memoria de calculo _ aba

MEMORIA DESCRIPTIVA DEL PROYECTO ESTRUCTURAL

MEMORIA DESCRIPTIVA DEL PROYECTO ESTRUCTURAL

PROYECTO : "MEJORAMIENTO Y AMPLIACION DE LA OFERTA DE SERVICIOS EDUCATIVOS

DE LA I.E. AUGUSTO BOURONCLE ACUÑA DE PUERTO MALDONADO"_________________________________________________________________________

EVALUACION DE LA ESTRUCTURA ACTUAL

ANTECEDENTES:El proyecto de esta Institucion Educativa, esta compuesta por la siguiente distribucion deambientes :

- ZONA ADMINISTRATIVA + LABORATORIO + BIBLIOTECA+AULA

- AULAS.

- COMEDOR

- SERVICIOS HIGUIENICOS- POLIDEPORTIVO

- OBRAS EXTERIORES: TANQUE ELEVADO + CISTERNA

- ACCESO PRINCIPAL

- CERCO PERIMETRICO

DE LA INSPECCION:Se ha verificado que el terreno es un amplio Recinto Rectangular, con construccionesexistentes, de los cuales, algunos seran refaccionados.

DEL ANALISIS ESTRUCTURALSe ha obtenido los siguientes criterios estructurales:

- SUPER ESTRUCTURASe ha obtenido un tipo de estructura aporticada en la mayoria de estas edificacioneslas cuales seran analizadas en ambas direcciones.Debido a que la distribucion en planta es regular, para la mayoria de los bloquesy solo algunos bloques rectangulares, estan separadas por la junta sismica respectiva.

- SUB ESTRUCTURALa Cimentacion es superficial convencional y esta conformado por zapatas aisladas y conectadas, cimientos corridos con sobrecimiento simples y/o reforzados.Según el tipo de terreno, se ha considerado los siguientes parametros de diseño

Caracteristicas de los Materiales:Concreto : f'c= 210 kg/cm²Acero: fy= 4200 kg/cm²Albañileria: f'm= 45 kg/cm²

Cargas Unitarias:Concreto Armado : = 2400 kg/m³Muros de Albañileria: = 1800 kg/m³

Cargas:CM = Carga MuertaLosa Aligerada = 300 kg/m²

CV = Carga VivaAulas : S/C= 350 kg/m²Corredores : S/C= 400 kg/m²Azotea : S/C= 150 kg/m²

CALCULOS DE PARAMETROS SISMICOS

DETERMINACION DEL FACTOR ZONA (Z):

TACNA CORRESPONDE A LA ZONA 3

ZONA FACTOR DE ZONA Z (g)2 0.3

DETERMINACION DEL FACTOR DE USO (U):

CATEGORIA FACTOR UA (Institucion Educativa) 1.5

DETERMINACION DEL FACTOR DE SUELO (S):

TIPO DESCRIPCION Tp (seg) SS2 Suelo Intermedio 0.60 1.2

DETERMINACION DEL FACTOR DE AMPLIFICACION SISMICA "C":

DETERMINACION DEL PERIODO FUNDAMENTAL

C = 2.5 (Tp/T) ; C< 2.5Tp = 0.60 SEG ; Ct = 35T= ht/Ct = (3.50+3.50)/35 = 0.20C = 2.5 (0.60/0.20) = 7.50C = 2.5

DETERMINACION DEL COEFICIENTE DE REDUCCION SISMICA "R"

SISTEMA ESTRUCTURAL Coef. De Reduccion R Limite de AlturaPORTICO DE C. A. 8 -----

Debe considerarse C/R el siguiente valor minimo:verificando : 2,5/8 = 0.31 > 0,10 OK!

CARGA SISMICA:Espectro de respuseta de Aceleracion de Diseño según norma E - 30 - 2003 = ZUSC/R g

ESPECTRO E - 030

3.000

2.500

2.000

1.500

1.000

0.500

0.0000.00 0.50 1.00 1.50 2.00

ESPECTRO DE DISEÑO SISMICO (N.T. E - 030)DIRECCION XX

CALCULO DE LA ACELERACION ESPECTRAL DATOS

FACTOR DE USO DE LA ZONA Z = 0.3FACTOR DE USO DE IMPORTANCIA U = 1.5FACTOR DE SUELO S = 1.2PERIODO DE VIBRACION DEL SUELO (Seg) Tp = 0.6COEFICIENTE SISMICO C = 2.5FACTOR DE REDUCCION R = 8ACELARACION DE LA GRAVEDAD g = 9.8

PERIODO DE VIBRACION FUNDAMENTAL DE LA ESTRUCTURA

ANALISIS DINAMICO

T C Ag Ag = Z.U.S.C/Rd .g

0.10 2.50 1.65 C = 2,5*(Tp/T)0.15 2.50 1.650.20 2.50 1.65 T = Hn/Ct0.25 2.50 1.650.30 2.50 1.65 Ct = 35 Porticos0.35 2.50 1.65 Ct = 45 Porticos y Placas0.40 2.50 1.65 Ct = 60 Porticos y Mamposteria0.45 2.50 1.650.50 2.50 1.65 Hn = Altura de Edificacion0.55 2.50 1.650.60 2.50 1.65 DATOS0.65 2.31 1.530.70 2.14 1.42 Hn = 7.000.75 2.00 1.32 Ct = 350.80 1.88 1.240.85 1.76 1.17 ANALISIS ESTATICO0.90 1.67 1.100.95 1.58 1.04 T = 0.201.00 1.50 0.99 C= 7.501.05 1.43 0.95 Ag = 1.651.10 1.36 0.901.15 1.30 0.861.20 1.25 0.831.25 1.20 0.791.30 1.15 0.761.35 1.11 0.741.40 1.07 0.711.45 1.03 0.681.50 1.00 0.661.55 0.97 0.641.60 0.94 0.621.65 0.91 0.601.70 0.88 0.581.75 0.86 0.571.80 0.83 0.55

1.85 0.81 0.54

DEL METODO DE ANALISIS ESTRUCTURAL

en donde se han modelado todos sus elementos estructurales de tal manera que alhacer correciones sucesivas, a sus giros y/o desplazamientos, se pueden hallar losmomentos y cortantes, utilizando las ecuaciones del metodo de deflexiones angulares.

COMBINACIONES DE ESFUERZOS PARA LA ESTRUCTURA

El Analisis Estructural para La Institucion Educativa, se ha empleado como una estructura tridimensional y se a utilizado las siguientes combinaciones de carga:

C1 = 1,4 CM + 1,7 CV C2 = 1,25 (CM + CV + CS) C3 = 1,25 (CM + CV - CS) C4 = 0,90 CM + 1,25 CS C5 = 0,90 CM - 1,25 CS

Con estos juegos de cargas se ha realizado las combinaciones para cada uno de los elementos para determinar sus esfuerzos y para verificar su resistencia de cada uno de ellas se ha empleado las ecuaciones proporcionaddas por la norma del NTE - 060 -98complementado con la Norma del ACI - 318 -99, asi mismo se ha utilizado la Norma de Albañileria NTE -70

ANALISIS SISMICO DINAMICOEl Analisis sismico dinamico empleado en este trabajo esta basado en el metodoespectral considerado en al norma NTE -030 - 2003, Considerando un analisis de masasconcentradas en el centro de masas, con 3 grados de libertad de oscilacion por nudo.

El modelo estara sometido a las diferentes simulaciones sismicas en cada uno de sus ejes, va permitir evaluar el comportamiento de la estructura y de cada uno de sus elementos por las fuerzas inerciales producidas por el espectro sismico, se esta conside-rando a la estructura de la siguiente manera:

- La super estructura se modela como una estructura reticular tridimensional, formada por columnas y vigas con una adecuada rigidez.

- La losa como una membrana que se considera como diafragma rigido y estara gobernada por tres grados de libertad, dos desplazamientos ortogonales y un giro alrededor del eje perpendicular al plano de la estructura.

- Se aplicara el modelo de masas concentradas, ubicado en el centro de masas de laestructura.

El metodo empleado en el presente proyecto esta basado en el Metodo de Takabeya,

MEMORIA DE CALCULO

MEMORIA DE CALCULO

1.00 RESULTADOS DEL ANALISIS ESTRUCTURAL:

Para determinar el diseño optimo de la estructura se ha realizado diferentes modelos, sea sometido a la estructura a las simulaciones del espectro sismico, con el fin de estudiar la respuesta al mismo de cada una de ellas y evaluar el comportamiento estructural de cada modelo y de acuerdo a los resultados se ha optado por el modelo mas ideal queofrezca la maxima seguridad, cumpla con las normas del diseño sismico y de concreto armado.

2.00 ESPECIFICACIONES TECNICAS:

MATERIALES:ACERO:ACERO ESTRUCTURAL CORRUGADO fy = 4200 kg/cm²ACERO LISO fy = 4200 kg/cm²

CONCRETO:CIMIENTOS CORRIDOS: f'c = 100 kg/cm² + 30% P.G. 6" maxSOBRECIMIENTOS : f'c = 140 kg/cm² + 25% P.G. 3" maxSOLADO DE ZAPATAS: Concreto: 1 : 12 C : H

COLUMNAS: f'c = 210 kg/cm² COLUMNAS DE AMARRE: f'c = 175 kg/cm² VIGAS Y LOSAS: f'c = 210 kg/cm² ZAPATAS: f'c = 210 kg/cm² ALBAÑILERIA: f'm = 45 kg/cm²

RECUBRIMIENTOS:ZAPATAS: 7,00 cmVIGAS Y VIGAS DE CIMENTACION: 3,00 cmCOLUMNAS Y MUROS DE CORTE: 3,00 cmVIGAS CHATAS Y LOSAS: 2,50 cmCOLUMNAS DE AMARRE: 2,50 cm

SUELO:

CAPACIDAD PORTANTE:PROFUNDIDAD DE DESPLANTE 1.60 mTIPO DE SUELO: LIMO-ARCILLOSOASENTAMIENTO MAXIMO: 1"

ESTRUCTURA:SISTEMA ESTRUCTURAL APORTICADO

SISMICIDAD:ESPECTRO DE RESPUESTA DE ACELERACION DE ACUERDO AN.T.E - 030 - 2003

PARAMETROS SISMICOS:FACTOR DE USO DE LA ZONA Z = 0.3

t= 0.85 kg/cm²

'= Z.U.S.C/Rd .g

FACTOR DE USO DE IMPORTANCIA U = 1.5FACTOR DE SUELO S = 1.2PERIODO DE VIBRACION DEL SUELO Tp = 0.6 segCOEFICIENTE SISMICO C = 2.5FACTOR DE REDUCCION R = 8ACELARACION DE LA GRAVEDAD g = 9.8

PERIODOS:T = 0.20 seg

DESPLAZAMIENTOS DE ENTREPISO:DESPLAZAMIENTO EN EJE X-X < 0,007DESPLAZAMIENTO EN EJE Y-Y < 0,007

ANALISIS SISMICO

1) BLOQUE 1

A) PESO DE LA ESTRUCTURA POR PISO :

PISO 1

LA + PT : 420 kg/m² × ### m² = 120132.60VIG VP-1: ### kg/m³ × 0.30 m ×### m × 10.40 m × 8 = 38937.60

VS-1: ### kg/m³ × 0.25 m ×### m × 28.90 m × 2 = 20808.00VS-2: ### kg/m³ × 0.25 m ×### m × 28.90 m × 1 = 6936.00

COL C-1: ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 10656.00C-2 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00

### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 3729.60C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00

### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 1864.80C-4 : ### kg/m³ × 0.25 m ×### m ×( 3.70 + 3.70 )/2 × 5 = 3885.00C-5 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 2 = 2664.00

TAB : 120 kg/m² × ### m² = 34323.60S/C : 250 kg/m² × ### m² ×### = 17876.88

272470.08

PISO 2

LMACIZ : ### kg/m³ × ### m² ×### m = 97018.56VIG VP-1: ### kg/m³ × 0.30 m ×### m × 10.40 m × 8 = 38937.60



### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 1864.80C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 2664.00

### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 932.40C-4 : ### kg/m³ × 0.25 m ×### m ×( 3.70 + 0.00 )/2 × 5 = 1942.50C-5 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 2 = 1332.00S/C : 80 kg/m² × ### m² ×### = 6737.40

187165.26

PESO TOTAL :

P = 459.64 TN

B) CALCULO DE FUERZAS SISMICAS

* CALCULO DE FUERZA CORTANTE BASAL :SE DETERMINA POR LA SIGUIENTE FORMULA :

V = Z × U × S × C/R × P

* CALCULO DEL COEFICIENTE DE AMPLIFICACION SISMICA (C) :

C = 2.5 (Tp/T) 1.25 ; C< 2.5Tp = 0.60 SEG ; Ct = 35T= ht/Ct = (3.70+3.70)/35 = 0.21C = 2.5 (0.60/0.21) = 7.14C = 2.5

C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 76.94 TN

* DISTRIBUCION DE FUERZAS SISMICAS :

SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0

LAS FUERZAS SISMICAS SE CALCULAN POR :

PISO Pi hi Pi × hi Fi1 272.47 3.70 1008.14 32.412 187.17 7.40 1385.02 44.53

2393.16

LAS RIGIDECES SE CALCULAN POR :

K = 210 b (h/H)³

n b h H K (Tn/cm)8 50.00 30.00 370.00 44.784 15.00 ### 370.00 248.754 15.00 65.00 370.00 68.315 35.00 25.00 370.00 11.342 50.00 30.00 370.00 11.19

Kxx = 384.378 30.00 50.00 370.00 124.384 30.00 50.00 370.00 62.194 30.00 50.00 370.00 62.195 25.00 35.00 370.00 22.222 30.00 50.00 370.00 31.09

Kyy = 302.06

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

2) BLOQUE 2


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 7459.20C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 10656.00


TAB : 120 kg/m² × ### m² = 69993.60S/C : 250 kg/m² × ### m² ×### = 36455.00

543398.00

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 8 = 3729.60C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 8 = 5328.00


S/C : 80 kg/m² × ### m² ×### = 12500.00324986.90

PESO TOTAL :

P = 868.38 TN



V = Z × U × S × C/R × P



C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 145.37 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 543.40 3.70 2010.57 ###2 324.99 7.40 2404.90 ###

4415.48


K = 210 b (h/H)³

n b h H K (Tn/cm)14 50.00 30.00 370.00 78.368 15.00 ### 370.00 497.508 15.00 65.00 370.00 136.639 35.00 25.00 370.00 20.414 50.00 30.00 370.00 22.39

Kxx = 755.2814 30.00 50.00 370.00 217.668 30.00 50.00 370.00 124.388 30.00 50.00 370.00 124.389 25.00 35.00 370.00 39.994 30.00 50.00 370.00 62.19

Kyy = 568.59

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

3) BLOQUE 3


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 3729.60C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00


TAB : 120 kg/m² × ### m² = 39168.00S/C : 250 kg/m² × ### m² ×### = 20400.00

301333.32

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 1864.80C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 2664.00


S/C : 80 kg/m² × ### m² ×### = 6737.40191039.58

PESO TOTAL :

P = 492.37 TN



V = Z × U × S × C/R × P



C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 82.42 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 301.33 3.70 1114.93 ###2 191.04 7.40 1413.69 ###

2528.63


K = 210 b (h/H)³

n b h H K (Tn/cm)8 50.00 30.00 370.00 44.784 15.00 ### 370.00 248.754 15.00 65.00 370.00 68.315 35.00 25.00 370.00 11.343 50.00 30.00 370.00 16.79

Kxx = 389.978 30.00 50.00 370.00 124.384 30.00 50.00 370.00 62.194 30.00 50.00 370.00 62.195 25.00 35.00 370.00 22.223 30.00 50.00 370.00 46.64

Kyy = 317.61

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

4) BLOQUE 4


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 6 = 5594.40C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 10656.00


TAB : 120 kg/m² × ### m² = 54816.00S/C : 250 kg/m² × ### m² ×### = 28550.00

431488.64

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 6 = 2797.20C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 8 = 5328.00

### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 8 = 1864.80C-4 : ### kg/m³ × 0.25 m ×### m ×( 3.70 + 0.00 )/2 × 6 = 2331.00C-5 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 2664.00S/C : 80 kg/m² × ### m² ×### = 9656.00

279328.04

PESO TOTAL :

P = 710.82 TN



V = Z × U × S × C/R × P



C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 118.99 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 431.49 3.70 1596.51 ###2 279.33 7.40 2067.03 ###

3663.54


K = 210 b (h/H)³

n b h H K (Tn/cm)10 50.00 30.00 370.00 55.976 15.00 ### 370.00 373.138 15.00 65.00 370.00 136.636 35.00 25.00 370.00 13.604 50.00 30.00 370.00 22.39

Kxx = 601.7110 30.00 50.00 370.00 155.476 30.00 50.00 370.00 93.288 30.00 50.00 370.00 124.386 25.00 35.00 370.00 26.66

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

4 30.00 50.00 370.00 62.19Kyy = 461.98

5) BLOQUE 5


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 2 = 1864.80C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00


TAB : 120 kg/m² × ### m² = 26850.00S/C : 250 kg/m² × ### m² ×### = 13984.38

212082.30

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 2 = 932.40C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 2664.00


S/C : 80 kg/m² × ### m² ×### = 4845.40139537.78

PESO TOTAL :

P = 351.62 TN



V = Z × U × S × C/R × P



C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 58.86 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 212.08 3.70 784.70 ###2 139.54 7.40 1032.58 ###

1817.28


K = 210 b (h/H)³

n b h H K (Tn/cm)6 50.00 30.00 370.00 33.582 15.00 ### 370.00 124.384 15.00 65.00 370.00 68.313 35.00 25.00 370.00 6.802 50.00 30.00 370.00 11.19

Kxx = 244.27

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

6 30.00 50.00 370.00 93.282 30.00 50.00 370.00 31.094 30.00 50.00 370.00 62.193 25.00 35.00 370.00 13.332 30.00 50.00 370.00 31.09

Kyy = 230.99

6) BLOQUE 6


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 6 = 5594.40C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00


TAB : 120 kg/m² × ### m² = 50457.60S/C : 250 kg/m² × ### m² ×### = 26280.00

384675.60

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 6 = 5594.40C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 5328.00


TAB : 120 kg/m² × ### m² = 50457.60S/C : 250 kg/m² × ### m² ×### = 26280.00

384675.60

PISO 3



COL C-1: ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 10 = 6660.00

C-2 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 6 = 3996.00### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 6 = 2797.20

C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 2664.00### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 932.40

C-4 : ### kg/m³ × 0.25 m ×### m ×( 3.70 + 0.00 )/2 × 6 = 2331.00C-5 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 2 = 1332.00

S/C : 80 kg/m² × ### m² ×### = 8841.20223315.40

PESO TOTAL :

P = 992.67 TN



V = Z × U × S × C/R × P


C = 2.5 (Tp/T) 1.25 ; C< 2.5Tp = 0.60 SEG ; Ct = 35T= ht/Ct = (3.70+2×3.70)/35 = 0.32C = 2.5 (0.60/0.32) = 4.69C = 2.5

C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 166.17 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 384.68 3.70 1423.30 ###2 384.68 7.40 2846.60 ###3 223.32 11.10 2478.80 ###

6748.70


K = 210 b (h/H)³

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)

n b h H K (Tn/cm)10 50.00 30.00 370.00 55.976 15.00 ### 370.00 373.134 15.00 65.00 370.00 68.316 35.00 25.00 370.00 13.602 50.00 30.00 370.00 11.19

Kxx = 522.2110 30.00 50.00 370.00 155.476 30.00 50.00 370.00 93.284 30.00 50.00 370.00 62.196 25.00 35.00 370.00 26.662 30.00 50.00 370.00 31.09

Kyy = 368.70

7) BLOQUE 7


PISO 1




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 3729.60C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 10656.00


TAB : 120 kg/m² × ### m² = 49137.60S/C : 250 kg/m² × ### m² ×### = 51185.00

404174.00

PISO 2




### kg/m³ × 0.15 m ×### m ×( 3.70 + 3.70 )/2 × 4 = 3729.60C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 3.70 )/2 × 8 = 10656.00


TAB : 120 kg/m² × ### m² = 49137.60S/C : 250 kg/m² × ### m² ×### = 51185.00

404174.00

PISO 3




### kg/m³ × 0.15 m ×### m ×( 3.70 + 0.00 )/2 × 4 = 1864.80C-3 : ### kg/m³ × 0.30 m ×### m ×( 3.70 + 0.00 )/2 × 8 = 5328.00


S/C : 80 kg/m² × ### m² ×### = 8853.20245640.98

PESO TOTAL :

P = 1053.99 TN



V = Z × U × S × C/R × P


C = 2.5 (Tp/T) 1.25 ; C< 2.5Tp = 0.60 SEG ; Ct = 35T= ht/Ct = (3.70+2×3.70)/35 = 0.32C = 2.5 (0.60/0.32) = 4.69C = 2.5

C/R = 0.31 >= 0.1 C/R = 0.31

* CALCULO DE V :

V = Z×U×S×C/R×PV = 0.30×1.50×1.20×0.31× P

V = 176.44 TN


SI T> 0.70 ; Fa = 0.07 T*V <= 0.15 * V0.39 > 0.70 ( No) ; Fa = 0


PISO Pi hi Pi × hi Fi1 404.17 3.70 1495.44 ###2 404.17 7.40 2990.89 ###3 245.64 11.10 2726.61 ###

7212.95

Fi = (Pi × hi) /∑(Pi × hi) × (V-Fa)


K = 210 b (h/H)³

n b h H K (Tn/cm)8 50.00 30.00 370.00 44.784 15.00 ### 370.00 248.758 15.00 65.00 370.00 136.635 35.00 25.00 370.00 11.342 50.00 30.00 370.00 11.19

Kxx = 452.688 30.00 50.00 370.00 124.384 30.00 50.00 370.00 62.198 30.00 50.00 370.00 124.385 25.00 35.00 370.00 22.222 30.00 50.00 370.00 31.09

Kyy = 364.25

PREDIMENSIONAMIENTO

3.00 PREDIMENSIONAMIENTO DE ELEMENTOS ESTRUCTURALES A) LOSA ALIGERADA:

PREDIMENSIONAMIENTO :

e = L/21 =4.10/21 = 0.20 = 0.20 m e = 20 cm

B) VIGAS PRINCIPALES:


- Para determinar el Peralte y el ancho de estas vigas, se usara:

S/C hL/11

250 - 350 L/10.5

L/10

a) VIGA : VP-1At = NP =4.10 3

hv = L/11 = 7.25/11 0.66 0.65 mbv = At (NP+5)/100 = 0.33 0.30 m VP: 30×65

b) VIGA : VP-2At = NP =2.05 3

hv = L/11 = 7.25/11 0.66 0.65 mbv = At (NP+5)/100 = 0.16 0.30 m VP: 30×65

VIGAS SECUNDARIAS:


a) VIGA : VS-1h 1= L/12 = 4.10/12 0.34 0.40 mh 2=0.75x bc = 0.60 0.60 0.60 m

b>= h/1.5 = 0.40/1.5 0.27 0.25 m VS-1: 25×60

b) VIGA : VS-2h 1= L/12 = 4.10/12 0.34 0.40 mh 2=0.75x bc = 0.60 0.60 0.60 m

b>= h/1.5 = 0.40/1.5 0.27 0.25 m VS-2: 25×60

bv = At . [ NP+5 ]/100

≤250

≥350

C) COLUMNAS :

a) COLUMNA: C-1 (3 PISOS) POR PUNZONAMIENTO:

- Para determinar las dimensiones de la columna, se usara:

f PISO S/C fPISO # 01 0.92 + (S/C)/2075 1 250 1.04

PISO INTERM. 0.90 + (S/C)/2075 2 250 1.02

PISO ULTIMO 0.86 + (S/C)/2020 3 150 0.93

f'c = 210 kg/cm²

3.00 Tn/m²

AT = 4.10 x 5.20 = 21.32 m²

Pu = 76.63 Tn

Ac = 3 . Pu/f'c = 1094.71 cm²

bc = bv = 30.00 cm

hc = Ac/bc = 36.49 cm

C -1 : 30 x 40POR RIGIDEZ:

b = 0.30 h = 0.40 H1 = ###Kc2 Kc1 = b.h^3 / (12. H1) x 100 0.43

b = 0.30 h = 0.40 H2 = ###Kv1 Kvol Kc2 = b.h^3 / (12. H2) x 100 0.43

b = 0.30 h = 0.65 L1 = ###Kc1 Kv1 = b.h^3 / (12. L1) x 1000 0.95

b = 0.30 h = 0.45 L2 = ###

Kvol = b.h^3 / (12. L2) x 1000 0.76

C/VOLADO 0.84 > 1.50

NO CUMPLE, AUMENTAR DIMENSION.

b = 0.30 h = 0.50 H1 = ###Kc2 Kc1 = b.h^3 / (12. H1) x 100 0.84

b = 0.30 h = 0.50 H2 = ###Kv1 Kvol Kc2 = b.h^3 / (12. H2) x 100 0.84

b = 0.30 h = 0.65 L1 = ###Kc1 Kv1 = b.h^3 / (12. L1) x 1000 0.95

b = 0.30 h = 0.45 L2 = ###

Kvol = b.h^3 / (12. L2) x 1000 0.76

C/VOLADO 1.65 > 1.50

COL: 30 x 50

∑ f=

1.2 . AT . ∑ f =

ѱ = ∑ Kc / 0.6(∑ Kv) =

ѱ = ∑ Kc / 0.6(∑ Kv) =

CUMPLE LA DIMENSION DEL NUCLEO.

Para hallar la longitud de las Alas se usara la expresion: e Lt = 24 AT NP Donde: Lt : Long total de todas las alas. (cm)

At : Area techada (m²)NP: Numero de pisos

e= 24*432*3/1220 e= 25.495082e= 25 cm

b2 b1 (cm) = h1 (cm)=

100 25

b2 (cm) = h2 (cm)=

h2 30 25

h1

b1

d) ZAPATAS AISLADAS:

ZAPATA: Z-1


DATOS : DATOS :

Pu = b (cm)= h (cm)= Pu = 78.45 0.85 30 50 41.23 1.00

tn kg/cm² tn kg/cm²

6.15 m²Az = (2m+b).(2m+h) 6.24 Az = (2m+b).(m+m = 1.05 m ZAP : 2.40 x 2.60 m = 0.90

ZAPATA: Z-2

PREDIMENSIONAMIENTO :DATOS :

Pu = b (cm)= h (cm)=50.00 0.85 30 50

tn kg/cm²

3.92 m²Az =(2.m + b).(m +h) 3.72m = 1.05 m ZAP : 2.40 x 1.55

σt = σt =

Az = Pu/(15.σt) = Az = Pu/(15.σt) =

σt =

Az = Pu/(15.σt) =

b (cm)= h (cm)=25 55

2.75 m²2.97

m ZAP : 2.05 x 1.45

4.00 DISEÑO DE ELEMENTOS ESTRUCTURALES a) LOSA ALIGERADA:

PREDIMENSIONAMIENTO :e = L/24 =4.10/24 = 0.20 m e = 20 cm

METRADO DE CARGAS :PESO DE LOSA ( e = 20 cms) : 300.00 KG/M²PESO DE PISO TERMINADO : 100.00 KG/M²

Wd = 400.00 KG/M²

SOBRECARGA : Wl = 350.00 KG/M²

CARGA ULTIMA : Wu = (1.5 x Wd + 1.8 x Wl) / 2.5Wu = 492.00 KG/M²Wu = 0.49 TN/M²

ENVOLVENTE DE MOMENTOS Y ACEROS : ( COEFICIENTES DEL ACI )

Ø 1/2"M(-) = 1/10 x Wu x L² = 0.83 TN/M² As(-) = 1.46 CM² : 1 Ø 1/2"+ 1 Ø 3/8" 1.14M(+) = 1/11 x Wu x L² = 0.75 TN/M² As(+) = 1.33 CM² : 1 Ø 1/2" 1.04

As min = 0.56 CM²

As temp . : Alambron de 1/4 @ 0.25

b) VIGAS PRINCIPALES Y SECUNDARIAS:

ENVOLVENTE DE MOMENTOS Y ACEROS : VP -1 VIGA = 30 x 3 PISOSDISEÑO

PISO N° 1 TN/M² portico CM² 3.56 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 42.27 As(-) = 20.79 4.00 Ø 1" 4.08 7.25 10.44 16.31M(+) = 14.89 As(+) = 7.32 2.00 Ø 1" 1.44 2.55 3.67 5.74

volado 2.92M(-) = 59.79 As(-) = 29.41 6.00 Ø 1" 5.77 10.25 14.76 23.06M(+) = 14.89 As(+) = 7.32 2.00 Ø 1" 1.44 2.55 3.67 5.74

PISO N° 2 porticoM(-) = 35.10 As(-) = 17.26 4.00 Ø 1" 3.39 6.02 8.67 13.54M(+) = 14.40 As(+) = 7.08 2.00 Ø 1" 1.39 2.47 3.56 5.56

voladoM(-) = 54.06 As(-) = 26.58 4.00 Ø 1"+ 2 Ø 3/4" 5.21 9.27 13.34 20.85M(+) = 14.40 As(+) = 7.08 2.00 Ø 5/8" 1.39 2.47 3.56 5.56

PISO N° 3 porticoM(-) = 16.90 As(-) = 8.31 3.00 Ø 3/4" 1.63 2.90 4.17 6.52M(+) = 11.81 As(+) = 5.81 2.00 Ø 3/4" +1 Ø 5/8" 1.14 2.03 2.92 4.56

voladoM(-) = 30.24 As(-) = 14.87 5.00 Ø 3/4" 2.92 5.18 7.47 11.67M(+) = 11.81 As(+) = 5.81 2.00 Ø 3/4" +1 Ø 5/8" 1.14 2.03 2.92 4.56

As min = 6.04 CM² 1.18 2.11 3.03 4.74

Est Ø 3/8 : 1 @ 0.05 4 @ 0.10 2 @0.15 RTO @ 0.20

ENVOLVENTE DE MOMENTOS Y ACEROS : VP -1a VIGA = 30 x2 PISOSDISEÑO

PISO N° 1 TN/M² portico CM² 2.73 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 28.34 As(-) = 13.94 3.00 Ø 1" 2.73 4.86 7.00 10.93M(+) = 14.62 As(+) = 7.19 3.00 Ø 1" 1.41 2.51 3.61 5.64

voladoM(-) = 45.00 As(-) = 22.13 5.00 Ø 1" 4.34 7.71 11.11 17.36M(+) = 14.62 As(+) = 7.19 2.00 Ø 1" +1 Ø 3/4" 1.41 2.51 3.61 5.64

PISO N° 2 porticoM(-) = 15.32 As(-) = 7.53 2.00 Ø 3/4" +1 Ø 5/8" 1.48 2.63 3.78 5.91M(+) = 11.69 As(+) = 5.75 3.00 Ø 3/4" 1.13 2.00 2.89 4.51

voladoM(-) = 28.05 As(-) = 13.80 5.00 Ø 3/4" 2.71 4.81 6.93 10.82M(+) = 11.69 As(+) = 5.75 2.00 Ø 3/4" +1 Ø 5/8" 1.13 2.00 2.89 4.51

As min = 6.04 CM² 1.18 2.11 3.03 4.74

Est Ø 3/8 : 1 @ 0.05 8 @ 0.10 5 @0.15 RTO @ 0.35

ENVOLVENTE DE MOMENTOS Y ACEROS : VP3 PISOSDISEÑO

PISO N° 1 TN/M² portico CM² VIGA = 30 x 65 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 23.49 As(-) = 11.55 5.00 Ø 3/4" 2.27 4.03 5.80 9.06M(+) = 9.50 As(+) = 4.67 2.00 Ø 3/4" +1 Ø 5/8" 0.92 1.63 2.34 3.66

volado VIGA = 30 x 65M(-) = 27.79 As(-) = 13.67 5.00 Ø 3/4" 2.68 4.76 6.86 10.72M(+) = 0.17 As(+) = 0.08 2.00 Ø 3/4" +1 Ø 5/8" 0.02 0.03 0.04 0.07

PISO N° 2 portico VIGA = 30 x 65M(-) = 20.51 As(-) = 10.09 3.00 Ø 3/4" +2 Ø 5/8" 1.98 3.52 5.06 7.91M(+) = 9.15 As(+) = 4.50 2.00 Ø 3/4" +1 Ø 5/8" 0.88 1.57 2.26 3.53

volado VIGA = 30 x 65M(-) = 22.43 As(-) = 11.03 3.00 Ø 3/4" +2 Ø 5/8" 2.16 3.84 5.54 8.65M(+) = 0.18 As(+) = 0.09 2.00 Ø 3/4" +1 Ø 5/8" 0.02 0.03 0.04 0.07


volado VIGA = 30 x 65M(-) = 11.64 As(-) = 5.72 2.00 Ø 3/4" +1 Ø 5/8" 1.12 2.00 2.87 4.49M(+) = -0.24 As(+) = -0.12 2.00 Ø 3/4" +1 Ø 5/8" -0.02 -0.04 -0.06 -0.09

As min = 6.04 CM² 1.18 2.11 3.03 4.74

Est Ø 3/8 : 1 @ 0.05 4 @ 0.10 2 @0.15 RTO @ 0.20

ENVOLVENTE DE MOMENTOS Y ACEROS : VP2 PISOSDISEÑO

PISO N° 1 TN/M² portico CM² VIGA = 30 x 65 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 21.00 As(-) = 10.33 3.00 Ø 3/4" +2 Ø 5/8" 2.03 3.60 5.18 8.10M(+) = 9.61 As(+) = 4.73 2.00 Ø 3/4" +1 Ø 5/8" 0.93 1.65 2.37 3.71

volado VIGA = 30 x 45M(-) = 12.41 As(-) = 9.08 3.00 Ø 3/4" +2 Ø 5/8" 1.78 3.16 4.56 7.12M(+) = 0.82 As(+) = 0.60 2.00 Ø 3/4" 0.12 0.21 0.30 0.47


volado VIGA = 30 x 45M(-) = 7.61 As(-) = 5.57 2.00 Ø 3/4" +1 Ø 5/8" 1.09 1.94 2.80 4.37M(+) = 0.33 As(+) = 0.24 2.00 Ø 3/4" +1 Ø 5/8" 0.05 0.08 0.12 0.19

As min = 6.04 CM² 1.18 2.11 3.03 4.74

Est Ø 3/8 : 1 @ 0.05 8 @ 0.10 5 @0.15 RTO @ 0.35

ENVOLVENTE DE MOMENTOS Y ACEROS : VS3 PISOSDISEÑO

PISO N° 1 TN/M² placa CM² VIGA = 25 x 60 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 17.39 As(-) = 9.32 4.00 Ø 1" 1.83 3.25 4.68 7.31M(+) = 2.22 As(+) = 1.19 2.00 Ø 1" 0.23 0.41 0.60 0.93

columna 0.44M(-) = 9.61 As(-) = 5.15 6.00 Ø 1" 1.01 1.79 2.58 4.04M(+) = 2.22 As(+) = 1.19 2.00 Ø 1" 0.23 0.41 0.60 0.93

PISO N° 2 placaM(-) = 15.14 As(-) = 8.11 4.00 Ø 1" 1.59 2.83 4.07 6.36M(+) = 2.16 As(+) = 1.16 2.00 Ø 1" 0.23 0.40 0.58 0.91

columnaM(-) = 9.01 As(-) = 4.83 4.00 Ø 1"+ 2 Ø 3/4" 0.95 1.68 2.42 3.79M(+) = 2.16 As(+) = 1.16 2.00 Ø 5/8" 0.23 0.40 0.58 0.91

As min = 4.62 CM² 0.91 1.61 2.32 3.62

PISO N° 3 placa VIGA = 25 x 65M(-) = 10.28 As(-) = 5.05 3.00 Ø 3/4" 0.99 1.76 2.54 3.96M(+) = 1.78 As(+) = 0.87 2.00 Ø 3/4" +1 Ø 5/8" 0.17 0.30 0.44 0.69

columnaM(-) = 5.10 As(-) = 2.51 5.00 Ø 3/4" 0.49 0.87 1.26 1.97M(+) = 1.78 As(+) = 0.87 2.00 Ø 3/4" +1 Ø 5/8" 0.17 0.30 0.44 0.69

As min = 6.04 CM² 1.18 2.11 3.03 4.74

Est Ø 3/8 : 1 @ 0.05 4 @ 0.10 2 @0.15 RTO @ 0.20

ENVOLVENTE DE MOMENTOS Y ACEROS : VS2 PISOSDISEÑO

PISO N° 1 TN/M² placa CM² VIGA = 25 x 60 Ø 1" Ø 3/4" Ø 5/8" Ø 1/2"M(-) = 11.31 As(-) = 6.06 2.00 Ø 3/4"+1 Ø5/8" 1.19 2.11 3.04 4.75M(+) = 2.20 As(+) = 1.18 2.00 Ø 3/4"+1 Ø5/8" 0.23 0.41 0.59 0.92

columnaM(-) = 6.77 As(-) = 3.63 2.00 Ø 3/4" 0.71 1.26 1.82 2.84M(+) = 2.20 As(+) = 1.18 2.00 Ø 3/4" 0.23 0.41 0.59 0.92

As min = 4.62 CM² 0.91 1.61 2.32 3.62

PISO N° 2 placa VIGA = 25 x 65M(-) = 9.26 As(-) = 4.55 2.00 Ø 3/4" 0.89 1.59 2.29 3.57M(+) = 2.17 As(+) = 1.07 2.00 Ø 3/4" 0.21 0.37 0.54 0.84

columnaM(-) = 5.03 As(-) = 2.47 2.00 Ø 3/4" 0.49 0.86 1.24 1.94M(+) = 2.17 As(+) = 1.07 2.00 Ø 3/4" 0.21 0.37 0.54 0.84

As min = 5.03 CM² 0.99 1.75 2.53 3.95

Est Ø 3/8 : 2 @ 0.05 6 @ 0.10 4 @0.15 RTO @ 0.30

c) COLUMNAS :

COLUMNA: C-1 995.5714

DATOS :Ø (cm) = d (cm)= r (cm)=

60 56 4

f'c = fy = Mu = Pu = : e = Mu/Pu 210.00 4200.00 32.54 71.74 : 45.36kg/cm² kg/cm² tn-m tn : cm

CALCULO DEL ACERO LONGITUDINAL :Usando la formula de WHITNEY :

Pu= 0.7 As'.fy 0.8 f'c.Ø² e/(d-r)+0.5 2.4 Ø.e/d²+1.18

71740 = 2142 . As' + 129755As' = -27.08 cm²

As = 2 . As' = -54.16 cm² 5.65

As min = 28.80 cm² As : 6 Ø 1"

Estribos: Zunchos @ 0.075

COLUMNA: C-2 995.5714

DATOS :b (cm) = h (cm)= d (cm)= r (cm)=

30 55 51 4



Pu= 0.7 As'.fy f'c.b.h e/(d-r)+0.5 3.h.e/d²+1.18

82736.02 = 2300 . As' + 69281As' = 5.85 cm²

As = 2 . As' = 11.70 cm² 4.08

As min = 16.50 cm² As : 6 Ø 3/4"+2 Ø 5/8"

Est Ø3/8 : 1 @ 0.05 6 @ 0.10 6 @0.15 RTO @ 0.30

COLUMNA: C-5 995.5714

DATOS :b (cm) = h (cm)= d (cm)= r (cm)=

30 50 46 4



Pu= 0.7 As'.fy f'c.b.h e/(d-r)+0.5 3.h.e/d²+1.18

9538.887 = 590 . As' + 15191As' = -9.57 cm²

As = 2 . As' = -19.14 cm² 5.23

As min = 15.00 cm² As : 4 Ø 3/4"+2 Ø 5/8"

Est Ø3/8 : 1 @ 0.05 4 @ 0.10 2 @0.15 RTO @ 0.30

d) ZAPATAS AISLADAS:

ZAPATA: Z-1


Pu = Ø (cm)= d (cm)=86.18 0.86 60 50

tn kg/cm²

6.68 m²Az =(2.m + Ø).(2.m + 6.76m = 1.00 m ZAP : 2.60 x 2.60

CALCULO DE ACERO :

0.0007

0.0018

As = 9.00 cm² s = 5.1 Ø²/As = 0.22 m²

σt =

Az = Pu/15/σt =

ρ = σt / 5000 .( m/d)² =

ρ min =

ρ (100).d =

As : Ø 5/8" a 0.20 m

ZAPATA: Z-2


Pu = b (cm)= h (cm)= d (cm)=86.16 0.86 35 55 50

tn kg/cm²

6.68 m²Az =(2.m + b).(m +h) 3.64m = 1.00 m ZAP : 2.35 x 1.55

CALCULO DE ACERO :

0.0007

0.0018

As = 9.00 cm²

σt =

Az = Pu/15/σt =

ρ = σt / 5000 .( m/d)² =

ρ min =

ρ (100).d =

s = 5.1 Ø²/As = 0.22 m²

As : Ø 5/8" a 0.20 m

ZAPATA: Z-3


Pu = b (cm)= h (cm)= d (cm)=1.83 0.75 35 35 50tn kg/cm²

0.16 m²Az =(2.m + b).(m +h) 3.17m = 1.00 m ZAP : 2.35 x 1.35

CALCULO DE ACERO :

0.0006

0.0018

σt =

Az = Pu/15/σt =

ρ = σt / 5000 .( m/d)² =

ρ min =

As = 9.00 cm² s = 5.1 Ø²/As = 0.22 m²

As : Ø 5/8" a 0.20 m

ρ (100).d =

ANALISIS DE PORTICO : VP-1

At = ------- b = hv = hc = S/C=3.80 ------- 0.30 0.65 0.50 250

AT = Z = U = S = C/R= Np =318.3 0.30 1.50 1.2 0.31 8

2.9125 2.796 1 2Wdt= 1.95 Tn/m Wdt= 1.86 S/C= S/C=

3 9.36 Wlt= 0.38 Tn/m Wlt= 0.38 100 100

9.36 -12.76 30 × 65 12.76 -12.58 30 × 42 *30 K= 0.95 30

3.70 × K= × K=M 50 0.84 4.1225 50 0.84 4.506

Wdt= 2.35 Tn/m Wdt= 2.08 S/C= S/C=2 6.94 Wlt= 0.95 Tn/m Wlt= 1.52 250 400

16.30 -18.06 30 × 65 18.06 -20.27 30 × 42 *30 K= 0.95 30

3.70 × K= × K= .M 50 0.84 4.1225 50 0.84 4.506


19.83 -18.06 30 × 65 18.06 -20.27 30 × 42 *30 K= 0.95 30

3.70 × K= × K=M 50 0.84 50 0.84

7.25 M 3.00 M

METODO DE TAKABEYA: VP-1

0.00 0.00

3 -3.58 3.56 -3.58 -0.05-0.26 -0.26 0.00-0.24 -0.24

0.00 -12.82 1.69 -0.75 -0.75-5.52 -12.82 4.07 3.02 0.08 2.22-7.15 -23.87 4.29 3.83 0.16 3.59-7.92 -29.48 4.39 4.21 0.21 4.13-8.28 -32.18 4.43 4.41 0.24 4.38-8.46 -33.49 4.45 4.52 0.25 4.50

-0.16 -0.16

2 -5.27 3.42 -5.27 0.42-0.18 -0.18 0.00-0.16 -0.16

0.00 -22.31 1.69 -0.75 -0.75-5.77 -22.31 3.96 5.14 1.44 4.35-7.75 -39.22 4.21 7.58 1.89 7.22-8.77 -47.79 4.34 8.82 2.09 8.65-9.28 -52.02 4.42 9.43 2.19 9.35-9.53 -54.08 4.45 9.73 2.23 9.69

-0.16 -0.16

1 -5.27 3.42 -5.27 0.42-0.18 -0.18 0.00-0.16 -0.16

0.00 -27.15 1.69 -0.75 -0.75-2.88 -27.15 4.10 7.10 0.84 5.95-3.71 -36.94 4.44 9.92 1.16 9.26-4.19 -41.54 4.60 11.23 1.34 10.91-4.45 -43.76 4.68 11.87 1.43 11.71-4.58 -44.84 4.72 12.19 1.48 12.11

ENVOLVENTE DE MOMENTOS Y CORTANTES: VP-1

-4.09 17.45-16.90 11.81 30.24 -12.588.72 -12.40 8.398.72

16.58 -7.77 -17.34 7.74

12.18 -7.77 -11.28 7.74-7.51 26.50-35.10 14.40 54.06 -20.2712.33 -17.56 13.5212.32

22.41 -11.61 -22.12 11.58

20.55 -11.61 -20.72 11.58-7.73 25.32-42.27 14.89 59.79 -20.2712.53 -17.36 13.5212.52

21.39 -13.27 -18.80 13.26

27.70 -13.27 -30.27 13.26

Mu = 27.70 Mu = 30.27 Pu = 33.58 Pu = 82.74

ANALISIS DE PORTICO : VP-2

At = ------- b = hv = hc = S/C=2.00 ------- 0.30 0.65 0.50 250

AT = Z = U = S = C/R= Np =318.30 0.30 1.50 1.2 0.31 8

1.81 1.81 1 2Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m S/C= S/C=

3 9.36 Wlt= 0.20 Wlt= 0.20 100 100

9.36 -7.93 30 × 65 7.93 -1.36 30 × 65 1.36 0.0030 K= 0.95 30 K= 2.29 30

3.70 × K= × K= × K=M 50 0.84 2.5475 50 0.84 2.71 50 0.84

Wdt= 1.54 Tn/m Wdt= 1.37 Tn/m S/C= S/C=2 6.94 Wlt= 0.50 Wlt= 0.80 250 400

16.30 -11.16 30 × 65 11.16 -2.03 30 × 65 2.03 0.0030 K= 0.95 30 K= 2.29 30

3.70 × K= × K= × K= .M 50 0.84 2.5475 50 0.84 2.71 50 0.84


19.83 -11.16 30 × 65 11.16 -2.03 30 × 65 2.03 0.0030 K= 0.95 30 K= 2.29 30

3.70 × K= × K= × K=M 50 0.84 50 0.84 50 0.84

7.25 M 3.00 M

METODO DE TAKABEYA: VP-2

0.00 0.00 0.00

3 -3.58 2.21 -8.16 -0.81 -6.27 -0.22-0.26 -0.12 -0.28 -0.37 0.00-0.24 -0.10 -0.13

0.00 -8.55 2.53 -0.50 -0.50 -0.50-1.06 -8.55 2.18 2.01 -0.79 0.65 0.25 0.91-1.49 -13.82 2.32 2.28 -0.91 0.74 0.30 1.33-1.58 -15.46 2.36 2.38 -0.92 0.74 0.30 1.42-1.61 -15.93 2.36 2.41 -0.92 0.75 0.31 1.44-1.63 -16.07 2.37 2.41 -0.92 0.76 0.31 1.44

-0.16 -0.09 -0.11

2 -5.27 2.12 -9.85 -0.93 -7.96 -0.26-0.18 -0.10 -0.23 -0.29 0.00-0.16 -0.09 -0.11

0.00 -14.88 2.53 -0.50 -0.50 -0.50-0.93 -14.88 1.91 3.43 -0.73 1.62 0.17 1.92-1.39 -23.17 1.99 4.51 -0.75 2.04 0.22 2.92-1.52 -25.94 2.00 4.88 -0.75 2.12 0.23 3.23-1.56 -26.83 2.01 4.99 -0.74 2.15 0.24 3.32-1.57 -27.11 2.01 5.02 -0.74 2.16 0.24 3.34

-0.16 -0.09 -0.11

1 -5.27 2.12 -9.85 -0.93 -7.96 -0.26-0.18 -0.10 -0.23 -0.29 0.00-0.16 -0.09 -0.11

0.00 -18.10 2.53 -0.50 -0.50 -0.50-0.47 -18.10 2.20 4.73 -0.90 2.23 0.13 2.65-0.72 -22.91 2.30 6.26 -0.93 2.56 0.21 3.85-0.79 -24.43 2.33 6.83 -0.94 2.59 0.23 4.26-0.81 -24.94 2.34 7.03 -0.94 2.59 0.24 4.40-0.82 -25.11 2.35 7.10 -0.94 2.59 0.24 4.44

ENVOLVENTE DE MOMENTOS Y CORTANTES: VP-2-4.32 8.42565082 -4.87 0.655-9.61 7.40 12.15 -11.64 -0.24 8.996.21 -6.91 3.60 -1.835.99 4.12

9.58 -4.50 -14.02 7.22 -8.97 4.43

7.07 -4.50 -12.68 7.22 -7.42 4.43-8.06 11.6566207 -4.88 1.432-19.61 9.15 20.51 -22.43 0.18 21.689.11 -9.36 4.31 -3.828.74 5.21

12.47 -6.34 -20.43 10.99 -14.2 7.43

11.00 -6.34 -20.24 10.99 -13.28 7.43-7.60 11.6025855 -5.77 0.999-23.49 9.50 23.22 -27.79 0.17 27.279.27 -9.20 4.24 -3.898.68 5.66

12.49 -7.84 -19.12 10.71 -13.98 8.63

16.50 -7.84 -20.51 10.71 -17.9 8.63

Mu = 16.50 Mu = 20.51 Mu = 17.94 Pu = 24.59 Pu = 37.62 Pu = 9.54

ANALISIS DE PORTICO : VP-1a

At = ------- b = hv = hc = S/C=3.80 ------- 0.30 0.65 0.50 250

AT = Z = U = S = C/R= Np =318.3 0.30 1.50 1.2 0.31 8

2.9125 2.706 1 2Wdt= 1.95 Tn/m Wdt= 1.78 S/C= S/C=

2 8.33 Wlt= 0.38 Tn/m Wlt= 0.38 100 100

8.33 -12.76 30 × 65 12.76 -12.17 30 × 42 *30 K= 0.95 30

3.70 × K= × K= .M 50 0.84 4.1225 50 0.84 4.416


13.04 -18.06 30 × 65 18.06 -19.87 30 × 42 *30 K= 0.95 30

3.70 × K= × K=M 50 0.84 50 0.84

7.25 M 3.00 M

METODO DE TAKABEYA: VP-1a

0.00 0.00

2 -3.58 3.56 -3.58 -0.16-0.26 -0.26 0.00-0.24 -0.24

0.00 -11.40 1.69 -0.75 -0.75-5.37 -11.40 4.06 2.69 -0.05 1.98-6.74 -20.79 4.21 3.37 0.09 3.16-7.35 -24.93 4.27 3.64 0.15 3.60-7.61 -26.67 4.29 3.77 0.17 3.77-7.72 -27.40 4.30 3.83 0.18 3.83

-0.16 -0.16

1 -5.27 3.42 -5.27 0.34-0.18 -0.18 0.00-0.16 -0.16

0.00 -17.85 1.69 -0.75 -0.75-2.83 -17.85 4.03 4.26 0.94 3.60-3.73 -23.75 4.26 5.95 1.24 5.56-4.12 -26.48 4.36 6.65 1.38 6.46-4.30 -27.69 4.40 6.94 1.43 6.86-4.37 -28.20 4.42 7.06 1.46 7.02

ENVOLVENTE DE MOMENTOS Y CORTANTES: VP-1a

-4.44 17.17-15.32 11.69 28.05 -12.178.80 -12.31 8.128.80

15.18 -7.49 -15.71 7.47

12.55 -7.49 -11.94 7.47-8.31 25.00-28.34 14.62 45.00 -19.8712.65 -17.24 13.2512.64

15.66 -9.07 -13.19 9.06

17.89 -9.07 -20.35 9.06

Mu = 17.89 Mu = 20.35 Pu = 21.45 Pu = 50.92

ANALISIS DE PORTICO : VP-2a

At = ------- b = hv = hc = S/C=2.00 ------- 0.30 0.65 0.50 250

AT = Z = U = S = C/R= Np =318.30 0.30 1.50 1.2 0.31 8

1.81 1.63 1 2Wdt= 1.25 Tn/m Wdt= 1.10 Tn/m S/C= S/C=

2 8.33 Wlt= 0.20 Wlt= 0.20 100 100

8.33 -7.93 30 × 65 7.93 -1.22 30 × 45 1.22 0.0030 K= 0.95 30 K= 0.76 30

3.70 × K= × K= × K=M 50 0.84 2.5475 50 0.84 2.53 50 0.84


13.04 -11.16 30 × 65 11.16 -1.90 30 × 45 1.90 0.0030 K= 0.95 30 K= 0.76 30

3.70 × K= × K= × K=M 50 0.84 50 0.84 50 0.84

7.25 M 3.00 M

METODO DE TAKABEYA: VP-2a

0.00 0.00 0.00

2 -3.58 2.21 -5.10 -1.31 -3.21 -0.38-0.26 -0.19 -0.15 -0.24 0.00-0.24 -0.17 -0.26

0.00 -7.60 2.53 -0.50 -0.50 -0.50-0.44 -7.60 2.17 1.79 -1.36 0.93 0.16 1.78-0.81 -13.60 2.26 2.29 -1.40 1.24 0.19 2.56-0.94 -16.04 2.29 2.52 -1.39 1.37 0.20 2.79-1.00 -17.03 2.29 2.60 -1.38 1.44 0.20 2.87-1.02 -17.42 2.30 2.62 -1.38 1.48 0.21 2.90

-0.16 -0.12 -0.17

1 -5.27 2.12 -6.79 -1.36 -4.90 -0.39-0.18 -0.14 -0.11 -0.16 0.00-0.16 -0.12 -0.17

0.00 -11.90 2.53 -0.50 -0.50 -0.50-0.18 -11.90 2.11 2.84 -1.37 1.91 -0.10 2.76-0.33 -15.66 2.18 3.98 -1.34 2.62 -0.02 4.20-0.41 -17.30 2.21 4.47 -1.33 2.88 0.02 4.82-0.45 -17.99 2.22 4.68 -1.32 2.98 0.03 5.08-0.46 -18.27 2.22 4.76 -1.32 3.02 0.04 5.19

ENVOLVENTE DE MOMENTOS Y CORTANTES: VP-2a

-4.89 7.48333014 -3.17 0.486-11.26 7.58 12.76 -7.61 0.33 6.016.35 -6.77 2.98 -1.916.20 3.34

11.16 -5.53 -13.98 7.19 -5.92 2.71

9.29 -5.53 -12.62 7.19 -4.13 2.71-8.20 10.7632661 -3.87 0.952-20.08 9.61 21.00 -12.41 0.82 11.139.11 -9.36 4.22 -3.378.88 4.77

10.75 -6.39 -12.95 7.39 -7.00 4.98

12.90 -6.39 -14.39 7.39 -11.4 4.98

Mu = 12.90 Mu = 14.39 Mu = 11.41 Pu = 15.46 Pu = 23.33 Pu = 5.28

ANALISIS DE PORTICO : VS-1

At = ------- b = hv = hc = S/C=1.60 ------- 0.25 0.60 1.00 250

AT = Z = U = S = C/R= Np =318.3 0.30 1.50 1.2 0.31 3

1.468 1.468 1.468 1.468 1.468 1.468 1.468Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m S/C=

3 25.51 Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m 100

25.51 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.0625 K= 1.40 50 K= 1.40 25 K= 1.40 50 K= 1.40 25 K= 1.40 50 K= 1.40 25 K= 1.40 50

3.70 L× K= × K= T× K= × K= T× K= × K= L× K= × K=M 65 1.55 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 65 1.55 2.063 30 0.30

Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m S/C=2 18.42 Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m 250

43.93 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.8925 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50

3.70 L× K= × K= T× K= × K= T× K= × K= L× K= × K=M 65 1.55 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 65 1.55 2.063 30 0.30


53.32 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.8925 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50

3.70 L× K= × K= T× K= × K= T× K= × K= L× K= × K=M 65 1.55 30 0.30 100 5.63 30 0.30 100 5.63 30 0.30 65 1.55 30 0.30

4.10 M 4.10 M 4.10 M 4.10 M 4.10 M 4.10 M 4.10 M

METODO DE TAKABEYA: VS-1

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

3 -5.88 0.35 -6.19 0.00 -16.84 0.00 -6.19 0.00 -16.84 0.00 -6.19 0.00 -8.67 0.00 -3.40 -0.60-0.24 -0.23 -0.23 -0.08 -0.08 -0.23 -0.23 -0.08 -0.08 -0.23 -0.23 -0.16 -0.16 -0.41-0.26 -0.05 -0.33 -0.05 -0.33 -0.05 -0.18 -0.09

0.00 -3.79 15.57 -0.15 -0.03 -0.54 -0.03 -0.54 -0.03 -0.15 -0.03-0.06 -3.79 0.27 1.00 -0.06 -0.04 0.03 1.27 0.00 -0.10 0.02 1.28 0.00 -0.10 0.11 0.69 -0.57 0.05-0.11 -7.95 0.33 1.65 -0.07 -0.28 0.04 2.06 -0.01 -0.37 0.03 2.07 -0.03 -0.24 0.10 1.20 -0.57 0.18-0.15 -10.88 0.33 2.13 -0.07 -0.42 0.04 2.60 -0.01 -0.52 0.04 2.60 -0.02 -0.33 0.11 1.52 -0.57 0.26-0.17 -12.93 0.34 2.45 -0.08 -0.51 0.05 2.96 -0.01 -0.62 0.05 2.96 -0.03 -0.38 0.11 1.75 -0.57 0.32-0.19 -14.36 0.34 2.68 -0.08 -0.57 0.05 3.21 -0.01 -0.69 0.05 3.21 -0.03 -0.42 0.11 1.90 -0.57 0.37

-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

2 -8.38 0.34 -5.61 0.00 -26.91 0.00 -5.61 0.00 -26.91 0.00 -5.61 0.00 -10.58 0.00 -3.41 -0.85-0.13 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.10 -0.10 -0.32-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

0.00 -6.52 15.57 -0.15 -0.03 -0.54 -0.03 -0.54 -0.03 -0.15 -0.03-0.05 -6.52 0.25 1.72 -0.04 0.22 0.02 1.88 0.00 0.20 0.02 1.88 0.00 0.20 0.09 1.39 -0.74 0.47-0.10 -12.57 0.27 3.02 -0.04 0.15 0.03 3.30 0.00 0.10 0.03 3.30 -0.01 0.19 0.08 2.48 -0.73 0.96-0.13 -16.72 0.28 3.97 -0.04 0.09 0.05 4.32 0.00 0.04 0.05 4.32 -0.01 0.18 0.09 3.24 -0.73 1.30-0.16 -19.58 0.29 4.64 -0.04 0.05 0.05 5.04 0.00 -0.02 0.05 5.03 -0.01 0.16 0.09 3.78 -0.73 1.53-0.18 -21.57 0.29 5.10 -0.04 0.01 0.06 5.54 0.00 -0.06 0.06 5.54 -0.01 0.15 0.10 4.16 -0.72 1.69

-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

1 -8.38 0.34 -5.61 0.00 -26.91 0.00 -5.61 0.00 -26.91 0.00 -5.61 0.00 -10.58 0.00 -3.41 -0.85-0.13 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.10 -0.10 -0.32-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

0.00 -7.92 15.57 -0.15 -0.03 -0.54 -0.03 -0.54 -0.03 -0.15 -0.03-0.03 -7.92 0.31 2.35 -0.05 0.31 0.01 2.62 0.00 0.26 0.01 2.62 0.00 0.26 0.09 1.88 -0.80 0.64-0.05 -11.43 0.33 3.83 -0.06 0.03 0.03 4.32 0.00 -0.06 0.02 4.32 -0.01 0.08 0.09 3.07 -0.80 1.07-0.06 -13.67 0.34 4.87 -0.06 -0.16 0.03 5.46 0.00 -0.27 0.03 5.46 -0.01 -0.03 0.10 3.86 -0.80 1.35-0.08 -15.17 0.34 5.58 -0.06 -0.28 0.04 6.24 0.00 -0.41 0.04 6.24 -0.01 -0.10 0.10 4.40 -0.80 1.55-0.08 -16.20 0.35 6.06 -0.06 -0.36 0.04 6.77 0.00 -0.50 0.04 6.77 -0.01 -0.15 0.11 4.77 -0.79 1.68

ENVOLVENTE DE MOMENTOS Y CORTANTES: VS-1-1.21 2.318 -2.20 2.097 -1.92 2.094 -2.02 2.175 -1.96 2.051 -1.97 2.335 -2.53 0.625-7.88 1.78 4.47 -5.10 1.24 10.28 -9.94 1.42 4.67 -4.58 1.30 10.16 -10.32 1.43 5.35 -3.45 1.23 7.05 -8.35 2.08 4.303.84 -2.18 1.75 -4.27 4.29 -1.72 1.65 -4.37 4.22 -1.80 2.13 -3.89 4.00 -2.022.74 3.03 2.97 2.97 2.99 2.92 3.47

7.25 -2.89 -4.82 2.56 13.31 -3.67 -4.87 2.58 -13.76 3.88 -4.65 2.47 10.10 -4.51 -4.25 2.20

3.43 -2.89 -4.64 2.56 0.26 -3.67 -4.67 2.58 -0.58 3.88 -4.47 2.47 6.59 -4.51 -3.90 2.20-2.29 3.121 -2.91 2.974 -2.76 2.951 -2.83 3.017 -2.77 2.936 -2.80 3.095 -3.47 1.407

-13.50 2.16 8.74 -9.01 1.84 15.14 -14.85 1.95 8.89 -8.77 1.86 15.10 -15.09 1.96 9.35 -7.70 1.83 12.39 -14.45 2.58 9.695.39 -3.07 2.73 -5.72 5.68 -2.78 2.68 -5.77 5.63 -2.83 3.08 -5.37 5.39 -3.074.03 4.21 4.18 4.18 4.19 4.16 4.73

9.37 -4.68 -6.76 3.68 20.86 -9.37 -6.80 3.71 -21.07 9.54 -6.57 3.58 13.32 -6.95 -5.75 3.12

7.96 -4.68 -6.88 3.68 13.82 -9.37 -6.93 3.71 -14.24 9.54 -6.66 3.58 12.39 -6.95 -5.78 3.12-2.19 3.139 -2.97 2.921 -2.79 2.933 -2.85 2.98 -2.81 2.904 -2.80 3.11 -3.52 1.264

-15.11 2.22 9.00 -9.61 1.83 17.39 -17.12 1.94 9.28 -9.19 1.87 17.29 -17.50 1.95 10.01 -7.72 1.82 13.42 -15.84 2.66 10.195.72 -2.74 2.33 -6.13 6.14 -2.32 2.25 -6.20 6.06 -2.40 2.84 -5.62 5.61 -2.854.00 4.24 4.19 4.20 4.21 4.15 4.78

7.23 -6.30 -5.21 2.78 14.95 -18.32 -5.25 2.80 -14.98 18.46 -5.05 2.72 10.50 -7.62 -4.41 2.46

16.07 -6.30 -5.08 2.78 52.83 -18.32 -5.10 2.80 -53.32 18.46 -5.00 2.72 17.71 -7.62 -4.68 2.46

Mu = 16.07 Mu = 5.08 Mu = 52.83 Mu = 5.10 Mu = 53.32 Mu = 5.00 Mu = 17.71 Mu = 4.68 Pu = 14.95 Pu = 14.79 Pu = 32.24 Pu = 13.40 Pu = 32.25 Pu = 15.08 Pu = 29.87 Pu = 7.94

S/C=

S/C=

S/C=

ANALISIS DE PORTICO : VS-1a

At = ------- b = hv = hc = S/C=1.60 ------- 0.25 0.60 0.90 250

AT = Z = U = S = C/R= Np =271 0.30 1.50 1.2 0.31 3

1.4675 1.47 1.47 1.47 1.43 1.43Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 0.98 Tn/m Wdt= 0.98 Tn/m S/C=

2 18.93 Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m 100

18.93 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.00 25 × 60 2.00 -2.00 25 × 60 2.00 0.0025 K= 1.40 50 K= 1.40 25 K= 1.40 50 K= 1.40 25 K= 1.10 50 K= 1.10 25

3.70 L× K= × K= T× K= × K= T× K= × K= L× K=M 65 1.55 2.0625 30 0.30 2.06 100 5.63 2.06 30 0.30 2.06 100 5.63 2.06 30 0.30 2.06 65 1.55

Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m Wdt= 1.25 Tn/m S/C=1 10.72 Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m Wlt= 0.40 Tn/m 250

29.65 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 0.0025 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25

3.70 L× K= × K= T× K= × K= T× K= × K= L× K=M 65 1.55 30 0.30 100 5.63 30 0.30 100 5.63 30 0.30 65 1.55

4.10 M 4.10 M 4.10 M 4.10 M 4.10 M 4.10 M

METODO DE TAKABEYA: VS-1a

0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 -5.88 0.35 -6.19 0.00 -16.84 0.00 -6.19 0.00 -16.25 0.00 -5.00 0.00 -5.29 -0.38-0.24 -0.23 -0.23 -0.08 -0.08 -0.23 -0.23 -0.09 -0.07 -0.22 -0.22 -0.21 0.00-0.26 -0.05 -0.33 -0.05 -0.35 -0.06 -0.29

0.00 -2.87 15.27 -0.15 -0.03 -0.55 -0.03 -0.55 -0.03 -0.150.01 -2.87 0.26 0.75 -0.06 -0.03 0.00 0.96 0.00 -0.08 -0.01 1.00 0.08 -0.05 -0.30 0.850.01 -6.04 0.28 1.27 -0.06 -0.22 0.00 1.60 0.00 -0.30 -0.01 1.66 0.06 -0.19 -0.31 1.460.01 -8.16 0.28 1.66 -0.06 -0.34 0.00 2.03 0.00 -0.43 -0.01 2.10 0.07 -0.29 -0.31 1.860.01 -9.61 0.28 1.92 -0.06 -0.42 0.00 2.32 0.00 -0.52 -0.01 2.40 0.07 -0.35 -0.31 2.130.01 -10.59 0.28 2.10 -0.06 -0.47 0.00 2.52 0.00 -0.58 -0.01 2.60 0.07 -0.39 -0.31 2.31

-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.18

1 -8.38 0.34 -5.61 0.00 -26.91 0.00 -5.61 0.00 -26.91 0.00 -5.61 0.00 -8.38 -0.34-0.13 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.13 0.00-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.18

0.00 -4.49 15.27 -0.15 -0.03 -0.55 -0.03 -0.55 -0.03 -0.150.00 -4.49 0.30 1.22 -0.06 0.16 0.00 1.33 0.00 0.14 0.00 1.32 0.06 0.14 -0.30 1.180.00 -6.34 0.30 2.03 -0.06 0.03 0.00 2.25 0.00 -0.01 0.00 2.24 0.06 0.01 -0.30 2.010.00 -7.59 0.30 2.60 -0.06 -0.08 0.00 2.87 0.00 -0.12 0.00 2.86 0.05 -0.08 -0.30 2.570.00 -8.44 0.30 2.99 -0.06 -0.15 0.00 3.30 0.00 -0.20 0.00 3.28 0.05 -0.15 -0.30 2.960.00 -9.02 0.30 3.25 -0.06 -0.19 0.00 3.59 0.00 -0.25 0.00 3.57 0.05 -0.19 -0.30 3.22

ENVOLVENTE DE MOMENTOS Y CORTANTES: VS-1a-1.35 2.28 -2.23 1.97 -2.05 2.06 -2.07 2.03 -1.95 2.14 -2.20 1.4 0.00-6.55 1.70 3.90 -4.43 1.30 8.35 -8.27 1.36 3.96 -4.08 1.37 8.49 -7.25 1.27 4.15 -3.89 1.61 6.053.66 -2.36 2.05 -3.96 4.06 -1.96 1.93 -4.08 3.69 -2.18 2.40 -3.462.78 3.07 3.00 3.02 2.89 3.13 ###

6.21 -2.88 -3.62 1.93 ### -4.37 -3.64 1.94 -10.2 4.05 3.57 -1.91 -5.65 2.67

4.45 -2.88 -3.53 1.93 5.05 -4.37 -3.55 1.94 -4.7 4.05 3.51 -1.91 -4.23 2.67-2.30 3.09 -3.01 2.83 -2.89 2.89 -2.89 2.88 -2.83 3.01 -3.10 2.3 0.00-9.2 2.17 6.24 -6.53 1.87 ### -10.5 1.91 6.28 -6.26 1.91 ### -10.5 1.87 6.50 -6.20 2.17 9.154.96 -3.50 3.26 -5.20 5.26 -3.20 3.21 -5.25 5.20 -3.26 3.51 -4.954.03 4.27 4.23 4.23 4.19 4.42 ###

4.82 -3.84 -2.89 1.54 ### -11.1 -2.90 1.54 -10.6 ### 2.90 -1.54 -4.92 3.88

9.39 -3.84 -2.82 1.54 ### -11.1 -2.82 1.54 -30.7 ### 2.82 -1.54 -9.43 3.88

Mu = 9.39 Mu = 2.82 Mu = 30.59 Mu = 2.82 Mu = 30.69 Mu = 2.82 Mu = 9.43 Pu = 8.61 Pu = 11.17 Pu = 18.48 Pu = 10.30 Pu = 18.22 Pu = 11.35 Pu = 8.41

S/C=

S/C=

ANALISIS DE PORTICO : VS-1b

At = ------- b = hv = hc = S/C=1.60 ------- 0.25 0.60 1.00 250

AT = Z = U = S = C/R= Np =318.3 0.30 1.50 1.2 0.31 3

1.8 1.8 1.8 1.8 1.468 1.468 1.468Wdt= 1.28 Tn/m Wdt= 1.28 Tn/m Wdt= 1.28 Tn/m Wdt= 1.28 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m Wdt= 1.01 Tn/m S/C=

2 22.20 Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m Wlt= 0.16 Tn/m 100

22.20 -2.52 25 × 65 2.52 -2.52 25 × 65 2.52 -2.52 25 × 65 2.52 -2.52 25 × 65 2.52 -2.06 25 × 65 2.06 -2.06 25 × 65 2.06 -2.06 25 × 65 2.0625 K= 1.40 50 K= 1.40 25 K= 1.40 50 K= 1.40 25 K= 1.40 50 K= 1.40 25 K= 1.40 50

3.70 L× K= × K= T× K= × K= T× K= × K= L× K= × K=M 65 1.55 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 100 5.63 2.063 30 0.30 2.063 65 1.55 2.063 30 0.30


34.78 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.89 -2.89 25 × 60 2.8925 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50 K= 1.10 25 K= 1.10 50

3.70 L× K= × K= T× K= × K= T× K= × K= L× K= × K=M 65 1.55 30 0.30 100 5.63 30 0.30 100 5.63 30 0.30 65 1.55 30 0.30

4.10 M 4.10 M 4.10 M 4.10 M 4.10 M 4.10 M 4.10 M

METODO DE TAKABEYA: VS-1b

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 -5.88 0.43 -6.19 0.00 -16.84 0.00 -6.19 0.00 -16.84 -0.03 -6.19 0.00 -8.67 0.00 -3.40 -0.60-0.24 -0.23 -0.23 -0.08 -0.08 -0.23 -0.23 -0.08 -0.08 -0.23 -0.23 -0.16 -0.16 -0.41-0.26 -0.05 -0.33 -0.05 -0.33 -0.05 -0.18 -0.09

0.00 -3.30 15.57 -0.15 -0.03 -0.54 -0.03 -0.54 -0.03 -0.15 -0.03-0.06 -3.30 0.35 0.87 -0.08 -0.03 0.03 1.11 0.00 -0.09 -0.01 1.11 0.00 -0.09 0.11 0.60 -0.57 0.05-0.11 -6.78 0.40 1.42 -0.09 -0.25 0.04 1.78 0.00 -0.33 0.00 1.79 -0.02 -0.21 0.10 1.03 -0.56 0.15-0.14 -8.99 0.41 1.82 -0.09 -0.37 0.05 2.21 0.00 -0.46 0.01 2.21 -0.02 -0.29 0.10 1.29 -0.56 0.22-0.17 -10.41 0.41 2.06 -0.09 -0.45 0.05 2.48 -0.01 -0.54 0.02 2.47 -0.02 -0.34 0.10 1.46 -0.56 0.26-0.18 -11.33 0.41 2.22 -0.09 -0.49 0.05 2.65 -0.01 -0.59 0.02 2.64 -0.02 -0.37 0.11 1.57 -0.56 0.29

-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

1 -8.38 0.34 -5.61 0.00 -26.91 0.00 -5.61 0.00 -26.91 0.00 -5.61 0.00 -10.58 0.00 -3.41 -0.85-0.13 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.04 -0.04 -0.20 -0.20 -0.10 -0.10 -0.32-0.18 -0.05 -0.21 -0.05 -0.21 -0.05 -0.15 -0.09

0.00 -5.17 15.57 -0.15 -0.03 -0.54 -0.03 -0.54 -0.03 -0.15 -0.03-0.03 -5.17 0.30 1.40 -0.05 0.19 0.01 1.53 0.00 0.16 0.02 1.53 0.00 0.16 0.08 1.13 -0.82 0.39-0.05 -7.23 0.31 2.30 -0.05 0.02 0.03 2.55 0.00 -0.02 0.03 2.55 -0.01 0.05 0.09 1.85 -0.81 0.64-0.07 -8.57 0.31 2.90 -0.05 -0.10 0.04 3.22 0.00 -0.15 0.04 3.22 -0.01 -0.02 0.10 2.31 -0.81 0.80-0.08 -9.45 0.32 3.30 -0.05 -0.17 0.04 3.65 0.00 -0.24 0.05 3.65 -0.02 -0.07 0.11 2.61 -0.81 0.91-0.09 -10.02 0.32 3.55 -0.05 -0.23 0.05 3.93 0.00 -0.29 0.05 3.93 -0.02 -0.10 0.11 2.81 -0.81 0.97

ENVOLVENTE DE MOMENTOS Y CORTANTES: VS-1b-1.50 2.838 -2.71 2.543 -2.38 2.579 -2.51 2.564 -2.03 2.031 -1.96 2.327 -2.54 0.642-7.00 2.17 4.55 -5.03 1.53 9.26 -8.96 1.72 4.64 -4.56 1.64 9.12 -8.90 1.39 4.70 -3.13 1.25 6.20 -7.33 2.07 3.644.29 -3.09 2.66 -4.72 4.74 -2.64 2.58 -4.80 4.03 -1.98 2.26 -3.76 3.91 -2.113.36 3.73 3.64 3.68 3.01 2.92 3.47

6.67 -3.01 -3.94 2.10 11.65 -4.34 -3.95 2.11 -12.41 4.70 -3.77 2.02 8.54 -4.10 -3.62 1.92

4.47 -3.01 -3.85 2.10 4.42 -4.34 -3.86 2.11 -4.99 4.70 -3.69 2.02 6.63 -4.10 -3.48 1.92-2.23 3.131 -2.95 2.935 -2.79 2.932 -2.84 3.001 -2.79 2.913 -2.80 3.112 -3.54 1.235-9.78 2.20 6.53 -6.77 1.83 11.31 -11.09 1.94 6.60 -6.50 1.87 11.30 -11.30 1.96 7.00 -5.66 1.82 9.16 -10.77 2.67 6.455.02 -3.44 3.12 -5.34 5.32 -3.13 3.06 -5.40 5.28 -3.18 3.37 -5.08 5.28 -3.184.01 4.23 4.19 4.19 4.20 4.15 4.79

5.37 -4.25 -3.24 1.73 12.18 -12.49 -3.25 1.73 -12.06 12.58 -3.14 1.69 7.01 -4.91 -2.97 1.62

10.36 -4.25 -3.16 1.73 34.04 -12.49 -3.16 1.73 -34.47 12.58 -3.11 1.69 11.18 -4.91 -3.02 1.62

Mu = 10.36 Mu = 3.16 Mu = 34.04 Mu = 3.16 Mu = 34.47 Mu = 3.11 Mu = 11.18 Mu = 3.02 Pu = 9.31 Pu = 12.31 Pu = 20.13 Pu = 11.40 Pu = 19.51 Pu = 10.80 Pu = 18.03 Pu = 5.28

S/C=

S/C=

ANALISIS DE LOSAS MACIZAS 2D: METODO PSEUDO 3M - DIR XX

ANCHO: At = 7.00 m

h1 = L1/40 = 0.10 mh = 0.12 m

METRADOS DE CARGA:PESO PROPIO : 2.40 x 1.00 x .12 = 0.29 Tn/m SOBRECARGA : 0.10 x 1.00 = 0.10 Tn/mACAB. IMPERMEAB: 0.10 x 1.00 = 0.10 Tn/m L = 0.10 Tn/mONDULINE: 0.010 x 1.00 = 0.01 Tn/m

D = 0.40 Tn/m

CARGA MUERTA: D = 0.40 Tn/m W1 = (1.5 D +1.8 L) = 0.78 Tn/m

CARGA VIVA: L = 0.10 Tn/m W2 = (1.5 D) = 0.60 Tn/m

W = 0.72 Tn/m 0.72 Tn/m 0.72 Tn/m 0.72 Tn/m 0.72 Tn/m 0.72 Tn/m

A B C D E F G3.80 M 3.80 M 3.80 M 3.80 M 3.80 M 3.80 M

-1.30 -1.30 -1.30 -1.30 -1.300.00 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.00

-0.97 -0.73 -0.79 -0.77 -1.10-1.11 -0.82 -0.90 -0.80 -1.10-1.09 -0.80 -0.90 -0.80 -1.10-1.10 -0.80 -0.90 -0.80 -1.10-1.10 -0.80 -0.90 -0.80 -1.10

M 0.00 0.81 -1.10 -1.10 0.35 -0.80 -0.80 0.45 -0.90 -0.90 0.45 -0.80 -0.80 0.35 -1.10 -1.10 0.81 0.00V 1.08 -1.65 1.44 -1.28 1.34 -1.39 1.39 -1.34 1.28 -1.44 1.65 -1.08


A B C D E F G3.80 M 3.80 M 3.80 M 3.80 M 3.80 M 3.80 M

-1.15 -1.15 -1.15 -1.15 -1.150.00 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.00

-0.86 -0.64 -0.70 -0.68 -0.97-0.98 -0.73 -0.79 -0.70 -0.97-0.96 -0.71 -0.79 -0.71 -0.97-0.97 -0.71 -0.79 -0.71 -0.97-0.97 -0.71 -0.79 -0.71 -0.97

M 0.00 0.86 -0.97 -0.97 0.16 -0.71 -0.71 0.55 -0.79 -0.79 0.25 -0.71 -0.71 0.46 -0.97 -0.97 0.57 0.00V 1.11 -1.62 1.12 -0.98 1.34 -1.39 1.07 -1.03 1.29 -1.43 1.30 -0.79


A B C D E F G3.80 M 3.80 M 3.80 M 3.80 M 3.80 M 3.80 M

-1.15 -1.15 -1.15 -1.15 -1.150.00 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.00

-0.86 -0.64 -0.70 -0.68 -0.97-0.98 -0.73 -0.79 -0.70 -0.97-0.96 -0.71 -0.79 -0.71 -0.97-0.97 -0.71 -0.79 -0.71 -0.97-0.97 -0.71 -0.79 -0.71 -0.97

M 0.00 0.57 -0.97 -0.97 0.46 -0.71 -0.71 0.25 -0.79 -0.79 0.55 -0.71 -0.71 0.16 -0.97 -0.97 0.86 0.00V 0.79 -1.30 1.43 -1.29 1.03 -1.07 1.39 -1.34 0.98 -1.12 1.62 -1.11

ENVOLVENTES DE MOMENTOS Y CORTANTES - DIR YY

-0.47 0.86 -1.10 -1.10 0.46 -0.80 -0.80 0.55 -0.90 -0.90 0.55 -0.80 -0.80 0.46 -1.10 -1.10 0.86 -0.471.11 -1.65 1.44 -1.29 1.34 -1.39 1.39 -1.34 1.29 -1.44 1.65 -1.11

ACEROS:

Asyy = 3.65 cm² = 0.35 m Ø 1/2 @ 0.36 m Asm = 2.97 cm² = 0.43 m Ø 1/2 @ 0.43 m

Asyy = Ø 1/2 @ 0.25 m

ANALISIS DE LOSAS MACIZAS 2D: METODO PSEUDO 3M DIR YY

ANCHO: At = 3.80 mC. MUERTA: D = 0.40 Tn/m W1 = (1.5 D +1.8 L) = 0.78 Tn/mC. VIVA: L = 0.10 Tn/m W2 = (1.5 D) = 0.60 Tn/m

W = 0.06 Tn/m

W = Wi . Km

B Km = At^4/(At^4+L^4)A CTE DE MARCUS

7.00 M

M 0.00 0.38 0.00V 0.22 -0.22

W = 0.05 Tn/m

B ACEROS:A

7.00 M Asyy = 5.31 cm² = 0.24 m Ø 1/2 @ 0.24 m Asm = 2.97 cm² = 0.43 m Ø 1/2 @ 0.43 m

M 0.00 0.29 0.00 Asyy = Ø 1/2 @ 0.20 m V 0.17 -0.17

ENVOLVENTES DE MOMENTOS Y CORTANTES - DIR YY

-1.59 0.38 -1.59

0.22 -0.22

ANALISIS DE LOSAS ALIGERADAS: METODO PSEUDO 3M

LOSA 01

CARGA MUERTA: D 0.40 Tn/m W1 = (1.5 D +1.8 L)/2.5 0.49 Tn/m

CARGA VIVA: L 0.35 Tn/m W2 = (1.5 D)/2.5 = 0.24 Tn/m

W = 0.49 Tn/m 0.49 Tn/m 0.49 Tn/m 0.49 Tn/m 0.49 Tn/m 0.49 Tn/m 0.49 Tn/m

A B C D E F G H5.45 M 5.95 M 5.95 M 5.95 M 5.95 M 5.95 M 5.45 M

-2.01 -2.18 -2.18 -2.18 -2.18 -2.010.00 0.26 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.00

-1.44 -1.27 -1.31 -1.30 -1.35 -1.66-1.68 -1.43 -1.49 -1.47 -1.40 -1.65-1.64 -1.39 -1.46 -1.46 -1.40 -1.64-1.65 -1.40 -1.46 -1.46 -1.40 -1.64-1.64 -1.40 -1.46 -1.46 -1.40 -1.64

M 0.00 1.10 -1.64 -1.64 0.66 -1.40 -1.40 0.75 -1.46 -1.46 0.72 -1.46 -1.46 0.75 -1.40 -1.40 0.66 -1.64 -1.64 1.10 0.00V 1.04 -1.64 1.50 -1.42 1.45 -1.47 1.46 -1.46 1.47 -1.45 1.42 -1.50 1.64 -1.04



-1.43 -1.62 -1.62 -1.62 -1.62 -1.430.00 0.26 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.00

-1.00 -0.96 -0.97 -0.97 -1.02 -1.16-1.18 -1.08 -1.11 -1.09 -1.06 -1.15-1.15 -1.06 -1.08 -1.08 -1.06 -1.15-1.15 -1.06 -1.08 -1.08 -1.06 -1.15-1.15 -1.06 -1.08 -1.08 -1.06 -1.15

M 0.00 1.30 -1.15 -1.15 -0.04 -1.06 -1.06 1.10 -1.08 -1.08 -0.02 -1.08 -1.08 1.10 -1.06 -1.06 -0.04 -1.15 -1.15 1.30 0.00

V 1.13 -1.55 0.73 -0.70 1.46 -1.47 0.71 -0.71 1.47 -1.46 0.70 -0.73 1.55 -1.13



-1.56 -1.62 -1.62 -1.62 -1.62 -1.560.00 0.26 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.00

-1.14 -0.93 -0.98 -0.97 -0.99 -1.30-1.32 -1.04 -1.12 -1.09 -1.02 -1.30-1.29 -1.02 -1.09 -1.09 -1.02 -1.30-1.30 -1.02 -1.09 -1.09 -1.02 -1.30-1.30 -1.02 -1.09 -1.09 -1.02 -1.30

M 0.00 0.36 -1.30 -1.30 1.02 -1.02 -1.02 0.01 -1.09 -1.09 1.09 -1.09 -1.09 0.01 -1.02 -1.02 1.02 -1.30 -1.30 0.36 0.00V 0.42 -0.89 1.51 -1.42 0.70 -0.73 1.46 -1.46 0.73 -0.70 1.42 -1.51 0.89 -0.42

ENVOLVENTES DE MOMENTOS Y CORTANTES

-0.61 1.30 -1.64 -1.64 1.02 -1.40 -1.40 1.10 -1.46 -1.46 1.09 -1.46 -1.46 1.10 -1.40 -1.40 1.02 -0.73 -1.64 1.30 -0.611.13 -1.64 1.51 -1.42 1.46 -1.47 1.46 -1.46 1.47 -1.46 1.42 -1.51 1.64 -1.13

ACEROS :

As(-) = 2.90 CM² = 2.28 Ø1/2 = 1 Ø 1/2" + 1 Ø3/8"As(+) = 2.29 CM² = 1.79 Ø1/2 = 1 Ø 1/2" + 1 Ø3/8"As m = 0.56 CM² =

LOSA 02

CARGA MUERTA: D 0.40 Tn/m W1 = (1.5 D +1.8 L1)/2.50.53 Tn/m

CARGA VIVA: L 1 0.40 Tn/m W2 = (1.5 D +1.8 L2)/2.50.60 Tn/m

CARGA VIVA: L2 0.50 Tn/m W3 = (1.5 D)/2.5 = 0.24 Tn/m

W = 0.53 Tn/m 0.53 Tn/m 0.53 Tn/m 0.60 Tn/m

A B C D E5.90 M 6.00 M 6.00 M 5.90 M

-2.34 -2.38 -2.490.00 0.25 0.25 0.25 0.25 0.25

-1.74 -1.32 -2.16-2.00 -1.33 -2.16-2.00 -1.34 -2.16-2.00 -1.34 -2.16-2.00 -1.34 -2.16

M 0.00 1.41 -2.00 -2.00 0.72 -1.34 -1.34 0.65 -2.16 -2.16 1.64 0.00V 1.22 -1.90 1.69 -1.47 1.45 -1.72 2.14 -1.40

W = 0.53 Tn/m 0.24 Tn/m 0.53 Tn/m 0.24 Tn/m

A B C D E5.90 M 6.00 M 6.00 M 5.90 M

-1.68 -1.73 -1.720.00 0.25 0.25 0.25 0.25 0.25

-1.25 -0.99 -1.47-1.43 -1.00 -1.46-1.43 -1.00 -1.46-1.43 -1.00 -1.46

-1.43 -1.00 -1.46

M 0.00 1.64 -1.43 -1.43 -0.13 -1.00 -1.00 1.15 -1.46 -1.46 0.44 0.00V 1.32 -1.80 0.79 -0.65 1.51 -1.66 0.96 -0.46

W = 0.24 Tn/m 0.53 Tn/m 0.24 Tn/m 0.60 Tn/m

A B C D E5.90 M 6.00 M 6.00 M 5.90 M

-1.72 -1.73 -1.840.00 0.25 0.25 0.25 0.25 0.25

-1.28 -0.95 -1.60-1.48 -0.96 -1.60 1.84-1.47 -0.96 -2.05 1.42-1.47 -0.85 -1.98-1.50 -0.86 -1.62

M 0.00 0.43 -1.50 -1.50 1.21 -0.86 -0.86 -0.13 -1.62 -1.62 1.86 0.00V 0.45 -0.96 1.69 -1.48 0.59 -0.85 2.05 -1.49

ENVOLVENTES DE MOMENTOS Y CORTANTES

-0.77 1.64 -2.00 -2.00 1.21 -1.34 -1.34 1.15 -2.16 -2.16 1.86 0.001.32 -1.90 1.69 -1.48 1.51 -1.72 2.14 -1.49

ACEROS :

As(-) = 3.80 CM² = 2.98 Ø1/2 = 2 Ø 1/2"As(+) = 3.29 CM² = 2.58 Ø1/2 = 1 Ø 1/2" + 1 Ø3/8"As m = 0.56 CM² =

FLEXO COMPRESION EN COLUMNAS

COLUMNA: C-1

DATOS : ab1 (cm) = h1 (cm)= f'c = fy = h1

30 50 210.00 4200.00kg/cm² kg/cm²

Mu = Pu = e = Mu/Pu 31.49 86.18 36.54 b1

tn-m tn cm

Ao = b1.h1 = 1500 cm²

Yc = h1/2 = 25.00 cm

As1 (cm²) = 2 Ø 3/4"+1 Ø 5/8" = 7.73 d1 (cm) = 4.00

As2 (cm²) = 2 Ø 5/8" = 3.98 d2 (cm) = 25.00

As3 (cm²) = 2 Ø 3/4"+1 Ø 5/8" = 7.73 d3 (cm) = 46.00

A = 19.44 cm²

Po = (0.85 .fc'. Ao + A .fy)/1000 = 349.41 tn

Cb = 6000 . d3 /(6000 + fy) = 27.06 cm

c = 27.059 cm

fs1 = 6000 . (c - d1)/c = 4200.00 kg/cm² F1 = 32.46 tn

fs2 = 6000 . (c - d2)/c = 456.52 kg/cm² F2 = 1.82 tn

fs3 = 6000 . (c - d3)/c = -4200.00 kg/cm² F3 = -32.46 tn

SF = 1.82 tn

a = 0.85 .c = 23.00 cm

Ac = b1 . a = 690.00 cm²

Yg = a/2 = 11.50 cm

Cc = 0.85. fc'.Ac/1000 = 123.17 tn

Pb = Cc + SF = 124.98 tn

F(0) = Cc F(i) = fs(i) . As(i)y(0) = Yc - Yg y(i) = Yc - d(i) M = F(i) .y (i)

F y M123.17 13.50 1662.7275

32.46 21.00 681.76

1.82 0.00 0.00

-32.46 -21.00 681.76

Mb = 30.26 tn-m

Vfx = (Pu/0.7 - Pb) / (Po - Pb) + (Mu/0.7/Mb)^1.5 <= 1.00

Vfx = 1.80 OK !!

COLUMNA: C-1 x-x b2


105 25 210.00 4200.00b2 (cm) = h2 (cm)= kg/cm² kg/cm²

35 30h1

Mu = Pu = e = Mu/Pu 31.49 86.18 36.54 b1tn-m tn cm

Ao = b1.h1 +b2.h2 = 3675 cm²

Yc =((b1.h1)(h1/2+h2) + (b2.h2)(h2/2))/Ao 34.64 cm

As1 (cm²) = 2 Ø 1"+ 1 Ø 3/4" = 13.07 d1 (cm) = 3.00

As2 (cm²) = 2 Ø 3/4"+ 2 Ø 5/8" = 9.72 d2 (cm) = 33.00

As3 (cm²) = 2 Ø 1"+ 1 Ø 3/4" + 2 Ø 5/8" = 17.05 d3 (cm) = 52.00

A = 39.84 cm²

Po = (0.85 .fc'. Ao + A .fy)/1000 = 823.33 tn

Cb = 6000 . d3 /(6000 + fy) = 30.59 cm

c = 30.588 cm

fs1 = 6000 . (c - d1)/c = 4200.00 kg/cm² F1 = 54.89 tn

fs2 = 6000 . (c - d2)/c = -473.08 kg/cm² F2 = -4.60 tn

fs3 = 6000 . (c - d3)/c = -4200.00 kg/cm² F3 = -71.62 tn

SF = -21.33 tn

a = 0.85 .c = 26.00 cm

Ac = b2 . a = 910.00 cm²

Yg = a/2 = 13.00 cm

Cc = 0.85. fc'.Ac/1000 = 162.44 tn

Pb = Cc + SF = 141.10 tn


F y M162.44 21.64 3515.5575

54.89 31.64 1736.84

-4.60 1.64 -7.56

-71.62 -17.36 1243.17

Mb = 64.88 tn-m


Vfx = 0.55 OK !!

COLUMNA: C-3 x-x b2


65 25 210.00 4200.00b2 (cm) = h2 (cm)= kg/cm² kg/cm²

30 30h1

Mu = Pu = e = Mu/Pu 21.29 39.66 53.68 b1tn-m tn cm

Ao = b1.h1 +b2.h2 = 2525 cm²

Yc =((b1.h1)(h1/2+h2) + (b2.h2)(h2/2))/Ao 32.70 cm

As1 (cm²) = 2 Ø 1" = 10.20 d1 (cm) = 3.00

As2 (cm²) = 3 Ø 5/8" = 5.98 d2 (cm) = 33.00

As3 (cm²) = 2 Ø 1"+ 1 Ø 5/8" = 12.19 d3 (cm) = 52.00

A = 28.37 cm²

Po = (0.85 .fc'. Ao + A .fy)/1000 = 569.86 tn

Cb = 6000 . d3 /(6000 + fy) = 30.59 cm

c = 30.588 cm

fs1 = 6000 . (c - d1)/c = 4200.00 kg/cm² F1 = 42.84 tn

fs2 = 6000 . (c - d2)/c = -473.08 kg/cm² F2 = -2.83 tn

fs3 = 6000 . (c - d3)/c = -4200.00 kg/cm² F3 = -51.21 tn

SF = -11.19 tn

a = 0.85 .c = 26.00 cm

Ac = b2 . a = 780.00 cm²

Yg = a/2 = 13.00 cm

Cc = 0.85. fc'.Ac/1000 = 139.23 tn

Pb = Cc + SF = 128.04 tn


F y M

139.23 19.70 2742.56

42.84 29.70 1272.26

-2.83 -0.30 0.85

-51.21 -19.30 988.40

Mb = 50.04 tn-m


Vfx = 0.31 OK !!

METODO DE PSEUDO 3M

VIGA DE CIMENTACION: VC-2

Pu 33.58 82.74

Wu = -16.04 Tn/m

R -58.16 -58.16Â -1528.40 -1528.40

A B7.25 M

M 0.00 -105.41 0.00V -58.16 58.16

ACEROS EN ZAPATAS COMBINADAS :

- ENVOLVENTE DE MOMENTOS Y ACEROS : Vc-1 (35 x 100)

M(-) = 105.41 TN/M² As(-) = 32.94 6 Ø 1" M(+) = 0.00 TN/M² As(+) = 0.00 3 Ø 1"

As min = 9.50 CM²

2 Est Ø 3/8 : 2 @ 0.05 [email protected] [email protected] RTO @ 0.20

DESPLAZAMIENTOS EN LA ESTRUCTURA

A continuacion mostraremos los desplazamientos producidos en cada uno de los

bloques que tengan o no, una junta sismica, teniendo en cuenta que los ejes X-X

estan en la direccion longitudinal de los bloques, y que los ejes Y-Y, son transversales.

1) BLOQUE 01

DIRECCION X-X

# PISO Fi (Tn) Ki (Tn/cm) Fi/Ki Xi (cm) Di

2 44.53 384.37 0.12 0.20 0.0005 D <= 0,007

1 32.41 384.37 0.08 0.08 0.0002 OK

1.20 cm

DIRECCION Y-Y


2 44.53 302.06 0.15 0.25 0.0009 D <= 0,007

1 32.41 302.06 0.11 0.11 0.0003 OK

1.53 cm

2) BLOQUE 02

DIRECCION X-X


2 79.17 755.28 0.10 0.19 0.0005 D <= 0,007

1 66.19 755.28 0.09 0.09 0.0002 OK

1.15 cm

DIRECCION Y-Y


2 79.17 568.59 0.14 0.26 0.0009 D <= 0,007

1 66.19 568.59 0.12 0.12 0.0003 OK

1.53 cm

∆xx =

∆yy =

∆xx =

∆yy =

3) BLOQUE 03

DIRECCION X-X


2 46.08 389.97 0.12 0.21 0.0006 D <= 0,007

1 36.34 389.97 0.09 0.09 0.0002 OK

1.27 cm

DIRECCION Y-Y


2 46.08 317.61 0.15 0.26 0.0009 D <= 0,007

1 36.34 317.61 0.11 0.11 0.0003 OK

1.56 cm

4) BLOQUE 04

DIRECCION X-X


2 67.14 601.71 0.11 0.20 0.0005 D <= 0,007

1 51.85 601.71 0.09 0.09 0.0002 OK

1.19 cm

DIRECCION Y-Y


2 67.14 461.98 0.15 0.26 0.0009 D <= 0,007

1 51.85 461.98 0.11 0.11 0.0003 OK

1.55 cm

∆xx =

∆yy =

∆xx =

∆yy =

5) BLOQUE 05

DIRECCION X-X


2 33.44 244.27 0.14 0.24 0.0007 D <= 0,007

1 25.42 244.27 0.10 0.10 0.0002 OK

1.45 cm

DIRECCION Y-Y


2 33.44 230.99 0.14 0.25 0.0009 D <= 0,007

1 25.42 230.99 0.11 0.11 0.0003 OK

1.53 cm

6) BLOQUE 06

DIRECCION X-X


3 61.04 522.21 0.12 0.32 0.0009 D <= 0,007

2 70.09 522.21 0.13 0.20 0.0006 OK

1 35.05 522.21 0.07 0.07 0.0001

1.21 cm

DIRECCION Y-Y


3 61.04 368.70 0.17 0.36 0.0013 D <= 0,007

2 70.09 368.70 0.19 0.29 0.0010 OK

1 35.05 368.70 0.10 0.10 0.0003

1.71 cm

∆xx =

∆yy =

∆xx =

∆yy =

7) BLOQUE 07

DIRECCION X-X


3 66.70 452.68 0.15 0.39 0.0011 D <= 0,007

2 73.16 452.68 0.16 0.24 0.0007 OK

1 36.58 452.68 0.08 0.08 0.0002

1.45 cm

DIRECCION Y-Y


3 66.70 364.25 0.18 0.38 0.0014 D <= 0,007

2 73.16 364.25 0.20 0.30 0.0011 OK

1 36.58 364.25 0.10 0.10 0.0003

1.81 cm

∆xx =

∆yy =

memoria de calculo _ aba

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