02 estimación del periodo de la estructura15 o
- 6. 𝑃𝑙𝑎𝑛𝑡𝑎 𝐵𝑎𝑗𝑎
𝑁𝑖𝑣𝑒𝑙 1
𝑁𝑖𝑣𝑒𝑙 2
𝑁𝑖𝑣𝑒𝑙 3
𝑁𝑖𝑣𝑒𝑙 4
𝑁𝑖𝑣𝑒𝑙 6
𝑁𝑖𝑣𝑒𝑙 5
𝑁𝑖𝑣𝑒𝑙 7
𝑋
z
𝑦
vigas: 90𝑥45 𝑐𝑚
𝐸 = 11000 𝑓´𝑐
𝑓´𝑐 = 250
𝑘𝑔
𝑐𝑚2
𝑐𝑜𝑙𝑢𝑚𝑛𝑎𝑠: 80𝑥80𝑐𝑚
𝑘0
𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻 = 4.3 𝑚
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑐=2733750 𝑐𝑚4
𝐼𝑣 = 3413333.33 𝑐𝑚4
- 7. 𝑃𝑙𝑎𝑛𝑡𝑎 𝐵𝑎𝑗𝑎
𝑁𝑖𝑣𝑒𝑙 1
𝑁𝑖𝑣𝑒𝑙 2
𝑁𝑖𝑣𝑒𝑙 3
𝑁𝑖𝑣𝑒𝑙 4
𝑁𝑖𝑣𝑒𝑙 6
𝑁𝑖𝑣𝑒𝑙 5
𝑁𝑖𝑣𝑒𝑙 7
𝑋
z
𝑦
vigas: 90𝑥45 𝑐𝑚
𝐸 = 11000 𝑓´𝑐
𝑓´𝑐 = 250
𝑘𝑔
𝑐𝑚2
𝑐𝑜𝑙𝑢𝑚𝑛𝑎𝑠: 80𝑥80𝑐𝑚
𝑘0
𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻 = 4.3 𝑚
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐 𝐼𝑐 𝐼𝑐𝐼𝑐
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑐=2733750 𝑐𝑚4
𝐼𝑣 = 3413333.33 𝑐𝑚4
𝐼𝑣 𝐼𝑣
𝐼𝑐𝐼𝑐 𝐼𝑐𝐻
𝐼 𝑚 = 71458333𝑐𝑚4
- 8. 𝑃𝑙𝑎𝑛𝑡𝑎 𝐵𝑎𝑗𝑎
𝑁𝑖𝑣𝑒𝑙 1
𝑁𝑖𝑣𝑒𝑙 2
𝑁𝑖𝑣𝑒𝑙 3
𝑁𝑖𝑣𝑒𝑙 4
𝑁𝑖𝑣𝑒𝑙 6
𝑁𝑖𝑣𝑒𝑙 5
𝑁𝑖𝑣𝑒𝑙 7
𝑌
Z
𝑋
vigas: 90𝑥45 𝑐𝑚
𝐸 = 11000 𝑓´𝑐
𝑓´𝑐 = 250
𝑘𝑔
𝑐𝑚2
𝑐𝑜𝑙𝑢𝑚𝑛𝑎𝑠: 80𝑥80𝑐𝑚
𝑘0
𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻 = 4.3 𝑚
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑐=2733750 𝑐𝑚4
𝐼𝑣 = 3413333.33 𝑐𝑚4
- 9. 𝑃𝑙𝑎𝑛𝑡𝑎 𝐵𝑎𝑗𝑎
𝑁𝑖𝑣𝑒𝑙 1
𝑁𝑖𝑣𝑒𝑙 2
𝑁𝑖𝑣𝑒𝑙 3
𝑁𝑖𝑣𝑒𝑙 4
𝑁𝑖𝑣𝑒𝑙 6
𝑁𝑖𝑣𝑒𝑙 5
𝑁𝑖𝑣𝑒𝑙 7
𝑌
Z
𝑋
vigas: 90𝑥45 𝑐𝑚
𝐸 = 11000 𝑓´𝑐
𝑓´𝑐 = 250
𝑘𝑔
𝑐𝑚2
𝑐𝑜𝑙𝑢𝑚𝑛𝑎𝑠: 80𝑥80𝑐𝑚
𝑘0
𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻 = 4.3 𝑚
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑐 𝐼𝑐𝐼𝑐 𝐼𝑐
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑣 𝐼𝑣 𝐼𝑣
𝐼𝑐=2733750 𝑐𝑚4
𝐼𝑣 = 3413333.33 𝑐𝑚4
𝐼𝑣
𝐼𝑐
𝐼𝑐
𝐻 𝑁𝑖𝑣𝑒𝑙 8
𝐼 𝑚 = 71458333𝑐𝑚4
- 10. RIGIDECES EN DIRECCION X
A B C D SUMA (Ton/m)
K0 37226.326 37226.326 37226.326 37226.326 148905.3038
K1 25247.2523 25247.2523 25247.2523 25247.2523 100989.0091
K2 24311.799 24311.799 24311.799 24311.799 97247.19591
K3 24311.799 24311.799 24311.799 24311.799 97247.19591
K4 24311.799 24311.799 24311.799 24311.799 97247.19591
K5 24311.799 24311.799 24311.799 24311.799 97247.19591
K6 24311.799 24311.799 24311.799 24311.799 97247.19591
K7 24311.799 24311.799 24311.799 24311.799 97247.19591
K8 13381.0151 13381.0151 26762.03024
RIGIDECES EN DIRECCION Y
1 2 3 4 5 6 7 SUMA (Ton/m)
K0 20227.2746 20227.2746 20227.2746 20227.27459 20227.2746 20227.2746 20227.2746 141590.9221
K1 13345.9107 13345.9107 13345.9107 13345.91073 13345.9107 13345.9107 13345.9107 93421.37513
K2 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K3 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K4 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K5 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K6 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K7 12762.543 12762.543 12762.543 12762.54302 12762.543 12762.543 12762.543 89337.80116
K8 7620.93707 7620.937068 7620.93707 22862.81121
- 11. Análisis Estático
DATOS DIRECCION (X,Y)
Q 2
c 0.45
F.I. 1.5
a´=(c/Q)*F.I. 0.3375
𝑭
𝒊=𝒂´
𝒘𝒊
𝒘𝒊∗𝒉𝒊
∗𝒘𝒊𝒉𝒊
Calculo de Fuerzas (Fi).
𝐶𝑂𝑀𝑃𝑅𝑂𝐵𝐴𝐶𝐼Ó𝑁
𝑉0
𝑊𝑇
= 0.3375
Nivel wi (Ton) hi (m) wi*hi Fi (Ton) Vi(Ton)
8 151.2 38.7 5851.9 102 102
7 1150.6 34.4 39581.5 689 790
6 1311.8 30.1 39486.1 687 1478
5 1311.8 25.8 33845.2 589 2066
4 1311.8 21.5 28204.3 491 2557
3 1311.8 17.2 22563.5 393 2950
2 1311.8 12.9 16922.6 294 3244
1 1311.8 8.6 11281.7 196 3440
PB. 1311.8 4.3 5640.9 98 3539
10484.6 203377.6
- 12. Determinación del periodo fundamental de
la estructura, en dos direcciones.
𝑻 = 𝟐𝝅
𝑾𝒊 𝑿𝒊
𝟐
𝒈 𝑭𝒊 𝑿𝒊
𝑇𝑋 = 1.205 𝑠𝑒𝑔.
𝑇𝑌 = 1.252 𝑠𝑒𝑔.
Kx(Ton/m) Vi/K(m) xi(cm) wi*xi^2(ton-cm2) Fi*xi(ton-cm) Tx
26762.0 0.0038 0.2 5.8 20.0
97247.2 0.0081 0.2 42.6 132.5
97247.2 0.0152 0.2 44.5 126.6
97247.2 0.0212 0.2 37.5 99.6
97247.2 0.0263 0.1 28.7 72.5
97247.2 0.0303 0.1 19.4 47.7
97247.2 0.0334 0.1 10.9 26.8
100989.0 0.0341 0.1 4.4 11.4
148905.0 0.0238 0.0 0.7 2.3 1.205
194.5 539.4
Ky(Ton/m) Vi/K(m) xi(cm) wi*xi^2(ton-cm2) Fi*xi(ton-cm) Ty
22863.0 0.0 0.2 6.8 21.7
89338.0 0.0 0.2 49.9 143.4
89338.0 0.0 0.2 52.2 137.0
89338.0 0.0 0.2 43.9 107.7
89338.0 0.0 0.2 33.5 78.4
89338.0 0.0 0.1 22.6 51.5
89338.0 0.0 0.1 12.6 28.9
93421.0 0.0 0.1 5.0 12.1
141591.0 0.0 0.0 0.8 2.5 1.2525
227.3 583.2
- 14. RIGIDEZ DE ENTREPISO EN DIRECCION X (Ton/m)
K0 148905 K1 100989 K2 97247 K3 97247 K4 97247 K5 97247 K6 97247 K7 97247 K8 26762
Matriz de rigidez lateral
Klat
K0 K1
K1
0
0
0
0
0
0
0
K1
K1 K2
K2
0
0
0
0
0
0
0
K2
K2 K3
K3
0
0
0
0
0
0
0
K3
K3 K4
K4
0
0
0
0
0
0
0
K4
K4 K5
K5
0
0
0
0
0
0
0
K5
K5 K6
K6
0
0
0
0
0
0
0
K6
K6 K7
K7
0
0
0
0
0
0
0
K7
K7 K8
K8
0
0
0
0
0
0
0
K8
K8
PROPIEDADES
Pesos en Toneladas Altura de entrepiso en m Modulo de elasticidad Ton/m2
w0 1311.8 H 4.30
w1 1311.8 E 14000 2500
w2 1311.8
w3 1311.8 E 7 10
5
w4 1311.8
w5 1311.8
w6 1311.8
w7 1150.6
w8 151.2
- 15. Matriz de masas (Ton*seg2)/m
M
w0
g
0
0
0
0
0
0
0
0
0
w1
g
0
0
0
0
0
0
0
0
0
w2
g
0
0
0
0
0
0
0
0
0
w3
g
0
0
0
0
0
0
0
0
0
w4
g
0
0
0
0
0
0
0
0
0
w5
g
0
0
0
0
0
0
0
0
0
w6
g
0
0
0
0
0
0
0
0
0
w7
g
0
0
0
0
0
0
0
0
0
w8
g
M
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
133.721
0
0
0
0
0
0
0
0
0
117.288
0
0
0
0
0
0
0
0
0
15.413
Matriz de Masas.
- 16. Frecuencias y Periodos.
Frecuencias
freq genvals Klat M( )
W
2
2.656 10
3
1.594 10
3
1.994 10
3
2.337 10
3
2.853 10
3
1.101 10
3
617.229
236.81
27.181
Periodos
T 2
W
T
0.122
0.157
0.141
0.13
0.118
0.189
0.253
0.408
1.205
- 17. MODOS
modos genvecs Klat M( )
modo
0
0.125
0.305
0.48
0.637
0.771
0.876
0.948
0.984
1
0
0.339
0.732
0.902
0.778
0.401
0.107
0.579
0.864
1
0
0.449
0.744
0.419
0.262
0.72
0.568
0.067
0.645
1
0
0.421
0.429
0.212
0.532
0.046
0.509
0.294
0.366
1
0
0.701
0.914
0.995
1
0.928
0.785
0.583
0.335
0.521
0
0.331
0.205
0.102
0.329
0.297
0.032
0.259
0.346
1
0
0.214
0.036
0.197
0.182
0.062
0.228
0.107
0.149
1
0
0.295
0.107
0.323
0.045
0.332
0.019
0.328
0.082
1
0
0.686
0.715
0.442
0.015
0.417
0.704
0.747
0.53
1
- 18. Modos en dirección X
1 0.5 0 0.5 1
2
4
6
8
10
modo 1
1 0.5 0 0.5 1
2
4
6
8
10
modo 2
1 0.5 0 0.5 1
2
4
6
8
10
modo 3
1 0.5 0 0.5 1
2
4
6
8
10
modo 4
1 0.5 0 0.5 1
2
4
6
8
10
modo 5
1 0.5 0 0.5 1
2
4
6
8
10
modo 6
1 0.5 0 0.5 1
2
4
6
8
10
modo 7
1 0.5 0 0.5 1
2
4
6
8
10
modo 8
1 0.5 0 0.5 1
2
4
6
8
10
modo 9
- 19. RIGIDEZ DE ENTREPISO EN DIRECCION Y (Ton/m)
K0 141591 K1 93422 K2 89338 K3 89338 K4 89338 K5 89338 K6 89338 K7 89338 K8 22863
Matriz de rigidez lateral
Klat
K0 K1
K1
0
0
0
0
0
0
0
K1
K1 K2
K2
0
0
0
0
0
0
0
K2
K2 K3
K3
0
0
0
0
0
0
0
K3
K3 K4
K4
0
0
0
0
0
0
0
K4
K4 K5
K5
0
0
0
0
0
0
0
K5
K5 K6
K6
0
0
0
0
0
0
0
K6
K6 K7
K7
0
0
0
0
0
0
0
K7
K7 K8
K8
0
0
0
0
0
0
0
K8
K8
Frecuencias
freq genvals Klat M( )
W
51.247
49.41
38.019
42.217
46.101
31.798
23.863
14.795
5.015
Periodos
Ty 2
W
Ty
0.123
0.127
0.165
0.149
0.136
0.198
0.263
0.425
1.253
- 20. Modos en dirección Y
1 0.5 0 0.5 1
2
4
6
8
10
modo 1
1 0.5 0 0.5 1
2
4
6
8
10
modo 2
1 0.5 0 0.5 1
2
4
6
8
10
modo 3
1 0.5 0 0.5 1
2
4
6
8
10
modo 4
1 0.5 0 0.5 1
2
4
6
8
10
modo 5
1 0.5 0 0.5 1
2
4
6
8
10
modo 6
1 0.5 0 0.5 1
2
4
6
8
10
modo 7
1 0.5 0 0.5 1
2
4
6
8
10
modo 8
1 0.5 0 0.5 1
2
4
6
8
10
modo 9
- 21. PERIODOS
M. Estático
M. Dinámico.
𝑇𝑋 = 1.205 𝑠𝑒𝑔.
𝑇𝑌 = 1.252 𝑠𝑒𝑔.
Tx
0.117
0.121
0.128
0.137
0.155
0.187
0.251
0.405
1.195
MODOS
Ty
0.123
0.127
0.165
0.149
0.136
0.198
0.263
0.425
1.253
- 22. Masas y Periodos calculados (3D).
Nivel Peso (ton)
Masa Traslacional
(Ton*s2/m)
Masa
Rotacional.
9 151.2 15.41 3012.7
8 1151 117.33 242789.1
7 1312 133.74 276750
6 1312 133.74 276750
5 1312 133.74 276750
4 1312 133.74 276750
3 1312 133.74 276750
2 1312 133.74 276750
P.B. 1312 133.74 276750
Modo Periodo (seg)
1 Transversal 1.1556
2 Longitudinal 1.081
3 Rotacional 1.0415
4 0.3572
5 0.3371
6 0.312
7 0.2015
8 0.1926
9 0.1769
10 0.1378
11 0.1323
12 0.1193