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Analisis estructural parte v
- 1. • • • ! " " • # $% • • • $ ! % & ! "# $% !& # " ! ' ' & ' ! !' % () * !& " ( )
- 2. + , -, . / , 0 * + , - ./ 012 , " # # " " # ' ! + 1 1 2 3 2 4 3 ! 4 ( " 5 . 6 . ! 2 " # ! # 3 6 . " . ! ! " . ! 7 . 8 9 ! " ! ! ! " . ! ! ( ) # # " 6 1 , . ! : $ # ! ) 0 ; $ <7.8" -7.8 " =7.8
- 3. 1$ 5 (& ; <7.8 -7.8 > ? $ * 6 ∆ ? 3 . ! > . - < > ? , . $ . ! > # > > . ! > =∆ ! =+∆=∆+∆ 3 . ! # ( . ' # . 7&8 . ! 6 54 54 =−=∆
- 4. 4 5 @ 87. !* 44 87 A < 876-. !* 5 444 = =−=→= = = == − −=∆ −= −= =∆ ∑ ∫ ∫ $ ! 4 5 A 54 54 = =+−
- 5. 5 $ 4 5 4 4 5 −= =Σ = =+−→=Σ =→=Σ 1$ 5 (? ; <7.8 -7.8 B , C B .B $
- 6.
- 7.
- 8. 1 $ $ D14542201 2 1 8 5 2 47840875D47A 54 44 =−=−=∆ −= −=∆ ∫∫ - -< >&1 &. >, , & 0 .&4 .4 4D5. , . # ' """" % A 014 @@@@@$ 00:4 4: 2 5 85D4787 5D4 5D4 5 1 5 4 1 4 4 = =+− =+= += −+−= −= −= −= −= −= = = ∫∫ ∑∫
- 9. : + , - (" ! ! 1$ 5 ( ? ; > ->? - $ 4 ) > " θ ( > ! θ ? > # θ ? ) >
- 10. 0 ( . ?,) > # -> - . ? ( 6 ( 7E8 ! =+θ ) >" . -> F # 6 6 >−<−>−<+>−<−= >−<−>−<+>−<−= == =+= =→= =→= ∑ ∑ 44159 44159 90D1A4 0 4A4 897 9 & & < , 6 -D
- 11. # 904 1449 4 4 0A 5 4 4 1A 9 == +=+= === θ θθθ < 6 ->B 7(# 8 ( ) 1 1 1 = =−→= =→= =→= ∑ ∑ ∑
- 12. 4 ( ) ( ) 9259 0 1 4 0 4 4 1 0 0 1 1 1 =+= ∗ ∗ + ∗ == = =+−→= = =−→= =→= =→= ∑ ∑ ∑ ∑ $! 550 92904 == =+ , + 6 2 7 1 3 * ? 3 ! 4 ( ! 5 2 . 6 . 9 6 . ! # - . 1 : , . . - ./ G ' 0 ( . 718 # H ) =7.8" <7.8 -7.8
- 13. 4 1$ 5 (& 3 <7.8 -7.8 B 9 I 5 B 4 > " , ? $ 6 3 . ! > 3 . ! 6 6 > 6 , ? ?$∆
- 14. 44 ! , =++∆ =++∆ $ $ $ #. # ' . $$ 1 5912 == −=∆=∆ F - ./ 20 == $ ! 2015912 2015912 =++− =++− $ # > B 42: 9J= , B 42: 9J= 3 , -
- 15. 45 1$ 5 (? B 1 I 5 B 5 * . B >. B B 2 I 4 B 4 - B -, B $ 4 K K
- 16. 42 < 6 . <6 - B < 6 -> B ! , '" " " "! $ $ $ $ 1 ? 5 1 87 1 87 @@ 44 44 == == − = − = =++ =++ θ θ θ θ
- 17. 49 $ ! 4 4 4 4 44 44 ? 511 87 151 87 "! " = = =++ − − =++ − − 1$5 ( & 3 <7.8 -7.8 !
- 18. 41 B 1 I5 B 5 - " -3" 3. ? $ 6 $$#$ 4∆=∆=∆ 6 - B
- 19. 4: 6 -> B 63. B ! , =+++∆ =+++ =+++ # # # # ### ### # # ### ###$ ### #$ θ θ
- 20. 40 8 2 2, . 3 1 - 2 - H - ) ' 0 4" C - " F # - 9 ! ' ( ! " ' ' 7$ 8 ( # ! G? • . G . • 3 ! • . . ! 7E8" ) • * ) " . " # ! " # • 3 ' ) " # ! . ! . 8 ! 8 ' ?∆ ! # 4 . 6 - " -6 ? - # " 6 8 7( 8 - 6 ? - 6
- 21. 4 - 6 "-6 ? ( ) " ' " # 6 8 78 ( . 8 - L ? - -6 L ? - 6 ! - L < , 6 B , K B - 8 6 -66 L ? - 6 6 - 6 L ? - ! -66 L 6 < , 6 # 8 3 # ∆ 6 ! - 6 L ? - # ∆ . 6 -6 L ? - 6 # ∆ . ϕ ? C " # 7 ) 8 ( ! - B - % E - L E - 6 LL -6 B -6 % E -6 L E -66 LL * 8 ? =Σ
- 22.
- 23. 5 $ ∆+++= ∆+++= ∆+++= ∆+++= % " ""! 1 24 1 42 @@ 124 142 4 4 θθ θθ θθ θθ " " #" # # ) . * ? $ <7.8 K -7.8 ( * ! (' $ () * $ # ( # 2959 51 4 1A4 4 5:9 0 A5 0 44 =∗= ===−= ==== * )9) * ! * ! ' : !
- 24. 54 =∆=∆=∆ == = /θθθ θ 9# 9) *! ;)$ < " =)>* $ ( / θ θθθ θ θθθ 9 4 95: 1 2495: 1 24 9 95: 1 4295: 1 42 +−= ∗++∗+−= ∆+++= += ∗++∗+= ∆+++= >, ( ( ) θθ θθθθ θθθθ 55 4 51 55 4 5142 1 51 42 1 51 1 42 ++−= ++=++= +++= ∆+++= 9# 9) * ! ?#) )5$) * ! * ! / : , 7E8 , " " ")! " # 0421 1911 9 11: 555 @555 1: @$ 555511: 5 4 29 5 51 9555511: 55 4 51 9 4 95: −= = − = −=+ =+++− =+Σ =Σ =+ =++++− =+Σ =Σ =Σ θ θ θ θ θθ θθ θθ θθθ
- 25. 55 $ . ! 0550 1911 9 95:=+= 29 0421 A 5 41911 A 5 51 0252 0421 A 5 1911 5 4 51 0252 1911 9 4 95: =+ −=−++−= =+ −=−++= −=+−= # ( > 4509A29 12529 29 052050 4 5 . == =+−= = − += >, 42052 4A4 552 :5:5521A4 552 1 05229 4 1A4 4 . =−= =−= = − −=
- 26. 52 * ? F# L B4 -* " > 9 3 B :0:4-* * $9) " 9 )@
- 27. 59 "!" # # 9 @@ 494 4 1A49 A 4 4940 4 5A49 A 4 25 4 21 4 =∆ =∆=∆=∆ ×== ×=== − − ( * !(' $ () * , ) 9# 9) * ! 2)$ < " =)>* A $ ( / 9 4195591: 4 1 24 8@79 4195591: 4 9A 5 1 42A 5 4940A:0:4 1 42 55 55 11 ++= ∆+++= =++ +++= ∆+++== − θθ θθ θθ θθ θθ $ ( / 9552 2410 0 9552 2410 0 9A 1 1 42A 1 4:4A:0:4 1 42 55 55 51 −+= −+= +++= ∆+++= − θθ θθ θθ θθ $ (
- 28. 51 ( ) 84@75591: 4 955591:4 42A 5 4940A:0:4 1 42 55 55 11 ## ## ## ### θθ θθ θθ θθ +== −+= +++= ∆+++= − 9# 9) * ! ?#) )5$) # / ( )59 41952 2559559 9552 2410 09 4195591: 4 555 5555 =++ =−++++ =+ θθθ θθθθ # 9555955952 2 5591: 49552 2410 0 555 5555 =++ =++−+ =+ # # # θθθ θθθθ , 7 8748758 728 # # M5 5 M1494 M415 M50 9 4199 4199 1: 4559 55955952 2 52 2559559 5591: 4 5 5 5 5 5 − − − − −= = = −= − = θ θ θ θ θ θ θ θ
- 29. 5: $ C .! # 255 555914941: 4 455951494410 041552 2 20595149452 2415410 0 2059 4194151: 450559 5555 5555 5555 5555 −=−∗+∗= −=−∗+∗= −=−∗+∗= =+∗+−∗= −− −− −− −− , 5N * ? ! B 1:9 . &1 2 # B 0 5 45 . &1 2 L B 4 -* B :0:4-* B 0 C*
- 30. 50 C , "3 θ " #θ "θ ( * ! (' $ () * ## ## # 914 914 4 95 4 == = ∗ =−= = = * )9) * ! * ! ' : ! ( ) ( )( )*+# =∆=∆=∆ == θθ 9# 9) * ! 2)$ " =)>* #(* / ( ) ( ) θθ θθ 5 1 5 1 142 5 1:90 04 5 1:90 = ∗ = = ∗ = − − ); ( ) ## ## ## θθ θθ θθ 411254014914 411254014914 42 9 450 50 914 55 55 1 5 ++−= ++= + ∗ += − #(* / ( ) ## ### θ θθ 5 5 1 14 04 5 1:90 = = ∗ = −
- 31. 5 ); ( ) ( ) () ( ) ( )9144112594014 24 9 450 50 914 4112594014914 42 9 450 50 914 555 11 5 555 1 5 # ## ## ## =+ + ∗ +−== ++= + ∗ += − − θθ θθ θθ θθ 9# 9) * ! ?#) )5$) * ! * ! : ( ) ( ) ( ) ( ) ( ) ( )54112542 4941125 1451125940149149401491441125 49144112594 14 511259401414914 5 5 M 5 5 # ### ### # # # # =++ =+++++− =++ =Σ −=+ =+++ =+ =Σ θθθ θθθθθ θθ θθθ H 7 8 748 758 # # M59 M21: M2:4 914 914 9401441125 4112542 4941125 4112594 14 5 5 5 5 − − − = −= −= − = θ θ θ θ θ θ $ . !
- 32. 2 91:4901:0 91:21:14 490594112521:94014914 1:021:940142:441125914 :5521:411252:494014914 1552:414 9012:40 −+−= =++ −=−∗= =∗+−∗+= −=−∗+−∗+−= =−∗+∗+= −=−∗= −=−∗= ### # # # # 1>$ )9 !9 * ( ! . " . " ! ) " # ' . " " ) . * ? # ! , B 0 C* *B 9 J= )B5 B 1:9. &1 2 B 9J=D 4 B 59 . &5 2 B 9 ( * ! (' $ () * 495 4 :90 0 4 == ==−= ==−= ## $ ,
- 33. 2 2$ ! )5$ ∆θθ " * )9) * ! * ! ' : ! < . 9# 9) * ! ;)$ " =)>* ( ) ( ) ,, ,, $ $ ,, , ,, , # # ∆+= ∆+= ∆+= ∆+= ++−=++−= ++=++= ∆++−= ∆++−= ∆++= ∆++= 55 55 555 4 555 4 555 555 014 1 2 00 1 4 :42249524 4 4 :42249542 4 4 014:90 1 2 0 00:90 1 4 0 θθ θθ θθθθ θθθθ θθ θθ 5 ! θ " ∆θ " # 5 9# 9) * ! ?#) )5$) ∆=∆=∆ == #θθ
- 34. 24 ( ) ( )( ) ( ) ( ) ( )449505912:4 01422:4495 940:45912 :422495014:90 5 5 M 5 5 # =∆++ =∆++++− =+ =Σ −=∆++ =+++∆++− =+ =Σ θθ θθθ θθ θθθ ! ! " ! ) ( ) 9 5 =−− =−− =Σ # #
- 35. 25 ( 6 !' . " 5 857 5 :9 8578979 ## # ### + = =−+ =Σ ++ = =−++ =Σ 5 :9 9:9 55 :9 9 ## ## ## =+++ =++++ = + − ++ − . ! ( ) ( ) 89@@@7:9542425425 :900014014:9000:90 5 5 =∆++ =∆++∆++∆++−∆++ θθ θθθθ H ! 7 8 748 798 5 2 5 5 :504 1 19 41 :9 495 94 542425425 05912:4 0:45912 − − − =∆ = −= − = ∆ θ θ θ θ $ C . ! - > B 5 0 J= -> B & 2 0 J= ->, B 2 04J= -,> B &5 0 J=
- 36. 22 -,3 B 50 J= -3, B 41 :5J= < > B 7& 2 0 E5 0 E:98D5 B 5 1:J= <3, B 75 0 E41 :58D5 B 52J= 1 $ )9 ! 9 * 9 #(* ! )*9 )* ! " ! ) ∆ " . " ! # ! " H" ! 6 * ? 3 B 0 C* B 1 . 1 2 B 40 0 . 1 = 4" $ 7&8 ) ∆ −=ϕ ϕ ?
- 37. 29 3 ? 2$ !)5 $ & ∆#θθ " ( * ! (' $ () * , ) . . 6 * )9) * ! ' : : 2)$ * # $ !
- 38. 21 [ ] [ ]∆+=∆++= ∆+=∆++= ∆= ∆ = ∆ = ∆= ∆ = ∆ = ∆−= ∆ =−= ∆= ∆ +=+= ∆+= ∆ += += == #" "-"! . ! ## # # 50849712 9 52849714 9 @@ 2 5 LLL LLL 2 5 LLL 2 9 L L9 2 L 49 1 2 5 1 LLL 49 22 L 49 9 2 9 9 L θθ θθ θ θ ϕ ϕ ϕ ϕ θθ
- 39. 2: [ ] [ ] [] 84@@711:49555 5:9495511: 8@755211::9 50495511: @@ 495511: 495511:8497142 1 5:9849712 2 5:99849714 2 # ## ## # # # # ## ### ### ### $""! θθ θθθ θθ θθθ θθ θθθθ θθ θθ +∆+ =∆++∆−+ =+ =Σ ++∆ =∆++∆−+ =+ =Σ ∆−+= ∆−+=∆−++= ∆+=∆++= ∆+=∆++= ! H
- 40. 20 85@7807847897 0 9 2 0 0 1 2 5 =++−− =Σ = = = = = = ## / / / / ! /# /# /# # . θ θ 3 , 82@7 9 897 82@7 9 897 + = =+− =Σ + = =+− =Σ 89@7 2 827 ## # ### # + = =+− =Σ $ 728798 758 81@704554 0847 2 897 9 =+++ =++ + − + − ## # ##
- 41. 2 . ! " "-"""% # # # # # # # # ## 25 2 94100:9 2:0 9 9:042: 0::9 00:9 941 2: 2: 9:04 @@@$ 245 4 402 04: 05:95245 4911:555 :955521: 8:@705:95245 0:94952410 = + = = + = −= = = −= = = − +=∆ −= −= = ∆ + + + =∆+ =∆++∆++∆++∆+ θ θ θ θ θθ θθθθ