calculo de la matriz de rigidez lateral de cada portico
TRANSCRIPT
CALCULO DE LA MATRIZ DE RIGIDEZ LATERAL DE CADA PORTICO
Por medio del cálculo Matricial de Estructuras calculamos la matriz de rigidez de la estructura, por medio del siguiente procedimiento:
1. Calculo de la Matriz de Rigidez en Coordenadas Locales de cada Miembro
k1
73398.058
0
0
73398.058
0
0
0
1996.854
3993.708
0
1996.854
3993.708
0
3993.708
10822.415
0
3993.708
5152.415
73398.058
0
0
73398.058
0
0
0
1996.854
3993.708
0
1996.854
3993.708
0
3993.708
5152.415
0
3993.708
10822.415
k2
73398.058
0
0
73398.058
0
0
0
1996.854
3993.708
0
1996.854
3993.708
0
3993.708
10822.415
0
3993.708
5152.415
73398.058
0
0
73398.058
0
0
0
1996.854
3993.708
0
1996.854
3993.708
0
3993.708
5152.415
0
3993.708
10822.415
k3
420000
0
0
420000
0
0
0
81871.345
122807.018
0
81871.345
122807.018
0
122807.018
324210.526
0
122807.018
44210.526
420000
0
0
420000
0
0
0
81871.345
122807.018
0
81871.345
122807.018
0
122807.018
44210.526
0
122807.018
324210.526
k4
420000
0
0
420000
0
0
0
81871.345
122807.018
0
81871.345
122807.018
0
122807.018
324210.526
0
122807.018
44210.526
420000
0
0
420000
0
0
0
81871.345
122807.018
0
81871.345
122807.018
0
122807.018
44210.526
0
122807.018
324210.526
k5
63000
0
0
63000
0
0
0
612.364
918.546
0
612.364
918.546
0
918.546
1850.319
0
918.546
905.319
63000
0
0
63000
0
0
0
612.364
918.546
0
612.364
918.546
0
918.546
905.319
0
918.546
1850.319
k6
63000
0
0
63000
0
0
0
612.364
918.546
0
612.364
918.546
0
918.546
1850.319
0
918.546
905.319
63000
0
0
63000
0
0
0
612.364
918.546
0
612.364
918.546
0
918.546
905.319
0
918.546
1850.319
2. Calculo de la Matriz de Transformación de cada miembro
3. Calculo de la Matriz de Ri de cada miembro
T1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
T2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
T3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
T4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
T5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
T6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
R1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0.15
1
R2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0.15
1
R3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
R4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4. Calculo de la Matriz de Rigidez en coordenadas globales de cada miembro
R5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
R6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
Ki
TiT R
iT k
i R
i T
i
K1
73398.058
0
0
73398.058
0
0
0
1996.854
5990.562
0
1996.854
4293.236
0
5990.562
20806.685
0
5990.562
10044.707
73398.058
0
0
73398.058
0
0
0
1996.854
5990.562
0
1996.854
4293.236
0
4293.236
10044.707
0
4293.236
12065.457
K2
73398.058
0
0
73398.058
0
0
0
1996.854
5990.562
0
1996.854
4293.236
0
5990.562
20806.685
0
5990.562
10044.707
73398.058
0
0
73398.058
0
0
0
1996.854
5990.562
0
1996.854
4293.236
0
4293.236
10044.707
0
4293.236
12065.457
K3
81871.345
0
122807.018
81871.345
0
122807.018
0
420000
0
0
420000
0
122807.018
0
324210.526
122807.018
0
44210.526
81871.345
0
122807.018
81871.345
0
122807.018
0
420000
0
0
420000
0
122807.018
0
44210.526
122807.018
0
324210.526
K4
81871.345
0
122807.018
81871.345
0
122807.018
0
420000
0
0
420000
0
122807.018
0
324210.526
122807.018
0
44210.526
81871.345
0
122807.018
81871.345
0
122807.018
0
420000
0
0
420000
0
122807.018
0
44210.526
122807.018
0
324210.526
K5
612.364
0
918.546
612.364
0
918.546
0
63000
0
0
63000
0
918.546
0
1850.319
918.546
0
905.319
612.364
0
918.546
612.364
0
918.546
0
63000
0
0
63000
0
918.546
0
905.319
918.546
0
1850.319
5. Ensamblaje de la matriz de rigidez del sistema en base a los grados de libertad libres y restringidos
K6
612.364
0
918.546
612.364
0
918.546
0
63000
0
0
63000
0
918.546
0
1850.319
918.546
0
905.319
612.364
0
918.546
612.364
0
918.546
0
63000
0
0
63000
0
918.546
0
905.319
918.546
0
1850.319
GL
2
3
5
6
8
9
11
12
GR
1
1
2
3
4
5
6
7
8
9
10
1
4
7
10
13
14
15
16
17
18
ArregloT 2 3 5 6 8 9 11 12 1 4 7 10 13 14 15 16 17 18( )
KT
841996.9
5990.6
1996.9
4293.2
420000
00000000
420000
0000
5990.6
669227.7
5990.6
10044.7
0
44210.5
0000
122807
0
122807
0
44210.5
000
1996.9
5990.6
127996.9
4293.2
00
63000
000000000
63000
0
4293.2
10044.7
4293.2
15766.1
000
905.3
000
918.5
000918.5
0
905.3
420000
000
421996.9
5990.6
1996.9
4293.2
0000000000
0
44210.5
00
5990.6
345017.2
5990.6
10044.7
122807
0
122807
0000000
00
63000
0
1996.9
5990.6
64996.9
4293.2
0000000000
000
905.3
4293.2
10044.7
4293.2
13915.8
0918.5
0
918.5
000000
00000
122807
00
237140.7
73398.1
81871.3
0
81871.3
0
122807
000
0000000918.5
73398.1
74622.8
0612.4
000612.4
0
918.5
0
122807
000
122807
00
81871.3
0
155269.4
73398.1
000000
000
918.5
000
918.5
0612.4
73398.1
74010.4
000000
0
122807
000000
81871.3
000
81871.3
0
122807
000
420000
000000000000
420000
0000
0
44210.5
000000
122807
000
122807
0
324210.5
000
000918.5
00000612.4
00000
612.4
0918.5
00
63000
0000000000000
63000
0
000
905.3
00000
918.5
00000918.5
0
1850.3
Extraemos las sub matrices de la matriz de rigidez global de la estructura
Seguidamente realizamos la condensación estática
Kuu
841996.854
5990.562
1996.854
4293.236
420000
0
0
0
5990.562
669227.737
5990.562
10044.707
0
44210.526
0
0
1996.854
5990.562
127996.854
4293.236
0
0
63000
0
4293.236
10044.707
4293.236
15766.095
0
0
0
905.319
420000
0
0
0
421996.854
5990.562
1996.854
4293.236
0
44210.526
0
0
5990.562
345017.211
5990.562
10044.707
0
0
63000
0
1996.854
5990.562
64996.854
4293.236
0
0
0
905.319
4293.236
10044.707
4293.236
13915.776
Kur
0
0
0
0
0
122807.02
0
0
0
0
0
0
0
0
0
918.55
0
122807.02
0
0
0
122807.02
0
0
0
0
0
918.55
0
0
0
918.55
0
122807.02
0
0
0
0
0
0
420000
0
0
0
0
0
0
0
0
44210.53
0
0
0
0
0
0
0
0
0
918.55
0
0
0
0
0
0
63000
0
0
0
0
0
0
0
0
905.32
0
0
0
0
Krr
237140.75
73398.06
81871.35
0
81871.35
0
122807.02
0
0
0
73398.06
74622.79
0
612.36
0
0
0
612.36
0
918.55
81871.35
0
155269.4
73398.06
0
0
0
0
0
0
0
612.36
73398.06
74010.42
0
0
0
0
0
0
81871.35
0
0
0
81871.35
0
122807.02
0
0
0
0
0
0
0
0
420000
0
0
0
0
122807.02
0
0
0
122807.02
0
324210.53
0
0
0
0
612.36
0
0
0
0
0
612.36
0
918.55
0
0
0
0
0
0
0
0
63000
0
0
918.55
0
0
0
0
0
918.55
0
1850.32
KCinicial Krr Kru Kuu1 Kur
Extraemos la sub matriz que se encuentra relacionada con los grados de libertad horizontales
CALCULO DE LA MATRIZ DE RIGIDEZ LATERAL DE LA ESTRUCTURA
KCinicial
192046.89
73162.95
39801.63
202.66
78847.19
995
121718.32
32.45
995
31.99
73162.95
74558
209.12
550.27
25.99
251.74
9.36
609.67
251.74
915.89
39801.63
209.12
93259.71
73112.98
19939.98
1544.02
7178.39
75.96
1544.02
74.87
202.66
550.27
73112.98
73895.81
82.43
477.73
29.67
52.52
477.73
51.77
78847.19
25.99
19939.98
82.43
58907.21
549.02
114539.93
108.42
549.02
106.86
995
251.74
1544.02
477.73
549.02
1547.55
197.65
225.99
1547.55
222.74
121718.32
9.36
7178.39
29.67
114539.93
197.65
321234.37
39.03
197.65
38.47
32.45
609.67
75.96
52.52
108.42
225.99
39.03
557.15
225.99
864.12
995
251.74
1544.02
477.73
549.02
1547.55
197.65
225.99
1547.55
222.74
31.99
915.89
74.87
51.77
106.86
222.74
38.47
864.12
222.74
1796.68
KC
192046.887
73162.948
39801.635
202.655
73162.948
74558
209.119
550.272
39801.635
209.119
93259.713
73112.977
202.655
550.272
73112.977
73895.807
kL
118883.938
1395.052
40010.754
752.928
40004.29
759.392
20146.736
782.83
kLT 118883.938
40004.29
1395.052
759.392
40010.754
20146.736
752.928
782.83
KL120278.99
40763.682
40763.682
20929.566
Kp1
120300
40760
40760
20930
Kp2
3505
1678
1678
1543
Kp3
164300
56030
56030
29320
Kp4
120300
40760
40760
20930
Kp5
3505
1678
1678
1543
Kp6
164300
56030
56030
29320
G1
0
0
1
0
7.1809
0
0
0
0
1
0
7.0811
G2
0
0
1
0
1.1809
0
0
0
0
1
0
1.0811
G3
0
0
1
0
4.8191
0
0
0
0
1
0
4.9189
G4
1
0
0
0
7.1809
0
0
1
0
0
0
7.0811
G5
1
0
0
0
1.1809
0
0
1
0
0
0
1.0811
G6
1
0
0
0
4.8191
0
0
1
0
0
0
4.9189
K
1
nPórticos
i
GiT Kp
i G
i
KL1
0
0
0
0
0
0
0
120300
863862.27
0
40760
288625.636
0
863862.27
6203308.575
0
292693.484
2072591.83
0
0
0
0
0
0
0
40760
292693.484
0
20930
148207.423
0
288625.636
2072591.83
0
148207.423
1049471.583
CALCULO DE LOS
DESPLAZAMIENTOS DE ENTRE PISO (DESPLAZAMIENTO DEL CENTRO DE MASA)
KL2
0
0
0
0
0
0
0
3505
4139.055
0
1678
1814.086
0
4139.055
4887.809
0
1981.55
2142.254
0
0
0
0
0
0
0
1678
1981.55
0
1543
1668.137
0
1814.086
2142.254
0
1668.137
1803.423
KL3
0
0
0
0
0
0
0
164300
791778.13
0
56030
275605.967
0
791778.13
3815657.986
0
270014.173
1328172.716
0
0
0
0
0
0
0
56030
270014.173
0
29320
144222.148
0
275605.967
1328172.716
0
144222.148
709414.324
K
288105
0
76223.194
98468
0
14833.755
0
288105
76223.194
0
98468
14833.755
76223.194
76223.194
20047708.741
24660.861
24660.861
6805813.598
98468
0
24660.861
51793
0
5653.412
0
98468
24660.861
0
51793
5653.412
14833.755
14833.755
6805813.598
5653.412
5653.412
3521378.66
Uo K1Fe
K
288105
0
76223.194
98468
0
14833.755
0
288105
76223.194
0
98468
14833.755
76223.194
76223.194
20047708.741
24660.861
24660.861
6805813.598
98468
0
24660.861
51793
0
5653.412
0
98468
24660.861
0
51793
5653.412
14833.755
14833.755
6805813.598
5653.412
5653.412
3521378.66
Fe
14.758
0
9.0762
25.436
0
15.6431
Uo
0.00062470903751
0.00000083079864
0.00000474310456
0.00167957559062
0.00000079929761
0.00001354226068
CALCULO DE LOS DESPLAZAMIENTOS DE CADA PORTICO
CALCULO DE LAS FUERZAS LATERALES EN CADA PORTICO
Ui GiUo
U1 G1Uo U2 G
2Uo U3 G
3Uo
U4 G4Uo U5 G
5Uo U6 G
6Uo
U10.00003322896087
0.0000950948045
U20.00000477033353
0.00001384124042
U30.00002368829382
0.00006741232367
U40.00065876879702
0.00177546969273
U50.00063031016968
0.00169421612865
U60.00060185154233
0.00161296256456
Fi kpi Ui
F1 Kp1U1 F2 Kp
2U2 F3 Kp
3U3
F4 Kp4U4 F5 Kp
5U5 F6 Kp
6U6
F10.121
0.636
F20.007
0.013
F30.115
0.649
F46.882
10.309
F50.634
1.557
F68.51
13.57