analisis estructural2 portico con apoyo empotrado
TRANSCRIPT
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PORTICO CON APOYO EMPOTRADO
E = 217370.65 Kg/cm^2
VIGAS = 25 50
CO!"MNAS = 25 25
#APATA I#$. = %0 %0
#APATA DER. = 100 100
1200 &g/m
1000&g
3
1200 &g/m
700 &g
'
5 m
NUMERACION DE NODOS Y BARRAS
1200 &g/m
1000&g
3
1200 &g/m
700 &g
7
65
%%
65
7
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'
5 m
FUERZAS TRANSMITIDAS EN LOS NODOS
(5) = (6) = *3000
(7) = (%) = *3000
*3000 &g *3000 &g
1000&g
*3000 &g *3000 3
700 &g
'
5 m
CALCULO DEL MEP
MEP = +,-!^2/12 = 2500
3 '
3 '
1 2
7
65
3 '
%%
3
65
7
'
1 2
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*250000 &g*cm 250000 &g*cm
3*250000 &g*cm 250000 &g*cm
'
5 m
la matriz de fuerzas atua!tes "sistema l#al$ e! l#s !#d#s e%trem#s de ad
EN LA BARRA ) Y *
(5 700 (7
(5) *3000 (7)
M5 = *250000 M7
(6 0 (%
(6) *3000 (%)
M6 250000 M%
matriz de tra!sf#rmai#! de ada &arra
0 1 0 0*1 0 0 0
0 0 1 0
T 0 0 0 0
0 0 0 *1
0 0 0 0
4 898 4:8 ;8 c; : 498(9m8c ) < 9c4?8 498
898 ;8 ?g8 c89 498(9m89 ;8 c9:8:8
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4m ;8 m849> : 498(9m8c + m849> :4:8:
1 0 0
0 1 0
T = 0 0 1
0 0 0
0 0 00 0 0
+ECTOR DE TODAS LAS FUERZAS ACTUANTES EN LA ESTRUCTURA
5 700
5) *3000
M5 *250000
6 0
6) *3000
M6 = 2500007 1000
7) *3000
M7 *250000
% 0
%) *3000
M% 250000
#!strui#! de la matriz l#al ,ara ada &arra
INICIO 3 INA! 5
ARRA 8+cm 8;4+cm !+cm A
3 25 25 '00 625
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
336'1.6'0625 1326.72515%61' 2653'5.03173%3 7075%675.13020% 'EF007
3 3)
336'1.6'0625 0 0
0 1326.72515%61' 2653'5
&3 = 0 2653'5.03173%2% 7EF007
*336'1.6'0625 0 0
0 *1326.72515%61 *2653'5
0 2653'5.03173%2% 'EF007
INICIO ' INA! 6
ARRA 8+cm 8;4+cm !+cm A
' 25 25 '00 625
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
336'1.6'0625 1326.72515%61' 2653'5.03173%3 7075%675.13020% 'EF007
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' 'Y
336'1.6'0625 0 0
0 1326.72515%61' 2653'5
K' = 0 2653'5.03173%2% 7EF007
*336'1.6'0625 0 0
0 *1326.72515%61 *2653'50 2653'5.03173%2% 'EF007
INICIO 5 INA! 7
ARRA 8+cm 8;4+cm !+cm A
5 25 25 300 625
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
'52%55.520%3333 31''.%300057%7 '7172'.500%6%1 '3''00.173611 5EF007
5 5Y
'52%55.520%333 0 00 31''.%300057%7 '71725
K5 = 0 '7172'.500%6%06 EF007
*'52%55.520%333 0 0
0 *31''.%300057%7 *'71725
0 '7172'.500%6%06 5EF007
INICIO 6 INA! %
ARRA 8+cm 8;4+cm !+cm A
6 25 25 300 625
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
'52%55.520%3333 31''.%300057%7 '7172'.500%6%1 '3''00.173611 5EF007
6 6Y
'52%55.520%333 0 0
0 31''.%300057%7 '71725
K6 = 0 '7172'.500%6%06 EF007
*'52%55.520%333 0 0
0 *31''.%300057%7 *'71725
0 '7172'.500%6%06 5EF007
INICIO 5 INA! 6
ARRA 8+cm 8;4+cm !+cm A
7 25 50 500 1250
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
5'3'26.625 5'3'.26625 135%566.5625 '52%55520.%3333 2EF00%
5 5Y
5'3'26.625 0 0
'@
5@
6@
5@
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0 5'3'.26625 1EF006
K7 = 0 135%566.5625 5EF00%
*5'3'26.625 0 0
0 *5'3'.26625 06
0 135%566.5625 2EF00%
INICIO 7 INA! %ARRA 8+cm 8;4+cm !+cm A
% 25 50 500 1250
AE/! 12EI/!^3 6EI/!^2 'EI/! 2EI/!
5'3'26.625 5'3'.26625 135%566.5625 '52%55520.%3333 2EF00%
7 7Y
5'3'26.625 0 0
0 5'3'.26625 1EF006
K% = 0 135%566.5625 5EF00%
*5'3'.26625 0 00 *5'3'.26625 06
0 135%566.5625 2EF00%
MATRIZ DE RI-IDES DEL SISTEMA -LOBAL
3 3Y R3
1326.72515%61 0 *2653'5
0 336'1.6'0625 0
K3 = *2653'5.03173%3 0 7EF007
*1326.72515%61 0 2653'5
0 *336'1.6'0625 0
*2653'5.03173%3 0 'EF007
' 'Y R'
1326.72515%61 0 *2653'5
0 336'1.6'0625 0
K' = *2653'5.03173%3 0 7EF007
*1326.72515%61 0 2653'5
0 *336'1.6'0625 0
*2653'5.03173%3 0 'EF007
5 5Y R5
31''.%300057%7 0 *'71725
0 '52%55.520%3333 0
K5 = *'7172'.500%6%1 0 EF007
*31''.%300057%7 0 '71725
0 *'52%55.520%333 0
*31''.%300057%7 0 5EF007
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6 6Y R6
31''.%300057%7 0 *'71725
0 '52%55.520%3333 0
K6 = *'7172'.500%6%1 0 EF007
*31''.%300057%7 0 '71725
0 *'52%55.520%333 0*'7172'.500%6%1 0 '71725
5 5Y R5
5'3'26.625 0 0
0 5'3'.26625 1EF006
&7 = 0 135%566.5625 5EF00%
*5'3'26.625 0 0
0 *5'3'.26625 06
0 135%566.5625 2EF00%
7 7Y R7
5'3'26.625 0 0
0 5'3'.26625 1EF006
K% = 0 135%566.5625 5EF00%
*5'3'.26625 0 0
0 *5'3'.26625 06
0 135%566.5625 2EF00%
MATRIZ ENSAMBLADA DE RI-IDECES "SISTEMA -LOBAL$
5 5Y R5
5'7%%.1%016'5 0 *20637
0 7731.'2770%33 1EF006
*20637.'612% 135%566.5625 6EF00%
*5'3'26.625 0 0
0 *5'3'.26625 06
K = 0 135%566.5625 2EF00%
*31''.%300057%7 0 '71725
0 *'52%55.520%333 0
*31''.%300057%7 0 5EF007
0 0 0
0 0 0
0 0 0
!A INVERSA DE !A MATRI# DE RIGIDE# RED"CIDA
5 5Y R5
0.00011%0231 *7.5''5E*007 2E*00%
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*'.77703E*007 2.2'03%E*006 *'E*00
3.%2''7715E*00% *'.66517'E*00 2E*00
0.0001171777 *7.556%%75E*007 2E*00%
'.777026E*007 1.'%75%50E*00% 'E*00
K^*1 = 1.720'52E*00% *'.'7761E*00 *7E*010
1.25130%2E*006 %.25032%10E*00 *7E*010
*6.%123%'3E*007 2.25677E*006 *'E*00*5.225326E*00% *'.3050553E*00 *2E*010
5.63'67%3'E*007 '.%531207E*00 6E*010
6.%123%'2E*007 1.%5%1'3'E*00% 'E*00
1.255166%E*007 *6.0%%0''0E*00 1E*010
CA!C"!O DE DESP!A#AMIENTOS +SISTEMA G!OA!
5 700
5) *3000
M5 *2500006 0
6) *3000
M6 = 250000
7 1000
7) *3000
M7 *250000
% 0
%) *3000
M% 250000
REEMP!A#ANDO !AS MATRICES RESPECTIVAS "=K^*1-
"5 0.0%'35
"5) *0.01%1
G5 *0.0005
"6 0.0%'6
"6) *0.0172
" = G6 = 0.00056
"7 0.00272
"7) *0.025
G7 *0.000%
"% *0.0007
"%) *0.0236
G% 0.000%5
MATRIZ DE RI-IDEZ DE LA ESTRUCTURA TOTAL
3 3Y R3
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1326.72515%61 0 *2653'5
0 336'1.6'0625 0
*2653'5.03173%3 0 7EF007
0 0 0
0 0 0
0 0 0
*1326.72515%61 0 2653'50 *336'1.6'0625 0
K = *2653'5.03173%3 0 'EF007
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 00 0 0
CON+ERSION DE LOS SISTEMAS -LOBALES OBTENIDOS AL SISTEMA LOCAL
PARA LA COLUMNA .
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V6 0 *1326.72515%61 *2653'5
M6 0 2653'5.03173%2% 'EF007
PARA LA COLUMNA 0
N5 '52%55.520%333 0 0
V5 0 31''.%300057%7 '71725M5 = 0 '7172'.500%6%06 EF007
N7 *'52%55.520%333 0 0
V7 0 *31''.%300057%7 *'71725
M7 0 '7172'.500%6%06 5EF007
PARA COLUMNA 1
N6 '52%55.520%333 0 0
V6 0 31''.%300057%7 '71725
M6 = 0 '7172'.500%6%06 EF007N% *'52%55.520%333 0 0
V% 0 *31''.%300057%7 *'71725
M% 0 '7172'.500%6%06 5EF007
PARA LA +I-A )
N5 5'3'26.625 0 0
V5 0 5'3'.26625 1EF006
M5 = 0 135%566.5625 5EF00%
N6 *5'3'26.625 0 0
V6 0 *5'3'.26625 06
M6 0 135%566.5625 2EF00%
PARA LA +I-A *
N7 5'3'26.625 0 0
V7 0 5'3'.26625 1EF006
M7 = 0 135%566.5625 5EF00%
N% *5'3'.26625 0 0
V% 0 *5'3'.26625 06
M% 0 135%566.5625 2EF00%
REACCIONES
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1 2
3%22.523'37'1 '2360
*27.2%3%305255
6157.7'35036% 5%'2.2'
DIAGRAMA DE ES"ER#O AIA!1%63.136'0001
110.1'367562 *110.2
*135.%5265722'
6157.7'35036%'
5%'2.236'203'05
DIAGRAMA DE "ER#A CORTANTE
110.1'367562
*%63.136'7''3
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110.1'367562
*27.2%3%305255 261.5%325116
DIAGRAMA DE MOMENTO !ECTOR
2035
*15''75.''0%1
*1350'7.'5137
13'%'6
*123%2.'31'5 *111371.01%700
*1'736.0615533 62273
3%22.523'37'06 '2360.251776'
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cm^2
cm^2
cm^2
cm^2
m
m
m
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m
&g
&g
m
m
Kg*m = 250000 &g*cm
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m
m
a &arra es la si'uie!te(
1000
*3000
= *250000
0
*3000
250000
0 0 0 *10 0 1 0
0 0 = 0 0
1 0 0 0
0 0 0 0
0 1 0 0
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0 0 0
0 0 0
0 0 0 = T^T
1 0 0
0 1 00 0 1
I E
32552.0%3 217370.65
5 5)
*336'1.6 0 0
0 *1326.725 2653'5
0 *2653'5 353733%
336'1.6' 0 0
0 1326.7252 *2653'5
0 *2653'5 7075%675
I E
32552.0%3 217370.65
5@
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6 6Y
*336'1.6 0 0
0 *1326.725 2653'5
0 *2653'5 353733%
336'1.6' 0 0
0 1326.7252 *2653'50 *2653'5 7075%675
I E
32552.0%3 217370.65
7 7Y
*'52%55.5 0 00 *31''.%3 '7172'.5
0 *'7172'.5 '7172'50
'52%55.52 0 0
0 31''.%3 *'7172'.5
0 *'7172'.5 '3''00
I E
32552.0%3 217370.65
% %Y
*'52%55.5 0 0
0 *31''.%3 '7172'.5
0 *'7172'.5 '7172'50
'52%55.52 0 0
0 31''.%3 *'7172'.5
0 '7172'50 '3''00
I E
260'16.67 217370.65
6 6Y
*5'3'26.6 0 0
6@
7@
%@
6@
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0 *5'3'.266 135%567
0 *135%567 760
5'3'26.63 0 0
0 5'3'.2663 *135%567
0 *135%567 521
I E
260'16.67 217370.65
% %Y
*5'3'26.6 0 0
0 *5'3'.266 135%567
0 *135%567 760
5'3'26.63 0 00 5'3'.2663 *135%567
0 *135%567 521
5 5Y R5
*1326.725 0 *2653'5 3
0 *336'1.6 0 3Y
2653'5 0 353733% R3
1326.7252 0 2653'5 5
0 336'1.6' 0 5Y
2653'5 0 7075%675 R5
6 6Y R6
*1326.725 0 *2653'5 '
0 *336'1.6 0 'Y
2653'5 0 353733% R'
1326.7252 0 2653'5 6
0 336'1.6' 0 6Y
2653'5 0 7075%675 R6
7 7Y R7
*31''.%3 0 *'7172'.55
0 *'52%55.5 0 5Y
'7172'.5 0 '7172'50R5
31''.%3 0 '7172'.5 7
0 '52%55.52 0 7Y
'7172'.5 0 '3''00R7
%@
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% %Y R%
*31''.%3 0 *'7172'.56
0 *'52%55.5 0 6Y
'7172'.5 0 '7172'50R6
31''.%3 0 '7172'.5 %
0 '52%55.52 0 %Y'7172'.5 0 '3''00R%
6 6Y R6
*5'3'26.6 0 0 5
0 *5'3'.266 135%567 5Y
0 *135%567 760 R5
5'3'26.63 0 0 6
0 5'3'.2663 *135%5676Y
0 *135%567 521 R6
% %Y R%
*5'3'26.6 0 0 7
0 *5'3'.266 135%567 7Y
0 *135%567 760 R7
5'3'26.63 0 0 %
0 5'3'.2663 *135%567%Y
0 *135%567 521 R%
6 6Y R6 7 7Y R7 %
*5'3'26.6 0 0 *31''.%3 0 *'7172'.5 0
0 *5'3'.266 135%567 0 *'52%55.5 0 0
0 *135%567 760 '7172'.5 0 '7172'50 0
5'7%%.1% 0 *20637.5 0 0 0 *31''.%3
0 7731.'3 *135%567 0 0 0 0
*20637.5 *135%567 06 0 0 0 '7172'.5
0 0 0 5'6571.'6 0 '7172'.5 *5'3'26.6
0 0 0 0 '5%2%.7 135%567 0
0 0 0 '7172'.5 135%567 '21 0
*31''.%3 0 '7172'.5 *5'3'.266 0 0 5'6571.'6
0 *'52%55.5 0 0 *5'3'.266 *135%567 0
*'7172'.5 0 '7172'.5 0 135%567 760 '7172'.5
6 6Y R6 7 7Y R7 %
0.0001171 7.55E*007 3.25E*00% 6.05E*007 *1.2E*006 7.52E*00% 1.1E*006
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*'.%E*007 1.'E*00% *5.0E*00 5.57E*00 2.3E*006 *5.2E*00 1.15E*00%
3.7%E*00% '.70E*00 *6.7E*010 *1.3E*00 *'.6E*00 *1.E*010 *6.'E*010
0.00011%1 7.56E*007 3.2E*00% 6.01E*007 *1.2E*006 7.3E*00% 1.1E*006
'.%0E*007 2.3E*006 '.%E*00 *5.6E*00 1.1E*00% 5.16E*00 *1.1E*00%
1.76E*00% '.'%E*00 1.%E*00 5.27E*010 *'.3E*00 1.77E*010 *%.'E*010
1.25E*006 *%.3E*00 *7.7E*010 1.%6E*006 1.02E*00% *3.6E*010 1.%5E*006
*6.E*007 1.%6E*00% *5.1E*00 7.6'E*00 5.13E*006 *.2E*00 1.5E*00%*5.3E*00% '.31E*00 7.'5E*011 *2.1E*00 *%.0E*00 2.23E*00 *1.6E*00
5.6%E*007 *'.E*00 *1.5E*00 2.03E*00% 6.0'E*00 .70E*010 1.%6E*006
6.%5E*007 2.3E*006 5.15E*00 *7.6E*00 2.52E*00% .1%E*00 *1.6E*00%
1.27E*007 6.0E*00 2.27E*011 1.32E*00 *1.0E*00% *%.1E*010 1.5'E*011
cm
cm
98:
cm
cm
98:
cm
cm
98:
cm
cm
98:
' 'Y R' 5 5Y R5 6
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0 0 0 *1326.725 0 *2653'5 0
0 0 0 0 *336'1.6 0 0
0 0 0 2653'5 0 353733% 0
1326.7252 0 *2653'5 0 0 0 *1326.725
0 336'1.6' 0 0 0 0 0
*2653'5 0 7075%675 0 0 0 2653'5
0 0 0 5'7%%.1% 0 *20637.5 *5'3'26.60 0 0 0 7731.'3 135%567 0
0 0 0 *20637.5 135%567 06 0
*1326.725 0 2653'5 *5'3'26.6 0 0 5'7%%.1%
0 *336'1.6 0 0 *5'3'.266 *135%567 0
*2653'5 0 353733% 0 135%567 760 *20637.5
0 0 0 *31''.%3 0 '7172'.5 0
0 0 0 0 *'52%55.5 0 0
0 0 0 *31''.%3 0 '7172'50 0
0 0 0 0 0 0 *31''.%3
0 0 0 0 0 0 00 0 0 0 0 0 *'7172'.5
0 0 0 0 0
0 0 0 0 0
0 0 0 - 0 = 0
0 1 0 0.0%'3'73 *0.01%131
*1 0 0 *0.01%13 *0.0%'3'7
0 0 1 *0.000525 *0.000525
0 0 0 0 0
0 0 0 0 0
0 0 0 - 0 = 0
0 1 0 0.0%'573 *0.017201
*1 0 0 *0.017201 *0.0%'57
0 0 1 0.000562% 0.000562%
0 0 0 0.0%'3'73 *0.01%131
0 0 0 *0.01%13 *0.0%'3'7
0 0 0 - *0.000525 = *0.000525
0 1 0 0.00272'' *0.025
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*1 0 0 *0.025 *0.00272'
0 0 1 *0.000761 *0.000761
0 0 0 0.0%'573 *0.017201
0 0 0 *0.017201 *0.0%'570 0 0 - 0.000562% = 0.000562%
0 1 0 *0.00070' *0.0235%1
*1 0 0 *0.0235%1 0.00070'2
0 0 1 0.000%'%' 0.000%'%'
0 0 0 0.0%'3'73 0.0%'3'73
0 0 0 *0.01%13 *0.01%13
0 0 0 - *0.000525 = *0.0005251 0 0 0.0%'573 0.0%'573
0 1 0 *0.017201 *0.017201
0 0 1 0.000562% 0.000562%
0 0 0 0.00272'' 0.00272''
0 0 0 *0.025 *0.025
0 0 0 - *0.000761 = *0.000761
1 0 0 *0.00070' *0.00070'
0 1 0 *0.0235%1 *0.0235%1
0 0 1 0.000%'%' 0.000%'%'
*336'1.6 0 0 0 6157.7''
0 *1326.725 2653'5 0 *27.2%3%3
0 *2653'5 353733% - 0 = 3%22.523
336'1.6' 0 0 *0.01%131 *6157.7'
0 1326.7252 *2653'5 *0.0%'3'7 27.2%3%31
0 *2653'5 7075%675 *0.000525 *1'736.06
*336'1.6 0 0 0 5%'2.236'
0 *1326.725 2653'5 0 261.5%325
0 *2653'5 353733% - 0 = '2360.252
336'1.6' 0 0 *0.017201 *5%'2.236
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0 1326.7252 *2653'5 *0.0%'57 *261.5%33
0 *2653'5 7075%675 0.000562% 62273.0'
*'52%55.5 0 0 *0.01%131 3110.7%37
0 *31''.%3 '7172'.5 *0.0%'3'7 *%63.13650 *'7172'.5 '7172'50 - *0.000525 = *123%2.
'52%55.52 0 0 *0.025 *3110.7%'
0 31''.%3 *'7172'.5 *0.00272' %63.136'%
0 *'7172'.5 '3''00 *0.000761 *1350'%
*'52%55.5 0 0 *0.017201 2%%%.3%7
0 *31''.%3 '7172'.5 *0.0%'57 37.'352
0 *'7172'.5 '7172'50- 0.000562%= 52%%1.063'52%55.52 0 0 *0.0235%1 *2%%%.3
0 31''.%3 *'7172'.5 0.00070'2 *37.'35
0 '7172'50 '3''00 0.000%'%' 00.'76
*5'3'26.6 0 0 0.0%'3'73 *135.%527
0 *5'3'.266 135%567 *0.01%13 '6.'6%'
0 *135%567 760 - *0.000525 = *111371
5'3'26.63 0 0 0.0%'573 135.%5266
0 5'3'.2663 *135%567 *0.017201 *'6.'6%
0 *135%567 521 0.000562% 13'%'5.%6
*5'3'26.6 0 0 0.00272'' 1%63.136'
0 *5'3'.266 135%567 *0.025 110.1''
0 *135%567 760 - *0.000761 = *15''75.'
5'3'26.63 0 0 *0.00070' *37.'36
0 5'3'.2663 *135%567 *0.0235%1 *110.1'
0 *135%567 521 0.000%'%' 2035.17
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261.5%325
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%Y R%
0 0 5
0 0 5Y
0 0 R5
0 *'7172'.56
*'52%55.5 0 6Y
0 '7172'50R6
0 0 7
*5'3'.266 135%567 7Y
*135%567 760 R7
0 '7172'.5%
'5%2%.7 *135%567%Y
*135%567 '21 R%
%Y R%
1.17E*006 7.1E*00% 5
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1.1E*00% *5.1E*005Y
'.60E*00 1.1E*010 R5
1.17E*006 7.32E*00% 6
2.3E*006 5.0%E*00 6Y
'.31E*00 *2.0E*010R6
*1.0E*00% *3.5E*0107
2.52E*00% *.0E*007Y%.00E*00 *.3E*010R7
*6.0E*00 *1.'E*00%
5.13E*006 .03E*00 %Y
1.0'E*00% 2.32E*00 R%
6Y R6 7 7Y R7 % %Y
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0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 *2653'5 0 0 0 0 0
*336'1.6 0 0 0 0 0 0
0 353733% 0 0 0 0 0
0 0 *31''.%3 0 *'7172'.5 0 0*5'3'.266 135%567 0 *'52%55.5 0 0 0
*135%567 760 '7172'.5 0 '7172'50 0 0
0 *20637.5 0 0 0 *31''.%3 0
7731.'3 *135%567 0 0 0 0 *'52%55.5
*135%567 06 0 0 0 '7172'.5 0
0 0 5'6571.'6 0 '7172'.5 *5'3'26.6 0
0 0 0 '5%2%.7 135%567 0 *5'3'.266
0 0 '7172'.5 135%567 '21 0 *135%567
0 '7172'.5 *5'3'.266 0 0 5'6571.'6 0
*'52%55.5 0 0 *5'3'.266 *135%567 0 '5%2%.70 '7172'.5 0 135%567 760 '7172'.5 *135%567
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700 *%35.%527
*3000 30'6.'7
* *250000 = 13%62
0 135.%5266
*3000 253.0503
250000 *11515'.1
1000 %63.136'
*3000 3110.1'
* *250000 = 552'.551
0 *37.'36
*3000 2%%.0%06
250000 *'006'.%3
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R%
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0 3
0 3Y
0 R3
0 '
0 'Y
0 R'
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0 R5
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'7172'50R6
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760 R7
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*135%567%Y'21 R%
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