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7/24/2019 Prctica Excel Mef 002
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INTRODUCCIN DE DATOS PRTICO Unidades
Altura Pilar 1 5 mAltura Pilar 2 6 m
Luz Jcena 1 m!n"ul# al$a %&&66'6525 rad
NUDOS CI(
Car"a re)arti*a CP +2 KN/ml
,ient# 1 nu*#2 2 KN,ient# 1 nu*#- KN
1
2
-
.
5
6/
'
&
1
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2 . 6 ' 1 12 1.
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0ARRAS
1 PILAR 2 12 6
2 J!CENA 2 612 /
- PILAR 12 /12 1
CAR3AS L4nea #riz#ntal 7
1 2 &2 12 &
L4nea ,ertical iz7 7
1 2 /2 2 &L4nea ,ertical *c8a 7
1 12 /2 12 &
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NODOS
1 2 12 2 6
- 12 /. 12 1
,IENTO NODO 2
1 62 2 6
,IENTO NODO -
1 12 /2 12 /
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0arra N#*# i N#*# 9 (aterial E :
1 1 2 #r;i"
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8 A I L#n"itu* !n"ul# Ra*
- & 6/5 5 & 1%5//&6-26'6 1' 5. 1.&%'/6 5%/15&-1-/5 %&&66'6525
- & 6/5 6 +& +1%5//&6-26'
mm mm mm4 mm =
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,ECTOR EN COORD LOCALES (ATRI> RO
NUDO 22? &&5%-/1&21 %&&5-/2,2? +11.&%-/&-.1.1& %&&5-/(2? +16666666%666666/
NUDO --? +&&5%-/1&21 %&&5-/2,-? +&&5%-/1&2&&& %&&5-/
(-? 16666666%666666/
S
IN,
IENTO
2? +&&5%-/1&21,2? +&&5%-/1&2&&&(2? +16666666%666666/
NUDO -
-? +&&5%-/1&21,-? +&&5%-/1&2&&&(-? 16666666%666666/
En e@ta )e@taa *eBni;#@ l#@ ect#re@ *e $uerza@ n#*ale@ e7*e en@a;:la9e "eneral *e la e@tructura% P#r e@te ;#ti#G la@"l#:ale@% Para c#nertirla@G ;ulti)lica;#@ *ic8# ect#r )#r la
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ACIN 0ARRA 2 ,ECTOR COORD 3LO0ALES
+%&&5. 2%&&5-/2 +1
1 +16666666%666666/
+%&&5. 1%1-6'6'-//2E+1-%&&5-/2 +1
1 16666666%666666/
uialente@ SO0RE NUDOS7ue *e@)uF@ utilizare;#@ en la ;atrizuerza@ actuante@ tienen 7ue e@tar eH)re@a*a@ en c##r*ena*a@;atriz *e r#taci
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La@ )e@taa@ 0ARRA n#@ @iren )ara *eBnir la@ ;atrice@ *e ri"i*e
A & I 6/5 E
(ATRI> RI3IDE> 0ARRA EJES LOCALES[K'] D1 *1 "ir#1 D2
N1? .&1. +.&1.
,1? 1/6&%. ..226
(1? ..226 1%./.E1
N2? +.&1. .&1.
,2? +1/6&%. +..226
(2? ..226 /-/1
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*e ca*a :arraG en e9e@ LOCALES M e9e@ 3LO0ALES
2/- ngulo 1%5//&6-- L 5
(ATRI> DE ROTACIN*2 "ir#2 [T] D1 *1
N1 % +1%
+1/6&%. ..226 1 1% %
+..226 /-/1 (1 % %
N2 % %
1/6&%. +..226 2 % %
+..226 1%./.E1 (2 % %
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"ir#1 D2 *2 "ir#2 [T]t
% % % % N1
% % % % 1
1% % % % (1
% % +1% % N2
% 1% % % 2
% % % 1% (2
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D1 *1 "ir#1 D2 *2 "ir#2
% 1% % % % %
+1% % % % % %
% % 1% % % %
% % % % 1% %
% % % +1% % %
% % % % % 1%
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[T]*[K'] D1 *1 "ir#1 D2
N1 -%12E+11 +1/6&%. +..226 +-%1E+11
1 .&1. 1%'-/E+1- 2%/&2E+1 +.&1.
(1 ..226 1%./.E1
N2 +-%1E+11 1/6&%. ..226 -%12E+11
2 +.&1. +1%'.E+1- +2%/&E+1 .&1.
(2 ..226 /-/1
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(ATRI> DE RI3IDE> 0ARRA*2 "ir#2 [K] D1 *1
1/6&%. +..226 N1 1/6&%. 2%&&&.E+11
+1%'.E+1- 2%/&2E+1 1 2%&&&.E+11 .&1.
+..226 /-/1 (1 +..226 2%/&2E+1
+1/6&%. ..226 N2 +1/6&%. +2%&&&E+11
1%'-/E+1- +2%/&E+1 2 +2%&&&E+11 +.&1.
+..226 1%./.E1 (2 +..226 2%/&2E+1
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EJES 3LO0ALES"ir#1 D2 *2 "ir#2
+..226 +1/6&%. +2%&&&E+11 +..226
2%/&1/E+1 +2%&&&E+11 +.&1. 2%/&1/E+1
1./.2 ..226 +2%/&E+1 /-/1
..226 1/6&%. 2%&&&.E+11 ..226
+2%/&1/E+1 2%&&&.E+11 .&1. +2%/&1/E+1
/-/1 ..226 +2%/&E+1 1./.2
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La@ )e@taa@ 0ARRA n#@ @iren )ara *eBnir la@ ;atrice@ *e ri"i*e
A 1' I 5. E
(ATRI> RI3IDE> 0ARRA EJES LOCALES
[K'] D2 *2 "ir#2 D-
N2? .''&61%2/5 +.''&61%2/5
,2? 1/.2%'-22/ '/5/62-%/62
(2? '/5/62-%/6 5'6/5-5--2
N-? +.''&61%2/5 .''&61%2/5
,-? +1/.2%'-22/ +'/5/62-%/6
(-? '/5/62-%/6 2&--/6/6516
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*e ca*a :arraG en e9e@ LOCALES M e9e@ 3LO0ALES
2/- n"ul# %&&66'65 L 1.&%'/56
*- "ir#- [T] D2 *2
N1 1% +%1
+1/.2%'-22/ '/5/62-%/6 1 %1 1%
+'/5/62-%/6 2%&-.E1 (1 % %
N2 % %
1/.2%'-22/ +'/5/62-%/6 2 % %
+'/5/62-%/6 5%'6'E1 (2 % %
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"ir#2 D- *- "ir#- [T]t
% % % % N1
% % % % 1
1% % % % (1
% 1% +%1 % N2
% %1 1% % 2
% % % 1% (2
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D2 *2 "ir#2 D- *- "ir#-
1% %1 % % % %
+%1 1% % % % %
% % 1% % % %
% % % 1% %1 %
% % % +%1 1% %
% % % % % 1%
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[T]*[K'] D2 *2 "ir#2 D-
N1 .'65-.%65- +1/-%.1'2&2 +'/1.16%1-. +.'65-.%65-
1 .'65-%.65- 1/-.%1'2&2 '/1.161%-. +.'65-%.65-
(1 '/5/62-%/6 5%'6'E1
N2 +.'65-.%65- 1/-%.1'2&2 '/1.16%1-. .'65-.%65-
2 +.'65-%.65- +1/-.%1'2&2 +'/1.161%-. .'65-%.65-
(2 '/5/62-%/6 2%&-.E1
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(ATRI> DE RI3IDE> 0ARRA
*- "ir#- [K] D2 *2
1/-%.1'2&2 +'/1.16%1-. N1 .'.1-/%--- .'2-&%..&'
+1/-.%1'2&2 '/1.161%-. 1 .'2-&%..&' 6566%///2.'
+'/5/62-%/6 2%&-.E1 (1 +'/1.16%1-. '/1.161%-.1
+1/-%.1'2&2 '/1.16%1-. N2 +.'.1-/%-- +.'2-&%..&'
1/-.%1'2&2 +'/1.161%-. 2 +.'2-&%..&' +6566%///25
+'/5/62-%/6 5%'6'E1 (2 +'/1.16%1-. '/1.161%-.1
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EJES 3LO0ALES
"ir#2 D- *- "ir#-
+'/1.16%1-.1 +.'.1-/%-- +.'2-&%..&' +'/1.16%1-.1
'/1.161%-.1. +.'2-&%..&' +6566%///25 '/1.161%-.1.
5'6/5-5--2 '/1.16%1-.1 +'/1.161%-. 2&--/6/6516
'/1.16%1-.1. .'.1-/%--- .'2-&%..&' '/1.16%1-.1.
+'/1.161%-.1 .'2-&%..&' 6566%///2.' +'/1.161%-.1
2&--/6/6516 '/1.16%1-.1 +'/1.161%-. 5'6/5-5--2
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La@ )e@taa@ 0ARRA n#@ @iren )ara *eBnir la@ ;atrice@ *e ri"i*e
A & I 6/5 E
(ATRI> RI3IDE> 0ARRA EJES LOCALES
[K'] D- *- "ir#- D.
N-? .&5 +.&5
,-? 12-%/5 -/125
(-? -/125 1%22&E1
N.? +.&5 .&5
,.? +12-%/5 +-/125
(.? -/125 61.25
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*e ca*a :arraG en e9e@ LOCALES M e9e@ 3LO0ALES
2/- n"ul# +1%5//&6-- L 6
*. "ir#. [T] D- *-
N1 % 1%
+12-%/5 -/125 1 +1% %
+-/125 61.25 (1 % %
N2 % %
12-%/5 +-/125 2 % %
+-/125 1%22&E1 (2 % %
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"ir#- D. *. "ir#. [T]t
% % % % N1
% % % % 1
1% % % % (1
% % 1% % N2
% +1% % % 2
% % % 1% (2
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D- *- "ir#- D. *. "ir#.
% +1% % % % %
1% % % % % %
% % 1% % % %
% % % % +1% %
% % % 1% % %
% % % % % 1%
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[T]*[K'] D- *- "ir#- D.
N1 2%5'5E+11 12-%/5 -/125 +2%5'E+11
1 +.&5 6%2/12E+1. 1%''1.E+1 .&5
(1 -/125 1%22&E1
N2 +2%5'E+11 +12-%/5 +-/125 2%5'5E+11
2 .&5 +6%2/1E+1. +1%''1E+1 +.&5
(2 -/125 61.25
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(ATRI> DE RI3IDE> 0ARRA
*. "ir#. [K] D- *-
+12-%/5 -/125 N1 12-%/5 +2%52E+11
+6%2/1E+1. 1%''1.E+1 1 +2%52E+11 .&5
+-/125 61.25 (1 -/125 1%''1.E+1
12-%/5 +-/125 N2 +12-%/5 2%522E+11
6%2/12E+1. +1%''1E+1 2 2%522E+11 +.&5
+-/125 1%22&E1 (2 -/125 1%''1.E+1
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EJES 3LO0ALES
"ir#- D. *. "ir#.
-/125 +12-%/5 2%522E+11 -/125
1%''1-/E+1 2%522E+11 +.&5 1%''1-/E+1
122'5 +-/125 +1%''1E+1 61.25
+-/125 12-%/5 +2%52E+11 +-/125
+1%''1-/E+1 +2%52E+11 .&5 +1%''1-/E+1
61.25 +-/125 +1%''1E+1 122'5
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(ATRI> DE RI3IDE> DE LA ESTRUCTURA EN COO
1 Q1 1 2
1 1/6&%. 2%&&&-5E+11 +..226 +1/6&%.
,1 -%E+11 .&1. 2%/1E+1 +-%E+11
(1 +..226 2%/&1/E+1 1%./E1 ..226
2 +1/6&%. +2%&&&-5E+11 ..226 .'5&6%-/
,2 +-%E+11 +.&1. +2%/E+1 .'2-&%.5
(2 +..226 2%/&1/E+1 /%-/E& -5511'.
- +.'.1-/%-
,- +.'2-&%.5
(- +'/1.16%1
.
,.
(.
(ATRI>
2 2 .'5&6%-/
,2 +1 .'2-&%.5
(2 +16666666%6/ -5511'.
UER>ASNODALES
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- 1%1-6'/E+1- +.'.1-/%-
,- +1 +.'2-&%.5
(- 16666666%66/ +'/1.16%1
$K
(ATRI>
2 %-&6'
+1 -%11E+/
+16666666%6/ +2%5E+'
1%1-6'/E+1- %-&61
+1 +5%E+/
16666666%66/ -%.E+&
$K H
UER>ASNODALES
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DENADAS 3LO0ALES
Q2 2 - Q- - .
+2%&&&-5E+11 +..226
+.&1. 2%/&1/1E+1
+2%/&1/E+1 /-/1
.'2-&%..&'2 -5511'-%'65& +.'.1-/%- +.'2-&%.5 +'/1.16%1-.1.
.&/&66%///25 '/1.161%-.1. +.'2-&%.5 +6566%/// '/1.161%-.1.
'/1.161%-.1. /-.1/-5--2 '/1.16%1- +'/1.161 2&--/6/6516
+.'2-&%..&'2 '/1.16%1-.1. .'5161%' .'2-&%.5 21&&'--%'65& +12-%/5
+6566%///2.'5 +'/1.161%-.1. .'2-&%.5 .1666%/' '/1.161%-.1. 2%5E+11
'/1.161%-.1. 2&--/6/6516 21&&'-. '/1.161 /&6-5--2 +-/125
+12-%/5 2%5E+11 +-/125 12-%/5
2%5E+11 +.&5 +1%''1-/E+1 +2%5E+11
-/125 1%''E+1 61.25 +-/125
ESULTANTE
.'2-&%..&'2 -5511'-%'65& +.'.1-/%- +.'2-&%.5 +'/1.16%1-.1.
.&/&66%///25 '/1.161%-.1. +.'2-&%.5 +6566%/// '/1.161%-.1.
'/1.161%-.1. /-.1/-5--2 '/1.16%1- +'/1.161 2&--/6/6516
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+.'2-&%..&'2 '/1.16%1-.1. .'5161%' .'2-&%.5 21&&'--%'65&
+6566%///2.'5 +'/1.161%-.1. .'2-&%.5 .1666%/' '/1.161%-.1.
'/1.161%-.1. 2&--/6/6516 21&&'-. '/1.161 /&6-5--2
K H
ESULTANTE
-%115-2E+/ +2%525E+' %-&61 +5%E+/ %- 2
2%-.-6&E+6 +1%'/.5&E+1 5%1-E+/ '%65E+& +1%'5./E+1 Q2
+1%'/.5&E+1 1%'-2.E+11 +2%5E+' 5%2.E+1 +/%2-2'E+12 2
%51- +2%522-E+' %-&/5 +/%.E+/ %- -
'%65-/'-E+& 5%2-'62E+1 +/%.E+/ 2%.5E+6 +5%21-E+1 Q-
+1%'5./E+1 +/%2-2'E+12 -%E+& +5%E+1 1%/2.'-E+11 -
K+1
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Q. .
2%522E+11 -/125
+.&5 1%''E+1
+1%''1.E+1 6%1.E&
+2%522E+11 +-/125
.&5 +1%&E+1
+1%''1.E+1 1%2-E1
(O,I(IENTOS EJES 3LO0ALES
2
Q2
2
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-
Q-
-
aK
(O,I(IENTOS EJES 3LO0ALES
1%2662-62.
+%1&//.&/
+%./1--
1%26.'16211
+%.2/1&..
%.1-/5-
aK
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0ARRA 1
TKt
% 1% % % %
+1% % % % %
% % 1% % %
% % % % 1%
% % % +1% %
% % % % %
0ARRA 2
TKt
1% %1 % % %
+%1 1% % % %
% % 1% % %
% % % 1% %1
% % % +%1 1%
% % % % %
0ARRA -
TKt
% +1% % % %
1% % % % %
% % 1% % %
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% % % % +1%
% % % 1% %
% % % % %
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COORDENADAS 3LO0ALES COORDENADAS LOCALES
% 1
% Q1
% 1
% 2 1%2662-62. +%1&//.&66
% Q2 +%1&//.&66 +1%2662-62.
1% 2 +%./1--- +%./1---
COORDENADAS 3LO0ALES COORDENADAS LOCALES
% 2 1%2662-62. 1%25/&'..6'
% Q2 +%1&//.&66 +%1.56/2.2
% 2 +%./1--- +%./1---
% - 1%26.'16211 1%25.2''.26
% Q- +%.2/1&.-' +%16'-61-.6
1% - %.1-/5- %.1-/5-
COORDENADAS 3LO0ALES COORDENADAS LOCALES
% - 1%26.'16211 %.2/1&.-'
% Q- +%.2/1&.-' 1%26.'16211
% - %.1-/5- %.1-/5-
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% .
% Q.
1% .
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0ARRA 1
K? (ATRI> DE RI3IDE> EN EJES LOCALES
D1 *1 "ir#1 D2 *2
N1? .&1. +.&1.
,1? 1/6&%. ..226 +1/6&%.
(1? ..226 1%./.E1 +..226
N2? +.&1. .&1.
,2? +1/6&%. +..226 1/6&%.
(2? ..226 /-/1 +..226
0ARRA 2
K? (ATRI> DE RI3IDE> EN EJES LOCALES
D2 *2 "ir#2 D- *-
N2? .''&61%2/5 +.''&61%2/5
,2? 1/.2%'-22/ '/5/62-%/6 +1/.2%'-22/
(2? '/5/62-%/6 5%'6'E1 +'/5/62-%/6
N-? +.''&61%2/5 .''&61%2/5
,-? +1/.2%'-22/ +'/5/62-%/6 1/.2%'-22/
(-? '/5/62-%/6 2%&-.E1 +'/5/62-%/6
0ARRA -
K? (ATRI> DE RI3IDE> EN EJES LOCALES
D- *- "ir#- D. *.
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N-? .&5 +.&5
,-? 12-%/5 -/125 +12-%/5
(-? -/125 1%22&E1 +-/125
N.? +.&5 .&5
,.? +12-%/5 +-/125 12-%/5
(.? -/125 61.25 +-/125
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(O,I(IENTOS (ULTIPLICACIN REACCIONES EN 0ARRAS
aK
"ir#2 E9e@ l#cale@
1 &/1/%.1'./ N1?
..226 Q1 155%5/11 ,1?
/-/1 1 2125'6-%'2 (1?
2 +%1&//.&/ +&/1/%.1'./ N2?
+..226 Q2 +1%2662-62. +155%5/11 ,2?
1%./.E1 2 +%./1-- +1-.'-2'%/6 (2?
(O,I(IENTOS (ULTIPLICACIN REACCIONES EN 0ARRAS
aK
"ir#- E9e@ l#cale@
2 1%25/&'../ 1'/%22121 &&5%-/1& N2?
'/5/62-%/6 Q2 +%1.56/2. +.6.%/1-. &&5%-/1& ,2?
2%&-.E1 2 +%./1-- +15-1'--' 16666666%/ (2?
- 1%25.2''.- +1'/%22121 &&5%-/1& N-?
+'/5/62-%/6 Q- +%16'-61-5 .6.%/1-. &&5%-/1& ,-?
5%'6'E1 - %.1-/5 16.'2&%/ +1666666/ (-?
(O,I(IENTOS (ULTIPLICACIN REACCIONES EN 0ARRAS
aK
"ir#. E9e@ l#cale@
$8i)
K
$8i)
K
$8i)
K
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- %.2/1&.. 1/.&-%6&' N-?
-/125 Q- 1%26.'1621 2565%5&5'2 ,-?
61.25 - %.1-/5 '&6/52/%6/ (-?
. +1/.&-%6&' N.?
+-/125 Q. +2565%5&5'2 ,.?
1%22&E1 . 6.26./%2- (.?
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ESUER>OS
EJES LOCALES
&/1/%.1'./--5
155%5/112&-
2125'6-%'1/2.
+&/1/%.1'./--5
+155%5/112&
+1-.'-2'%/6/&
ESUER>OS
EJES LOCALES
2'2%25'-&'22&
&.'5%65''61/--
1-.'-2'%/6/'&
+'12%1'.1/'&
1.15%'.&.2./
+61'6-/%15&&
ESUER>OS
EJES LOCALES
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1/.&-%6&'/16
2565%5&5'16/61
'&6/52/%6/6.2
+1/.&-%6&'/2
+2565%5&5'16/6
6.26./%22&&2-
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ESCALA DE REPRESENTACIN %1
MOMENTOS PILAR IZQ. JCENA PILAR DER.
Kn Knm Kn
+2%126 +1%-.' +6%.26L' +2%2& &%115 +.%52L. +1%&-1 16%.22 +2%5/'-L' +1%'-. 2%5/2 +%65-L2 +1%/-/ 21%56/ 1%2/15L' +1%6. 1&%.5 -%1&5
-L. +1%5.- 1.%'6 5%11&/L' +1%..6 5%612 /%.-
L +1%-.' +6%1& '%&6'
Tra;#@ Re@ulta*# 0arra 0arra Recta entre*e :arra ;#;ent#@ c##r*ena*a c##r*ena*a ;#;ent#@
a:@#luta "rBc# eHter;#@
Knm m m +1%-.' 2% +1%-.'
L' 1%256 -%25 +1%&-2L. 2%512 .%5 +2%516-L' -%/6& 5%/5 +-%1L2 5%25 /% +-%6'-5L' 6%2'1 '%25 +.%26/-L. /%5-/ &%5 +.%'51/L' '%/&. 1%/5 +5%.-5
L +6%1& 1%5 12% +6%1&
0ARRA 1Tra;#@ Re@ulta*# Recta entre Recta entre L4nea*e :arra ;#;ent#@ ;#;ent#@ ;#;ent#@ *e cierre
eHter;#@ eHter;#@ in$eri#r
Knm Knm gr!" inici# +2%126 +2%126 1%/& H
L' +2%2& 2%L. +1%&-1 M
+2
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-L' +1%'-. 1%L2 +1%/-/ Bnal5L' +1%6. H-L. +1%5.- 1%/'//L' +1%..6 M
L +1%-.' +1%-.' 1%'/ 1%
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0ARRA 2(#;ent# (#;ent# 0arra (#;ent# L4nea L4nea)ar:#la al#re@ c##r*ena*a c##r*ena*a *e cierre *e cierrei@#@ttica "rBc# "rBc# iz7uier*a *erec8a
#Nm m inici# inici#% +1%-.' 6% 6%1-5 H H
11%./ &%115 6%125 5%21. 2% 12%1'%&-' 16%.22 6%25 .%6' M M2-%6/2 2%5/2 6%-/5 .%-1' 6% /%25%25 21%56/ 6%5 .%-.- Bnal Bnal2-%6/2 1&%.5 6%625 .%6'5 H H1'%&-' 1.%'6 6%/5 5%-.1 2% 12%11%./ 5%612 6%'/5 6%-1. M M% +6%1& /% /%62 6%1-5 /%62
0ARRA -L4nea Re@ulta*# Recta entre Recta entre L4nea L4nea
*e cierre ;#;ent#@ ;#;ent#@ ;#;ent#@ *e cierre *e cierre@u)eri#r eHter;#@ eHter;#@ in$eri#r @u)eri#r
inici# Knm Knm gr!" inici# inici#H +6%.26 +6%.26 11%-6 H H
2% +.%52 12% 12%M +2%5/' M M
2 . 6 ' 1 12 1.
1
2
-
.
5
6
/
'
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6% +%65- 1% /%Bnal 1%2/1 Bnal Bnal
H -%1&5 H H1%'65 5%11& 11%-5/ 12%'&/
M /%.- M M6% '%&6' '%&6' 12%& 1% /%
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AILES
ESCALA DE REPRESENTACIN %1
MOMENTOS PILAR IZQ. JCENA PILAR DER.
Kn Kn Kn
&%/1/ 2%'2L' &%/1/L. &%/1/-L' &%/1/L2 &%/1/
5L' &%/1/-L. &%/1//L' &%/1/
L &%/1/
0ARRA 1 0ARRA 2
Recta *e aHil 2%&/ 1% Recta *e aHil
2%&/ 6%Cierre N#*# 1 2% 1% Cierre N#*# 2
2%&/ 1%Cierre N#*# 2 2% 6% Cierre N#*# -
2%&/ 6%
+2
1
2
-
.
5
6
/
'
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0ARRA -
2% 6%2' Recta *e aHil
Cierre N#*# -
Cierre N#*# .
. 6 ' 1 12 1.
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