Cargas,Analisis Estatico y Dinamico

INGENIERIA ANTISISMICA UNPRG - ING CIVIL

Juan Manuel Chero Damian

MEMORIA DESCRIPTIVA

UBICACIÓN DEL PROYECTO

- DEPARTAMENTO : LIMA- PROVINCIA: LIMA- DISTRITO : LOS OLIVOS

USO DE LA EDIFICACION

- USO : VIVIENDA COMERCIO

SISTEMA CONSTRUCTIVO: PORTICOS DE CONCRETO ARMADO

ALTURA TOTAL (hn): 16.625 m : medido desde el nivel de terreno natural

ESTUDIO DE SUELO:- Grava arenosa bien graduada- capacidad admisible = 4 kg/cm2- profundidad minima de cimentacion = 1.20 m

CARACTERISTICAS DE LOS MATERIALES

- CONCRETO ARMADO:- f'c = 210 kg/cm2

- ACERO DE REFUERZO:- fy = 4200 kg/cm2- E = 2000000 kg/cm2

PREDIMENSIONAMIENTO Y METRADO DE CARGAS

JUAN MANUEL CHERO DAMIAN INGENIERIA CIVIL-UNPRG

SISTEMA: PORTICOS DE CONCRETO ARMADONUMERO DE PISOS DEL EDIFICIO N = 6MATERIALES:

fy = 4200.000 kg/cm2Es = 2100000.000 kg/cm2f'c = 210.000 kg/cm2E = 217370.651 kg/cm2Peso Espec. Conc. = 2400.000 kg/m3Peso Espec. Tab. = 14.000 kg/(m2xcm)Peso Espec. Alb. = 14.000 kg/(m2xcm)

LOSA MACIZA:Luz mayor : = 6.000 m 40predimensionado h = 0.150 mvalor asumido h = 0.150 mPeso = 360.000 kg/m2

ACABADOSPeso = 100.000 kg/m2

SOBRECARGAVivienda = 200.000 kg/m2Azotea = 100.000 kg/m2

cargas por tabiqueria repartidaSEGUNDO PISOespesor del tabique = 0.150 marea equivalente = 131.762 m2peso = 27670.020 kgarea techada = 178.670 m2peso tab.equivalente = 154.867 kg/m2

3ERO, 4TO, 5TO Y 6TO PISOespesor del tabique = 0.150 marea equivalente = 159.218 m2peso = 33435.780 kgarea de losa = 175.010 m2peso tab.equivalente = 191.051 kg/m2

RESUMENcarga muertaPeso de losa maciza = 360.000 kg/m2peso de tabiqueria = 154.867 kg/m2 para 1 y 2 pisopeso de tabiqueria = 191.051 kg/m2 para 3,4,5,6 pisosPeso de acabados = 100.000 kg/m2carga vivasobrecarga vivienda = 200.000 kg/m2sobrecarga azotea = 100.000 kg/m2

espesor del muro perimetral e = 0.250 maltura del muro perimetral h = 2.500 m

coeficiente α:ℎ=𝑙𝑢𝑧/α



PREDIMENSIONAMIENTO

PREDIMENSIONAMIENTO DE LOSA MACIZALuz mayor : = 6.000 m 40predimensionado h = 0.150 mvalor asumido h = 0.150 m

PREDIMENSIONAMIENTO DE VIGASLn : luz libreWu : carga ultima en kg/cm2

determinacion de la carga ultimacarga muertaPeso de losa maciza = 360.000 kg/m2peso de tabiqueria = 191.051 kg/m2 Wu = 1251.471 kg/m2Peso de acabados = 100.000 kg/m2 = 0.125 kg/cm2

Wcm = 651.051 kg/m2carga vivasobrecarga vivienda = 200.000 kg/m2

Wcv = 200.000 kg/m2

luz libre en direccion y-y (mayor) Ln = 5.850 mh = 0.517 m

asumiendo h = 0.500 m 0.50ancho minimo b = 0.250 mentonces b x h = 0.50 x 0.25 m

0.25

luz libre en direccion x-x (mayor) Ln = 5.250 mh = 0.464 m

asumiendo h = 0.500 m 0.50ancho minimo b = 0.250 mentonces b x h = 0.50 x 0.25 m

0.25

PREDIMENSIONAMIENTO DE COLUMNASPara el predimensionamiento de columnas se utilizara el metodo del areatributaria

d = dimension de la seccion en la direccion delanalisis sismico de la columna.

b = la otra dimension de la seccion de la columnaP = Carga total que soporta la columna (ver Tabla 1)n = valor que depende del tipo de columna (ver Tabla 1)f'c=Resistencia del concreto a la compresion.

TIPO C1 Columna interior P = 1.1 * PG(para los primeros pisos) N < 3 pisos n = 0.3

TIPO C1 Columna interior P = 1.1 * PG(para los 4 ultimos pisos N > 4 pisos n = 0.25

superiores)

TIPO C2, C3Columnas extremas de P = 1.25 * PGporticos interiores n = 0.25 TABLA 1

coeficiente α:ℎ=𝑙𝑢𝑧/αℎ=𝐿𝑛/(4/√𝑊𝑢)

𝑊𝑢=1.4∗Wcm+1.7∗Wcv

𝑏∗𝑑=𝑃/(𝑛∗𝑓^′ 𝑐)



TIPO C4 Columna de esquinaP = 1.5 * PGn = 0.2

PG = Peso debido a la carga por gravedadP = Peso debido a la carga de sismo

COLUMNA DE ESQUINA (A-1) TIPO C4

piso elemento carga unitaria peso parcial

losa 360.000 kg/m2 5.083 m2 1829.700 kgacabados 100.000 kg/m2 6.283 m2 628.270 kgtabiqueria 191.051 kg/m2 0.000 m2 0.000 kgmuro 875.000 kg/m 0.000 m 0.000 kgviga x-x 300.000 kg/m 2.930 m 879.000 kgviga y-y 300.000 kg/m 2.150 m 645.000 kgcolumna 150.000 kg/m 2.500 m 375.000 kgsobrecarga 100.000 kg/m2 6.283 m2 628.270 kg

PD 4356.970 kgPL 628.270 kg


PD 34989.940 kg para columnas sePL 5026.160 kg esta asumiendo

losa 360.000 kg/m2 5.083 m2 1829.700 kg el ancho minimoacabados 100.000 kg/m2 6.283 m2 628.270 kgtabiqueria 154.867 kg/m2 5.083 m2 787.110 kgmuro 875.000 kg/m 5.080 m 4445.000 kgviga x-x 300.000 kg/m 2.930 m 879.000 kgviga y-y 300.000 kg/m 2.150 m 645.000 kgcolumna 150.000 kg/m 3.700 m 555.000 kg

acumuladosobrecarga 200.000 kg/m2 6.283 m2 1256.540 kg

PD 9769.080 kg 49115.990 kgPL 1256.540 kg 6910.970 kg

TOTAL 56026.960 kg

= 2000.963 cm2

asumiendo un ancho b = 0.400 mentonces h = 0.500 masumiendo h = 0.500 m 0.50

b x h = 0.40 x 0.50

0.40

A o L tributaria

6to

5,4,3,2,

piso

1 PISO




COLUMNA DE ESQUINA (C-1) TIPO C4



PD 3518.280 kgPL 478.380 kg





PD 7499.417 kg 37716.488 kgPL 956.760 kg 5262.180 kg

TOTAL 42978.668 kg

= 1534.952 cm2


b x h = 0.30 x 0.50

0.30

A o L tributaria

6TO

5,4,3,2,

piso

1 PISO




COLUMNA DE ESQUINA (A-5) TIPO C4



PD 4983.926 kgPL 767.810 kg





PD 8974.059 kg 50053.746 kgPL 1535.620 kg 8445.910 kg

TOTAL 58499.656 kg

= 2089.273 cm2


b x h = 0.40 x 0.50

0.40

A o L tributaria

6TO

5,4,3,2,

piso

1 PISO




COLUMNA DE ESQUINA (C-5) TIPO C4



PD 5732.231 kgPL 695.310 kg





PD 8183.024 kg 46749.179 kgPL 1390.620 kg 7648.410 kg

TOTAL 54397.589 kg

= 1942.771 cm2


b x h = 0.40 x 0.50

A o L tributaria

6TO

5,4,3,2,

piso

1 PISO




0.40

COLUMNA INTERIOR (B-4) TIPO C1

elemento carga unitaria peso parcial


PD 15068.799 kgPL 1923.940 kg





PD 20084.100 kg 117303.092 kgPL 3847.880 kg 21163.340 kg

TOTAL 138466.432 kg

= 2417.668 cm2

asumiendo un ancho b = 0.400 m

A o L tributaria

6TO

5,4,3,2,

piso

1 PSIO




entonces h = 0.604 masumiendo h = 0.600 m 0.60

b x h = 0.40 x 0.60

0.40

COLUMNA INTERIOR (B-3) TIPO C1



PD 13228.572 kgPL 2321.940 kg





PD 17614.308 kg 103564.745 kgPL 4643.880 kg 25541.340 kg

TOTAL 129106.085 kg

A o L tributaria

AZOTEA

5,4,3,2,

piso

1 PISO




= 2254.233 cm2


b x h = 0.40 x 0.60

0.40

COLUMNA LATERAL (A-3) TIPO C2 Y C3



PD 8925.400 kgPL 1484.800 kg





PD 16226.676 kg 88143.113 kgPL 3217.600 kg 16580.800 kg

TOTAL 104723.913 kg

A o L tributaria

AZOTEA

5,4,3,2,

piso

1 PISO




= 2493.427 cm2


b x h = 0.40 x 0.60

0.40

COLUMNA LATERAL (A-4) TIPO C2 Y C3



PD 9274.058 kgPL 1559.510 kg





A o L tributaria

AZOTEA

5,4,3,2,

piso

1 PISO




PD 16366.002 kg 88825.420 kgPL 3246.740 kg 17282.330 kg

TOTAL 106107.750 kg

= 2526.375 cm2


b x h = 0.40 x 0.60

0.40

COLUMNA LATERAL (C-4) TIPO C2 Y C3



PD 7137.308 kgPL 1126.400 kg



losa 360.000 kg/m2 10.465 m2 3767.508 kg el ancho minimoacabados 100.000 kg/m2 12.349 m2 1234.880 kgtabiqueria 154.867 kg/m2 10.465 m2 1620.726 kgmuro 875.000 kg/m 5.000 m 4375.000 kgviga x-x 300.000 kg/m 1.980 m 594.000 kg

1 PISO

A o L tributaria

AZOTEA

5,4,3,2,

piso

1 PISO




viga y-y 300.000 kg/m 5.550 m 1665.000 kgcolumna 150.000 kg/m 3.700 m 555.000 kg


PD 13812.114 kg 74167.105 kgPL 2469.760 kg 12607.360 kg

TOTAL 86774.465 kg

= 2066.059 cm2


b x h = 0.40 x 0.60

0.40

RESUMEN

COLUMNAS

COLUM. DIMENSIONES ESQUEMA

A-1b 0.40 mh 0.50 m

C-1b 0.30 mh 0.50 m

A-5b 0.40 mh 0.50 m

C-5b 0.40 mh 0.50 m

A-2,C-2b 0.40 m hh 0.60 m

A-3,C-3b 0.40 m bh 0.60 m

A-4,C-4b 0.40 mh 0.60 m

B-1,B-5b 0.40 mh 0.60 m

B-2,3,4b 0.40 mh 0.60 m

1 PISO


V- 101

V- 101

V- 101

V- 101

V- 101

V- 101

V-102

V-102

V-102

V-102

V-102V-102



VIGAS

TIPO DIMENSIONES ESQUEMA

V-101b 0.25 mh 0.50 m

V-102b 0.25 mh 0.50 m h

b

V- 101 V- 10

1

V- 101

V- 101 V- 10

1

V- 101

V-102V-102

V-102V-102



METRADO DE CARGAS

CARGAS UNITARIAS

LOSA MACIZAh t Pe Peso

0.150 m 2400.000 kg/m3 0.360 Tn/m2

h b Pe Peso0.500 m 0.25 m 2400.000 kg/m3 0.300 Tn/m

VIGA V-103h b Pe Peso

0.000 m 0.25 m 2400.000 kg/m3 0.000 Tn/m

COLUMNA C1h b Pe Peso

0.500 m 0.40 m 2400.000 kg/m3 0.480 Tn/m

COLUMNA C2h b Pe Peso

0.600 m 0.40 m 2400.000 kg/m3 0.576 Tn/m

MURO H=2.5 mh t Pe Peso

2.500 m 0.250 m 14 kg/(m2xcm) 0.875 Tn/m

MURO H=1.2 mh t Pe Peso

1.200 m 0.250 m 14 kg/(m2xcm) 0.420 Tn/m

MURO H=0.90mh t Pe Peso

0.900 m 0.250 m 14 kg/(m2xcm) 0.315 Tn/m

MURO H=0.60mh t Pe Peso

0.600 m 0.250 m 14 kg/(m2xcm) 0.210 Tn/m

TABIQUERIA 0.155 Tn/m2 para 1 y 2 pisoTABIQUERIA 0.191 Tn/m2 para 3,4,5 y 6 piso

ACABADOS 0.100 Tn/m2

SOBRECARGA VIVIENDA 0.200 Tn/m2

SOBRECARGA AZOTEA 0.100 Tn/m2

VIGA V-101 y V-102



PESO POR PISO

LOSA MACIZANIVEL AREA peso peso en piso TOTAL

2,3,4,5,6 148.448 m 0.360Tn/m2 53.441 Tn321.964 Tn1ro 152.108 m 0.360Tn/m2 54.759 Tn

NIVEL LONG.PROM peso peso en piso6to 106.250 m 0.300 Tn/m 31.875 Tn

1,2,3,4,5 126.250 m 0.300 Tn/m 37.875 TnNIVEL LONG.PROM peso peso en piso TOTAL

221.250 Tn

COLUMNA C1 peso altura Nro peso entrep.6to 0.480 Tn/m 2.50 m 4 4.800 TnENTREP.5,4,3,2 0.480 Tn/m 2.50 m 4 4.800 TnENTREP.1 0.480 Tn/m 3.70 m 4 7.104 TnCOLUMNA C2 peso altura Nro peso entrep.6to 0.576 Tn/m 2.50 m 11 15.840 TnENTREP.5,4,3,2 0.576 Tn/m 2.50 m 11 15.840 TnENTREP.1 0.576 Tn/m 3.70 m 11 23.443 TnCOLUMNA C3 peso altura Nro peso entrep.

0.000 Tn TOTAL0.000 Tn

133.747 Tn0.000 Tn

ACABADOSNIVEL AREA peso peso en piso TOTAL

2,3,4,5,6 175.010 m 0.100Tn/m2 17.501 Tn105.372 Tn1ero 178.670 m 0.100Tn/m2 17.867 Tn

TABIQUERIANIVEL AREA peso peso en piso TOTAL

2,3,4,5 148.448 m 0.191Tn/m2 28.361 Tn137.001 Tn1ero 152.108 m 0.155Tn/m2 23.556 Tn

MURO 2.5 m peso longitud Nro peso entrep.1 y 2 0.875 Tn/m 57.20 m 50.050 TnENTREP 6,5,4,3 0.875 Tn/m 53.68 m 46.970 TnMURO 1.2 m peso longitud Nro peso entrep.1 y 2 0.420 Tn/m 0.00 m 0.000 TnENTREP 6,5,4,3 0.420 Tn/m 0.00 m 0.000 TnMURO 0.6 m peso longitud Nro peso entrep. TOTAL1 y 2 0.210 Tn/m 0.00 m 0.000 Tn

237.930 TnENTREP 6,5,4,3 0.210 Tn/m 0.00 m 0.000 Tn

SOBRECARGA

NIVEL AREA peso peso en piso TOTAL6to 175.010 m 0.100Tn/m2 17.501 Tn

193.243 Tn2,3,4,5 175.010 m 0.200Tn/m2 35.002 Tn

1ro 178.670 m 0.200Tn/m2 35.734 Tn

VIGA V-101 y V-102



CARGA TOTAL 1350.507 Tn

RESUMEN DEL METRADO DE CARGAS

PISO 1 PISO 2 PISO 3 PISO 4 PISO 5 PISO 6 PISO

ELEMENTO UNIDADLOSA MACIZA Tn 54.76 53.44 53.44 53.44 53.44 53.44VIGAS Tn 37.88 37.88 37.88 37.88 37.88 37.88COLUMNAS Tn 30.55 20.64 20.64 20.64 20.64 20.64ACABADOS Tn 17.87 17.50 17.50 17.50 17.50 17.50TABIQUERIA Tn 23.56 28.36 28.36 28.36 28.36 0.00MUROS Tn 0.00 50.05 46.97 46.97 46.97 46.97S/C Tn 35.73 35.00 35.00 35.00 35.00 17.50PESO Tn 200.34 242.87 239.79 239.79 239.79 193.93AREA m2 178.67 175.01 175.01 175.01 175.01 175.01

PESO TOTAL (Tn) 1350.507

PESO/m2 Tn/m2 ### ### ### ### ### ###

MASA Tn*s2/m ### ### ### ### ### ###

PISO 1 PISO 2 PISO 3 PISO 4 PISO 5 PISO 6 PISO PROMEDIO

ELEMENTO UNIDADVIGAS Tn/m2 0.212 0.216 0.216 0.216 0.216 0.216 0.216COLUMNAS Tn/m2 0.171 0.118 0.118 0.118 0.118 0.118 0.127MUROS Tn/m2 0.000 0.286 0.268 0.268 0.268 0.268 0.227

INGENIERIA ANTISISMICA UNPRG-ING CIVIL


W6 = 147.00 Tn

2.75 m

W5 = 213.54 Tn

2.75 m

W4 = 213.54 Tn

2.75 m

W3 = 213.54 Tn

2.75 m

W2 = 212.68 Tn

2.75 m

W1 = 218.63 Tn

Wt = 1218.92 Tn2.88 m

1.50 m

- categoria de la edificacion: C : edificaciones comunes- porcentaje de sobrecarga: 25.00 %- % sobrecarga azotea: 25.00 %

ANALISIS SISMICO ESTATICO: (NORMA E-030)



AREA Xm YmAo 200 5 10A1 -3.688 1.73 15A2 -13.04 7.78 14.2A3 -8.108 4.38 7

Xm= 4.891 mYm= 9.717 m

X

A2

A1

A3

Ao



Y

AREA Xm YmAo 200 5 10A1 -3.688 1.73 15A2 -13.04 7.78 14.2A3 -8.108 4.38 7A4 -1.84 1.05 8.38A5 -1.82 9.05 8.05

Xm= 4.888 mYm= 9.750 m

X

A2

A1

A3

Ao

A4A5



Y

CALCULO DE LAS RIGIDECES POR WILBUR

DIRECCION X-X: PORTICO EJE 1-1 Y 5-5

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m

1.50 m

A B C



la altura de las columnas del primer piso es: h= 3.875 m

PRIMER PISO TERCER PISO

SEGUNDO PISO CUARTO PISO



QUINTO PISO SEXTO PISO

formulas de Wilbur empleadas para el calculo de las rigideces laterales

PARA EL PRIMER NIVEL PARA EL SEXTO NIVEL

considerando columnas empotradas en la cimentacion

PARA EL SEGUNDO NIVEL

considerando columnas empotradas

en la cimentacion

PARA LOS PISOS INTERMEDIOS

𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)

𝑹_𝟐=(𝟒𝟖∗𝑬)/(𝑫_𝟐∗𝒉_𝟐 )𝑫_𝟐=(𝟒∗𝒉_𝟐)/(∑▒ 〖𝑲𝒄〗 _𝟐 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)+(𝒉_𝟐+𝒉_𝟑)/(∑▒ 〖𝑲𝒕〗 _𝟐 )

𝑹_𝟔=(𝟒𝟖∗𝑬)/(𝑫_𝟔∗𝒉_𝟔 )𝑫_𝟔=(𝟒∗𝒉_𝟔)/(∑▒ 〖𝑲𝒄〗 _𝟔 )+( ∗〖𝟐 𝒉〗 _𝟓+𝒉_𝟔)/(∑▒ 〖𝑲𝒕〗 _𝟓 )+𝒉_𝟔/(∑▒ 〖𝑲𝒕〗 _𝟔 )



- m,n,o identifican a 3 niveles consecutivos de abajo hacia arriba- Ktn = rigidez a flexion de vigas- Kcn= rigidez a flexion de columnas- hn= altura de entrepiso

DIRECCION X-X: PORTICO EJE 2-2, 3-3 Y 4-4

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m

1.50 m

𝑹_𝒏=(𝟒𝟖∗𝑬)/(𝑫_𝒏∗𝒉_𝒏 )𝑫_𝟐=(𝟒∗𝒉_𝒏)/(∑▒ 〖𝑲𝒄〗 _𝒏 )+(𝒉_𝒎+𝒉_𝒏)/(∑▒ 〖𝑲𝒕〗 _𝒎 )+(𝒉_𝒏+𝒉_𝒐)/(∑▒ 〖𝑲𝒕〗 _𝒏 )



A B C












𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)

𝑹_𝟐=(𝟒𝟖∗𝑬)/(𝑫_𝟐∗𝒉_𝟐 )




en la cimentacion



DIRECCION Y-Y: PORTICO EJE A-A Y C-C

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m





1.50 m

1 2 3 4 5









𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐) 𝑹_𝟔=(𝟒𝟖∗𝑬)/(𝑫_𝟔∗𝒉_𝟔 )






en la cimentacion



DIRECCION Y-Y: PORTICO EJE B-B

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)






2.88 m

1.50 m

1 2 3 4 5















en la cimentacion



RESUMEN DE RIGIDECES

R6=63.032R5=63.032R4=63.032R3=63.032 R2=64.881R1=62.05

R6=28.24R5=28.24R4=28.24R3=28.24R2=27.892R1=22.159

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=64.867R5=64.867R4=64.867R3=64.867R2=68.055R1=69.062

YRY Ym

R6=63.032R5=63.032R4=63.032R3=63.032R2=64.881R1=62.05

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)






color rojo rigideces direccion x-xcolor azul rigideces direccion y-y

CALCULO DEL CORTANTE BASALDEPARTAMENTO : LAMBAYEQUEPROVINCIA: LAMBAYEQUEDISTRITO : LAMBAYEQUEUSO : VIVIENDA COMERCIO

SISTEMA CONSTRUCTIVO: PORTICOS DE CONCRETO ARMADOALTURA TOTAL (hn): 16.625 m

XR

X

Xm

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=28.24R5=28.24R4=28.24R3=28.24R2=27.892R1=22.159



DISTRIBUCION DE FUERZA SISMICA EN ALTURA SIN CONSIDERAR TORSION

45.746 Tn 45.746 Tn

55.461 Tn 101.208 Tn

44.469 Tn 145.677 Tn

𝑭𝒊=(𝑾𝒊∗𝒉𝒊∗(𝑽−𝑭𝒂))/(∑▒ ∗〖𝑾𝒊 𝒉𝒊〗 )



33.477 Tn 179.153 Tn

22.394 Tn 201.547 Tn

11.766 Tn 213.313 Tn

- T > 0.7 seg - no cumplen las distorsiones: son mayores a 0.007

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




CALCULO DEL NUEVO CORTANTE BASAL Y FUERZAS EN ALTURA CON T=0.99 seg

la fuerza Fa se adicionara al ultimo nivel


52.144 Tn 52.144 Tn

46.925 Tn 99.070 Tn

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




37.625 Tn 136.694 Tn

28.324 Tn 165.019 Tn

18.947 Tn 183.966 Tn

9.955 Tn 193.921 Tn


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))





la fuerza Fa se adicionara al ultimo nivel


55.505 Tn 55.505 Tn

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




52.231 Tn 107.737 Tn

41.879 Tn 149.616 Tn

31.527 Tn 181.143 Tn

21.090 Tn 202.232 Tn

11.081 Tn 213.313 Tn


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




CORTANTES TRASLACIONALES

55.505 Tn 55.505 Tn 6.573 cm

52.231 Tn 107.737 Tn 6.187 cm

41.879 Tn 149.616 Tn 5.437 cm

31.527 Tn 181.143 Tn 4.397 cm

21.090 Tn 202.232 Tn 3.137 cm

11.081 Tn 213.313 Tn 1.762 cm

FUERZAS CORTANTES DESPLAZAMIENTOSTEORICOS X-X

TORSION EN PLANTA

R6=28.24R5=28.24R4=28.24R3=28.24R2=27.892R1=22.159

YRY Ym

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




R6=63.032R5=63.032R4=63.032R3=63.032 R2=64.881R1=62.05

R6=28.24R5=28.24R4=28.24R3=28.24R2=27.892R1=22.159

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=64.867R5=64.867R4=64.867R3=64.867R2=68.055R1=69.062

XR

X

Xm

R6=63.032R5=63.032R4=63.032R3=63.032R2=64.881R1=62.05

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=29.093R5=29.093R4=29.093R3=29.093R2=30.692R1=25.59

R6=28.24R5=28.24R4=28.24R3=28.24R2=27.892R1=22.159











(FUERZA SISMICA TRASLACIONAL)





CORTANTES FINALES CONSIDERANDO TRASLACION YTORSION






60.302 Tn 60.302 Tn 7.126 cm

56.745 Tn 117.047 Tn 6.707 cm

45.498 Tn 162.546 Tn 5.893 cm

34.252 Tn 196.797 Tn 4.792 cm

22.939 Tn 219.736 Tn 3.393 cm

11.174 Tn 230.910 Tn 1.907 cm

FUERZAS CORTANTES DESPLAZAMIENTOS

CORTANTES Y DEPLAZAMIENTOS CONSIDERANDO CORTANTE TRASLACIONAL Y TORSIONAL PARA TODA LA ESTRUCTURA EN DIRECCION X-X

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))



TEORICOS X-X

FACTOR DE SEGURIDAD AL VOLTEO EN DIRECCION X-X

MOMENTOS DESESTABILIZADORES

nivel Fi ubicación Mi6 60.302 Tn 18.125 m 1092.974 Tn.m5 56.745 Tn 15.375 m 872.454 Tn.m4 45.498 Tn 12.625 m 574.412 Tn.m3 34.252 Tn 9.875 m 338.239 Tn.m2 22.939 Tn 7.125 m 163.440 Tn.m1 11.174 Tn 4.375 m 48.886 Tn.m

suma 3090.406 Tn.m

MOMENTOS ESTABILIZADORES

nivel Pi ubicación Mi6 147.000 Tn 4.712 m 692.664 Tn.m5 213.540 Tn 4.712 m 1006.200 Tn.m4 213.540 Tn 4.712 m 1006.200 Tn.m3 213.540 Tn 4.712 m 1006.200 Tn.m2 212.680 Tn 4.712 m 1002.148 Tn.m1 218.630 Tn 4.709 m 1029.529 Tn.m

suma 5742.942 Tn.m

Fsv= 5742.942 Tn.m = 1.86 > 1.5 : OK3090.406 Tn.m




57.196 Tn 57.196 Tn 4.863 cm

53.823 Tn 111.019 Tn 4.564 cm

43.155 Tn 154.174 Tn 3.982 cm

32.488 Tn 186.662 Tn 3.175 cm

21.845 Tn 208.507 Tn 2.197 cm

12.271 Tn 220.778 Tn 1.143 cm

FUERZAS CORTANTES DESPLAZAMIENTOSTEORICOS Y-Y

CORTANTES Y DEPLAZAMIENTOS CONSIDERANDO CORTANTE TRASLACIONAL Y TORSIONAL PARA TODA LA ESTRUCTURA EN DIRECCION Y-Y

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))



FACTOR DE SEGURIDAD AL VOLTEO EN DIRECCION Y-Y



suma 2939.188 Tn.m



suma 11877.353 Tn.m

Fsv= 11877.353 Tn.m = 4.04 > 1.5 : OK2939.188 Tn.m



DISTRIBUCION DE FUERZAS PARA CADA PORTICO

DIRECCION X -X

PORTICO EJE 1-1 PORTICO EJE 2-2

12.094 Tn 12.424 Tn

12.143 Tn 11.691 Tn

9.736 Tn 9.374 Tn

7.330 Tn 7.057 Tn

4.612 Tn 5.042 Tn

2.130 Tn 2.632 Tn


11.410 Tn 11.741 Tn



10.737 Tn 11.049 Tn

8.609 Tn 8.859 Tn

6.481 Tn 6.669 Tn

4.469 Tn 4.620 Tn

2.379 Tn 2.272 Tn

PORTICO EJE 5-5

11.823 Tn

11.125 Tn

8.920 Tn

6.715 Tn

4.195 Tn

1.761 Tn

DIRECCION Y -Y

PORTICO EJE A-A PORTICO EJE B - B

18.876 Tn 18.972 Tn



17.762 Tn 17.853 Tn

14.242 Tn 14.315 Tn

10.721 Tn 10.776 Tn

7.143 Tn 7.314 Tn

3.888 Tn 4.069 Tn

PORTICO EJE C-C

19.349 Tn

18.207 Tn

14.599 Tn

10.990 Tn

7.389 Tn

4.313 Tn

INGENIERIA ANTISIMICA UNPRG - ING CIVIL

Juan Manuel chero Damian

W6 = 147.00 Tn

2.75 m

W5 = 213.54 Tn

2.75 m

W4 = 213.54 Tn

2.75 m

W3 = 213.54 Tn

2.75 m

W2 = 212.68 Tn

2.75 m

W1 = 218.63 Tn

Wt = 1218.92 Tn2.88 m

1.50 m

- categoria de la edificacion: C : edificaciones comunes- porcentaje de sobrecarga: 25.00 %- % sobrecarga azotea: 25.00 %

ANALISIS SISMICO ESTATICO: (NORMA E-030)



AREA Xm YmAo 200 5 10A1 -3.688 1.73 15A2 -13.04 7.78 14.2A3 -8.108 4.38 7

Xm= 4.891 mYm= 9.717 m

X

A2

A1

A3

Ao



Y

AREA Xm YmAo 200 5 10A1 -3.688 1.73 15A2 -13.04 7.78 14.2A3 -8.108 4.38 7A4 -1.84 1.05 8.38A5 -1.82 9.05 8.05

Xm= 4.888 mYm= 9.750 m

X

A2

A1

A3

Ao

A4A5



Y

CALCULO DE LAS RIGIDECES POR WILBUR


2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m

1.50 m

A B C




ancho colaborante para las vigas perimetrales

TERCER PISO

ADOPTANDO :B = 0.65 m

PRIMER PISO

CUARTO PISO

SEGUNDO PISO









en la cimentacion


𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)







DIRECCION X-X: PORTICO EJE 2-2

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m

1.50 m




A B C


para el tramo A-B las vigas tendran un ancho colaborante de seccion en T y para el tramo B-Ctendra una ancho colaborante de seccion en L

TRAMO A-B TRAMO B-C

ADOPTANDO :B = 1.30 m ADOPTANDO :B = 0.55 m

PRIMER PISO SEGUNDO PISO



TERCER PISO SEXTO PISO

CUARTO PISO

PARA EL PRIMER NIVEL




en la cimentacion

QUINTO PISO PARA LOS PISOS INTERMEDIOS


𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)





- m,n,o ident. a 3 niveles consecutivos de abajo hacia arriba- Ktn = rigidez a flexion de vigas- Kcn= rigidez a flexion de columnas- hn= altura de entrepiso

PARA EL SEXTO NIVEL


2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

2.88 m





1.50 m

A B C


LA VIGA TENDRA UN ANCHO COLABORANTEDE SECCION EN T

TERCER PISO


CUARTO PISO

PRIMER PISO



QUINTO PISO

SEGUNDO PISO

SEXTO PISO






en la cimentacion

𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)







DIRECCION Y-Y: PORTICO EJE A-A

2.75 m

2.75 m

2.75 m

2.75 m

2.75 m

𝑫_𝟐=(𝟒∗𝒉_𝟐)/(∑▒ 〖𝑲𝒄〗 _𝟐 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)+(𝒉_𝟐+𝒉_𝟑)/(∑▒ 〖𝑲𝒕〗 _𝟐 )𝑹_𝒏=(𝟒𝟖∗𝑬)/(𝑫_𝒏∗𝒉_𝒏 )𝑫_𝟐=(𝟒∗𝒉_𝒏)/(∑▒ 〖𝑲𝒄〗 _𝒏 )+(𝒉_𝒎+𝒉_𝒏)/(∑▒ 〖𝑲𝒕〗 _𝒎 )+(𝒉_𝒏+𝒉_𝒐)/(∑▒ 〖𝑲𝒕〗 _𝒏 )



2.88 m

1.50 m

1 2 3 4 5


ancho colaborante para las vigas perimetrales

TERCER PISO


PRIMER PISO

CUARTO PISO



SEGUNDO PISO

QUINTO PISO





en la cimentacion

SEXTO PISOPARA LOS PISOS INTERMEDIOS

- m,n,o identifican a 3 niveles consecutivos de abajo hacia arriba- Ktn = rigidez a flexion de vigas


𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)





- Kcn= rigidez a flexion de columnas- hn= altura de entrepiso

PARA EL SEXTO NIVEL

DIRECCION Y-Y: PORTICO EJE B-B

2.75 m

2.75 m

2.75 m

2.75 m




2.75 m

2.88 m

1.50 m

1 2 3 4 5


PRIMER PISOLA VIGA TENDRA UN ANCHO COLABORANTEDE SECCION EN T 1-2 Y 4-5


SEGUNDO PISO



LA VIGA TENDRA UN ANCHO COLABORANTEDE SECCION EN L 2-3 Y 3-4

TERCER PISO

SEXTO PISO

CUARTO PISO



CUARTO PISO


considerando columnas empotradas en la cimentacionPARA EL SEGUNDO NIVEL


en la cimentacion


QUINTO PISO


PARA EL SEXTO NIVEL

DIRECCION Y-Y: PORTICO EJE C-C

2.75 m

2.75 m

2.75 m


𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)𝑹_𝟐=(𝟒𝟖∗𝑬)/(𝑫_𝟐∗𝒉_𝟐 )𝑫_𝟐=(𝟒∗𝒉_𝟐)/(∑▒ 〖𝑲𝒄〗 _𝟐 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)+(𝒉_𝟐+𝒉_𝟑)/(∑▒ 〖𝑲𝒕〗 _𝟐 )


𝑹_𝟔=(𝟒𝟖∗𝑬)/(𝑫_𝟔∗𝒉_𝟔 ) 𝑫_𝟔=(𝟒∗𝒉_𝟔)/(∑▒ 〖𝑲𝒄〗 _𝟔 )+( ∗〖𝟐 𝒉〗 _𝟓+𝒉_𝟔)/(∑▒ 〖𝑲𝒕〗 _𝟓 )+𝒉_𝟔/(∑▒ 〖𝑲𝒕〗 _𝟔 )



2.75 m

2.75 m

2.88 m

1.50 m

1 2 3 4 5


ancho colaborante para las vigas perimetrales TERCER PISO


para el tramo 2-3 se considerara seccion rectangular

PRIMER PISO



PRIMER PISO

CUARTO PISO

SEGUNDO PISO

QUINTO PISO


SEXTO PISO




en la cimentacion


𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)






PARA EL SEXTO NIVEL

RESUMEN DE RIGIDECES

𝑫_𝟐=(𝟒∗𝒉_𝟐)/(∑▒ 〖𝑲𝒄〗 _𝟐 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)+(𝒉_𝟐+𝒉_𝟑)/(∑▒ 〖𝑲𝒕〗 _𝟐 )𝑹_𝒏=(𝟒𝟖∗𝑬)/(𝑫_𝒏∗𝒉_𝒏 )𝑫_𝟐=(𝟒∗𝒉_𝒏)/(∑▒ 〖𝑲𝒄〗 _𝒏 )+(𝒉_𝒎+𝒉_𝒏)/(∑▒ 〖𝑲𝒕〗 _𝒎 )+(𝒉_𝒏+𝒉_𝒐)/(∑▒ 〖𝑲𝒕〗 _𝒏 )


R6=37.746R5=37.746R4=37.746R3=37.746R2=36.717R1=25.465

YRY Ym




CALCULO DEL CORTANTE BASALDEPARTAMENTO : LIMAPROVINCIA: LIMADISTRITO : LOS OLIVOSUSO : VIVIENDA COMERCIO


ESTUDIO DE SUELO:- Grava arenosa bien graduada

R6=91.849R5=91.849R4=91.849R3=91.849R2=91.209R1=74.885

R6=50.989R5=50.989R4=50.989R3=50.989R2=51.836R1=47.41

R6=106.182R5=106.182R4=106.82R3=106.82R2=105.768R1=88.315

XR

X

Xm

R6=84.941R5=84.941R4=84.941R3=84.941R2=84.879R1=72.035

R6=58.218R5=58.218R4=58.218R3=58.218R2=58.436R1=50.663

R6=58.218R5=58.218R4=58.218R3=58.218R2=58.436R1=50.663

R6=37.746R5=37.746R4=37.746R3=37.746R2=36.717R1=25.465



- capacidad admisible = 4 kg/cm2- profundidad minima de cimentacion = 1.20 m





27.517 Tn 27.517 Tn

33.360 Tn 60.877 Tn

26.748 Tn 87.625 Tn

20.748 Tn 107.761 Tn

13.470 Tn 121.231 Tn

7.077 Tn 128.308 Tn


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))





la la la fuerza Fa se adicionara al ultimo nivel


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




20.370 Tn 20.370 Tn

19.524 Tn 39.894 Tn

15.654 Tn 55.548 Tn

11.785 Tn 67.332 Tn

7.883 Tn 75.216 Tn

4.142 Tn 79.357 Tn


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))





la la la fuerza Fa se adicionara al ultimo nivel


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




21.760 Tn 21.760 Tn

21.209 Tn 42.970 Tn

17.006 Tn 59.975 Tn

12.802 Tn 72.777 Tn

8.564 Tn 81.341 Tn

4.499 Tn 85.840 Tn


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))




CORTANTES TRASLACIONALES

21.760 Tn 21.760 Tn 1.579 cm

21.209 Tn 42.970 Tn 1.489 cm

17.006 Tn 59.975 Tn 1.312 cm

12.802 Tn 72.777 Tn 1.065 cm

8.564 Tn 81.341 Tn 0.766 cm

4.499 Tn 85.840 Tn 0.430 cm


𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))



TORSION EN PLANTA

R6=91.849R5=91.849R4=91.849R3=91.849R2=91.209R1=74.885

R6=37.746R5=37.746R4=37.746R3=37.746R2=36.717R1=25.465

R6=50.989R5=50.989R4=50.989R3=50.989R2=51.836R1=47.41

R6=106.182R5=106.182R4=106.82R3=106.82R2=105.768R1=88.315

XR

YR

X

Y Ym

Xm

R6=84.941R5=84.941R4=84.941R3=84.941R2=84.879R1=72.035

R6=58.218R5=58.218R4=58.218R3=58.218R2=58.436R1=50.663

R6=58.218R5=58.218R4=58.218R3=58.218R2=58.436R1=50.663

R6=37.746R5=37.746R4=37.746R3=37.746R2=36.717R1=25.465




CENTRO DE MASAS

R6=37.746R5=37.746R4=37.746R3=37.746R2=36.717R1=25.465









(FUERZA SISMICA TRASLACIONAL)





CORTANTES FINALES CONSIDERANDO TRASLACION Y TORSION






23.706 Tn 23.706 Tn 1.724 cm

23.175 Tn 46.880 Tn 1.626 cm

18.578 Tn 65.458 Tn 1.433 cm

CORTANTES Y DEPLAZAMIENTOS CONSIDERANDO CORTANTE TRASLACIONAL Y TORSIONAL PARA TODA LA ESTRUCTURA EN DIRECCION X-X

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))



13.985 Tn 79.443 Tn 1.163 cm

9.368 Tn 88.811 Tn 0.836 cm

4.964 Tn 93.775 Tn 0.470 cm


FACTOR DE SEGURIDAD AL VOLTEO EN DIRECCION X-X



suma 1247.101 Tn.m



suma 5742.942 Tn.m

Fsv= 5742.942 Tn.m = 4.61 > 1.5 : OK1247.101 Tn.m




22.352 Tn 22.352 Tn 1.392 cm

21.848 Tn 44.200 Tn 1.313 cm

17.517 Tn 61.717 Tn 1.156 cm

CORTANTES Y DEPLAZAMIENTOS CONSIDERANDO CORTANTE TRASLACIONAL Y TORSIONAL PARA TODA LA ESTRUCTURA EN DIRECCION Y-Y

𝑻=𝟐𝝅√((∑▒〖𝑷𝒊∗〖〗𝑫𝒊 ^𝟐 〗 )/(𝒈∗∑▒〖𝑭𝒊∗𝑫〗𝒊 ))



13.187 Tn 74.904 Tn 0.938 cm

8.840 Tn 83.744 Tn 0.674 cm

4.806 Tn 88.550 Tn 0.376 cm

FUERZAS CORTANTES DESPLAZAMIENTOSTEORICOS Y-Y

FACTOR DE SEGURIDAD AL VOLTEO EN DIRECCION Y-Y



suma 1176.428 Tn.m



suma 11877.353 Tn.m

Fsv= 11877.353 Tn.m = 10.10 > 1.5 : OK1176.428 Tn.m



DISTRIBUCION DE FUERZAS PARA CADA PORTICO

DIRECCION X -X


4.047 Tn 5.086 Tn

3.957 Tn 4.972 Tn

3.172 Tn 3.986 Tn

2.388 Tn 3.000 Tn

1.557 Tn 2.123 Tn



0.622 Tn 1.762 Tn


5.300 Tn 5.516 Tn

5.181 Tn 5.392 Tn

4.154 Tn 4.323 Tn

3.127 Tn 3.254 Tn

2.110 Tn 2.183 Tn

1.202 Tn 1.115 Tn

PORTICO EJE 5-5

3.756 Tn

3.672 Tn

2.944 Tn

2.216 Tn

1.394 Tn

0.263 Tn

DIRECCION Y -Y



PORTICO EJE A-A PORTICO EJE B - B

7.318 Tn 8.194 Tn

7.153 Tn 8.009 Tn

5.735 Tn 6.422 Tn

4.317 Tn 4.834 Tn

2.863 Tn 3.236 Tn

1.423 Tn 1.713 Tn

PORTICO EJE C-C

6.840 Tn

6.686 Tn

5.361 Tn

4.035 Tn

2.741 Tn

1.670 Tn



PORTICO EJE 1-1

4.047 Tn 4.047 Tn

3.957 Tn 8.004 Tn

3.172 Tn 11.176 Tn

2.388 Tn 13.564 Tn

1.557 Tn 15.121 Tn

0.622 Tn 15.743 Tn

1 2 3

PARA EL PRIMER PISO PARA LOS DEMAS PISOS

688.172 969.697825.806 1163.636688.172 969.697

713.193977.338

DIAGRAMA DE MOMENTOS PARA CADA PORTICO UTILIZANDO EL METODO DE BOWMAN



CORTANTE POR ENTREPISO Y POR COLUMNAS Y VIGAS

1.707 Tn 2.340 Tn V PARA COLUMNAS

Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn

0.854 Tn 0.854 Tn 1.170 Tn V PARA VIGAS

0.854 Tn 1.170 Tn 1.170 TnVt= 4.0470 Tn

2.024 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


1.688 Tn 2.314 Tn 2.314 TnVt= 8.0040 Tn

4.002 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.357 Tn 3.231 Tn 3.231 TnVt= 11.1760 Tn

5.588 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.861 Tn 3.921 Tn 3.921 TnVt= 13.5640 Tn

6.782 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.190 Tn 4.371 Tn 4.371 TnVt= 15.1210 Tn

7.561 Tn

3.321 Tn 4.551 Tn

2.88 m

2.460 Tn 2.952 Tn 2.460 Tn V PARA COLUMNAS

1.660 Tn 1.660 Tn 2.275 TnVc= 7.8715 Tn

4.120 Tn 2.275 Tn 4.735 Tn

6.888 Tn V PARA VIGAS

Vt= 7.8715 Tn1.50 m

A B C



DIAGRAMA DE MOMENTOS PARA COLUMNAS

1.53 Tn.m 3.62 Tn.m 2.09 Tn.m

2.75 m

0.82 Tn.m

2.79 Tn.m 6.60 Tn.m 3.82 Tn.m

1.95 Tn.m 1.13 Tn.m

2.75 m

1.86 Tn.m

3.57 Tn.m 8.45 Tn.m 4.89 Tn.m

4.40 Tn.m 2.55 Tn.m

2.75 m

2.92 Tn.m

3.93 Tn.m 9.33 Tn.m 5.39 Tn.m

6.92 Tn.m 4.00 Tn.m

2.75 m

3.93 Tn.m

4.39 Tn.m 10.40 Tn.m 6.01 Tn.m

9.33 Tn.m 5.39 Tn.m

2.75 m

4.39 Tn.m

6.39 Tn.m 10.68 Tn.m 7.34 Tn.m

10.40 Tn.m 6.01 Tn.m

2.88 m

1.50 m

9.58 Tn.m 11.01 Tn.m

16.01 Tn.m

A B C




DIAGRAMA DE MOMENTOS PARA VIGAS

1.25 Tn.m 2.09 Tn.m

2.75 m 1.53 Tn.m 1.71 Tn.m

2.95 Tn.m 4.94 Tn.m

2.75 m 3.61 Tn.m 4.04 Tn.m

4.44 Tn.m 7.43 Tn.m

2.75 m 5.42 Tn.m 6.08 Tn.m

5.61 Tn.m 9.39 Tn.m

2.75 m 6.85 Tn.m 7.68 Tn.m

6.81 Tn.m 11.40 Tn.m

2.75 m 8.32 Tn.m 9.33 Tn.m

8.81 Tn.m 13.35 Tn.m

2.88 m 10.77 Tn.m 10.92 Tn.m

1.50 m

A 5.55 m B 4.05 m C



PORTICO EJE 2-2

5.086 Tn 5.086 Tn

4.972 Tn 10.058 Tn

3.986 Tn 14.044 Tn

3.000 Tn 17.044 Tn

2.123 Tn 19.167 Tn

1.762 Tn 20.929 Tn

1 2 3


1858.065 2618.1821858.065 2618.1821858.065 2618.182



906.981914.042



Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


1.267 Tn 1.276 Tn 1.276 TnVt= 5.0860 Tn

2.543 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.505 Tn 2.524 Tn 2.524 TnVt= 10.0580 Tn

5.029 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.497 Tn 3.525 Tn 3.525 TnVt= 14.0440 Tn

7.022 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


4.244 Tn 4.278 Tn 4.278 TnVt= 17.0440 Tn

8.522 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


4.773 Tn 4.810 Tn 4.810 TnVt= 19.1670 Tn

9.584 Tn

5.212 Tn 5.253 Tn

2.88 m


2.606 Tn 2.606 Tn 2.626 TnVc= 10.4645 Tn

6.094 Tn 2.626 Tn 6.114 Tn


Vt= 10.4645 Tn1.50 m



A B C


2.26 Tn.m 4.55 Tn.m 2.28 Tn.m

2.75 m

1.22 Tn.m

4.13 Tn.m 8.30 Tn.m 4.17 Tn.m

2.45 Tn.m 1.23 Tn.m

2.75 m

2.76 Tn.m

5.29 Tn.m 10.62 Tn.m 5.33 Tn.m

5.53 Tn.m 2.78 Tn.m

2.75 m

4.33 Tn.m

5.84 Tn.m 11.72 Tn.m 5.88 Tn.m

8.69 Tn.m 4.36 Tn.m

2.75 m

5.84 Tn.m

6.56 Tn.m 13.18 Tn.m 6.61 Tn.m

11.72 Tn.m 5.88 Tn.m

2.75 m

6.56 Tn.m

9.45 Tn.m 13.52 Tn.m 9.48 Tn.m

13.18 Tn.m 6.61 Tn.m

2.88 m

1.50 m

14.17 Tn.m 14.22 Tn.m



20.27 Tn.m

A B C



1.85 Tn.m 2.28 Tn.m

2.75 m 2.26 Tn.m 1.87 Tn.m

4.38 Tn.m 5.39 Tn.m

2.75 m 5.35 Tn.m 4.41 Tn.m

6.58 Tn.m 8.11 Tn.m

2.75 m 8.05 Tn.m 6.63 Tn.m

8.32 Tn.m 10.24 Tn.m

2.75 m 10.16 Tn.m 8.38 Tn.m

10.14 Tn.m 12.50 Tn.m

2.75 m 12.40 Tn.m 10.22 Tn.m

13.10 Tn.m 16.09 Tn.m

2.88 m 16.01 Tn.m 13.17 Tn.m



1.50 m

A 5.55 m B 4.05 m C

PORTICO EJE 3-3

5.300 Tn 5.300 Tn

5.181 Tn 10.481 Tn

4.154 Tn 14.635 Tn

3.127 Tn 17.762 Tn

2.110 Tn 19.872 Tn

1.202 Tn 21.074 Tn

1 2 3


1858.065 2618.182



1858.065 2618.1821858.065 2618.182

906.9811242.9



Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


1.118 Tn 1.532 Tn 1.532 TnVt= 5.3000 Tn

2.650 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.211 Tn 3.030 Tn 3.030 TnVt= 10.4810 Tn

5.240 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.087 Tn 4.230 Tn 4.230 TnVt= 14.6350 Tn

7.317 Tn

7.493 Tn ### V PARA COLUMNAS

Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.747 Tn 5.134 Tn 5.134 TnVt= 17.7620 Tn

8.881 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


4.192 Tn 5.744 Tn 5.744 TnVt= 19.8720 Tn

9.936 Tn

4.445 Tn 6.092 Tn

2.88 m




2.223 Tn 2.223 Tn 3.046 TnVc= 10.5370 Tn

5.735 Tn 3.046 Tn 6.558 Tn


Vt= 10.5370 Tn1.50 m

A B C


2.00 Tn.m 4.74 Tn.m 2.74 Tn.m

2.75 m

1.08 Tn.m

3.65 Tn.m 8.65 Tn.m 5.00 Tn.m

2.55 Tn.m 1.47 Tn.m

2.75 m

2.43 Tn.m

4.67 Tn.m 11.07 Tn.m 6.40 Tn.m

5.76 Tn.m 3.33 Tn.m

2.75 m

3.82 Tn.m

5.15 Tn.m 12.21 Tn.m 7.06 Tn.m

9.06 Tn.m 5.24 Tn.m

2.75 m

5.15 Tn.m

5.76 Tn.m 13.66 Tn.m 7.90 Tn.m

12.21 Tn.m 7.06 Tn.m

2.75 m

5.76 Tn.m

8.89 Tn.m 13.61 Tn.m 10.17 Tn.m

13.66 Tn.m 7.90 Tn.m

2.88 m



1.50 m

13.33 Tn.m 15.25 Tn.m

20.42 Tn.m

A B C



1.64 Tn.m 2.74 Tn.m

2.75 m 2.00 Tn.m 2.24 Tn.m

3.87 Tn.m 6.47 Tn.m

2.75 m 4.72 Tn.m 5.30 Tn.m

5.81 Tn.m 9.73 Tn.m

2.75 m 7.10 Tn.m 7.96 Tn.m

7.34 Tn.m 12.29 Tn.m

2.75 m 8.97 Tn.m 10.06 Tn.m

8.93 Tn.m 14.96 Tn.m

2.75 m 10.92 Tn.m 12.24 Tn.m

11.99 Tn.m 18.06 Tn.m



2.88 m 14.65 Tn.m 14.78 Tn.m

1.50 m

A 5.55 m B 4.05 m C

PORTICO EJE 4-4

5.516 Tn 5.516 Tn

5.392 Tn 10.908 Tn

4.323 Tn 15.231 Tn

3.254 Tn 18.485 Tn

2.183 Tn 20.668 Tn

1.115 Tn 21.783 Tn

1 2 3




1858.065 2618.1821858.065 2618.1821858.065 2618.182

906.9811242.9



Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


1.164 Tn 1.594 Tn 1.594 TnVt= 5.5160 Tn

2.758 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.301 Tn 3.153 Tn 3.153 TnVt= 10.9080 Tn

5.454 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.213 Tn 4.403 Tn 4.403 TnVt= 15.2310 Tn

7.616 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


3.899 Tn 5.343 Tn 5.343 TnVt= 18.4850 Tn

9.243 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn




4.360 Tn 5.974 Tn 5.974 TnVt= 20.6680 Tn

###4.595 Tn 6.297 Tn

2.88 m


2.297 Tn 2.297 Tn 3.148 TnVc= 10.8915 Tn

5.928 Tn 3.148 Tn 6.779 Tn


Vt= 10.8915 Tn1.50 m

A B C


2.08 Tn.m 4.93 Tn.m 2.85 Tn.m

2.75 m

1.12 Tn.m

3.80 Tn.m 9.00 Tn.m 5.20 Tn.m

2.65 Tn.m 1.53 Tn.m

2.75 m

2.53 Tn.m

4.86 Tn.m 11.52 Tn.m 6.66 Tn.m

6.00 Tn.m 3.47 Tn.m

2.75 m

3.98 Tn.m

5.36 Tn.m 12.71 Tn.m 7.35 Tn.m

9.42 Tn.m 5.45 Tn.m

2.75 m

5.36 Tn.m

5.99 Tn.m 14.21 Tn.m 8.21 Tn.m

12.71 Tn.m 7.35 Tn.m



2.75 m

5.99 Tn.m

9.19 Tn.m 14.07 Tn.m 10.51 Tn.m

14.21 Tn.m 8.21 Tn.m

2.88 m

1.50 m

13.78 Tn.m 15.76 Tn.m

21.10 Tn.m

A B C



1.70 Tn.m 2.85 Tn.m

2.75 m 2.08 Tn.m 2.33 Tn.m

4.02 Tn.m 6.74 Tn.m

2.75 m 4.92 Tn.m 5.51 Tn.m

6.05 Tn.m 10.13 Tn.m

2.75 m 7.39 Tn.m 8.29 Tn.m

7.64 Tn.m 12.80 Tn.m

2.75 m 9.34 Tn.m 10.47 Tn.m



9.29 Tn.m 15.56 Tn.m

2.75 m 11.36 Tn.m 12.73 Tn.m

12.42 Tn.m 18.72 Tn.m

2.88 m 15.18 Tn.m 15.32 Tn.m

1.50 m

A 5.55 m B 4.05 m C

PORTICO EJE 5-5

3.756 Tn 3.756 Tn

3.672 Tn 7.428 Tn

2.944 Tn 10.372 Tn

2.216 Tn 12.588 Tn

1.394 Tn 13.982 Tn

0.263 Tn 14.245 Tn



1 2 3


688.172 969.697825.806 1163.636688.172 969.697

713.193977.338



Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


0.792 Tn 1.086 Tn 1.086 TnVt= 3.7560 Tn

1.878 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


1.567 Tn 2.147 Tn 2.147 TnVt= 7.4280 Tn

3.714 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.188 Tn 2.998 Tn 2.998 TnVt= 10.3720 Tn

5.186 Tn




Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.655 Tn 3.639 Tn 3.639 TnVt= 12.5880 Tn

6.294 Tn


Vc= 0.0000 Tn2.75 m 0.000 Tn 0.000 Tn 0.000 Tn


2.949 Tn 4.042 Tn 4.042 TnVt= 13.9820 Tn

###3.005 Tn 4.118 Tn

2.88 m


1.502 Tn 1.502 Tn 2.059 TnVc= 7.1225 Tn

3.728 Tn 2.059 Tn 4.285 Tn


Vt= 7.1225 Tn1.50 m

A B C


1.42 Tn.m 3.36 Tn.m 1.94 Tn.m

2.75 m

0.76 Tn.m

2.59 Tn.m 6.13 Tn.m 3.54 Tn.m

1.81 Tn.m 1.05 Tn.m

2.75 m

1.72 Tn.m

3.31 Tn.m 7.84 Tn.m 4.53 Tn.m

4.09 Tn.m 2.36 Tn.m

2.75 m

2.71 Tn.m



3.65 Tn.m 8.65 Tn.m 5.00 Tn.m

6.42 Tn.m 3.71 Tn.m

2.75 m

3.65 Tn.m

4.06 Tn.m 9.61 Tn.m 5.56 Tn.m

8.65 Tn.m 5.00 Tn.m

2.75 m

4.06 Tn.m

5.78 Tn.m 9.66 Tn.m 6.64 Tn.m

9.61 Tn.m 5.56 Tn.m

2.88 m

1.50 m

8.67 Tn.m 9.96 Tn.m

14.49 Tn.m

A B C



1.16 Tn.m 1.94 Tn.m

2.75 m 1.42 Tn.m 1.59 Tn.m

2.74 Tn.m 4.59 Tn.m

2.75 m 3.35 Tn.m 3.75 Tn.m

4.12 Tn.m 6.90 Tn.m



2.75 m 5.03 Tn.m 5.64 Tn.m

5.20 Tn.m 8.71 Tn.m

2.75 m 6.36 Tn.m 7.13 Tn.m

6.31 Tn.m 10.56 Tn.m

2.75 m 7.71 Tn.m 8.64 Tn.m

8.05 Tn.m 12.20 Tn.m

2.88 m 9.83 Tn.m 9.98 Tn.m

1.50 m

A 5.55 m B 4.05 m C

PORTICO EJE A-A

7.318 Tn 7.318 Tn

7.153 Tn 14.471 Tn

5.735 Tn 20.206 Tn

4.317 Tn 24.523 Tn



2.863 Tn 27.386 Tn

1.423 Tn 28.809 Tn

1 2 3 4 5


1075.269 1515.1521858.065 2618.1821858.065 2618.1821858.065 2618.1821075.269 1515.152

713.1931058.314908.769668.854889.434


1.318 Tn 1.132 Tn 0.833 Tn 1.108 Tn V PARA COLUMNAS

Vc= 2.9272 Tn2.75 m 0.407 Tn 0.704 Tn 0.704 Tn 0.704 Tn 0.407 Tn

0.659 Tn 0.659 Tn 0.566 Tn 0.417 Tn 0.554 Tn V PARA VIGAS1.067 Tn 0.566 Tn 0.417 Tn 0.554 Tn 0.961 Tn Vt= 4.3908 Tn

1.929 Tn 1.687 Tn 1.675 Tn






3.815 Tn 3.335 Tn 3.311 TnVt= 8.6826 Tn




5.326 Tn 4.657 Tn 4.624 Tn




6.464 Tn 5.652 Tn 5.611 Tn




8.051 Tn 6.312 Tn 6.266 Tn

2.595 Tn 2.228 Tn 1.640 Tn 2.181 Tn

2.88 m

2.807 Tn 4.851 Tn 4.851 Tn 4.851 Tn 2.807 Tn V PARA COLUMNAS1.297 Tn 1.297 Tn 1.114 Tn 0.820 Tn 1.090 Tn Vc= 20.1663 Tn4.104 Tn 1.114 Tn 0.820 Tn 1.090 Tn 3.897 Tn


Vt= 8.6427 Tn1.50 m

1 2 3 4 5



1.91 Tn.m 3.45 Tn.m 3.01 Tn.m 2.99 Tn.m ###

2.75 m

1.03 Tn.m

3.48 Tn.m 6.29 Tn.m 5.50 Tn.m 5.46 Tn.m ###

1.86 Tn.m 1.62 Tn.m 1.61 Tn.m 0.93 Tn.m

2.75 m



2.32 Tn.m

4.45 Tn.m 8.06 Tn.m 7.04 Tn.m 6.99 Tn.m ###

4.20 Tn.m 3.67 Tn.m 3.64 Tn.m 2.09 Tn.m

2.75 m

3.64 Tn.m

4.91 Tn.m 8.89 Tn.m 7.77 Tn.m 7.72 Tn.m ###

6.59 Tn.m 5.76 Tn.m 5.72 Tn.m 3.28 Tn.m

2.75 m

4.91 Tn.m

6.63 Tn.m ### 8.68 Tn.m 8.62 Tn.m ###

8.89 Tn.m 7.77 Tn.m 7.72 Tn.m 4.43 Tn.m

2.75 m

6.63 Tn.m

6.36 Tn.m ### ### ### ###

### 8.68 Tn.m 8.62 Tn.m 4.95 Tn.m

2.88 m

1.50 m

9.54 Tn.m ### ### 9.06 Tn.m

###

A B C C C

la altura de las columnas del primer piso es: h= ###


1.56 Tn.m 1.89 Tn.m 1.59 Tn.m ###

2.75 m 1.91 Tn.m 1.89 Tn.m 1.59 Tn.m 1.41 Tn.m

3.69 Tn.m 4.46 Tn.m 3.75 Tn.m ###



2.75 m 4.51 Tn.m 4.46 Tn.m 3.75 Tn.m 3.32 Tn.m

5.54 Tn.m 6.71 Tn.m 5.64 Tn.m ###

2.75 m 6.77 Tn.m 6.71 Tn.m 5.64 Tn.m 5.00 Tn.m

7.00 Tn.m 8.48 Tn.m 7.13 Tn.m ###

2.75 m 8.56 Tn.m 8.48 Tn.m 7.13 Tn.m 6.31 Tn.m

9.45 Tn.m ### 8.66 Tn.m ###

2.75 m ### ### 8.66 Tn.m 7.67 Tn.m

### ### ### ###

2.88 m ### ### ### 8.99 Tn.m

1.50 m

1 2 3 4 5


PORTICO EJE B-B

8.194 Tn 8.194 Tn



8.009 Tn 16.203 Tn

6.422 Tn 22.625 Tn

4.834 Tn 27.459 Tn

3.236 Tn 30.695 Tn

1.713 Tn 32.408 Tn

1 2 3 4 5


1858.065 2618.1821858.065 2618.1821858.065 2618.1821858.065 2618.1821858.065 2618.182

713.1931329.773908.769668.8541117.575







2.023 Tn 1.619 Tn 1.747 Tn




4.000 Tn 3.202 Tn 3.454 Tn




5.585 Tn 4.470 Tn 4.823 Tn




6.778 Tn 5.426 Tn 5.853 Tn




8.746 Tn 6.065 Tn 6.543 Tn

3.212 Tn 2.195 Tn 1.616 Tn 2.700 Tn

2.88 m



Vt= 9.7224 Tn1.50 m

1 2 3 4 5



2.62 Tn.m 3.62 Tn.m 2.89 Tn.m 3.12 Tn.m ###



2.75 m

1.41 Tn.m

4.79 Tn.m 6.60 Tn.m 5.28 Tn.m 5.70 Tn.m ###

1.95 Tn.m 1.56 Tn.m 1.68 Tn.m 1.29 Tn.m

2.75 m

3.19 Tn.m

6.13 Tn.m 8.45 Tn.m 6.76 Tn.m 7.29 Tn.m ###

4.40 Tn.m 3.52 Tn.m 3.80 Tn.m 2.91 Tn.m

2.75 m

5.01 Tn.m

6.76 Tn.m 9.32 Tn.m 7.46 Tn.m 8.05 Tn.m ###

6.91 Tn.m 5.53 Tn.m 5.97 Tn.m 4.57 Tn.m

2.75 m

6.76 Tn.m

9.17 Tn.m ### 8.34 Tn.m 9.00 Tn.m ###

9.32 Tn.m 7.46 Tn.m 8.05 Tn.m 6.17 Tn.m

2.75 m

9.17 Tn.m

9.52 Tn.m ### 9.99 Tn.m ### ###

### 8.34 Tn.m 9.00 Tn.m 6.89 Tn.m

2.88 m

1.50 m

### ### ### ###

###

A B C C C



2.15 Tn.m 1.47 Tn.m 1.17 Tn.m ###



2.75 m 2.62 Tn.m 1.47 Tn.m 1.17 Tn.m 1.96 Tn.m

5.07 Tn.m 3.47 Tn.m 2.75 Tn.m ###

2.75 m 6.20 Tn.m 3.47 Tn.m 2.75 Tn.m 4.63 Tn.m

7.63 Tn.m 5.22 Tn.m 4.14 Tn.m ###

2.75 m 9.32 Tn.m 5.22 Tn.m 4.14 Tn.m 6.95 Tn.m

9.64 Tn.m 6.60 Tn.m 5.23 Tn.m ###

2.75 m ### 6.60 Tn.m 5.23 Tn.m 8.79 Tn.m

### 8.31 Tn.m 6.36 Tn.m ###

2.75 m ### 8.31 Tn.m 6.36 Tn.m ###

### 7.96 Tn.m 6.27 Tn.m ###

2.88 m ### 7.96 Tn.m 6.27 Tn.m ###

1.50 m

1 2 3 4 5


PORTICO EJE C-C



PORTICO EJE C-C

PORTICO EJE C-C

6.840 Tn 6.840 Tn

6.686 Tn 13.526 Tn

5.361 Tn 18.887 Tn

4.035 Tn 22.922 Tn

2.741 Tn 25.663 Tn

1.670 Tn 27.333 Tn

1 2 3 4 5


1075.269 1515.1521858.065 2618.1821858.065 2618.1821858.065 2618.1821075.269 1515.152

713.1931058.314566.123668.854889.434







1.705 Tn 1.454 Tn 1.663 Tn




3.372 Tn 2.876 Tn 3.288 Tn




4.709 Tn 4.016 Tn 4.591 Tn




5.715 Tn 4.874 Tn 5.572 Tn




7.391 Tn 5.457 Tn 6.239 Tn

2.727 Tn 1.459 Tn 1.723 Tn 2.292 Tn

2.88 m



Vt= 8.1999 Tn1.50 m

1 2 3 4 5





1.90 Tn.m 3.05 Tn.m 2.60 Tn.m 2.97 Tn.m ###

2.75 m

1.02 Tn.m

3.47 Tn.m 5.56 Tn.m 4.75 Tn.m 5.43 Tn.m ###

1.64 Tn.m 1.40 Tn.m 1.60 Tn.m 0.92 Tn.m

2.75 m

2.31 Tn.m

4.44 Tn.m 7.12 Tn.m 6.07 Tn.m 6.94 Tn.m ###

3.71 Tn.m 3.16 Tn.m 3.62 Tn.m 2.08 Tn.m

2.75 m

3.63 Tn.m

4.90 Tn.m 7.86 Tn.m 6.70 Tn.m 7.66 Tn.m ###

5.83 Tn.m 4.97 Tn.m 5.68 Tn.m 3.26 Tn.m

2.75 m

4.90 Tn.m

6.85 Tn.m ### 7.50 Tn.m 8.58 Tn.m ###

7.86 Tn.m 6.70 Tn.m 7.66 Tn.m 4.40 Tn.m

2.75 m

6.85 Tn.m

6.24 Tn.m ### 9.60 Tn.m ### ###

### 7.50 Tn.m 8.58 Tn.m 4.92 Tn.m

2.88 m

1.50 m

9.36 Tn.m ### ### 8.86 Tn.m

###

A B C C C





1.55 Tn.m 1.49 Tn.m 1.58 Tn.m ###

2.75 m 1.90 Tn.m 1.49 Tn.m 1.58 Tn.m 1.40 Tn.m

3.68 Tn.m 3.53 Tn.m 3.73 Tn.m ###

2.75 m 4.49 Tn.m 3.53 Tn.m 3.73 Tn.m 3.30 Tn.m

5.53 Tn.m 5.31 Tn.m 5.60 Tn.m ###

2.75 m 6.75 Tn.m 5.31 Tn.m 5.60 Tn.m 4.96 Tn.m

6.98 Tn.m 6.71 Tn.m 7.08 Tn.m ###

2.75 m 8.53 Tn.m 6.71 Tn.m 7.08 Tn.m 6.27 Tn.m

9.61 Tn.m 8.41 Tn.m 8.61 Tn.m ###

2.75 m ### 8.41 Tn.m 8.61 Tn.m 7.63 Tn.m

### 9.83 Tn.m 9.96 Tn.m ###

2.88 m ### 9.83 Tn.m 9.96 Tn.m 8.86 Tn.m

1.50 m

1 2 3 4 5




DIMENSIONAMIENTO DE PLACAS

esfuerzo adm. vs= 6.53 kg/cm²Vbasal= 128308.000 kgAnecesaria= 3.341 m2

area de columnas: b h A (m2) cantidad A (total)0.3 0.5 0.150 m2 4 0.600 m20.4 0.6 0.240 m2 11 2.640 m2

TOTAL 3.240 m2

area de placas necesaria: 0.101 m2- espesor de placa adoptado : 0.15 m- longitud necesaria : 0.67 m en cada dirección

se adoptaran dos pares de placas en cada direccion con dimensiones de:

b = 0.15 m numero de placas: 4 (ver plano)L = 1.50 m

altura de entre piso: h= 2.75 m

- PESO A ADICIONAR POR PLACA A CADA NIVEL: P = 1.48 Tn por placa- inercia de cada placa I = 4218750.0 cm4 por placa

NIVEL ALTURA PESO ANTERIOR NUEVO PESO6 2.75 m 147.00 Tn 149.97 Tn5 2.75 m 213.54 Tn 219.48 Tn4 2.75 m 213.54 Tn 219.48 Tn3 2.75 m 213.54 Tn 219.48 Tn2 2.75 m 212.68 Tn 218.62 Tn1 2.88 m 218.63 Tn 224.57 Tn

TOTAL 1218.92 Tn 1251.59 Tn

CALCULO DEL NUEVO PESO DE LA ESTRUCTURA TENIENDO EN CUENTA EL PESO DE LAS PLACAS

𝐴=(1.7∗𝑉𝑏𝑎𝑠𝑎𝑙)/(.85∗0.53∗√(𝑓^′ 𝑐))



CALCULO DEL NUEVO CORTANTE BASAL

DEPARTAMENTO : LIMAPROVINCIA: LIMADISTRITO : LOS OLIVOSUSO : VIVIENDA COMERCIO


ESTUDIO DE SUELO:- Grava arenosa bien graduada- capacidad admisible = 4 kg/cm2- profundidad minima de cimentacion = 1.20 m

VALOR ESPECIFICACION

Z 0.4 ZONA 3U 1 EDIFICACION COMUNS1 1 SUELO MUY RIGIDOTp 0.4 SUELO MUY RIGIDOhn 16.625 m ALTURA DE EDIFICACIONCt 45 DUALT 0.369 PERIODO FUNDAMENTAL <0.7C 2.707 TOMAMOS C=2.5R 7 CONCRETO ARMADO: DUALC/R 0.387 ES MAYOR QUE 0.125

FACTOR 0.142857PESO 1251.594 TnV 178.799 Tn

FUERZA SISMICA POR PISO

NIVEL hi (m) Pixhi INC CORT.

6 149.97 16.63 2493.2072 0.213 38.12 38.125 219.48 13.88 3045.2668 0.260 46.56 84.684 219.48 11.13 2441.7004 0.209 37.33 122.023 219.48 8.38 1838.134 0.157 28.11 150.122 218.62 5.63 1229.7171 0.105 18.80 168.931 224.57 2.88 645.65098 0.055 9.87 178.80

TOTAL 1251.59 11693.677 178.80

COEF. SISMICO

Pi (Tn)

F. SISM.

𝑭𝒊=(𝑷𝒊∗𝒉𝒊∗(𝑽−𝑭𝒂))/(∑▒ ∗〖𝑷𝒊 𝒉𝒊〗 )

PR

ZUSCV



Fa= 0 dado que T < 0.7

CALCULO DE LA NUEVA RIGIDEZ LATERAL TENIENDO EN CUENTA LA RIGIDEZ DE LAS PLACAS POR EL METODO DE WILBUR



RIGIDEZ LATERAL DEL PORTICO 2-2

- RIGIDEZ DE COLUMNAS PARA EL SEXTO NIVEL

PARA PRIMER PISOA 1858.065 cm4B 1858.065 cm4C 1858.065 cm4

PLACA 9642.857 cm4 15217.052 cm4

PARA LOS DEMAS PISOS RIGIDECES LATERALES PARA CADA NIVELA 2618.182 cm4B 2618.182 cm4C 2618.182 cm4 NIVEL ALTURA D RIGIDEZ LATERAL

PLACA 15340.909 cm4 23195.455 cm4 6 2.75 m 0.651 58238.332 kg/cm5 2.75 m 0.651 58238.332 kg/cm

- RIGIDEZ DE VIGAS 4 2.75 m 0.651 58238.332 kg/cm3 2.75 m 0.651 58238.332 kg/cm

PARA TODOS LOS PISOS 2 2.75 m 0.580 65404.340 kg/cmAB 906.981 cm4 1 4.38 m 0.346 68996.280 kg/cmBC 914.042 cm4 1821.023 cm4





en la cimentacion



𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)







RIGIDEZ LATERAL DEL PORTICO 4 - 4

- RIGIDEZ DE COLUMNAS PARA EL SEXTO NIVEL

PARA PRIMER PISOA 1858.065 cm4B 1858.065 cm4C 1858.065 cm4

PLACA 9642.857 cm4 15217.052 cm4

PARA LOS DEMAS PISOS RIGIDECES LATERALES PARA CADA NIVELA 2618.182 cm4B 2618.182 cm4C 2618.182 cm4 NIVEL ALTURA D RIGIDEZ LATERAL

PLACA 15340.909 cm4 23195.455 cm4 6 2.75 m 0.559 67863.465 kg/cm5 2.75 m 0.559 67863.465 kg/cm

- RIGIDEZ DE VIGAS 4 2.75 m 0.559 67863.465 kg/cm3 2.75 m 0.559 67863.465 kg/cm

PARA TODOS LOS PISOS 2 2.75 m 0.512 74145.868 kg/cmAB 906.981 cm4 1 4.38 m 0.323 73729.942 kg/cmBC 1242.900 cm4 2149.881 cm4





en la cimentacion



𝑫_𝟐=(𝟒∗𝒉_𝒏)/(∑▒ 〖𝑲𝒄〗 _𝒏 )+(𝒉_𝒎+𝒉_𝒏)/(∑▒ 〖𝑲𝒕〗 _𝒎 )+(𝒉_𝒏+𝒉_𝒐)/(∑▒ 〖𝑲𝒕〗 _𝒏 )

𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)


𝑹_𝒏=(𝟒𝟖∗𝑬)/(𝑫_𝒏∗𝒉_𝒏 )





RIGIDEZ LATERAL DEL PORTICO A - A

- RIGIDEZ DE COLUMNAS- m,n,o ident. a 3 niveles consecutivos de abajo hacia arriba

PARA PRIMER PISO - Ktn = rigidez a flexion de vigas1 1075.269 cm4 - Kcn= rigidez a flexion de columnas2 1858.065 cm4 - hn= altura de entrepiso3 1858.065 cm44 1858.065 cm45 1075.269 cm4

PLACA 9642.857 cm4 17367.590 cm4

PARA LOS DEMAS PISOS PARA EL SEXTO NIVEL1 1515.152 cm42 2618.182 cm43 2618.182 cm44 2618.182 cm45 1515.152 cm4

PLACA 15340.909 cm4 26225.759 cm4

- RIGIDEZ DE VIGAS RIGIDECES LATERALES PARA CADA NIVEL

PARA TODOS LOS PISOS12 1058.314 cm4 NIVEL ALTURA D RIGIDEZ LATERAL23 908.769 cm4 6 2.75 m 0.354 107188.006 kg/cm34 668.854 cm4 5 2.75 m 0.354 107188.006 kg/cm45 889.434 cm4 3525.371 cm4 4 2.75 m 0.354 107188.006 kg/cm

3 2.75 m 0.354 107188.006 kg/cm2 2.75 m 0.341 111186.297 kg/cm1 4.38 m 0.244 97722.180 kg/cm







𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)

𝑹_𝟐=(𝟒𝟖∗𝑬)/(𝑫_𝟐∗𝒉_𝟐 )




en la cimentacion


RIGIDEZ LATERAL DEL PORTICO C - C

- RIGIDEZ DE COLUMNAS- m,n,o ident. a 3 niveles consecutivos de abajo hacia arriba

PARA PRIMER PISO - Ktn = rigidez a flexion de vigas1 1075.269 cm4 - Kcn= rigidez a flexion de columnas2 1858.065 cm4 - hn= altura de entrepiso3 1858.065 cm44 1858.065 cm45 1075.269 cm4

PLACA 9642.857 cm4 17367.590 cm4

PARA LOS DEMAS PISOS PARA EL SEXTO NIVEL1 1515.152 cm42 2618.182 cm43 2618.182 cm44 2618.182 cm45 1515.152 cm4

PLACA 15340.909 cm4 26225.759 cm4

- RIGIDEZ DE VIGAS RIGIDECES LATERALES PARA CADA NIVEL

PARA TODOS LOS PISOS12 1058.314 cm4 NIVEL ALTURA D RIGIDEZ LATERAL23 566.123 cm4 6 2.75 m 0.388 97897.434 kg/cm34 668.854 cm4 5 2.75 m 0.388 97897.434 kg/cm45 889.434 cm4 3182.725 cm4 4 2.75 m 0.388 97897.434 kg/cm

3 2.75 m 0.388 97897.434 kg/cm2 2.75 m 0.369 102922.192 kg/cm1 4.38 m 0.255 93652.986 kg/cm







𝑹_𝟏=(𝟒𝟖∗𝑬)/(𝑫_𝟏∗𝒉_𝟏 ) 𝑫_𝟏=(𝟒∗𝒉_𝟏)/(∑▒ 〖𝑲𝒄〗 _𝟏 )+(𝒉_𝟏+𝒉_𝟐)/(∑▒ 〖𝑲𝒕〗 _𝟏 +(∑▒ 〖𝑲𝒄〗 _𝟏 )/𝟏𝟐)





en la cimentacion


RESUMEN DE RIGIDECES LATERALES PARA CADA PORTICO Y PARA TODA LA ESTRUCTURA

DIRECCION X-X

EJE 1 2 3 4 5NIVEL

6 37745.719 kg/cm 58238.332 kg/cm 58218.359 kg/cm 67863.465 kg/cm 37745.719 kg/cm 259.812 Tn/cm5 37745.719 kg/cm 58238.332 kg/cm 58218.359 kg/cm 67863.465 kg/cm 37745.719 kg/cm 259.812 Tn/cm4 37745.719 kg/cm 58238.332 kg/cm 58218.359 kg/cm 67863.465 kg/cm 37745.719 kg/cm 259.812 Tn/cm3 37745.719 kg/cm 58238.332 kg/cm 58218.359 kg/cm 67863.465 kg/cm 37745.719 kg/cm 259.812 Tn/cm2 36716.659 kg/cm 65404.340 kg/cm 58435.676 kg/cm 74145.868 kg/cm 36716.659 kg/cm 271.419 Tn/cm1 25464.962 kg/cm 68996.280 kg/cm 50662.930 kg/cm 73729.942 kg/cm 25464.962 kg/cm 244.319 Tn/cm

DIRECCION Y-Y

EJE A B CNIVEL

6 107188.006 kg/cm 106181.822 kg/cm 97897.434 kg/cm 311.267 Tn/cm5 107188.006 kg/cm 106181.822 kg/cm 97897.434 kg/cm 311.267 Tn/cm4 107188.006 kg/cm 106181.822 kg/cm 97897.434 kg/cm 311.267 Tn/cm3 107188.006 kg/cm 106181.822 kg/cm 97897.434 kg/cm 311.267 Tn/cm2 111186.297 kg/cm 105768.035 kg/cm 102922.192 kg/cm 319.877 Tn/cm1 97722.180 kg/cm 88314.949 kg/cm 93652.986 kg/cm 279.690 Tn/cm

RIGIDEZ TOTAL X-X

RIGIDEZ TOTAL Y-Y





DETERMINACION DE LAS FORMAS MODALES

gravedad = 9.81 m/s^2

DIRECCION X - X

1471.180 KN1.4997 Tn

F62548.752 KN/cm

2153.086 KN2.1948 Tn

F52548.752 KN/cm

2153.086 KN2.1948 Tn

F42548.752 KN/cm

2153.086 KN2.1948 Tn

F32548.752 KN/cm

2144.627 KN2.1862 Tn

F22662.622 KN/cm

2203.073 KN2.2457 Tn

F1

2396.770 KN/cm

5059.393 -2662.622 0.000 0.000 0.000 0.000

-2662.622 5211.374 -2548.752 0.000 0.000 0.000[K] = 0.000 -2548.752 5097.503 -2548.752 0.000 0.000

0.000 0.000 -2548.752 5097.503 -2548.752 0.000

0.000 0.000 0.000 -2548.752 5097.503 -2548.752

0.000 0.000 0.000 0.000 -2548.752 2548.752



2.2457 0 0 0 0 00 2.1862 0 0 0 0

[m] = 0 0 2.1948 0 0 00 0 0 2.1948 0 00 0 0 0 2.1948 00 0 0 0 0 1.4997

=

5059.39 -2.246w² -2662.62 0.00 0.00 0.00 0.00

-2662.62 5211.37 -2.186w² -2548.75 0.00 0.00 0.00

= 0.00 -2548.75 5097.50 -2.195w² -2548.75 0.00 0.00

0.00 0.00 -2548.75 5097.50 -2.195w² -2548.75 0.00

0.00 0.00 0.00 -2548.75 5097.50 -2.195w² -2548.75

0.00 0.00 0.00 0 -2548.75 2548.75 -1.500w²

= 7.7845E+01 * w^12 -1.0356E+06 * w^10 + 5.1465E+09 * w^8 -1.1730E+13 * w^6 + 1.2013E+16 * w^4 -4.4704E+18 * w^2 + 2.6930E+20

MODIFICAR VALORES

valores característicos

w1 = 8.596 rad/s 73.888 rad/sw2 = 25.091 rad/s 629.539 rad/sw3 = 39.951 rad/s 1596.116 rad/sw4 = 52.511 rad/s 2757.443 rad/sw5 = 61.651 rad/s 3800.831 rad/sw6 = 66.678 rad/s 4445.984 rad/s

|[K] - W²[m]|

w1² =w2² =w3² =w4² =w5² =w6² =



FORMAS MODALES PARA: W1^2 = 73.888 rad/s

ɸ11 4893.459 -2662.622 0.000 0.000 0.000 0.000

ɸ12 -2662.622 5049.843 -2548.752 0.000 0.000 0.000

=ɸ13

x0.000 -2548.752 4935.335 -2548.752 0.000 0.000

= 0ɸ14 0.000 0.000 -2548.752 4935.335 -2548.752 0.000

ɸ15 0.000 0.000 0.000 -2548.752 4935.335 -2548.752

ɸ16 0.000 0.000 0.000 0.000 -2548.752 2437.944

4893.459 *ɸ11 + -2662.622 *ɸ12 + 0.000 *ɸ13 + 0.000 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

-2662.622 *ɸ11 + 5049.843 *ɸ12 + -2548.752 *ɸ13 + 0.000 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + -2548.752 *ɸ12 + 4935.335 *ɸ13 + -2548.752 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + -2548.752 *ɸ13 + 4935.335 *ɸ14 + -2548.752 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + 0.000 *ɸ13 + -2548.752 *ɸ14 + 4935.335 *ɸ15 + -2548.752 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + 0.000 *ɸ13 + 0.000 *ɸ14 + -2548.752 *ɸ15 + 2437.944 *ɸ16 = 0

1.000

ɸ12 = 1.838

ɸ13 = 2.597

ɸ14 = 3.190

ɸ15 = 3.581

ɸ16 = 3.744

h ɸ16.625 3.74413.875 3.58111.125 3.1908.375 2.5975.625 1.8382.875 1.000

0 0.000

asumiendo: ɸ11 =

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18




ɸ21 3645.609 -2662.622 0.000 0.000 0.000 0.000

ɸ22 -2662.622 3835.098 -2548.752 0.000 0.000 0.000

=ɸ23

x0.000 -2548.752 3715.799 -2548.752 0.000 0.000

= 0ɸ24 0.000 0.000 -2548.752 3715.799 -2548.752 0.000

ɸ25 0.000 0.000 0.000 -2548.752 3715.799 -2548.752

ɸ26 0.000 0.000 0.000 0.000 -2548.752 1604.648

3645.609 *ɸ21 + -2662.622 *ɸ22 + 0.000 *ɸ23 + 0.000 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

-2662.622 *ɸ21 + 3835.098 *ɸ22 + -2548.752 *ɸ23 + 0.000 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + -2548.752 *ɸ22 + 3715.799 *ɸ23 + -2548.752 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + -2548.752 *ɸ23 + 3715.799 *ɸ24 + -2548.752 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + 0.000 *ɸ23 + -2548.752 *ɸ24 + 3715.799 *ɸ25 + -2548.752 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + 0.000 *ɸ23 + 0.000 *ɸ24 + -2548.752 *ɸ25 + 1604.648 *ɸ26 = 0

1.000

ɸ22 = 1.369

ɸ23 = 1.016

ɸ24 = 0.111

ɸ25 = -0.853

ɸ26 = -1.355

h ɸ16.625 -1.35513.875 -0.85311.125 0.1118.375 1.0165.625 1.3692.875 1.000

asumiendo: ɸ21 =

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



0.000 0.000


ɸ31 1474.926 -2662.622 0.000 0.000 0.000 0.000

ɸ32 -2662.622 1722.002 -2548.752 0.000 0.000 0.000

=ɸ33

x0.000 -2548.752 1594.368 -2548.752 0.000 0.000

= 0ɸ34 0.000 0.000 -2548.752 1594.368 -2548.752 0.000

ɸ35 0.000 0.000 0.000 -2548.752 1594.368 -2548.752

ɸ36 0.000 0.000 0.000 0.000 -2548.752 155.098

1474.926 *ɸ31 + -2662.622 *ɸ32 + 0.000 *ɸ33 + 0.000 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

-2662.622 *ɸ31 + 1722.002 *ɸ32 + -2548.752 *ɸ33 + 0.000 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + -2548.752 *ɸ32 + 1594.368 *ɸ33 + -2548.752 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + -2548.752 *ɸ33 + 1594.368 *ɸ34 + -2548.752 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + 0.000 *ɸ33 + -2548.752 *ɸ34 + 1594.368 *ɸ35 + -2548.752 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + 0.000 *ɸ33 + 0.000 *ɸ34 + -2548.752 *ɸ35 + 155.098 *ɸ36 = 0

1.000

ɸ32 = 0.554

ɸ33 = -0.670

ɸ34 = -0.973

ɸ35 = 0.062

ɸ36 = 1.012

h ɸ16.625 1.01213.875 0.06211.125 -0.9738.375 -0.670

asumiendo: ɸ31 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



5.625 0.5542.875 1.0000.000 0.000


ɸ41 -1133.115 -2662.622 0.000 0.000 0.000 0.000

ɸ42 -2662.622 -816.848 -2548.752 0.000 0.000 0.000

=ɸ43

x0.000 -2548.752 -954.496 -2548.752 0.000 0.000

= 0ɸ44 0.000 0.000 -2548.752 -954.496 -2548.752 0.000

ɸ45 0.000 0.000 0.000 -2548.752 -954.496 -2548.752

ɸ46 0.000 0.000 0.000 0.000 -2548.752 -1586.513

-1133.115 *ɸ41 + -2662.622 *ɸ42 + 0.000 *ɸ43 + 0.000 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

-2662.622 *ɸ41 + -816.848 *ɸ42 + -2548.752 *ɸ43 + 0.000 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + -2548.752 *ɸ42 + -954.496 *ɸ43 + -2548.752 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + -2548.752 *ɸ43 + -954.496 *ɸ44 + -2548.752 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + 0.000 *ɸ43 + -2548.752 *ɸ44 + -954.496 *ɸ45 + -2548.752 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + 0.000 *ɸ43 + 0.000 *ɸ44 + -2548.752 *ɸ45 + -1586.513 *ɸ46 = 0

1.000

ɸ42 = -0.426

ɸ43 = -0.908

ɸ44 = 0.766

ɸ45 = 0.622

ɸ46 = -0.998

h ɸ16.625 -0.99813.875 0.622

asumiendo: ɸ41 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



11.125 0.7668.375 -0.9085.625 -0.4262.875 1.0000.000 0.000


ɸ51 -3476.295 -2662.622 0.000 0.000 0.000 0.000

ɸ52 -2662.622 -3097.864 -2548.752 0.000 0.000 0.000

=ɸ53

x0.000 -2548.752 -3244.510 -2548.752 0.000 0.000

= 0ɸ54 0.000 0.000 -2548.752 -3244.510 -2548.752 0.000

ɸ55 0.000 0.000 0.000 -2548.752 -3244.510 -2548.752

ɸ56 0.000 0.000 0.000 0.000 -2548.752 -3151.253

-3476.295 *ɸ51 + -2662.622 *ɸ52 + 0.000 *ɸ53 + 0.000 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

-2662.622 *ɸ51 + -3097.864 *ɸ52 + -2548.752 *ɸ53 + 0.000 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + -2548.752 *ɸ52 + -3244.510 *ɸ53 + -2548.752 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + -2548.752 *ɸ53 + -3244.510 *ɸ54 + -2548.752 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + 0.000 *ɸ53 + -2548.752 *ɸ54 + -3244.510 *ɸ55 + -2548.752 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + 0.000 *ɸ53 + 0.000 *ɸ54 + -2548.752 *ɸ55 + -3151.253 *ɸ56 = 0

1.000

ɸ52 = -1.306

ɸ53 = 0.542

ɸ54 = 0.615

ɸ55 = -1.326

ɸ56 = 1.072

h ɸ

asumiendo: ɸ51 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



16.625 1.07213.875 -1.32611.125 0.6158.375 0.5425.625 -1.3062.875 1.0000.000 0.000


ɸ61 -4925.142 -2662.622 0.000 0.000 0.000 0.000

ɸ62 -2662.622 -4508.274 -2548.752 0.000 0.000 0.000

=ɸ63

x0.000 -2548.752 -4660.484 -2548.752 0.000 0.000

= 0ɸ64 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000

ɸ65 0.000 0.000 0.000 -2548.752 -4660.484 -2548.752

ɸ66 0.000 0.000 0.000 0.000 -2548.752 -4118.772

-4925.142 *ɸ61 + -2662.622 *ɸ62 + 0.000 *ɸ63 + 0.000 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

-2662.622 *ɸ61 + -4508.274 *ɸ62 + -2548.752 *ɸ63 + 0.000 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + -2548.752 *ɸ62 + -4660.484 *ɸ63 + -2548.752 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + -2548.752 *ɸ63 + -4660.484 *ɸ64 + -2548.752 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + 0.000 *ɸ63 + -2548.752 *ɸ64 + -4660.484 *ɸ65 + -2548.752 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + 0.000 *ɸ63 + 0.000 *ɸ64 + -2548.752 *ɸ65 + -4118.772 *ɸ66 = 0

1.000

ɸ62 = -1.850

ɸ63 = 2.227

ɸ64 = -2.223

ɸ65 = 1.837

ɸ66 = -1.137

asumiendo: ɸ61 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18



h ɸ16.625 -1.13713.875 1.83711.125 -2.2238.375 2.2275.625 -1.8502.875 1.0000.000 0.000

DETERMINACION DE LOS FACTORES DE PARTICIPACION MODAL

NORMALIZACION DE LOS MODOS

2.246* 1.000² + 2.186* 1.838² + 2.195* 2.597² + 2.195* 3.190² + 2.195* 3.581² + 1.500* 3.744²= 9.794073

2.246* 1.000² + 2.186* 1.369² + 2.195* 1.016² + 2.195* 0.111² + 2.195* -0.853² + 1.500* -1.355²= 3.603708

2.246* 1.000² + 2.186* 0.554² + 2.195* -0.670² + 2.195* -0.973² + 2.195* 0.062² + 1.500* 1.012²= 2.743349

2.246* 1.000² + 2.186* -0.426² + 2.195* -0.908² + 2.195* 0.766² + 2.195* 0.622² + 1.500* -0.998²= 2.842909

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18

〖 𝑖ɸ 〗^𝑛= /ɸ√(∑▒〖 ∗〖〖 ɸ𝑖〗 ^2 〗 )

√(∑▒ ∗〖𝑚𝑖 〖 ɸ1〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ2〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ3〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ4〗^2 〗 )=



2.246* 1.000² + 2.186* -1.306² + 2.195* 0.542² + 2.195* 0.615² + 2.195* -1.326² + 1.500* 1.072²= 3.609522

2.246* 1.000² + 2.186* -1.850² + 2.195* 2.227² + 2.195* -2.223² + 2.195* 1.837² + 1.500* -1.137²= 6.387536

0.102 0.277 0.365 0.352 0.277 0.1570.188 0.380 0.202 -0.150 -0.362 -0.2900.265 0.282 -0.244 -0.319 0.150 0.3490.326 0.031 -0.355 0.269 0.170 -0.3480.366 -0.237 0.022 0.219 -0.367 0.2880.382 -0.376 0.369 -0.351 0.297 -0.178

FACTORES DE PARTICIPACION MODAL

FPM1 = 2.246* 0.102 + 2.186* 0.188 + 2.195* 0.265 + 2.195* 0.326 + 2.195* 0.366 + 1.500* 0.382 = 3.3120FPM2 = 2.246* 0.277 + 2.186* 0.380 + 2.195* 0.282 + 2.195* 0.031 + 2.195* -0.237 + 1.500* -0.376 = 1.0565FPM3 = 2.246* 0.365 + 2.186* 0.202 + 2.195* -0.244 + 2.195* -0.355 + 2.195* 0.022 + 1.500* 0.369 = 0.5474FPM4 = 2.246* 0.352 + 2.186* -0.150 + 2.195* -0.319 + 2.195* 0.269 + 2.195* 0.219 + 1.500* -0.351 = 0.3057FPM5 = 2.246* 0.277 + 2.186* -0.362 + 2.195* 0.150 + 2.195* 0.170 + 2.195* -0.367 + 1.500* 0.297 = 0.1747FPM6 = 2.246* 0.157 + 2.186* -0.290 + 2.195* 0.349 + 2.195* -0.348 + 2.195* 0.288 + 1.500* -0.178 = 0.0844

DETERMINACION DE LA ACELERACION ESPECTRAL


Z 0.4 ZONA 3

COEF. SISMICO

√(∑▒ ∗〖𝑚𝑖 〖 ɸ4〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ5〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ6〗^2 〗 )=

〖 1ɸ〗^𝑛=

〖 2ɸ〗^𝑛=

〖 3ɸ〗^𝑛=

〖 4ɸ〗^𝑛=

〖 5ɸ〗^𝑛=

〖 6ɸ〗^𝑛=

〖〗𝐹𝑃𝑀 _𝑖=∑▒∗〖〖𝑚𝑖 𝑖ɸ 〗^𝑛

〗

𝑆𝑎𝑖=𝑍𝑈𝑆𝐶/𝑅∗𝑔



U 1 EDIFICACION COMUNS2 1 SUELO MUY RIGIDOTp 0.4 SUELO MUY RIGIDOR 7 CONCRETO ARMADO: DUAL

w T C Sai8.596 rad/s 0.73096 1.368 76.690 cm/s²

25.091 rad/s 0.25042 2.500 140.143 cm/s²39.951 rad/s 0.15727 2.500 140.143 cm/s²52.511 rad/s 0.11965 2.500 140.143 cm/s²61.651 rad/s 0.10192 2.500 140.143 cm/s²66.678 rad/s 0.09423 2.500 140.143 cm/s²

DETERMINACION DE LA FUERZA SISMICA

2.2457 0.1021 58.240 KN2.1862 0.1876 104.195 KN

F1 = 3.312 * 2.1948*

0.2651 * 76.690 cm/s² = 147.796 KN2.1948 0.3257 181.581 KN2.1948 0.3656 203.813 KN1.4997 0.3822 145.593 KN

2.2457 0.2775 92.266 KN2.1862 0.3799 122.978 KN

F2 = 1.056 * 2.1948*

0.2818 * 140.143 cm/s² = 91.573 KN2.1948 0.0309 10.040 KN

𝑇=2𝜋/𝑤 𝐶≤2.5∗𝑇𝑝/𝑇

𝐹𝑖=𝐹𝑃𝑀𝑖∗𝑚𝑖∗〖 𝑖ɸ 〗^𝑛∗𝑆𝑎𝑖



2.1948 -0.2368 -76.936 KN1.4997 -0.3761 -83.500 KN

2.2457 0.3645 62.795 KN2.1862 0.2019 33.862 KN

F3 = 0.547 * 2.1948*

-0.2444 * 140.143 cm/s² = -41.144 KN2.1948 -0.3548 -59.733 KN2.1948 0.0224 3.778 KN1.4997 0.3688 42.430 KN

2.2457 0.3518 33.848 KN2.1862 -0.1497 -14.022 KN

F4 = 0.306 * 2.1948*

-0.3195 * 140.143 cm/s² = -30.046 KN2.1948 0.2693 25.330 KN2.1948 0.2186 20.560 KN1.4997 -0.3512 -22.569 KN

2.2457 0.2770 15.231 KN2.1862 -0.3617 -19.358 KN

F5 = 0.175 * 2.1948*

0.1502 * 140.143 cm/s² = 8.071 KN2.1948 0.1705 9.160 KN2.1948 -0.3672 -19.732 KN1.4997 0.2970 10.904 KN

2.2457 0.1566 4.160 KN2.1862 -0.2896 -7.491 KN

F6 = 0.084 * 2.1948*

0.3487 * 140.143 cm/s² = 9.055 KN2.1948 -0.3480 -9.037 KN2.1948 0.2876 7.470 KN1.4997 -0.1779 -3.158 KN



NIVEL F1 F2 F3 F4 F5 F6 Fd Fd

1 58.240 KN 92.266 KN 62.795 KN 33.848 KN 15.231 KN 4.160 KN 50.936 KN 98.485 KN 149.421 KN 15.232 Tn2 104.195 KN 122.978 KN 33.862 KN -14.022 KN -19.358 KN -7.491 KN 67.011 KN 124.947 KN 191.958 KN 19.568 Tn3 147.796 KN 91.573 KN -41.144 KN -30.046 KN 8.071 KN 9.055 KN 71.635 KN 136.186 KN 207.821 KN 21.185 Tn4 181.581 KN 10.040 KN -59.733 KN 25.330 KN 9.160 KN -9.037 KN 58.787 KN 145.136 KN 203.923 KN 20.787 Tn5 203.813 KN -76.936 KN 3.778 KN 20.560 KN -19.732 KN 7.470 KN 82.128 KN 164.899 KN 247.027 KN 25.181 Tn6 145.593 KN -83.500 KN 42.430 KN -22.569 KN 10.904 KN -3.158 KN 66.431 KN 131.214 KN 197.645 KN 20.147 Tn

DETERMINACION DEL CORTANTE

12.5159 0.1021 324.581 KN10.2702 0.1876 489.491 KN

Q1 = 3.312 * 8.0840*

0.2651 * 76.690 cm/s² = 544.374 KN5.8892 0.3257 487.234 KN3.6945 0.3656 343.076 KN1.4997 0.3822 145.593 KN

DETERMINACION DE LA FUERZA DE DISEÑO APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

𝐹𝑑=0.25∗∑▒〖 |𝐹𝑖|+0.75√(∑▒〖〗𝐹𝑖^2 )〗

𝑄𝑖=𝐹𝑃𝑀𝑖∗ ∅〖〗𝑖 ^𝑛∗∑▒ ∗〖𝑚𝑖 𝑆𝑎𝑖〗

0.25 iF 20.75 iF



12.5159 0.2775 514.218 KN10.2702 0.3799 577.727 KN

Q2 = 1.056 * 8.0840*

0.2818 * 140.143 cm/s² = 337.289 KN5.8892 0.0309 26.940 KN3.6945 -0.2368 -129.505 KN1.4997 -0.3761 -83.500 KN

12.5159 0.3645 349.970 KN10.2702 0.2019 159.077 KN

Q3 = 0.547 * 8.0840*

-0.2444 * 140.143 cm/s² = -151.546 KN5.8892 -0.3548 -160.281 KN3.6945 0.0224 6.360 KN1.4997 0.3688 42.430 KN

12.5159 0.3518 188.641 KN10.2702 -0.1497 -65.874 KN

Q4 = 0.306 * 8.0840*

-0.3195 * 140.143 cm/s² = -110.668 KN5.8892 0.2693 67.967 KN3.6945 0.2186 34.609 KN1.4997 -0.3512 -22.569 KN

12.5159 0.2770 84.885 KN10.2702 -0.3617 -90.940 KN

Q5 = 0.175 * 8.0840*

0.1502 * 140.143 cm/s² = 29.727 KN5.8892 0.1705 24.580 KN3.6945 -0.3672 -33.214 KN1.4997 0.2970 10.904 KN

12.5159 0.1566 23.186 KN10.2702 -0.2896 -35.193 KN

Q6 = 0.084 * 8.0840*

0.3487 * 140.143 cm/s² = 33.354 KN



Q6 = 0.084 *5.8892 * -0.3480

* 140.143 cm/s² =-24.250 KN

3.6945 0.2876 12.574 KN1.4997 -0.1779 -3.158 KN

DETERMINACION DEL CORTANTE APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

NIVEL Q1 Q2 Q3 Q4 Q5 Q6 Q Q


DETERMINACION DE LOS DESPLAZAMIENTOS

0.1021 0.351 cm 0.2770 0.00178 cm0.1876 0.645 cm -0.3617 -0.00233 cm

X1 = 3.312 * 76.6898 *0.2651 = 0.911 cm X5 = 0.175 * 140.143 *

0.1502 = 0.00097 cm

Q=0.25∗∑▒〖𝑄𝑖 +0.75√(∑▒〖〗𝑄𝑖 ^2 )〗

𝑄𝑖=(𝐹𝑃𝑀𝑖∗ ∅〖〗𝑖 ^𝑛∗𝑆𝑎𝑖)/〖〗𝑤𝑖 ^2

0.25 iQ 20.75 iQ



X1 = 3.312 * 76.6898 * 0.3257=

1.120 cmX5 = 0.175 * 140.143 * 0.1705

=0.00110 cm

73.8879 0.3656 1.257 cm 3800.8307 -0.3672 -0.00237 cm0.3822 1.314 cm 0.2970 0.00191 cm

0.2775 0.065 cm 0.1566 0.00042 cm0.3799 0.089 cm -0.2896 -0.00077 cm

X2 = 1.056 * 140.143*

0.2818 = 0.066 cm X6 = 0.084 * 140.143 *0.3487 = 0.00093 cm

0.0309 0.007 cm -0.3480 -0.00093 cm629.5392 -0.2368 -0.056 cm 4445.9838 0.2876 0.00077 cm

-0.3761 -0.088 cm -0.1779 -0.00047 cm

0.3645 0.018 cm0.2019 0.010 cm

X3 = 0.547 * 140.143 *-0.2444 = -0.012 cm-0.3548 -0.017 cm

1596.1164 0.0224 0.001 cm0.3688 0.018 cm

0.3518 0.005 cm-0.1497 -0.002 cm

X4 = 0.306 * 140.143 *-0.3195 = -0.005 cm0.2693 0.004 cm

2757.4430 0.2186 0.003 cm-0.3512 -0.005 cm

NIVEL X1 X2 X3 X4 X5 X6 X 0.75*R*X

DETERMINACION DE LOS DESPLAZAMIENTOS APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

Q=0.25∗∑▒〖 |𝑋𝑖|+0.75√(∑▒〖〗𝑋𝑖 ^2 )〗0.25 iX 20.75 iX



1 0.3510 cm 0.0653 cm 0.0175 cm 0.0055 cm 0.0018 cm 0.0004 cm 0.1060 cm 0.2681 cm 0.3741 cm 1.9639 cm2 0.6450 cm 0.0894 cm 0.0097 cm -0.0023 cm -0.0023 cm -0.0008 cm 0.1850 cm 0.4885 cm 0.6734 cm 3.5355 cm3 0.9114 cm 0.0663 cm -0.0117 cm -0.0050 cm 0.0010 cm 0.0009 cm 0.2461 cm 0.6854 cm 0.9315 cm 4.8905 cm4 1.1197 cm 0.0073 cm -0.0171 cm 0.0042 cm 0.0011 cm -0.0009 cm 0.2833 cm 0.8399 cm 1.1232 cm 5.8968 cm5 1.2568 cm -0.0557 cm 0.0011 cm 0.0034 cm -0.0024 cm 0.0008 cm 0.3298 cm 0.9435 cm 1.2733 cm 6.6847 cm6 1.3139 cm -0.0884 cm 0.0177 cm -0.0055 cm 0.0019 cm -0.0005 cm 0.3526 cm 0.9878 cm 1.3403 cm 7.0367 cm

DETERMINACION DE LAS DISTORCIONES

NIVEL 0.75*R*X Δr H DISTORSION VERIFICACION

6 7.0367 cm 0.3520 cm 275.0 cm 0.0013 CUMPLE < 0.0075 6.6847 cm 0.7879 cm 275.0 cm 0.0029 CUMPLE < 0.0074 5.8968 cm 1.0063 cm 275.0 cm 0.0037 CUMPLE < 0.0073 4.8905 cm 1.3550 cm 275.0 cm 0.0049 CUMPLE < 0.0072 3.5355 cm 1.5715 cm 275.0 cm 0.0057 CUMPLE < 0.0071 1.9639 cm 1.9639 cm 287.5 cm 0.0068 CUMPLE < 0.007



FORMAS MODALES DIRECCION X-X

PARA W1^2 = 73.888 rad/s PARA W2^2 = 629.539 rad/s PARA W3^2 = 1596.116 rad/s

ɸ h ɸ h ɸ h3.7436 16.625 -1.3552 16.625 1.0118 16.6253.5808 13.875 -0.8532 13.875 0.0616 13.8753.1902 11.125 0.1113 11.125 -0.9733 11.1252.5966 8.375 1.0155 8.375 -0.6704 8.3751.8378 5.625 1.3692 5.625 0.5539 5.6251.0000 2.875 1.0000 2.875 1.0000 2.8750.0000 0 0.0000 0 0.0000 0

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



FORMAS MODALES DIRECCION X-X


ɸ h ɸ h ɸ h-0.9985 16.625 1.0720 16.625 -1.1366 16.6250.6215 13.875 -1.3256 13.875 1.8371 13.8750.7657 11.125 0.6154 11.125 -2.2227 11.125-0.9083 8.375 0.5422 8.375 2.2272 8.375-0.4256 5.625 -1.3056 5.625 -1.8497 5.6251.0000 2.875 1.0000 2.875 1.0000 2.8750.0000 0 0.0000 0 0.0000 0

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18



FORMAS MODALES DIRECCION Y-Y


ɸ h ɸ h ɸ h3.6238 16.625 -1.3285 16.625 0.9976 16.6253.4693 13.875 -0.8432 13.875 0.0698 13.8753.0985 11.125 0.0927 11.125 -0.9529 11.1252.5344 8.375 0.9791 8.375 -0.6787 8.3751.8123 5.625 1.3421 5.625 0.5192 5.6251.0000 2.875 1.0000 2.875 1.0000 2.8750.0000 0 0.0000 0 0.0000 0

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



FORMAS MODALES DIRECCION Y-Y


ɸ h ɸ h ɸ h-0.9929 16.625 1.1080 16.625 -1.2624 16.6250.6038 13.875 -1.3533 13.875 2.0326 13.8750.7796 11.125 0.5849 11.125 -2.4356 11.125-0.8793 8.375 0.6216 8.375 2.3987 8.375-0.4689 5.625 -1.3625 5.625 -1.9285 5.6251.0000 2.875 1.0000 2.875 1.0000 2.8750.0000 0 0.0000 0 0.0000 0

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18



-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18



DETERMINACION DE LAS FORMAS MODALES

gravedad = 9.81 m/s^2

DIRECCION Y - Y

1471.180 KN1.4997 Tn

F63053.532 KN/cm

2153.086 KN2.1948 Tn

F53053.532 KN/cm

2153.086 KN2.1948 Tn

F43053.532 KN/cm

2153.086 KN2.1948 Tn

F33053.532 KN/cm

2144.627 KN2.1862 Tn

F23137.989 KN/cm

2203.073 KN2.2457 Tn

F1

2743.760 KN/cm

5881.749 -3137.989 0.000 0.000 0.000 0.000

-3137.989 6191.521 -3053.532 0.000 0.000 0.000[K] = 0.000 -3053.532 6107.064 -3053.532 0.000 0.000

0.000 0.000 -3053.532 6107.064 -3053.532 0.000

0.000 0.000 0.000 -3053.532 6107.064 -3053.532

0.000 0.000 0.000 0.000 -3053.532 3053.532



2.2457 0 0 0 0 00 2.1862 0 0 0 0

[m] = 0 0 2.1948 0 0 00 0 0 2.1948 0 00 0 0 0 2.1948 00 0 0 0 0 1.4997

=

5881.75 -2.246w² -3137.99 0.00 0.00 0.00 0.00

-3137.99 6191.52 -2.186w² -3053.53 0.00 0.00 0.00

= 0.00 -3053.53 6107.06 -2.195w² -3053.53 0.00 0.00

0.00 0.00 -3053.53 6107.06 -2.195w² -3053.53 0.00

0.00 0.00 0.00 -3053.53 6107.06 -2.195w² -3053.53

0.00 0.00 0.00 0 -3053.53 3053.53 -1.500w²

= 7.7845E+01 * w^12 -1.2327E+06 * w^10 + 7.2856E+09 * w^8 -1.9732E+13 * w^6 + 2.3978E+16 * w^4 -1.0563E+19 * w^2 + 7.4853E+20

MODIFICAR VALORES

valores característicos

w1 = 9.315 rad/s 86.774 rad/sw2 = 27.271 rad/s 743.688 rad/sw3 = 43.515 rad/s 1893.547 rad/sw4 = 57.221 rad/s 3274.195 rad/sw5 = 67.252 rad/s 4522.892 rad/sw6 = 72.896 rad/s 5313.754 rad/s

|[K] - W²[m]|

w1² =w2² =w3² =w4² =w5² =w6² =




ɸ11 5686.877 -3137.989 0.000 0.000 0.000 0.000

ɸ12 -3137.989 6001.819 -3053.532 0.000 0.000 0.000

=ɸ13

x0.000 -3053.532 5916.614 -3053.532 0.000 0.000

= 0ɸ14 0.000 0.000 -3053.532 5916.614 -3053.532 0.000

ɸ15 0.000 0.000 0.000 -3053.532 5916.614 -3053.532

ɸ16 0.000 0.000 0.000 0.000 -3053.532 2923.400

5686.877 *ɸ11 + -3137.989 *ɸ12 + 0.000 *ɸ13 + 0.000 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

-3137.989 *ɸ11 + 6001.819 *ɸ12 + -3053.532 *ɸ13 + 0.000 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + -3053.532 *ɸ12 + 5916.614 *ɸ13 + -3053.532 *ɸ14 + 0.000 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + -3053.532 *ɸ13 + 5916.614 *ɸ14 + -3053.532 *ɸ15 + 0.000 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + 0.000 *ɸ13 + -3053.532 *ɸ14 + 5916.614 *ɸ15 + -3053.532 *ɸ16 = 0

0.000 *ɸ11 + 0.000 *ɸ12 + 0.000 *ɸ13 + 0.000 *ɸ14 + -3053.532 *ɸ15 + 2923.400 *ɸ16 = 0

1.000

ɸ12 = 1.812

ɸ13 = 2.534

ɸ14 = 3.098

ɸ15 = 3.469

ɸ16 = 3.624

h ɸ16.625 3.62413.875 3.46911.125 3.0988.375 2.5345.625 1.8122.875 1.000

0 0.000

asumiendo: ɸ11 =

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18




ɸ21 4211.618 -3137.989 0.000 0.000 0.000 0.000

ɸ22 -3137.989 4565.698 -3053.532 0.000 0.000 0.000

=ɸ23

x0.000 -3053.532 4474.828 -3053.532 0.000 0.000

= 0ɸ24 0.000 0.000 -3053.532 4474.828 -3053.532 0.000

ɸ25 0.000 0.000 0.000 -3053.532 4474.828 -3053.532

ɸ26 0.000 0.000 0.000 0.000 -3053.532 1938.243

4211.618 *ɸ21 + -3137.989 *ɸ22 + 0.000 *ɸ23 + 0.000 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

-3137.989 *ɸ21 + 4565.698 *ɸ22 + -3053.532 *ɸ23 + 0.000 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + -3053.532 *ɸ22 + 4474.828 *ɸ23 + -3053.532 *ɸ24 + 0.000 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + -3053.532 *ɸ23 + 4474.828 *ɸ24 + -3053.532 *ɸ25 + 0.000 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + 0.000 *ɸ23 + -3053.532 *ɸ24 + 4474.828 *ɸ25 + -3053.532 *ɸ26 = 0

0.000 *ɸ21 + 0.000 *ɸ22 + 0.000 *ɸ23 + 0.000 *ɸ24 + -3053.532 *ɸ25 + 1938.243 *ɸ26 = 0

1.000

ɸ22 = 1.342

ɸ23 = 0.979

ɸ24 = 0.093

ɸ25 = -0.843

ɸ26 = -1.328

h ɸ16.625 -1.32813.875 -0.84311.125 0.0938.375 0.9795.625 1.3422.875 1.000

asumiendo: ɸ21 =

0.0000 2.0000 4.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



0.000 0.000


ɸ31 1629.329 -3137.989 0.000 0.000 0.000 0.000

ɸ32 -3137.989 2051.916 -3053.532 0.000 0.000 0.000

=ɸ33

x0.000 -3053.532 1951.131 -3053.532 0.000 0.000

= 0ɸ34 0.000 0.000 -3053.532 1951.131 -3053.532 0.000

ɸ35 0.000 0.000 0.000 -3053.532 1951.131 -3053.532

ɸ36 0.000 0.000 0.000 0.000 -3053.532 213.829

1629.329 *ɸ31 + -3137.989 *ɸ32 + 0.000 *ɸ33 + 0.000 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

-3137.989 *ɸ31 + 2051.916 *ɸ32 + -3053.532 *ɸ33 + 0.000 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + -3053.532 *ɸ32 + 1951.131 *ɸ33 + -3053.532 *ɸ34 + 0.000 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + -3053.532 *ɸ33 + 1951.131 *ɸ34 + -3053.532 *ɸ35 + 0.000 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + 0.000 *ɸ33 + -3053.532 *ɸ34 + 1951.131 *ɸ35 + -3053.532 *ɸ36 = 0

0.000 *ɸ31 + 0.000 *ɸ32 + 0.000 *ɸ33 + 0.000 *ɸ34 + -3053.532 *ɸ35 + 213.829 *ɸ36 = 0

1.000

ɸ32 = 0.519

ɸ33 = -0.679

ɸ34 = -0.953

ɸ35 = 0.070

ɸ36 = 0.998

h ɸ16.625 0.99813.875 0.07011.125 -0.9538.375 -0.679

asumiendo: ɸ31 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



5.625 0.5192.875 1.0000.000 0.000


ɸ41 -1471.250 -3137.989 0.000 0.000 0.000 0.000

ɸ42 -3137.989 -966.405 -3053.532 0.000 0.000 0.000

=ɸ43

x0.000 -3053.532 -1079.096 -3053.532 0.000 0.000

= 0ɸ44 0.000 0.000 -3053.532 -1079.096 -3053.532 0.000

ɸ45 0.000 0.000 0.000 -3053.532 -1079.096 -3053.532

ɸ46 0.000 0.000 0.000 0.000 -3053.532 -1856.691

-1471.250 *ɸ41 + -3137.989 *ɸ42 + 0.000 *ɸ43 + 0.000 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

-3137.989 *ɸ41 + -966.405 *ɸ42 + -3053.532 *ɸ43 + 0.000 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + -3053.532 *ɸ42 + -1079.096 *ɸ43 + -3053.532 *ɸ44 + 0.000 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + -3053.532 *ɸ43 + -1079.096 *ɸ44 + -3053.532 *ɸ45 + 0.000 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + 0.000 *ɸ43 + -3053.532 *ɸ44 + -1079.096 *ɸ45 + -3053.532 *ɸ46 = 0

0.000 *ɸ41 + 0.000 *ɸ42 + 0.000 *ɸ43 + 0.000 *ɸ44 + -3053.532 *ɸ45 + -1856.691 *ɸ46 = 0

1.000

ɸ42 = -0.469

ɸ43 = -0.879

ɸ44 = 0.780

ɸ45 = 0.604

ɸ46 = -0.993

h ɸ16.625 -0.99313.875 0.604

asumiendo: ɸ41 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



11.125 0.7808.375 -0.8795.625 -0.4692.875 1.0000.000 0.000


ɸ51 -4275.502 -3137.989 0.000 0.000 0.000 0.000

ɸ52 -3137.989 -3696.262 -3053.532 0.000 0.000 0.000

=ɸ53

x0.000 -3053.532 -3819.721 -3053.532 0.000 0.000

= 0ɸ54 0.000 0.000 -3053.532 -3819.721 -3053.532 0.000

ɸ55 0.000 0.000 0.000 -3053.532 -3819.721 -3053.532

ɸ56 0.000 0.000 0.000 0.000 -3053.532 -3729.329

-4275.502 *ɸ51 + -3137.989 *ɸ52 + 0.000 *ɸ53 + 0.000 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

-3137.989 *ɸ51 + -3696.262 *ɸ52 + -3053.532 *ɸ53 + 0.000 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + -3053.532 *ɸ52 + -3819.721 *ɸ53 + -3053.532 *ɸ54 + 0.000 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + -3053.532 *ɸ53 + -3819.721 *ɸ54 + -3053.532 *ɸ55 + 0.000 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + 0.000 *ɸ53 + -3053.532 *ɸ54 + -3819.721 *ɸ55 + -3053.532 *ɸ56 = 0

0.000 *ɸ51 + 0.000 *ɸ52 + 0.000 *ɸ53 + 0.000 *ɸ54 + -3053.532 *ɸ55 + -3729.329 *ɸ56 = 0

1.000

ɸ52 = -1.362

ɸ53 = 0.622

ɸ54 = 0.585

ɸ55 = -1.353

ɸ56 = 1.108

h ɸ

asumiendo: ɸ51 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18



16.625 1.10813.875 -1.35311.125 0.5858.375 0.6225.625 -1.3622.875 1.0000.000 0.000


ɸ61 -6051.574 -3137.989 0.000 0.000 0.000 0.000

ɸ62 -3137.989 -5425.216 -3053.532 0.000 0.000 0.000

=ɸ63

x0.000 -3053.532 -5555.494 -3053.532 0.000 0.000

= 0ɸ64 0.000 0.000 -3053.532 -5555.494 -3053.532 0.000

ɸ65 0.000 0.000 0.000 -3053.532 -5555.494 -3053.532

ɸ66 0.000 0.000 0.000 0.000 -3053.532 -4915.364

-6051.574 *ɸ61 + -3137.989 *ɸ62 + 0.000 *ɸ63 + 0.000 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

-3137.989 *ɸ61 + -5425.216 *ɸ62 + -3053.532 *ɸ63 + 0.000 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + -3053.532 *ɸ62 + -5555.494 *ɸ63 + -3053.532 *ɸ64 + 0.000 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + -3053.532 *ɸ63 + -5555.494 *ɸ64 + -3053.532 *ɸ65 + 0.000 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + 0.000 *ɸ63 + -3053.532 *ɸ64 + -5555.494 *ɸ65 + -3053.532 *ɸ66 = 0

0.000 *ɸ61 + 0.000 *ɸ62 + 0.000 *ɸ63 + 0.000 *ɸ64 + -3053.532 *ɸ65 + -4915.364 *ɸ66 = 0

1.000

ɸ62 = -1.928

ɸ63 = 2.399

ɸ64 = -2.436

ɸ65 = 2.033

ɸ66 = -1.262

asumiendo: ɸ61 =

-2.0000 0.0000 2.00000

2

4

6

8

10

12

14

16

18

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18



h ɸ16.625 -1.26213.875 2.03311.125 -2.4368.375 2.3995.625 -1.9282.875 1.0000.000 0.000

DETERMINACION DE LOS FACTORES DE PARTICIPACION MODAL

NORMALIZACION DE LOS MODOS

2.246* 1.000² + 2.186* 1.812² + 2.195* 2.534² + 2.195* 3.098² + 2.195* 3.469² + 1.500* 3.624²= 9.523898

2.246* 1.000² + 2.186* 1.342² + 2.195* 0.979² + 2.195* 0.093² + 2.195* -0.843² + 1.500* -1.328²= 3.537506

2.246* 1.000² + 2.186* 0.519² + 2.195* -0.679² + 2.195* -0.953² + 2.195* 0.070² + 1.500* 0.998²= 2.709681

2.246* 1.000² + 2.186* -0.469² + 2.195* -0.879² + 2.195* 0.780² + 2.195* 0.604² + 1.500* -0.993²= 2.834734

-5.0000 0.0000 5.00000

2

4

6

8

10

12

14

16

18

〖 𝑖ɸ 〗^𝑛= /ɸ√(∑▒ ∗〖〖𝑚𝑖 𝑖ɸ〗^2 〗 )

√(∑▒ ∗〖𝑚𝑖 〖 ɸ1〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ2〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ3〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ4〗^2 〗 )=



2.246* 1.000² + 2.186* -1.362² + 2.195* 0.622² + 2.195* 0.585² + 2.195* -1.353² + 1.500* 1.108²= 3.709916

2.246* 1.000² + 2.186* -1.928² + 2.195* 2.399² + 2.195* -2.436² + 2.195* 2.033² + 1.500* -1.262²= 6.890694

0.105 0.283 0.369 0.353 0.270 0.1450.190 0.379 0.192 -0.165 -0.367 -0.2800.266 0.277 -0.250 -0.310 0.168 0.3480.325 0.026 -0.352 0.275 0.158 -0.3530.364 -0.238 0.026 0.213 -0.365 0.2950.380 -0.376 0.368 -0.350 0.299 -0.183

FACTORES DE PARTICIPACION MODAL

FPM1 = 2.246* 0.105 + 2.186* 0.190 + 2.195* 0.266 + 2.195* 0.325 + 2.195* 0.364 + 1.500* 0.380 = 3.3200FPM2 = 2.246* 0.283 + 2.186* 0.379 + 2.195* 0.277 + 2.195* 0.026 + 2.195* -0.238 + 1.500* -0.376 = 1.0430FPM3 = 2.246* 0.369 + 2.186* 0.192 + 2.195* -0.250 + 2.195* -0.352 + 2.195* 0.026 + 1.500* 0.368 = 0.5347FPM4 = 2.246* 0.353 + 2.186* -0.165 + 2.195* -0.310 + 2.195* 0.275 + 2.195* 0.213 + 1.500* -0.350 = 0.2956FPM5 = 2.246* 0.270 + 2.186* -0.367 + 2.195* 0.168 + 2.195* 0.158 + 2.195* -0.365 + 1.500* 0.299 = 0.1635FPM6 = 2.246* 0.145 + 2.186* -0.280 + 2.195* 0.348 + 2.195* -0.353 + 2.195* 0.295 + 1.500* -0.183 = 0.0750

DETERMINACION DE LA ACELERACION ESPECTRAL


Z 0.4 ZONA 3

COEF. SISMICO

√(∑▒ ∗〖𝑚𝑖 〖 ɸ4〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ5〗^2 〗 )=√(∑▒ ∗〖𝑚𝑖 〖 ɸ6〗^2 〗 )=

〖 1ɸ〗^𝑛=

〖 2ɸ〗^𝑛=

〖 3ɸ〗^𝑛=

〖 4ɸ〗^𝑛=

〖 5ɸ〗^𝑛=

〖 6ɸ〗^𝑛=

〖〗𝐹𝑃𝑀 _𝑖=∑▒∗〖〖𝑚𝑖 𝑖ɸ 〗^𝑛

〗

𝑆𝑎𝑖=𝑍𝑈𝑆𝐶/𝑅∗𝑔



U 1 EDIFICACION COMUNS2 1 SUELO MUY RIGIDOTp 0.4 SUELO MUY RIGIDOR 7 CONCRETO ARMADO: DUAL

w T C Sai9.32 rad/s 0.67451 1.483 83.108 cm/s²

27.27 rad/s 0.23040 2.500 140.143 cm/s²43.51 rad/s 0.14439 2.500 140.143 cm/s²57.22 rad/s 0.10981 2.500 140.143 cm/s²67.25 rad/s 0.09343 2.500 140.143 cm/s²72.90 rad/s 0.08619 2.500 140.143 cm/s²

DETERMINACION DE LA FUERZA SISMICA

2.2457 0.1050 65.063 KN2.1862 0.1903 114.783 KN

F1 = 3.320 * 2.1948*

0.2661 * 83.108 cm/s² = 161.154 KN2.1948 0.3253 197.021 KN2.1948 0.3643 220.601 KN1.4997 0.3805 157.444 KN

2.2457 0.2827 92.790 KN2.1862 0.3794 121.233 KN

F2 = 1.043 * 2.1948*

0.2768 * 140.143 cm/s² = 88.792 KN2.1948 0.0262 8.410 KN

𝑇=2𝜋/𝑤 𝐶≤2.5∗𝑇𝑝/𝑇

𝐹𝑖=𝐹𝑃𝑀𝑖∗𝑚𝑖∗〖 𝑖ɸ 〗^𝑛∗𝑆𝑎𝑖



2.1948 -0.2384 -76.467 KN1.4997 -0.3755 -82.316 KN

2.2457 0.3690 62.110 KN2.1862 0.1916 31.394 KN

F3 = 0.535 * 2.1948*

-0.2505 * 140.143 cm/s² = -41.200 KN2.1948 -0.3517 -57.844 KN2.1948 0.0258 4.240 KN1.4997 0.3681 41.375 KN

2.2457 0.3528 32.821 KN2.1862 -0.1654 -14.980 KN

F4 = 0.296 * 2.1948*

-0.3102 * 140.143 cm/s² = -28.204 KN2.1948 0.2750 25.006 KN2.1948 0.2130 19.367 KN1.4997 -0.3503 -21.763 KN

2.2457 0.2695 13.870 KN2.1862 -0.3673 -18.396 KN

F5 = 0.163 * 2.1948*

0.1676 * 140.143 cm/s² = 8.426 KN2.1948 0.1577 7.928 KN2.1948 -0.3648 -18.344 KN1.4997 0.2986 10.262 KN

2.2457 0.1451 3.424 KN2.1862 -0.2799 -6.429 KN

F6 = 0.075 * 2.1948*

0.3481 * 140.143 cm/s² = 8.028 KN2.1948 -0.3535 -8.151 KN2.1948 0.2950 6.802 KN1.4997 -0.1832 -2.887 KN



NIVEL F1 F2 F3 F4 F5 F6 Fd Fd


DETERMINACION DEL CORTANTE

12.5159 0.1050 362.605 KN10.2702 0.1903 539.228 KN

Q1 = 3.320 * 8.0840*

0.2661 * 83.108 cm/s² = 593.577 KN5.8892 0.3253 528.665 KN3.6945 0.3643 371.334 KN1.4997 0.3805 157.444 KN

DETERMINACION DE LA FUERZA DE DISEÑO APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

𝐹𝑑=0.25∗∑▒〖 |𝐹𝑖|+0.75√(∑▒〖〗𝐹𝑖^2 )〗

𝑄𝑖=𝐹𝑃𝑀𝑖∗ ∅〖〗𝑖 ^𝑛∗∑▒ ∗〖〗𝑚𝑖 𝑆𝑎𝑖

0.25 iF 20.75 iF



12.5159 0.2827 517.135 KN10.2702 0.3794 569.530 KN

Q2 = 1.043 * 8.0840*

0.2768 * 140.143 cm/s² = 327.047 KN5.8892 0.0262 22.567 KN3.6945 -0.2384 -128.717 KN1.4997 -0.3755 -82.316 KN

12.5159 0.3690 346.150 KN10.2702 0.1916 147.481 KN

Q3 = 0.535 * 8.0840*

-0.2505 * 140.143 cm/s² = -151.753 KN5.8892 -0.3517 -155.211 KN3.6945 0.0258 7.137 KN1.4997 0.3681 41.375 KN

12.5159 0.3528 182.919 KN10.2702 -0.1654 -70.374 KN

Q4 = 0.296 * 8.0840*

-0.3102 * 140.143 cm/s² = -103.884 KN5.8892 0.2750 67.099 KN3.6945 0.2130 32.600 KN1.4997 -0.3503 -21.763 KN

12.5159 0.2695 77.300 KN10.2702 -0.3673 -86.423 KN

Q5 = 0.163 * 8.0840*

0.1676 * 140.143 cm/s² = 31.037 KN5.8892 0.1577 21.274 KN3.6945 -0.3648 -30.878 KN1.4997 0.2986 10.262 KN

12.5159 0.1451 19.084 KN10.2702 -0.2799 -30.200 KN

Q6 = 0.075 * 8.0840*

0.3481 * 140.143 cm/s² = 29.568 KN



Q6 = 0.075 *5.8892 * -0.3535

* 140.143 cm/s² =-21.872 KN

3.6945 0.2950 11.450 KN1.4997 -0.1832 -2.887 KN

DETERMINACION DEL CORTANTE APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

NIVEL Q1 Q2 Q3 Q4 Q5 Q6 Q Q


DETERMINACION DE LOS DESPLAZAMIENTOS

0.1050 0.334 cm 0.2695 0.00137 cm0.1903 0.605 cm -0.3673 -0.00186 cm

X1 = 3.320 * 83.1084 *0.2661 = 0.846 cm X5 = 0.163 * 140.143 *

0.1676 = 0.00085 cm

Q=0.25∗∑▒〖𝑄𝑖 +0.75√(∑▒〖〗𝑄𝑖 ^2 )〗

𝑄𝑖=(𝐹𝑃𝑀𝑖∗ ∅〖〗𝑖 ^𝑛∗𝑆𝑎𝑖)/〖〗𝑤𝑖 ^2

0.25 iQ 20.75 iQ



X1 = 3.320 * 83.1084 * 0.3253=

1.035 cmX5 = 0.163 * 140.143 * 0.1577

=0.00080 cm

86.7736 0.3643 1.158 cm 4522.8920 -0.3648 -0.00185 cm0.3805 1.210 cm 0.2986 0.00151 cm

0.2827 0.056 cm 0.1451 0.00029 cm0.3794 0.075 cm -0.2799 -0.00055 cm

X2 = 1.043 * 140.143 *0.2768 = 0.054 cm X6 = 0.075 * 140.143 *

0.3481 = 0.00069 cm0.0262 0.005 cm -0.3535 -0.00070 cm

743.6875 -0.2384 -0.047 cm 5313.7539 0.2950 0.00058 cm-0.3755 -0.074 cm -0.1832 -0.00036 cm

0.3690 0.015 cm0.1916 0.008 cm

X3 = 0.535 * 140.143 *-0.2505 = -0.010 cm-0.3517 -0.014 cm

1893.5473 0.0258 0.001 cm0.3681 0.015 cm

0.3528 0.004 cm-0.1654 -0.002 cm

X4 = 0.296 * 140.143 *-0.3102 = -0.004 cm0.2750 0.003 cm

3274.1947 0.2130 0.003 cm-0.3503 -0.004 cm

NIVEL X1 X2 X3 X4 X5 X6 X 0.75*R*X

DETERMINACION DE LOS DESPLAZAMIENTOS APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

Q=0.25∗∑▒〖 |𝑋𝑖|+0.75√(∑▒〖〗𝑋𝑖 ^2 )〗0.25 iX 20.75 iX



1 0.3339 cm 0.0556 cm 0.0146 cm 0.0045 cm 0.0014 cm 0.0003 cm 0.0989 cm 0.2541 cm 0.3530 cm 1.8532 cm2 0.6051 cm 0.0746 cm 0.0076 cm -0.0021 cm -0.0019 cm -0.0006 cm 0.1710 cm 0.4573 cm 0.6283 cm 3.2986 cm3 0.8462 cm 0.0544 cm -0.0099 cm -0.0039 cm 0.0008 cm 0.0007 cm 0.2265 cm 0.6360 cm 0.8625 cm 4.5281 cm4 1.0345 cm 0.0052 cm -0.0139 cm 0.0035 cm 0.0008 cm -0.0007 cm 0.2612 cm 0.7760 cm 1.0371 cm 5.4449 cm5 1.1583 cm -0.0468 cm 0.0010 cm 0.0027 cm -0.0018 cm 0.0006 cm 0.3026 cm 0.8694 cm 1.1720 cm 6.1531 cm6 1.2099 cm -0.0738 cm 0.0146 cm -0.0044 cm 0.0015 cm -0.0004 cm 0.3225 cm 0.9092 cm 1.2317 cm 6.4662 cm

DETERMINACION DE LAS DISTORCIONES

NIVEL 0.75*R*X Δr H DISTORSION VERIFICACION

6 6.4662 cm 0.3131 cm 275.0 cm 0.0011 CUMPLE < 0.0075 6.1531 cm 0.7082 cm 275.0 cm 0.0026 CUMPLE < 0.0074 5.4449 cm 0.9168 cm 275.0 cm 0.0033 CUMPLE < 0.0073 4.5281 cm 1.2295 cm 275.0 cm 0.0045 CUMPLE < 0.0072 3.2986 cm 1.4454 cm 275.0 cm 0.0053 CUMPLE < 0.0071 1.8532 cm 1.8532 cm 287.5 cm 0.0064 CUMPLE < 0.007

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