Edificio 8 Pisos Analisis Dinamico Y Estatico 4o4c4e
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CALCULOS GENERALES APELLIDO: NOMBRE:
URRUCHI SANCHEZ DIEGO E.
DATOS GENERALES: Especificaciones f’c = 210 kg/cm2 fy = 4200 kg/cm2 UBICACIÓN : HUANCAYO USO : HOSPITAL TIPO DE SUELO :TIPO 3
FACTOR Z = FACTOR U = FACTOR S = Tp = FACTOR R =
TIPO DE ESTR. : MIXTO
L1 L2 Lint X Lint Y
= = = =
f´c = S/C (hospital) = S/C azotea = Acabados = Tabiqueria = Concreto =
7 5 6 3.5 210 400 100 100 210 2400
m m m m
C1
Kg/cm2 Kg/m2 Kg/m2 Kg/m2 Kg/m2 kg/m3
ALTURAS DE ENTREPISO Nº de pisos H1 = H2 = H3 = H4 = H5 = H6 = H7 = H8 =
8 4.3 3.5 3.5 3.5 3.5 3.5 3.5 3.0
0.3 1.5 1.4 0.9 7
m m m m m m m m
LOSA ALIGERADA:
C6
C3
C4
C5
C3
C4
C5
C1
PREDIMENSIONAMIENTO 1.-
C2
C2
C6
L1/L2=
1.40
TIPO DE LOSA: ALIGERADA ESPESOR DE LA LOSA: ALIGERADA e losa = 0.28 m e asumido= 0.30 m S/C losa = 400 Kg/m2 2.-
VIGAS:
2.1 VIGAS V-1 h viga = b viga = h(m) = b(m) =
12 vigas 0.5 m 0.25 m 0.5 m 0.25 m
2.2 VIGAS V-2 h viga = b viga = h(m) = b(m) =
6 vigas 0.35 m 0.18 m 0.35 m 0.2 m
2.3 VIGAS V-3 h viga = b viga = h(m) = b(m) =
16 vigas 0.7 m 0.35 m 0.7 m 0.35 m
2.4 VIGAS V-4 h viga = b viga = h(m) = b(m) =
4 vigas 0.6 m 0.3 m 0.6 m 0.3 m
3.-
C1
C2
V-3
C6
V-3
V-1
V-1
C3
V-1
C4
C5
V-3
V-3
V-2
V-
V-2 V-3
C3
V-
V-2 V-3
C4
V-1
V-1
V-1 V-3 C1
V-
C5
V-3
VC6
C2
COLUMNAS AREA TRIBUTARIA COLUMNA C-1 C-2 C-3 C-4 C-5 C-6 Total Techado
AREA 8.750 17.500 14.875 29.750 27.625 16.250 459.00
C 1 m2 m2 m2 m2 m2 m2 m2
C 2
C
METRADO Peso S/C Peso Acabados Peso Tabiqueria Peso Aligerado (30cm)
Tipo de Columna C-1 C-2, C-3, C-6 C-4 , C-5
3.1 COLUMNA C-1 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
400 100 210 420
Kg/m2 Kg/m2 Kg/m2 Kg/m2
P
C 3
C 4
C 5
n 1.50 1.25 1.10
0.20 0.25 0.30
4 columnas 2808.0 Kg 1102.5 Kg 875.0 Kg 1837.5 Kg 3500.0 Kg
3.4 COLUMNA C-4 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 10123 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3.2 COLUMNA C-2 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
2892.29 cm2 3000 m 0.6 m 0.5 m 4 columnas 4866.0 Kg 2205.0 Kg 1750.0 Kg 3675.0 Kg 7000.0 Kg
3.5 COLUMNA C-5 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 19496.0 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3.3 COLUMNA C-3
3713.52 cm2 4200 m 0.7 m 0.6 m 4 columnas
3.6 COLUMNA C-6
3402.0 Kg 1874.3 Kg 1487.5 Kg 3123.8 Kg 5950.0 Kg
Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
4.-
Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 15837.5 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3016.67 cm2 3500 m 0.5 m 0.7 m
PLACAS: e=
0.25
m
VERIFICACION DE LA CONFIGURACION EN PLANTA 1.* 2.* * * *
IRREGULARIDAD EN PLANTA: No existe discontinuidades en planta mayores al 50%. IRREGULARIDAD EN ALTURA: No existe una irregularidad de rigidecez considerables . No existe una irregularidad en masa ,pues entres pisos adyacentes no existe una diferencia del 50% en peso. No existe irregularidad vertical ,pues todos los porticos tienen las mismas dimensiones No existe disontinuidad de elementos verticales. CONCLUSION:
C4
V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 )
C5
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C5
C4 V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 ) V-2 (0.35x0.20)
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0 .7 0x 0 .3 5)
C3
C5 V -3 (0.7 0x0 .3 5)
V -3 (0
C5
V -3 (0 . V-2 (0.35x0.20)
C4 V -3 (0 .7 0x 0 .3 5)
C2 V -3 (0.7 0 x0 .3 5)
V-2 (0.35x0.20)
C3
V-1 (0.50x0.25)
V-1 (0.50x0.25)
No presenta discontinuidades significativas tanto en planta como en elevacion C2 C6 C6 por loVque considera ESTRUCTURA V -4 (0.60x 0.30 ) -3 (0 .7 0xse 0 .3 5) V -3 (0 .70 x 0.3 5REGULAR )
V-1 (0.50x0.25)
*
C1
V -3 (0.7 0x0 .3 5)
C4
V -3 (0 .
V -3 (0 .7 0x 0 .3 5)
C1
C5
V-2 (0.35x0.20)
C4
V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 )
C6
V -3 (0.7 0x0 .3 5)
V-1 (0.50x0.25)
V-1 (0.50x0.25)
V -3 (0.7 0x0 .3 5)
C2
V-2 (0.35x0.20)
V -4 (0.60x 0.30 )
C5
C6
V -3 (0 .
V-1 (0.50x0.25)
V -3 (0.7 0x0 .3 5)
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C4
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0 .7 0x 0 .3 5)
C3
V -3 (0 .
C2
C6
C6
C2
C1
C5
C5
C4
C3
C5
C5
C4
C3
C6
C6
C2
C1
C6
V-3
C6
V-4 V-1
C5
V-4 V-2 V-4 V-1
V-3
V-4
C 6
V-3
V-3
C4
V-2 V-3
V-1 V-3
C6
C3
V-2
V-1
C6
C 2
C5
V-1
C4
V-3
V-2 C5
V-3 V-1
C5
V-3
C1
V-3
V-1
V-3
C2
C3
V-1 V-3
C2
C1
C 4
C 5
4 columnas 5160.0 Kg 3748.5 Kg 2975.0 Kg 6247.5 Kg 11900.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
30031.0 Kg 4194.81 cm2 4200 m 0.7 m 0.6 m 4 columnas 4398.0 Kg 3480.8 Kg 2762.5 Kg 5801.3 Kg 11050.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
27492.5 Kg 3840.22 cm2 4200 m 0.7 m 0.6 m 4 columnas
4104.0 Kg 2047.5 Kg 1625.0 Kg 3412.5 Kg 6500.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
17689.0 Kg 3369.33 cm2 3500 m 0.7 m 0.5 m
iferencia del
C2
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C3
C4 V -3 (0.70 x0 .35) V-2 (0.35x0.20)
V-2 (0.35x0.20)
7 0x 0 .35)
7 0x 0 .35)
C1 V -3 (0.70 x0.3 5)
7 0x0 .35)
C4
V -3 (0.70 x0 .35)
C3
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0.70 x0 .35)
V-1 (0.50x0.25)
C4
C3 V-1 (0.50x0.25)
7 0x 0 .35)
V -3 (0.70 x0 .35)
7 0x 0 .35)
C2
C1
METRADO DE CARGAS POR PISO DATOS: P.E. Concreto = S/C (hospital) = S/C azotea =
2400 kg/m3 400 kg/m2 100 kg/m2
Acabados = Tabiqueria = P. aligerado = espesor alig =
100 kg/m2 210 kg/m2 420 kg/m2 0.30 m
H1 H2 H3 H4 H5 H6 H7 H8
= = =
4.30 m L(V-1) = 3.50 m L(V-2) = 3.50 m L(V-3) =
5.0 m 3.5 m 7.0 m
= = = = =
3.50 m L(V-4) = 3.50 m 3.50 m 3.50 m 3.00 m
6.0 m
METRADO 1ER PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1 V-2 V-3 V-4
= = = = = = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x x x x x
0.25 0.25 0.25
x x x
400 x
0.50 0.60 0.70 0.60 0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x x x x x
x
3.90 3.90 3.90 3.90 3.90 3.90 5.0 3.5 7.0 6.0 34.0 34.0 34.0 3.90 3.90 3.90
x x x x x x x x x x
x x x
4 4 4 4 4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = = = = = =
= =
METRADO 2DO PISO - 6TO PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1
= = = = = = =
2400 2400 2400 2400 2400 2400 2400
x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5
x x x x x x x
0.50 0.60 0.70 0.60 0.60 0.50 0.25
x x x x x x x
3.50 3.50 3.50 3.50 3.50 3.50 5.0
x x x x x x x
4 4 4 4 4 4 12
= = = = = = =
V-2 = V-3 = V-4 = Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x
0.35 0.7 0.6
x x x
0.25 0.25 0.25
x x x
400 x
0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x
x
3.5 7.0 6.0 34.0 34.0 34.0 3.50 3.50 3.50
x x x
x x x
6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = =
= =
METRADO 7MO PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1 V-2 V-3 V-4
= = = = = = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x x x x x
0.25 0.25 0.25
x x x
400 x
0.50 0.60 0.70 0.60 0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x x x x x
x
3.25 3.25 3.25 3.25 3.25 3.25 5.0 3.5 7.0 6.0 34.0 34.0 34.0 3.25 3.25 3.25
x x x x x x x x x x
x x x
4 4 4 4 4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = = = = = =
= =
METRADO 8VO PISO (AZOTEA) PCM Peso columnas
C-1 C-2 C-3 C-4
= = = =
2400 2400 2400 2400
x x x x
0.60 0.70 0.50 0.70
x x x x
0.50 0.60 0.70 0.60
x x x x
1.50 1.50 1.50 1.50
x x x x
4 4 4 4
= = = =
Peso vigas
C-5 C-6 V-1 V-2 V-3 V-4
= = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x
100 x
0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x
0.25 0.25 0.25
x x x
0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x
x
1.50 1.50 5.0 3.5 7.0 6.0 34.0 34.0 34.0 1.50 1.50 1.50
x x x x x x
x x x
4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = =
= =
MASA TOTAL DEL
α= PCM 1º 2º 3º 4º 5º
11.23 Ton. 15.72 Ton. 13.1 Ton. 15.72 Ton. 15.72 Ton. 13.1 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 16.38 Ton. 32.76 Ton. 14.04 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
10.08 Ton. 14.11 Ton. 11.76 Ton. 14.11 Ton. 14.11 Ton. 11.76 Ton. 18 Ton.
6º 7º 8º TOTAL
580.6164 565.4580 565.4580 565.4580 565.4580 565.4580 555.9840 489.6660 ###
3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 14.7 Ton. 29.4 Ton. 12.6 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
9.36 Ton. 13.1 Ton. 10.92 Ton. 13.1 Ton. 13.1 Ton. 10.92 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 13.65 Ton. 27.3 Ton. 11.7 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
4.32 Ton. 6.05 Ton. 5.04 Ton. 6.05 Ton.
6.05 Ton. 5.04 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 6.3 Ton. 12.6 Ton. 5.4 Ton. ### Ton.
45.9 Ton. 45.9 Ton.
MASA TOTAL DEL EDIFICIO - PISO X PISO
0.5 PCV
g= Pi
183.60 672.416 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 647.784 Ton. 45.90 512.616 Ton. 1331.10 5119.106 Ton.
9.81 m/seg2 Mi
### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2
A
B
C
D
1
2
3
4
5
6
C1
C2
C6
C6
C2
C1
C3
C4
C5
C3
C4
C5
C1
f'c = E =
C2
C5
RIGIDEZC6LATERALC6
C4
C3
C4
C3
C2
C1
210 kg/cm2 ### kg/cm2
Fórmulas:
DIMENSIONES DE COLUMNAS h(cm) b(cm)
C-1 C-2 C-3 C-4 C-5 C-6
60 70 50 70 70 70
50 60 70 60 60 50
Area (cm2)
3000 4200 3500 4200 4200 3500
Inercia (cm4)
900000 1715000 ### 1715000 1715000 ###
alt. Piso1 (cm)
430 430 430 430 430 430
alt. Piso2-7 alt piso8 Krelat. Piso1 Krelat. Piso2-7 (cm) (cm)
350 350 350 350 350 350
300 2093.023 300 3988.372 300 1695.736 300 3988.372 300 3988.372 300 3323.643
DIMENSIONES DE VIGAS h(cm) b(cm)
V-1 V-2 V-3 V-4
50 35 70 60
Area (cm2) Inercia (cm4)Long. (cm) Krelat.
25 20 35 30
1250 260416.67 700 71458.33 2450 ### 1800 540000
500 520.83 350 204.17 700 1429.17 600 900
2571.429 4900.000 2083.333 4900.000 4900.000 4083.333
Fórmulas de Muto:
6 C1
C3
C3
PÓRTICO 1 y 6 COLUMNA Kraya 0.25 C1 0.43 C3 0.43 C3 0.25 C1
C1
PORT. 1 PORT. 6 Krelat. Piso8
3000.000 5716.667 2430.556 5716.667 5716.667 4763.889
Kempot Piso1 Kempot Piso2-7 Kempot Piso8 (ton/cm)
29.527 56.265 23.922 56.265 56.265 46.888
(ton/cm)
54.755 104.338 44.361 104.338 104.338 86.948
(ton/cm)
86.948 165.685 70.444 165.685 165.685 138.071
PÓRTICO 2 y 5 COLUMNA Kraya 0.13 C2 0.18 C4 0.18 C4 C2
0.13 PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.16 C6 0.18 C5 0.18 C5 0.16 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.68 C1 0.72 C2 0.7 C6 0.7 C6 0.72 C2 0.68 C1
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.84 C3 0.72 C4 0.58 C5 0.58 C5 0.72 C4 0.84 C3
PORT. B PORT. C PISOS 2 - 7 PÓRTICO 1 y 6 COLUMNA Kraya 0.2 C1 0.35 C3 0.35 C3 0.2 C1
PORT. 1 PORT. 6
PÓRTICO 2 y 5 COLUMNA Kraya 0.11 C2 0.15 C4 0.15 C4 0.11 C2
PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.13 C6 0.15 C5 0.15 C5 0.13 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.56 C1 0.58 C2 0.57 C6 0.57 C6 0.58 C2 0.56 C1
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.69 C3 0.58 C4 0.48 C5 0.48 C5
C4 C3
0.58 0.69 PORT. B PORT. C
PÓRTICO 1 y 6 COLUMNA Kraya 0.17 C1 0.3 C3 0.3 C3 0.17 C1
PORT. 1 PORT. 6
PÓRTICO 2 y 5 COLUMNA Kraya 0.09 C2 0.13 C4 0.13 C4 0.09 C2
PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.11 C6 0.13 C5 0.13 C5 0.11 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.48 C1 0.5 C2 0.49 C6
C6 C2 C1
0.49 0.5 0.48
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.84 C3 0.72 C4 0.58 C5 0.58 C5 0.72 C4 0.84 C3
PORT. B PORT. C
PISO 1
a
KL (ton/cm)
0.33 0.38 0.38 0.33
KL = KL =
527.37 ton/cm 527.37 ton/cm
a
KL (ton/cm)
0.3 0.31 0.31 0.3 KL = KL =
16.65 ### 17.58 16.65 68.47 ton/cm 68.47 ton/cm
a
KL (ton/cm)
0.3 0.31 0.31 0.3 KL = KL =
9.83 9.14 9.14 9.83
14.28 ### 17.58 14.28 63.72 ton/cm 63.72 ton/cm
PLACA
E t h L KL =
### ton/cm2 25 cm 430 cm 350 cm 489.43 ton/cm
a
KL (ton/cm)
0.44 0.45 0.44 0.44 0.45 0.44
13.02 ### 20.85 20.85 25.2 13.02
PLACA PORT. A
E t h L KL =
### ton/cm2 25 cm 430 cm 700 cm 1961.79 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
### ton/cm2 25 cm 430 cm 600 cm 1500.2 ton/cm
2079.92 ton/cm 1618.33 ton/cm
a
KL (ton/cm)
0.47 0.45 0.42 0.42 0.45 0.47
11.3 ### 23.6 23.6 25.2 11.3
KL = KL =
120.2 ton/cm 120.2 ton/cm
PISOS 2 - 7
a
KL (ton/cm)
0.09 0.15 0.15 0.09
KL = KL =
5.04 6.57 6.57 5.04
799.54 ton/cm 799.54 ton/cm
PLACA
E t h L KL =
### ton/cm2 25 cm 350 cm 350 cm 776.32 ton/cm
a
KL (ton/cm)
0.05 0.07 0.07 0.05 KL = KL =
5.27 ### 7.19 5.27 24.91 ton/cm 24.91 ton/cm
a
KL (ton/cm)
0.06 0.07 0.07 0.06 KL = KL =
5.21 ### 7.19 5.21 24.8 ton/cm 24.8 ton/cm
a
KL (ton/cm)
0.22 0.23 0.22 0.22 0.23 0.22
11.91 ### 19.29 19.29 23.56 11.91
PLACA PORT. A
E t h L KL =
### ton/cm2 25 cm 350 cm 700 cm 2717.13 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
2826.66 ton/cm 2245.65 ton/cm
a
KL (ton/cm)
0.26 0.23 0.19 0.19
11.33 ### 20.04 20.04
### ton/cm2 25 cm 350 cm 600 cm 2136.13 ton/cm
0.23 0.26 KL = KL =
23.56 11.33 109.85 ton/cm 109.85 ton/cm
PISO 8
a
KL (ton/cm)
0.08 0.13 0.13 0.08
KL = KL =
6.94 9.14 9.14 6.94
PLACA
E t h L KL =
### ton/cm2 25 cm 300 cm 350 cm 1067.56 ton/cm
1099.73 ton/cm 1099.73 ton/cm
a
KL (ton/cm)
0.04 0.06 0.06 0.04 KL = KL =
7.22 ### 9.88 7.22 34.2 ton/cm 34.2 ton/cm
a
KL (ton/cm)
0.05 0.06 0.06 0.05 KL = KL =
7.16 ### 9.88 7.16 34.07 ton/cm 34.07 ton/cm
a
KL (ton/cm)
0.19 0.2 0.2
16.73 ### 27.12
PLACA PORT. A
E t h
### ton/cm2 25 cm 300 cm
0.2 0.2 0.19
27.12 33.14 16.73
L KL =
700 cm 3395.18 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
3549.15 ton/cm 2871.1 ton/cm
a
KL (ton/cm)
0.3 0.26 0.23 0.23 0.26 0.3 KL = KL =
20.88 ### 37.45 37.45 43.71 20.88 204.08 ton/cm 204.08 ton/cm
### ton/cm2 25 cm 300 cm 600 cm 2717.13 ton/cm
CUADRO DE RESUMEN DE RIGIDEZ LATERAL RIGIDEZ LATERAL EJE Y
PISO 1
PISO 2
PISO 3
PISO 4
PISO 5
PISO 6
PISO 7
PORTICO KL(Ton/cm) 1 527.37 2 68.47 3 63.72 4 63.72 5 68.47 6 527.37 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8
RIGIDEZ LATERAL EJE X
PISO 1
PISO 2
PISO 3
PISO 4
PISO 5
PISO 6
PISO 7
PISO 8
PORTICO KL(Ton/cm) A 2079.92 B 120.2 C 120.2 D 1618.33 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 3549.15 B 204.08 C 204.08 D 2871.1
RIGIDEZ LATERAL POR
PISO PISO PISO PISO PISO PISO PISO PISO
1 2 3 4 5 6 7 8
PISO 7
PISO 8
4 5 6 1 2 3 4 5 6
24.8 24.91 799.54 1099.73 34.2 34.07 34.07 34.2 1099.73
RIGIDEZ LATERAL POR PISO EJE Y EJE X (ton/cm) (ton/cm) 1319.126 3938.656 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 2336.001 6828.408
PERIODOS Y FORMAS DE MODO DE VIBRACION - STODOLA
m 8
MASAS POR PISO Pi
m 7
m 6
8 1ºk 2º 3º 4º 5ºk 7 6º 7º 8º TOTAL
672.416 657.258 657.258 657.258 657.258 657.258 647.784 512.616 5119.106
Mi
0.685440 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.660330 ton-cm/seg2 0.522544 ton-cm/seg2 5.218253 ton-cm/seg2
k 6 m 5 RIGIDECES POR PISO EJE Y EJE X k 5 (ton/cm) (ton/cm)
m 4
m 3
m 2
m 1
PISO 1 PISO 2 PISO 3 k 4 PISO 4 PISO 5 PISO 6 PISO 7 PISO 8 k 3
1319.126 1698.497 1698.497 1698.497 1698.497 1698.497 1698.497 2336.001
3938.656 5292.013 5292.013 5292.013 5292.013 5292.013 5292.013 6828.408
RIGIDECES POR PISO PISO KL (ton/cm) 1 5257.780 k 2 2 6990.510 3 6990.510 4 6990.510 5 6990.510 1 6990.510 6k 7 6990.510 8 9164.410
m8 = m =
0.523
k8 = k =
9164.410
m8 m7 m6 m5 m4 m3 m2 m1
= = = = = = = =
1m 1.26 m 1.28 m 1.28 m 1.28 m 1.28 m 1.28 m 1.31 m
k8 k7 k6 k5 k4 k3 k2 k1
1k 0.76 k 0.76 k 0.76 k 0.76 k 0.76 k 0.76 k 0.57 k
k (ton/cm)
0.57
m (ton*seg2/cm) {X} {FI} {V} {ΔX} {XC} {X} {FI} {V} {ΔX}
1.31 1 1.31 43.8
{X} {FI} {V}
28.92
{XC} {X} {FI} {V} {ΔX} {XC} {X}
28.92
33.45 120.37 2.38 3.05
0
22.36 33.31 119.91 2.38 3.05
25.4 36.18 86.56 1.72 2.2
27.6 50.38 50.38 1
22.47
25.42 36.2 86.6 1.72 2.2
27.61 50.38 50.38 1 1.31
{ΔX}
34.68 124.52 2.38 3.06
36.34 86.92 1.72 2.2
0
23.37
25.52
27.62 50.4 50.4 1 1.31
{XC}
26.46
27.73
28.93
36.08 52.33 184.32 2.42 3.1
37.59 89.84 1.72 2.2
50.59 50.59 1 1.31
{ΔX}
39.92
28.68
29.04
0.76
1.28 3 3.85
55.69 131.99 1.73 2.22
52.25 52.25 1 1.31
{FI} {V}
42.49
29.99
{X}
0.76
1.28 2 2.56
76.31 76.31 1 1.31
{XC} {X} {FI} {V} {ΔX} {XC}
0.76
22.35 33.29 119.85 2.38 3.05
25.4 36.18 86.56 1.72
{ф1 } =
0
22.35 33.29 119.85 2.38
1 1.72 2.38 2.96 3.44
3.81 4.05 4.13
PERIODOS Y FORMAS DE MODO CRITERIO PARA ASUMIR "Wi"
w2 = w2 =
m (ton*seg2/cm)
k (ton/cm)
93.29 rad/seg 93.29 rad/seg
0.685
0.670
5257.780
{ΔX} {V}
### 1 63.95 1
{X} {FI}
F1 F2 F3 F4 F5 F6
5257.78
0.670
### 1.74 108.94 0.74
5193.83
1 3 5 7 9 11
6990.510 2.47 154.41 0.73
5084.89
4930.48
POLINOMIO CARACTERISTICO
M=
0.685440 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 0.669988 0 0 0 0.669988 0 0 0 0 0 0 0 0 0
K=
MATRIZ EJE Y 3017.624 ### 0 -1698.497 3396.995 ### 0 ### 3396.995 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 ### 4034.499 ### 0 ### 2336.001
0.76
1.28 4 5.13
0.76
1.28 5 6.41 30.95
47.28 231.6 3.04 3.89
24.54
19.47
29.44 149.82 2.96 3.8
0 18.56
29.3 149.15 2.96 3.8 29.29 149.14 2.96
0
24.32 173.47 3.44 4.41 24.32 173.46 3.44
DETERMINANDO EL PERIODO T1
12.21 205.12 4.05 5.13
0
18.54 192.01 3.81 4.89
0
4.14 208.38 4.13 4.13
4.13 12.13 204.14 4.05 5.12
9.26 18.53 192 3.81
4.16 209.29 4.14 4.14 4.14
12.14 204.24 4.05 5.12
9.26
14.14
4.38 217.41 4.16 4.16 4.16
9.26
14.14
18.56
12.83 213.03 4.08 5.15
18.65 192.92 3.81 4.89 18.55 192.1 3.81 4.89
8 334.41 4.38 4.38 4.38
9.31
14.15 24.34 173.55 3.44 4.41
8 8
22.08 326.41 4.28 5.41
19.53 200.2 3.83 4.91
24.45 174.27 3.44 4.42
1
8
9.79
14.23
18.57
1.26 7 8.85
32.16 304.33 3.99 5.11
25.52 180.67 3.46 4.43
1
16.85
14.9
18.66
29.31 149.22 2.96 3.8
1.28 6 7.69
40.56 272.17 3.57 4.57
30.62 155.15 2.97 3.81
0.76
4.13 208.27 4.13 4.13 4.13
12.13 204.13 4.05
4.13 208.26 4.13
∑ XNC
∑ XC
23.5
w₁ = T₁ =
1183.76
18.66 rad/seg 0.34 seg
RMAS DE MODO DE VIBRACION - HOLTZER
W1 W2 W3 W4 W5 W6
0.669988
18.66 55.98 93.29 130.61 167.93 205.24
###
### 3.18 198.5 0.71
### 3.85 240.81 0.68
4731.98
0 0 0 0 0 0 0.660330 0 0
0.669988
0 0 0 0 0 0 0 ### 0
###
6990.510 4.5 280.96 0.64
4491.18
0.522544
9164.410 5.1 314.02 0.6
4210.21
5.52 269.22 0.43 3896.2
K=
MATRIZ EJE X ### ### ### ### 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 ### ### ###
mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k
F-V=
-3626.98
0 0 0 0 0 0 ### 6828.408
ESPECTRO DE RESPUESTA DE ACELERACIONES HYO PROYECTO
: TRABAJO ESCALONADO DE INGENIERIA ANTISISMICA
FECHA
: AGOSTO 2011
PARAMETROS DE Z SITIO 1 - 2 - 3 ZONA =
2
Z=
0.30
CONDICIONES GEOTECNICAS S S1-S2-S3 TIPO =
S3
S=
1.40
CATEGORIA DE U LA EDIFICACION A-B-C USO =
A
Tp = U=
0.90 1.50
SISTEMA ESTRUCTURAL Rd 9.5-8.7-6-4 R=
7.000
800.00 700.00
Sa (cm/seg2)
600.00 500.00 400.00 300.00 200.00 100.00 0.00
T ESPECTRO DE RESPUESTAS DE ACELERACIONES (NORMA E-030, 2003 RNE) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1
PERIODO (seg)
1
1
2
C
2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.2500 2.0455 1.8750 1.7308 1.6071 1.5000
Sa
220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 198.6525 180.5932 165.5438 152.8096 141.8946 132.4350
2.
PERIODOS Y FORMAS DE VIBRACION
De la ecuación dinámica
MODOS EN EL EJE Y 1 2 3 4 5 6 7 ω² = 85.389 759.626 2053.584 3833.553 5867.623 7839.594 9399.354 ω= 9.241 27.561 45.316 61.916 76.600 88.541 96.950 T= 0.68 0.23 0.14 0.1 0.08 0.07 0.06 1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.7422
-1.5084
0.2296
-1.8621
-2.0165
-1.4733 1671.8636
2.4257 3.0275
-3.5649 -4.2946
-0.8880 -0.6628
-0.4143 1.3256
2.4435 -2.1562
2.1527 -1.5973
3.5273
-4.2609
0.5647
-1.4383
1.2385
3.9083 4.1577 4.2387
-4.0389 -0.5452 3.3902
0.9382 -0.1070 -0.7510
1.9950 -0.7411 -1.1855
0.0412 -1.3089 1.1872
-0.0013 -0.3311
0.0009 -548.2067 0.0047 0.0340 0.0000
0.0004 -0.8963 ###
MODOS EN EL EJE X 1 2 3 4 5 6 7 ω² = 262.599 2336.391 6318.730 11802.979 18078.109 24170.954 29015.554 ω= 16.2 48.34 79.49 108.64 134.45 155.47 170.34 T=
0.39
0.13
0.08
0.06
0.05
0.04
0.04
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.7103
-1.5754
0.2155
-1.7156
-2.0139
2.3636
-3.6848
-0.8910
-0.5046
2.3703
2.9385 3.4156 3.7791 4.0171
-4.4871 -4.4543 -4.1239 -0.4946
-0.6661 0.5542 0.9463 -0.0756
1.3161 -1.3433 1.8624 -0.6311
-1.9526 0.8974 0.4508 -1.6519
4.0994
3.5304
-0.7813
-1.1933
1.3535
-1.2874 1671.8636 1.6230
-0.0013
-1.1267 -0.3311 0.0007 -548.2067 0.0039 0.0004 0.0283 -0.8963 0.0000
###
GRAFICOS DE MODOS EJE Y
EJE X
MODO 1
MODO 1
MODO 1
MODO 1
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0.0000
2.0000
4.0000
6.0000
0.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
4.0000
6.0000
MODO 2
MODO 2
-5.0000
2.0000
-5.0000
MODO 3
0.0000
5.0000
MODO 3
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
6
6
5
5
4
4
3
3
2
2
1
1
-1.0000 0.0000 1.0000 2.0000
-1.0000 0.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
-2.0000 0.0000
MODO 5 9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
-5.0000
MODO 6 9
2.0000
4.0000
MODO 5
9
-5.0000
2.0000
MODO 4
MODO 4
-5.0000
1.0000
0.0000
5.0000
MODO 6 9
MODO 6
MODO 6
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-2.0000 0.0000 2.0000 4.0000
-2.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
2000.0000
2.0000
MODO 7
MODO 7
-2000.0000
0.0000
-2000.0000
0.0000
2000.0000
MODO 8
MODO 8 9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
4
4
3
3
2
2
1
1
-1.0000 0.0000 1.0000 2.0000
-1.0000 0.0000
1.0000
2.0000
3º
CALCULO DE LOS FACTORES DE PARTICIPACION MODAL (FPM)
EJE Y 8
1ER MODO 1.0000 1.7422 2.4257
10495.166 102.446 0.06
{ф1 } =
3.0275
1.0000
3.5273
-0.0008
3.9083
-0.0006 -0.3289
4.1577 4.2387
{ф1 }T =
1.0000
1.7422
2.4257
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
1.17
1.63
0.0003 0.0002 -0.8943 0.0007
8
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
[M] =
31890.874
MODO 1
178.58 0.04
[M] *{ф1 }T =
0.69
1.0000
[M] *{ф1 }T *{ф1 }=
52.17
{ф1 }T *{m}=
15.45
-0.0008 -0.0006 -0.3289 0.0003 0.0002 -0.8943
1.0000
0.0007
-1.5084
FPM1 =
2DO MODO
-3.5649 1
{ф } =
-4.2946 -4.2609
{ф1 }T =
1.0000 -1.5084 -3.5649
-4.0389 -0.5452 3.3902
0.68544
0.685440
0
0
MODO 1
0000
0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0 0 0 0 0 0 0
### 0 0 0 0 0 0
0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.01
-2.39
[M] *{ф1 }T *{ф1 }=
52.38
{ф1 }T *{m}=
-9.74
[M] =
6.0000
FPM2 =
3ER MODO 1.0000
MODO 2
0.2296 -0.8880
{ф1 } =
-0.6628 0.5647 0.9382
{ф1 }T =
1.0000
0.2296 -0.8880
-0.1070 -0.7510
5.0000
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
MODO 3
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
0.15
-0.59
[M] *{ф1 }T *{ф1 }=
2.65
{ф1 }T *{m}=
0.34
[M] =
4TO MODO 1.0000
FPM3 =
0000
-1.8621 -0.4143
{ф1 } =
2.0000
MODO 4
0000
1.3256 -1.4383 1.9950 -0.7411 -1.1855
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.25
-0.28
[M] *{ф1 }T *{ф1 }=
9.45
{ф1 }T *{m}=
-0.69
[M] =
4.0000
1.0000 -2.0165 2.4435
{ф1 } =
MODO 6
FPM4 =
5TO MODO
MODO 5
5.0000
1.0000 -1.8621 -0.4143
-2.1562 1.2385 0.0412 -1.3089 1.1872
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
[M] =
[M] *{ф1 }T =
1.0000 -2.0165
2.4435
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
0.69
-1.35
1.64
MODO 6 [M] *{ф1 }T *{ф1 }=
13.42
{ф1 }T *{m}=
0.14
FPM5 =
6TO MODO 1.0000 -1.4733 2.1527
{ф1 } =
2.0000
MODO 7
-1.5973 0.0009 0.0047 0.0340 0.0000
{ф1 }T =
1.0000 -1.4733
2.1527
0.68544
0.685440
0
0
0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0 0 0 0 0 0 0
### 0 0 0 0 0 0
0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-0.99
1.44
[M] *{ф1 }T *{ф1 }=
6.95
{ф1 }T *{m}=
0.1
[M] =
2000.0000
FPM6 = FPM1 FPM2 FPM3 FPM4 FPM5 FPM6 FPMtotal
MODO 8
EJE X 1ER MODO 1.0000 1.7103 2.3636
29.609 18.597 12.989 7.274 1.046 1.390 70.904
0000
{ф1 } = 2.0000
2.9385 3.4156 3.7791 4.0171 4.0994
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000
1.7103
2.3636
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
1.15
1.58
[M] *{ф1 }T *{ф1 }=
49
{ф1 }T *{m}=
15
[M] =
FPM1 =
2DO MODO 1.0000 -1.5754 -3.6848
{ф1 } =
-4.4871 -4.4543 -4.1239 -0.4946 3.5304
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000 -1.5754 -3.6848
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.06
-2.47
[M] *{ф1 }T *{ф1 }=
56.3
[M] =
{ф1 }T *{m}=
-10.07
FPM2 =
3ER MODO 1.0000 0.2155 -0.8910
{ф1 } =
-0.6661 0.5542 0.9463 -0.0756 -0.7813
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000
0.2155 -0.8910
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
0.14
-0.6
[M] *{ф1 }T *{ф1 }=
2.67
{ф1 }T *{m}=
0.33
[M] =
FPM3 =
4TO MODO 1.0000 -1.7156 -0.5046
{ф1 } =
1.3161 -1.3433 1.8624 -0.6311 -1.1933
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999
{ф1 }T =
[M] =
1.0000 -1.7156 -0.5046
0.685440 0 0 0 0
0 ### 0 0 0
0 0 ### 0 0
0.66999 0.66033 0.52254
0 0 0
0 0 0
0 0 0
[M] *{ф1 }T =
0.69
-1.15
-0.34
[M] *{ф1 }T *{ф1 }=
8.53
{ф1 }T *{m}=
-0.61
FPM4 =
5TO MODO 1.0000 -2.0139 2.3703
{ф1 } =
-1.9526 0.8974 0.4508 -1.6519 1.3535
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000 -2.0139
2.3703
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.35
1.59
[M] *{ф1 }T *{ф1 }=
13.16
{ф1 }T *{m}=
0.14
[M] =
FPM5 =
6TO MODO 1.0000 -1.2874 1.6230
{ф1 } =
-1.1267 0.0007 0.0039
{ф1 }T =
1.0000 -1.2874
1.6230
0.0283 0.0000
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-0.86
1.09
[M] *{ф1 }T *{ф1 }=
4.41
{ф1 }T *{m}=
0.18
[M] =
FPM6 = FPM1 FPM2 FPM3 FPM4 FPM5 FPM6 FPMtotal
30.613 17.895 12.478 7.186 1.032 4.017 73.220
4º
CALCULO DE LA ACELERACION ES Parametros Sísmicos Z= 0.3
3.0275
3.5273
3.9083
4.1577
U=
1.5
S=
1.4
R=
7.0
4.2387
MODO 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 ###
T1 = C= C= MODO 2 T2 = C= C= MODO 3 T3 =
2.03
2.36
2.62
2.75
2.21
C= C= MODO 4
0.2961
29.609
T4 = C= C= MODO 5
-4.2946 -4.2609 -4.0389 -0.5452
T5 = C= C=
3.3902
MODO 6 T6 = C= C= 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 ###
MODO 1 T1 = C= C= MODO 2 T2 =
-2.88
-2.85
-2.71
-0.36
1.77
C= C= MODO 3
-0.1860
18.597
T3 = C= C= MODO 4
-0.6628
0.5647
T4 = C= C=
0.9382 -0.1070 -0.7510
MODO 5 T5 = C= C= 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 ###
-0.44
0.38
0.63
-0.07
-0.39
0.1299
12.989
MODO 6 T6 = C= C=
1.3256 -1.4383
1.9950 -0.7411 -1.1855
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 ###
0.89
-0.96
1.34
-0.49
-0.62
0.0412 -1.3089
1.1872
-0.0727
7.274
-2.1562
1.2385
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 ###
-1.44
0.83
0.03
-0.86
0.62
0.0105
1.046
-1.5973
0.0009
0.0047
0.0340
0.0000
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 ###
-1.07
0
0
0.02
0
0.0139 % % % % % % %
1.390
como es mayor a 70% analizamos con estos 6 modos
2.9385
3.4156
3.7791
4.0171
4.0994
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 ###
1.97
2.29
2.53
2.65
2.14
-4.4871 -4.4543 -4.1239 -0.4946
3.5304
0.3061
30.613
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 ###
-3.01
-2.98
-2.76
-0.33
1.84
-0.1789
17.895
-0.6661
0.5542
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 ###
-0.45
0.37
0.63
-0.05
-0.41
0.1248
1.3161 -1.3433
0 0 0 ### 0
0 0 0 0 ###
0.9463 -0.0756 -0.7813
12.478
1.8624 -0.6311 -1.1933
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 ###
0.88
-0.9
1.25
-0.42
-0.62
0.4508 -1.6519
1.3535
-0.0719
7.186
-1.9526
0.8974
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 ###
-1.31
0.6
0.3
-1.09
0.71
0.0283
0.0000
0.0103
-1.1267
0.0007
1.032
0.0039
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 ###
-0.75
0
0
0.02
0
0.0402 % % % % % % %
4.017
como es mayor a 70% analizamos con estos 6 modos
O DE LA ACELERACION ESPECTRAL
5º
CALCULO DEL VECTOR DE D
os Sísmicos g=
981
Tp =
0.9
C <=
2.5
MODO 1 2 3 4
EJE Y
5 6
0.680 3.31 2.5
MODO 1 Sa =
220.73 cm/seg2 {ф1 } =
0.228 9.87 2.5
Sa =
220.73 cm/seg2
Sa =
220.73 cm/seg2
0.139 16.23 2.5
MODO 2
{ф1 } =
0.101 22.17 2.5
Sa =
220.73 cm/seg2
0.082 27.43 2.5
Sa =
220.73 cm/seg2
0.071 31.71 2.5
MODO 3
{ф1 } =
Sa =
220.73 cm/seg2
EJE X
0.388 5.8 2.5
MODO 4 Sa =
220.73 cm/seg2 {ф1 } =
0.130 17.31 2.5
0.079 28.47 2.5
Sa =
220.73 cm/seg2
MODO 5 Sa =
220.73 cm/seg2 {ф1 } =
0.058 38.9 2.5
Sa =
220.73 cm/seg2
0.047 48.15 2.5
Sa =
220.73 cm/seg2
MODO 6
{ф1 } =
0.040 55.67 2.5
Sa =
220.73 cm/seg2
MODO 1 2 3 4 5 6
MODO 1
{ф1 } =
MODO 2
{ф1 } =
MODO 3
{ф1 } =
MODO 4
{ф1 } =
MODO 5
{ф1 } =
MODO 6
{ф1 } =
=
CORRECCION POR 0.75
{ X }=
VERIFICACION: "Desplazam
EJE PISO 1 2 3 4 5 6 7 8
=
CORRECCION POR 0.75
{ X }=
VERIFICACION: "Desplazam
EJE PISO 1 2 3 4 5 6 7 8
CALCULO DEL VECTOR DE DESPLAZAMIENTOS
EJE Y FPM 0.2961 -0.1860
Sa 220.73 220.73
W2 85.389 759.626
0.1299
220.73
2053.584
-0.0727
220.73
3833.553
0.0105
220.73
5867.623
0.0139
220.73
7839.594
1.0000 1.7422 2.4257 3.0275
{X1 }=
3.5273 3.9083 4.1577 4.2387
1.0000 -1.5084 -3.5649
{X1 }=
-4.2609 -4.0389 -0.5452 3.3902
1.0000 0.2296 -0.6628 0.5647 0.9382
-0.05 cm 0.08 cm 0.19 cm 0.23 cm 0.23 cm 0.22 cm 0.03 cm -0.18 cm
-4.2946
-0.8880
0.77 cm 1.33 cm 1.86 cm 2.32 cm 2.7 cm 2.99 cm 3.18 cm 3.24 cm
{X1 }=
0.01 cm 0 cm -0.01 cm -0.01 cm 0.01 cm 0.01 cm
-0.1070 -0.7510
0 cm -0.01 cm
1.0000 -1.8621 -0.4143 1.3256
0 cm 0.01 cm 0 cm -0.01 cm 0.01 cm
{X1 }=
-1.4383
-0.01 cm 0 cm 0 cm
1.9950 -0.7411 -1.1855
1.0000 -2.0165 2.4435 -2.1562
{X1 }=
1.2385 0.0412 -1.3089 1.1872
1.0000 -1.4733 2.1527
{X1 }=
-1.5973 0.0009 0.0047 0.0340 0.0000
EJE X FPM
Sa
W2
0.3061
220.73
262.599
-0.1789 0.1248 -0.0719 0.0103
220.73 220.73 220.73 220.73
2336.391 6318.730 ### ###
0.0402
220.73
###
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 1.7103 2.3636 2.9385 3.4156 3.7791 4.0171 4.0994
1.0000 -1.5754 -3.6848 -4.4871 -4.4543 -4.1239
{X1 }=
{X1 }=
-0.4946 3.5304
0.26 cm 0.44 cm 0.61 cm 0.76 cm 0.88 cm 0.97 cm 1.03 cm 1.05 cm
-0.02 cm 0.03 cm 0.06 cm 0.08 cm 0.08 cm 0.07 cm 0.01 cm -0.06 cm
-0.7813
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 -1.7156 -0.5046 1.3161 -1.3433 1.8624 -0.6311 -1.1933
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 0.2155 -0.8910 -0.6661 0.5542 0.9463 -0.0756
1.0000 -2.0139 2.3703 -1.9526 0.8974
{X1 }=
{X1 }=
{X1 }=
0 cm 0 cm 0 cm 0 cm 0 cm
-1.6519
0 cm 0 cm
1.3535
0 cm
1.0000 -1.2874 1.6230 -1.1267
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
0.4508
{X1 }=
0.0007 0.0039 0.0283 0.0000
COMBINACION MODAL DE LA NORMA NTE-030
EJE Y 0.84 1.43 2.07 2.57 2.94
=
3.23 3.22 3.44
0.77 1.34 1.87 2.33 2.71
{ X }=
3 3.18 3.25
0.78514 cm 1.35876 cm 1.91618 cm 2.38793 cm 2.76820 cm 3.05722 cm 3.19090 cm 3.29779 cm
CORRECCION POR 0.75 x R ……..SEGUN NTE-030 0 cm 0.00 m 4.12 cm 4.30 m 7.13 cm 7.80 m 10.06 cm 11.30 m 12.54 cm Hacum. = 14.80 m 14.53 cm 18.30 m 16.05 cm 21.80 m 16.75 cm 25.30 m 17.31 cm 28.30 m
DESPLAZAMIE 30.00 28.30 25.30
25.00
21.80 20.00 18.30
VERIFICACION: "Desplazamientos Laterales" H (m)
15.00
10.00
14.80 11.30
D IE
18.30 H (m)
EJE Y H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 4.12 NO CUMPLE! 3.5 2.45 3.01 NO CUMPLE! 3.5 2.45 2.93 NO CUMPLE! 3.5 2.45 2.48 NO CUMPLE! 3.5 2.45 2 OK! 3.5 2.45 1.52 OK! 3.5 2.45 0.7 OK! 3.0 2.10 0.56 OK!
15.00
14.80 11.30
10.00
7.80 5.00
4.30
0.00 0.00 5
=
1.04 1.12
0.26 0.44 0.61 0.76 0.88 0.97 1.03 1.06
CORRECCION POR 0.75 x R ……..SEGUN NTE-030 0 cm 0.00 m 1.38 cm 3.50 m 2.35 cm 7.80 m 3.29 cm 11.30 m 4.09 cm Hacum. = 14.80 m 4.73 cm 18.30 m 5.22 cm 21.80 m 5.44 cm 25.30 m 5.63 cm 28.30 m
VERIFICACION: "Desplazamientos Laterales" EJE X H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 1.38 OK! 3.5 2.45 0.97 OK! 3.5 2.45 0.94 OK! 3.5 2.45 0.8 OK! 3.5 2.45 0.64 OK! 3.5 2.45 0.48 OK! 3.5 2.45 0.22 OK! 3.0
2.10
0.19
OK!
15
desplaz. (cm)
EJE X 0.28 0.47 0.68 0.84 0.96 1.05
10
{ X }=
0.26353 cm 0.44833 cm 0.62752 cm 0.77925 cm 0.90119 cm 0.99339 cm 1.03610 cm 1.07232 cm
20
D IE
DESPLAZAMIENTO EN Y
28.30 25.30 21.80 18.30 14.80 11.30
DESPLAZAM IENTO EN Y
18.30 14.80 11.30 7.80
4.30
0 5
10
15
laz. (cm)
20
DESPLAZAM IENTO EN Y
6º
CALCULO DEL VECTOR DE FUERZAS SISMICAS
EJE Y
EJE X
MODO 1 2 3 4 5
FPM 0.2961 -0.1860 0.1299 -0.0727 0.0105
Sa 220.73 220.73 220.73 220.73 220.73
MODO 1 2 3 4 5
FPM 0.3061 -0.1789 0.1248 -0.0719 0.0103
Sa 220.73 220.73 220.73 220.73 220.73
6
0.0139
220.73
6
0.0402
220.73
{m} =
0.69 0.67 0.67 0.67 0.67 0.67 0.66 0.52
MODO 1
{F1 }=
44.8 76.28 106.21 132.56 154.45 171.13 179.43 144.75
MODO 1
{F1 }=
MODO 2
{F1 }=
-28.14 41.48 98.04 118.11 117.18
46.31 77.42 107 133.03 154.63 171.08 179.23 144.74
MODO 2
{F1 }=
-27.07 41.69 97.51 118.74 117.88
111.07 14.78 -72.72
109.13 12.9 -72.87
MODO 3
{F1 }=
19.65 4.41 -17.06 -12.73 10.85 18.02 -2.03 -11.25
MODO 3
{F1 }=
MODO 4
{F1 }=
-11.01 20.03 4.46 -14.26 15.47 -21.46 7.86 9.95
MODO 4
{F1 }=
MODO 5
{F1 }=
1.58 -3.12 3.78 -3.33 1.92 0.06 -1.99 1.43
{F1 }=
-10.87 18.23 5.36 -13.99 14.27 -19.79 6.61 9.89 MODO 5
{F1 }=
MODO 6 2.1 -3.03 4.42 -3.28 0 0.01 0.07 0
18.88 3.98 -16.44 -12.29 10.23 17.46 -1.38 -11.24
1.56 -3.07 3.62 -2.98 1.37 0.69 -2.48 1.61 MODO 6
{F1 }=
6.08 -7.65 9.64 -6.69 0 0.02 0.17 0
COMBINACION MODAL DE LA NORMA NTE-030 COMBINACIÓ N MODAL : COMBINACIÓ N MODAL : 0.25 ∑i { F{} F=}0=.25 ∑F
F i + 0.75 ∑i 2F i + 0.75 ∑ F EJE Y
107.27 148.35 61 . 804 .804233.97 tonton 61 i 62.119 ton , .119284.28 ton , ∑∑F i F= == 62 74 . 788 74 ton 299.86 .788 ton 321.76 206.15 240.1
{ Fi }=
69.98 104.09 167.79 205.04 221.06 234.89 186.71 182.04
2
57.55 89.33 40 .458ton ton .458 145.73 2 40 2 i 48 .974 ton 48.974 ton ∑ ∑F i F== =178.63 56 .079 56 194.8 ton .079 ton 205.93 180.23 162.69
tn tn tn tn tn tn tn tn
COMBINACIÓ N MODAL : COMBINACIÓ N MODAL : 0.25 ∑i { F{} F=}0=.25 ∑F
F i + 0.75 ∑i 2F i + 0.75 ∑ F EJE X
2
110.78 58.24 152.04 90.27 61 . 804 ton 40 .458ton ton .458 146.16 .804239.58 61 ton 2 40 i i 2 62.119 ton , 48 .974 ton .119287.72 48.974 ton ton , ∑∑F i F= == 62 ∑ ∑F i F== =179.43 74.788 ton 56 .079 298.38 74 195.23 ton .788 ton 56.079 ton 318.18 204.64 202.77 179.84 240.36 162.75 1 8 2 . 1 5 t n 1 8 5 . 5 7 t n
1 8 2 . 1 5 t n
1 8 5 . 5 7 t n
2 3 3 . 0 3 t n
{ Fi }=
71.38 tn 105.71 2 tn 2 1 . 0 1 t n 169.52 tn 206.51 2 tn 0 6 . 5 1 t n 221.01 tn 6 9 . 5 2 t n 233.031 tn 185.57 tn 0 5 . 7 1 t n 182.151 tn 7 1 . 3 8 t n
7º
CALCULO DEL VECTOR DE CORTANTES
{ V } = [ S] . { F } i
i
[S] = MATRIZ CUADRADA SUPERIOR
1 0 0 0 0 0 0 0
[S]=
1 1 0 0 0 0 0 0
EJE Y
1 1 1 0 0 0 0 0
1 1 1 1 0 0 0 0
1 1 1 1 1 0 0 0
1 1 1 1 1 1 0 0
1 1 1 1 1 1 1 0
EJE X
1009.61 tn 964.82 tn 888.53 tn {V1 }= 782.32 tn 649.76 tn 495.31 tn 324.18 tn 144.75 tn
1013.46 tn 967.14 tn 889.72 tn {V1 }= 782.71 tn 649.69 tn 495.06 tn 323.98 tn 144.74 tn
399.81 tn 427.95 tn 386.46 tn 288.42 tn 170.32 tn 53.14 tn -57.94 tn -72.72 tn
397.92 tn 424.99 tn 383.3 tn 285.78 tn 167.04 tn 49.17 tn -59.97 tn -72.87 tn
{V2 }=
{V3 }=
9.87 tn -9.79 tn -14.2 tn 2.86 tn 15.59 tn
{V2 }=
{V3 }=
9.19 tn -9.69 tn -13.66 tn 2.78 tn 15.07 tn
1 1 1 1 1 1 1 1
4.75 tn -13.28 tn -11.25 tn
4.84 tn -12.62 tn -11.24 tn
11.04 tn 22.04 tn 2.01 tn -2.45 tn 11.81 tn -3.66 tn 17.8 tn 9.95 tn
9.72 tn 20.59 tn 2.36 tn -3 tn 10.98 tn -3.29 tn 16.5 tn 9.89 tn
{V4 }=
{V5 }=
{V6 }=
{V4 }=
0.32 tn -1.26 tn 1.86 tn -1.92 tn 1.42 tn -0.5 tn -0.56 tn 1.43 tn
0.31 tn -1.25 tn 1.82 tn -1.8 tn 1.18 tn -0.19 tn -0.87 tn 1.61 tn
{V5 }=
0.3 tn -1.81 tn 1.22 tn -3.2 tn 0.08 tn 0.08 tn 0.07 tn 0 tn
1.57 tn -4.51 tn 3.14 tn -6.5 tn 0.19 tn 0.19 tn 0.17 tn 0 tn
{V6 }=
COMBINACIÓ NCOMBINACION MODAL : MODAL DE LA NORMA NTE-030
{V}
= 0.25
∑
V i + 0.75
∑
Vi
2
EJE Y
∑
1430.95 .473 1427.65 147
Vi
ton = 115 .497 ton 74 .788 ton
1085.99 1055.74
,
∑
Vi
2
1172.23 tn 129 .257 tn 1148.72
ton = 101 .665 ton 56 .079 ton
∑
ton 147 .473 ton 147 .473 1294.28 i V i = 115V .497 ton , 1081.17 == 115 .497 ton 74 .788 ton 848.98 74.788 ton
∑
∑, V i
2
557.43 413.83 240.1
.257 129 969.05 2 == 101 .665 833.81 Vi 56 .079 671.99
∑
498.19 330.06 162.69
ton 129 .257 ton1050.36 tn ton { Vi = 101 .665 }=ton 895.65 tn ton 56.079 ton 716.24 tn
513.00 tn 351.00 tn 182.04 tn
1 8 2 . 0 4 t n
3 5 1 . 0 0 t n
5 1 3 . 0 0 t n
7 1 6 . 2 4 t n
8 9 5 . 6 5 t n
1 0 5 0 . 3 6 t n
1 1 4 8 . 7 2 t n
COMBINACIÓN MODAL :
1 1 7 2 . 2 3 t n
COMBINACIÓ N MODAL :
{ V} { V } = 0.25 ∑
∑
Vi
∑ + 0.75
= 0.25
Vi
1432.17 1428.17 .473 ton ton1294 147 .473 147 i 1082.57 = ∑ 115V .497== ton .497, ton 115 844.16 74 .788 ton 74.788 ton 552.74 414.1 240.36
∑,
V i + 0.75 2 ∑X V i EJE
Vi
2
∑
Vi
1088.86 1056.66 968.88 .257 129 2 i = 833.29 = = ∑101V.665 671.08 56 .079 497.53 330.14 162.75
2
129.257 ton ton }= 101.665{ Vi ton ton ton56.079 ton
1 8 2 . 1 5 t n
3 5 1 . 1 3 t n
5 1 1 . 3 3 t n
7 1 4 . 3 5 t n
8 9 5 . 6 1 t n
1 0 5 0 . 1 6 t n
1174.69 tn 1149.53 tn 1050.16 tn 895.61 tn 714.35 tn 511.33 tn 351.13 tn 182.15 tn
7 1 4 . 3 5 t n
8 9 5 . 6 1 t n
1 0 5 0 . 1 6 t n
1 1 4 9 . 5 3 t n
1 1 7 4 . 6 9 t n
8º
CALCULO DEL VECTOR DE MOMENTOS
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
EJE Y
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 3.50 0.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
EJE X
3497.1 tn-m 3304.48 tn-m 3037.48 tn-m {V1 }= 2665.74 tn-m 2201.77 tn-m 1661.21 tn-m 1062.25 tn-m 434.26 tn-m
3511.78 tn-m 3312.63 tn-m 3041.64 tn-m {V1 }= 2667.13 tn-m 2201.54 tn-m 1660.35 tn-m 1061.55 tn-m 434.23 tn-m
1413.19 tn-m 1534.17 tn-m 1388.98 tn-m {V2 }= 1045.84 tn-m 632.46 tn-m
1407.48 tn-m 1523.9 tn-m 1377.98 tn-m {V2 }= 1036.68 tn-m 621.08 tn-m
{V3 }=
{V4 }=
{V5 }=
{V6 }=
222.34 tn-m -166.42 tn-m -218.15 tn-m
208.51 tn-m -173.45 tn-m -218.6 tn-m
55.88 tn-m -28.63 tn-m -44.06 tn-m 15.64 tn-m 60.2 tn-m 22.23 tn-m -40.85 tn-m -33.76 tn-m
52.89 tn-m -28.28 tn-m -42.2 tn-m 15.34 tn-m 58.36 tn-m 22.57 tn-m -38.55 tn-m -33.73 tn-m
24.85 tn-m 72.17 tn-m 2.07 tn-m -13.53 tn-m 36.37 tn-m -17.78 tn-m 57.34 tn-m 29.84 tn-m
1.68 tn-m -5.12 tn-m 5.79 tn-m -7.43 tn-m 4.24 tn-m -2.46 tn-m -2.69 tn-m 4.3 tn-m
2.72 tn-m -6.32 tn-m 4.28 tn-m -11.21 tn-m 0.28 tn-m 0.28 tn-m 0.24 tn-m 0 tn-m
{V3 }=
{V4 }=
{V5 }=
{V6 }=
20.38 tn-m 67.13 tn-m 3.32 tn-m -15.45 tn-m 33.5 tn-m -16.46 tn-m 52.8 tn-m 29.67 tn-m
1.53 tn-m -5.19 tn-m 5.57 tn-m -7.09 tn-m 3.34 tn-m -1.45 tn-m -3.86 tn-m 4.83 tn-m
10.36 tn-m -15.77 tn-m 10.99 tn-m -22.75 tn-m 0.68 tn-m 0.66 tn-m 0.58 tn-m 0 tn-m
COMBINACION MODAL DE LA NORMA NTE-030
COMBINACIÓ N MODAL :
{ M}
COMBINACIÓ N MODAL : COMBINACIÓ N MODAL :
{ M}
∑
= 0.25
∑
{ M}
= 0.25
∑
= 0.25
M i + 0.75
∑
M
+ 0.75
i
∑
M i + 0.75
M ∑ EJE Y 2
i
4995.42 3772.34 4950.89 3644.08 1087 . 968 ton − m 1087 . 968 ton − m −m 1066 .918 1087 .968 ton4482.66 3340.29 2 i 2863.67 i i = 3759.39 = M = 604 . 224 ton − m , M = 604i .224 ton −m , M = 520 .843 = ton604 .224 ∑ton − m , M 2291.9 2935.33 224 . 364 − m 168 .236 224 .364 ton − m 224 1926.29 1676.26 .364 1329.78 ton − m 1077.51 COMBINACIÓ N MODAL : 720.29 488.07
∑
∑
∑
Mi
∑
M
i
2
2
4078.11 tn-m 3970.78 tn-m 1066 . 918 ton −m 3625.89 tn-m ton − m 2 2 i }= .843 3087.60 tn-m M − m ={ Mi520 −m ton i ton M = 168 .236 ton 2452.76 tn-m ton − m −m 1738.77 tn-m 1140.58 tn-m 546.13 tn-m
∑
COMBINACIÓ N MODAL :
{ M}
∑
M
i
= 0.25
1087 .968 i = 604 .224M 224 .364
∑
∑
{ M}
= 0.25
M i + 0.75
5004.42 4952.9 1087 4481.71 ton − m .968 =ton3764.45 −604 m .224 , = ton2918.49 m .364 −224 1910.01 1330.8 721.07
∑
M i + 0.75
∑EJEM X i
2
∑
3783.77 3647.1 ton − m 1066 .918 3339.52 2 i ton −∑m M ,== 2861.7 520 .843 2288.46 ton − m 168 .236 1673.62 1077.62 488.25
∑
Mi
2
4088.94 tn-m 3973.55 tn-m 1066 . 918 m ton −tn-m ton − m 3625.06 i 2 520}= .843 m 3087.39 ton −tn-m Mton − =m { Mi ton − m m 168.2362445.97 ton −tn-m 1732.72 tn-m 1140.92 tn-m 546.45 tn-m
546.13 tn-m
546.45 tn-m
1140.58 tn-m
1140.92 tn-m
1738.77 tn-m
1732.72 tn-m
2452.76 tn-m
2445.97 tn-m
3087.60 tn-m
3087.39 tn-m
3625.89 tn-m
3625.06 tn-m
3970.78 tn-m
3973.55 tn-m
4078.11 tn-m
4088.94 tn-m
1066 .918 520 .843 168 .236
3625.89 tn-m
3625.06 tn-m
3970.78 tn-m
3973.55 tn-m
4078.11 tn-m
4088.94 tn-m
EJE Y
EJE X
1º
FORMULACION MATRICIAL PARA EL ANÁLISIS ESTATICO
V=
Z .U. S . C . PT R
....... (1)
Parametros Sísmicos Z= U= S= R=
0.3 1.5 1.4 7.0
W1 =
672.416
W2 = W3 = W4 = W5 = W6 = W7 = W8 = PT =
657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 647.784 Ton 512.616 Ton 5119.106 Ton
Además
(Huancayo) (Hospital)
Ton
0.4
C <=
2.5
k1 =
1319
k2 = k3 = k4 = k5 = k6 = k7 = k8 =
1698 1698 1698 1698 1698 1698 2336
tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm
h1 h2 h3 h4 h5 h6 h7 h8
= = = = = = = =
Hn
≥
C/R T=
CT = T= C=
Tp = (Sistema Mixto)
0.13
hn/CT (Periodo Fundamental) 45 (sist. Mixto) 0.629 seg.
1.59
C= V=
732.59 Ton.
1.59
4.30 3.50 3.50 3.50 3.50 3.50 3.50 3.00 28.30
2º
DISTRIBUCION DE "V" EN ALTURA
Fi =
w i . hi
. V
n
∑w .h i
Fi: Fuerza sísmica en el nivel i Pi: Peso del nivel i Hi: Altura del nivel i, suma de la mitad de c/piso
i
V: Cortante basal en la base del edificio
1
V=
3º
732.590 Tn
Nivel 1 2 3 4
Pi (ton) 672.416 657.258 657.258 657.258
5 6 7 8
657.258 657.258 647.784 512.616
total
5119.106
FUERZA POR CADA PISO hi (m) Pi*hi Fi (Ton) 4.300 2891.391 147.165 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 3.500 3.500 3.000
2300.403 2300.403 2267.244 1537.848
117.085 117.085 115.397 78.273
14393.406
732.590
VECTOR DE FUERZAS SISMICAS
147.165 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 115.397 ton 78.273 ton 4º
VECTOR DE FUERZAS CORTANTES
732.590 ton 585.425 ton 468.340 ton 351.255 ton 234.170 ton 117.085 ton 115.397 ton 78.273 ton
V(Ton) 732.590 585.425 468.340 351.255 234.170 117.085 115.397 78.273
5º
d de c/piso
VECTOR DE DESPLAZAMIENTOS
∆Xi = NIVEL 1 2 3 4 5 6 7 8
Vi , Ki
Xi = Xi −1 + ∆Xi
Vi
Ki
∆Xi
Xi
(ton)
(Tn/cm)
(cm)
(cm)
0.555
0.555
0.345 0.276 0.207 0.138 0.069 0.068
0.900 1.176 1.383 1.520 1.589 1.657
0.034
1.691
732.59 585.43 468.34 351.26 234.17 117.09 115.40 78.27
1319 1698 1698 1698 1698 1698 1698 2336
Corregidos por 0.75R
=
6º
0.75
*
7*
VERIFICACION "DESPLAZAMIENTOS LATERALES"
EJE Y PISO 1 2 3 4 5 6 7 8 7º
H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 2.916 OK! 3.5 2.45 1.810 OK! 3.5 2.45 1.448 OK! 3.5 2.45 1.086 OK! 3.5 2.45 0.724 OK! 3.5 2.45 0.362 OK! 3.5 2.45 0.357 OK! 3.0 2.10 0.176 OK!
VECTOR DE MOMENTOS DE VOLTEO
{ M} = [ H ] .{ V } i
i
0.555 0.900 1.176 1.383 1.520 1.589 1.657 1.691
=
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
{M }=
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
1er piso 2do piso 3er piso 4to piso 5to piso 6to piso 7mo piso 8vo piso
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
9935.81 Tn/m 6785.67 Tn/m 4736.69 Tn/m 3097.5 Tn/m 1868.1 Tn/m 1048.51 Tn/m 638.71 Tn/m 234.82 Tn/m
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 3.50 0.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
2.916 4.725 6.173 7.259 7.982 8.344 8.701 8.877
cm cm cm cm cm cm cm cm
OK! OK! NO NO NO NO OK!
OK!
1º
FORMULACION MATRICIAL PARA EL ANÁLISIS ESTATICO
V=
Z .U. S . C . PT R
....... (1)
Parametros Sísmicos Z= U= S= R=
0.3 1.5 1.4 7.0
W1 =
672.416
W2 = W3 = W4 = W5 = W6 = W7 = W8 = PT =
657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 647.784 Ton 512.616 Ton 5119.106 Ton
Además
(Huancayo) (Hospital)
Ton
0.4
C <=
2.5
k1 =
3939
k2 = k3 = k4 = k5 = k6 = k7 = k8 =
5292 5292 5292 5292 5292 5292 6828
tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm
h1 h2 h3 h4 h5 h6 h7 h8
= = = = = = = =
Hn
≥
C/R T=
CT = T= C=
Tp = (Sistema Mixto)
0.13
hn/CT (Periodo Fundamental) 45 (sist. Mixto) 0.629 seg.
1.59
C= V=
732.59 Ton.
1.59
4.30 3.50 3.50 3.50 3.50 3.50 3.50 3.00 28.30
2º
DISTRIBUCION DE "V" EN ALTURA
Fi =
w i . hi
. V
n
∑ w .h i
Fi: Fuerza sísmica en el nivel i Pi: Peso del nivel i Hi: Altura del nivel i, suma de la mitad de c/piso
i
V: Cortante basal en la base del edificio
1
V=
3º
732.590 Tn
Nivel 1 2 3 4
Pi (ton) 672.416 657.258 657.258 657.258
5 6 7 8
657.258 657.258 647.784 512.616
total
5119.106
FUERZA POR CADA PISO hi (m) Pi*hi Fi (Ton) 4.300 2891.391 147.165 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 3.500 3.500 3.000
2300.403 2300.403 2267.244 1537.848
117.085 117.085 115.397 78.273
14393.406
732.590
VECTOR DE FUERZAS SISMICAS
147.165 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 115.397 ton 78.273 ton 4º
VECTOR DE FUERZAS CORTANTES
732.590 ton 585.425 ton 468.340 ton 351.255 ton 234.170 ton 117.085 ton 115.397 ton 78.273 ton
V(Ton) 732.590 585.425 468.340 351.255 234.170 117.085 115.397 78.273
5º
d de c/piso
VECTOR DE DESPLAZAMIENTOS
Vi Ki
∆Xi = NIVEL 1 2 3 4 5 6 7 8
Xi = Xi −1 + ∆Xi
,
Vi
Ki
∆Xi
Xi
(ton)
(Tn/cm)
(cm)
(cm)
0.186
0.186
0.111 0.088 0.066 0.044 0.022 0.022
0.297 0.385 0.451 0.496 0.518 0.540
0.011
0.551
732.59 585.43 468.34 351.26 234.17 117.09 115.40 78.27
3939 5292 5292 5292 5292 5292 5292 6828
Corregidos por 0.75R
=
6º
0.75
*
7*
VERIFICACION "DESPLAZAMIENTOS LATERALES"
EJE Y PISO 1 2 3 4 5 6 7 8 7º
H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 0.977 OK! 3.5 2.45 0.581 OK! 3.5 2.45 0.465 OK! 3.5 2.45 0.348 OK! 3.5 2.45 0.232 OK! 3.5 2.45 0.116 OK! 3.5 2.45 0.114 OK! 3.0 2.10 0.060 OK!
VECTOR DE MOMENTOS DE VOLTEO
{ M} = [ H ] .{ V } i
i
0.186 0.297 0.385 0.451 0.496 0.518 0.540 0.551
=
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
{M }=
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
1er piso 2do piso 3er piso 4to piso 5to piso 6to piso 7mo piso 8vo piso
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
9935.81 Tn/m 6785.67 Tn/m 4736.69 Tn/m 3097.5 Tn/m 1868.1 Tn/m 1048.51 Tn/m 638.71 Tn/m 234.82 Tn/m
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 0.00 3.00
0.977 1.557 2.022 2.370 2.603 2.719 2.833 2.893
cm cm cm cm cm cm cm cm
OK! OK! NO NO NO NO OK!
OK!
CALCULO DEL CENTRO DE MASA CON EL AUTOCAD CENTRO DE MASA Piso Xm Ym 1 17.00 7.00 2 17.00 7.00 3 17.00 7.00 4 17.00 7.00 5 17.00 7.00 6 17.00 7.00 7 17.00 7.00 8 17.00 7.00
CENTRO DE RIGIDEZ
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C
Y(m) 0 7 14 20 27 34 0 0 0
PRIMER PISO X(m) KL(Ton/cm) K*Y K*X 0 527.37 0 0 0 68.47 479.29 0 0 63.72 892.06 0 0 63.72 1274.37 0 0 68.47 1848.69 0 0 527.37 17930.73 0 0 2079.92 0 0 5 120.2 0 601.02 8.5 120.2 0 1021.73 13.5 1618.33 0 21847.46
17 m 5.96 m SEGUNDO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0 0 24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 5 109.85 0 8.5 109.85 0
K*X 0 0 0 0 0 0 0 549.26 933.74
D
0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1
Y(m) 0
13.5
2245.65
0 30316.29
17 m 6.01 m
TERCER PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
CUARTO PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
QUINTO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0
K*X 0
2 3 4 5 6 A B C D
7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C
Y(m) 0 7 14 20 27 34 0 0 0
0 0 0 0 0 0 5 8.5 13.5
24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 0 109.85 0 549.26 109.85 0 933.74 2245.65 0 30316.29
17 m 6.01 m
SEXTO PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
SEPTIMO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0 0 24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 5 109.85 0 8.5 109.85 0
K*X 0 0 0 0 0 0 0 549.26 933.74
D
0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
13.5
2245.65
17 m 6.01 m
OCTAVO PISO X(m) KL(Ton/cm) K*Y K*X 0 1099.73 0 0 0 34.2 239.38 0 0 34.07 477.01 0 0 34.07 681.45 0 0 34.2 923.32 0 0 1099.73 37390.86 0 0 3549.15 0 0 5 204.08 0 1020.38 8.5 204.08 0 1734.65 13.5 2871.1 0 38759.92
17 m 6.08 m
RESUMEN CENTRO DE RIGIDECES PISO 1 2 3 4 5 6 7 8
0 30316.29
X(m) 17.00 17.00 17.00 17.00 17.00 17.00 17.00 17.00
Y(m) 5.96 6.01 6.01 6.01 6.01 6.01 6.01 6.08
CALCULO DE EXCENTRICIDADES EXCENTRICIDAD DIRECTA: CENTRO MASAS PISO Xm(m) Ym(m) 1 17.00 7.00 2 17.00 7.00 3 17.00 7.00 4 17.00 7.00 5 17.00 7.00 6 17.00 7.00 7 17.00 7.00 8 17.00 7.00
CENTRO DE RIGIDECES PISO Xg(m) Yg(m) 1 17.00 5.96 2 17.00 6.01 3 17.00 6.01 4 17.00 6.01 5 17.00 6.01 6 17.00 6.01 7 17.00 6.01 8 17.00 6.08 EXCENTRICIDAD ACCIDENTAL:
EXCENTRICIDAD DIRECTA: PISO 1 2 3 4 5 6 7 8
ex 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ey 1.04 0.99 0.99 0.99 0.99 0.99 0.99 0.92
EXCENTRICIDAD REAL PISO 1 2 3 4 5 6 7 8
ex 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68
ey 2.74 2.69 2.69 2.69 2.69 2.69 2.69 2.62
DX = DY =
34 13.5
PISO 1 2 3 4 5 6 7 8
ex 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68
m m ey 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70
PORTICO 1 SEGUNDO PISO EJE "Y"
CARGA MUERTA
1218 kg
CARGA VIVA
750 kg
CARGA ULTIMA
CUANTIA MINIMA
3177 kg/m
f´c
fy
0.0024 As min
210 b
4200 d
3.913
30
54
B W
Mu(ton-m) 0.0250
CUANTIA As(-)
4.07412
ø
W 0.9
Mu(ton-m) 0.0529
0.0013
CUANTIA
2.029 cm2
As(-)
W
Mu(ton-m) 0.0223
CUANTIA As
3.63990
ø 0.9 0.0011 1.810 cm2
8.46231
Y"
CARGA MUERTA
1218 kg
CARGA VIVA
750 kg
CARGA ULTIMA
CUANTIA MINIMA
3177 kg/m
f´c
fy
0.0024 As min
210 b
d
3.913
C
4200
30
54
C
ø
W 0.9 0.0026 CUANTIA 4.282 As(-)
Mu(ton-m) 0.0655
10.40632
ø
W 0.9
0.0401
0.0033
CUANTIA
5.306 cm2
As(-)
W
Mu(ton-m) 0.0363
CUANTIA As
5.8627
ø 0.9 0.0018 2.938 cm2
D Mu(ton-m) 6.4613
ø 0.9 0.0020 3.245 cm2
JUNTA SISMICA ALTURA HOSPITAL = 28.30 m ALTURA EDIFICIO VECINO 30.00 = m S> Fórmula:
3.00 cm
S = 3 + 0.004 ( h - 500 ) S= h= S=
junta de separación sísmica altura del edificio en cm. 13 cm
Cada uno de los edificios se retirará de los límites de propiedad adyacentes distancias no menores que 2/3 del desplazamiento máximo calculado ni menores que S/2 Retiro Hospital = Retiro Hospital = Retiro Hospital = Retiro Edif. vecino =
5.92 cm 6.5 cm 6.5 cm 6.5 cm
URRUCHI SANCHEZ DIEGO E.
DATOS GENERALES: Especificaciones f’c = 210 kg/cm2 fy = 4200 kg/cm2 UBICACIÓN : HUANCAYO USO : HOSPITAL TIPO DE SUELO :TIPO 3
FACTOR Z = FACTOR U = FACTOR S = Tp = FACTOR R =
TIPO DE ESTR. : MIXTO
L1 L2 Lint X Lint Y
= = = =
f´c = S/C (hospital) = S/C azotea = Acabados = Tabiqueria = Concreto =
7 5 6 3.5 210 400 100 100 210 2400
m m m m
C1
Kg/cm2 Kg/m2 Kg/m2 Kg/m2 Kg/m2 kg/m3
ALTURAS DE ENTREPISO Nº de pisos H1 = H2 = H3 = H4 = H5 = H6 = H7 = H8 =
8 4.3 3.5 3.5 3.5 3.5 3.5 3.5 3.0
0.3 1.5 1.4 0.9 7
m m m m m m m m
LOSA ALIGERADA:
C6
C3
C4
C5
C3
C4
C5
C1
PREDIMENSIONAMIENTO 1.-
C2
C2
C6
L1/L2=
1.40
TIPO DE LOSA: ALIGERADA ESPESOR DE LA LOSA: ALIGERADA e losa = 0.28 m e asumido= 0.30 m S/C losa = 400 Kg/m2 2.-
VIGAS:
2.1 VIGAS V-1 h viga = b viga = h(m) = b(m) =
12 vigas 0.5 m 0.25 m 0.5 m 0.25 m
2.2 VIGAS V-2 h viga = b viga = h(m) = b(m) =
6 vigas 0.35 m 0.18 m 0.35 m 0.2 m
2.3 VIGAS V-3 h viga = b viga = h(m) = b(m) =
16 vigas 0.7 m 0.35 m 0.7 m 0.35 m
2.4 VIGAS V-4 h viga = b viga = h(m) = b(m) =
4 vigas 0.6 m 0.3 m 0.6 m 0.3 m
3.-
C1
C2
V-3
C6
V-3
V-1
V-1
C3
V-1
C4
C5
V-3
V-3
V-2
V-
V-2 V-3
C3
V-
V-2 V-3
C4
V-1
V-1
V-1 V-3 C1
V-
C5
V-3
VC6
C2
COLUMNAS AREA TRIBUTARIA COLUMNA C-1 C-2 C-3 C-4 C-5 C-6 Total Techado
AREA 8.750 17.500 14.875 29.750 27.625 16.250 459.00
C 1 m2 m2 m2 m2 m2 m2 m2
C 2
C
METRADO Peso S/C Peso Acabados Peso Tabiqueria Peso Aligerado (30cm)
Tipo de Columna C-1 C-2, C-3, C-6 C-4 , C-5
3.1 COLUMNA C-1 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
400 100 210 420
Kg/m2 Kg/m2 Kg/m2 Kg/m2
P
C 3
C 4
C 5
n 1.50 1.25 1.10
0.20 0.25 0.30
4 columnas 2808.0 Kg 1102.5 Kg 875.0 Kg 1837.5 Kg 3500.0 Kg
3.4 COLUMNA C-4 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 10123 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3.2 COLUMNA C-2 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
2892.29 cm2 3000 m 0.6 m 0.5 m 4 columnas 4866.0 Kg 2205.0 Kg 1750.0 Kg 3675.0 Kg 7000.0 Kg
3.5 COLUMNA C-5 Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 19496.0 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3.3 COLUMNA C-3
3713.52 cm2 4200 m 0.7 m 0.6 m 4 columnas
3.6 COLUMNA C-6
3402.0 Kg 1874.3 Kg 1487.5 Kg 3123.8 Kg 5950.0 Kg
Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
4.-
Peso viga Peso losa Peso acabados Peso tabiquería Peso S/C
PESO TOTAL = CARGA MUERTA + CARGA VIVA 15837.5 Kg PESO TOTAL =
PESO TOTAL = CARGA MUERTA + PESO TOTAL =
Area req = Area real = Dimension =
Area req = Area real = Dimension =
3016.67 cm2 3500 m 0.5 m 0.7 m
PLACAS: e=
0.25
m
VERIFICACION DE LA CONFIGURACION EN PLANTA 1.* 2.* * * *
IRREGULARIDAD EN PLANTA: No existe discontinuidades en planta mayores al 50%. IRREGULARIDAD EN ALTURA: No existe una irregularidad de rigidecez considerables . No existe una irregularidad en masa ,pues entres pisos adyacentes no existe una diferencia del 50% en peso. No existe irregularidad vertical ,pues todos los porticos tienen las mismas dimensiones No existe disontinuidad de elementos verticales. CONCLUSION:
C4
V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 )
C5
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C5
C4 V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 ) V-2 (0.35x0.20)
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0 .7 0x 0 .3 5)
C3
C5 V -3 (0.7 0x0 .3 5)
V -3 (0
C5
V -3 (0 . V-2 (0.35x0.20)
C4 V -3 (0 .7 0x 0 .3 5)
C2 V -3 (0.7 0 x0 .3 5)
V-2 (0.35x0.20)
C3
V-1 (0.50x0.25)
V-1 (0.50x0.25)
No presenta discontinuidades significativas tanto en planta como en elevacion C2 C6 C6 por loVque considera ESTRUCTURA V -4 (0.60x 0.30 ) -3 (0 .7 0xse 0 .3 5) V -3 (0 .70 x 0.3 5REGULAR )
V-1 (0.50x0.25)
*
C1
V -3 (0.7 0x0 .3 5)
C4
V -3 (0 .
V -3 (0 .7 0x 0 .3 5)
C1
C5
V-2 (0.35x0.20)
C4
V -3 (0.7 0x0 .3 5)
V -4 (0.60x 0.30 )
C6
V -3 (0.7 0x0 .3 5)
V-1 (0.50x0.25)
V-1 (0.50x0.25)
V -3 (0.7 0x0 .3 5)
C2
V-2 (0.35x0.20)
V -4 (0.60x 0.30 )
C5
C6
V -3 (0 .
V-1 (0.50x0.25)
V -3 (0.7 0x0 .3 5)
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C4
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0 .7 0x 0 .3 5)
C3
V -3 (0 .
C2
C6
C6
C2
C1
C5
C5
C4
C3
C5
C5
C4
C3
C6
C6
C2
C1
C6
V-3
C6
V-4 V-1
C5
V-4 V-2 V-4 V-1
V-3
V-4
C 6
V-3
V-3
C4
V-2 V-3
V-1 V-3
C6
C3
V-2
V-1
C6
C 2
C5
V-1
C4
V-3
V-2 C5
V-3 V-1
C5
V-3
C1
V-3
V-1
V-3
C2
C3
V-1 V-3
C2
C1
C 4
C 5
4 columnas 5160.0 Kg 3748.5 Kg 2975.0 Kg 6247.5 Kg 11900.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
30031.0 Kg 4194.81 cm2 4200 m 0.7 m 0.6 m 4 columnas 4398.0 Kg 3480.8 Kg 2762.5 Kg 5801.3 Kg 11050.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
27492.5 Kg 3840.22 cm2 4200 m 0.7 m 0.6 m 4 columnas
4104.0 Kg 2047.5 Kg 1625.0 Kg 3412.5 Kg 6500.0 Kg
TOTAL = CARGA MUERTA + CARGA VIVA
17689.0 Kg 3369.33 cm2 3500 m 0.7 m 0.5 m
iferencia del
C2
V-1 (0.50x0.25)
V-1 (0.50x0.25)
C3
C4 V -3 (0.70 x0 .35) V-2 (0.35x0.20)
V-2 (0.35x0.20)
7 0x 0 .35)
7 0x 0 .35)
C1 V -3 (0.70 x0.3 5)
7 0x0 .35)
C4
V -3 (0.70 x0 .35)
C3
V-2 (0.35x0.20)
V-2 (0.35x0.20)
V -3 (0.70 x0 .35)
V-1 (0.50x0.25)
C4
C3 V-1 (0.50x0.25)
7 0x 0 .35)
V -3 (0.70 x0 .35)
7 0x 0 .35)
C2
C1
METRADO DE CARGAS POR PISO DATOS: P.E. Concreto = S/C (hospital) = S/C azotea =
2400 kg/m3 400 kg/m2 100 kg/m2
Acabados = Tabiqueria = P. aligerado = espesor alig =
100 kg/m2 210 kg/m2 420 kg/m2 0.30 m
H1 H2 H3 H4 H5 H6 H7 H8
= = =
4.30 m L(V-1) = 3.50 m L(V-2) = 3.50 m L(V-3) =
5.0 m 3.5 m 7.0 m
= = = = =
3.50 m L(V-4) = 3.50 m 3.50 m 3.50 m 3.00 m
6.0 m
METRADO 1ER PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1 V-2 V-3 V-4
= = = = = = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x x x x x
0.25 0.25 0.25
x x x
400 x
0.50 0.60 0.70 0.60 0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x x x x x
x
3.90 3.90 3.90 3.90 3.90 3.90 5.0 3.5 7.0 6.0 34.0 34.0 34.0 3.90 3.90 3.90
x x x x x x x x x x
x x x
4 4 4 4 4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = = = = = =
= =
METRADO 2DO PISO - 6TO PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1
= = = = = = =
2400 2400 2400 2400 2400 2400 2400
x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5
x x x x x x x
0.50 0.60 0.70 0.60 0.60 0.50 0.25
x x x x x x x
3.50 3.50 3.50 3.50 3.50 3.50 5.0
x x x x x x x
4 4 4 4 4 4 12
= = = = = = =
V-2 = V-3 = V-4 = Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x
0.35 0.7 0.6
x x x
0.25 0.25 0.25
x x x
400 x
0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x
x
3.5 7.0 6.0 34.0 34.0 34.0 3.50 3.50 3.50
x x x
x x x
6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = =
= =
METRADO 7MO PISO PCM Peso columnas
Peso vigas
C-1 C-2 C-3 C-4 C-5 C-6 V-1 V-2 V-3 V-4
= = = = = = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x x x x x
0.60 0.70 0.50 0.70 0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x x x x x
0.25 0.25 0.25
x x x
400 x
0.50 0.60 0.70 0.60 0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x x x x x
x
3.25 3.25 3.25 3.25 3.25 3.25 5.0 3.5 7.0 6.0 34.0 34.0 34.0 3.25 3.25 3.25
x x x x x x x x x x
x x x
4 4 4 4 4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = = = = = =
= =
METRADO 8VO PISO (AZOTEA) PCM Peso columnas
C-1 C-2 C-3 C-4
= = = =
2400 2400 2400 2400
x x x x
0.60 0.70 0.50 0.70
x x x x
0.50 0.60 0.70 0.60
x x x x
1.50 1.50 1.50 1.50
x x x x
4 4 4 4
= = = =
Peso vigas
C-5 C-6 V-1 V-2 V-3 V-4
= = = = = =
Peso losa aligerado Peso acabado Tabiquería móvil Placas Pl(V-2) Pl(V-3) Pl(V-4)
PCV S/C Hospital
2400 2400 2400 2400 2400 2400 420 100 210 2400 2400 2400
x x x x x x x x x x x x
100 x
0.70 0.70 0.5 0.35 0.7 0.6
x x x x x x
0.25 0.25 0.25
x x x
0.60 0.50 0.25 0.2 0.35 0.3 13.5 13.5 13.5 3.5 7.0 6.0
13.5
x x x x x x x x x x x x
x
1.50 1.50 5.0 3.5 7.0 6.0 34.0 34.0 34.0 1.50 1.50 1.50
x x x x x x
x x x
4 4 12 6 16 4
2 2 1 PD
34.0 PL
= = = = = = = = = = = = =
= =
MASA TOTAL DEL
α= PCM 1º 2º 3º 4º 5º
11.23 Ton. 15.72 Ton. 13.1 Ton. 15.72 Ton. 15.72 Ton. 13.1 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 16.38 Ton. 32.76 Ton. 14.04 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
10.08 Ton. 14.11 Ton. 11.76 Ton. 14.11 Ton. 14.11 Ton. 11.76 Ton. 18 Ton.
6º 7º 8º TOTAL
580.6164 565.4580 565.4580 565.4580 565.4580 565.4580 555.9840 489.6660 ###
3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 14.7 Ton. 29.4 Ton. 12.6 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
9.36 Ton. 13.1 Ton. 10.92 Ton. 13.1 Ton. 13.1 Ton. 10.92 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 13.65 Ton. 27.3 Ton. 11.7 Ton. ### Ton.
183.6 Ton. 183.60 Ton.
4.32 Ton. 6.05 Ton. 5.04 Ton. 6.05 Ton.
6.05 Ton. 5.04 Ton. 18 Ton. 3.53 Ton. 65.86 Ton. 10.37 Ton. 192.78 Ton. 45.9 Ton. 96.39 Ton. 6.3 Ton. 12.6 Ton. 5.4 Ton. ### Ton.
45.9 Ton. 45.9 Ton.
MASA TOTAL DEL EDIFICIO - PISO X PISO
0.5 PCV
g= Pi
183.60 672.416 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 657.258 Ton. 183.60 647.784 Ton. 45.90 512.616 Ton. 1331.10 5119.106 Ton.
9.81 m/seg2 Mi
### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2 ### ton-m/seg2
A
B
C
D
1
2
3
4
5
6
C1
C2
C6
C6
C2
C1
C3
C4
C5
C3
C4
C5
C1
f'c = E =
C2
C5
RIGIDEZC6LATERALC6
C4
C3
C4
C3
C2
C1
210 kg/cm2 ### kg/cm2
Fórmulas:
DIMENSIONES DE COLUMNAS h(cm) b(cm)
C-1 C-2 C-3 C-4 C-5 C-6
60 70 50 70 70 70
50 60 70 60 60 50
Area (cm2)
3000 4200 3500 4200 4200 3500
Inercia (cm4)
900000 1715000 ### 1715000 1715000 ###
alt. Piso1 (cm)
430 430 430 430 430 430
alt. Piso2-7 alt piso8 Krelat. Piso1 Krelat. Piso2-7 (cm) (cm)
350 350 350 350 350 350
300 2093.023 300 3988.372 300 1695.736 300 3988.372 300 3988.372 300 3323.643
DIMENSIONES DE VIGAS h(cm) b(cm)
V-1 V-2 V-3 V-4
50 35 70 60
Area (cm2) Inercia (cm4)Long. (cm) Krelat.
25 20 35 30
1250 260416.67 700 71458.33 2450 ### 1800 540000
500 520.83 350 204.17 700 1429.17 600 900
2571.429 4900.000 2083.333 4900.000 4900.000 4083.333
Fórmulas de Muto:
6 C1
C3
C3
PÓRTICO 1 y 6 COLUMNA Kraya 0.25 C1 0.43 C3 0.43 C3 0.25 C1
C1
PORT. 1 PORT. 6 Krelat. Piso8
3000.000 5716.667 2430.556 5716.667 5716.667 4763.889
Kempot Piso1 Kempot Piso2-7 Kempot Piso8 (ton/cm)
29.527 56.265 23.922 56.265 56.265 46.888
(ton/cm)
54.755 104.338 44.361 104.338 104.338 86.948
(ton/cm)
86.948 165.685 70.444 165.685 165.685 138.071
PÓRTICO 2 y 5 COLUMNA Kraya 0.13 C2 0.18 C4 0.18 C4 C2
0.13 PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.16 C6 0.18 C5 0.18 C5 0.16 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.68 C1 0.72 C2 0.7 C6 0.7 C6 0.72 C2 0.68 C1
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.84 C3 0.72 C4 0.58 C5 0.58 C5 0.72 C4 0.84 C3
PORT. B PORT. C PISOS 2 - 7 PÓRTICO 1 y 6 COLUMNA Kraya 0.2 C1 0.35 C3 0.35 C3 0.2 C1
PORT. 1 PORT. 6
PÓRTICO 2 y 5 COLUMNA Kraya 0.11 C2 0.15 C4 0.15 C4 0.11 C2
PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.13 C6 0.15 C5 0.15 C5 0.13 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.56 C1 0.58 C2 0.57 C6 0.57 C6 0.58 C2 0.56 C1
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.69 C3 0.58 C4 0.48 C5 0.48 C5
C4 C3
0.58 0.69 PORT. B PORT. C
PÓRTICO 1 y 6 COLUMNA Kraya 0.17 C1 0.3 C3 0.3 C3 0.17 C1
PORT. 1 PORT. 6
PÓRTICO 2 y 5 COLUMNA Kraya 0.09 C2 0.13 C4 0.13 C4 0.09 C2
PORT. 2 PORT. 5
PÓRTICO 3 y 4 COLUMNA Kraya 0.11 C6 0.13 C5 0.13 C5 0.11 C6
PORT. 3 PORT. 4
PÓRTICO A y D COLUMNA Kraya 0.48 C1 0.5 C2 0.49 C6
C6 C2 C1
0.49 0.5 0.48
PORT. A PORT. D
PÓRTICO B y C COLUMNA Kraya 0.84 C3 0.72 C4 0.58 C5 0.58 C5 0.72 C4 0.84 C3
PORT. B PORT. C
PISO 1
a
KL (ton/cm)
0.33 0.38 0.38 0.33
KL = KL =
527.37 ton/cm 527.37 ton/cm
a
KL (ton/cm)
0.3 0.31 0.31 0.3 KL = KL =
16.65 ### 17.58 16.65 68.47 ton/cm 68.47 ton/cm
a
KL (ton/cm)
0.3 0.31 0.31 0.3 KL = KL =
9.83 9.14 9.14 9.83
14.28 ### 17.58 14.28 63.72 ton/cm 63.72 ton/cm
PLACA
E t h L KL =
### ton/cm2 25 cm 430 cm 350 cm 489.43 ton/cm
a
KL (ton/cm)
0.44 0.45 0.44 0.44 0.45 0.44
13.02 ### 20.85 20.85 25.2 13.02
PLACA PORT. A
E t h L KL =
### ton/cm2 25 cm 430 cm 700 cm 1961.79 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
### ton/cm2 25 cm 430 cm 600 cm 1500.2 ton/cm
2079.92 ton/cm 1618.33 ton/cm
a
KL (ton/cm)
0.47 0.45 0.42 0.42 0.45 0.47
11.3 ### 23.6 23.6 25.2 11.3
KL = KL =
120.2 ton/cm 120.2 ton/cm
PISOS 2 - 7
a
KL (ton/cm)
0.09 0.15 0.15 0.09
KL = KL =
5.04 6.57 6.57 5.04
799.54 ton/cm 799.54 ton/cm
PLACA
E t h L KL =
### ton/cm2 25 cm 350 cm 350 cm 776.32 ton/cm
a
KL (ton/cm)
0.05 0.07 0.07 0.05 KL = KL =
5.27 ### 7.19 5.27 24.91 ton/cm 24.91 ton/cm
a
KL (ton/cm)
0.06 0.07 0.07 0.06 KL = KL =
5.21 ### 7.19 5.21 24.8 ton/cm 24.8 ton/cm
a
KL (ton/cm)
0.22 0.23 0.22 0.22 0.23 0.22
11.91 ### 19.29 19.29 23.56 11.91
PLACA PORT. A
E t h L KL =
### ton/cm2 25 cm 350 cm 700 cm 2717.13 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
2826.66 ton/cm 2245.65 ton/cm
a
KL (ton/cm)
0.26 0.23 0.19 0.19
11.33 ### 20.04 20.04
### ton/cm2 25 cm 350 cm 600 cm 2136.13 ton/cm
0.23 0.26 KL = KL =
23.56 11.33 109.85 ton/cm 109.85 ton/cm
PISO 8
a
KL (ton/cm)
0.08 0.13 0.13 0.08
KL = KL =
6.94 9.14 9.14 6.94
PLACA
E t h L KL =
### ton/cm2 25 cm 300 cm 350 cm 1067.56 ton/cm
1099.73 ton/cm 1099.73 ton/cm
a
KL (ton/cm)
0.04 0.06 0.06 0.04 KL = KL =
7.22 ### 9.88 7.22 34.2 ton/cm 34.2 ton/cm
a
KL (ton/cm)
0.05 0.06 0.06 0.05 KL = KL =
7.16 ### 9.88 7.16 34.07 ton/cm 34.07 ton/cm
a
KL (ton/cm)
0.19 0.2 0.2
16.73 ### 27.12
PLACA PORT. A
E t h
### ton/cm2 25 cm 300 cm
0.2 0.2 0.19
27.12 33.14 16.73
L KL =
700 cm 3395.18 ton/cm
PLACA PORT. D
E t h L KL = KL = KL =
3549.15 ton/cm 2871.1 ton/cm
a
KL (ton/cm)
0.3 0.26 0.23 0.23 0.26 0.3 KL = KL =
20.88 ### 37.45 37.45 43.71 20.88 204.08 ton/cm 204.08 ton/cm
### ton/cm2 25 cm 300 cm 600 cm 2717.13 ton/cm
CUADRO DE RESUMEN DE RIGIDEZ LATERAL RIGIDEZ LATERAL EJE Y
PISO 1
PISO 2
PISO 3
PISO 4
PISO 5
PISO 6
PISO 7
PORTICO KL(Ton/cm) 1 527.37 2 68.47 3 63.72 4 63.72 5 68.47 6 527.37 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8 4 24.8 5 24.91 6 799.54 1 799.54 2 24.91 3 24.8
RIGIDEZ LATERAL EJE X
PISO 1
PISO 2
PISO 3
PISO 4
PISO 5
PISO 6
PISO 7
PISO 8
PORTICO KL(Ton/cm) A 2079.92 B 120.2 C 120.2 D 1618.33 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 2826.66 B 109.85 C 109.85 D 2245.65 A 3549.15 B 204.08 C 204.08 D 2871.1
RIGIDEZ LATERAL POR
PISO PISO PISO PISO PISO PISO PISO PISO
1 2 3 4 5 6 7 8
PISO 7
PISO 8
4 5 6 1 2 3 4 5 6
24.8 24.91 799.54 1099.73 34.2 34.07 34.07 34.2 1099.73
RIGIDEZ LATERAL POR PISO EJE Y EJE X (ton/cm) (ton/cm) 1319.126 3938.656 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 1698.497 5292.013 2336.001 6828.408
PERIODOS Y FORMAS DE MODO DE VIBRACION - STODOLA
m 8
MASAS POR PISO Pi
m 7
m 6
8 1ºk 2º 3º 4º 5ºk 7 6º 7º 8º TOTAL
672.416 657.258 657.258 657.258 657.258 657.258 647.784 512.616 5119.106
Mi
0.685440 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.669988 ton-cm/seg2 0.660330 ton-cm/seg2 0.522544 ton-cm/seg2 5.218253 ton-cm/seg2
k 6 m 5 RIGIDECES POR PISO EJE Y EJE X k 5 (ton/cm) (ton/cm)
m 4
m 3
m 2
m 1
PISO 1 PISO 2 PISO 3 k 4 PISO 4 PISO 5 PISO 6 PISO 7 PISO 8 k 3
1319.126 1698.497 1698.497 1698.497 1698.497 1698.497 1698.497 2336.001
3938.656 5292.013 5292.013 5292.013 5292.013 5292.013 5292.013 6828.408
RIGIDECES POR PISO PISO KL (ton/cm) 1 5257.780 k 2 2 6990.510 3 6990.510 4 6990.510 5 6990.510 1 6990.510 6k 7 6990.510 8 9164.410
m8 = m =
0.523
k8 = k =
9164.410
m8 m7 m6 m5 m4 m3 m2 m1
= = = = = = = =
1m 1.26 m 1.28 m 1.28 m 1.28 m 1.28 m 1.28 m 1.31 m
k8 k7 k6 k5 k4 k3 k2 k1
1k 0.76 k 0.76 k 0.76 k 0.76 k 0.76 k 0.76 k 0.57 k
k (ton/cm)
0.57
m (ton*seg2/cm) {X} {FI} {V} {ΔX} {XC} {X} {FI} {V} {ΔX}
1.31 1 1.31 43.8
{X} {FI} {V}
28.92
{XC} {X} {FI} {V} {ΔX} {XC} {X}
28.92
33.45 120.37 2.38 3.05
0
22.36 33.31 119.91 2.38 3.05
25.4 36.18 86.56 1.72 2.2
27.6 50.38 50.38 1
22.47
25.42 36.2 86.6 1.72 2.2
27.61 50.38 50.38 1 1.31
{ΔX}
34.68 124.52 2.38 3.06
36.34 86.92 1.72 2.2
0
23.37
25.52
27.62 50.4 50.4 1 1.31
{XC}
26.46
27.73
28.93
36.08 52.33 184.32 2.42 3.1
37.59 89.84 1.72 2.2
50.59 50.59 1 1.31
{ΔX}
39.92
28.68
29.04
0.76
1.28 3 3.85
55.69 131.99 1.73 2.22
52.25 52.25 1 1.31
{FI} {V}
42.49
29.99
{X}
0.76
1.28 2 2.56
76.31 76.31 1 1.31
{XC} {X} {FI} {V} {ΔX} {XC}
0.76
22.35 33.29 119.85 2.38 3.05
25.4 36.18 86.56 1.72
{ф1 } =
0
22.35 33.29 119.85 2.38
1 1.72 2.38 2.96 3.44
3.81 4.05 4.13
PERIODOS Y FORMAS DE MODO CRITERIO PARA ASUMIR "Wi"
w2 = w2 =
m (ton*seg2/cm)
k (ton/cm)
93.29 rad/seg 93.29 rad/seg
0.685
0.670
5257.780
{ΔX} {V}
### 1 63.95 1
{X} {FI}
F1 F2 F3 F4 F5 F6
5257.78
0.670
### 1.74 108.94 0.74
5193.83
1 3 5 7 9 11
6990.510 2.47 154.41 0.73
5084.89
4930.48
POLINOMIO CARACTERISTICO
M=
0.685440 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 0.669988 0 0 0 0.669988 0 0 0 0 0 0 0 0 0
K=
MATRIZ EJE Y 3017.624 ### 0 -1698.497 3396.995 ### 0 ### 3396.995 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 ### 4034.499 ### 0 ### 2336.001
0.76
1.28 4 5.13
0.76
1.28 5 6.41 30.95
47.28 231.6 3.04 3.89
24.54
19.47
29.44 149.82 2.96 3.8
0 18.56
29.3 149.15 2.96 3.8 29.29 149.14 2.96
0
24.32 173.47 3.44 4.41 24.32 173.46 3.44
DETERMINANDO EL PERIODO T1
12.21 205.12 4.05 5.13
0
18.54 192.01 3.81 4.89
0
4.14 208.38 4.13 4.13
4.13 12.13 204.14 4.05 5.12
9.26 18.53 192 3.81
4.16 209.29 4.14 4.14 4.14
12.14 204.24 4.05 5.12
9.26
14.14
4.38 217.41 4.16 4.16 4.16
9.26
14.14
18.56
12.83 213.03 4.08 5.15
18.65 192.92 3.81 4.89 18.55 192.1 3.81 4.89
8 334.41 4.38 4.38 4.38
9.31
14.15 24.34 173.55 3.44 4.41
8 8
22.08 326.41 4.28 5.41
19.53 200.2 3.83 4.91
24.45 174.27 3.44 4.42
1
8
9.79
14.23
18.57
1.26 7 8.85
32.16 304.33 3.99 5.11
25.52 180.67 3.46 4.43
1
16.85
14.9
18.66
29.31 149.22 2.96 3.8
1.28 6 7.69
40.56 272.17 3.57 4.57
30.62 155.15 2.97 3.81
0.76
4.13 208.27 4.13 4.13 4.13
12.13 204.13 4.05
4.13 208.26 4.13
∑ XNC
∑ XC
23.5
w₁ = T₁ =
1183.76
18.66 rad/seg 0.34 seg
RMAS DE MODO DE VIBRACION - HOLTZER
W1 W2 W3 W4 W5 W6
0.669988
18.66 55.98 93.29 130.61 167.93 205.24
###
### 3.18 198.5 0.71
### 3.85 240.81 0.68
4731.98
0 0 0 0 0 0 0.660330 0 0
0.669988
0 0 0 0 0 0 0 ### 0
###
6990.510 4.5 280.96 0.64
4491.18
0.522544
9164.410 5.1 314.02 0.6
4210.21
5.52 269.22 0.43 3896.2
K=
MATRIZ EJE X ### ### ### ### 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 ### ### ###
mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k mw₁² mw₁² mw₁²/k mw₁²/k mw₁²/k
F-V=
-3626.98
0 0 0 0 0 0 ### 6828.408
ESPECTRO DE RESPUESTA DE ACELERACIONES HYO PROYECTO
: TRABAJO ESCALONADO DE INGENIERIA ANTISISMICA
FECHA
: AGOSTO 2011
PARAMETROS DE Z SITIO 1 - 2 - 3 ZONA =
2
Z=
0.30
CONDICIONES GEOTECNICAS S S1-S2-S3 TIPO =
S3
S=
1.40
CATEGORIA DE U LA EDIFICACION A-B-C USO =
A
Tp = U=
0.90 1.50
SISTEMA ESTRUCTURAL Rd 9.5-8.7-6-4 R=
7.000
800.00 700.00
Sa (cm/seg2)
600.00 500.00 400.00 300.00 200.00 100.00 0.00
T ESPECTRO DE RESPUESTAS DE ACELERACIONES (NORMA E-030, 2003 RNE) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1
PERIODO (seg)
1
1
2
C
2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.2500 2.0455 1.8750 1.7308 1.6071 1.5000
Sa
220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 220.7250 198.6525 180.5932 165.5438 152.8096 141.8946 132.4350
2.
PERIODOS Y FORMAS DE VIBRACION
De la ecuación dinámica
MODOS EN EL EJE Y 1 2 3 4 5 6 7 ω² = 85.389 759.626 2053.584 3833.553 5867.623 7839.594 9399.354 ω= 9.241 27.561 45.316 61.916 76.600 88.541 96.950 T= 0.68 0.23 0.14 0.1 0.08 0.07 0.06 1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.7422
-1.5084
0.2296
-1.8621
-2.0165
-1.4733 1671.8636
2.4257 3.0275
-3.5649 -4.2946
-0.8880 -0.6628
-0.4143 1.3256
2.4435 -2.1562
2.1527 -1.5973
3.5273
-4.2609
0.5647
-1.4383
1.2385
3.9083 4.1577 4.2387
-4.0389 -0.5452 3.3902
0.9382 -0.1070 -0.7510
1.9950 -0.7411 -1.1855
0.0412 -1.3089 1.1872
-0.0013 -0.3311
0.0009 -548.2067 0.0047 0.0340 0.0000
0.0004 -0.8963 ###
MODOS EN EL EJE X 1 2 3 4 5 6 7 ω² = 262.599 2336.391 6318.730 11802.979 18078.109 24170.954 29015.554 ω= 16.2 48.34 79.49 108.64 134.45 155.47 170.34 T=
0.39
0.13
0.08
0.06
0.05
0.04
0.04
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.7103
-1.5754
0.2155
-1.7156
-2.0139
2.3636
-3.6848
-0.8910
-0.5046
2.3703
2.9385 3.4156 3.7791 4.0171
-4.4871 -4.4543 -4.1239 -0.4946
-0.6661 0.5542 0.9463 -0.0756
1.3161 -1.3433 1.8624 -0.6311
-1.9526 0.8974 0.4508 -1.6519
4.0994
3.5304
-0.7813
-1.1933
1.3535
-1.2874 1671.8636 1.6230
-0.0013
-1.1267 -0.3311 0.0007 -548.2067 0.0039 0.0004 0.0283 -0.8963 0.0000
###
GRAFICOS DE MODOS EJE Y
EJE X
MODO 1
MODO 1
MODO 1
MODO 1
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0.0000
2.0000
4.0000
6.0000
0.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
4.0000
6.0000
MODO 2
MODO 2
-5.0000
2.0000
-5.0000
MODO 3
0.0000
5.0000
MODO 3
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
6
6
5
5
4
4
3
3
2
2
1
1
-1.0000 0.0000 1.0000 2.0000
-1.0000 0.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
-2.0000 0.0000
MODO 5 9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
5.0000
-5.0000
MODO 6 9
2.0000
4.0000
MODO 5
9
-5.0000
2.0000
MODO 4
MODO 4
-5.0000
1.0000
0.0000
5.0000
MODO 6 9
MODO 6
MODO 6
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-2.0000 0.0000 2.0000 4.0000
-2.0000
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 0.0000
2000.0000
2.0000
MODO 7
MODO 7
-2000.0000
0.0000
-2000.0000
0.0000
2000.0000
MODO 8
MODO 8 9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
4
4
3
3
2
2
1
1
-1.0000 0.0000 1.0000 2.0000
-1.0000 0.0000
1.0000
2.0000
3º
CALCULO DE LOS FACTORES DE PARTICIPACION MODAL (FPM)
EJE Y 8
1ER MODO 1.0000 1.7422 2.4257
10495.166 102.446 0.06
{ф1 } =
3.0275
1.0000
3.5273
-0.0008
3.9083
-0.0006 -0.3289
4.1577 4.2387
{ф1 }T =
1.0000
1.7422
2.4257
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
1.17
1.63
0.0003 0.0002 -0.8943 0.0007
8
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
[M] =
31890.874
MODO 1
178.58 0.04
[M] *{ф1 }T =
0.69
1.0000
[M] *{ф1 }T *{ф1 }=
52.17
{ф1 }T *{m}=
15.45
-0.0008 -0.0006 -0.3289 0.0003 0.0002 -0.8943
1.0000
0.0007
-1.5084
FPM1 =
2DO MODO
-3.5649 1
{ф } =
-4.2946 -4.2609
{ф1 }T =
1.0000 -1.5084 -3.5649
-4.0389 -0.5452 3.3902
0.68544
0.685440
0
0
MODO 1
0000
0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0 0 0 0 0 0 0
### 0 0 0 0 0 0
0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.01
-2.39
[M] *{ф1 }T *{ф1 }=
52.38
{ф1 }T *{m}=
-9.74
[M] =
6.0000
FPM2 =
3ER MODO 1.0000
MODO 2
0.2296 -0.8880
{ф1 } =
-0.6628 0.5647 0.9382
{ф1 }T =
1.0000
0.2296 -0.8880
-0.1070 -0.7510
5.0000
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
MODO 3
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
0.15
-0.59
[M] *{ф1 }T *{ф1 }=
2.65
{ф1 }T *{m}=
0.34
[M] =
4TO MODO 1.0000
FPM3 =
0000
-1.8621 -0.4143
{ф1 } =
2.0000
MODO 4
0000
1.3256 -1.4383 1.9950 -0.7411 -1.1855
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.25
-0.28
[M] *{ф1 }T *{ф1 }=
9.45
{ф1 }T *{m}=
-0.69
[M] =
4.0000
1.0000 -2.0165 2.4435
{ф1 } =
MODO 6
FPM4 =
5TO MODO
MODO 5
5.0000
1.0000 -1.8621 -0.4143
-2.1562 1.2385 0.0412 -1.3089 1.1872
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
[M] =
[M] *{ф1 }T =
1.0000 -2.0165
2.4435
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
0.69
-1.35
1.64
MODO 6 [M] *{ф1 }T *{ф1 }=
13.42
{ф1 }T *{m}=
0.14
FPM5 =
6TO MODO 1.0000 -1.4733 2.1527
{ф1 } =
2.0000
MODO 7
-1.5973 0.0009 0.0047 0.0340 0.0000
{ф1 }T =
1.0000 -1.4733
2.1527
0.68544
0.685440
0
0
0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0 0 0 0 0 0 0
### 0 0 0 0 0 0
0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-0.99
1.44
[M] *{ф1 }T *{ф1 }=
6.95
{ф1 }T *{m}=
0.1
[M] =
2000.0000
FPM6 = FPM1 FPM2 FPM3 FPM4 FPM5 FPM6 FPMtotal
MODO 8
EJE X 1ER MODO 1.0000 1.7103 2.3636
29.609 18.597 12.989 7.274 1.046 1.390 70.904
0000
{ф1 } = 2.0000
2.9385 3.4156 3.7791 4.0171 4.0994
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000
1.7103
2.3636
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
1.15
1.58
[M] *{ф1 }T *{ф1 }=
49
{ф1 }T *{m}=
15
[M] =
FPM1 =
2DO MODO 1.0000 -1.5754 -3.6848
{ф1 } =
-4.4871 -4.4543 -4.1239 -0.4946 3.5304
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000 -1.5754 -3.6848
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.06
-2.47
[M] *{ф1 }T *{ф1 }=
56.3
[M] =
{ф1 }T *{m}=
-10.07
FPM2 =
3ER MODO 1.0000 0.2155 -0.8910
{ф1 } =
-0.6661 0.5542 0.9463 -0.0756 -0.7813
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000
0.2155 -0.8910
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
0.14
-0.6
[M] *{ф1 }T *{ф1 }=
2.67
{ф1 }T *{m}=
0.33
[M] =
FPM3 =
4TO MODO 1.0000 -1.7156 -0.5046
{ф1 } =
1.3161 -1.3433 1.8624 -0.6311 -1.1933
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999
{ф1 }T =
[M] =
1.0000 -1.7156 -0.5046
0.685440 0 0 0 0
0 ### 0 0 0
0 0 ### 0 0
0.66999 0.66033 0.52254
0 0 0
0 0 0
0 0 0
[M] *{ф1 }T =
0.69
-1.15
-0.34
[M] *{ф1 }T *{ф1 }=
8.53
{ф1 }T *{m}=
-0.61
FPM4 =
5TO MODO 1.0000 -2.0139 2.3703
{ф1 } =
-1.9526 0.8974 0.4508 -1.6519 1.3535
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
{ф1 }T =
1.0000 -2.0139
2.3703
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-1.35
1.59
[M] *{ф1 }T *{ф1 }=
13.16
{ф1 }T *{m}=
0.14
[M] =
FPM5 =
6TO MODO 1.0000 -1.2874 1.6230
{ф1 } =
-1.1267 0.0007 0.0039
{ф1 }T =
1.0000 -1.2874
1.6230
0.0283 0.0000
0.68544 0.66999 0.66999 {m} = 0.66999 0.66999 0.66999 0.66033 0.52254
0.685440 0 0 0 0 0 0 0
0 ### 0 0 0 0 0 0
0 0 ### 0 0 0 0 0
[M] *{ф1 }T =
0.69
-0.86
1.09
[M] *{ф1 }T *{ф1 }=
4.41
{ф1 }T *{m}=
0.18
[M] =
FPM6 = FPM1 FPM2 FPM3 FPM4 FPM5 FPM6 FPMtotal
30.613 17.895 12.478 7.186 1.032 4.017 73.220
4º
CALCULO DE LA ACELERACION ES Parametros Sísmicos Z= 0.3
3.0275
3.5273
3.9083
4.1577
U=
1.5
S=
1.4
R=
7.0
4.2387
MODO 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 ###
T1 = C= C= MODO 2 T2 = C= C= MODO 3 T3 =
2.03
2.36
2.62
2.75
2.21
C= C= MODO 4
0.2961
29.609
T4 = C= C= MODO 5
-4.2946 -4.2609 -4.0389 -0.5452
T5 = C= C=
3.3902
MODO 6 T6 = C= C= 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 ###
MODO 1 T1 = C= C= MODO 2 T2 =
-2.88
-2.85
-2.71
-0.36
1.77
C= C= MODO 3
-0.1860
18.597
T3 = C= C= MODO 4
-0.6628
0.5647
T4 = C= C=
0.9382 -0.1070 -0.7510
MODO 5 T5 = C= C= 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 ###
-0.44
0.38
0.63
-0.07
-0.39
0.1299
12.989
MODO 6 T6 = C= C=
1.3256 -1.4383
1.9950 -0.7411 -1.1855
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 ###
0.89
-0.96
1.34
-0.49
-0.62
0.0412 -1.3089
1.1872
-0.0727
7.274
-2.1562
1.2385
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 ###
-1.44
0.83
0.03
-0.86
0.62
0.0105
1.046
-1.5973
0.0009
0.0047
0.0340
0.0000
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 ###
-1.07
0
0
0.02
0
0.0139 % % % % % % %
1.390
como es mayor a 70% analizamos con estos 6 modos
2.9385
3.4156
3.7791
4.0171
4.0994
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 ###
1.97
2.29
2.53
2.65
2.14
-4.4871 -4.4543 -4.1239 -0.4946
3.5304
0.3061
30.613
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 ###
-3.01
-2.98
-2.76
-0.33
1.84
-0.1789
17.895
-0.6661
0.5542
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 ###
-0.45
0.37
0.63
-0.05
-0.41
0.1248
1.3161 -1.3433
0 0 0 ### 0
0 0 0 0 ###
0.9463 -0.0756 -0.7813
12.478
1.8624 -0.6311 -1.1933
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 ###
0.88
-0.9
1.25
-0.42
-0.62
0.4508 -1.6519
1.3535
-0.0719
7.186
-1.9526
0.8974
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 ###
-1.31
0.6
0.3
-1.09
0.71
0.0283
0.0000
0.0103
-1.1267
0.0007
1.032
0.0039
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 ###
-0.75
0
0
0.02
0
0.0402 % % % % % % %
4.017
como es mayor a 70% analizamos con estos 6 modos
O DE LA ACELERACION ESPECTRAL
5º
CALCULO DEL VECTOR DE D
os Sísmicos g=
981
Tp =
0.9
C <=
2.5
MODO 1 2 3 4
EJE Y
5 6
0.680 3.31 2.5
MODO 1 Sa =
220.73 cm/seg2 {ф1 } =
0.228 9.87 2.5
Sa =
220.73 cm/seg2
Sa =
220.73 cm/seg2
0.139 16.23 2.5
MODO 2
{ф1 } =
0.101 22.17 2.5
Sa =
220.73 cm/seg2
0.082 27.43 2.5
Sa =
220.73 cm/seg2
0.071 31.71 2.5
MODO 3
{ф1 } =
Sa =
220.73 cm/seg2
EJE X
0.388 5.8 2.5
MODO 4 Sa =
220.73 cm/seg2 {ф1 } =
0.130 17.31 2.5
0.079 28.47 2.5
Sa =
220.73 cm/seg2
MODO 5 Sa =
220.73 cm/seg2 {ф1 } =
0.058 38.9 2.5
Sa =
220.73 cm/seg2
0.047 48.15 2.5
Sa =
220.73 cm/seg2
MODO 6
{ф1 } =
0.040 55.67 2.5
Sa =
220.73 cm/seg2
MODO 1 2 3 4 5 6
MODO 1
{ф1 } =
MODO 2
{ф1 } =
MODO 3
{ф1 } =
MODO 4
{ф1 } =
MODO 5
{ф1 } =
MODO 6
{ф1 } =
=
CORRECCION POR 0.75
{ X }=
VERIFICACION: "Desplazam
EJE PISO 1 2 3 4 5 6 7 8
=
CORRECCION POR 0.75
{ X }=
VERIFICACION: "Desplazam
EJE PISO 1 2 3 4 5 6 7 8
CALCULO DEL VECTOR DE DESPLAZAMIENTOS
EJE Y FPM 0.2961 -0.1860
Sa 220.73 220.73
W2 85.389 759.626
0.1299
220.73
2053.584
-0.0727
220.73
3833.553
0.0105
220.73
5867.623
0.0139
220.73
7839.594
1.0000 1.7422 2.4257 3.0275
{X1 }=
3.5273 3.9083 4.1577 4.2387
1.0000 -1.5084 -3.5649
{X1 }=
-4.2609 -4.0389 -0.5452 3.3902
1.0000 0.2296 -0.6628 0.5647 0.9382
-0.05 cm 0.08 cm 0.19 cm 0.23 cm 0.23 cm 0.22 cm 0.03 cm -0.18 cm
-4.2946
-0.8880
0.77 cm 1.33 cm 1.86 cm 2.32 cm 2.7 cm 2.99 cm 3.18 cm 3.24 cm
{X1 }=
0.01 cm 0 cm -0.01 cm -0.01 cm 0.01 cm 0.01 cm
-0.1070 -0.7510
0 cm -0.01 cm
1.0000 -1.8621 -0.4143 1.3256
0 cm 0.01 cm 0 cm -0.01 cm 0.01 cm
{X1 }=
-1.4383
-0.01 cm 0 cm 0 cm
1.9950 -0.7411 -1.1855
1.0000 -2.0165 2.4435 -2.1562
{X1 }=
1.2385 0.0412 -1.3089 1.1872
1.0000 -1.4733 2.1527
{X1 }=
-1.5973 0.0009 0.0047 0.0340 0.0000
EJE X FPM
Sa
W2
0.3061
220.73
262.599
-0.1789 0.1248 -0.0719 0.0103
220.73 220.73 220.73 220.73
2336.391 6318.730 ### ###
0.0402
220.73
###
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 1.7103 2.3636 2.9385 3.4156 3.7791 4.0171 4.0994
1.0000 -1.5754 -3.6848 -4.4871 -4.4543 -4.1239
{X1 }=
{X1 }=
-0.4946 3.5304
0.26 cm 0.44 cm 0.61 cm 0.76 cm 0.88 cm 0.97 cm 1.03 cm 1.05 cm
-0.02 cm 0.03 cm 0.06 cm 0.08 cm 0.08 cm 0.07 cm 0.01 cm -0.06 cm
-0.7813
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 -1.7156 -0.5046 1.3161 -1.3433 1.8624 -0.6311 -1.1933
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
1.0000 0.2155 -0.8910 -0.6661 0.5542 0.9463 -0.0756
1.0000 -2.0139 2.3703 -1.9526 0.8974
{X1 }=
{X1 }=
{X1 }=
0 cm 0 cm 0 cm 0 cm 0 cm
-1.6519
0 cm 0 cm
1.3535
0 cm
1.0000 -1.2874 1.6230 -1.1267
0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm
0.4508
{X1 }=
0.0007 0.0039 0.0283 0.0000
COMBINACION MODAL DE LA NORMA NTE-030
EJE Y 0.84 1.43 2.07 2.57 2.94
=
3.23 3.22 3.44
0.77 1.34 1.87 2.33 2.71
{ X }=
3 3.18 3.25
0.78514 cm 1.35876 cm 1.91618 cm 2.38793 cm 2.76820 cm 3.05722 cm 3.19090 cm 3.29779 cm
CORRECCION POR 0.75 x R ……..SEGUN NTE-030 0 cm 0.00 m 4.12 cm 4.30 m 7.13 cm 7.80 m 10.06 cm 11.30 m 12.54 cm Hacum. = 14.80 m 14.53 cm 18.30 m 16.05 cm 21.80 m 16.75 cm 25.30 m 17.31 cm 28.30 m
DESPLAZAMIE 30.00 28.30 25.30
25.00
21.80 20.00 18.30
VERIFICACION: "Desplazamientos Laterales" H (m)
15.00
10.00
14.80 11.30
D IE
18.30 H (m)
EJE Y H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 4.12 NO CUMPLE! 3.5 2.45 3.01 NO CUMPLE! 3.5 2.45 2.93 NO CUMPLE! 3.5 2.45 2.48 NO CUMPLE! 3.5 2.45 2 OK! 3.5 2.45 1.52 OK! 3.5 2.45 0.7 OK! 3.0 2.10 0.56 OK!
15.00
14.80 11.30
10.00
7.80 5.00
4.30
0.00 0.00 5
=
1.04 1.12
0.26 0.44 0.61 0.76 0.88 0.97 1.03 1.06
CORRECCION POR 0.75 x R ……..SEGUN NTE-030 0 cm 0.00 m 1.38 cm 3.50 m 2.35 cm 7.80 m 3.29 cm 11.30 m 4.09 cm Hacum. = 14.80 m 4.73 cm 18.30 m 5.22 cm 21.80 m 5.44 cm 25.30 m 5.63 cm 28.30 m
VERIFICACION: "Desplazamientos Laterales" EJE X H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 1.38 OK! 3.5 2.45 0.97 OK! 3.5 2.45 0.94 OK! 3.5 2.45 0.8 OK! 3.5 2.45 0.64 OK! 3.5 2.45 0.48 OK! 3.5 2.45 0.22 OK! 3.0
2.10
0.19
OK!
15
desplaz. (cm)
EJE X 0.28 0.47 0.68 0.84 0.96 1.05
10
{ X }=
0.26353 cm 0.44833 cm 0.62752 cm 0.77925 cm 0.90119 cm 0.99339 cm 1.03610 cm 1.07232 cm
20
D IE
DESPLAZAMIENTO EN Y
28.30 25.30 21.80 18.30 14.80 11.30
DESPLAZAM IENTO EN Y
18.30 14.80 11.30 7.80
4.30
0 5
10
15
laz. (cm)
20
DESPLAZAM IENTO EN Y
6º
CALCULO DEL VECTOR DE FUERZAS SISMICAS
EJE Y
EJE X
MODO 1 2 3 4 5
FPM 0.2961 -0.1860 0.1299 -0.0727 0.0105
Sa 220.73 220.73 220.73 220.73 220.73
MODO 1 2 3 4 5
FPM 0.3061 -0.1789 0.1248 -0.0719 0.0103
Sa 220.73 220.73 220.73 220.73 220.73
6
0.0139
220.73
6
0.0402
220.73
{m} =
0.69 0.67 0.67 0.67 0.67 0.67 0.66 0.52
MODO 1
{F1 }=
44.8 76.28 106.21 132.56 154.45 171.13 179.43 144.75
MODO 1
{F1 }=
MODO 2
{F1 }=
-28.14 41.48 98.04 118.11 117.18
46.31 77.42 107 133.03 154.63 171.08 179.23 144.74
MODO 2
{F1 }=
-27.07 41.69 97.51 118.74 117.88
111.07 14.78 -72.72
109.13 12.9 -72.87
MODO 3
{F1 }=
19.65 4.41 -17.06 -12.73 10.85 18.02 -2.03 -11.25
MODO 3
{F1 }=
MODO 4
{F1 }=
-11.01 20.03 4.46 -14.26 15.47 -21.46 7.86 9.95
MODO 4
{F1 }=
MODO 5
{F1 }=
1.58 -3.12 3.78 -3.33 1.92 0.06 -1.99 1.43
{F1 }=
-10.87 18.23 5.36 -13.99 14.27 -19.79 6.61 9.89 MODO 5
{F1 }=
MODO 6 2.1 -3.03 4.42 -3.28 0 0.01 0.07 0
18.88 3.98 -16.44 -12.29 10.23 17.46 -1.38 -11.24
1.56 -3.07 3.62 -2.98 1.37 0.69 -2.48 1.61 MODO 6
{F1 }=
6.08 -7.65 9.64 -6.69 0 0.02 0.17 0
COMBINACION MODAL DE LA NORMA NTE-030 COMBINACIÓ N MODAL : COMBINACIÓ N MODAL : 0.25 ∑i { F{} F=}0=.25 ∑F
F i + 0.75 ∑i 2F i + 0.75 ∑ F EJE Y
107.27 148.35 61 . 804 .804233.97 tonton 61 i 62.119 ton , .119284.28 ton , ∑∑F i F= == 62 74 . 788 74 ton 299.86 .788 ton 321.76 206.15 240.1
{ Fi }=
69.98 104.09 167.79 205.04 221.06 234.89 186.71 182.04
2
57.55 89.33 40 .458ton ton .458 145.73 2 40 2 i 48 .974 ton 48.974 ton ∑ ∑F i F== =178.63 56 .079 56 194.8 ton .079 ton 205.93 180.23 162.69
tn tn tn tn tn tn tn tn
COMBINACIÓ N MODAL : COMBINACIÓ N MODAL : 0.25 ∑i { F{} F=}0=.25 ∑F
F i + 0.75 ∑i 2F i + 0.75 ∑ F EJE X
2
110.78 58.24 152.04 90.27 61 . 804 ton 40 .458ton ton .458 146.16 .804239.58 61 ton 2 40 i i 2 62.119 ton , 48 .974 ton .119287.72 48.974 ton ton , ∑∑F i F= == 62 ∑ ∑F i F== =179.43 74.788 ton 56 .079 298.38 74 195.23 ton .788 ton 56.079 ton 318.18 204.64 202.77 179.84 240.36 162.75 1 8 2 . 1 5 t n 1 8 5 . 5 7 t n
1 8 2 . 1 5 t n
1 8 5 . 5 7 t n
2 3 3 . 0 3 t n
{ Fi }=
71.38 tn 105.71 2 tn 2 1 . 0 1 t n 169.52 tn 206.51 2 tn 0 6 . 5 1 t n 221.01 tn 6 9 . 5 2 t n 233.031 tn 185.57 tn 0 5 . 7 1 t n 182.151 tn 7 1 . 3 8 t n
7º
CALCULO DEL VECTOR DE CORTANTES
{ V } = [ S] . { F } i
i
[S] = MATRIZ CUADRADA SUPERIOR
1 0 0 0 0 0 0 0
[S]=
1 1 0 0 0 0 0 0
EJE Y
1 1 1 0 0 0 0 0
1 1 1 1 0 0 0 0
1 1 1 1 1 0 0 0
1 1 1 1 1 1 0 0
1 1 1 1 1 1 1 0
EJE X
1009.61 tn 964.82 tn 888.53 tn {V1 }= 782.32 tn 649.76 tn 495.31 tn 324.18 tn 144.75 tn
1013.46 tn 967.14 tn 889.72 tn {V1 }= 782.71 tn 649.69 tn 495.06 tn 323.98 tn 144.74 tn
399.81 tn 427.95 tn 386.46 tn 288.42 tn 170.32 tn 53.14 tn -57.94 tn -72.72 tn
397.92 tn 424.99 tn 383.3 tn 285.78 tn 167.04 tn 49.17 tn -59.97 tn -72.87 tn
{V2 }=
{V3 }=
9.87 tn -9.79 tn -14.2 tn 2.86 tn 15.59 tn
{V2 }=
{V3 }=
9.19 tn -9.69 tn -13.66 tn 2.78 tn 15.07 tn
1 1 1 1 1 1 1 1
4.75 tn -13.28 tn -11.25 tn
4.84 tn -12.62 tn -11.24 tn
11.04 tn 22.04 tn 2.01 tn -2.45 tn 11.81 tn -3.66 tn 17.8 tn 9.95 tn
9.72 tn 20.59 tn 2.36 tn -3 tn 10.98 tn -3.29 tn 16.5 tn 9.89 tn
{V4 }=
{V5 }=
{V6 }=
{V4 }=
0.32 tn -1.26 tn 1.86 tn -1.92 tn 1.42 tn -0.5 tn -0.56 tn 1.43 tn
0.31 tn -1.25 tn 1.82 tn -1.8 tn 1.18 tn -0.19 tn -0.87 tn 1.61 tn
{V5 }=
0.3 tn -1.81 tn 1.22 tn -3.2 tn 0.08 tn 0.08 tn 0.07 tn 0 tn
1.57 tn -4.51 tn 3.14 tn -6.5 tn 0.19 tn 0.19 tn 0.17 tn 0 tn
{V6 }=
COMBINACIÓ NCOMBINACION MODAL : MODAL DE LA NORMA NTE-030
{V}
= 0.25
∑
V i + 0.75
∑
Vi
2
EJE Y
∑
1430.95 .473 1427.65 147
Vi
ton = 115 .497 ton 74 .788 ton
1085.99 1055.74
,
∑
Vi
2
1172.23 tn 129 .257 tn 1148.72
ton = 101 .665 ton 56 .079 ton
∑
ton 147 .473 ton 147 .473 1294.28 i V i = 115V .497 ton , 1081.17 == 115 .497 ton 74 .788 ton 848.98 74.788 ton
∑
∑, V i
2
557.43 413.83 240.1
.257 129 969.05 2 == 101 .665 833.81 Vi 56 .079 671.99
∑
498.19 330.06 162.69
ton 129 .257 ton1050.36 tn ton { Vi = 101 .665 }=ton 895.65 tn ton 56.079 ton 716.24 tn
513.00 tn 351.00 tn 182.04 tn
1 8 2 . 0 4 t n
3 5 1 . 0 0 t n
5 1 3 . 0 0 t n
7 1 6 . 2 4 t n
8 9 5 . 6 5 t n
1 0 5 0 . 3 6 t n
1 1 4 8 . 7 2 t n
COMBINACIÓN MODAL :
1 1 7 2 . 2 3 t n
COMBINACIÓ N MODAL :
{ V} { V } = 0.25 ∑
∑
Vi
∑ + 0.75
= 0.25
Vi
1432.17 1428.17 .473 ton ton1294 147 .473 147 i 1082.57 = ∑ 115V .497== ton .497, ton 115 844.16 74 .788 ton 74.788 ton 552.74 414.1 240.36
∑,
V i + 0.75 2 ∑X V i EJE
Vi
2
∑
Vi
1088.86 1056.66 968.88 .257 129 2 i = 833.29 = = ∑101V.665 671.08 56 .079 497.53 330.14 162.75
2
129.257 ton ton }= 101.665{ Vi ton ton ton56.079 ton
1 8 2 . 1 5 t n
3 5 1 . 1 3 t n
5 1 1 . 3 3 t n
7 1 4 . 3 5 t n
8 9 5 . 6 1 t n
1 0 5 0 . 1 6 t n
1174.69 tn 1149.53 tn 1050.16 tn 895.61 tn 714.35 tn 511.33 tn 351.13 tn 182.15 tn
7 1 4 . 3 5 t n
8 9 5 . 6 1 t n
1 0 5 0 . 1 6 t n
1 1 4 9 . 5 3 t n
1 1 7 4 . 6 9 t n
8º
CALCULO DEL VECTOR DE MOMENTOS
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
EJE Y
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 3.50 0.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
EJE X
3497.1 tn-m 3304.48 tn-m 3037.48 tn-m {V1 }= 2665.74 tn-m 2201.77 tn-m 1661.21 tn-m 1062.25 tn-m 434.26 tn-m
3511.78 tn-m 3312.63 tn-m 3041.64 tn-m {V1 }= 2667.13 tn-m 2201.54 tn-m 1660.35 tn-m 1061.55 tn-m 434.23 tn-m
1413.19 tn-m 1534.17 tn-m 1388.98 tn-m {V2 }= 1045.84 tn-m 632.46 tn-m
1407.48 tn-m 1523.9 tn-m 1377.98 tn-m {V2 }= 1036.68 tn-m 621.08 tn-m
{V3 }=
{V4 }=
{V5 }=
{V6 }=
222.34 tn-m -166.42 tn-m -218.15 tn-m
208.51 tn-m -173.45 tn-m -218.6 tn-m
55.88 tn-m -28.63 tn-m -44.06 tn-m 15.64 tn-m 60.2 tn-m 22.23 tn-m -40.85 tn-m -33.76 tn-m
52.89 tn-m -28.28 tn-m -42.2 tn-m 15.34 tn-m 58.36 tn-m 22.57 tn-m -38.55 tn-m -33.73 tn-m
24.85 tn-m 72.17 tn-m 2.07 tn-m -13.53 tn-m 36.37 tn-m -17.78 tn-m 57.34 tn-m 29.84 tn-m
1.68 tn-m -5.12 tn-m 5.79 tn-m -7.43 tn-m 4.24 tn-m -2.46 tn-m -2.69 tn-m 4.3 tn-m
2.72 tn-m -6.32 tn-m 4.28 tn-m -11.21 tn-m 0.28 tn-m 0.28 tn-m 0.24 tn-m 0 tn-m
{V3 }=
{V4 }=
{V5 }=
{V6 }=
20.38 tn-m 67.13 tn-m 3.32 tn-m -15.45 tn-m 33.5 tn-m -16.46 tn-m 52.8 tn-m 29.67 tn-m
1.53 tn-m -5.19 tn-m 5.57 tn-m -7.09 tn-m 3.34 tn-m -1.45 tn-m -3.86 tn-m 4.83 tn-m
10.36 tn-m -15.77 tn-m 10.99 tn-m -22.75 tn-m 0.68 tn-m 0.66 tn-m 0.58 tn-m 0 tn-m
COMBINACION MODAL DE LA NORMA NTE-030
COMBINACIÓ N MODAL :
{ M}
COMBINACIÓ N MODAL : COMBINACIÓ N MODAL :
{ M}
∑
= 0.25
∑
{ M}
= 0.25
∑
= 0.25
M i + 0.75
∑
M
+ 0.75
i
∑
M i + 0.75
M ∑ EJE Y 2
i
4995.42 3772.34 4950.89 3644.08 1087 . 968 ton − m 1087 . 968 ton − m −m 1066 .918 1087 .968 ton4482.66 3340.29 2 i 2863.67 i i = 3759.39 = M = 604 . 224 ton − m , M = 604i .224 ton −m , M = 520 .843 = ton604 .224 ∑ton − m , M 2291.9 2935.33 224 . 364 − m 168 .236 224 .364 ton − m 224 1926.29 1676.26 .364 1329.78 ton − m 1077.51 COMBINACIÓ N MODAL : 720.29 488.07
∑
∑
∑
Mi
∑
M
i
2
2
4078.11 tn-m 3970.78 tn-m 1066 . 918 ton −m 3625.89 tn-m ton − m 2 2 i }= .843 3087.60 tn-m M − m ={ Mi520 −m ton i ton M = 168 .236 ton 2452.76 tn-m ton − m −m 1738.77 tn-m 1140.58 tn-m 546.13 tn-m
∑
COMBINACIÓ N MODAL :
{ M}
∑
M
i
= 0.25
1087 .968 i = 604 .224M 224 .364
∑
∑
{ M}
= 0.25
M i + 0.75
5004.42 4952.9 1087 4481.71 ton − m .968 =ton3764.45 −604 m .224 , = ton2918.49 m .364 −224 1910.01 1330.8 721.07
∑
M i + 0.75
∑EJEM X i
2
∑
3783.77 3647.1 ton − m 1066 .918 3339.52 2 i ton −∑m M ,== 2861.7 520 .843 2288.46 ton − m 168 .236 1673.62 1077.62 488.25
∑
Mi
2
4088.94 tn-m 3973.55 tn-m 1066 . 918 m ton −tn-m ton − m 3625.06 i 2 520}= .843 m 3087.39 ton −tn-m Mton − =m { Mi ton − m m 168.2362445.97 ton −tn-m 1732.72 tn-m 1140.92 tn-m 546.45 tn-m
546.13 tn-m
546.45 tn-m
1140.58 tn-m
1140.92 tn-m
1738.77 tn-m
1732.72 tn-m
2452.76 tn-m
2445.97 tn-m
3087.60 tn-m
3087.39 tn-m
3625.89 tn-m
3625.06 tn-m
3970.78 tn-m
3973.55 tn-m
4078.11 tn-m
4088.94 tn-m
1066 .918 520 .843 168 .236
3625.89 tn-m
3625.06 tn-m
3970.78 tn-m
3973.55 tn-m
4078.11 tn-m
4088.94 tn-m
EJE Y
EJE X
1º
FORMULACION MATRICIAL PARA EL ANÁLISIS ESTATICO
V=
Z .U. S . C . PT R
....... (1)
Parametros Sísmicos Z= U= S= R=
0.3 1.5 1.4 7.0
W1 =
672.416
W2 = W3 = W4 = W5 = W6 = W7 = W8 = PT =
657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 647.784 Ton 512.616 Ton 5119.106 Ton
Además
(Huancayo) (Hospital)
Ton
0.4
C <=
2.5
k1 =
1319
k2 = k3 = k4 = k5 = k6 = k7 = k8 =
1698 1698 1698 1698 1698 1698 2336
tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm
h1 h2 h3 h4 h5 h6 h7 h8
= = = = = = = =
Hn
≥
C/R T=
CT = T= C=
Tp = (Sistema Mixto)
0.13
hn/CT (Periodo Fundamental) 45 (sist. Mixto) 0.629 seg.
1.59
C= V=
732.59 Ton.
1.59
4.30 3.50 3.50 3.50 3.50 3.50 3.50 3.00 28.30
2º
DISTRIBUCION DE "V" EN ALTURA
Fi =
w i . hi
. V
n
∑w .h i
Fi: Fuerza sísmica en el nivel i Pi: Peso del nivel i Hi: Altura del nivel i, suma de la mitad de c/piso
i
V: Cortante basal en la base del edificio
1
V=
3º
732.590 Tn
Nivel 1 2 3 4
Pi (ton) 672.416 657.258 657.258 657.258
5 6 7 8
657.258 657.258 647.784 512.616
total
5119.106
FUERZA POR CADA PISO hi (m) Pi*hi Fi (Ton) 4.300 2891.391 147.165 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 3.500 3.500 3.000
2300.403 2300.403 2267.244 1537.848
117.085 117.085 115.397 78.273
14393.406
732.590
VECTOR DE FUERZAS SISMICAS
147.165 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 115.397 ton 78.273 ton 4º
VECTOR DE FUERZAS CORTANTES
732.590 ton 585.425 ton 468.340 ton 351.255 ton 234.170 ton 117.085 ton 115.397 ton 78.273 ton
V(Ton) 732.590 585.425 468.340 351.255 234.170 117.085 115.397 78.273
5º
d de c/piso
VECTOR DE DESPLAZAMIENTOS
∆Xi = NIVEL 1 2 3 4 5 6 7 8
Vi , Ki
Xi = Xi −1 + ∆Xi
Vi
Ki
∆Xi
Xi
(ton)
(Tn/cm)
(cm)
(cm)
0.555
0.555
0.345 0.276 0.207 0.138 0.069 0.068
0.900 1.176 1.383 1.520 1.589 1.657
0.034
1.691
732.59 585.43 468.34 351.26 234.17 117.09 115.40 78.27
1319 1698 1698 1698 1698 1698 1698 2336
Corregidos por 0.75R
=
6º
0.75
*
7*
VERIFICACION "DESPLAZAMIENTOS LATERALES"
EJE Y PISO 1 2 3 4 5 6 7 8 7º
H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 2.916 OK! 3.5 2.45 1.810 OK! 3.5 2.45 1.448 OK! 3.5 2.45 1.086 OK! 3.5 2.45 0.724 OK! 3.5 2.45 0.362 OK! 3.5 2.45 0.357 OK! 3.0 2.10 0.176 OK!
VECTOR DE MOMENTOS DE VOLTEO
{ M} = [ H ] .{ V } i
i
0.555 0.900 1.176 1.383 1.520 1.589 1.657 1.691
=
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
{M }=
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
1er piso 2do piso 3er piso 4to piso 5to piso 6to piso 7mo piso 8vo piso
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
9935.81 Tn/m 6785.67 Tn/m 4736.69 Tn/m 3097.5 Tn/m 1868.1 Tn/m 1048.51 Tn/m 638.71 Tn/m 234.82 Tn/m
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 3.50 0.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
2.916 4.725 6.173 7.259 7.982 8.344 8.701 8.877
cm cm cm cm cm cm cm cm
OK! OK! NO NO NO NO OK!
OK!
1º
FORMULACION MATRICIAL PARA EL ANÁLISIS ESTATICO
V=
Z .U. S . C . PT R
....... (1)
Parametros Sísmicos Z= U= S= R=
0.3 1.5 1.4 7.0
W1 =
672.416
W2 = W3 = W4 = W5 = W6 = W7 = W8 = PT =
657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 657.258 Ton 647.784 Ton 512.616 Ton 5119.106 Ton
Además
(Huancayo) (Hospital)
Ton
0.4
C <=
2.5
k1 =
3939
k2 = k3 = k4 = k5 = k6 = k7 = k8 =
5292 5292 5292 5292 5292 5292 6828
tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm tn/cm
h1 h2 h3 h4 h5 h6 h7 h8
= = = = = = = =
Hn
≥
C/R T=
CT = T= C=
Tp = (Sistema Mixto)
0.13
hn/CT (Periodo Fundamental) 45 (sist. Mixto) 0.629 seg.
1.59
C= V=
732.59 Ton.
1.59
4.30 3.50 3.50 3.50 3.50 3.50 3.50 3.00 28.30
2º
DISTRIBUCION DE "V" EN ALTURA
Fi =
w i . hi
. V
n
∑ w .h i
Fi: Fuerza sísmica en el nivel i Pi: Peso del nivel i Hi: Altura del nivel i, suma de la mitad de c/piso
i
V: Cortante basal en la base del edificio
1
V=
3º
732.590 Tn
Nivel 1 2 3 4
Pi (ton) 672.416 657.258 657.258 657.258
5 6 7 8
657.258 657.258 647.784 512.616
total
5119.106
FUERZA POR CADA PISO hi (m) Pi*hi Fi (Ton) 4.300 2891.391 147.165 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 2300.403 117.085 3.500 3.500 3.500 3.000
2300.403 2300.403 2267.244 1537.848
117.085 117.085 115.397 78.273
14393.406
732.590
VECTOR DE FUERZAS SISMICAS
147.165 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 117.085 ton 115.397 ton 78.273 ton 4º
VECTOR DE FUERZAS CORTANTES
732.590 ton 585.425 ton 468.340 ton 351.255 ton 234.170 ton 117.085 ton 115.397 ton 78.273 ton
V(Ton) 732.590 585.425 468.340 351.255 234.170 117.085 115.397 78.273
5º
d de c/piso
VECTOR DE DESPLAZAMIENTOS
Vi Ki
∆Xi = NIVEL 1 2 3 4 5 6 7 8
Xi = Xi −1 + ∆Xi
,
Vi
Ki
∆Xi
Xi
(ton)
(Tn/cm)
(cm)
(cm)
0.186
0.186
0.111 0.088 0.066 0.044 0.022 0.022
0.297 0.385 0.451 0.496 0.518 0.540
0.011
0.551
732.59 585.43 468.34 351.26 234.17 117.09 115.40 78.27
3939 5292 5292 5292 5292 5292 5292 6828
Corregidos por 0.75R
=
6º
0.75
*
7*
VERIFICACION "DESPLAZAMIENTOS LATERALES"
EJE Y PISO 1 2 3 4 5 6 7 8 7º
H(m) 0.007*hi(cm) X(cm) CONDICION 4.3 3.01 0.977 OK! 3.5 2.45 0.581 OK! 3.5 2.45 0.465 OK! 3.5 2.45 0.348 OK! 3.5 2.45 0.232 OK! 3.5 2.45 0.116 OK! 3.5 2.45 0.114 OK! 3.0 2.10 0.060 OK!
VECTOR DE MOMENTOS DE VOLTEO
{ M} = [ H ] .{ V } i
i
0.186 0.297 0.385 0.451 0.496 0.518 0.540 0.551
=
{ M} = [ H ] .{ V } i
i
[H] = Matriz cuadrada, diagonal superior cuyos coeficientes corresponden a los valores de las alturas de los entrepisos.
[H]=
4.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00
{M }=
3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00
1er piso 2do piso 3er piso 4to piso 5to piso 6to piso 7mo piso 8vo piso
3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00
9935.81 Tn/m 6785.67 Tn/m 4736.69 Tn/m 3097.5 Tn/m 1868.1 Tn/m 1048.51 Tn/m 638.71 Tn/m 234.82 Tn/m
3.50 3.50 3.50 3.50 3.50 0.00 0.00 0.00
3.50 3.50 3.50 3.50 3.50 3.50 0.00 0.00
3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 3.50 3.00 0.00 3.00
0.977 1.557 2.022 2.370 2.603 2.719 2.833 2.893
cm cm cm cm cm cm cm cm
OK! OK! NO NO NO NO OK!
OK!
CALCULO DEL CENTRO DE MASA CON EL AUTOCAD CENTRO DE MASA Piso Xm Ym 1 17.00 7.00 2 17.00 7.00 3 17.00 7.00 4 17.00 7.00 5 17.00 7.00 6 17.00 7.00 7 17.00 7.00 8 17.00 7.00
CENTRO DE RIGIDEZ
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C
Y(m) 0 7 14 20 27 34 0 0 0
PRIMER PISO X(m) KL(Ton/cm) K*Y K*X 0 527.37 0 0 0 68.47 479.29 0 0 63.72 892.06 0 0 63.72 1274.37 0 0 68.47 1848.69 0 0 527.37 17930.73 0 0 2079.92 0 0 5 120.2 0 601.02 8.5 120.2 0 1021.73 13.5 1618.33 0 21847.46
17 m 5.96 m SEGUNDO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0 0 24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 5 109.85 0 8.5 109.85 0
K*X 0 0 0 0 0 0 0 549.26 933.74
D
0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1
Y(m) 0
13.5
2245.65
0 30316.29
17 m 6.01 m
TERCER PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
CUARTO PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
QUINTO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0
K*X 0
2 3 4 5 6 A B C D
7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C
Y(m) 0 7 14 20 27 34 0 0 0
0 0 0 0 0 0 5 8.5 13.5
24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 0 109.85 0 549.26 109.85 0 933.74 2245.65 0 30316.29
17 m 6.01 m
SEXTO PISO X(m) KL(Ton/cm) K*Y K*X 0 799.54 0 0 0 24.91 174.34 0 0 24.8 347.2 0 0 24.8 496 0 0 24.91 672.44 0 0 799.54 27184.49 0 0 2826.66 0 0 5 109.85 0 549.26 8.5 109.85 0 933.74 13.5 2245.65 0 30316.29
17 m 6.01 m
SEPTIMO PISO X(m) KL(Ton/cm) K*Y 0 799.54 0 0 24.91 174.34 0 24.8 347.2 0 24.8 496 0 24.91 672.44 0 799.54 27184.49 0 2826.66 0 5 109.85 0 8.5 109.85 0
K*X 0 0 0 0 0 0 0 549.26 933.74
D
0
XR1 = YR1 =
PORTICO 1 2 3 4 5 6 A B C D
Y(m) 0 7 14 20 27 34 0 0 0 0
XR1 = YR1 =
13.5
2245.65
17 m 6.01 m
OCTAVO PISO X(m) KL(Ton/cm) K*Y K*X 0 1099.73 0 0 0 34.2 239.38 0 0 34.07 477.01 0 0 34.07 681.45 0 0 34.2 923.32 0 0 1099.73 37390.86 0 0 3549.15 0 0 5 204.08 0 1020.38 8.5 204.08 0 1734.65 13.5 2871.1 0 38759.92
17 m 6.08 m
RESUMEN CENTRO DE RIGIDECES PISO 1 2 3 4 5 6 7 8
0 30316.29
X(m) 17.00 17.00 17.00 17.00 17.00 17.00 17.00 17.00
Y(m) 5.96 6.01 6.01 6.01 6.01 6.01 6.01 6.08
CALCULO DE EXCENTRICIDADES EXCENTRICIDAD DIRECTA: CENTRO MASAS PISO Xm(m) Ym(m) 1 17.00 7.00 2 17.00 7.00 3 17.00 7.00 4 17.00 7.00 5 17.00 7.00 6 17.00 7.00 7 17.00 7.00 8 17.00 7.00
CENTRO DE RIGIDECES PISO Xg(m) Yg(m) 1 17.00 5.96 2 17.00 6.01 3 17.00 6.01 4 17.00 6.01 5 17.00 6.01 6 17.00 6.01 7 17.00 6.01 8 17.00 6.08 EXCENTRICIDAD ACCIDENTAL:
EXCENTRICIDAD DIRECTA: PISO 1 2 3 4 5 6 7 8
ex 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ey 1.04 0.99 0.99 0.99 0.99 0.99 0.99 0.92
EXCENTRICIDAD REAL PISO 1 2 3 4 5 6 7 8
ex 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68
ey 2.74 2.69 2.69 2.69 2.69 2.69 2.69 2.62
DX = DY =
34 13.5
PISO 1 2 3 4 5 6 7 8
ex 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68
m m ey 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70
PORTICO 1 SEGUNDO PISO EJE "Y"
CARGA MUERTA
1218 kg
CARGA VIVA
750 kg
CARGA ULTIMA
CUANTIA MINIMA
3177 kg/m
f´c
fy
0.0024 As min
210 b
4200 d
3.913
30
54
B W
Mu(ton-m) 0.0250
CUANTIA As(-)
4.07412
ø
W 0.9
Mu(ton-m) 0.0529
0.0013
CUANTIA
2.029 cm2
As(-)
W
Mu(ton-m) 0.0223
CUANTIA As
3.63990
ø 0.9 0.0011 1.810 cm2
8.46231
Y"
CARGA MUERTA
1218 kg
CARGA VIVA
750 kg
CARGA ULTIMA
CUANTIA MINIMA
3177 kg/m
f´c
fy
0.0024 As min
210 b
d
3.913
C
4200
30
54
C
ø
W 0.9 0.0026 CUANTIA 4.282 As(-)
Mu(ton-m) 0.0655
10.40632
ø
W 0.9
0.0401
0.0033
CUANTIA
5.306 cm2
As(-)
W
Mu(ton-m) 0.0363
CUANTIA As
5.8627
ø 0.9 0.0018 2.938 cm2
D Mu(ton-m) 6.4613
ø 0.9 0.0020 3.245 cm2
JUNTA SISMICA ALTURA HOSPITAL = 28.30 m ALTURA EDIFICIO VECINO 30.00 = m S> Fórmula:
3.00 cm
S = 3 + 0.004 ( h - 500 ) S= h= S=
junta de separación sísmica altura del edificio en cm. 13 cm
Cada uno de los edificios se retirará de los límites de propiedad adyacentes distancias no menores que 2/3 del desplazamiento máximo calculado ni menores que S/2 Retiro Hospital = Retiro Hospital = Retiro Hospital = Retiro Edif. vecino =
5.92 cm 6.5 cm 6.5 cm 6.5 cm
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