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8/17/2019 Examen Porticos Ana2
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Coordenadas:
Nodo x y Δx Δy θz
1 8.5 3 Δ1 Δ2 θ3
2 4 3 Δ4 Δ5 θ6
3 0 3 Δ7 Δ8 θ9
4 8.5 0 Δ10 Δ11 θ12
5 4 0 Δ13 Δ14 θ156 0 0 Δ16 Δ17 θ18
Cargas:
Tipo Nodo i Nodo ! "
#iga 1 1 2 4.5 0
#iga 2 2 3 4 $300
Co%&'na 1 1 4 3 0
Co%&'na 2 2 5 3 0Co%&'na 3 3 6 3 0
(a)riz de *igidez
#+,- 1
Nodo x y Δx Δy
N&do i 1 8.5 3 Δ1 Δ2
N&do 2 4 3 Δ4 Δ5
! 4.5 ' se//ion:
$1 0.3 -y 0 0.4 +
#+,- 2
Nodo x y Δx Δy
N&do i 2 4 3 Δ4 Δ5
N&do 3 0 3 Δ7 Δ8
! 4 ' se//ion:$1 0.3 -
y 0 0.4 +
COLUMNA 1
Nodo x y Δx Δy
x
x
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N&do i 1 8.5 3 Δ1 Δ2
N&do 4 8.5 0 Δ10 Δ11
! 3 ' se//ion:
0 0.3 -
y $1 0.4 +
COLUMNA 2
Nodo x y Δx Δy
N&do i 2 4 3 Δ1 Δ2
N&do 5 4 0 Δ10 Δ11
! 3 ' se//ion:
0 0.3 -
y $1 0.4 +
COLUMNA 3
Nodo x y Δx Δy
N&do i 3 0 3 Δ7 Δ8
N&do 6 0 0 Δ16 Δ17
! 3 ' se//ion:0 0.6 -
y $1 0.4 +
Δ1 Δ2 θ3 Δ4 Δ5
5898.66667 0 448 $5600 0
0 16844.2469 $99.5555556 0 $44.2469136
448 $99.5555556 1194.66667 0 99.5555556$5600 0 0 11900 0
0 $44.2469136 99.5555556 0 107.246914
0 $99.5555556 149.333333 0 $26.4444444
0 0 0 $6300 0
0 0 0 0 $63
0 0 0 0 $126
x
x
x
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x y (z
1 2 (3
4 5 (6
7 8 (9
10 11 (12
13 14 (1516 17 (18
*- +#-!NT *- +#-!NT
is). nor'a% 1 +N+C+-! nor'a% 2 +N-!
$600 2.25 2 $720 5 $300
$240 2 5 $240 8 $240
0 0 10 0 1 0
0 0 13 0 4 00 0 16 0 7 0
(-T*+ *+,+:
θz 5600 0 0
θ3 0 44.2469136 99.5555556
θ6 ; 0 99.5555556 298.666667
$5600 0 0
0 $44.2469136 $99.5555556
0.12 '2 0 99.5555556 149.3333330.0016'4
210000 <g='2
θz 6300 0 0
θ6 0 63 126
θ9 ; 0 126 336
$6300 0 0
0 $63 $1260.12 '2 0 126 168
0.0016 '4
210000 <g='2
θz 8400 0 0
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θ3 0 149.333333 224
θ12 ; 0 224 448
$8400 0 0
0 $149.333333 $224
0.12 '2 0 224 224
0.0016 '4
210000 <g='2
θz 8400 0 0
θ3 0 149.333333 224
θ12 ; 0 224 448
$8400 0 0
0 $149.333333 $224
0.12 '2 0 224 224
0.0016 '4
210000 <g='2
θz 16800 0 0
θ9 0 298.666667 448
θ18 ; 0 448 896
$16800 0 0
0 $298.666667 $4480.24 '2 0 448 448
0.0032 '4
210000 <g='2
θ6 Δ7 Δ8 θ9
0 0 0 0 Δ1
$99.5555556 0 0 0 Δ2
149.333333 0 0 0 θ30 $6300 0 0 Δ4
$26.4444444 0 $63 $126 Δ5
634.666667 0 126 168 θ6
0 6598.66667 0 448 Δ7
126 0 16863 126 Δ8
168 448 126 1232 θ9
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(ini/ia% (>na%
(3 300 (6 $300
(6 200 (9 $200
(12 0 (3 0
(9 0 (6 0(9 0 (6 0
$5600 0 0
0 $44.2469135802 99.5555555556
0 $99.5555555556 149.3333333333
5600 0 0
0 44.2469135802 $99.5555555556
0 $99.5555555556 298.6666666667
$6300 0 0
0 $63 126
0 $126 168
6300 0 0
0 63 $1260 $126 336
$8400 0 0
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0 $149.3333333333 224
0 $224 224
8400 0 0
0 149.3333333333 $224
0 $224 448
$8400 0 0
0 $149.3333333333 224
0 $224 224
8400 0 0
0 149.3333333333 $224
0 $224 448
$16800 0 0
0 $298.6666666667 448
0 $448 448
16800 0 0
0 298.6666666667 $4480 $448 896
0.004198 $0.000005 $0.001665 0.004110
$0.000005 0.000060 0.000004 $0.000005
$0.001665 0.000004 0.001615 $0.0016250.004110 $0.000005 $0.001625 0.004199
$0.000121 0.000028 $0.000988 $0.000207
0.000805 0.000009 $0.000567 0.000803
0.004031 $0.000005 $0.001589 0.004119
0.000005 0.000000 $0.000004 0.000005
$0.001589 0.000004 0.000554 $0.001629
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$1 0 0
0 $1 0
0 0 1
T 0 0 0
0 0 0
0 0 0
$1 0 0
0 $1 0
0 0 1
T 0 0 0
0 0 00 0 0
0 $1 0
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1 0 0
0 0 1
T 0 0 0
0 0 0
0 0 0
0 $1 0
1 0 0
0 0 1
T 0 0 0
0 0 0
0 0 0
0 $1 0
1 0 0
0 0 1
T 0 0 0
0 0 00 0 0
$0.000121 0.000805 0.004031 0.000005
0.000028 0.000009 $0.000005 0.000000
$0.000988 $0.000567 $0.001589 $0.000004$0.000207 0.000803 0.004119 0.000005
0.011846 0.000391 $0.000283 0.000032
0.000391 0.001862 0.000801 $0.000009
$0.000283 0.000801 0.004198 0.000005
0.000032 $0.000009 0.000005 0.000060
0.001258 $0.000504 $0.001665 $0.000004
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0 0 0 $1
0 0 0 0
0 0 0 0
$1 0 0 T?T 0
0 $1 0 0
0 0 1 0
0 0 0 $1
0 0 0 0
0 0 0 0
$1 0 0 T?T 0
0 $1 0 00 0 1 0
0 0 0 0
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0 0 0 $1
0 0 0 0
0 $1 0 T?T 0
1 0 0 0
0 0 1 0
0 0 0 0
0 0 0 $1
0 0 0 0
0 $1 0 T?T 0
1 0 0 0
0 0 1 0
0 0 0 0
0 0 0 $1
0 0 0 0
0 $1 0 T?T 0
1 0 0 00 0 1 0
$0.001589 1 0 Δ1
0.000004 2 $720 Δ2
0.000554 (3 300 θ3$0.001629 4 0 Δ4
0.001258 5 $540 Δ5
$0.000504 (6 $100 θ6
$0.001665 7 0 Δ7
$0.000004 8 $240 Δ8
0.001615 (9 $200 θ9
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0 0 0 0 0
$1 0 0 0 0
0 1 0 0 0
0 0 $1 0 0
0 0 0 $1 0
0 0 0 0 1
0 0 0 0 0
$1 0 0 0 0
0 1 0 0 0
0 0 $1 0 0
0 0 0 $1 00 0 0 0 1
1 0 0 0 0
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0 0 0 0 0
0 1 0 0 0
0 0 0 1 0
0 0 $1 0 0
0 0 0 0 1
1 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 0 0 1 0
0 0 $1 0 0
0 0 0 0 1
1 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 0 0 1 0
0 0 $1 0 00 0 0 0 1
$0.19415215
$0.05825767
0.96219846$0.12753105
$7.01150445
$0.47070482
$0.0683123
$0.03102805
$0.78722216
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Δ1 Δ2 θ3 Δ4 Δ5
5600 0 0 $5600 0
0 44.2469136 $99.5555556 0 $44.2469136
<@T?TA;ATB 0 $99.5555556 298.666667 0 99.5555556
$5600 0 0 5600 0
0 $44.2469136 99.5555556 0 44.2469136
0 $99.5555556 149.333333 0 99.5555556
Δ4 Δ5 θ6 Δ7 Δ8
6300 0 0 $6300 0
0 63 $126 0 $63
<@T?TA;ATB 0 $126 336 0 126
$6300 0 0 6300 0
0 $63 126 0 630 $126 168 0 126
Δ1 Δ2 θ3 Δ10 Δ11
149.333333 0 224 $149.333333 0
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0 8400 0 0 $8400
<@T?TA;ATB 224 0 448 $224 0
$149.333333 0 $224 149.333333 0
0 $8400 0 0 8400
224 0 224 $224 0
Δ1 Δ2 θ3 Δ10 Δ11
149.333333 0 224 $149.333333 0
0 8400 0 0 $8400
<@T?TA;ATB 224 0 448 $224 0
$149.333333 0 $224 149.333333 0
0 $8400 0 0 8400
224 0 224 $224 0
Δ7 Δ8 θ9 Δ16 Δ17
298.666667 0 448 $298.666667 0
0 16800 0 0 $16800
<@T?TA;ATB 448 0 896 $448 0
$298.666667 0 $448 298.666667 0
0 $16800 0 0 16800448 0 448 $448 0
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θ6
0 Δ1 $0.19415215 $373.078136
$99.5555556 Δ2 $0.05825767 258.728787
149.333333 θ3 0.96219846 $475.149659
0 Δ4 $0.12753105 373.078136
99.5555556 Δ5 $7.01150445 $258.728787
298.666667 θ6 $0.47070482 $689.129883
θ9
0 Δ4 $0.12753105 $373.078136
$126 Δ5 $7.01150445 $281.271213
168 θ6 $0.47070482 589.129883
0 Δ7 $0.0683123 373.078136
126 Δ8 $0.03102805 281.271213336 θ9 $0.78722216 535.954969
θ12
224 Δ1 $0.19415215 186.539068
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0 Δ2 $0.05825767 $489.364394
224 θ3 0.96219846 387.57483
$224 Δ10 0 $186.539068
0 Δ11 0 489.364394
448 θ12 0 172.042374
θ12
224 Δ1 $0.19415215 186.539068
0 Δ2 $0.05825767 $489.364394
224 θ3 0.96219846 387.57483
$224 Δ10 0 $186.539068
0 Δ11 0 489.364394
448 θ12 0 172.042374
θ18
448 Δ7 $0.0683123 $373.078136
0 Δ8 $0.03102805 $521.271213
448 θ9 $0.78722216 $735.954969
$448 Δ16 0 373.078136
0 Δ17
0 521.271213896 θ18 0 $383.279439
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C!(N-
0.3
0.4
! 3 θ1
5000000 (i 10666.6667
+ 0.0016 (D 5333.33333
+ 8000 5333.33333
C!(N-
0.3 0.4
! 3 θ2
5000000 Mi 10666.6667
+ 0.0016 Mf 5333.33333
+ 8000 F 5333.33333
C!(N-
0.6
0.4
! 3 θ3 5000000 Mi 21333.3333
+ 0.0032 Mf 10666.6667
+ 16000 F 10666.6667
#+,-
0.3
0.4
! 4 θ1
5000000 Mi 8000
+ 0.0016 Mf 4000+ 8000
#+,-
0.3
0.4
! 4.5 θ2
5000000 (i 7111.11111
+ 0.0016 (D 3555.55556
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+ 8000
M1 = $270 θ1 θ2
M2 = 68.75 18666.6667 4000
M3 = 568.75 4000 25777.7778
P = 500 0 3555.55556
5333.33333 5333.33333
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Mθ
θ4 Δ
5333.33333 5333.33333 θ1 $0.02608845 $50.415676
10666.6667 5333.33333 θ4 0 88.7227362
5333.33333 3555.56 Δ 0.04272397 12.7690201
θ5 Δ
5333.33333 5333.33333 θ2 $0.00271918 198.8566
10666.6667 5333.33333 θ5 0 213.358874
5333.33333 3555.56 Δ 0.04272397 137.405158
θ6 Δ10666.6667 10666.6667 θ3 0.00431353 547.744211
21333.3333 10666.6667 θ6 0 501.733254
10666.6667 7111.11 Δ 0.04272397 349.825822
θ2
4000 θ1 $0.02608845 $219.584324
8000 θ2 $0.00271918 $126.10722
θ3
3555.55556θ2 $0.00271918 $3.99937978
7111.11111θ3 0.00431353 21.0057887
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θ3 Δ
0 5333.33333 θ1 θ1 = $0.02608845
3555.55556 5333.33333 θ2 θ2 = $0.00271918
28444.4444 10666.6667 θ3 θ3 = 0.00431353
10666.6667 14222.22 Δ Δ = 0.04272397
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MOM. EQUIVALEN MOMENTO EQUIV
E 0 $50.415676
E 0 88.7227362
E
E 0 198.8566
E 0 213.358874
E 0 547.744211
E 0 501.733254
E 270 50.415676
E $270 $396.10722
E 568.75 564.75062
E $568.75 $547.744211
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