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Analisis estructural parte 3

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Análisis estructural.

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Analisis estructural parte 3

  1. 1. ! " # " $ % &% ' " ( " % ) " $ % &%& ( ( " * + " ( ( ,--.*/ 0% &%# * 1 2* 3 4 " ( " " *5 ! , " / " 6 ( 0% ' " ( % 7 " " , /4 " 6 ( 0 + % &%8 ) " 3 9 , " " , , " 6 ( % &%: * " " 3 9 + "$ , 6 ! " , , ( *5 ! , ( % #% 9 , " , ! ( " % ! " #$ % & ' (& $) 9 ( , % ! ! % ( *
  2. 2. ; ),< * "+3 * ),<" "3=== * == ><,)> >>3=!= * = * = *55 ,5= ,-3,5= ) < ) < ) < ) < ? ? )<)5< ? ? )< )< = = ? ? ## ∫ ∫ ∫ ∫ −= =− = = == == ∫=5θ " 5θ " ( ) , <! " " * 5 , " % < ( 3 1 /@0 3 5θ /@0 " % 1 /@0 + 3 5θ /20 " ! + , ( ) % ∫= = = = = ) < ? ? )5< * = > ><> >)" * = *= * = == 9 5θ 3 ) ( " A < " )%
  3. 3. B ∫ 3 + " *5 < , ) <% ( " 5θ < )! " ! <! + " *5 < , )% 5θ /1 < , )0C & 5θ /1 < , )0C # # ! & 3 ) < , ) % " " 6 θ , ( " !5∆ + " ! % % " 5θ , ( " !5∆ " 7 % 9 + " *5 " ! " 5θ + " % ( " <% " %
  4. 4. D % - 3 E , ( ' " .&F*G% #
  5. 5. ;F :%H &F=8 5#C&H &F8CD &F== F= '=== 8 ' &8&8 ''5 #&''5 −−−−− =→−== = +==−= 9 " I :H, #%FC##%H &F&%HC#; &F, /#%F0/&%H0, ' 88 ' #&''5 −= −= +==∆ −− % - E , , ( %
  6. 6. ;& I <55< <5 < <<5 == F= === ∆=∆ =− = −= J 3 " 6 , ! , , " + % 8# == # * F # 0/ * 888 8#&<5 # # −−−=++=−= ≥ −−= =− − + #F:B &D B &D K B &8 8B 8 8 # # B &8 B 8 8 # && = && = 8 # H 8 L B 8 ? :: * ? 888 5< 8#&5< 8 8 5 −−=−= −+−+−= ++= −= −=− = = = ! . " < " " ! " " 6 ! " , % ( " ∆'5 , ' , %
  7. 7. ;# 5∆ −=θ θ " % 5θθθ += + ( " ∆)5 ) ! 6 " % '5)5) '5 ), E' ∆−∆=−= ∆== % - E , ( ) &#B ; M #&#B DH &#B 8 M # H M = === === :: 8 * : 8 * 8 '5 ## '5 #&'5 '5 )5) ))5 & = += += −= += −= −−= =
  8. 8. ;8 θ 8#&#B ; &#B 8 = &#B 8 = === ) &#B ;M = ### ) # &)5 )5) # '5 −=−= == += −=−= #H 8 , H&# ; H&# ), H&# ;5: H&# ) &#&#B 8 ) &# ) 8 ) 88 ) 8 '5 8 # &)5 −= −=−= =∆= = = =∆= ! / 0- 1 2 31 9 " , " ! ( ,% " 6 , ( %
  9. 9. ;: N3 " 6 * ?5O OO5 L= ==F=== = →−=−=−= % - 3 ( N , '% N ' &#B H = # : 8 & 8 # :& 8 &#B ; = ==== === # ' # ' #&'5' ''5 = ++−= ++=+= −=
  10. 10. ;H F%HHD B&#B H P=F= P===& &#B H = &#B H = ## : 8 & 8 # :& 8 = ??= 5==J ## 'N N''5 # ' 8 5' 5' ##&&5' 5'' =→= =→= =−= = = += += = ' 3 P. B# : # = 8 5 # 5 F&:H%F 8 HHD%FC# B 0HHD%F/ 8 # P = === θ θ % - E ( % Q " R&F?88! . ;%F; &F2H : ! . #FFS ! . FOG5 %
  11. 11. ; F%&8B,:%#D &FD%H: &F=PP P, ) :%#D &F= : 8C8 C&%DFB &F : 8 = D%H: &F H 8 CF%&HDPP P =PP P =PP P F%&HD= 8 HC# C:%;; &F 8 # = 'I " :%;; &F # &%DFB &FCH = &%DFB &F 8 &%DFB &FC8 = 80#8:/808F/8F*/ 0 80#8:/80F/FQ/ 0 #8:OG', F',/H0F/80/ %H0 FT* ## 5' # 5' # &5' # <5' <5' <5' # #<5' # # #<5' # # &'5 ## F =−−=+= −= −== −=−= = = −= −== −= − == −= − == −+−+−= −+−+−= = =− = −− − − − − − − − − ! 4 " 3 ( % 3 &% " " ! " , , + , + + % " + + , " % #% < " I ( " , ! % 8% 9 6 " + ! + " , + + %
  12. 12. ;; :% 9 6 " *5 , " , ( % H% ) ( , ( 1 2* % % - ( ', " % " " " % 5 56 /9 + + " 0% 9 " ', ( B : 8 C : 8 #8 # # : 5 8 &5 8# & # # −= −== −=      − = −= −= −= θ θ 5 5& / + + 0 B 8 F 8B 8 8 # C #8 # ## 05/ 8: 555 8 5 # #5 # # = =+ − =+= = == =      = = = = ∆ θθθ θ θ
  13. 13. ;B + ' $ " #$ 6 78#$ $ ) J * &B B% + + , " " ! + " 6 , " " " ! " " *5 % " " " ! " " ! , ! " " *5 ! , " ! , ( " % 9 " ( % ∫ ∫ ∫∫ ∫ ∫∫ ∫ = −= = −=       =       = = = = = =→= == Q* Q Q * Q ""9 * , * , =, ,5= */ 05= */ 05= *5 == &5U *5&5UN 9 " " " " " . *5 6 , " 3
  14. 14. ;D ∫ ∫∫ ∫∫       == == < + 3 = =θ ! ( " " 6 ( " " Q% θ . Q + ( " ! " * ( " " % , . * 4 " ! Q , *% −= = −= # # 4 ( *5 θ , ( ,% == = = # # θ θ 6 + , " " % 9 9 9- 3 9 ( ( ! " " + ! , , % 9 3 G , " ( " ! " " , ! " + %
  15. 15. BF 1 3 I ( , ( " ! " " + Q , *% 9 3 " , ( , ! " " ( % ,- 2 " , ( , ! , " " , + + * , + + Q% " " + + ( " *5 ! ! " + % */@0 " " ! ( ,/@0 + " % Q/@0 " θ /@0 % Q " Q " " % Q " Q " " + %
  16. 16. B& % ! < , " *5 " + ) " " " *5 " " " ! /@0 " + , /20 + % . < , " " / + , + 0% / θ " Q " , /) ( 0 " ! + * " %
  17. 17. B# % - 3 ( 6 % ! :B8 B# 8 F ## 8 # & # − === − === =Σ −−= 5θ 8B: ; , B ; :B 5#0/, FT* : 8 &' ' −=      − =+= =
  18. 18. B8 % - 3 ( , " % &.HF &F; : .#FFS Q " < " " # : : &FHF &F&#H F 8 H # HCH%&# 0H%#/CHCH%&# 8 H H # HC#H 0&F/HF F &F&FH − − = == =+      ++      ++− =Σ −−= θ
  19. 19. B: % - 4 " 4' 4 % ) " *5 "
  20. 20. BH Q " < " : ; 8 # 8 # : 8 : ; B& B #; # & # & F 8 # 8 # C # 8 # 8 # 8 # # & 8 # C 88 # 8 # C # 8 # 8 # F F 888 −=−−−= −=−= = =+ =    −    +    =Σ ==
  21. 21. B % - 4 ( % 9 ( % *3 9 " 4 % #5 # −−= ) " *5 . Q " " $ 4 ,.4),. 5# , *'.*<.* " $%" θθθθθθ =→=−= 55 F
  22. 22. B; Q<'Q # # '<'< && # & & 'Q'Q == "< 8 * 8 # # * 4= # * &# # : # * 4= = = − == −=+ − == 5B* #8 & B 8 * & #8 * &8# * 8 * # * & &# &# # # & # #& &# & # #& #&& # = >>       + = =      + =      + =− * " + % J 6 % 6 2 3
  23. 23. BB 9' )' / + + (" 0 ) + (" % Q " 3 & '# && ' & # '& & # & ' '' ''5 # E =M # E # E = 3< & =M &# #: = 3< == F= === # # & & == == == == = = −=
  24. 24. BD 8∆ 9 " + " '3       + ==       + =       + = += =+ === & # # # # & # # # # #& & # # & # # 8 & # & # &8# # 8 # 8 ' #8 & B 8 E* #8 & B 8 E #8 E & 8 E # E & MMM +>> 8 E 8 # # E M=

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