 mm051 = ft: . 02

.mm 052 = wb mm 005 = h mm 05 = 'sd = sd mm 008 = fb (. ) . mNk 002 = dM

:

0.610080548.6

1120020112

2

6

=

. ft < x =

. ft < mm 27 = 054 61.0 = x: mm 054 = d ( : xam,dcM < dM )xamx < x

63

3mm 601 52.65 = 2003 055 5.0 2054 008 5.0 = 0S : xamx 3mm 601 0.63 = 0S 46.0 = xam,cS

mm 511 = xamx 3mm 601 0.63 = xam,cS = )xamx 5.0 054( xamx 008 xamx < x ft < xamx

:h / fb 2

(10.50.61)0.540.530831mm s== A002

8.4 . 03 , ,

mm06= sd mm 007 = h mm 053 = wb mm 056 = fb mm 052 = ft: mNk 0021 = dM

. ( )

: ? xam,dcM > dM

3mm 601 503.011 = 2093 003 5.0 2046 056 5.0 = 0S mNk 8.719 = dcf xam,cS = xam,dcM 3mm 601 06.07 = 0S 46.0 = xam,cS

.'sA xam,dcM > dM :ft xamx

mm 202 = xamx 3mm 601 06.07 = )xamx 5.0 046( xamx 056 = fcS 613.0 = 046/202 = xam ft < xamx

73

2.282 = 8.7190021= dM: mNk

2(0.460.50)0.537631mm s

== A'282.2

2(10.50.613)0.460.53763166843326mm s

=+=+= A7631719.8

9.4 . 03

.mNk 0011 = dM

:

: xam,dcM > dM = 2084 004 5.0 2036 057 5.0 = 0S 3mm 601 67.201

mNk 4.558 = dcf xam,cS = xam,dcM 3mm 601 08.56 = 0S 46.0 = xam,cS :ft xamx . 'sA xam,dcM > dM

xam,cS < 3mm 601 44.26 = )57 - 036( 051 057 = )ft 5.0 d( ft fb = fcS : xamx ft > xamx

= )xamx 5.0 - d( xamx wb + )ft5.0 - d( ft )wb - fb( = 601 08.56 = xam,cS )xamx 5.0 - 036( xamx 053 + )57 036( 051 )053 057( =

dfM dwM mm 071 = xamx = 6-01 0.31 )071 5.0 036( 071 053 = dwM:

mNk 6.124

83

mNk 8.334 = 6.124 4.558 = dwM xam,dcM = dfM 2:

(0.360.50)0.535021mm s= A'0011558.4

=

] [

:

20534465mm s

=++= A5021(057053)05105307131.0

2(0.360.50.71)0.538465mm s

124.6(0.360.570)0.53

=++= A5021334.8

01.4 . - 03 .

. . mNk 005 = dM

:

: 'sA 3mm 601 45.27 = 2024 005 5.0 2045 008 5.0 = 0S

. mNk 5.306 = dcf 0S 46.0 = xam,dcM :ft xamx

3mm 601 80.64 = )06 045( 021 008 = )ft 5.0 d( ft fb = fcS .ft > xamx fcS > 3mm 601 34.64 = 0S 46.0 = xam,cS

0.8100804531.0

1120050112

2

6

=

: ft < x =

93

: ft < mm 2.79 = 045 81.0 = x2

(10.50.81)0.450.537092mm s== A005

11.4 .

( ) ( z ) - y , z

( 71.4 ) . x zy . a71.4 - ( y )ydM ( x )xdM, , - ) ( ydM )xdM ,

. ( b71.4 . zy

71.4

. , , , , , ,

04

. .

. :

, , ( ) : .

, ) "(."

, , , , ( a71.4) ydM xdM ,

, ,

. . ,

. (. 5 )

- , , . . , ,

, , ( )

. [(1] )

y x , h b . - ) , 81.4 ,

ydM x xdM . - yd y ( b = sd + xd ) xd x . y

( .h = sd + yd)

, , , " " " "

:

14

81.4

:

( 65.4)

x

yd

y

xd

dM

d) M

x

y

yd

xd

dd

M ( M

:qe,xdM - " "

( 75.4)

x

yd xd,qexdyd

d =+ MM0.57M

. x ( 65.4) : , (65.4)

( 85.4)

x

yd

y

xd

dM

d ) < M

x

y

yd

xd

dd

M (< M

: qe,ydM - " " ( 95.4)

y

xd yd,qeydxd

=+ MM0.57Md

( 85.4) ( 75.4) , -

24

" ) " (.

: 03 , a91.4 ', 005/004 mNk 001 = ydM mNk 002 = xdM .

, sd, . . . ' 04

91.4

: 534.0 = 064/002 = yd / xdM mm 064 = yd mm 063 = xd

: , (65.4) 872.0 = xd/ydM . mNk 692 = 063/064 001 57.0 + 002 = qe,xdM

) . dM + dcM = dM - , x , (xdM

. mm 4102 = )53.0 24.0(/692 = sA: , sd - yd b91.4 223+ 522 ,

34

RITA nmuloC : . - : ' 52 8

( ) .

21.4

1.21.4,

[(. 1] ) [. 1]

. 6 ,

, . ,

. ,

( . b02.4- a02.4 ) , (c02.4 )

. ) , .

(. [ 1 ]1 664 "

[.8] [ 4] [ 1] sd D , 6

, :

=+ M0.562DAf0.01Af dsdsgdc ) (( 06.4) (. ) gA:

44

, D 1.0 = sd: , . gA30.0 < sA < gA 400.0 ' 052 ( 06.4) . b02.4 a02.4

02.4

- , .

: . 61 6 6 03

. mm 04 = sd . mm 004=D ?

: 2mm 006521 = gA . =sA 2mm 0021

' 761 . 6900.0 = gA/sA : .

54

mNk 38.16 = 6-01 ) 31 006521 01.0 + 053 0021( 004 562.0 = dM RITA nmuloC :

. ' 61 6 " 0121 - . - ,

2.21.4 ,

(.12.4 ) .

12.4

- sA: ) . gA 10.0 sA:

gA . gA300.0 ( .

: . dsf sD sA 57.0 = dM( 16.4)

sd 2 - D = sD: sD57.0 ( 16.4)

. .

64

: . 223 03 mm 004

(. 22.4 ) 016 . ' 05

: mNk 8.98 = 6-01 )05 2 - 004( 053 083 3 57.0 = dM

22.4

1.43

( 7 6 ) ( 5.3 )

(. 02 ) , , . , ,

. 2.4 c/c c :

. (52.4 ) uc .

. 7 ,

74

,(tnemenifnoc) ,

( ) .

(. ) 2

(:26.4) kcf 32f 2k3kwkc

(26.4) 1 . w

( ) w .2.4 42.4 32.4

32.4

( ) w D )32.4 .

: w ( s d ( 36.4)

dc

sds

dc2

sdsf w

fd4A

14df == dAf

84

. , .

n . s (42.4 ) ib .s

42.4

(46.4) 2

2i

d n =1n(b6)

. ' - n: .' 002 , ib 42.4 32.4 d

)ds

2 (56.4) = s(11

(d5.0 ' 002 ) s

: 66.4 26.4

2f 2k3kwnskc (66.4) 1

s 2.4 . 4 52.4 : w n

94

w n s - 2.4 d C B A 338.0 877.0 766.0 333.0 n

1s(/2d)1s(/2d) 1s(/2d) 1s(/2d) s

ds 21A

ds 9.33A

ds 6.38A

ds 4A

ds

dcf w

f

sA . 42.4 32.4 s d: ' 6

: c,kcf

:0.50f 2kkc ( 76.4)

=+ f1.0f5.0 kc,ckc2k

: >0.50f 2kkc ( 86.4)

=+ f1.521f2.5 kc,ckc2k :52.4 2.4 c/c

"( " )2.4 52.4 . 3 2 ,

: c.uc 5.3 c,cc 2 [ :4]

2

kc

3kc,cf) cc,c

f ( 96.4) = 201(

05

52.4

( 07.4)

kc

32kf uc,c

=+ 3.5010.2

, ,

. , 0.2 = c -

. 664 " , .

.07.4 96.4

15

. 5

1.5 .

. ,

, , (.5.5 )

dN dM 1.5' )

, (. , sA ,

, d h . sA sA sA

. sd sd ,

, 1.5' . ,

, .

6.1 1.5 . 51.1

2 6.1 . . ( ) 5.3 " "

01 61.1 . " "

, , ,

.

1

1.5

- 1.5 AC B' C' .

. , AB - 2

'A B . A'A )A'A

+ (.01 DC 4 AC 3 ,

DC . : .

2 5.3 DC . EF , ""

5.3 : EF' EF DC 2 " " . 5.5/5.2 G

1.5' ( 6.1 " ) " ,

(. 51.1 )

2

.

, . 2.5 , margaiD noitcaretnI

) ( ) , (. ) (

2.5

, 2.5 0' .

. .

2.5 1.5 ,

. :

, , ( 1.5 )

3

. , " " , ,

" " . " " .

2.5 , ,

, , "" .

- . ( 6.1 " )"

)41.1 , ( . - gninedrah niarts

51.1 , , .

. [.82] [ 9] ,

. , . , ,

. , .

. d (. ytilibitapmoc niarts)

, : . . '

.1.5

[. 9] : dM 53 = 'sd = sd' ' 004/002

. 03 . dN

4

. 1.5 [. 1] ,

, )

(.

1.5 sA )( s )( c :

)2mm( sA )2mm(

dN )Nk(

dM )mNk(

54.81 0 331 0 400.2+ 204.0 -

0.452 0 6432 5901 557.1+ 596.1- 001 0 668 *292 497.1+ 520.1-

06 006 *292 *292 941.0+ 498.0- 001 002 036 *292 536.4+ 988.1- 001 033 734 005 618.1+ 543.1- 001 033 805 *292 876.1+ 224.1-

.%4.0 ( ) -*

3.5

1.3.5 )

( . ( ) .

. (. )

: . etamitlu

5

" " .

) . ( 5.5

.

. . (. " )" ,

.

. , y

. h = y + y: . y - .

( . a3.5 ) ,

, . b3.5 , ,

.

3.5

6

. .

, . . ( , )

. 5-2

2.3.5

de dN a4.5

dN . sA sA . ) de dN = ( dM

: .

. sA :dsM

] )sd y( + de [ dN = dsM( 1.5) :

( ) . . dsM dN sA

. .

. xam,dcM dsM . xam,dcM dsM = dM( 2.5)

snimsds

d(dd')fA' s

= A'M( 3.5)

:

s,nimds

d

nimds

dc,xamfA ss

Nzf

M ( 4.5) =+ AA'

.xam,dcM nimz

7

4.5

xam,dcM dsM . : , nimsA

)sd d ( dsf nimsA = dM( 5.5) :

dM dsM = dcM( 6.5) :sA z dcM

s,nimds

d

ds

dcfA ssnim

Nzf

( 7.5) =+ AA'M

d/sd2 < . z , . . sd d = z . :

. dsM = dcM . nimsA ' . nimsA ( 7.5) sA

. '

8

z xam,dcM dcM . "

:4 . dcf 2d b )5.0 1( = dcM dcf 2d b 23.0 = xam,dcM

2/h = 'y = y: d )5.0 1 ( = z :( 4.5) ( 3.5) xam,dcM > dsM,

s,nimds

d

ds

xamdcfA ss

Nf

( 8.5) =+ AA'bdf

(:7.5) ( 9.5) sA xam,dcM dsM s,nim

ds

d

ds

dcfA ssnim

Nf

( 9.5) =+ AA'bdf

: :

dsf sA dsf sA + dcf db = dN( 01.5) : ( )

)sd d( dsf sA + dcf 2db )2/-1( = ] )sd 2/h( + de [ dN( 11.5) ,

, . ( 11.5) ( 01.5)

, .

.

3.3.5

1.3.5 .

)

9

. ( . .

. , ,

, . a5.5 . .

.

5.5

: . b5.5

) (:2.3.5

] )sd y( + de [ dN = dsM( 1.5) . xam,dcM dsM .

xam,dcM dsM = dM( 2.5)

snimsds

d(dd')fA' s

= A'M( 3.5)

( 4.5) :

01

s,nimds

d

nimds

dc,xamfA ss

Nzf

M ( 4.5) =+ AA'

. ( )

. ( 4.5) .

. :

.b5.5 :'dsM

] de )sd y([ dN = 'dsM( 21.5) . sA

.- xam'dcM :'dcM 'dsM : xam'dcM > 'dsM

xam'dcM - 'dsM = 'dM( 31.5) : sA

s,nimsds

d(dd')fA s

= AM' ( 41.5)

, ( 41.5) sA ( 41.5) ( 31.5) , .

. ". " " "

.

.

. ,

11

sA ,

xam < (. 8.5) ( 4.5) (. 9.5) ( 7.5)

.z dcM

4.3.5

, .

, .

6.5

de dN a6.5

. sA :dsM . sA

21

] )sd y( de [ dN = dsM ( 51.5) . dsM

. sA

: xam,dcM > dsM . xam,dcM dsM = dM( 61.5)

:

snimsds

d(dd)`fA' s

= A'M( 71.5)

:, dN

s,nimds

d

nimds

dc,xamfA ss

Nzf

M=++ AA'

dsnimdss MA'f(dd')

( 81.5)

. nimsA xam,dcM dsM . :

=( 91.5) :

( 02.5) = MMM dcdsd

(: z ) xam,dcM dcM

s,nimds

d

ds

dcfA ssnim

Nzf

( 12.5) =++ AA'M

( 12.5) ( 51.5)

: d ) 5.0 1 ( = z 2/h = y = y

dcf 2db ) 5.0 1 ( = dcM dcf 2db 23.0 = xam,dcM

31

, :

dsf sA + dsf sA - dcf db = dN( 22.5) : ( )

)sd d( dsf sA + dcf 2db )5.0 1 ( = ])sd 2/h( de [ dN( 32.5)

5.3.5

: .

.

7.5

, , , ,

( : 7.5 ) :

41

s,nimds

d

s

sdfA s

N(dd') A(y'd')e

( 42.5) =+

snimds

d

s

sdfA' s

N(dd') A'(yd)e

( 52.5) =

' 1.5

. 03 , mm 006/003 . m 5.0 , Nk 0001

. . 400.0 = nim = nim

:

m 55.0 = d aPM = 0.31 = dcf apM 053 = dsf 055 003 400.0 = nim,'sA = nim,sA 2mm 066 =

mNk 5.773 = 6-01 0.31 2055 003 23.0 = xam,dcM xam,dcM > mNk 057 = ])50.0-03.0( + 5.0[ 0001 = dsM

mNk 5.273 = 5.773 057 = dM2

(0.550.50)0.538212mm s== A'273.5

:

: 2

0.538712154275822771mm s0001

0.080.550.53 =+=+= A8212773.5

51

2.5 . 12 . 02 mm 006/052

6.0 Nk 063 . . 400.0 = nim = nim . '

?

:

aPM 002 = dsf sA aPM 6.8 = dcf 055 052 400.0 =nim,'sA=nim,sA 2mm 055 =

mNk 802 = 6-01 6.8 2055 052 23.0 = xam,dcM mNk 4.101 = )50.0 55.0( 02.0 705 2 = dM

mNk 603 = ])50.0 03.0( + 6.0[ 063 = dsM xam,dcM ~ mNk 6.402 = 4.101 603 = dM - dsM = dcM

20.5397592319201978mm s

063(10.050.04)0.550.53

402.60.53=+=+= A41010.02

3.5 . 03 ' 006/003

.mNk 081 = dM Nk 008 = dN - . 400.0 = nim = nim

61

:

aPM 053 = dsf aPM 0.31 = dcf 055 003 400.0 = nim'sA = nim,sA 2mm 066 = mNk 5.773 = 6-01 0.31 2055 003 23.0 = xam,dcM 522.0 = 008/081 = de m

mNk 083 = ])50.0 03.0( + 522.0[ 008 = dsM 2mm 066 = nimsA = sA . sA xam,dcM dsM

mNk 5.511 = )50.0 55.0( 53.0 066 = dM (:62.0= ) sA

20.5306621516822411mm s

008(10.50.62)0.550.53

=+=+= A066352.3

: sA : sA xam,dcM < dsM mNk 02 = ]522.0 )50.0 03.0([ 008 = dsM

2mm 066 = nim,sA = sA: , sA

4.5 . 02 ' 006/004

.' 05 . Nk 0003 .400.0 = nim = nim.

: mm 045 = d .aPM 053 = dsf aPM 6.8 = dcf

2mm 468 = 045 004 400.0 = nim,'sA = nim,sA

mNk 123 = 6-01 6.8 2045 004 23.0 = xam,dcM

71

mNk 078 = ])60.0 3.0( + 50.0 [ 0003 = dsM

2 mNk 945 = 123 - 078 = dM(0.450.60)0.538623mm s

== A'945

mNk 075 = ]50.0 )60.0-03.0[ 0003 = dsM: sA 2

(0.450.60)0.532841mm s== A942

mNk 942 = 123 075 = dM 5.5

. 03 ', 005/052 .mNk 042 = dM Nk 003 = dN

. . 400.0 = nim = nim

:

m 8.0 = 003/042 = de mm 054 = d aPM 053 = dsf aPM 7.21 = dcf 2mm 054 = 054 052 400.0 = nim'sA = nim,sA

81

mNk 6.012 = 6-01 0.31 2054 052 23.0 = xam,dcM xam,dcM < mNk 081 = ])50.0 52.0( 8.0 [ 003 = dsM

mNk 36 = )50.0-54.0( 53.0 054 = dM: =71.0 mNk 711 = 36 081 = dM - dsM = dcM:

20.530542187589112mm s

003(10.50.71)0.540.53

=++=++= A054711

2mm 054 = nimsA = sA

6.5 . 03 . mm 005/003

Nk 004 = dN . aPM 002 = dsf ? . m 1.0=de

:

:

20.020051mm s

0040.540.50

= A0.520.500.01 =+

s,nim2

0.02005mmA s004

0.540.50=< A'0.520.500.01

=

nim,sA 2mm 045 = 054 003 400.0 nimsA 2mm 0261 = )005/045( 0051 = sA:

91

.

7.5 2mm 0002 03 mm 006/003

. mm 05 = 'sd = sd ? . ' 226.0

: .aPM 053 = dsf aPM 0.31 = dcf. 2mm 0002 = 'sA = sA

- : (:xam= - )

dsf sA dsfsA + dcfdbxam = dN: )sd-d(dsfsA + xam,dcM = ])sd-2/h(+de[dN:

. . 'sA sA .

. sA sA : sA 2mm 0002 = sA

02

053 )0002 sA( + 0.31 055 003 xam = dN )05-055( 053 sA + 0.31 2055 003 23.0 = ]052+226[ dN

. . sA .2mm 1481 = sA sA , Nk 5.208 = dN:

4.5

1.4.5 .

4 .

. ,

) (

. .

. b8.5 a8.5 . .

) 0S ( 0S 46.0 ,cS .

dN y

0S . y :

12

8.5

sfwfw

2fwffw

c

yd 0(bb)tbd

(bb)t(d0.5t)0.5bdA+= S

( 62.5) =+

. , y y . ( 62.5) 0S

2.4.5 .

wb .

.

1.2.4.5 . 9.5'

sA :dsM

( 72.5) =+ dsdds MNe(yd)] [ : dM xam,dcM > dsM

22

snimsds

d(dd')fA' s

= A'M ( 82.5)

9.5

, xam,dcM ) sA ,xamx

( :ft xamx

( 92.5)s,nim

ds

d

ds

fxamdcfA ss

Nf

bxf=+ AA'

:ft > xamx

(

] [s,nim

dsds

fwfwxamff ss

(bb)tbxf =++03.5) NA dcd AA'

2.4.5

[(.1] 5.1 )dwb ,

2.

32

. 01.5 (. 72.5) dsM sA

(.82.5) sA

01.5

, , sA

. nim,sA" " " " xam,dcM 'dsM

, , ( 03.5) ( 92.5) :'dsM 'sA .

] de )'sd - 'y ( [ dN = 'dsM( 13.5)

: ( ) xam,dcM > 'dsM

( 23.5)s,nim

sds(dd')fA s

A= M'M dsdc,xam

4.5

3.4.5

3.

1.

,

(. )

42

( 'y y) :dsM ( 6.5 )sA

] ) sd y ( de [ dN = dsM( 33.5) (.82.5) 'sA ( :ft xamx ), ( 43.5) sA

s,nimds

d

ds

fxamdcfA ss

Nf

bxf=++ AA'

: ft > xamx

( 43.5)

] [( s,nim

dsds

fff ss

(bNA wfwxamdcd AA'

=+53.5) ++ b)tbxf

2. 3.4.5

'

( )

. )

( (.52.5) ( 42.5)

8.5

. 03 ,

.(

:

.m 5.0 Nk 0031

) . 400.0 =nim=nim

:

=+= 06)06804864mm 003006005003

+ y06006003(05606)003005(052 =++

52

0S 233=864-008 = 'y2mm 601 42.531 = 2047 003+)051-047(003)003-006( = 0S:

mm

:xam,cS

3mm 601 455.68 = 0S 46.0 = xam,cS

:m,dcM

( + 5.0[ 0031 = dsM M

xa mNk 5211 = 0.31 601 455.68 = dcf xam,cS = xam,dcM

xam,dcM > mNk 0811 = ])60.0 864.0 nim'sA < 2mm 132 = )53.0 86.0(/55 = 'sA mNk 55 = 5211-0811 = d

2mm 888 = 047 003 400.0 = nimsA = sA: mNk 3.112 = )60.0 47.0( 53.0 888 = dM :dM

mNk 7.869 = 3.112 0811 = dcM:

]0.62: 00604731

12 2869.701 == 2 1[16

)mm 003=( f . 62.0 = xt < mm 391 = 047: 2

s888103441735741mm: =+ A888006391310031053053

=+=

62

9.5 . 03 ,

. 400.0 = nim= nim. mNk 0231 Nk 0021 .

:

(: )

004mm008051055004

+= y008051(00757)055004572 =+

: 0S mm 003 = 004 007 = y 3mm 601 85.901 = 004 2026 5.0 + )57-026( 051 )004-008( = 0S

3mm 601 31.07 = 0S 46.0 = xam,cS: :

mNk 219 = 0.31 31.07 = dcf xam,cS = xam,dcM :

xam,dcM > mNk 4071 = ])80.0-004.0( + 01.1[ 0021 = dsM : dM

mNk 297 = 2194071 = dM2

(0.260.60)0.531404mm s== A'297

:

: . xamx

72

ft > mm 361 = xamx )xamx 5.0 026( xamx 008 = 601 31.07 = xam,cS . xamx

)xamx 5.0-026( xamx 004 + )57-026( 051 )004-008( = 601 31.07 = xam,cS .ft mm 671 = xamx:

: 2

0.531404348492435545mm s31.00021

053 =++=+= A8414(008004)051004671

01.5 . 02 .

Nk 0052 . 400.0 = nim= nim . . ' 001

:

: aPM 053 = dsf aPM 6.8 = dcf

904mm006052003054

+= y006052(007521)003054522 =+

: 0S . mm 192 = 904 007 = y 3mm 601 14.79 = 2036 003 5.0 + )521-036( 052 )003-006( = 0S

3mm 601 243.26 = 0S 46.0 = xam,cS: :

mNk 635 = 6.8 243.26 = dcf xam,cS = xam,dcM

82

: xam,dcM > mNk 3901 = ])70.0 904.0( + 001.0[ 0052 = dsM

.sA s,nim

2(0.360.60)0.532972mmA` s

=> A`3901635: =

ft xamx . - xam,cS > 3mm 601 57.57 = )521 036 ( 052 006 = fcS

(. )ft < xamx: )xamx 5.0 -036( xamx 006 = 601 243.26 = xam,cS: xam

.m 591.0 = xamx : sA

20.535741mm s

0052(0.360.05.591)0.53

=+= A2972635

:dsM sA: mNk5.723 = ]60.001.0192.0[ 0052 =dsM

. sA mNk 823 = 6.8 2036 003 23.0 = xamdcM 2mm 657 = 036 003 400.0 = nim,sA = sA

5.5

. .

) . (

. ( a11.5 )

) , , (.b11.5

92

, , ,

(. . ,

11.5

,

: .

- , , , ,

. . " "

.

. -

)

03

, (. ( a21.5 )

(. b21.5 ) .

21.5

1.5.5

dN : . a21.5 xe ( ye dN = xdM: )x ye

(. xe dN = ydM : )y .

: ( 63.5)

N dxdydd01

N1

N1

N=+ 1

( ) - dN: ye - xdN

.0 = xe

13

xe - ydN .0 = ye

: - 0dN dsf sA + hb dcf = 0dN

[ 92 ]relserB " ydM dN margaid noitcaretni . a31.5

dN margaid noitcaretni . . 2.5 1.5 - . xdM

. 0dN ( 054) relserB.

( b31.5 ) . b31.5

(. )%51

31.5

:11.5 . 03 ' 005/053 mm 54=sd . mm 612 mm 02

23

mm051=ye dN . ?' mm001=xe

: . ( 63.5)

ydN xdN ( 63.5) . 024 618 0dN Nk 6.5723 = 3-01 ] 053 6582 + 005 053 0.31 [ = . 0dN mm 001 = xe xdN

. y . mm 54=sd mm 005=b mm 053=h A 2mm 8201 = 'sA = s - y

: mNk 391 = 0.31 2503 005 23.0 = xam,dcM mNk 55.39 = 62.0 53.0 8201 = dM: xdN 32.0 = ])540.0-571.0 + 01.0[ xdN = dsM:

Nk 6421 = xdN: mm 051 = ye ydN

. y . mm 54=sd mm 053=b mm 005=h A 2mm 8201 = 'sA = s - y

: mNk 4.103 = 0.31 2554 053 23.0 = xam,dcM mNk 25.741 = 14.0 53.0 8201 = dM: ydN 553.0 = ])540.0-52.0 + 51.0[ ydN = dsM:

Nk 5621 = ydN: :( 63.5)

5723.61

56211

64211

N1

d

Nk 777 = dN: =+

33

2.5.5

dN : . b21.5 xe ( ye dN = xdM: )x ye

(. xe dN = ydM : )y .

, 5891 [ 6] , 2891

( 11.4 ) . .

) ". " , (

.

x ) ( 41.5 ) ( :

( 73.5)

x

yd

y

xd

dM

d M

41.5

:qe,xdM

43

( 83.5)

x

yd xd,qexdNyd

d =+ MMM

:, (73.5)

( 93.5)

x

yd

y

xd

dM

d < M

:qe,ydM ( 04.5)

y

xd yd,qeydNxd

=+ MMMd

sd xe dN = ydM ye dN = xdM: .

. , xam,dcM 2 qe,ydM qe,xdM [ 1] : 2.5 -N

N - 2.5 2.1 0.1 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0dcf hb/dN

83.005.026.086.047.008.068.009.058.008.057.0 N

:21.5 . 04 mm 006/003

. mm 812 mm 52 dN . mm 053 = ye mm 052 = xe:

?"

53

: 52.0 dN = ydM: ydM 53.0 dN = xdM: xdM

dN 636.0 = 55.0 / 53.0 dN = yd/xdM: dN 0.1 = 52.0 / 52.0 dN = xd/ydM

: qe,ydM xd/ydM < yd/xdM: N - dN yd/xd N xdM + ydM = qe,ydM

: . : 438.0 = N . 561.0 = )dcf hb( / dN . Nk 025 = dN

dN 383.0 = dN)55.0/52.0 53.0 438.0( + dN 52.0 = qe,ydM : dsM sA

mNk 152 = dN 384.0 = ]50.0 - 51.0 + 383.0 [ dN = dsM ( mNk 14) 'sA mNk 012 = xamdcM

: