ejercicios de analisis estructural ii-metodo matricial
TRANSCRIPT
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1)CALCULO de [k]
BARRA L(m) EA(cte) k = EA/L
1 3 1 0.33
2 3 1 0.33
3 3 1 0.33
4 3 1 0.33
5 3 1 0.33
6 3 1 0.33
7 3 1 0.33
8 3 1 0.33
3 1 0.33
10 3 1 0.33
11 3 1 0.33
2) !ALORE" U#$%AR$O"
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3) CALCULO &E [']
B C D E Fnudos
[ 1 ]= [ 8 ]= [ 6 ]=[(64*0.50/0.87)]
[ 2 ]= [ 3 ]= [ 11 ]= [ ]= [ 5 ]=[(6
[ 10 ]= [ 7 ]= [ 4 ]=[(64*0.50/(+0.87
〖 1][ 〗 ,0- ,^ 0- ,0- ,0-
[ 2]〗 ^ 〖 2][ 〗 ,0- ,0- ,0-^ ,0- +〖 [ 3]〗 ^ 〖 3][ 〗 ^ ,0- ,0-
,0- ,0- 〖+ [ 4]〗 ^ 〖 4][ 〗 ,0-^ ,0- ,0- ,0-〖 [ 5]〗 ^ 〖+ [ 5]〗 ^ ,0-,0- ,0- 〖 [ 6]〗 ^ ,0-
〖+ 6][ 〗 ,0-^ ,0- +〖 7][ 〗 ^ ,0- ,0- 〖 [ 7]〗 ^
,0- 〖 [ 8]〗 ,0- ,0- ,0-^
,0- ,0- ,0- ,0- 〖 ][ 〗 ^
+ 10][ 〗 ,0- ,0- ,0- ,0-^
,0- ,0- ,0- ,0- ,0- 〖
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0.5
1
0
0
0[a]= 0
0
0
0
0.5
0
0.330
0
0
0
[k]= 00
0
0
0
0
0.5
0.87
0
0
0
0
0
0
0
0
0
0
〖 ][ 〗 ^ =
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0.17
0.2
0
00
0
0
0
0
0
0
barras 01
234 0.55 06 0.337 08 09 010 011 0
G 00
0.08
0.145
.0E15
5.22E15
.0E15
1.57E16
.0E15
2.61E16
6.02E00
3.13E16
4.11E00
〖 ][ 〗 ]^ [ =
]=[
〖 ][ 〗 ^(!" = − − − − − − − − − − −
*1/0)]
)]
,0-
,0-,0-
,0-
,0-
+〖 8][ 〗 ^
+〖 [ ]〗 ^
〖 [ 10]〗 ^
1[ 1]〗 ^
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2.0E16
2.50E00
1.04E16
2.30E171.32E17
2.30E17
3.6E17
2.30E17
6.61E17
6.60E01
7.3E17
1.65E01
5.28E17
1.15E012.64E17
0
32
64
128
4.55
0
64
64
4.6
0
11.4
0
10.67
][ =
]=[
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21.33
42.67
16.52
0
21.33
21.33
1.650
3.83
10.67
010.67
0
0
37.12
4.82
37.12
4.20
18.56
12.84
18.56
]=[
]=[
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0.87 0 0 0
0 1 0 0
0 1 0 1
0 0 0 0.5
0 0 0 00 0 0 0.5
0 0.5 0.87 0
0 0.5 0.87 0
0 0 0 0
0.87 0 0 0
0 0 0 0
0 0 0 00.33 0 0 0
0 0.33 0 0
0 0 0.33 0
0 0 0 0.33
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 0 0 0
1 1 0 0
0 0 0 0
0 1 0.5 0
0 0 0.87 0
0 0 0.5 1
0 0 0.87 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
]=[ 〖 ][ 〗 ^ ] ][ [
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0.33 0 0 0
0 0 0 0
0.33 0.33 0 0
0 0 0 00 0.33 0.17 0
0 0 0.2 0
0 0 0.17 0.33
0 0 0.2 0
0 0 0 0.33
0 0 0 0
0 0 0 0
0 0 0 0
0 0.33 0 0
0.50 0 0 0
0 0.83 0 0.33
0 0 0.50 0
0 0.33 0 0.5
0 0 0 0
0 0 0 0.08
0 0 0 0.145
0 0.08 0.15 0.08
0 0.145 0.25 0.15
0.145 0.08 0.15 0
0.2523 0.145 0.25 0
5.22E15 .0E15 1.57E16 .0E15
3.00E15 5.22E15 .01E15 5.22E15
5.22E15 .0E15 1.57E16 .0E15
.01E15 1.57E16 2.70E16 1.57E16
5.22E15 .0E15 1.57E16 .0E15
1.50E16 2.61E16 4.50E16 2.61E16
3.05E00 4.1E00 6.46E00 4.6E00
1.80E16 3.13E16 5.40E16 3.13E16
2.40E00 2.74E00 3.43E00 3.43E00
]=[ 〖 ][ 〗(+1)
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1.20E16 2.0E16 3.60E16 2.0E16
1.44E00 2.50E00 8.62E01 2.50E00
6.00E15 1.04E16 1.80E16 1.04E16
]= ] ][ [ [
[]=[ ] []
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#E$F%C&C%')
$E&CC%*E+
0.5 0.87 0
0 0 0
0 0 0
0 0 0.5
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
& E
]=[ 〖 ][ 〗 ]^ [
]=[ 〖〖 [ 〗 ]_ 〗 ]^ [
〖 [ 〗 ]=_
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0 0 0 0
0 0 0 0
0 0 0 0
0.87 0.5 0.87 0
0 1 0 10.87 0 0 0.5
0 0 0 0.5
0 0 0 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0.33 0 0 0
0 0.33 0 0
0 0 0.33 0
0 0 0 0.33
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0.5 0.5 0
0 0.87 0.87 0
0.5 0 0 0
0.87 0 0 0
0 0 0 0
0 0 0 0
0.5 0.5 0 1
0.87 0.87 0 0
0 0 0.5 1
0 0 0.87 0
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6.00E16 2.70E00 7.21E16 4.20E00
2.87E01 3.00E00 0.00E00 3.00E00
3.00E16 3.75E01 3.60E16 3.75E01
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BARRA
0 10 20 3
0.87 40 50 60 70 80 90 100 11
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0 0 0 0
0 0 0 0
0.5 1 0 0
0.87 0 0 0
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0 0 0
0 0 0
0 0 0
0 0 0
0 0 00.87 0 0
0.87 0 0
0 0.5 0.87
0 1 0
0 0.5 0.87
0 1 0
0 00 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0.33 0
0 0.33
0.5 0
0.87 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0.5 1
0.87 0
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0.17 0
0.2 0
0 0
0 00 0
0 0
0 0
0 0
0 0
0 0
0.17 0.33
0.2 0
0 0.08 0.15
0 0.15 0.25
0.15 0.08 0.15
0.25 0.15 0.25
0.15 0 0
0.25 0 0
0 0 0
0 0 0
0 0.33 0
0.50 0 0
0 0.83 0
0 0 0.50
2.0E16 5.21E01 1.04E16
1.20E16 3.00E01 6.00E15
2.0E16 5.21E01 1.04E16
3.60E16 2.55E00 1.80E16
2.0E16 5.21E01 1.04E16
6.00E16 5.40E00 3.00E16
4.87E00 3.00E00 4.51E00
7.21E16 6.82E00 3.60E16
0.00E00 3.00E00 2.74E00
][ =
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4.80E16 3.7E00 2.40E16
5.75E01 3.00E00 1.15E00
2.40E16 1.13E00 1.20E16
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0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
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0
0
0
0
0
0
0
0
0
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8
0
6
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C,-C.-* DE [a] / [k]
B&$$& -(s" E (kbs2" & = s21 25 2000 10
2 25 2000 10
3 20 2000 10
4 20 2000 10
5 15 2000 10
#&-*$E+ .%&$%*+
=
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0.8
[a]= 00.6
11600.00
[k]= 00
0.8
0.6
280.00
660
12644.00
132.00
7.5756E005
k = E&- 4.42087E00611600
11600
14500 0.0008841733
14500 0.000847333
1333.3333333333
]=[ 〖 ][
〖 ][ 〗 ^ =
〖 ][ 〗 ]^ [ =
]=[
]=[ 〖 ][ 〗(
〖 ][ 〗 ^(!" = − − − − − − − − − − −
] [ =
]= ] ][ [ [
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0.00122
0.00085
0.00015
14.10
.83
2.14
#E$F%C&C%'
10
20
$E&CC%*E+
0.8 0.6
0 00 0
&
0.8 0
0.6 0
0 0
0 10 0
0 0
1128846000 $E&CC983
]= ] ][ [ [
[ ]= 〖 ][ 〗 ^
]=[
][ =
][ =
]=[
〖 [ 〗 ]_ =
〖〖 [ 〗 ]_ 〗 ^ =
]=[
0
. !!
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128171
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0.6
1
0.8
0 0
11600.00 0
0 14500.00
0 0.6
1 0.8
0 8700.00
11600.00 11600.00
132.00
25056.00
4.42087E006 10
4.01562E005 20
] ]^ [ [
1) ][
]=[
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C
B&$$&+0 0 0 0 1
0 1 0 0 20 0 0.6 0.8 3
B C
$E&CC%*E+
0
0
0
00.6
0.8
%*E+
[]
〖〖 [ 〗 ]_ 〗 ]^ [
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1 C&-C.-* DE [a] / [k]
B&$$& - (" E& (:;" k = E&-1 5 1 0.2
2 5 1 0.23 5 1 0.2
4 5 1 0.2
5 5.83 1 0.17
6 3 1 0.33
7 5.83 1 0.17
8 5.83 1 0.17
3 1 0.33
10 5.83 1 0.17
11 5.36 1 0.1
12 5.36 1 0.1
13 5 1 0.2
11 #EC*$E+ .%&$%*+
2 ]= [ [ 2 ]= [ 3 ]= [ 4 ]=[(64* 1/0) ]
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F.E$
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0
0
0
0
0
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43/64
-
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0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0.2 0.2 0
0 0 0
0 0.2 0.2
0 0 0
0 0 0.2
0 0 0
0 0 0
0 0 0
0 0 00 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0.4 0 0.2
0 0.33 0
0.2 0 0.65
0 0 0
0 0 0.2
0 0 0
0 0 0
0 0 0
0 0 0.13
0 0 0.08
0 0 0
0 0 0
0 0 0.13
0 0.33 0.08
5.00E00 4.63E00 5.00E00
〖 ][ 〗 ]^ [ =
]=[
1)]
1)]
0.37))]
/0.37)]
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4.56E00 2.67E15 .11E00
5.00E00 .26E00 1.00E01
6.80E01 5.34E15 1.36E00
5.00E00 .3E00 1.00E01
3.20E00 8.01E15 6.3E00
5.00E00 .57E00 1.00E01
7.07E00 1.07E16 1.41E012.70E00 1.58E15 5.40E00
3.20E00 8.01E15 6.3E00
1.16E00 2.64E15 2.32E00
6.80E01 5.34E15 1.36E00
2.70E00 1.58E15 5.40E00
4.56E00 2.67E15 .11E00
.36841738431.040832E017
18.7368347686
2.081664E017
41.03127728
3.12246E017
61.8680028351
4.163328E017
6.172375E016
3.12246E017
1.031332E017
2.081664E017
6.172375E016
1.040832E017
.37
.37
22.36
20.77
72
0
24
0
64
〖 ][ 〗(+1) =
]=[
]=[
c
c
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0
8
0
0
1.87
1.87
4.47
4.15
12.35
04.12
0.00
21.333333333
0
1.4
0.00
0
#E$%F%C&C%')
0.00
0.00
0.4
2.10
0.32
21.33
4.15
0.00
0.00
21.33
1.3
0.55
5.6
7.85
]=[ [
]=[
c
][ =
c
]=[
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$E&CC%*E+ E -*+ &*>*+
1 0 0
0 0 0
0 0 0
0 0 1
0.86 0.51 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0.860 0 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
12.4
6.30
4.15
0
[ ]= 〖〖 [〗 ]_ 〗 ^ [
〖 [〗 _
]=
〖〖 [〗 ]_ 〗 ^ =
]=[ c
-
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0 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 1 0 1 0
0 0 0 0 00 0 0 0 0
0.51 0 0 0 0
0.51 0 0 0 0
0 0 1 0 0
0 0 0 0.86 0.51
0 0 0 0 0
0 0 0 0 0
1 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0.2 0 0 0 0
0 0.17 0 0 0
0 0 0.33 0 0
0 0 0 0.17 0
0 0 0 0 0.17
0 0 0 0 00 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0.86 0.86
0 0 0 0.51 0.51
1 0 0 0 0
0 0 0 0 0
1 0 0 0 0
0 0 0 0 0
0 0 0 0 0.86
]=[ 〖 ][ 〗 ] ]^ [ [
-
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0 0 0 0 0.51
0 0 0 0 0
0 0 0 0 0
0 0.86 0 0.86 0
0 0.51 1 0.51 0
0 0 0 0 0
0 0 0.33 0 0
0 0 0 0.15 0.15
0 0 0 0.0 0.0
0.2 0 0 0 0
0 0 0 0 0
0.2 0 0 0 0
0 0 0 0 0
0 0 0 0 0.150 0 0 0 0.0
0 0 0 0 0
0 0 0 0 0
0 0.15 0 0.15 0
0 0.0 0.33 0.0 0
0 0 0 0 0
0 0 0 0 0
0 0.2 0 0 0
0.2 0 0 0 0
0 0.4 0 0.2 0
0 0 0.33 0 0
0 0.2 0 0.33 0.08
0 0 0 0.08 0.04
0.08 0 0 0.13 0.08
0.04 0 0.33 0.08 0.04
0 0 0 0 0
0.2 0 0 0 0
0.08 0 0 0 0
0.04 0 0 0 0
1.8E00 5.00E00 3.50E00 5.00E00 6.10E00
]=[ 〖 ][ 〗(+1) ][
-
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-
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][
][ 〗
]^ [
-
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0
0
0
0
0
0
0
0
0
0.510
0
0
0 0.86 0 0 0
0 0.51 0 0 0
1 0 0 0 0
0 0 0 0 0
]
c
-
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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 0 0 0.860 0 0 0 0
0 0 0 0 0.86
0.86 0.51 0 0 0
0 1 0 0 0
0.86 0.51 0 0 0
0 0 0.3 0.37 0.3
0.3 0.37 0.3 0.37 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0.33 0 0 0 00 0.17 0 0 0
0 0 0.1 0 0
0 0 0 0.1 0
0 0 0 0 0.2
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 1
0 0 0 0 0
1 0 0 0 0
0 0.86 0 0 0
0 0.51 0 0 0
0 0.86 0 0.3 0
-
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1 0.51 0 0.37 0
0 0 0.3 0.3 0
0 0 0.37 0.37 1
0 0 0.3 0 0
0 0 0.37 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0.2
0 0 0 0 0
0.33 0 0 0 0
0 0.15 0 0 0
0 0.0 0 0 0
0 0.15 0 0.17 00.33 0.0 0 0.07 0
0 0 0.17 0.17 0
0 0 0.07 0.07 0.2
0 0 0.17 0 0
0 0 0.07 0 0
0 0 0 0 0
0 0 0 0 0
0.13 0.08 0 0 0.13
0.08 0.04 0 0.2 0.08
0 0 0 0 0
0 0.33 0 0 0
0.13 0.08 0 0 0
0.08 0.04 0 0 0
0.42 0.06 0.16 0.06 0
0.06 0.45 0.06 0.03 0
0.16 0.06 0.32 0 0.16
0.06 0.03 0 0.25 0.06
0 0 0.16 0.06 0.42
0 0 0.06 0.03 0.06
2.8E00 3.50E00 1.27E00 1.8E00 2.53E00
c
-
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1.58E15 8.01E15 2.64E15 5.34E15 1.58E15
5.5E00 7.00E00 2.54E00 3.5E00 5.05E00
3.17E15 1.60E16 5.2E15 1.07E16 3.17E15
6.3E00 8.87E00 2.72E00 5.82E00 5.01E00
4.75E15 2.40E16 7.3E15 1.60E16 4.75E15
6.0E00 1.03E01 2.4E00 7.78E00 5.07E00
6.33E15 3.20E16 1.06E16 2.14E16 6.33E15.3E14 4.75E15 1.57E15 3.17E15 .3E14
4.75E15 2.40E16 7.3E15 1.60E16 4.75E15
1.57E15 7.3E15 2.62E15 5.2E15 1.57E15
3.17E15 1.60E16 5.2E15 1.07E16 3.17E15
.3E14 4.75E15 1.57E15 3.17E15 .3E14
1.58E15 8.01E15 2.64E15 5.34E15 1.58E15
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58/64
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0 0 0 0 0
0 0 0 0 0
0 0.86 0 0 0
0 0.51 0 0 0
c
-
8/17/2019 Ejercicios de Analisis Estructural II-metodo Matricial
60/64
0
0
0
0
0.511
0.51
0
0
0
0.37
0
0
-
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61/64
0
0.33
0.08
0.04
0
0
0
0
0
0
0.06
0.03
0.06
0.45
4.63E00
c
-
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2.67E15
.26E00
5.34E15
.3E00
8.01E15
.57E00
1.07E161.58E15
8.01E15
2.64E15
5.34E15
1.58E15
2.67E15
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63/64
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