Memoria Est. 2

CARRETERA: Autopista México - QuerétaroTRAMO: Palmillas - QuerétaroORIGEN: MéxicoFECHA: Mayo 2012

SECRETARIA DE COMUNICACIONES Y TRANSPORTES

DIRECCION GENERAL DE CARRETERAS

FEDERALES

ENTRONQUE “ENT. AEROPUERTO Y CARRETERA MEXICO - QUERETARO ESTRUCTURA 2”

KM. 192+000.00

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E N T R O N Q U E “ A E R O P Ú E R T O E S T . 2 ”

CONTENIDO

1.-Memoria Descriptiva.................................................................................................................3

1.1.- Descripcion de la estructura...................................................................................................3

1.2.- Analisis de cargas...................................................................................................................7

1.3.- Análisis de la estructura.........................................................................................................8

1.4.- Grupos de cargas....................................................................................................................8

1.5.- Criterios de deformaciones..................................................................................................10

1.6.- Analisis Sismico....................................................................................................................10

1.7.- Metodo simplificado............................................................................................................11

1.8.- Metodo Cuasidinamico........................................................................................................12

1.8.1.- Periodo de vibracion de la estructura...............................................................................12

1.8.2.- Fuerza equivalente............................................................................................................13

1.9.- Carga viva vehicular.............................................................................................................14

1.9.- Referencias...........................................................................................................................15

2.-Bajada de cargas de la superestructura..................................................................................17

2.1.- tramo 1-2.............................................................................................................................17

2.2.- tramo 2-3.............................................................................................................................18

2.3.- tramo 3-4.............................................................................................................................19

3.-Analisis de la Losa....................................................................................................................20

3.1.- tramo 1-2.............................................................................................................................20

3.2.- tramo 2-3.............................................................................................................................25

3.3.- tramo 3-4.............................................................................................................................30

4.-Analisis de las Trabes..............................................................................................................35

4.1.- Diseño de la trabe AASHTO, (claro 32.6 mts.) TRamo 1-2.................................................35

4.1.1.- Carga viva..........................................................................................................................35

4.1.2.- Analisis de la Trabe TRAMO 1-2........................................................................................38


4.2.1.- Carga viva..........................................................................................................................57


E N T . “ A E R O P U E R T O Y C A R R E T E R A M E X I C O Q U E R E T A R O ”

M e m o r i a D e s c r i p t i v aCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

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4.3.1.- Carga viva..........................................................................................................................79


5.- ESTRUCTURACION DE LAS COLUMNAS.................................................................................101

5.1- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA EL EJE 1......................................101

5.2- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA LAS COLUMNAS DEL EJE 2..........108

5.3- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA LAS COLUMNAS DEL EJE 3..........115

5.4- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA EL EJE 4......................................122

6 - ESTRUCTURACION DE CABEZALES.............................................................................................129

6.1 - ESTRUCTURACION DE CABEZAL PARA EL EJE 1.......................................................................129






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1.-MEMORIA DESCRIPTIVA

En el presente documento se agrupan todas y cada una de las Consideraciones, Análisis y Cálculos utilizados para el diseño de los elementos que en conjunto forman la Estructura del Entronque denominado “AEROPUERTO Y CARRETERA MEXICO QUERETARO”:

CARRETERA: Autopista México - QuerétaroTRAMO: Palmillas – QuerétaroORIGEN: México

1.1.- DESCRIPCION DE LA ESTRUCTURA

Una vez aprobada la solución ante la dependencia y tomando como base las condiciones topográficas, geológicas y de mecánica de suelos en la zona del Entronque “AEROPUERTO Y CARRETERA MEXICO QUERETARO” ubicado en el km. 192+000.00. Se estudiaron las características para la estructura del entronque.

Figura 1.- Sección Transversal del Entronque.



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La estructura se proyectó de la siguiente manera:

El Plano General se realizó en base a los datos proporcionados por STOM S.A. DE C.V. en campo, como son topografía y mecánica de suelos.

Se determinó una estructura sin esviaje y en curva para la cual la geometría se calculó por el método de geometría analítica., así mismo, se obtuvo el alineamiento vertical y las superficies terminadas de concreto.

Las trabes se analizaron mediante hojas de cálculo en Excel determinando los factores de concentración de carga por el método de las normas AASHTO y los esfuerzos permitidos.

La superestructura se proyecta con una losa que tiene un ancho variable. En todos los tramos las losas son de concreto armado, con un peralte de 20 cm. (Revisar los planos estructurales No.10 al No.23).

• Para todos los tramos, las losas se encuentran apoyadas sobre trabes simplemente apoyadas. Son de concreto presforzado, “Tipo AASHTO IV”. (Revisar planos estructurales No.24 al No.36).

Todas las trabes se diseñaron de acuerdo a las especificaciones de la AASHTO (American Association of State Highway and Transportation Officials).



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Características de los materiales a emplear:

Guarnición Concreto de fć= 250 kg/cm² Acero de refuerzo de LE > 4200 kg/cm²

Parapeto

Tubo de acero galvanizado 8.9 (31/2”) de diámetro cédula 40 Tubo de acero galvanizado 7.6 (3”) de diámetro cédula 40 Acero A-36 Pernos de 2.54 Ø (3/4”) con tuerca

Superestructura losa y diafragmas.

Acero de refuerzo, de LE > 4200 kg/cm² Varillas C con rosca en sus extremos de LE > 4200 kg/cm² Acero A-36 (placas, tuercas y rondanas) Concreto de fć= 250 kg/cm² Ductos de 2.5 Ø x 1.09 m. Drenes de 7.6 Ø

Superestructura trabes.

Acero de presfuerzo, torones de 1.27 Ø de LR> 19000 kg/cm² Acero de refuerzo de LE > 4200 kg/cm² Cable tipo CASCABEL galvanizado serie G-37 con alma de acero de 1.59 Ø

para izado Concreto de fć= 400 kg/cm² y 450 kg/cm²

Apoyos.

Neopreno dureza shore 60 (ft = 100 kg/cm²) Acero estructural A-36

Junta de dilatación.

Acero de refuerzo de LE > 4200 kg/cm²



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Sikaflex 1-A o similar Cartón Asfaltado de 4 cm de espesor Acero Estructural A-36

La subestructura se resolvió de la siguiente manera:

Los apoyos están conformados por 2 cargaderos en los extremos. (Véanse detalles en los planos estructurales No.37, 38 y 51) Con las características geométricas descritas anteriormente, se pueden definir los factores de distribución de las cargas, los factores de impacto, etc.; con ello, es posible ser congruentes con la filosofía de diseño original del proyecto.

Características de los materiales a emplear:

Subestructura.

Acero de refuerzo de LE > 4200 kg/cm² Concreto de fć= 250 kg/cm² en corona, diafragmas, bancos y topes y

pantallas en estribos Placas de neopreno de 35x35x5.7 Cartón Asfaltado de 2 cm. de espesor

Columnas de 150 colados en el lugar (Caballetes eje 1 y eje 8)

Acero de refuerzo de LE > 4200 kg/cm² Concreto de fć= 250 kg/cm² en : Excavaciones

Columnas de 200 colados en el lugar (Pilas ejes 2 al 7)

Acero de refuerzo de LE > 4200 kg/cm² Concreto de fć= 250 kg/cm² en : Excavaciones

Accesos.

Terraplén retenido Muro de retención Carpeta asfáltica Riego de impregnación en carpeta Acero de refuerzo de LE > 4200 kg/cm² Concreto de fć= 250 kg/cm² en postes y guarniciones



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Defensa de tubo de acero galvanizado Acero estructural A-36

Figura 2.- Elevación de pilas Ejes centrales



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1.2.- ANALISIS DE CARGAS

Para la revisión estructural de los elementos que forman el paso, se consideraron tres grupos de cargas:

• Cargas permanentes: Cargas muertas y empuje de tierras.• Cargas variables: Cargas vivas: impacto y fuerza centrífuga.• Cargas eventuales: Sismo.

Todas ellas se encuentran definidas en las Normas para proyectos de Puentes y Estructuras de la Secretaría de Comunicaciones y Transportes (N-PRY-CAR-6-01-003/01).Para el cálculo del peso propio de los elementos que forman el Entronque AEROPUERTO, se utilizó el peso volumétrico de los materiales de uso común en México, de acuerdo a las especificaciones en la norma de la S.C.T.

1.3.- ANÁLISIS DE LA ESTRUCTURA

El análisis se realizó para cada uno de los elementos de forma individual:

• Losa.• Trabes.• Caballetes.• Columnas Circulares

1.4.- GRUPOS DE CARGAS

Los elementos estructurales se diseñaron para resistir, en condiciones de seguridad, todos los grupos de carga que sean aplicables al tipo de estructura y a las condiciones particulares del sitio en donde se ubique ésta. Cada grupo de carga se integra por la combinación de cargas permanentes, variables y eventuales, que sean aplicadas:

Combinación de cargas permanentes:

(CPN)= β CMCM+β ETET

Combinación de carga variable:



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(CV N) =βV(V+I)βFCFC

Combinación de carga eventual:

(CE N) = βVEVE+βVCVVCV+βSS+βFLFL+βACT(A+ C +T) +βPLPL+βSPSP

Dónde:



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1.5.- CRITERIOS DE DEFORMACIONES

La deflexión por carga viva de los elementos horizontales de piso no excederá en ningún caso los valores de 1/360 del claro, ni claro/240 + 0.5 (cm) para carga total, calculados al centro del mismo.

1.6.- ANALISIS SISMICO

De acuerdo a la ubicación de la estructura y su uso, conforme a la norma de proyectos para carreteras emitida por la S.C.T., el Entronque AEROPUERTO se clasifica como:



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Dónde:

I CORRESPONDE A TERRENO FIRMEII CORRESPONDE A TERRENO INTERMEDIOIII CORRESPONDE A TERRENO BLANDO



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1.7.- METODO SIMPLIFICADO

Este método es aplicable a estructuras que según su comportamiento sísmico, son del Tipo 1s. El análisis se realiza en dos direcciones ortogonales horizontales, considerando para cada una de ellas el efecto de una fuerza horizontal equivalente (S) independiente, aplicada en el centro de gravedad de la estructura y sus efectos se combinan como se indica en la Cláusula M. de la Norma N-PRY-CAR-6-01-005/01. Dicha fuerza horizontal se determina mediante la siguiente expresión:

Dónde:

S= Fuerza horizontal equivalente, (kN)c= Ordenada máxima del espectro sísmico correspondiente a la zona sísmica donde se ubique la estructura y al tipo de suelo en que se desplantara, (adimensional)Q= Factor de comportamiento sísmico, (adimensional)W= Peso de estructura, (kN)

La relación c/Q no debe ser menor que la ordenada al origen del espectro sísmico correspondiente (ao), según la zona sísmica donde se ubique la estructura y el tipo de suelo

en que se desplantará.

1.8.- METODO CUASIDINAMICO

Este método es aplicable a estructuras que, según su comportamiento sísmico, son de los Tipos 1s o 2s. Igual que en método simplificado, el análisis se realiza en dos direcciones ortogonales horizontales considerando para cada una de ellas el efecto de una fuerza horizontal equivalente (S’) independiente, aplicada en el centro de gravedad de la estructura y sus efectos se combinan como se indica en la Cláusula M. de la Norma N-



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PRY-CAR-6- 01-005/01. Dicha fuerza horizontal se determina en función del periodo de vibración (T) de la estructura, como sigue:

1.8.1.- PERIODO DE VIBRACION DE LA ESTRUCTURA

El periodo de vibración (T) de la estructura, que es el periodo natural correspondiente al primer modo de vibración en la dirección horizontal que se analice, puede determinarse por cualquier método de análisis dinámico reconocido. En estructuras de los Tipos 1s y 2s, puede calcularse aproximadamente con la siguiente fórmula:

Dónde:

T =Periodo de vibración de la estructura, (s)W =Peso de la estructura, (kN)K =Rigidez de la estructura (Kn/cm), que vale:

Dónde:

F=Fuerza estática horizontal de valor arbitrario, aplicada en el centro de gravedad de la estructura y en la dirección del análisis, (kN)Δ=Desplazamiento de la estructura en la dirección de análisis ocasionada por la fuerza F.

1.8.2.- FUERZA EQUIVALENTE

La fuerza horizontal equivalente (S’) que se utiliza en el método cuasidinámico, se determina mediante la expresión:



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Dónde:

S’= Fuerza horizontal equivalente, (kN)a= Ordenada en el espectro sísmico correspondiente a la zona sísmica donde se ubique la estructura y al tipo de suelo en que se desplanta, para el periodo de vibración T de la estructura.W= Peso de estructura, (kN)Q’= Factor de comportamiento sísmico modificado, (adimensional), que vale:

Dónde:

Ta=Periodo de vibración inferior del intervalo de resonancia del espectro sísmico correspondiente a la zona sísmica donde se ubique la estructura y al tipo de suelo que se desplantará.

1.9.- CARGA VIVA VEHICULAR

La S.C.T. en la Ley General de Vías de Comunicación contempla tres sistemas de cargas para considerarse en el proyecto estructural de puentes o estructuras similares, éstas se muestran a continuación.



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1.9.- REFERENCIAS

Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Ejecución de Proyectos de nuevos Puentes y Estructuras Similares”.México 2001, (N-PRY-CAR-6-01-003/01).



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Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Características Generales del Proyecto”.México 2001, (N-PRY-CAR-6-01-003/01).

Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Cargas y Acciones”. México 2001, (N-PRY-CAR-6-01-001/01).



Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Viento”. México 2001, (N-PRY-CAR-6-01-004/01).

Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Sismo”. México 2001, (N-PRY-CAR-6-01-005/01).

Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Combinaciones de Cargas”. México 2001, (N-PRY-CAR-6-01-006/01).

Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Distribución de Cargas”. México 2001, (N-PRY-CAR-6-01-007/04).


Secretaría de Comunicaciones y Trasportes,Normas de Proyectos para Carreteras, Proyectos de nuevos puentes y estructuras similares, “Presentación del Proyecto de Nuevos Puentes y Estructuras Similares”.México 2001, (N-PRY-CAR-6-01-009/04).

Normas AASHTO



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Términos de referencia

Planos de kms.

Estudios topográficos

Estudios geotécnicos

Especificaciones para proyectos de puentes

Manual de la A.C.I.

Manual del proyecto geométrico de carreteras

Manual de fórmulas técnicasRalp b. PeckWalter e. Hanson



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2.-BAJADA DE CARGAS DE LA SUPERESTRUCTURA

2.1.- TRAMO 1-2

Area del Diafragma (m2)

1.24

2.767

2.322

Distancia del paño de la trabe al eje de apoyo

IZQ.

524.622

6 30.00

262.31117.144

ANALISIS DE CARGA MUERTA POR TRABE

0.300

0.036

84.667

W Carpeta (Ton/m)

0.672

Σ Carga Muerta Claro

(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.194 0.015

0.000

W Guarnicion, Camellon (Ton/m)

W Diafragma

(Ton/m)

1 0.251

2 0.000 0.029

42.334

2.322 71.057 35.529

W Losa (Ton/m)

0.024

0.000

0.000

0.672 0.403 1.194 0.024

0.0291.194

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.300

Longitud de la Trabe (m)

Altura de la Losa (m)

Altura de la Carpeta

Asfaltica (m)

30.60 0.20 0.12

Distancia entre trabes

Ancho de volado

DATOS

1.40 2.40

Peso del Parapeto (Ton/ml)

Area del Zoclo (m2)

Area de la Guarnicion

(m2)

Area del Deflector

(m2)

0.000.50 0.010 0.24 0.036 0.00

0.036

2.767

W Parapeto (Ton/m)

W Zoclo (Ton/m)

42.3347 0.672 0.251 1.194 84.667

0.024 0.000 35.529

4 0.672 0.403 1.194 0.024 0.000 0.029 35.529

3

2.322 71.057

0.5760.024 0.015

2.322 71.0570.672 0.403

5 0.672 0.403 1.194 0.024 0.000 0.029 0.000 2.322 71.057 35.529

0.029 0.0006 0.672 0.403 1.194 0.024 0.000 71.057 35.529

2.2.- TRAMO 2-3


B a j a d a d e C a r g a sCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

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1.24

2.767

2.322


IZQ.

524.622

6 30.00

262.31117.144


0.300

0.036

84.667

W Carpeta (Ton/m)

0.672


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.194 0.015

0.000


W Diafragma

(Ton/m)

1 0.251

2 0.000 0.029

42.334

2.322 71.057 35.529

W Losa (Ton/m)

0.024

0.000

0.000

0.672 0.403 1.194 0.024

0.0291.194

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.300




Asfaltica (m)

30.60 0.20 0.12


Ancho de volado

DATOS

1.40 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.000.50 0.010 0.24 0.036 0.00

0.036

2.767

W Parapeto (Ton/m)

W Zoclo (Ton/m)

42.3347 0.672 0.251 1.194 84.667

0.024 0.000 35.529

4 0.672 0.403 1.194 0.024 0.000 0.029 35.529

3

2.322 71.057

0.5760.024 0.015

2.322 71.0570.672 0.403

5 0.672 0.403 1.194 0.024 0.000 0.029 0.000 2.322 71.057 35.529

0.029 0.0006 0.672 0.403 1.194 0.024 0.000 71.057 35.529

2.3.- TRAMO 3-4


1.24

2.767

2.322


IZQ.

524.622

6 30.00

262.31117.144


0.300

0.036

84.667

W Carpeta (Ton/m)

0.672


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.194 0.015

0.000


W Diafragma

(Ton/m)

1 0.251

2 0.000 0.029

42.334

2.322 71.057 35.529

W Losa (Ton/m)

0.024

0.000

0.000

0.672 0.403 1.194 0.024

0.0291.194

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.300




Asfaltica (m)

30.60 0.20 0.12


Ancho de volado

DATOS

1.40 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.000.50 0.010 0.24 0.036 0.00

0.036

2.767

W Parapeto (Ton/m)

W Zoclo (Ton/m)

42.3347 0.672 0.251 1.194 84.667

0.024 0.000 35.529

4 0.672 0.403 1.194 0.024 0.000 0.029 35.529

3

2.322 71.057

0.5760.024 0.015

2.322 71.0570.672 0.403

5 0.672 0.403 1.194 0.024 0.000 0.029 0.000 2.322 71.057 35.529

0.029 0.0006 0.672 0.403 1.194 0.024 0.000 71.057 35.529

2.4.- TRAMO 4-5



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1.24

2.728

2.282


IZQ.

549.798

7 31.09

274.89916.865


0.305

0.036

88.920

W Carpeta (Ton/m)

0.648


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.194 0.014

0.000


W Diafragma

(Ton/m)

1 0.236

2 0.000 0.027

44.460

2.282 74.391 37.196

W Losa (Ton/m)

0.024

0.000

0.000

0.648 0.389 1.194 0.024

0.0271.194

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.757




Asfaltica (m)

32.60 0.20 0.12


Ancho de volado

DATOS

1.35 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.000.50 0.010 0.24 0.036 0.00

0.036

2.728

W Parapeto (Ton/m)

W Zoclo (Ton/m)

44.4607 0.648 0.236 1.194 88.920

0.024 0.000 37.196

4 0.648 0.389 1.194 0.024 0.000 0.027 37.196

3

2.282 74.391

0.5760.024 0.014

2.282 74.3910.648 0.389

5 0.648 0.389 1.194 0.024 0.000 0.027 0.000 2.282 74.391 37.196

0.027 0.0006 0.648 0.389 1.194 0.024 0.000 74.391 37.196

2.5.- TRAMO 5-6

0.031 0.000 2.875 117.317 58.6595 0.672 0.403 1.662 0.108 0.000

2.875 117.3170.672 0.403

2.875 117.317

0.5760.108

58.659

4 0.672 0.403 1.662 0.108 0.000 0.031 58.659

3 0.108 0.000

75.0806 0.898 0.386 1.662 0.015 150.160

0.69 0.045 0.24 0.036 0.47

0.036

3.680

W Parapeto (Ton/m)

W Zoclo (Ton/m)


Ancho de volado

DATOS

1.40 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.00




Asfaltica (m)

40.80 0.20 0.12

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.400

W Losa (Ton/m)

0.108

0.000

0.000

0.672 0.403 1.662 0.108

0.0311.662

1 0.386

2 0.000 0.031

75.080

2.875 117.317 58.659


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.662 0.015

0.000


W Diafragma

(Ton/m)

6 40.00

384.79518.862


0.400

0.036

150.160

W Carpeta (Ton/m)

0.898


IZQ.

769.590


1.74

3.680



21


2.6.- TRAMO 6-7

0.031 0.000 2.875 117.317 58.6595 0.672 0.403 1.662 0.108 0.000

2.875 117.3170.672 0.403

2.875 117.317

0.5760.108

58.659

4 0.672 0.403 1.662 0.108 0.000 0.031 58.659

3 0.108 0.000

75.0806 0.898 0.386 1.662 0.015 150.160

0.69 0.045 0.24 0.036 0.47

0.036

3.680

W Parapeto (Ton/m)

W Zoclo (Ton/m)


Ancho de volado

DATOS

1.40 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.00




Asfaltica (m)

40.80 0.20 0.12

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.400

W Losa (Ton/m)

0.108

0.000

0.000

0.672 0.403 1.662 0.108

0.0311.662

1 0.386

2 0.000 0.031

75.080

2.875 117.317 58.659


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.662 0.015

0.000


W Diafragma

(Ton/m)

6 40.00

384.79518.862


0.400

0.036

150.160

W Carpeta (Ton/m)

0.898


IZQ.

769.590


1.74

3.680



22


2.7.- TRAMO 7-8

0.031 0.000 2.875 117.317 58.6595 0.672 0.403 1.662 0.108 0.000

2.875 117.3170.672 0.403

2.875 117.317

0.5760.108

58.659

4 0.672 0.403 1.662 0.108 0.000 0.031 58.659

3 0.108 0.000

75.0806 0.898 0.386 1.662 0.015 150.160

0.69 0.045 0.24 0.036 0.47

0.036

3.680

W Parapeto (Ton/m)

W Zoclo (Ton/m)


Ancho de volado

DATOS

1.40 2.40


Area del Zoclo (m2)


(m2)

Area del Deflector

(m2)

0.00




Asfaltica (m)

40.80 0.20 0.12

Concreto

(Ton/m3)

Numero de Trabe

Area de la

Trabe (m2)

W Trabe (Ton/m)

Σ Carga Muerta

por metro (Ton/m)

Numero de trabes

Longituid del claro


DER.

0.400

W Losa (Ton/m)

0.108

0.000

0.000

0.672 0.403 1.662 0.108

0.0311.662

1 0.386

2 0.000 0.031

75.080

2.875 117.317 58.659


(Ton/m)

Σ Carga Muerta Eje

(Ton/m)

0.5761.662 0.015

0.000


W Diafragma

(Ton/m)

6 40.00

384.79518.862


0.400

0.036

150.160

W Carpeta (Ton/m)

0.898


IZQ.

769.590


1.74

3.680



23


3.-ANALISIS DE LA LOSA

3.1.- TRAMO 1-2


A n á l i s i s d e l a L o s aCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

24


= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10

Vcm = w L = tn/m x m Tn/m2 2

250

2400

Concreto de la losa f´c Peso vol del concreto asfáltico

kg/cm²

kg/cm²

Peso vol del concreto Ancho de patín

0.66

Ancho del patín inferior de la viga

m

m

1.40

0.20

0.20

0.03

Espesor de losa entre vigas Espesor de losa en volado

Ancho total de la losa

Recubrimiento del acero de refuerzo Espesor de carpeta

mm

9.00

7No. de vigas

0.12

pzas.

kg/m3

m

Ancho de la guarnición 0.53

Ton/m

Ton/m0.12

Separación entre vigas

0.00 Acero de refuerzo f y

m

0.56

4200

0.20

0.062

0.288Ton/m3

m

kg/m3

Ton/m

DISEÑO DE LOSA INTERMEDIA

DISEÑO DE LOSA DE SUPERESTRUCTURA

DATOS GENERALES:

m

m

0.346

0.900

Distancia entre trabe y trabe

Solicitaciones de carga muerta:

Wcm 0.768

0.480Losa 2.4

2400

mAncho de la banqueta

2.4

Ton/m3

100.768 0.900

0.768

Carpeta asfaltica

0.900



25


Carga viva del camion

Para un Camiòn HS-20P = TonL = m

Mcv = L + x P

Mcv = m + x Ton = Ton-m/m

=

x = Ton-m/m

Calculo del factor de impacto AASTHO 3.8.2.1

I =L + 38

I = = = % De la Carga viva (Maximo 30%) + 38

Por lo tanto

I =

Mcv + I = Ton-m/m x =

= P x I = x = Ton2 2

Obteniendo momento y cortante ùltimo con la combinaciòn de carga viva y carga muerta

= Ton-m/m β = =

Mu = ( Mcm + β Mcv+i )

Mu = ( + 1.7 x ) Mu = Ton-m/m

Vu = ( Vcm + β Vcv )

Vu = ( + 1.7 x ) Vu = Ton

Mcv x F. Continuidad= 1.126 0.8 0.9

Para mas de 2 trabes, Factor de Continuidad 0.8 AASHTO 3.24.3.1

0.61

0.900

1.300

0.900

15.24

0.900

0.900

1.1255

7.260

0.062

0.346

1.3

1.3

1.3

1.3

Mcv + I 1.171

1.3Vcv

10.67

2.617

39.18

1.67

1.300

9.74

Solicitaciones de carga viva

15.24

7.2609.74

0.39

4.719

1.171

Caso A : Refuerzo Principal Perpendicular al eje del camio (seccion 3.24.3.1 AASHTO)

Ton-m/m

7.260

5/3

4.719

1.171

0.61



26


Diseñando un metro de ancho de losa al centro de trabes en el sentido transversal

### cm##

cm

DATOS As min=b = cm fy d

fy = kg/cm² Asmin =fc = kg/cm²Ø = Flexiòn Proponiendo varillas

Ø = Cortante No. 4 @ 20 cm Av = cm2

d = cm As = Av = cm = cm As =

MR = Ø As fy (d-a/2)

Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN

Se colocaran varillas # 4 @ 20 cm

67 % AASHTO 3.24.10.2

S= m % = =S= ft √ S Proponiendo varillas de

No. 4 = cm2

As = xAs = cm2 S = Av

As

S = cm

Se colocaran varillas del No. 4 @ 51 cm

1.27

Acero longitudinal por distribucion, se colocara el un porcentaje no mayor a:

428992.91

4200

6.35

As fy

3.74

Calculo del momento resistente en el centro

2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

128.030.9002.953

0.67 3.742.507

1.26

1.26

4.290 2.617

0.9 4200

6.35Espesor Losa

100s

50.65

100

220



27


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =

SOLICITACIONES POR CARGA VIVA EN EL VOLADO

CARGA VIVA VEHICULAR P = Ton (AASHTO SECCIÒN 3,14,1,1)X = m Eje de la trabe a eje de la llanta de un HS-20

La llanta a 30 cm de la guarnicion, no genera momentos negativos en el volado

X = mE = X +

Mcv = Pv x X E = m Ancho de distribucion de la cargaen el volado

Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m


β = (AASHTO SECCIÒN 3,24,2,2) Solo en el voladoMu = ( Mcm + β Mcv)Mu = x ( + 1.0 x ) Mu = Tn-m/m

Vu = ( Vcm + β Vcv )Vu = x ( + 1.0 x ) Vu = Tn/m

Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.220

00.282

0.502

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.502 0.000 0.653

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143

DISEÑO DE LOSA EN VOLADO

Peso Brazo

0.459

0.418

Wcm 1.443

0.675

Momento

0

0.480 Ton/m

ANALISIS DE CARGA MUERTA:

Losa 0.20 Ton/m3

Ton/m

Guarnicion y parapeto Ton/m

Carpeta asfaltica 0.12 2.4 Ton/m3 0.288 Ton/m

2.4



28


Diseñando un metro de ancho de losa en el volado en el sentido transversal

### cm##

cmDATOS As min=

b = cm fy dfy = kg/cm²fc = kg/cm² Asmin =Ø = FlexiònØ = Cortanted = cm Proponiendo varillas

= cm No. 4 @ 20 cm Av = cm2

Rec. Superior = cm As = cm2

CALCULO DEL MOMENTO RESISTENTE EN EL VOLADO


Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN

As minimo necesario = cm2

Se acepta y se colocaran varillas No. 4 @ 20 cm

REVISION POR CORTANTE

VCR = Ø x x b x d √ f`c

VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN

ACERO LONGITUDINAL POR DISTRIBUCIÓN SE COLOCARÁ EL SIGUIENTE PORCENTAJE (SECCIÓN 3.24.10.2 )

S= m Ancho del volado% = = % S= ft

√ SAs = x 67 %

As = cm2

Proponiendo varillas de

No. 4 Av = cm2

S = AvAs

Se colocaran varillas del No. 4 @ 30 cmS = cm

ACERO POR CONTRACCIÒN Y TEMPERATURA DE ACUERDO A LA AASHTO SECCION 8,20,1


As = cm2/m No. 4 Av = cm

2

S = Av xAs cm ≈ 30 cm

Se colocaran varillas del No. 4 @ 30 cm2.65 S = 47.92

0.4591.506

428992.912

El porcentaje de acero no debera ser mayor del

1.27

100

13.18 10.133

220 179.277

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.653

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 0.93 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



29


3.2.- TRAMO 2-3

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.66


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas

0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

0.56

4200

0.20

0.062

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.346

0.900



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 0.900

0.768

Carpeta asfaltica

0.900



30




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

0.900

1.300

0.900

15.24

0.900

0.900

1.1255

7.260

0.062

0.346

1.3

1.3

1.3

1.3

Mcv + I 1.171

1.3Vcv

10.67

2.617

39.18

1.67

1.300

9.74


15.24

7.2609.74

0.39

4.719

1.171


Ton-m/m

7.260

5/3

4.719

1.171

0.61



31



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

3.74


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

128.030.9002.953

0.67 3.742.507

1.26

1.26

4.290 2.617

0.9 4200

6.35Espesor Losa

100s

50.65

100

220



32


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.220

00.282

0.502

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.502 0.000 0.653

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.459

0.418

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



33




34



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %

As = cm2


No. 4 Av = cm2

S = AvAs





2



0.4591.506

428992.912


1.27

100

13.18 10.133

220 179.277

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.653

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 0.93 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



35


3.3.- TRAMO 3-4

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.66


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas

0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

0.56

4200

0.20

0.062

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.346

0.900



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 0.900

0.768

Carpeta asfaltica

0.900



36




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

0.900

1.300

0.900

15.24

0.900

0.900

1.1255

7.260

0.062

0.346

1.3

1.3

1.3

1.3

Mcv + I 1.171

1.3Vcv

10.67

2.617

39.18

1.67

1.300

9.74


15.24

7.2609.74

0.39

4.719

1.171


Ton-m/m

7.260

5/3

4.719

1.171

0.61



37



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

3.74


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

128.030.9002.953

0.67 3.742.507

1.26

1.26

4.290 2.617

0.9 4200

6.35Espesor Losa

100s

50.65

100

220



38


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.220

00.282

0.502

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.502 0.000 0.653

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.459

0.418

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



39




40



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %

As = cm2


No. 4 Av = cm2

S = AvAs





2



0.4591.506

428992.912


1.27

100

13.18 10.133

220 179.277

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.653

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 0.93 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



41


3.4.- TRAMO 4-5

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.66


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas 0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

0.56

4200

0.20

0.062

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.346

0.900



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 0.900

0.768

Carpeta asfaltica

0.900



42




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

0.900

1.300

0.900

15.24

0.900

0.900

1.1255

7.260

0.062

0.346

1.3

1.3

1.3

1.3

Mcv + I 1.171

1.3Vcv

10.67

2.617

39.18

1.67

1.300

9.74

15.24

7.2609.74

0.39

4.719

1.171



Ton-m/m

7.260

5/3

4.719

1.171

0.61



43




44



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

3.74


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

128.030.9002.953

0.67 3.742.507

1.26

1.26

4.290 2.617

0.9 4200

6.35Espesor Losa

100s

50.65

100

220



45


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.220

00.282

0.502

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.502 0.000 0.653

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.459

0.418

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



46




47



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %

As = cm2 Proponiendo varillas de

No. 4 Av = cm2

S = AvAs




As = cm2/m No. 4 Av = cm2



0.4591.506

428992.912


1.27

100

13.18 10.133

220 179.277

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.653

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 0.93 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



48


3.5.- TRAMO 5-6

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.71


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas 0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

1.07

4200

0.20

0.151

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.538

1.400



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 1.400

0.768

Carpeta asfaltica

1.400



49




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

1.400

1.300

1.199

15.24

1.400

1.400

1.4982

7.260

0.151

0.538

1.3

1.3

1.3

1.3

Mcv + I 1.558

1.3Vcv

10.92

3.572

38.68

1.67

1.300

9.74

15.24

7.2609.74

0.39

4.719

1.558



Ton-m/m

7.260

5/3

4.719

1.558

0.61



50



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

5.11


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

102.651.4004.593

0.67 5.113.422

1.26

1.26

4.290 3.572

0.9 4200

6.35Espesor Losa

100s

37.11

100

220



51


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.226

00.317

0.543

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.543 0.000 0.706

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.47

0.47

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



52




53



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %


No. 4 Av = cm2

S = AvAs







0.4701.542

428992.912


1.27

100

13.18 10.133

220 177.166

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.706

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 1.01 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



54


3.6.- TRAMO 6-7

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.71


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas 0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

1.07

4200

0.20

0.151

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.538

1.400



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 1.400

0.768

Carpeta asfaltica

1.400



55




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

1.400

1.300

1.199

15.24

1.400

1.400

1.4982

7.260

0.151

0.538

1.3

1.3

1.3

1.3

Mcv + I 1.558

1.3Vcv

10.92

3.572

38.68

1.67

1.300

9.74

15.24

7.2609.74

0.39

4.719

1.558



Ton-m/m

7.260

5/3

4.719

1.558

0.61



56



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

5.11


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

102.651.4004.593

0.67 5.113.422

1.26

1.26

4.290 3.572

0.9 4200

6.35Espesor Losa

100s

37.11

100

220



57


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.226

00.317

0.543

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.543 0.000 0.706

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.47

0.47

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



58




59



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %


No. 4 Av = cm2

S = AvAs







0.4701.542

428992.912


1.27

100

13.18 10.133

220 177.166

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.706

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 1.01 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



60


3.7.- TRAMO 7-8

= == == =

= == == =

==

=

1.- m x =

2.- m x =

=

Donde: L =

L = m

Mcm = w L2 = tn/m x ( )2m = Tn/m10


250

2400


kg/cm²

kg/cm²


0.71


m

m

1.40

0.20

0.20

0.03




mm

9.00

7No. de vigas 0.12

pzas.

kg/m3

m


Ton/m

Ton/m0.12



m

1.07

4200

0.20

0.151

0.288Ton/m3

m

kg/m3

Ton/m



DATOS GENERALES:

m

m

0.538

1.400



Wcm 0.768

0.480Losa 2.4

2400


2.4

Ton/m3

100.768 1.400

0.768

Carpeta asfaltica

1.400



61




Mcv = L + x P


=

x = Ton-m/m


I =L + 38


Por lo tanto

I =


= P x I = x = Ton2 2


= Ton-m/m β = =


Mu = ( + 1.7 x ) Mu = Ton-m/m


Vu = ( + 1.7 x ) Vu = Ton



0.61

1.400

1.300

1.199

15.24

1.400

1.400

1.4982

7.260

0.151

0.538

1.3

1.3

1.3

1.3

Mcv + I 1.558

1.3Vcv

10.92

3.572

38.68

1.67

1.300

9.74

15.24

7.2609.74

0.39

4.719

1.558



Ton-m/m

7.260

5/3

4.719

1.558

0.61



62



### cm##

cm






Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m = Ton-m

MR > Mu

Ton-m > Ton-m BIEN


67 % AASHTO 3.24.10.2


No. 4 = cm2


As

S = cm


1.27


428992.91

4200

6.35

As fy

5.11


2

250

Rec. Inferior

100

4200

1.5

Peralte 20

18.5

0.85

0.85 1006.35

4.290

100Mu

0.9

2500.9

1.270.85

cm2

102.651.4004.593

0.67 5.113.422

1.26

1.26

4.290 3.572

0.9 4200

6.35Espesor Losa

100s

37.11

100

220



63


1.- m x = x m =

2.- m x = x m =3.- = x m =

= =




X = mE = X +


Mcv = x = Ton-m/m

= PvE Mcv = tn-m/m

= = Ton/mVcv = Tn/m




Ton-m/m

Ton-m/m

Ton-m/m

Ton-m/mMcm

7.260.000

0.226

00.317

0.543

1.14

1.3 1.443 6.352 10.133

1.1 6.352

1.01.31.3 0.543 0.000 0.706

1.3

E7.26 0.000 0

1.1

Vcv 0.000

Vcv 7.26 6.352

0.0000.8 1.143


Peso Brazo

0.47

0.47

Wcm 1.443

0.675

Momento

0

0.480 Ton/m


Losa 0.20 Ton/m3

Ton/m



2.4



64




65



### cm##

cmDATOS As min=


= cm No. 4 @ 20 cm Av = cm2




Donde a =b fc

a = x =x x

MR = x x ( 19 - ) = kg-m

MR = tn-m

MR > Mu

tn-m > tn-m BIEN





VCR = x x ## x 19 x √

VCR = Tn

> Vu

tn-m > tn-m BIEN



√ SAs = x 67 %


No. 4 Av = cm2

S = AvAs







0.4701.542

428992.912


1.27

100

13.18 10.133

220 177.166

29.85

2.65 1.27

100 S = 100 1.27

0.67

0.53

0.85 0.53 250

13.18

VCR

6.35

4.255

1.27

0.9 6.35 4200 1.26

24.290

4.290 0.706

6.35

1.5 6.35

As fy0.85

6.35 4200 1.260.85 100 250

250 1.01 cm20.9

0.85Peralte 19

20.00Espesor losa

100Mu

100 0.94200



66


4.-ANALISIS DE LAS TRABES

4.1.- DISEÑO DE LA TRABE AASHTO, (CLARO 30.6 MTS.) TRAMO 1-2

4.1.1.- CARGA VIVA

Camion de diseño:T3-S2-R4

1.- Tomando en cuenta un carril cargado

1.000

0.330

Datos

Viga Ri Ri x FR1 0.330

Analisis

Excentricidad (m)

Factor de reduccion

No. De vigas Separacion (m)

1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143

METODO DE ENGESSER COURBON PARA REPARTO TRANSVERSAL

6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2


A n á l i s i s d e l a s T r a b e sCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

67


2.- Tomando en cuenta dos carriles cargados

Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2

T4 0.349 54.030 18.862

DESCARGA TOTAL =

Incremento por impacto =

54.03054.0300.464

132.031

25.06628.168T1

Longitud de la Trabe (m)=

Longitud de la Trabe (ft)=

FACTOR DE DISTRIBUCIÓN DE

CARGA POR TRABE

T7 0.177 54.030 9.555

0.521

30.600100.394

Analisis

T3 0.407

DESCARGA DE CAMION

DESGARGA FACTORIZADA

0.222

1.222

T5 0.292 54.030

54.030T2

Datos

54.030 12.65715.760

21.964

T6 0.234

25

50

LI



68


4.1.2.- ANALISIS DE LA TRABE TRAMO 1-2

12.1 36.2 165.0

0.45x / L 0.05

MOMENTO0.0 kL 0.50

DEFLECTOR Y DIAFRAGMAS

45.3

0.40

65.8

245.88

362.43239.01

51.6 57.8

190.40

277.73

1.7

78.377.5

188.94

204.81

43.5 44.941.3

66.1

1.6

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 8.63.0

0.0 8.8 25.6

GUARNICIÓN Y PARAPETO

C. VIVA CAMIÓN HS-20

C. VIVA CAMIÓN T3S2R4

C. VIVA CAMIÓN T3S3

CARGA VIVA TRABE

x / L

CARGA VIVA TRABE

SOLICITACIONES POR TRABE

6.4

207.24108.78 138.51 158.46

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




265.35262.87

196.0192.6

0.0

0.01 39.53 79.0413.18

316.46

12.00

10.4

6.0

0.2

202.39

0.0

3.1 2.1

140.54102.23

0.0

29.60 29.05 27.97 26.34 14.93

0.0

9.2 2.8 1.8

10.6

0.0

0.40 0.45 0.50

6.00

0.1

4.6

13.50 15.00

Reacción

21.45 13.30

3.7

19.82 18.19 16.56

1.8 0.0

5.4 3.6

0.2

2.4

0.1

4.8 4.2 3.0

8.9 8.3 7.3 5.5

0.2

10.1 9.3 8.4 7.3

5.8

17.9 17.3 16.1 14.4

6.3

0.00.2 0.2 0.1 0.1

0.05 0.10 0.15 0.20

0.0 0.68 1.50 3.00 4.50

0.01

0.01

177.1

69.44 138.87

72.4

23.15

17.04

144.80.0

51.11

0.0 0.6 1.4 1.50.9 1.1 1.30.3

44.1

75.2

0.0 68.2

39.9 50.1

1.7

0.0 29.0

71.3

38.116.3 23.1 34.0

15.00

68.6 86.1 100.9 113.0 122.4

9.00

129.2 133.2 134.648.4

4.50 6.00 13.50

58.70.0 5.1 14.9 28.2

0.20

0.0 0.68 1.50 3.00

4.5

14.1 12.2

0.25 0.30

7.50

178.41

205.12

0.1

24.8

376.02

15.66

0.35

369.43339.65

260.38

62.7

12.0010.50

3.6

9.1

35.1 68.9

0.30

5.4

CORTANTE

13.1

0.0 kL

188.998.5 124.6

0.35

9.00

7.2

0.25

12.6

7.50 10.50

27.09 20.42

231.38

23.40

0.9

4.2

0.61.8 1.2

1.0

24.71

10.8 9.0

23.08

5.2

17.4542.40 38.53 34.66 30.78

27.16 24.86 22.56 20.26 17.9636.36 34.06 31.76

16.028.2 27.5 26.1 24.1 22.1 20.1 18.1

38.66

178.86

0.10 0.15

54.03 52.73 50.15 46.28

29.4637.90

0.22

9.36

18.26

10.65

3.83

29.60

54.03

38.66

0.00



69




70


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI

m CONCRETO f´C = kg/cm²

ACERO fY = kg/cm²

PERALTE = cm Ancho alma= cm

Ancho Patín Losa = cm Ancho Patín Inf. = cm

% kg/cm² f y = 4,200 kg/cm2

ES = kg/cm² fSR = 14,250 kg/cm2

0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L

COMPRESIÓN fC = 240.0 kg/cm²

TENSIÓN fT = -16.00 kg/cm²

0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-15.661

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO

ULTIMOPASA POR MOMENTO

ULTIMO

PASA POR MOMENTO

ULTIMO

44

42

44PASA POR MOMENTO


ULTIMO

30

36

42

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

24

Suma

4

8

12

18

6 0

0 0

0

Fibra Sup. Fibra Inf.

Esfuerzos Servicio


23.22%4.32%

Esfuerzos Trans.

PÉRDIDAS DE TENSIÓN

FINALESINICIALES

Longitud de Enductado

0.0 L 0

Distancia del paño inferor de la trabe al Toron

5 10 15

REACCIONES

0.68

0.05 L 1.50

0.10 L 3.00

0 0 0

8

31.5

8 0 0 3.459

4.426

-12.189

215.6070 0

0.15 L 4.50

ESFUERZOS PERMISIBLES

6 0 0

8 0 0

44

0.25 L 7.50

0.30 L 9.00

0 0 0

0 0 0

Distancia5 10 15 20


30

15.00

1.3500

0.1026

0.49740.61500.9000

9.00

10.50

12.00

13.50

1.5500

0.2058

0.70610.8618

6.00

7.50

41.500 -14.886

10.65

36.20

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

1.50

3.00

4.50

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

12

12

12

12

fSMAX = 138.575

fSMIN =

fI MAX =

-15.67

218.8

BIEN POR MOMENTO RESISTENTE

0.50 L 15.00

-1.651

135.980

138.575

76.474

20 25

-9.280

-8.398

-9.188

12

34.185

52.990 -6.250 31.414

-14.6730 0 0

0

0.40 L 12.00

0.45 L 13.50

10.50

A LA TRANSFERENCIA

EN SERVICIO

RESUMEN DE RESULTADOS

0.20 L 6.00

0.572

14.1218.07 16.0526.15 24.13 22.10

12

12

18.488128.848 56.914

91.179

105.093

120.380

0.00

8 0 0

004

12.07 72.40

0.0 L

28.17

0

157.218

9.10

12 0

12

-15.675

00

12

187.201 14.445

0 0

216.416

12

12

12

-11.885

12

124.60

12 12

12

6

0

06

12

99.662 36.947

164.98

14.562

-11.023

31.67272.089 10.548

177.07

19.119

12

12

12

27.49

0

12

0

20.09

12

12

216.369

98.50

1.00

144.79

0.75

192.60 196.03188.95

4

4

6

6

14.144

210.723 -0.987

218.832 129.796 -6.382

-15.056

6

6

6

2

HR = 55

MÓDULO DE ELASTICICIDAD DEL ACERO

ton/mton/m

LOSA, ZOCLO CARPETA GUAR., PARA, DEFL. Y DIAF.

EC =

CARGAS

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140

HUMEDAD RELATIVA PROMEDIO ANUAL

12.20

ESFUERZO DEL

CONCRETO fCi EN LA

TRANSFERENCIA =400 kg/cm²

CONCRETO f´C = 450

ACERO DE

PRESFUERZO frg =19,000 kg/cm²

ton/m

DISEÑO DE TRABES DE CONCRETO PRETENSADAS

30.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA

MÓDULO DE ELASTICIDAD DEL CONCRETO ESF. DEL ACERO DE REF.

TRABE4200

BAJA RELAJACIÓN

TENSAR ACERO ( 1.5 f ) A

1.19 ton/m

PESO PROPIO

0.70

LOSA

ton/m0.25 2.77

20

66

SUMA DE CARGA MUERTA CARGA VIVA EQUIVALENTE

ton/m 1.740.63



71


DATOS PARA OBTENCIÓN DE PÉRDIDAS EN TRABES PRETENSADAS

HUMEDAD RELATIVA PROMEDIO ANUAL HR = 55 %

MÓDULO DE ELASTICIDAD DEL ACERO ES = 2,100,000 kg/cm²

MÓDULO DE ELASTICIDAD DEL CONCRETO EC = 302,000 kg/cm²

Dfs = CC + AE + CRC + CRS

Dfs = Pérdida total de tensión por deformación en el concreto en kg/cm² CC = Pérdida por contracción del concreto en kg/cm² AE = Pérdida por acortamiento elástico en kg/cm²

CRC = Pérdida debida al escurrimiento plástico del concreto en kg/cm²

CRS = Pérdida por relajación del acero en kg/cm²

X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

fs -106.46 -61.99 -36.78 -5.38 6.76 25.09 92.56 117.97 146.83 156.50

f i 614.19 1054.74 1081.00 1317.28 1569.68 1816.90 1760.44 1826.70 1802.55 1794.46

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 58.750 99.960 101.890 122.910 145.391 166.521 161.924 167.712 165.760 165.107

fs 15.880 30.087 42.619 53.483 62.672 70.196 76.046 80.222 82.731 83.570

f i -18.135 -34.361 -48.675 -61.083 -71.578 -80.171 -86.851 -91.623 -94.489 -95.444

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -17.038 -31.589 -44.258 -54.431 -62.917 -69.084 -74.841 -78.521 -80.977 -81.795

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 408.52565 695.08334 708.50549 854.67236 1010.9955 1157.9275 1125.9636 1166.2063 1152.6381 1148.092893

CRC (kg/cm²) = 585.73578 978.38993 912.87286 1093.9053 1304.2722 1514.6645 1419.2078 1462.8926 1422.2864 1408.714836

CRS (kg/cm²) = 250.92365 202.63517 204.56881 180.9005 154.74984 129.53703 137.50626 131.29775 134.68488 135.8179739

AE + CRC + CRS 1245.19 1876.11 1825.95 2129.48 2470.02 2802.13 2682.68 2760.40 2709.61 2692.63

% fPU = 8.74 13.17 12.81 14.94 17.33 19.66 18.83 19.37 19.01 18.90

% fPU TOTAL = 13.06 17.49 17.13 19.26 21.65 23.99 23.15 23.69 23.34 23.22

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,389 11,758 11,808 11,505 11,164 10,832 10,952 10,874 10,925 10,942

(fPU - fSE)AS* = 22 44 58 82 110 142 137 147 145 144

X 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000



72


0 1.5 3 4.5 6 7.5 9 10.5 12 13.5 15

0

20

40

60

80

100

120

140

160

PÉRDIDAS DEL PRESFUERZO

LONGITUD MEDIA TRABE (en metros)

FU

ER

ZA

(e

n t

on

ela

da

s)



73


permisible

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

permisible

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

GRÁFICA DE ESFUERZOS A LA TRANSFERENCIA

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD ( m )

FIBRA SUPERIOR ( VIGA )

-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD (m)

FIBRA INFERIOR ( VIGA )



74


GRÁFICA DE ESFUERZOS EN SERVICIO

Esfzo. Inf. Viga permisible permisible Esfzo. tope Viga

x0.00 0.000 34.18484409 -33.94 247.50 -14.88640475

0.05 1.500 31.67191973 -33.94 247.50 10.54792737

0.10 3.000 19.11917723 -33.94 247.50 36.94664256

0.15 4.500 18.48836805 -33.94 247.50 56.91390295

0.20 6.000 14.56200247 -33.94 247.50 76.47421063

0.25 7.500 14.44508456 -33.94 247.50 91.17885051

0.30 9.000 14.1435935 -33.94 247.50 105.0926799

0.35 10.500 -0.987094465 -33.94 247.50 120.3798701

0.40 12.000 -6.381574919 -33.94 247.50 129.7960632

0.45 13.500 -12.18859772 -33.94 247.50 135.9802937

0.50 15.000 -15.05624186 -33.94 247.50 138.5752084

-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




75


Trabes pretensadas, Cálculo de Esfuerzos y Momento Resistente

Sección = 0.5 L Momento carga muerta + camión T3 S2 R4 Combinación = (CM+CV+I)

w

AL CENTRO DEL CLARO

30.00

CARGAS MomentosPeso propio 1.19 ton/m 134.55 ton-mLosa 0.70 ton/m 78.30 ton-mAsfalto 0.25 ton/m 45.33 ton-m 17100Parapeto + banqueta 0.63 ton/m 70.53 ton-mCarga Viva Equivalente 1.74 ton/m 196.03 ton-m

CALIDAD DE MATERIALESf'c tensado = 400 kg/cm² Pérdidas p* = 0.002915468

% DE ESFUERZOS f'c = 450 kg/cm² Iniciales Totales p = 0.000315419

PERMISIBLES = 100.00% frg = 19000 kg/cm² 4.32% 23.22% f S = 4,200 kg/cm²

SECCION SIMPLE SECCION COMPUESTA POR RUPTURA PRESFUERZO:Y TORONES CANTIDAD

H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12

A = 0.4974 m² A = 0.7061 m² b equiv= 104.35 cm 20 15 12Yi = 0.6150 m Yi = 0.8618 m d* = 143.18 cm 20 8Ys = 0.7350 m Ys = 0.6882 m p* = 0.00292 s/u 25 0Si = 0.1668 m³ Si viga = 0.2388 m³ fsu = 17100.0 kg/cm² 30 0Ss = 0.1396 m³ Ss viga = 0.4216 m³ cent as p = 11.82 cm 4.426

ycable = 11.818 Ss losa = 0.2991 m³ Refuerzo: As = 4.97 cm² Total = 44

Fuerza de cable = 620.73 ton Ys viga = 0.4882 m d = 151.00 cma = 21.58

Elemento estructural Esfuerzos en trabe Esfuerzos en losa Secc.

ETAPA P (ton) e (m) M (ton-m) Inferior Inf. acum. Superior Sup. acum. Inferior Inf. acum. Superior Sup. acum. S

Po.Po Viga 0.00 0.00 134.55 -806.4 -806.4 963.8 963.8 0.0 0.0 0.0 0.0 I

Presfuerzo Incl. 10% Pérd. 593.908 0.50 0.00 2962.5 2156.1 -919.5 44.3 0.0 0.0 0.0 0.0 M

Losa 0.00 0.00 78.30 -469.3 1686.8 560.9 605.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -117.291 0.74 0.00 -531.3 1155.4 40.8 645.9 40.8 40.8 125.5 125.5 C

Asfal + Parapeto 0.00 0.00 115.86 -485.1 670.3 274.8 920.7 274.8 315.6 387.4 513.0 O

Carga viva + I 0.00 0.00 196.03 -820.9 -150.6 465.0 1385.8 465.0 780.6 655.5 1168.5 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= -15.06 Sup. acum= 138.58 Inf. acum= 78.06 Sup acum= 116.85 P

Esf. adm. kg/cm²: AL TENSADO EN SERVICIO OBSERVACIONES

Compresión 240.00 180.00

Tensión: con/sin refzo. -31.92 -15.92 -33.77 0.00 Colocar acero de refuerzo OK

REV POR RESIST. Momento último Momento resistente OBSERVACIONES

MOMENTO 852.71 ton-m 931.04 ton-m PASA POR MOMENTO ULTIMO



76




w

30.00

CARGAS MomentosPeso propio 1.19 ton/m 133.20 ton-m

Losa 0.70 ton/m 77.51 ton-mAsfalto 0.25 ton/m 44.88 ton-m

Parapeto 0.63 ton/m 69.83 ton-mCarga Viva Equivalente 1.74 ton/m 192.60 ton-m


% DE ESFUERZOS f'c = 450 kg/cm² Iniciales Diferidas p = 0.000179054



H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12

A = 0.4974 m² A = 0.7061 m² b equiv= 104.35 cm 15 12Yi = 0.6150 m Yi = 0.8618 m d* = 143.18 cm 20 8Ys = 0.7350 m Ys = 0.6882 m p* = 0.00292 s/u 25 0Si = 0.1668 m³ Si viga = 0.2388 m³ fsu = 17100.0 kg/cm² 30 0Ss = 0.1396 m³ Ss viga = 0.4216 m³ cent as p = 11.82 cm





Po.Po Viga 0.00 0.00 133.20 -798.3 -798.3 954.1 954.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.51 -464.6 1699.6 555.2 589.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -118.03 0.74 0.00 -534.7 1164.9 41.0 630.8 41.0 41.0 126.3 126.3 C

Asfal + Parapeto 0.00 0.00 114.71 -480.3 684.6 272.1 902.9 272.1 313.1 383.6 509.9 O

Carga viva + I 0.00 0.00 192.60 -806.5 -121.9 456.9 1359.8 456.9 770.0 644.0 1153.9 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= -12.19 Sup. acum= 135.98 Inf. acum= 77.00 Sup. acum= 115.39 P



Tensión: con/sin refzo. -31.92 -15.92 -33.77 0.00 Colocar acero de refuerzo





77




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 129.17 -774.2 -774.2 925.2 925.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 75.16 -450.5 1737.8 538.4 544.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -120.24 0.74 0.00 -544.7 1193.1 41.8 585.9 41.8 41.8 128.7 128.7 C

Asfal + Parapeto 0.00 0.00 111.23 -465.8 727.4 263.8 849.8 263.8 305.7 371.9 500.6 O

Carga viva + I 0.00 0.00 188.95 -791.2 -63.8 448.2 1298.0 448.2 753.9 631.8 1132.5 M









78




w

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f'c tensado = 400 kg/cm² Pérdidas p* = 0.002775394




H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 122.44 -733.8 -733.8 877.0 877.0 0.0 0.0 0.0 0.0 I

Presfuerzo Incl. 10% Pérd. 566.91 0.50 0.00 2841.1 2107.2 -893.5 -16.5 0.0 0.0 0.0 0.0 M

Losa 0.00 0.00 71.25 -427.0 1680.2 510.4 493.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -111.55 0.75 0.00 -507.1 1173.1 39.8 533.7 39.8 39.8 120.8 120.8 C

Asfal + Parapeto 0.00 0.00 105.43 -441.5 731.6 250.1 783.8 250.1 289.9 352.5 473.4 O

Carga viva + I 0.00 0.00 177.07 -741.5 -9.9 420.0 1203.8 420.0 709.9 592.1 1065.5 M







CALIDAD DE MATERIALES



79




80




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 113.02 -677.4 -677.4 809.6 809.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 65.77 -394.2 1769.5 471.1 387.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -116.51 0.75 0.00 -529.7 1239.8 41.6 428.7 41.6 41.6 126.2 126.2 C

Asfal + Parapeto 0.00 0.00 97.32 -407.5 832.3 230.9 659.6 230.9 272.4 325.4 451.7 O

Carga viva + I 0.00 0.00 164.98 -690.8 141.4 391.4 1050.9 391.4 663.8 551.7 1003.3 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= 14.14 Sup. acum= 105.09 Inf. acum= 66.38 Sup. acum= 100.33 P



Tensión: con/sin refzo. -31.92 -15.92 -33.77 0.00 BIEN






81




w

30.00








H = 1.3500 m H = 1.5500 m As* = 35.64 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12


ycable = 10.000 cm Ss losa = 0.2991 m³ Refuerzo: As = 2.84 cm² Total = 36

Fuerza de cable = 507.87 ton Ys viga = 0.4882 m d = 152.00 cma = 17.51 cm



Po.Po Viga 0.00 0.00 100.91 -604.8 -604.8 722.8 722.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 58.72 -351.9 1520.1 420.6 327.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -88.03 0.76 0.00 -405.5 1114.6 34.4 362.2 34.4 34.4 99.6 99.6 C

Asfal + Parapeto 0.00 0.00 86.89 -363.8 750.7 206.1 568.3 206.1 240.5 290.6 390.1 O

Carga viva + I 0.00 0.00 144.79 -606.3 144.5 343.5 911.8 343.5 584.0 484.2 874.3 M










82




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H = 1.3500 m H = 1.5500 mts. As* = 29.70 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 86.11 -516.1 -516.1 616.8 616.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 50.11 -300.3 1271.8 358.9 267.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -63.25 0.77 0.00 -294.0 977.9 26.2 293.3 26.2 26.2 73.7 73.7 C

Asfal + Parapeto 0.00 0.00 74.15 -310.5 667.4 175.9 469.2 175.9 202.1 247.9 321.6 O

Carga viva + I 0.00 0.00 124.60 -521.8 145.6 295.6 764.7 295.6 497.7 416.7 738.3 M










83




w

30








H = 1.3500 m H = 1.5500 mts. As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 68.62 -411.3 -411.3 491.5 491.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 39.93 -239.3 1049.2 286.0 175.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -43.38 0.79 0.00 -204.4 844.8 19.5 195.3 19.5 19.5 52.7 52.7 C

Asfal + Parapeto 0.00 0.00 59.09 -247.4 597.3 140.2 335.5 140.2 159.7 197.6 250.3 O

Carga viva + I 0.00 0.00 98.50 -412.5 184.9 233.7 569.1 233.7 393.4 329.4 579.7 M










84




w

30








H = 1.3500 m H = 1.5500 mts. As* = 17.82 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 6






Po.Po Viga 0.00 0.00 48.44 -290.3 -290.3 347.0 347.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 28.19 -169.0 827.7 201.9 83.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -33.43 0.80 0.00 -158.7 669.0 15.7 98.8 15.7 15.7 41.5 41.5 C

Asfal + Parapeto 0.00 0.00 41.71 -174.7 494.3 98.9 197.7 98.9 114.7 139.5 181.0 O

Carga viva + I 0.00 0.00 72.40 -303.2 191.2 171.7 369.5 171.7 286.4 242.1 423.1 M










85




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H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 25.57 -153.3 -153.3 183.2 183.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 14.88 -89.2 631.7 106.6 -40.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.79 0.81 0.00 -71.2 560.5 7.5 -32.6 7.5 7.5 19.2 19.2 C

Asfal + Parapeto 0.00 0.00 22.01 -92.2 468.3 52.2 19.6 52.2 59.7 73.6 92.8 O

Carga viva + I 0.00 0.00 36.20 -151.6 316.7 85.9 105.5 85.9 145.6 121.1 213.9 M










86



Sección = Un peralte Momento carga muerta + camión T3 S2 R4 Combinación = (CM+CV+I)

w

30.00






PERMISIBLES = #¡REF! frg = 19000 kg/cm² 4.32% 23.22% f S = 4,200 kg/cm²


H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 8.82 -52.9 -52.9 63.2 63.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 5.13 -30.7 499.2 36.7 -120.0 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -21.33 0.81 0.00 -102.7 396.5 10.9 -109.1 10.9 10.9 27.7 27.7 C

Asfal + Parapeto 0.00 0.00 7.59 -31.8 364.7 18.0 -91.1 18.0 28.9 25.4 53.1 O

Carga viva + I 0.00 0.00 12.07 -50.5 314.1 28.6 -62.5 28.6 57.5 40.4 93.4 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= 31.41 Sup. acum= -6.25 Inf. acum= 5.75 Sup. acum= 9.34 P









87



Sección = 0 L Momento carga muerta + camión T3 S2 R4 Combinación = (CM+CV+I)

w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 5.64 cm² 5 4

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 415.0 0.0 -156.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -15.19 0.81 0.00 -73.1 341.9 7.7 -148.9 7.7 7.7 19.7 19.7 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 341.9 0.0 -148.9 0.0 7.7 0.0 19.7 O

Carga viva + I 0.00 0.00 0.00 0.0 341.8 0.0 -148.9 0.0 7.7 0.0 19.7 M










88


DISEÑO POR CORTANTE DE TRABES PRETENSADAS

x en metros 0.675 1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

MCM 21.54 62.46 118.34 167.64 210.37 246.52 276.11 299.12 315.56 325.42 328.71

MCV 12.07 36.20 72.40 98.50 124.60 144.79 164.98 177.07 188.95 192.60 196.03

MU en ton-m 54.15 159.63 310.70 431.35 543.46 634.19 716.40 772.51 819.62 840.34 852.06

VCM 42.35 39.38 35.05 30.65 26.27 21.88 17.51 13.13 8.74 4.36 0.00

VCV 27.49 26.15 24.13 22.10 20.09 18.07 16.05 14.12 12.20 10.65 9.10

VU en ton 114.62 107.84 97.84 87.74 77.67 67.59 57.53 47.67 37.79 28.74 19.71

VC 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37

VU-VC 85.95 79.17 69.49 59.55 49.77 39.88 30.09 20.23 10.42 1.37 -7.66

E#3@ 8.85 9.60 10.94 12.77 15.28 19.07 25.27 37.59 72.97 554.86 -99.33

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 148.33 147.50 146.00 145.00 143.57 143.57 143.18 143.18 143.18

Vud/Mu <= 1.0 1.00 1.00 0.47 0.30 0.21 0.15 0.12 0.09 0.07 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37

f(0.16 raiz(f́ c) + 49Vud/Mu)bwd 133.60 133.60 66.27 45.37 33.80 27.03 22.07 18.88 16.13 14.10 12.21

f1.3 raiz(f́ c)bwd 70.32 70.32 69.54 69.15 68.45 67.98 67.31 67.31 67.13 67.13 67.13

VC considerado 70.32 70.32 66.27 45.37 33.80 27.71 27.44 27.44 27.37 27.37 27.37

VS = VU-VC 44.30 37.52 31.57 42.36 43.87 39.88 30.09 20.23 10.42 1.37 0.01

Separación de Estribos #4 en cm 30.6 36.1 42.5 31.5 30.1 32.9 43.1 64.2 124.2 944.4 129425.5

Separación Max. Estribos #4 en cm 85.20 85.20 85.20 85.20 85.20 85.20 85.20 85.20 85.20 85.20 85.20

Separación a usar @ 15 OK @ 15 OK @ 15 OK @ 20 OK @ 20 OK @ 20 OK @ 30 OK @ 30 OK @ 30 OK @ 40 OK @ 40 OK



89



4.2.1.- CARGA VIVA



1.000

0.330

Datos


Analisis

Excentricidad (m)

Factor de reduccion


1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143


6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2



90



Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2

T4 0.349 54.030 18.862

DESCARGA TOTAL =


54.03054.0300.464

132.031

25.06628.168T1




CARGA POR TRABE

T7 0.177 54.030 9.555

0.521

30.600100.394

Analisis

T3 0.407

DESCARGA DE CAMION


0.222

1.222

T5 0.292 54.030

54.030T2

Datos

54.030 12.65715.760

21.964

T6 0.234

25

50

LI



91



12.1 36.2 165.0

0.45x / L 0.05

MOMENTO0.0 kL 0.50


45.3

0.40

65.8

245.88

362.43239.01

51.6 57.8

190.40

277.73

1.7

78.377.5

188.94

204.81

43.5 44.941.3

66.1

1.6

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 8.63.0

0.0 8.8 25.6





CARGA VIVA TRABE

x / L

CARGA VIVA TRABE


6.4

207.24108.78 138.51 158.46

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




265.35262.87

196.0192.6

0.0

0.01 39.53 79.0413.18

316.46

12.00

10.4

6.0

0.2

202.39

0.0

3.1 2.1

140.54102.23

0.0

29.60 29.05 27.97 26.34 14.93

0.0

9.2 2.8 1.8

10.6

0.0

0.40 0.45 0.50

6.00

0.1

4.6

13.50 15.00

Reacción

21.45 13.30

3.7

19.82 18.19 16.56

1.8 0.0

5.4 3.6

0.2

2.4

0.1

4.8 4.2 3.0

8.9 8.3 7.3 5.5

0.2

10.1 9.3 8.4 7.3

5.8

17.9 17.3 16.1 14.4

6.3

0.00.2 0.2 0.1 0.1

0.05 0.10 0.15 0.20

0.0 0.68 1.50 3.00 4.50

0.01

0.01

177.1

69.44 138.87

72.4

23.15

17.04

144.80.0

51.11

0.0 0.6 1.4 1.50.9 1.1 1.30.3

44.1

75.2

0.0 68.2

39.9 50.1

1.7

0.0 29.0

71.3

38.116.3 23.1 34.0

15.00

68.6 86.1 100.9 113.0 122.4

9.00

129.2 133.2 134.648.4

4.50 6.00 13.50

58.70.0 5.1 14.9 28.2

0.20

0.0 0.68 1.50 3.00

4.5

14.1 12.2

0.25 0.30

7.50

178.41

205.12

0.1

24.8

376.02

15.66

0.35

369.43339.65

260.38

62.7

12.0010.50

3.6

9.1

35.1 68.9

0.30

5.4

CORTANTE

13.1

0.0 kL

188.998.5 124.6

0.35

9.00

7.2

0.25

12.6

7.50 10.50

27.09 20.42

231.38

23.40

0.9

4.2

0.61.8 1.2

1.0

24.71

10.8 9.0

23.08

5.2

17.4542.40 38.53 34.66 30.78

27.16 24.86 22.56 20.26 17.9636.36 34.06 31.76

16.028.2 27.5 26.1 24.1 22.1 20.1 18.1

38.66

178.86

0.10 0.15

54.03 52.73 50.15 46.28

29.4637.90

0.22

9.36

18.26

10.65

3.83

29.60

54.03

38.66

0.00



92




93


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-15.661

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

44

42

44PASA POR MOMENTO


ULTIMO

30

36

42

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

24

Suma

4

8

12

18

6 0

0 0

0


Esfuerzos Servicio


23.22%4.32%

Esfuerzos Trans.


FINALESINICIALES


0.0 L 0


5 10 15

REACCIONES

0.68

0.05 L 1.50

0.10 L 3.00

0 0 0

8

31.5

8 0 0 3.459

4.426

-12.189

215.6070 0

0.15 L 4.50


6 0 0

8 0 0

44

0.25 L 7.50

0.30 L 9.00

0 0 0

0 0 0

Distancia5 10 15 20


30

15.00

1.3500

0.1026

0.49740.61500.9000

9.00

10.50

12.00

13.50

1.5500

0.2058

0.70610.8618

6.00

7.50

41.500 -14.886

10.65

36.20

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

1.50

3.00

4.50

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

12

12

12

12

fSMAX = 138.575

fSMIN =

fI MAX =

-15.67

218.8


0.50 L 15.00

-1.651

135.980

138.575

76.474

20 25

-9.280

-8.398

-9.188

12

34.185

52.990 -6.250 31.414

-14.6730 0 0

0

0.40 L 12.00

0.45 L 13.50

10.50

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 6.00

0.572

14.1218.07 16.0526.15 24.13 22.10

12

12

18.488128.848 56.914

91.179

105.093

120.380

0.00

8 0 0

004

12.07 72.40

0.0 L

28.17

0

157.218

9.10

12 0

12

-15.675

00

12

187.201 14.445

0 0

216.416

12

12

12

-11.885

12

124.60

12 12

12

6

0

06

12

99.662 36.947

164.98

14.562

-11.023

31.67272.089 10.548

177.07

19.119

12

12

12

27.49

0

12

0

20.09

12

12

216.369

98.50

1.00

144.79

0.75

192.60 196.03188.95

4

4

6

6

14.144

210.723 -0.987

218.832 129.796 -6.382

-15.056

6

6

6

2

HR = 55


ton/mton/m


EC =

CARGAS

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140


12.20

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m


30.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


TRABE4200

BAJA RELAJACIÓN


1.19 ton/m

PESO PROPIO

0.70

LOSA

ton/m0.25 2.77

20

66


ton/m 1.740.63



94










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

fs -106.46 -61.99 -36.78 -5.38 6.76 25.09 92.56 117.97 146.83 156.50

f i 614.19 1054.74 1081.00 1317.28 1569.68 1816.90 1760.44 1826.70 1802.55 1794.46

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 58.750 99.960 101.890 122.910 145.391 166.521 161.924 167.712 165.760 165.107

fs 15.880 30.087 42.619 53.483 62.672 70.196 76.046 80.222 82.731 83.570

f i -18.135 -34.361 -48.675 -61.083 -71.578 -80.171 -86.851 -91.623 -94.489 -95.444

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -17.038 -31.589 -44.258 -54.431 -62.917 -69.084 -74.841 -78.521 -80.977 -81.795

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 408.52565 695.08334 708.50549 854.67236 1010.9955 1157.9275 1125.9636 1166.2063 1152.6381 1148.092893

CRC (kg/cm²) = 585.73578 978.38993 912.87286 1093.9053 1304.2722 1514.6645 1419.2078 1462.8926 1422.2864 1408.714836

CRS (kg/cm²) = 250.92365 202.63517 204.56881 180.9005 154.74984 129.53703 137.50626 131.29775 134.68488 135.8179739

AE + CRC + CRS 1245.19 1876.11 1825.95 2129.48 2470.02 2802.13 2682.68 2760.40 2709.61 2692.63

% fPU = 8.74 13.17 12.81 14.94 17.33 19.66 18.83 19.37 19.01 18.90

% fPU TOTAL = 13.06 17.49 17.13 19.26 21.65 23.99 23.15 23.69 23.34 23.22

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,389 11,758 11,808 11,505 11,164 10,832 10,952 10,874 10,925 10,942

(fPU - fSE)AS* = 22 44 58 82 110 142 137 147 145 144

X 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000



95


0 1.5 3 4.5 6 7.5 9 10.5 12 13.5 15

0

20

40

60

80

100

120

140

160



FU

ER

ZA

(e

n t

on

ela

da

s)



96


permisible

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

permisible

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


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD (m)




97




x0.00 0.000 34.18484409 -33.94 247.50 -14.88640475

0.05 1.500 31.67191973 -33.94 247.50 10.54792737

0.10 3.000 19.11917723 -33.94 247.50 36.94664256

0.15 4.500 18.48836805 -33.94 247.50 56.91390295

0.20 6.000 14.56200247 -33.94 247.50 76.47421063

0.25 7.500 14.44508456 -33.94 247.50 91.17885051

0.30 9.000 14.1435935 -33.94 247.50 105.0926799

0.35 10.500 -0.987094465 -33.94 247.50 120.3798701

0.40 12.000 -6.381574919 -33.94 247.50 129.7960632

0.45 13.500 -12.18859772 -33.94 247.50 135.9802937

0.50 15.000 -15.05624186 -33.94 247.50 138.5752084

-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




98




w

AL CENTRO DEL CLARO

30.00






H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 134.55 -806.4 -806.4 963.8 963.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 78.30 -469.3 1686.8 560.9 605.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -117.291 0.74 0.00 -531.3 1155.4 40.8 645.9 40.8 40.8 125.5 125.5 C

Asfal + Parapeto 0.00 0.00 115.86 -485.1 670.3 274.8 920.7 274.8 315.6 387.4 513.0 O

Carga viva + I 0.00 0.00 196.03 -820.9 -150.6 465.0 1385.8 465.0 780.6 655.5 1168.5 M









99




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 133.20 -798.3 -798.3 954.1 954.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.51 -464.6 1699.6 555.2 589.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -118.03 0.74 0.00 -534.7 1164.9 41.0 630.8 41.0 41.0 126.3 126.3 C

Asfal + Parapeto 0.00 0.00 114.71 -480.3 684.6 272.1 902.9 272.1 313.1 383.6 509.9 O

Carga viva + I 0.00 0.00 192.60 -806.5 -121.9 456.9 1359.8 456.9 770.0 644.0 1153.9 M









100




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 129.17 -774.2 -774.2 925.2 925.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 75.16 -450.5 1737.8 538.4 544.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -120.24 0.74 0.00 -544.7 1193.1 41.8 585.9 41.8 41.8 128.7 128.7 C

Asfal + Parapeto 0.00 0.00 111.23 -465.8 727.4 263.8 849.8 263.8 305.7 371.9 500.6 O

Carga viva + I 0.00 0.00 188.95 -791.2 -63.8 448.2 1298.0 448.2 753.9 631.8 1132.5 M









101




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 122.44 -733.8 -733.8 877.0 877.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 71.25 -427.0 1680.2 510.4 493.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -111.55 0.75 0.00 -507.1 1173.1 39.8 533.7 39.8 39.8 120.8 120.8 C

Asfal + Parapeto 0.00 0.00 105.43 -441.5 731.6 250.1 783.8 250.1 289.9 352.5 473.4 O

Carga viva + I 0.00 0.00 177.07 -741.5 -9.9 420.0 1203.8 420.0 709.9 592.1 1065.5 M










102




103




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 113.02 -677.4 -677.4 809.6 809.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 65.77 -394.2 1769.5 471.1 387.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -116.51 0.75 0.00 -529.7 1239.8 41.6 428.7 41.6 41.6 126.2 126.2 C

Asfal + Parapeto 0.00 0.00 97.32 -407.5 832.3 230.9 659.6 230.9 272.4 325.4 451.7 O

Carga viva + I 0.00 0.00 164.98 -690.8 141.4 391.4 1050.9 391.4 663.8 551.7 1003.3 M










104




w

30.00








H = 1.3500 m H = 1.5500 m As* = 35.64 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 100.91 -604.8 -604.8 722.8 722.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 58.72 -351.9 1520.1 420.6 327.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -88.03 0.76 0.00 -405.5 1114.6 34.4 362.2 34.4 34.4 99.6 99.6 C

Asfal + Parapeto 0.00 0.00 86.89 -363.8 750.7 206.1 568.3 206.1 240.5 290.6 390.1 O

Carga viva + I 0.00 0.00 144.79 -606.3 144.5 343.5 911.8 343.5 584.0 484.2 874.3 M










105




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 29.70 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 86.11 -516.1 -516.1 616.8 616.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 50.11 -300.3 1271.8 358.9 267.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -63.25 0.77 0.00 -294.0 977.9 26.2 293.3 26.2 26.2 73.7 73.7 C

Asfal + Parapeto 0.00 0.00 74.15 -310.5 667.4 175.9 469.2 175.9 202.1 247.9 321.6 O

Carga viva + I 0.00 0.00 124.60 -521.8 145.6 295.6 764.7 295.6 497.7 416.7 738.3 M










106




w

30








H = 1.3500 m H = 1.5500 mts. As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 68.62 -411.3 -411.3 491.5 491.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 39.93 -239.3 1049.2 286.0 175.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -43.38 0.79 0.00 -204.4 844.8 19.5 195.3 19.5 19.5 52.7 52.7 C

Asfal + Parapeto 0.00 0.00 59.09 -247.4 597.3 140.2 335.5 140.2 159.7 197.6 250.3 O

Carga viva + I 0.00 0.00 98.50 -412.5 184.9 233.7 569.1 233.7 393.4 329.4 579.7 M










107




w

30








H = 1.3500 m H = 1.5500 mts. As* = 17.82 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 6






Po.Po Viga 0.00 0.00 48.44 -290.3 -290.3 347.0 347.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 28.19 -169.0 827.7 201.9 83.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -33.43 0.80 0.00 -158.7 669.0 15.7 98.8 15.7 15.7 41.5 41.5 C

Asfal + Parapeto 0.00 0.00 41.71 -174.7 494.3 98.9 197.7 98.9 114.7 139.5 181.0 O

Carga viva + I 0.00 0.00 72.40 -303.2 191.2 171.7 369.5 171.7 286.4 242.1 423.1 M










108




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 25.57 -153.3 -153.3 183.2 183.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 14.88 -89.2 631.7 106.6 -40.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.79 0.81 0.00 -71.2 560.5 7.5 -32.6 7.5 7.5 19.2 19.2 C

Asfal + Parapeto 0.00 0.00 22.01 -92.2 468.3 52.2 19.6 52.2 59.7 73.6 92.8 O

Carga viva + I 0.00 0.00 36.20 -151.6 316.7 85.9 105.5 85.9 145.6 121.1 213.9 M










109




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 8.82 -52.9 -52.9 63.2 63.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 5.13 -30.7 499.2 36.7 -120.0 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -21.33 0.81 0.00 -102.7 396.5 10.9 -109.1 10.9 10.9 27.7 27.7 C

Asfal + Parapeto 0.00 0.00 7.59 -31.8 364.7 18.0 -91.1 18.0 28.9 25.4 53.1 O

Carga viva + I 0.00 0.00 12.07 -50.5 314.1 28.6 -62.5 28.6 57.5 40.4 93.4 M










110




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 5.64 cm² 5 4

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 415.0 0.0 -156.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -15.19 0.81 0.00 -73.1 341.9 7.7 -148.9 7.7 7.7 19.7 19.7 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 341.9 0.0 -148.9 0.0 7.7 0.0 19.7 O

Carga viva + I 0.00 0.00 0.00 0.0 341.8 0.0 -148.9 0.0 7.7 0.0 19.7 M










111



x en metros 0.675 1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

MCM 21.54 62.46 118.34 167.64 210.37 246.52 276.11 299.12 315.56 325.42 328.71

MCV 12.07 36.20 72.40 98.50 124.60 144.79 164.98 177.07 188.95 192.60 196.03

MU en ton-m 54.15 159.63 310.70 431.35 543.46 634.19 716.40 772.51 819.62 840.34 852.06

VCM 42.35 39.38 35.05 30.65 26.27 21.88 17.51 13.13 8.74 4.36 0.00

VCV 27.49 26.15 24.13 22.10 20.09 18.07 16.05 14.12 12.20 10.65 9.10

VU en ton 114.62 107.84 97.84 87.74 77.67 67.59 57.53 47.67 37.79 28.74 19.71

VC 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37

VU-VC 85.95 79.17 69.49 59.55 49.77 39.88 30.09 20.23 10.42 1.37 -7.66

E#3@ 8.85 9.60 10.94 12.77 15.28 19.07 25.27 37.59 72.97 554.86 -99.33

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 148.33 147.50 146.00 145.00 143.57 143.57 143.18 143.18 143.18

Vud/Mu <= 1.0 1.00 1.00 0.47 0.30 0.21 0.15 0.12 0.09 0.07 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37


f1.3 raiz(f́ c)bwd 70.32 70.32 69.54 69.15 68.45 67.98 67.31 67.31 67.13 67.13 67.13

VC considerado 70.32 70.32 66.27 45.37 33.80 27.71 27.44 27.44 27.37 27.37 27.37

VS = VU-VC 44.30 37.52 31.57 42.36 43.87 39.88 30.09 20.23 10.42 1.37 0.01






112



4.3.1.- CARGA VIVA



1.000

0.330

Datos


Analisis

Excentricidad (m)

Factor de reduccion


1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143


6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2



113



Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2

T4 0.349 54.030 18.862

DESCARGA TOTAL =


54.03054.0300.464

132.031

25.06628.168T1




CARGA POR TRABE

T7 0.177 54.030 9.555

0.521

30.600100.394

Analisis

T3 0.407

DESCARGA DE CAMION


0.222

1.222

T5 0.292 54.030

54.030T2

Datos

54.030 12.65715.760

21.964

T6 0.234

25

50

LI



114



12.1 36.2 165.0

0.45x / L 0.05

MOMENTO0.0 kL 0.50


45.3

0.40

65.8

245.88

362.43239.01

51.6 57.8

190.40

277.73

1.7

78.377.5

188.94

204.81

43.5 44.941.3

66.1

1.6

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 8.63.0

0.0 8.8 25.6





CARGA VIVA TRABE

x / L

CARGA VIVA TRABE


6.4

207.24108.78 138.51 158.46

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




265.35262.87

196.0192.6

0.0

0.01 39.53 79.0413.18

316.46

12.00

10.4

6.0

0.2

202.39

0.0

3.1 2.1

140.54102.23

0.0

29.60 29.05 27.97 26.34 14.93

0.0

9.2 2.8 1.8

10.6

0.0

0.40 0.45 0.50

6.00

0.1

4.6

13.50 15.00

Reacción

21.45 13.30

3.7

19.82 18.19 16.56

1.8 0.0

5.4 3.6

0.2

2.4

0.1

4.8 4.2 3.0

8.9 8.3 7.3 5.5

0.2

10.1 9.3 8.4 7.3

5.8

17.9 17.3 16.1 14.4

6.3

0.00.2 0.2 0.1 0.1

0.05 0.10 0.15 0.20

0.0 0.68 1.50 3.00 4.50

0.01

0.01

177.1

69.44 138.87

72.4

23.15

17.04

144.80.0

51.11

0.0 0.6 1.4 1.50.9 1.1 1.30.3

44.1

75.2

0.0 68.2

39.9 50.1

1.7

0.0 29.0

71.3

38.116.3 23.1 34.0

15.00

68.6 86.1 100.9 113.0 122.4

9.00

129.2 133.2 134.648.4

4.50 6.00 13.50

58.70.0 5.1 14.9 28.2

0.20

0.0 0.68 1.50 3.00

4.5

14.1 12.2

0.25 0.30

7.50

178.41

205.12

0.1

24.8

376.02

15.66

0.35

369.43339.65

260.38

62.7

12.0010.50

3.6

9.1

35.1 68.9

0.30

5.4

CORTANTE

13.1

0.0 kL

188.998.5 124.6

0.35

9.00

7.2

0.25

12.6

7.50 10.50

27.09 20.42

231.38

23.40

0.9

4.2

0.61.8 1.2

1.0

24.71

10.8 9.0

23.08

5.2

17.4542.40 38.53 34.66 30.78

27.16 24.86 22.56 20.26 17.9636.36 34.06 31.76

16.028.2 27.5 26.1 24.1 22.1 20.1 18.1

38.66

178.86

0.10 0.15

54.03 52.73 50.15 46.28

29.4637.90

0.22

9.36

18.26

10.65

3.83

29.60

54.03

38.66

0.00



115




116


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-15.661

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

44

42

44PASA POR MOMENTO


ULTIMO

30

36

42

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

24

Suma

4

8

12

18

6 0

0 0

0


Esfuerzos Servicio


23.22%4.32%

Esfuerzos Trans.


FINALESINICIALES


0.0 L 0


5 10 15

REACCIONES

0.68

0.05 L 1.50

0.10 L 3.00

0 0 0

8

31.5

8 0 0 3.459

4.426

-12.189

215.6070 0

0.15 L 4.50


6 0 0

8 0 0

44

0.25 L 7.50

0.30 L 9.00

0 0 0

0 0 0

Distancia5 10 15 20


30

15.00

1.3500

0.1026

0.49740.61500.9000

9.00

10.50

12.00

13.50

1.5500

0.2058

0.70610.8618

6.00

7.50

41.500 -14.886

10.65

36.20

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

1.50

3.00

4.50

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

12

12

12

12

fSMAX = 138.575

fSMIN =

fI MAX =

-15.67

218.8


0.50 L 15.00

-1.651

135.980

138.575

76.474

20 25

-9.280

-8.398

-9.188

12

34.185

52.990 -6.250 31.414

-14.6730 0 0

0

0.40 L 12.00

0.45 L 13.50

10.50

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 6.00

0.572

14.1218.07 16.0526.15 24.13 22.10

12

12

18.488128.848 56.914

91.179

105.093

120.380

0.00

8 0 0

004

12.07 72.40

0.0 L

28.17

0

157.218

9.10

12 0

12

-15.675

00

12

187.201 14.445

0 0

216.416

12

12

12

-11.885

12

124.60

12 12

12

6

0

06

12

99.662 36.947

164.98

14.562

-11.023

31.67272.089 10.548

177.07

19.119

12

12

12

27.49

0

12

0

20.09

12

12

216.369

98.50

1.00

144.79

0.75

192.60 196.03188.95

4

4

6

6

14.144

210.723 -0.987

218.832 129.796 -6.382

-15.056

6

6

6

2

HR = 55


ton/mton/m


EC =

CARGAS

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140


12.20

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m


30.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


TRABE4200

BAJA RELAJACIÓN


1.19 ton/m

PESO PROPIO

0.70

LOSA

ton/m0.25 2.77

20

66


ton/m 1.740.63



117










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

fs -106.46 -61.99 -36.78 -5.38 6.76 25.09 92.56 117.97 146.83 156.50

f i 614.19 1054.74 1081.00 1317.28 1569.68 1816.90 1760.44 1826.70 1802.55 1794.46

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 58.750 99.960 101.890 122.910 145.391 166.521 161.924 167.712 165.760 165.107

fs 15.880 30.087 42.619 53.483 62.672 70.196 76.046 80.222 82.731 83.570

f i -18.135 -34.361 -48.675 -61.083 -71.578 -80.171 -86.851 -91.623 -94.489 -95.444

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.118 0.118

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -17.038 -31.589 -44.258 -54.431 -62.917 -69.084 -74.841 -78.521 -80.977 -81.795

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 408.52565 695.08334 708.50549 854.67236 1010.9955 1157.9275 1125.9636 1166.2063 1152.6381 1148.092893

CRC (kg/cm²) = 585.73578 978.38993 912.87286 1093.9053 1304.2722 1514.6645 1419.2078 1462.8926 1422.2864 1408.714836

CRS (kg/cm²) = 250.92365 202.63517 204.56881 180.9005 154.74984 129.53703 137.50626 131.29775 134.68488 135.8179739

AE + CRC + CRS 1245.19 1876.11 1825.95 2129.48 2470.02 2802.13 2682.68 2760.40 2709.61 2692.63

% fPU = 8.74 13.17 12.81 14.94 17.33 19.66 18.83 19.37 19.01 18.90

% fPU TOTAL = 13.06 17.49 17.13 19.26 21.65 23.99 23.15 23.69 23.34 23.22

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,389 11,758 11,808 11,505 11,164 10,832 10,952 10,874 10,925 10,942

(fPU - fSE)AS* = 22 44 58 82 110 142 137 147 145 144

X 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000



118


0 1.5 3 4.5 6 7.5 9 10.5 12 13.5 15

0

20

40

60

80

100

120

140

160



FU

ER

ZA

(e

n t

on

ela

da

s)



119


permisible

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

permisible

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


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

LONGITUD (m)




120




x0.00 0.000 34.18484409 -33.94 247.50 -14.88640475

0.05 1.500 31.67191973 -33.94 247.50 10.54792737

0.10 3.000 19.11917723 -33.94 247.50 36.94664256

0.15 4.500 18.48836805 -33.94 247.50 56.91390295

0.20 6.000 14.56200247 -33.94 247.50 76.47421063

0.25 7.500 14.44508456 -33.94 247.50 91.17885051

0.30 9.000 14.1435935 -33.94 247.50 105.0926799

0.35 10.500 -0.987094465 -33.94 247.50 120.3798701

0.40 12.000 -6.381574919 -33.94 247.50 129.7960632

0.45 13.500 -12.18859772 -33.94 247.50 135.9802937

0.50 15.000 -15.05624186 -33.94 247.50 138.5752084

-50

0

50

100

150

200

250

300

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 1.500 3.000 4.500 6.000 7.500 9.000 10.500 12.000 13.500 15.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




121




w

AL CENTRO DEL CLARO

30.00






H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 134.55 -806.4 -806.4 963.8 963.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 78.30 -469.3 1686.8 560.9 605.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -117.291 0.74 0.00 -531.3 1155.4 40.8 645.9 40.8 40.8 125.5 125.5 C

Asfal + Parapeto 0.00 0.00 115.86 -485.1 670.3 274.8 920.7 274.8 315.6 387.4 513.0 O

Carga viva + I 0.00 0.00 196.03 -820.9 -150.6 465.0 1385.8 465.0 780.6 655.5 1168.5 M









122




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 133.20 -798.3 -798.3 954.1 954.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.51 -464.6 1699.6 555.2 589.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -118.03 0.74 0.00 -534.7 1164.9 41.0 630.8 41.0 41.0 126.3 126.3 C

Asfal + Parapeto 0.00 0.00 114.71 -480.3 684.6 272.1 902.9 272.1 313.1 383.6 509.9 O

Carga viva + I 0.00 0.00 192.60 -806.5 -121.9 456.9 1359.8 456.9 770.0 644.0 1153.9 M









123




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 129.17 -774.2 -774.2 925.2 925.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 75.16 -450.5 1737.8 538.4 544.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -120.24 0.74 0.00 -544.7 1193.1 41.8 585.9 41.8 41.8 128.7 128.7 C

Asfal + Parapeto 0.00 0.00 111.23 -465.8 727.4 263.8 849.8 263.8 305.7 371.9 500.6 O

Carga viva + I 0.00 0.00 188.95 -791.2 -63.8 448.2 1298.0 448.2 753.9 631.8 1132.5 M









124




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 122.44 -733.8 -733.8 877.0 877.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 71.25 -427.0 1680.2 510.4 493.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -111.55 0.75 0.00 -507.1 1173.1 39.8 533.7 39.8 39.8 120.8 120.8 C

Asfal + Parapeto 0.00 0.00 105.43 -441.5 731.6 250.1 783.8 250.1 289.9 352.5 473.4 O

Carga viva + I 0.00 0.00 177.07 -741.5 -9.9 420.0 1203.8 420.0 709.9 592.1 1065.5 M










125




126




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 113.02 -677.4 -677.4 809.6 809.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 65.77 -394.2 1769.5 471.1 387.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -116.51 0.75 0.00 -529.7 1239.8 41.6 428.7 41.6 41.6 126.2 126.2 C

Asfal + Parapeto 0.00 0.00 97.32 -407.5 832.3 230.9 659.6 230.9 272.4 325.4 451.7 O

Carga viva + I 0.00 0.00 164.98 -690.8 141.4 391.4 1050.9 391.4 663.8 551.7 1003.3 M










127




w

30.00








H = 1.3500 m H = 1.5500 m As* = 35.64 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 100.91 -604.8 -604.8 722.8 722.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 58.72 -351.9 1520.1 420.6 327.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -88.03 0.76 0.00 -405.5 1114.6 34.4 362.2 34.4 34.4 99.6 99.6 C

Asfal + Parapeto 0.00 0.00 86.89 -363.8 750.7 206.1 568.3 206.1 240.5 290.6 390.1 O

Carga viva + I 0.00 0.00 144.79 -606.3 144.5 343.5 911.8 343.5 584.0 484.2 874.3 M










128




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 29.70 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 86.11 -516.1 -516.1 616.8 616.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 50.11 -300.3 1271.8 358.9 267.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -63.25 0.77 0.00 -294.0 977.9 26.2 293.3 26.2 26.2 73.7 73.7 C

Asfal + Parapeto 0.00 0.00 74.15 -310.5 667.4 175.9 469.2 175.9 202.1 247.9 321.6 O

Carga viva + I 0.00 0.00 124.60 -521.8 145.6 295.6 764.7 295.6 497.7 416.7 738.3 M










129




w

30








H = 1.3500 m H = 1.5500 mts. As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 68.62 -411.3 -411.3 491.5 491.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 39.93 -239.3 1049.2 286.0 175.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -43.38 0.79 0.00 -204.4 844.8 19.5 195.3 19.5 19.5 52.7 52.7 C

Asfal + Parapeto 0.00 0.00 59.09 -247.4 597.3 140.2 335.5 140.2 159.7 197.6 250.3 O

Carga viva + I 0.00 0.00 98.50 -412.5 184.9 233.7 569.1 233.7 393.4 329.4 579.7 M










130




w

30








H = 1.3500 m H = 1.5500 mts. As* = 17.82 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 6






Po.Po Viga 0.00 0.00 48.44 -290.3 -290.3 347.0 347.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 28.19 -169.0 827.7 201.9 83.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -33.43 0.80 0.00 -158.7 669.0 15.7 98.8 15.7 15.7 41.5 41.5 C

Asfal + Parapeto 0.00 0.00 41.71 -174.7 494.3 98.9 197.7 98.9 114.7 139.5 181.0 O

Carga viva + I 0.00 0.00 72.40 -303.2 191.2 171.7 369.5 171.7 286.4 242.1 423.1 M










131




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 25.57 -153.3 -153.3 183.2 183.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 14.88 -89.2 631.7 106.6 -40.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.79 0.81 0.00 -71.2 560.5 7.5 -32.6 7.5 7.5 19.2 19.2 C

Asfal + Parapeto 0.00 0.00 22.01 -92.2 468.3 52.2 19.6 52.2 59.7 73.6 92.8 O

Carga viva + I 0.00 0.00 36.20 -151.6 316.7 85.9 105.5 85.9 145.6 121.1 213.9 M










132




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 8.82 -52.9 -52.9 63.2 63.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 5.13 -30.7 499.2 36.7 -120.0 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -21.33 0.81 0.00 -102.7 396.5 10.9 -109.1 10.9 10.9 27.7 27.7 C

Asfal + Parapeto 0.00 0.00 7.59 -31.8 364.7 18.0 -91.1 18.0 28.9 25.4 53.1 O

Carga viva + I 0.00 0.00 12.07 -50.5 314.1 28.6 -62.5 28.6 57.5 40.4 93.4 M










133




w

30.00








H = 1.3500 m H = 1.5500 mts. As* = 5.64 cm² 5 4

Ix = 0.1026 m4Ix = 0.2058 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 415.0 0.0 -156.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -15.19 0.81 0.00 -73.1 341.9 7.7 -148.9 7.7 7.7 19.7 19.7 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 341.9 0.0 -148.9 0.0 7.7 0.0 19.7 O

Carga viva + I 0.00 0.00 0.00 0.0 341.8 0.0 -148.9 0.0 7.7 0.0 19.7 M










134



x en metros 0.675 1.50 3.00 4.50 6.00 7.50 9.00 10.50 12.00 13.50 15.00

MCM 21.54 62.46 118.34 167.64 210.37 246.52 276.11 299.12 315.56 325.42 328.71

MCV 12.07 36.20 72.40 98.50 124.60 144.79 164.98 177.07 188.95 192.60 196.03

MU en ton-m 54.15 159.63 310.70 431.35 543.46 634.19 716.40 772.51 819.62 840.34 852.06

VCM 42.35 39.38 35.05 30.65 26.27 21.88 17.51 13.13 8.74 4.36 0.00

VCV 27.49 26.15 24.13 22.10 20.09 18.07 16.05 14.12 12.20 10.65 9.10

VU en ton 114.62 107.84 97.84 87.74 77.67 67.59 57.53 47.67 37.79 28.74 19.71

VC 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37

VU-VC 85.95 79.17 69.49 59.55 49.77 39.88 30.09 20.23 10.42 1.37 -7.66

E#3@ 8.85 9.60 10.94 12.77 15.28 19.07 25.27 37.59 72.97 554.86 -99.33

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 148.33 147.50 146.00 145.00 143.57 143.57 143.18 143.18 143.18

Vud/Mu <= 1.0 1.00 1.00 0.47 0.30 0.21 0.15 0.12 0.09 0.07 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.37 27.37


f1.3 raiz(f́ c)bwd 70.32 70.32 69.54 69.15 68.45 67.98 67.31 67.31 67.13 67.13 67.13

VC considerado 70.32 70.32 66.27 45.37 33.80 27.71 27.44 27.44 27.37 27.37 27.37

VS = VU-VC 44.30 37.52 31.57 42.36 43.87 39.88 30.09 20.23 10.42 1.37 0.01






135




136


4.4.- DISEÑO DE LA TRABE AASHTO, (CLARO 30.6 MTS.) TRAMO 4-5 T 1, 2

4.4.1.- CARGA VIVA



137




1.000

0.330

Datos


Analisis

Excentricidad (m)

Factor de reduccion


1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143


6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2


Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2



138


T4 0.367 33.720 12.360

DESCARGA TOTAL =


33.72033.7200.487

86.523

16.42618.459T1




CARGA POR TRABE

T7 0.186 33.720 6.262

0.547

15.76051.706

Analisis

T3 0.427

DESCARGA DE CAMION


0.283

1.283

T5 0.306 33.720

33.720T2

Datos

33.720 8.29510.328

14.393

T6 0.246

25

50

LI



139



60.7 14.7 45.7

0.45x / L 0.05

MOMENTO0.0 kL 0.50


9.9

0.40

14.3

84.77

95.7667.50

12.2 13.0

76.30

78.21

1.4

17.117.0

58.40

78.97

9.5 9.89.2

14.9

1.4

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 2.51.3

0.0 3.9 7.6





CARGA VIVA TRABE

x / L

CARGA VIVA TRABE


2.9

78.8848.51 56.35 65.84

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




87.1387.21

53.853.4

0.0

0.01 21.89 32.83110.95

83.56

5.70

4.8

2.8

0.4

79.16

0.0

1.3 1.0

54.3037.01

0.0

26.28 25.20 24.11 23.02 11.18

0.0

4.4 1.2 0.9

6.6

0.0

0.40 0.45 0.50

2.85

0.1

2.0

6.41 7.12

Reacción

17.59 10.15

1.7

16.51 14.33 13.25

0.6 0.0

2.4 1.7

0.4

1.1

0.2

2.2 1.8 1.3

4.1 3.8 3.5 2.6

0.4

4.5 4.1 3.8 3.2

5.6

8.5 8.0 7.4 6.8

2.9

0.10.3 0.3 0.2 0.2

0.05 0.10 0.15 0.20

0.0 0.68 0.71 1.42 2.14

0.01

0.01

50.2

26.92 40.38

22.1

13.46

12.34

42.80.0

24.68

0.0 0.5 0.1 1.30.8 0.9 1.10.4

9.9

16.4

0.0 15.5

9.5 10.9

1.4

0.0 6.3

15.8

8.33.6 5.5 7.7

7.12

16.9 19.4 23.7 25.5 28.2

4.27

29.1 30.2 30.410.9

2.14 2.85 6.41

13.30.0 2.2 4.2 6.1

0.20

0.0 0.68 0.71 1.42

2.0

8.6 7.9

0.25 0.30

3.56

70.59

74.00

0.2

5.6

98.33

9.65

0.35

97.4791.69

87.90

14.4

5.704.99

1.7

6.0

8.6 15.5

0.30

2.3

CORTANTE

3.9

0.0 kL

52.432.0 37.0

0.35

4.27

3.4

0.25

5.7

3.56 4.99

15.75 12.12

79.52

14.52

0.3

1.9

0.20.7 0.6

0.3

20.85

5.1 4.0

19.77

2.2

10.9224.72 22.92 19.77 18.20

18.65 17.29 14.59 13.24 10.8527.47 25.97 22.89

10.018.5 17.5 16.5 15.5 13.5 12.5 10.8

30.56

62.94

0.10 0.15

33.72 31.92 30.12 28.32

21.3629.02

0.22

4.82

9.41

5.30

1.86

26.28

33.72

30.56

0.00



140




141


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.05 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.05 L



0.05 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-7.831

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

12

12

12PASA POR MOMENTO


ULTIMO

8

10

12

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

6

Suma

2

4

6

6

0 0

0 0

0


Esfuerzos Servicio


12.76%4.32%

Esfuerzos Trans.


FINALESINICIALES


0.0 L 0


5 10 15

REACCIONES

0.68

0.05 L 0.71

0.10 L 1.42

0 0 0

0

31.5

0 0 0 -11.356

-11.249

18.849

69.2240 0

0.15 L 2.14


0 0 0

0 0 0

12

0.25 L 3.56

0.30 L 4.27

0 0 0

0 0 0

Distancia5 10 15 20


30

7.12

1.3500

0.1026

0.49740.61500.9000

4.27

4.99

5.70

6.41

1.5500

0.2075

0.71090.8657

2.85

3.56

20.750 -7.661

6.63

14.74

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

0.71

1.42

2.14

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

0

0

0

0

fSMAX =

fI MIN =

20.504

-3.593 PASA

fSMIN =

fI MAX =

-14.72

72.1


0.50 L 7.12

-12.796

20.204

20.504

12.738

20 25

-10.485

-14.723

-8.075

0

19.117

26.795 8.593 -3.593

-11.0860 0 0

0

0.40 L 5.70

0.45 L 6.41

4.99

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 2.85

-12.115

8.6210.82 9.9716.49 15.50 13.53

0

12

6.25633.602 13.527

14.494

11.973

16.815

0.00

4 0 0

002

60.74 22.10

0.0 L

18.46

0

46.631

5.98

0 0

0

-8.195

00

0

58.617 18.863

0 0

69.314

0

0

0

-8.665

12

36.95

10 0

0

0

0

00

8

37.156 3.428

45.74

13.997

-4.417

25.21839.182 -2.795

50.19

17.506

12

12

12

17.47

0

6

0

12.55

6

6

72.131

31.97

1.00

42.81

0.75

53.36 53.8252.42

2

2

28.221

70.519 22.627

69.949 18.581 20.542

18.472

2

2

2

HR = 55


ton/mton/m


EC =

CARGAS

GEOMETRÍA

302,000

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

135


7.95

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 400

ACERO DE


ton/m


14.25CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


TRABE4200

BAJA RELAJACIÓN


1.19 ton/m

PESO PROPIO

0.67

LOSA

ton/m0.24 2.74

20

66


ton/m 2.120.64



142










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

0.71 1.42 2.14 2.85 3.56 4.27 4.99 5.70 6.41 7.12

fs -90.73 -66.52 -24.04 -53.90 -71.30 -106.96 -87.69 -80.89 -73.29 -72.22

f i 338.47 391.30 282.67 395.18 497.25 614.61 598.49 592.79 586.44 585.54

ytorones 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 32.257 37.435 27.131 37.854 47.619 58.788 57.307 56.784 56.200 56.118

fs 4.594 6.653 10.264 11.825 14.455 15.265 17.166 17.739 18.393 18.478

f i -5.325 -7.711 -11.898 -13.708 -16.755 -17.534 -19.897 -20.561 -21.315 -21.419

ytorones 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -5.005 -7.248 -11.183 -12.885 -15.748 -16.476 -18.702 -19.326 -20.034 -20.132

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 239.7941 278.27996 201.68631 281.39937 353.99025 437.01881 426.00808 422.11953 417.78072 417.1667407

CRC (kg/cm²) = 352.05655 398.4809 247.29289 364.05925 461.19692 590.12711 556.776 546.13016 534.1682 532.4880652

CRS (kg/cm²) = 279.48077 273.31096 288.52973 274.72011 262.60413 247.85477 250.6234 251.54454 252.57652 252.7219277

AE + CRC + CRS 871.33 950.07 737.51 920.18 1077.79 1275.00 1233.41 1219.79 1204.53 1202.38

% fPU = 6.11 6.67 5.18 6.46 7.56 8.95 8.66 8.56 8.45 8.44

% fPU TOTAL = 10.44 10.99 9.50 10.78 11.88 13.27 12.98 12.88 12.77 12.76

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,763 12,684 12,897 12,714 12,556 12,359 12,401 12,414 12,430 12,432

(fPU - fSE)AS* = 9 9 8 12 17 22 22 22 22 22

X 0.712 1.425 2.137 2.849 3.562 4.274 4.986 5.698 6.411 7.123



143


0 0.7123 1.4246 2.1369 2.8492 3.5615 4.2738 4.9861 5.6984 6.4107 7.123

0

5

10

15

20

25



FU

ER

ZA

(e

n t

on

ela

da

s)



144


Esfzo. Inf. Vigapermisiblepermisible

21 ## ##39 ## ##37 ## ##34 ## ##47 ## ##59 ## ##72 ## ##71 ## ##70 ## ##69 ## ##69 ## ##

permisibleEsfzo. tope Vigapermisible

## -8 #### -11 #### -9 #### -4 #### -8 #### -10 #### -15 #### -13 #### -12 #### -11 #### -11 ##


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

0.000 0.712 1.425 2.137 2.849 3.562 4.274 4.986 5.698 6.411 7.123

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

0.000 0.712 1.425 2.137 2.849 3.562 4.274 4.986 5.698 6.411 7.123

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




145




x0.00 0.000 19.1166682 -32.00 220.00 -7.660789864

0.05 0.712 25.21800549 -32.00 220.00 -2.7947359

0.10 1.425 17.5058868 -32.00 220.00 3.428496944

0.15 2.137 6.255996479 -32.00 220.00 13.52677397

0.20 2.849 13.99710674 -32.00 220.00 12.73835932

0.25 3.562 18.8628879 -32.00 220.00 14.49429433

0.30 4.274 28.22148876 -32.00 220.00 11.97280551

0.35 4.986 22.62692337 -32.00 220.00 16.81482105

0.40 5.698 20.54157671 -32.00 220.00 18.58072174

0.45 6.411 18.84920017 -32.00 220.00 20.20351678

0.50 7.123 18.47171233 -32.00 220.00 20.50410152

-50

0

50

100

150

200

250

0.000 0.712 1.425 2.137 2.849 3.562 4.274 4.986 5.698 6.411 7.123

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

0.000 0.712 1.425 2.137 2.849 3.562 4.274 4.986 5.698 6.411 7.123

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




146




w

AL CENTRO DEL CLARO

14.25






H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0

A = 0.4974 m² A = 0.7109 m² b equiv= 106.73 cm 106.726871 15 0Yi = 0.6150 m Yi = 0.8657 m d* = 150.00 cm 20 0Ys = 0.7350 m Ys = 0.6843 m p* = 0.00074 s/u 25 0Si = 0.1668 m³ Si viga = 0.2396 m³ fsu = 17100.0 kg/cm² 30 0Ss = 0.1396 m³ Ss viga = 0.4284 m³ cent as p = 5.00 cm #####





Po.Po Viga 0.00 0.00 30.35 -181.9 -181.9 217.4 217.4 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 17.05 -102.2 590.1 122.1 9.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.284 0.82 0.00 -68.7 521.3 7.1 16.7 7.1 7.1 18.3 18.3 C

Asfal + Parapeto 0.00 0.00 26.84 -112.0 409.3 62.7 79.4 62.7 69.8 88.5 106.9 O

Carga viva + I 0.00 0.00 53.82 -224.6 184.7 125.6 205.0 125.6 195.4 177.5 284.4 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= 18.47 Sup. acum= 20.50 Inf. acum= 19.54 Sup acum= 28.44 P



Tensión: con/sin refzo. -29.86 -14.89 -31.84 0.00 BIEN OK





147




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 30.20 -181.0 -181.0 216.3 216.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 16.98 -101.8 591.4 121.6 8.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.31 0.82 0.00 -68.8 522.5 7.1 15.2 7.1 7.1 18.4 18.4 C

Asfal + Parapeto 0.00 0.00 26.69 -111.4 411.2 62.3 77.5 62.3 69.4 88.0 106.4 O

Carga viva + I 0.00 0.00 53.36 -222.7 188.5 124.5 202.0 124.5 194.0 176.0 282.4 M









148




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 29.14 -174.7 -174.7 208.7 208.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 16.37 -98.1 601.4 117.3 -3.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.49 0.82 0.00 -69.7 531.7 7.2 3.3 7.2 7.2 18.6 18.6 C

Asfal + Parapeto 0.00 0.00 25.76 -107.5 424.2 60.1 63.4 60.1 67.3 85.0 103.6 O

Carga viva + I 0.00 0.00 52.42 -218.8 205.4 122.4 185.8 122.4 189.7 172.9 276.5 M









149




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 28.19 -169.0 -169.0 201.9 201.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 15.84 -94.9 610.3 113.5 -14.5 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.65 0.82 0.00 -70.5 539.8 7.3 -7.2 7.3 7.3 18.8 18.8 C

Asfal + Parapeto 0.00 0.00 24.93 -104.0 435.7 58.2 51.0 58.2 65.5 82.2 101.0 O

Carga viva + I 0.00 0.00 50.19 -209.5 226.3 117.2 168.1 117.2 182.6 165.6 266.6 M










150




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 25.50 -152.8 -152.8 182.7 182.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 14.32 -85.8 635.5 102.6 -44.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -15.15 0.82 0.00 -72.9 562.6 7.5 -37.1 7.5 7.5 19.4 19.4 C

Asfal + Parapeto 0.00 0.00 21.45 -89.5 473.1 50.1 13.0 50.1 57.6 70.8 90.2 O

Carga viva + I 0.00 0.00 45.74 -190.9 282.2 106.8 119.7 106.8 164.4 150.9 241.1 M










151




152




w

14.25








H = 1.3500 m H = 1.5500 m As* = 9.90 cm² 5 10

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 23.74 -142.3 -142.3 170.0 170.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 13.34 -80.0 506.2 95.6 -9.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -10.67 0.82 0.00 -51.3 454.9 5.3 -4.0 5.3 5.3 13.7 13.7 C

Asfal + Parapeto 0.00 0.00 20.99 -87.6 367.3 49.0 45.0 49.0 54.3 69.2 82.9 O

Carga viva + I 0.00 0.00 42.81 -178.7 188.6 99.9 144.9 99.9 154.2 141.2 224.1 M










153




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 19.43 -116.5 -116.5 139.2 139.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 10.91 -65.4 400.9 78.1 -2.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -7.29 0.82 0.00 -35.1 365.9 3.6 1.0 3.6 3.6 9.4 9.4 C

Asfal + Parapeto 0.00 0.00 17.18 -71.7 294.2 40.1 41.1 40.1 43.7 56.7 66.0 O

Carga viva + I 0.00 0.00 36.95 -154.2 140.0 86.3 127.4 86.3 130.0 121.9 187.9 M










154




w

14.246








H = 1.3500 m H = 1.5500 mts. As* = 5.94 cm² 5 6

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 10.93 -65.5 -65.5 78.3 78.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 6.14 -36.8 334.8 44.0 -42.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -5.64 0.82 0.00 -27.1 307.6 2.8 -39.9 2.8 2.8 7.2 7.2 C

Asfal + Parapeto 0.00 0.00 9.66 -40.3 267.3 22.5 -17.3 22.5 25.4 31.9 39.1 O

Carga viva + I 0.00 0.00 22.10 -92.2 175.1 51.6 34.3 51.6 77.0 72.9 112.0 M










155




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 5.94 cm² 5 6

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 7.55 -45.3 -45.3 54.1 54.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 4.24 -25.4 366.4 30.4 -80.5 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -5.18 0.82 0.00 -24.9 341.5 2.6 -77.9 2.6 2.6 6.6 6.6 C

Asfal + Parapeto 0.00 0.00 6.67 -27.8 313.7 15.6 -62.3 15.6 18.1 22.0 28.6 O

Carga viva + I 0.00 0.00 14.74 -61.5 252.2 34.4 -27.9 34.4 52.5 48.6 77.3 M










156




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 3.96 cm² 5 4

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 3.91 -23.4 -23.4 28.0 28.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 2.19 -13.1 254.8 15.7 -66.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -4.76 0.82 0.00 -22.9 231.9 2.4 -63.9 2.4 2.4 6.1 6.1 C

Asfal + Parapeto 0.00 0.00 3.45 -14.4 217.5 8.1 -55.8 8.1 10.4 11.4 17.5 O

Carga viva + I 0.00 0.00 60.74 -253.5 -35.9 141.8 85.9 141.8 152.2 200.3 217.8 M










157




w

14.25








H = 1.3500 m H = 1.5500 mts. As* = 2.82 cm² 5 2

Ix = 0.1026 m4Ix = 0.2075 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 207.5 0.0 -78.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -3.39 0.82 0.00 -16.3 191.2 1.7 -76.6 1.7 1.7 4.4 4.4 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 191.2 0.0 -76.6 0.0 1.7 0.0 4.4 O

Carga viva + I 0.00 0.00 0.00 0.0 191.2 0.0 -76.6 0.0 1.7 0.0 4.4 M










158



x en metros 0.675 0.71 1.42 2.14 2.85 3.56 4.27 4.99 5.70 6.41 7.12

MCM 9.55 18.46 26.73 41.24 47.52 58.07 61.27 68.96 71.27 73.87 74.24

MCV 60.74 14.74 22.10 31.97 36.95 42.81 45.74 50.19 52.42 53.36 53.82

MU en ton-m 144.01 55.93 82.64 122.88 141.84 168.25 178.76 198.40 206.23 211.64 213.13

VCM 22.42 18.04 16.65 13.88 12.49 9.70 8.31 5.54 4.16 1.38 0.00

VCV 17.47 16.49 15.50 13.53 12.55 10.82 9.97 8.62 7.95 6.63 5.98

VU en ton 67.01 59.18 55.23 47.36 43.42 36.06 32.39 25.88 22.63 16.17 12.95

VC 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03

VU-VC 39.98 32.15 28.20 20.33 16.39 9.03 5.36 -1.15 -4.40 -10.86 -14.08

E#3@ 19.02 23.65 26.96 37.40 46.39 84.22 141.76 -661.96 -172.68 -70.01 -54.01

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

Vud/Mu <= 1.0 0.70 1.00 1.00 0.58 0.46 0.32 0.27 0.20 0.16 0.11 0.09

Vc = f0.53*raiz(f́ c)bwd 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03 27.03


f1.3 raiz(f́ c)bwd 66.30 66.30 66.30 66.30 66.30 66.30 66.30 66.30 66.30 66.30 66.30

VC considerado 66.30 66.30 66.30 66.30 65.54 48.33 42.12 32.61 28.72 27.03 27.03

VS = VU-VC 0.71 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01






159




160


4.5.- DISEÑO DE LA TRABE AASHTO, (CLARO 30.6 MTS.) TRAMO 4-5 T 3, 4

4.5.1.- CARGA VIVA



161




1.000

0.330

Datos


Analisis

Excentricidad (m)

Factor de reduccion


1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143


6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2


Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2



162


T4 0.354 48.580 17.187

DESCARGA TOTAL =


48.58048.5800.470

120.311

22.84125.667T1




CARGA POR TRABE

T7 0.179 48.580 8.707

0.528

25.86084.843

Analisis

T3 0.412

DESCARGA DE CAMION


0.238

1.238

T5 0.296 48.580

48.580T2

Datos

48.580 11.53414.361

20.014

T6 0.237

25

50

LI



163



10.5 31.5 118.6

0.45x / L 0.05

MOMENTO0.0 kL 0.50


28.8

0.40

41.8

189.53

257.75168.95

34.9 38.1

150.80

202.28

1.1

49.849.5

127.25

159.99

27.7 28.626.6

43.5

1.1

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 6.52.3

0.0 7.0 20.0





CARGA VIVA TRABE

x / L

CARGA VIVA TRABE


5.4

161.9181.09 109.04 127.45

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




200.38199.43

140.8139.0

0.0

0.01 37.48 62.4712.50

224.51

9.74

8.2

4.7

0.2

158.18

0.0

2.3 1.6

102.2178.83

0.0

28.90 28.25 26.95 25.64 13.91

0.0

7.5 2.1 1.5

9.1

0.0

0.40 0.45 0.50

4.87

0.1

3.6

10.96 12.17

Reacción

20.43 12.60

3.0

19.12 17.17 15.86

1.2 0.0

4.2 2.8

0.2

1.9

0.1

3.8 3.4 2.3

7.2 6.6 6.0 4.5

0.2

7.9 7.2 6.5 5.9

5.5

14.6 14.0 12.8 11.6

4.9

0.00.1 0.1 0.1 0.1

0.05 0.10 0.15 0.20

0.0 0.68 1.22 2.43 3.65

0.01

0.01

129.2

59.68 99.46

52.5

19.90

15.77

106.90.0

47.30

0.0 0.4 0.9 1.00.5 0.7 0.90.3

29.0

47.8

0.0 45.1

24.0 31.9

1.1

0.0 18.5

45.9

24.210.4 13.9 22.2

12.17

42.7 56.7 68.2 74.5 81.6

7.30

85.1 88.1 88.631.9

3.65 4.87 10.96

38.30.0 3.9 11.2 17.9

0.20

0.0 0.68 1.22 2.43

3.6

12.1 10.9

0.25 0.30

6.09

139.73

160.99

0.1

16.3

266.55

13.96

0.35

263.03244.45

198.01

41.8

9.748.52

2.9

8.0

21.8 45.4

0.30

4.1

CORTANTE

10.2

0.0 kL

136.267.2 89.3

0.35

7.30

5.8

0.25

10.5

6.09 8.52

22.92 17.29

176.80

20.54

0.6

3.3

0.41.3 0.9

0.7

24.34

8.7 7.0

22.38

3.9

15.1337.78 33.20 29.17 26.49

25.00 23.16 20.40 18.56 15.8034.20 32.36 30.52

14.025.7 24.8 23.2 21.6 20.0 17.5 15.4

36.96

137.28

0.10 0.15

48.58 47.03 43.93 40.83

27.7636.04

0.22

7.91

15.44

8.69

3.05

28.90

48.58

36.96

0.00



164




165


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.03 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.03 L



0.03 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-15.661

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

34

28

32PASA POR MOMENTO


ULTIMO

20

24

24

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

16

Suma

4

4

8

12

0 0

0 0

0


Esfuerzos Servicio


21.59%4.32%

Esfuerzos Trans.


FINALESINICIALES


0.0 L 0


5 10 15

REACCIONES

0.68

0.05 L 1.22

0.10 L 2.43

0 0 0

0

31.5

0 0 0 -14.913

-14.505

23.861

181.6040 0

0.15 L 3.65


0 0 0

0 0 0

34

0.25 L 6.09

0.30 L 7.30

0 0 0

0 0 0

Distancia5 10 15 20


30

12.17

1.3500

0.1026

0.49740.61500.9000

7.30

8.52

9.74

10.96

1.5500

0.2032

0.69860.8555

4.87

6.09

41.500 -14.926

9.14

31.53

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

1.22

2.43

3.65

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

0

4

0

10

fSMAX = 77.198

fSMIN =

fI MAX =

-15.66

181.9


0.50 L 12.17

-8.862

75.999

77.198

47.327

20 25

-11.310

-6.840

-10.478

12

34.805

24.973 1.283 11.029

-7.6660 0 0

0

0.40 L 9.74

0.45 L 10.96

8.52

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 4.87

-13.483

12.1115.41 14.0023.21 21.57 19.96

10

12

20.80189.348 32.004

58.299

69.333

74.810

0.00

4 0 0

004

10.51 52.55

0.0 L

25.67

0

108.454

7.99

4 0

8

-6.018

00

12

129.087 16.121

0 0

181.946

8

12

12

-10.124

12

89.26

12 12

12

0

0

00

12

68.283 22.990

118.62

16.441

-11.472

15.70446.289 12.560

129.16

15.933

12

12

12

24.85

0

12

0

17.54

12

8

125.347

67.23

1.00

106.87

0.75

138.97 140.83136.18

4

4

4

4

4.045

146.976 9.733

170.781 74.612 20.128

22.453

4

2

4

4

HR = 55


ton/mton/m


EC =

CARGAS

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

135


10.85

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m


24.35CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


TRABE4200

BAJA RELAJACIÓN


1.19 ton/m

PESO PROPIO

0.67

LOSA

ton/m0.24 2.73

20

66


ton/m 1.900.63



166










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

1.22 2.43 3.65 4.87 6.09 7.30 8.52 9.74 10.96 12.17

fs -49.82 -60.97 -63.39 -42.39 -39.64 5.05 -6.46 -43.98 -53.92 -49.84

f i 391.76 722.31 753.19 910.65 1083.39 1045.99 1230.67 1437.09 1532.93 1529.52

ytorones 0.050 0.050 0.063 0.070 0.075 0.075 0.086 0.094 0.097 0.097

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 37.540 69.330 71.539 86.123 102.100 98.816 115.212 133.424 141.885 141.597

fs 12.176 19.441 26.006 34.557 41.554 45.354 49.766 51.835 53.647 53.995

f i -13.881 -22.162 -29.642 -39.393 -47.366 -51.699 -56.728 -59.086 -61.152 -61.550

ytorones 0.050 0.050 0.063 0.070 0.075 0.075 0.086 0.094 0.097 0.097

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -13.040 -20.820 -27.398 -36.053 -43.063 -47.003 -50.839 -52.377 -53.964 -54.315

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 261.04257 482.09592 497.45333 598.87119 709.96926 687.13442 801.1416 927.78341 986.61526 984.6145908

CRC (kg/cm²) = 359.20508 686.22252 666.67343 781.10853 923.76127 856.77421 1026.6661 1234.4503 1324.8711 1318.958944

CRS (kg/cm²) = 276.99849 238.54229 237.984 222.12046 203.87802 209.51085 189.61554 166.56215 156.15792 156.6535987

AE + CRC + CRS 897.25 1406.86 1402.11 1602.10 1837.61 1753.42 2017.42 2328.80 2467.64 2460.23

% fPU = 6.30 9.87 9.84 11.24 12.90 12.30 14.16 16.34 17.32 17.26

% fPU TOTAL = 10.62 14.19 14.16 15.56 17.22 16.63 18.48 20.66 21.64 21.59

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,737 12,227 12,232 12,032 11,797 11,881 11,617 11,305 11,167 11,174

(fPU - fSE)AS* = 12 24 32 44 58 56 73 93 104 104

X 1.217 2.435 3.652 4.869 6.087 7.304 8.521 9.738 10.956 12.173



167


0 1.2173 2.4346 3.6519 4.8692 6.0865 7.3038 8.5211 9.7384 10.9557 12.173

0

20

40

60

80

100

120



FU

ER

ZA

(e

n t

on

ela

da

s)



168


Esfzo. Inf. Vigapermisiblepermisiblex## 41 ## #### 46 ## #### 68 ## #### 89 ## #### ## ## #### ## ## #### ## ## #### ## ## #### ## ## #### ## ## #### ## ## ##

permisibleEsfzo. tope Vigapermisiblex## ## -16 #### ## -8 #### ## -10 #### ## -11 #### ## -10 #### ## -11 #### ## -7 #### ## -9 #### ## -13 #### ## -15 #### ## -15 ##


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 1.217 2.435 3.652 4.869 6.087 7.304 8.521 9.738 10.956 12.173

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 1.217 2.435 3.652 4.869 6.087 7.304 8.521 9.738 10.956 12.173

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




169




x0.00 0.000 34.80539945 -33.94 247.50 -14.92589839

0.05 1.217 15.70418788 -33.94 247.50 12.56015166

0.10 2.435 15.93323143 -33.94 247.50 22.99029264

0.15 3.652 20.80131936 -33.94 247.50 32.00419992

0.20 4.869 16.4413527 -33.94 247.50 47.32735377

0.25 6.087 16.12051698 -33.94 247.50 58.29916091

0.30 7.304 4.045082593 -33.94 247.50 69.33302032

0.35 8.521 9.732583668 -33.94 247.50 74.80953844

0.40 9.738 20.12788322 -33.94 247.50 74.61220307

0.45 10.956 23.86064704 -33.94 247.50 75.9987768

0.50 12.173 22.45326 -33.94 247.50 77.19780756

-50

0

50

100

150

200

250

300

0.000 1.217 2.435 3.652 4.869 6.087 7.304 8.521 9.738 10.956 12.173

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 1.217 2.435 3.652 4.869 6.087 7.304 8.521 9.738 10.956 12.173

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




170




w

AL CENTRO DEL CLARO

24.35






H = 1.3500 m H = 1.5500 mts. As* = 33.66 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12

A = 0.4974 m² A = 0.6986 m² b equiv= 100.62 cm 100.623059 15 10Yi = 0.6150 m Yi = 0.8555 m d* = 145.29 cm 20 0Ys = 0.7350 m Ys = 0.6945 m p* = 0.00230 s/u 25 0Si = 0.1668 m³ Si viga = 0.2375 m³ fsu = 17100.0 kg/cm² 30 0Ss = 0.1396 m³ Ss viga = 0.4109 m³ cent as p = 9.71 cm #####





Po.Po Viga 0.00 0.00 88.64 -531.3 -531.3 634.9 634.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 49.80 -298.5 1517.6 356.7 211.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -82.811 0.76 0.00 -383.0 1134.6 34.3 246.0 34.3 34.3 96.2 96.2 C

Asfal + Parapeto 0.00 0.00 75.29 -317.0 817.5 183.2 429.2 183.2 217.6 257.3 353.5 O

Carga viva + I 0.00 0.00 140.83 -593.0 224.5 342.7 772.0 342.7 560.3 481.4 834.9 M

E S T A D O F I N A L E N kg / cm ² Inf. acum= 22.45 Sup. acum= 77.20 Inf. acum= 56.03 Sup acum= 83.49 P



Tensión: con/sin refzo. -31.92 -15.92 -33.77 0.00 BIEN OK





171




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 33.66 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 88.07 -527.8 -527.8 630.8 630.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 49.48 -296.6 1522.9 354.4 205.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -83.06 0.76 0.00 -384.2 1138.7 34.4 239.7 34.4 34.4 96.4 96.4 C

Asfal + Parapeto 0.00 0.00 74.80 -315.0 823.8 182.0 421.8 182.0 216.5 255.7 352.1 O

Carga viva + I 0.00 0.00 138.97 -585.2 238.6 338.2 760.0 338.2 554.7 475.0 827.1 M









172




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 31.68 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 85.09 -510.0 -510.0 609.5 609.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 47.81 -286.6 1421.3 342.5 207.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -73.78 0.76 0.00 -342.2 1079.0 31.2 238.8 31.2 31.2 86.5 86.5 C

Asfal + Parapeto 0.00 0.00 72.27 -304.3 774.7 175.9 414.7 175.9 207.1 247.0 333.5 O

Carga viva + I 0.00 0.00 136.18 -573.4 201.3 331.4 746.1 331.4 538.5 465.5 799.0 M









173




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 27.72 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 81.59 -489.0 -489.0 584.4 584.4 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 45.90 -275.1 1194.7 328.8 240.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -55.92 0.77 0.00 -261.3 933.3 24.7 264.9 24.7 24.7 67.1 67.1 C

Asfal + Parapeto 0.00 0.00 69.39 -292.2 641.2 168.9 433.8 168.9 193.6 237.2 304.3 O

Carga viva + I 0.00 0.00 129.16 -543.8 97.3 314.3 748.1 314.3 507.9 441.5 745.7 M










174




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 74.46 -446.3 -446.3 533.4 533.4 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 41.83 -250.7 1002.8 299.6 231.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -41.66 0.78 0.00 -196.6 806.2 19.5 250.7 19.5 19.5 51.5 51.5 C

Asfal + Parapeto 0.00 0.00 63.24 -266.3 539.9 153.9 404.6 153.9 173.4 216.2 267.7 O

Carga viva + I 0.00 0.00 118.62 -499.5 40.5 288.7 693.3 288.7 462.1 405.5 673.1 M










175




w

24.35








H = 1.3500 m H = 1.5500 m As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 68.22 -408.9 -408.9 488.7 488.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 38.33 -229.7 1061.1 274.6 161.5 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -43.66 0.78 0.00 -206.0 855.2 20.4 181.9 20.4 20.4 54.0 54.0 C

Asfal + Parapeto 0.00 0.00 57.93 -243.9 611.2 141.0 322.9 141.0 161.4 198.0 252.0 O

Carga viva + I 0.00 0.00 106.87 -450.0 161.2 260.1 583.0 260.1 421.5 365.3 617.3 M










176




177




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 19.80 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 8






Po.Po Viga 0.00 0.00 56.73 -340.0 -340.0 406.4 406.4 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 31.87 -191.0 893.5 228.3 123.5 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -31.72 0.79 0.00 -150.3 743.2 15.2 138.7 15.2 15.2 39.8 39.8 C

Asfal + Parapeto 0.00 0.00 48.19 -202.9 540.3 117.3 256.0 117.3 132.5 164.7 204.5 O

Carga viva + I 0.00 0.00 89.26 -375.9 164.4 217.2 473.3 217.2 349.8 305.1 509.6 M










178




w

24.346








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 31.92 -191.3 -191.3 228.6 228.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 17.93 -107.5 575.4 128.4 27.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -16.71 0.81 0.00 -80.6 494.8 8.8 36.0 8.8 8.8 22.1 22.1 C

Asfal + Parapeto 0.00 0.00 27.11 -114.2 380.6 66.0 102.0 66.0 74.8 92.7 114.8 O

Carga viva + I 0.00 0.00 52.55 -221.3 159.3 127.9 229.9 127.9 202.7 179.6 294.4 M










179




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 20.00 -119.9 -119.9 143.3 143.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 11.23 -67.3 395.6 80.4 3.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -7.11 0.81 0.00 -34.3 361.3 3.8 7.5 3.8 3.8 9.4 9.4 C

Asfal + Parapeto 0.00 0.00 16.98 -71.5 289.8 41.3 48.9 41.3 45.1 58.0 67.4 O

Carga viva + I 0.00 0.00 31.53 -132.8 157.0 76.7 125.6 76.7 121.8 107.8 175.2 M










180




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 3.96 cm² 5 4

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 6.95 -41.7 -41.7 49.8 49.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 3.90 -23.4 226.4 27.9 -32.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -9.74 0.81 0.00 -47.0 179.4 5.2 -27.1 5.2 5.2 12.9 12.9 C

Asfal + Parapeto 0.00 0.00 5.89 -24.8 154.6 14.3 -12.8 14.3 19.5 20.1 33.0 O

Carga viva + I 0.00 0.00 10.51 -44.3 110.3 25.6 12.8 25.6 45.1 35.9 69.0 M










181




w

24.35








H = 1.3500 m H = 1.5500 mts. As* = 5.64 cm² 5 4

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 415.0 0.0 -156.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -13.88 0.81 0.00 -66.9 348.1 7.3 -149.3 7.3 7.3 18.3 18.3 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 348.1 0.0 -149.3 0.0 7.3 0.0 18.3 O

Carga viva + I 0.00 0.00 0.00 0.0 348.1 0.0 -149.3 0.0 7.4 0.0 18.4 M










182



x en metros 0.675 1.22 2.43 3.65 4.87 6.09 7.30 8.52 9.74 10.96 12.17

MCM 16.74 48.21 76.96 102.93 136.79 164.48 179.53 196.88 205.17 212.35 213.73

MCV 10.51 31.53 52.55 67.23 89.26 106.87 118.62 129.16 136.18 138.97 140.83

MU en ton-m 44.54 130.99 213.91 279.48 371.23 445.39 490.40 535.78 561.78 577.16 582.99

VCM 34.68 30.87 28.06 25.26 21.05 16.83 14.03 9.81 7.00 2.79 0.00

VCV 24.85 23.21 21.57 19.96 17.54 15.41 14.00 12.11 10.85 9.14 7.99

VU en ton 98.92 90.42 83.22 76.09 65.37 55.27 48.57 38.99 32.62 23.42 17.32

VC 28.67 28.67 28.67 28.43 28.29 28.19 28.19 27.99 27.83 27.77 27.77

VU-VC 70.25 61.75 54.55 47.66 37.08 27.08 20.38 11.00 4.78 -4.35 -10.45

E#3@ 10.82 12.31 13.94 15.96 20.51 28.08 37.32 69.10 159.00 -174.83 -72.77

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 150.00 148.75 148.00 147.50 147.50 146.43 145.63 145.29 145.29

Vud/Mu <= 1.0 1.00 1.00 0.58 0.40 0.26 0.18 0.15 0.11 0.08 0.06 0.04

Vc = f0.53*raiz(f́ c)bwd 28.67 28.67 28.67 28.43 28.29 28.19 28.19 27.99 27.83 27.77 27.77


f1.3 raiz(f́ c)bwd 70.32 70.32 70.32 69.74 69.38 69.15 69.15 68.65 68.27 68.12 68.12

VC considerado 70.32 70.32 70.32 58.76 40.67 31.00 28.19 27.99 27.83 27.77 27.77

VS = VU-VC 28.60 20.10 12.90 17.33 24.70 24.27 20.38 11.00 4.78 0.01 0.01






183




184


4.6.- DISEÑO DE LA TRABE AASHTO, (CLARO 32.6 MTS.) TRAMO 4-5 T 5, 6,7

4.5.1.- CARGA VIVA



185




1.000

0.330

Datos


Analisis

Excentricidad (m)

Factor de reduccion


1.00 7.00 1.40

0.205

0.143

Carga (P)

7

0.2682

3

-0.044

4

2.446 1.00

0.268

-0.044

5 0.080 0.080

0.205

0.143


6 0.018 0.018

S

e

n

in

n

PRi 1

2161

2


Separacion (m)

2.00

4 0.286 0.286

1 0.427 0.427

3 0.333 0.333

2

Excentricidad (m)

0.380

Ri x FR

0.380

1.00

Factor de reduccion

0.92

Carga (P)

1.407.00

7 0.145 0.145

Datos

AnalisisViga Ri

No. De vigas

5 0.239 0.239

2.000

6 0.192 0.192

S

e

n

in

n

PRi 1

2161

2



186


DESCARGA TOTAL =


55.49055.490

T4 0.347 55.490 19.272

0.176

0.462

134.903

25.61128.780T1




CARGA POR TRABE

T755.490 12.933

0.519

32.600106.955

Analisis

T3 0.404

DESCARGA DE CAMION


0.216

1.216

T5 0.290 55.490

55.490T2

Datos

16.102

22.441

55.490 9.763T6 0.233

25

50

LI



187



12.0 36.6 175.0

0.45x / L 0.05

MOMENTO0.0 kL 0.50


45.3

0.40

70.5

261.88

394.50260.50

57.5 64.2

201.38

300.88

82.163.1

1.9

86.084.8

211.69

221.50

43.5 44.941.3

74.8

1.8

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 8.63.0

0.0 9.1 26.6

0.0





CARGA VIVA TRABE

x / L

CARGA VIVA TRABE


6.8

223.62118.59 146.11 167.88

x

PESO PROPIO



LOSA + ZOCLO

CARPETA




289.22286.65

213.9211.6

0.0

0.01 39.03 88.1913.02

337.43

12.43

10.8

6.0

0.2

215.12

0.0

3.6 2.3

153.92114.74

0.0

29.78 29.29 28.30 26.33 15.46

0.0

9.8 3.3 2.1

11.4

0.0

0.40 0.45 0.50

6.22

0.1

5.0

13.99 15.54

Reacción

21.88 13.49

4.2

20.40 18.92 16.94

2.3 0.0

5.4 3.6

0.2

2.4

0.1

4.8 4.2 3.0

9.5 8.9 7.7 5.9

0.2

10.4 9.8 8.5 7.5

5.8

19.1 18.6 17.4 15.1

6.5

0.10.2 0.2 0.1 0.1

0.05 0.10 0.15 0.20

0.0 0.68 1.55 3.11 4.66

0.01

0.01

190.0

70.49 158.66

82.3

23.05

16.95

156.10.0

50.84

0.0 0.7 1.6 1.71.0 1.2 1.40.3

49.60.0 77.2

44.2 54.4

1.9

0.0 29.0

76.5

38.116.3 23.1 34.0

15.54

78.7 96.9 112.5 125.5 136.1

9.33

146.2 150.8 153.158.1

4.66 6.22 13.99

5.1 14.9 32.6

0.20

0.0 0.68 1.55 3.11

4.7

15.4 13.1

0.25 0.30

7.77

187.14

218.71

0.1

29.7

412.35

16.12

0.35

407.88366.32

278.94

69.6

12.4310.88

4.1

9.4

40.3 78.3

0.30

6.4

CORTANTE

13.6

0.0 kL

204.6109.8 135.1

0.35

9.33

8.1

0.25

13.3

7.77 10.88

29.66 21.99

244.01

25.18

1.2

4.6

0.61.8 1.2

1.3

24.85

11.6 9.9

23.36

5.5

18.2243.75 40.23 36.71 33.18

27.97 25.84 23.79 21.00 18.9137.03 34.24 32.15

17.228.8 28.2 27.0 24.5 22.7 20.9 19.0

39.12

189.70

0.10 0.15

55.49 54.32 51.97 47.27

30.0638.42

0.22

9.98

19.46

10.95

3.85

29.78

55.49

39.12

0.00



188




189


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

-15.661

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

46

42

44PASA POR MOMENTO


ULTIMO

30

36

42

PASA POR MOMENTO



ULTIMO

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

24

Suma

4

8

12

18

6 0

0 0

0


Esfuerzos Servicio


22.90%4.32%

Esfuerzos Trans.


FINALESINICIALES


0.0 L 0


5 10 15

REACCIONES

0.68

0.05 L 1.55

0.10 L 3.11

0 0 0

10

31.5

10 0 0 13.497

15.102

-29.148

216.6430 0

0.15 L 4.66


6 0 0

8 0 0

46

0.25 L 7.77

0.30 L 9.33

0 0 0

0 0 0

Distancia5 10 15 20


30

15.54

1.3500

0.1026

0.49740.61500.9000

9.33

10.88

12.43

13.99

1.5500

0.2032

0.69860.8555

6.22

7.77

41.500 -14.870

11.41

36.56

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

0.68

0.05 L

0.10 L

0.15 L

0.20 L

0

1.55

3.11

4.66

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

12

12

12

12

fSMAX = 163.602

fSMIN =

fI MAX =

-15.66

218.0


0.50 L 15.54

8.120

160.173

163.602

92.358

20 25

-1.007

0.563

-1.488

12

34.296

52.798 -5.865 31.311

-13.9560 0 0

0

0.40 L 12.43

0.45 L 13.99

10.88

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 6.22

12.771

15.3819.04 17.2126.95 24.52 22.69

12

12

3.854122.788 72.185

108.199

123.083

140.439

0.00

8 0 0

004

11.96 82.29

0.0 L

28.78

0

150.775

9.45

12 0

12

-15.445

00

12

180.279 -0.809

0 0

217.986

12

12

12

-4.987

12

135.11

12 12

12

6

0

06

12

93.891 51.314

175.01

-0.005

-3.782

30.59171.490 11.895

190.00

5.132

12

12

12

28.17

0

12

0

20.87

12

12

208.871

109.79

1.00

156.05

0.75

211.55 213.87204.61

4

4

6

6

-1.210

202.548 -18.551

208.625 154.711 -28.108

-32.354

6

6

6

2

2

HR = 55


ton/mton/m


EC =

CARGAS

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

135


13.06

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m


31.09CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


TRABE4200

BAJA RELAJACIÓN


1.19 ton/m

PESO PROPIO

0.67

LOSA

ton/m0.24 2.73

20

66


ton/m 1.770.63



190










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

1.55 3.11 4.66 6.22 7.77 9.33 10.88 12.43 13.99 15.54

fs -99.30 6.99 35.64 71.62 89.49 114.70 190.27 239.95 250.38 266.43

f i 608.20 997.03 1020.40 1252.85 1500.45 1741.92 1678.69 1724.63 1803.42 1790.00

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.122 0.122

h 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350 1.350

fcr (kg/cm²) 58.199 94.814 96.569 117.410 139.594 160.416 155.268 159.466 166.337 165.261

fs 16.178 34.745 47.352 58.397 67.834 75.804 82.162 88.081 90.872 92.177

f i -18.436 -39.239 -53.621 -66.210 -76.970 -86.017 -93.229 -99.828 -102.987 -104.435

ytorones 0.050 0.067 0.075 0.090 0.100 0.114 0.114 0.118 0.122 0.122

h 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

fcd (kg/cm²) -17.320 -36.057 -48.735 -58.975 -67.628 -74.086 -80.297 -85.501 -87.761 -88.992

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 404.6968 659.29919 671.50865 816.42624 970.68589 1115.4786 1079.6803 1108.8697 1156.6505 1149.16283

CRC (kg/cm²) = 577.1529 885.36162 817.68633 996.09627 1201.7338 1406.3962 1301.1436 1315.0878 1381.7215 1360.179815

CRS (kg/cm²) = 251.73568 210.865 213.02782 189.61557 163.90773 139.19534 148.0378 144.42165 136.31188 138.1377313

AE + CRC + CRS 1233.59 1755.53 1702.22 2002.14 2336.33 2661.07 2528.86 2568.38 2674.68 2647.48

% fPU = 8.66 12.32 11.95 14.05 16.40 18.67 17.75 18.02 18.77 18.58

% fPU TOTAL = 12.98 16.64 16.27 18.37 20.72 23.00 22.07 22.34 23.09 22.90

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,401 11,879 11,932 11,632 11,298 10,973 11,105 11,066 10,960 10,987

(fPU - fSE)AS* = 22 42 55 78 105 136 131 139 150 149

X 1.554 3.109 4.663 6.217 7.772 9.326 10.880 12.434 13.989 15.543



191


0 1.5543 3.1086 4.6629 6.2172 7.7715 9.3258 10.8801 12.4344 13.9887 15.543

0

20

40

60

80

100

120

140

160



FU

ER

ZA

(e

n t

on

ela

da

s)



192


Esfzo. Inf. Vigapermisiblepermisiblex

## ## 41 ## #### ## 71 ## #### ## 94 ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## ##

permisibleEsfzo. tope Vigapermisiblex## ## -16 #### ## -14 #### ## -5 #### ## -4 #### ## -1 #### ## -1 #### ## 1 #### ## 8 #### ## 13 #### ## 13 #### ## 15 ##


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 1.554 3.109 4.663 6.217 7.772 9.326 10.880 12.434 13.989 15.543

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 1.554 3.109 4.663 6.217 7.772 9.326 10.880 12.434 13.989 15.543

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




193




x0.00 0.000 34.2960576 -33.94 247.50 -14.8700436

0.05 1.554 30.59066026 -33.94 247.50 11.8949683

0.10 3.109 5.132050078 -33.94 247.50 51.31406699

0.15 4.663 3.854373829 -33.94 247.50 72.18512319

0.20 6.217 -0.004521975 -33.94 247.50 92.35842758

0.25 7.772 -0.80883952 -33.94 247.50 108.1986594

0.30 9.326 -1.210121067 -33.94 247.50 123.0827891

0.35 10.880 -18.5512417 -33.94 247.50 140.4392621

0.40 12.434 -28.10787962 -33.94 247.50 154.7113827

0.45 13.989 -29.14806014 -33.94 247.50 160.1726278

0.50 15.543 -32.35438328 -33.94 247.50 163.6024494

-50

0

50

100

150

200

250

300

0.000 1.554 3.109 4.663 6.217 7.772 9.326 10.880 12.434 13.989 15.543

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 1.554 3.109 4.663 6.217 7.772 9.326 10.880 12.434 13.989 15.543

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




194




w

AL CENTRO DEL CLARO

31.09






H = 1.3500 m H = 1.5500 mts. As* = 45.54 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 153.08 -917.5 -917.5 1096.5 1096.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 86.02 -515.5 1650.9 616.1 767.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -120.566 0.73 0.00 -545.1 1105.8 42.7 809.9 42.7 42.7 129.8 129.8 C

Asfal + Parapeto 0.00 0.00 125.59 -528.8 577.0 305.6 1115.5 305.6 348.4 429.3 559.1 O

Carga viva + I 0.00 0.00 213.87 -900.5 -323.5 520.5 1636.0 520.5 868.9 731.0 1290.1 M









195




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 45.54 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 150.84 -904.1 -904.1 1080.5 1080.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 84.75 -508.0 1671.9 607.1 742.0 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -121.81 0.73 0.00 -550.7 1121.2 43.2 785.2 43.2 43.2 131.2 131.2 C

Asfal + Parapeto 0.00 0.00 123.95 -521.9 599.3 301.7 1086.9 301.7 344.8 423.7 554.8 O

Carga viva + I 0.00 0.00 211.55 -890.8 -291.5 514.9 1601.7 514.9 859.7 723.1 1277.9 M









196




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 43.56 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 146.20 -876.3 -876.3 1047.2 1047.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 82.14 -492.3 1593.9 588.4 716.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -111.88 0.74 0.00 -507.5 1086.5 40.6 756.7 40.6 40.6 121.8 121.8 C

Asfal + Parapeto 0.00 0.00 120.16 -506.0 580.5 292.4 1049.1 292.4 333.1 410.7 532.6 O

Carga viva + I 0.00 0.00 204.61 -861.6 -281.1 498.0 1547.1 498.0 831.0 699.4 1231.9 M









197




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 136.08 -815.6 -815.6 974.7 974.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 76.45 -458.2 1567.3 547.6 628.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -105.15 0.74 0.00 -478.7 1088.6 39.2 668.0 39.2 39.2 115.9 115.9 C

Asfal + Parapeto 0.00 0.00 112.59 -474.1 614.5 274.0 942.0 274.0 313.2 384.8 500.7 O

Carga viva + I 0.00 0.00 190.00 -800.0 -185.5 462.4 1404.4 462.4 775.6 649.4 1150.2 M










198




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 41.58 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 125.53 -752.4 -752.4 899.2 899.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 70.53 -422.7 1666.0 505.2 510.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -110.65 0.74 0.00 -503.7 1162.3 41.2 552.1 41.2 41.2 122.0 122.0 C

Asfal + Parapeto 0.00 0.00 103.89 -437.5 724.8 252.8 804.9 252.8 294.1 355.1 477.1 O

Carga viva + I 0.00 0.00 175.01 -736.9 -12.1 425.9 1230.8 425.9 720.0 598.2 1075.3 M










199




200




w

31.09








H = 1.3500 m H = 1.5500 m As* = 35.64 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 112.46 -674.0 -674.0 805.6 805.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 63.12 -378.3 1424.5 452.1 442.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -83.27 0.76 0.00 -384.1 1040.4 33.9 476.0 33.9 33.9 95.8 95.8 C

Asfal + Parapeto 0.00 0.00 92.95 -391.4 649.0 226.2 702.2 226.2 260.1 317.7 413.6 O

Carga viva + I 0.00 0.00 156.05 -657.1 -8.1 379.8 1082.0 379.8 639.9 533.4 947.0 M










201




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 29.70 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 96.86 -580.5 -580.5 693.8 693.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 54.42 -326.2 1181.6 389.8 374.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -59.46 0.77 0.00 -276.8 904.8 25.7 400.6 25.7 25.7 70.5 70.5 C

Asfal + Parapeto 0.00 0.00 79.78 -335.9 568.9 194.2 594.8 194.2 219.8 272.7 343.2 O

Carga viva + I 0.00 0.00 135.11 -568.9 0.0 328.8 923.6 328.8 548.7 461.8 805.0 M










202




w

31.086








H = 1.3500 m H = 1.5500 mts. As* = 23.76 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 12






Po.Po Viga 0.00 0.00 78.73 -471.9 -471.9 563.9 563.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 44.23 -265.1 962.8 316.8 279.0 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -40.44 0.78 0.00 -190.8 772.0 18.9 297.9 18.9 18.9 50.0 50.0 C

Asfal + Parapeto 0.00 0.00 64.39 -271.1 500.9 156.7 454.6 156.7 175.6 220.1 270.1 O

Carga viva + I 0.00 0.00 109.79 -462.3 38.5 267.2 721.9 267.2 442.8 375.3 645.4 M










203




w

31.086








H = 1.3500 m H = 1.5500 mts. As* = 17.82 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 6






Po.Po Viga 0.00 0.00 58.07 -348.0 -348.0 416.0 416.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 32.62 -195.5 743.4 233.7 183.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -31.28 0.79 0.00 -148.7 594.7 15.3 199.1 15.3 15.3 39.6 39.6 C

Asfal + Parapeto 0.00 0.00 46.76 -196.9 397.8 113.8 312.9 113.8 129.1 159.8 199.4 O

Carga viva + I 0.00 0.00 82.29 -346.5 51.3 200.3 513.1 200.3 329.3 281.3 480.7 M










204




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 11.88 cm² 5 12

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 26.57 -159.2 -159.2 190.3 190.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 14.93 -89.5 625.4 106.9 -32.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.65 0.81 0.00 -70.7 554.7 7.8 -24.9 7.8 7.8 19.4 19.4 C

Asfal + Parapeto 0.00 0.00 22.53 -94.9 459.9 54.8 30.0 54.8 62.6 77.0 96.4 O

Carga viva + I 0.00 0.00 36.56 -153.9 305.9 89.0 118.9 89.0 151.6 125.0 221.4 M










205




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 7.92 cm² 5 8

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 9.14 -54.8 -54.8 65.5 65.5 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 5.13 -30.7 497.2 36.7 -117.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -20.97 0.81 0.00 -101.1 396.1 11.1 -106.6 11.1 11.1 27.7 27.7 C

Asfal + Parapeto 0.00 0.00 7.75 -32.6 363.5 18.9 -87.7 18.9 30.0 26.5 54.2 O

Carga viva + I 0.00 0.00 11.96 -50.3 313.1 29.1 -58.6 29.1 59.1 40.9 95.1 M










206




w

31.09








H = 1.3500 m H = 1.5500 mts. As* = 5.64 cm² 5 4

Ix = 0.1026 m4Ix = 0.2032 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 415.0 0.0 -156.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -14.93 0.81 0.00 -72.0 343.0 7.9 -148.7 7.9 7.9 19.7 19.7 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 343.0 0.0 -148.7 0.0 7.9 0.0 19.7 O

Carga viva + I 0.00 0.00 0.00 0.0 343.0 0.0 -148.7 0.0 7.9 0.0 19.8 M










207



x en metros 0.675 1.55 3.11 4.66 6.22 7.77 9.33 10.88 12.43 13.99 15.54

MCM 22.02 64.03 137.45 187.35 231.06 268.53 299.95 325.12 348.50 359.54 364.68

MCV 11.96 36.56 82.29 109.79 135.11 156.05 175.01 190.00 204.61 211.55 213.87

MU en ton-m 54.53 162.46 356.98 481.44 593.12 687.21 769.13 834.31 896.38 925.76 937.47

VCM 44.53 41.72 36.27 32.04 27.80 23.56 19.33 15.10 9.67 5.41 0.00

VCV 28.17 26.95 24.52 22.69 20.87 19.04 17.21 15.38 13.06 11.41 9.45

VU en ton 118.93 112.64 100.27 90.81 81.35 71.89 62.42 52.96 40.86 31.75 20.47

VC 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.30 27.30

VU-VC 90.26 83.97 71.92 62.62 53.45 44.17 34.98 25.52 13.50 4.45 -6.82

E#3@ 8.42 9.06 10.57 12.14 14.23 17.21 21.74 29.80 56.34 170.99 -111.44

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 150.00 150.00 148.33 147.50 146.00 145.00 143.57 143.57 143.18 142.83 142.83

Vud/Mu <= 1.0 1.00 1.00 0.42 0.28 0.20 0.15 0.12 0.09 0.07 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 28.67 28.67 28.35 28.19 27.91 27.71 27.44 27.44 27.37 27.30 27.30


f1.3 raiz(f́ c)bwd 70.32 70.32 69.54 69.15 68.45 67.98 67.31 67.31 67.13 66.96 66.96

VC considerado 70.32 70.32 60.04 42.70 32.78 27.71 27.44 27.44 27.37 27.30 27.30

VS = VU-VC 48.61 42.31 40.23 48.12 48.57 44.17 34.98 25.52 13.50 4.45 0.01






208



4.7.1.- CARGA VIVA




5 0.027 0.027

4

2.446 1.00

0.306

-0.066-0.066

0.213

0.120

Carga (P)

6

0.3062

3

Analisis

Excentricidad (m)

Factor de reduccion


1.00 6.00 1.50

Datos


1.000

0.400

0.213

0.120

S

e

n

in

n

PRi 1

2161

2



209



5 0.228 0.228

2.000

No. De vigas

6 0.158 0.158

Datos

AnalisisViga Ri

Carga (P)

1.506.000.92

Excentricidad (m)

0.439

Ri x FR

0.439

1.00

Factor de reduccion

4 0.298 0.298

1 0.509 0.509

3 0.368 0.368

2

2.00

Separacion (m)

S

e

n

in

n

PRi 1

2161

2



210


16.292T5 0.272 59.870

59.870

T1T2

26.318

DESCARGA DE CAMION


0.193

1.193

T6 0.188 59.870 11.280

0.607

40.800133.858

Analisis

T3 0.440

DatosLongitud de la Trabe (m)=



CARGA POR TRABE

DESCARGA TOTAL =


59.87059.8700.523

142.868

31.33036.343

T4 0.356 59.870 21.305

25

50

LI




211


30.35

59.87

40.50

0.00

33.90

20.51

7.87

0.31

12.48

40.50

253.57

0.10 0.15

59.87 58.05 56.20 51.59

31.1939.40

36.3 35.2 34.1 31.3 29.1 26.8

19.6938.31 35.57 33.38

22.424.6

47.90 44.21 40.52 36.83

29.00 26.81

288.2

325.59

28.52

1.2

8.1

25.31

20.0 16.8

23.75

10.1

0.35

12.00

13.6

0.25

23.2

10.00

122.4

0.30

9.6

CORTANTE

22.2

0.0 kL

332.2181.1 221.8

569.78

17.50

0.35

562.34524.66

370.18

112.4

16.0014.00

6.4

0.25 0.30

10.00

245.23

292.47

0.3

16.8 64.1

0.20

0.0 0.92 2.00 4.00

61.0 128.7

6.00 8.00 18.00

150.9 193.977.0

20.00

176.0 217.2 252.3 281.3 308.9

12.00

324.2 333.3 336.4

105.0 129.9

3.0

0.0 4.9

184.8

64.657.9

0.0 18.7

1.9 2.30.5

79.00.0 121.311.4

0.01

318.5

103.58 218.44

132.6

51.79

35.45

257.10.0

70.91

0.05 0.10 0.15 0.20

0.0 0.92 2.00 4.00

33.6 32.0 30.4 26.4

12.0

0.10.2 0.2 0.2 0.2

19.2 18.2 15.8 13.9

7.4 7.0 5.3 3.9

11.1 9.6 7.3

0.3

Reacción

22.20 14.05

5.0

20.65 18.71 17.15

3.2 0.0

0.45 0.50

8.00

0.1

6.1

18.00 20.00

2.2 1.54.6

15.1

0.0

12.8

32.22 24.83 21.14

19.6 17.3

24.07 21.88

20.1

7.7

0.3

0.7

6.00

1.9

0.3

3.1

0.1

6.1

345.9341.4

0.0

28.79 26.85 15.61

14.00 16.00

0.0

0.40

30.35 29.57

11.7

280.13

0.0 0.0

5.7 3.8

380.35378.19



LOSA + ZOCLO

CARPETA



CARGA VIVA TRABE


8.5

288.74155.75 191.38 220.37

x

PESO PROPIO






CARGA VIVA TRABE

x / L

0.01 53.39

2.9

365.31

91.8 102.3

547.31

26.70

0.01

0.0

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 14.07.2

36.5

3.0

201.2199.4

298.28

286.65

74.4 76.570.9

118.0

474.85

168.2

356.33

113.46 269.18

29.5 40.4

1.1 2.5 2.81.6

77.2

0.40 0.45

0.0 31.3

0.05

MOMENTO

0.0 kL 0.50x / L


423.48

31.4 62.9

205.84150.13

12.2 3.5 2.3



212


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

0.39 3.68

20

0.71


ton/m 1.730.63

TRABE4200

BAJA RELAJACIÓN


1.66 ton/m

PESO PROPIO

1.01

LOSA

ton/m


40.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


17.31

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140


HR = 55


ton/mton/m


EC =

CARGAS

7

6

5

6

2

-29.590

9

4

-22.131

211.603 -25.477

225.868 161.725 -26.825

4

4

186.924

181.07

1.00

257.07

0.75

341.36 345.87332.24

13

13

13

35.24

0

13

0

26.84

13

13

81.052 56.001

288.25

-8.332

8.316

12.91453.574 23.563

318.49

-0.263

13

221.76

13 13

13

11

0

09

13

13

166.151 -16.940

0 0

236.650

13

13

13

5.569

36.34

0

132.018

12.83

13 5

13

-4.825

00

0.01

9 0 0

005

31.44 132.60

0.0 L

-7.470113.729 82.971

4

122.482

138.242

153.675

22.034

19.5624.60 22.3634.12 31.32 29.08

13

13

0.40 L 16.00

0.45 L 18.00

14.00

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 8.00

13

31.708

40.433 9.231 12.350

-2.2540 0 0

0

20.562

166.868

169.195

99.251

20 25

14.887

17.706

13.561

7

3


0.50 L 20.00

fSMAX =

fI MIN =

169.195

-29.590 PASA

fSMIN =

fI MAX =

-11.18

236.6

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

13

13

13

13

0.92

0.05 L

0.10 L

0.15 L

0.20 L

0

2.00

4.00

6.00

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

2.0300

0.4662

0.90161.1584

8.00

10.00

39.536 -10.193

15.07

62.88

20.00

1.8300

0.3038

0.69290.92600.9000

12.00

14.00

16.00

18.00

Distancia5 10 15 20


30

0.25 L 10.00

0.30 L 12.00

0 0 0

0 0 0

0.15 L 6.00


13 7 0

13 11 0

66

31.5

13 11 3 23.058

23.966

-26.979

235.72011 3

REACCIONES

0.92

0.05 L 2.00

0.10 L 4.00

7 0 0

13


FINALESINICIALES


0.0 L 0


5 10 15


Esfuerzos Servicio


24.49%4.32%

Esfuerzos Trans.

22

13 0

0 0

0

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

31

Suma

5

9

13

59

63PASA POR MOMENTO


ULTIMO

37

46

52

PASA POR MOMENTO



ULTIMO

-11.182

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

66



213










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

fs 2.38 95.65 136.94 197.94 222.33 257.61 292.72 311.19 323.50 332.58

f i 447.64 864.85 932.98 1078.22 1364.83 1536.42 1742.81 1862.37 1953.62 1944.32

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830

fcr (kg/cm²) 43.547 83.523 89.509 103.142 129.290 144.907 163.201 173.791 181.663 180.888

fs 16.155 29.757 46.513 51.019 66.790 74.462 81.780 85.819 88.241 89.053

f i -20.257 -35.277 -58.342 -60.920 -83.750 -93.368 -102.546 -107.610 -110.646 -111.666

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030

fcd (kg/cm²) -19.360 -33.020 -53.843 -55.555 -75.205 -83.034 -89.849 -93.620 -95.579 -96.460

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 302.81027 580.79056 622.41701 717.21157 899.03656 1007.6316 1134.8379 1208.4837 1263.2188 1257.828231

CRC (kg/cm²) = 387.04598 771.14173 697.21115 848.81552 1025.0423 1157.6472 1329.4622 1430.1604 1510.9014 1495.430958

CRS (kg/cm²) = 271.42968 224.42686 223.96075 206.90107 179.90723 162.41748 141.1061 128.70662 119.19605 120.508634

AE + CRC + CRS 961.29 1576.36 1543.59 1772.93 2103.99 2327.70 2605.41 2767.35 2893.32 2873.77

% fPU = 6.75 11.06 10.83 12.44 14.76 16.33 18.28 19.42 20.30 20.17

% fPU TOTAL = 11.07 15.38 15.15 16.76 19.09 20.66 22.60 23.74 24.62 24.49

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,673 12,058 12,091 11,861 11,530 11,307 11,029 10,867 10,741 10,760

(fPU - fSE)AS* = 20 48 66 87 124 152 188 211 229 228

X 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000



214


0 2 4 6 8 10 12 14 16 18 20

0

50

100

150

200

250



FU

ER

ZA

(e

n t

on

ela

da

s)



215



## ## 40 ## #### ## 54 ## #### ## 81 ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## ##

permisibleEsfzo. tope Vigapermisiblex## ## -11 #### ## -2 #### ## 6 #### ## 8 #### ## 14 #### ## 15 #### ## 18 #### ## 21 #### ## 22 #### ## 23 #### ## 24 ##


-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




216




x0.00 0.000 31.707786 -33.94 247.50 -10.19311523

0.05 2.000 12.91360261 -33.94 247.50 23.56252132

0.10 4.000 -0.262990035 -33.94 247.50 56.00122372

0.15 6.000 -7.469785946 -33.94 247.50 82.97053987

0.20 8.000 -8.331860494 -33.94 247.50 99.25078201

0.25 10.000 -16.93983924 -33.94 247.50 122.482223

0.30 12.000 -22.13102411 -33.94 247.50 138.2421642

0.35 14.000 -25.47744212 -33.94 247.50 153.6747735

0.40 16.000 -26.82513331 -33.94 247.50 161.7250355

0.45 18.000 -26.97922378 -33.94 247.50 166.8678529

0.50 20.000 -29.59002659 -33.94 247.50 169.1950126

-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




217




w

AL CENTRO DEL CLARO

40.00






H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 336.38 -1025.2 -1025.2 1000.9 1000.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 201.20 -613.2 1744.0 598.7 838.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -187.772 1.00 0.00 -677.0 1067.0 63.5 901.8 63.5 63.5 144.4 144.4 C

Asfal + Parapeto 0.00 0.00 202.60 -503.4 563.5 291.9 1193.7 291.9 355.4 378.8 523.2 O

Carga viva + I 0.00 0.00 345.87 -859.4 -295.9 498.3 1692.0 498.3 853.6 646.7 1169.9 M









218




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 333.33 -1016.0 -1016.0 991.8 991.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 199.37 -607.7 1758.8 593.2 823.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -189.05 1.00 0.00 -681.6 1077.2 63.9 887.7 63.9 63.9 145.4 145.4 C

Asfal + Parapeto 0.00 0.00 200.74 -498.8 578.4 289.2 1176.9 289.2 353.1 375.3 520.7 O

Carga viva + I 0.00 0.00 341.36 -848.2 -269.8 491.8 1668.7 491.8 844.9 638.2 1158.9 M









219




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 62.37 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 324.18 -988.1 -988.1 964.6 964.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 193.90 -591.0 1667.7 576.9 797.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -172.60 1.01 0.00 -625.3 1042.4 60.1 857.4 60.1 60.1 135.0 135.0 C

Asfal + Parapeto 0.00 0.00 195.23 -485.1 557.3 281.3 1138.6 281.3 341.3 365.0 500.0 O

Carga viva + I 0.00 0.00 332.24 -825.6 -268.3 478.6 1617.3 478.6 820.0 621.2 1121.2 M









220




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 58.41 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 308.92 -941.6 -941.6 919.2 919.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 184.77 -563.2 1552.9 549.8 755.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -152.18 1.02 0.00 -554.0 998.9 54.5 809.9 54.5 54.5 121.0 121.0 C

Asfal + Parapeto 0.00 0.00 186.05 -462.3 536.6 268.0 1077.9 268.0 322.5 347.8 468.9 O

Carga viva + I 0.00 0.00 318.49 -791.4 -254.8 458.8 1536.7 458.8 781.4 595.4 1064.3 M










221




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 51.48 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 281.28 -857.3 -857.3 836.9 836.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 168.24 -512.8 1356.5 500.6 677.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -119.83 1.03 0.00 -440.6 915.8 45.5 723.1 45.5 45.5 98.6 98.6 C

Asfal + Parapeto 0.00 0.00 169.39 -420.9 494.9 244.0 967.2 244.0 289.5 316.7 415.3 O

Carga viva + I 0.00 0.00 288.25 -716.3 -221.3 415.3 1382.4 415.3 704.8 538.9 954.2 M










222




223




w

40.00








H = 1.8300 m H = 2.0300 m As* = 45.54 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 252.29 -769.0 -769.0 750.7 750.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 150.90 -459.9 1201.6 449.0 597.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -95.82 1.04 0.00 -354.6 846.9 37.7 635.6 37.7 37.7 80.6 80.6 C

Asfal + Parapeto 0.00 0.00 151.95 -377.6 469.4 218.9 854.5 218.9 256.6 284.1 364.7 O

Carga viva + I 0.00 0.00 257.07 -638.8 -169.4 370.3 1224.8 370.3 627.0 480.6 845.3 M










224




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 36.63 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 217.21 -662.0 -662.0 646.3 646.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 129.92 -396.0 924.2 386.6 522.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -64.94 1.06 0.00 -243.3 680.9 27.2 549.4 27.2 27.2 56.8 56.8 C

Asfal + Parapeto 0.00 0.00 85.81 -213.2 467.7 123.6 673.0 123.6 150.9 160.4 217.2 O

Carga viva + I 0.00 0.00 221.76 -551.0 -83.3 319.5 992.5 319.5 470.3 414.6 631.8 M










225




w

40








H = 1.8300 m H = 2.0300 mts. As* = 30.69 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 176.02 -536.5 -536.5 523.7 523.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 105.00 -320.0 817.3 312.4 395.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -47.37 1.07 0.00 -178.7 638.6 20.6 416.2 20.6 20.6 42.3 42.3 C

Asfal + Parapeto 0.00 0.00 106.00 -263.4 375.2 152.7 568.9 152.7 173.3 198.2 240.5 O

Carga viva + I 0.00 0.00 181.07 -449.9 -74.7 260.8 829.7 260.8 434.1 338.5 579.0 M










226




w

40








H = 1.8300 m H = 2.0300 mts. As* = 21.78 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 9






Po.Po Viga 0.00 0.00 128.74 -392.4 -392.4 383.1 383.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.00 -234.7 575.8 229.1 284.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -34.33 1.09 0.00 -130.9 444.9 15.7 300.5 15.7 15.7 31.8 31.8 C

Asfal + Parapeto 0.00 0.00 47.52 -118.1 326.9 68.5 369.0 68.5 84.2 88.8 120.6 O

Carga viva + I 0.00 0.00 132.60 -329.5 -2.6 191.0 560.0 191.0 275.2 247.9 368.5 M










227




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 12.87 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 61.03 -186.0 -186.0 181.6 181.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 36.50 -111.2 424.5 108.6 86.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -12.37 1.11 0.00 -47.8 376.7 6.0 92.1 6.0 6.0 11.9 11.9 C

Asfal + Parapeto 0.00 0.00 36.75 -91.3 285.4 52.9 145.0 52.9 59.0 68.7 80.6 O

Carga viva + I 0.00 0.00 62.88 -156.2 129.1 90.6 235.6 90.6 149.6 117.6 198.2 M










228




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 8.91 cm² 5 9

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 31.28 -95.3 -95.3 93.1 93.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 18.71 -57.0 347.3 55.7 7.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -25.61 1.11 0.00 -98.9 248.4 12.5 19.9 12.5 12.5 24.7 24.7 C

Asfal + Parapeto 0.00 0.00 18.82 -46.8 201.6 27.1 47.0 27.1 39.6 35.2 59.8 O

Carga viva + I 0.00 0.00 31.44 -78.1 123.5 45.3 92.3 45.3 84.9 58.8 118.6 M










229




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 7.05 cm² 5 5

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 395.4 0.0 -111.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -20.26 1.11 0.00 -78.3 317.1 9.9 -101.9 9.9 9.9 19.5 19.5 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 O

Carga viva + I 0.00 0.00 0.01 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 M










230



x en metros 0.915 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

MCM 68.81 134.28 253.26 387.02 432.94 555.14 618.91 679.74 713.31 733.44 740.18

MCV 31.44 62.88 132.60 181.07 221.76 257.07 288.25 318.49 332.24 341.36 345.87

MU en ton-m 157.57 310.80 616.54 895.43 1043.30 1278.66 1429.12 1573.71 1647.15 1693.08 1711.63

VCM 70.49 66.95 58.12 51.09 44.04 36.97 29.94 21.12 14.08 7.02 0.00

VCV 35.24 34.12 31.32 29.08 26.84 24.60 22.36 19.56 17.31 15.07 12.83

VU en ton 167.99 160.95 143.41 129.42 115.39 101.35 87.36 69.83 55.81 41.78 27.80

VC 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86

VU-VC 130.14 123.11 105.96 92.28 78.45 64.76 50.95 33.71 19.82 5.92 -8.06

E#3@ 5.84 6.18 7.18 8.24 9.69 11.74 14.92 22.56 38.36 128.38 -94.39

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 198.00 198.00 195.95 194.29 193.27 191.48 190.50 189.02 188.32 187.62 187.62

Vud/Mu <= 1.0 1.00 1.00 0.46 0.28 0.21 0.15 0.12 0.08 0.06 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86


f1.3 raiz(f́ c)bwd 92.82 92.82 91.87 91.09 90.61 89.77 89.31 88.61 88.29 87.96 87.96

VC considerado 92.82 92.82 85.71 56.66 45.57 36.60 36.41 36.13 35.99 35.86 35.86

VS = VU-VC 75.16 68.13 57.70 72.76 69.83 64.76 50.95 33.71 19.82 5.92 0.01






231



4.8.1.- CARGA VIVA




5 0.027 0.027

4

2.446 1.00

0.306

-0.066-0.066

0.213

0.120

Carga (P)

6

0.3062

3

Analisis

Excentricidad (m)

Factor de reduccion


1.00 6.00 1.50

Datos


1.000

0.400

0.213

0.120

S

e

n

in

n

PRi 1

2161

2



232



5 0.228 0.228

2.000

No. De vigas

6 0.158 0.158

Datos

AnalisisViga Ri

Carga (P)

1.506.000.92

Excentricidad (m)

0.439

Ri x FR

0.439

1.00

Factor de reduccion

4 0.298 0.298

1 0.509 0.509

3 0.368 0.368

2

2.00

Separacion (m)

S

e

n

in

n

PRi 1

2161

2



233


16.292T5 0.272 59.870

59.870

T1T2

26.318

DESCARGA DE CAMION


0.193

1.193

T6 0.188 59.870 11.280

0.607

40.800133.858

Analisis

T3 0.440




CARGA POR TRABE

DESCARGA TOTAL =


59.87059.8700.523

142.868

31.33036.343

T4 0.356 59.870 21.305

25

50

LI




234


30.35

59.87

40.50

0.00

33.90

20.51

7.87

0.31

12.48

40.50

253.57

0.10 0.15

59.87 58.05 56.20 51.59

31.1939.40

36.3 35.2 34.1 31.3 29.1 26.8

19.6938.31 35.57 33.38

22.424.6

47.90 44.21 40.52 36.83

29.00 26.81

288.2

325.59

28.52

1.2

8.1

25.31

20.0 16.8

23.75

10.1

0.35

12.00

13.6

0.25

23.2

10.00

122.4

0.30

9.6

CORTANTE

22.2

0.0 kL

332.2181.1 221.8

569.78

17.50

0.35

562.34524.66

370.18

112.4

16.0014.00

6.4

0.25 0.30

10.00

245.23

292.47

0.3

16.8 64.1

0.20

0.0 0.92 2.00 4.00

61.0 128.7

6.00 8.00 18.00

150.9 193.977.0

20.00

176.0 217.2 252.3 281.3 308.9

12.00

324.2 333.3 336.4

105.0 129.9

3.0

0.0 4.9

184.8

64.657.9

0.0 18.7

1.9 2.30.5

79.00.0 121.311.4

0.01

318.5

103.58 218.44

132.6

51.79

35.45

257.10.0

70.91

0.05 0.10 0.15 0.20

0.0 0.92 2.00 4.00

33.6 32.0 30.4 26.4

12.0

0.10.2 0.2 0.2 0.2

19.2 18.2 15.8 13.9

7.4 7.0 5.3 3.9

11.1 9.6 7.3

0.3

Reacción

22.20 14.05

5.0

20.65 18.71 17.15

3.2 0.0

0.45 0.50

8.00

0.1

6.1

18.00 20.00

2.2 1.54.6

15.1

0.0

12.8

32.22 24.83 21.14

19.6 17.3

24.07 21.88

20.1

7.7

0.3

0.7

6.00

1.9

0.3

3.1

0.1

6.1

345.9341.4

0.0

28.79 26.85 15.61

14.00 16.00

0.0

0.40

30.35 29.57

11.7

280.13

0.0 0.0

5.7 3.8

380.35378.19



LOSA + ZOCLO

CARPETA



CARGA VIVA TRABE


8.5

288.74155.75 191.38 220.37

x

PESO PROPIO






CARGA VIVA TRABE

x / L

0.01 53.39

2.9

365.31

91.8 102.3

547.31

26.70

0.01

0.0

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 14.07.2

36.5

3.0

201.2199.4

298.28

286.65

74.4 76.570.9

118.0

474.85

168.2

356.33

113.46 269.18

29.5 40.4

1.1 2.5 2.81.6

77.2

0.40 0.45

0.0 31.3

0.05

MOMENTO

0.0 kL 0.50x / L


423.48

31.4 62.9

205.84150.13

12.2 3.5 2.3



235


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

0.39 3.68

20

0.71


ton/m 1.730.63

TRABE4200

BAJA RELAJACIÓN


1.66 ton/m

PESO PROPIO

1.01

LOSA

ton/m


40.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


17.31

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140


HR = 55


ton/mton/m


EC =

CARGAS

7

6

5

6

2

-29.590

9

4

-22.131

211.603 -25.477

225.868 161.725 -26.825

4

4

186.924

181.07

1.00

257.07

0.75

341.36 345.87332.24

13

13

13

35.24

0

13

0

26.84

13

13

81.052 56.001

288.25

-8.332

8.316

12.91453.574 23.563

318.49

-0.263

13

221.76

13 13

13

11

0

09

13

13

166.151 -16.940

0 0

236.650

13

13

13

5.569

36.34

0

132.018

12.83

13 5

13

-4.825

00

0.01

9 0 0

005

31.44 132.60

0.0 L

-7.470113.729 82.971

4

122.482

138.242

153.675

22.034

19.5624.60 22.3634.12 31.32 29.08

13

13

0.40 L 16.00

0.45 L 18.00

14.00

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 8.00

13

31.708

40.433 9.231 12.350

-2.2540 0 0

0

20.562

166.868

169.195

99.251

20 25

14.887

17.706

13.561

7

3


0.50 L 20.00

fSMAX =

fI MIN =

169.195

-29.590 PASA

fSMIN =

fI MAX =

-11.18

236.6

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

13

13

13

13

0.92

0.05 L

0.10 L

0.15 L

0.20 L

0

2.00

4.00

6.00

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

2.0300

0.4662

0.90161.1584

8.00

10.00

39.536 -10.193

15.07

62.88

20.00

1.8300

0.3038

0.69290.92600.9000

12.00

14.00

16.00

18.00

Distancia5 10 15 20


30

0.25 L 10.00

0.30 L 12.00

0 0 0

0 0 0

0.15 L 6.00


13 7 0

13 11 0

66

31.5

13 11 3 23.058

23.966

-26.979

235.72011 3

REACCIONES

0.92

0.05 L 2.00

0.10 L 4.00

7 0 0

13


FINALESINICIALES


0.0 L 0


5 10 15


Esfuerzos Servicio


24.49%4.32%

Esfuerzos Trans.

22

13 0

0 0

0

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

31

Suma

5

9

13

59

63PASA POR MOMENTO


ULTIMO

37

46

52

PASA POR MOMENTO



ULTIMO

-11.182

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

66



236










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

fs 2.38 95.65 136.94 197.94 222.33 257.61 292.72 311.19 323.50 332.58

f i 447.64 864.85 932.98 1078.22 1364.83 1536.42 1742.81 1862.37 1953.62 1944.32

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830

fcr (kg/cm²) 43.547 83.523 89.509 103.142 129.290 144.907 163.201 173.791 181.663 180.888

fs 16.155 29.757 46.513 51.019 66.790 74.462 81.780 85.819 88.241 89.053

f i -20.257 -35.277 -58.342 -60.920 -83.750 -93.368 -102.546 -107.610 -110.646 -111.666

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030

fcd (kg/cm²) -19.360 -33.020 -53.843 -55.555 -75.205 -83.034 -89.849 -93.620 -95.579 -96.460

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 302.81027 580.79056 622.41701 717.21157 899.03656 1007.6316 1134.8379 1208.4837 1263.2188 1257.828231

CRC (kg/cm²) = 387.04598 771.14173 697.21115 848.81552 1025.0423 1157.6472 1329.4622 1430.1604 1510.9014 1495.430958

CRS (kg/cm²) = 271.42968 224.42686 223.96075 206.90107 179.90723 162.41748 141.1061 128.70662 119.19605 120.508634

AE + CRC + CRS 961.29 1576.36 1543.59 1772.93 2103.99 2327.70 2605.41 2767.35 2893.32 2873.77

% fPU = 6.75 11.06 10.83 12.44 14.76 16.33 18.28 19.42 20.30 20.17

% fPU TOTAL = 11.07 15.38 15.15 16.76 19.09 20.66 22.60 23.74 24.62 24.49

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,673 12,058 12,091 11,861 11,530 11,307 11,029 10,867 10,741 10,760

(fPU - fSE)AS* = 20 48 66 87 124 152 188 211 229 228

X 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000



237


0 2 4 6 8 10 12 14 16 18 20

0

50

100

150

200

250



FU

ER

ZA

(e

n t

on

ela

da

s)



238



## ## 40 ## #### ## 54 ## #### ## 81 ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## ##



-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




239




x0.00 0.000 31.707786 -33.94 247.50 -10.19311523

0.05 2.000 12.91360261 -33.94 247.50 23.56252132

0.10 4.000 -0.262990035 -33.94 247.50 56.00122372

0.15 6.000 -7.469785946 -33.94 247.50 82.97053987

0.20 8.000 -8.331860494 -33.94 247.50 99.25078201

0.25 10.000 -16.93983924 -33.94 247.50 122.482223

0.30 12.000 -22.13102411 -33.94 247.50 138.2421642

0.35 14.000 -25.47744212 -33.94 247.50 153.6747735

0.40 16.000 -26.82513331 -33.94 247.50 161.7250355

0.45 18.000 -26.97922378 -33.94 247.50 166.8678529

0.50 20.000 -29.59002659 -33.94 247.50 169.1950126

-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




240




w

AL CENTRO DEL CLARO

40.00






H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 336.38 -1025.2 -1025.2 1000.9 1000.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 201.20 -613.2 1744.0 598.7 838.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -187.772 1.00 0.00 -677.0 1067.0 63.5 901.8 63.5 63.5 144.4 144.4 C

Asfal + Parapeto 0.00 0.00 202.60 -503.4 563.5 291.9 1193.7 291.9 355.4 378.8 523.2 O

Carga viva + I 0.00 0.00 345.87 -859.4 -295.9 498.3 1692.0 498.3 853.6 646.7 1169.9 M









241




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 333.33 -1016.0 -1016.0 991.8 991.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 199.37 -607.7 1758.8 593.2 823.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -189.05 1.00 0.00 -681.6 1077.2 63.9 887.7 63.9 63.9 145.4 145.4 C

Asfal + Parapeto 0.00 0.00 200.74 -498.8 578.4 289.2 1176.9 289.2 353.1 375.3 520.7 O

Carga viva + I 0.00 0.00 341.36 -848.2 -269.8 491.8 1668.7 491.8 844.9 638.2 1158.9 M









242




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 62.37 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 324.18 -988.1 -988.1 964.6 964.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 193.90 -591.0 1667.7 576.9 797.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -172.60 1.01 0.00 -625.3 1042.4 60.1 857.4 60.1 60.1 135.0 135.0 C

Asfal + Parapeto 0.00 0.00 195.23 -485.1 557.3 281.3 1138.6 281.3 341.3 365.0 500.0 O

Carga viva + I 0.00 0.00 332.24 -825.6 -268.3 478.6 1617.3 478.6 820.0 621.2 1121.2 M









243




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 58.41 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 308.92 -941.6 -941.6 919.2 919.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 184.77 -563.2 1552.9 549.8 755.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -152.18 1.02 0.00 -554.0 998.9 54.5 809.9 54.5 54.5 121.0 121.0 C

Asfal + Parapeto 0.00 0.00 186.05 -462.3 536.6 268.0 1077.9 268.0 322.5 347.8 468.9 O

Carga viva + I 0.00 0.00 318.49 -791.4 -254.8 458.8 1536.7 458.8 781.4 595.4 1064.3 M










244




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 51.48 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 281.28 -857.3 -857.3 836.9 836.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 168.24 -512.8 1356.5 500.6 677.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -119.83 1.03 0.00 -440.6 915.8 45.5 723.1 45.5 45.5 98.6 98.6 C

Asfal + Parapeto 0.00 0.00 169.39 -420.9 494.9 244.0 967.2 244.0 289.5 316.7 415.3 O

Carga viva + I 0.00 0.00 288.25 -716.3 -221.3 415.3 1382.4 415.3 704.8 538.9 954.2 M










245




246




w

40.00








H = 1.8300 m H = 2.0300 m As* = 45.54 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 252.29 -769.0 -769.0 750.7 750.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 150.90 -459.9 1201.6 449.0 597.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -95.82 1.04 0.00 -354.6 846.9 37.7 635.6 37.7 37.7 80.6 80.6 C

Asfal + Parapeto 0.00 0.00 151.95 -377.6 469.4 218.9 854.5 218.9 256.6 284.1 364.7 O

Carga viva + I 0.00 0.00 257.07 -638.8 -169.4 370.3 1224.8 370.3 627.0 480.6 845.3 M










247




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 36.63 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 217.21 -662.0 -662.0 646.3 646.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 129.92 -396.0 924.2 386.6 522.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -64.94 1.06 0.00 -243.3 680.9 27.2 549.4 27.2 27.2 56.8 56.8 C

Asfal + Parapeto 0.00 0.00 85.81 -213.2 467.7 123.6 673.0 123.6 150.9 160.4 217.2 O

Carga viva + I 0.00 0.00 221.76 -551.0 -83.3 319.5 992.5 319.5 470.3 414.6 631.8 M










248




w

40








H = 1.8300 m H = 2.0300 mts. As* = 30.69 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 176.02 -536.5 -536.5 523.7 523.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 105.00 -320.0 817.3 312.4 395.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -47.37 1.07 0.00 -178.7 638.6 20.6 416.2 20.6 20.6 42.3 42.3 C

Asfal + Parapeto 0.00 0.00 106.00 -263.4 375.2 152.7 568.9 152.7 173.3 198.2 240.5 O

Carga viva + I 0.00 0.00 181.07 -449.9 -74.7 260.8 829.7 260.8 434.1 338.5 579.0 M










249




w

40








H = 1.8300 m H = 2.0300 mts. As* = 21.78 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 9






Po.Po Viga 0.00 0.00 128.74 -392.4 -392.4 383.1 383.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.00 -234.7 575.8 229.1 284.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -34.33 1.09 0.00 -130.9 444.9 15.7 300.5 15.7 15.7 31.8 31.8 C

Asfal + Parapeto 0.00 0.00 47.52 -118.1 326.9 68.5 369.0 68.5 84.2 88.8 120.6 O

Carga viva + I 0.00 0.00 132.60 -329.5 -2.6 191.0 560.0 191.0 275.2 247.9 368.5 M










250




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 12.87 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 61.03 -186.0 -186.0 181.6 181.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 36.50 -111.2 424.5 108.6 86.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -12.37 1.11 0.00 -47.8 376.7 6.0 92.1 6.0 6.0 11.9 11.9 C

Asfal + Parapeto 0.00 0.00 36.75 -91.3 285.4 52.9 145.0 52.9 59.0 68.7 80.6 O

Carga viva + I 0.00 0.00 62.88 -156.2 129.1 90.6 235.6 90.6 149.6 117.6 198.2 M










251




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 8.91 cm² 5 9

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 31.28 -95.3 -95.3 93.1 93.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 18.71 -57.0 347.3 55.7 7.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -25.61 1.11 0.00 -98.9 248.4 12.5 19.9 12.5 12.5 24.7 24.7 C

Asfal + Parapeto 0.00 0.00 18.82 -46.8 201.6 27.1 47.0 27.1 39.6 35.2 59.8 O

Carga viva + I 0.00 0.00 31.44 -78.1 123.5 45.3 92.3 45.3 84.9 58.8 118.6 M










252




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 7.05 cm² 5 5

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 395.4 0.0 -111.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -20.26 1.11 0.00 -78.3 317.1 9.9 -101.9 9.9 9.9 19.5 19.5 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 O

Carga viva + I 0.00 0.00 0.01 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 M










253



x en metros 0.915 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

MCM 68.81 134.28 253.26 387.02 432.94 555.14 618.91 679.74 713.31 733.44 740.18

MCV 31.44 62.88 132.60 181.07 221.76 257.07 288.25 318.49 332.24 341.36 345.87

MU en ton-m 157.57 310.80 616.54 895.43 1043.30 1278.66 1429.12 1573.71 1647.15 1693.08 1711.63

VCM 70.49 66.95 58.12 51.09 44.04 36.97 29.94 21.12 14.08 7.02 0.00

VCV 35.24 34.12 31.32 29.08 26.84 24.60 22.36 19.56 17.31 15.07 12.83

VU en ton 167.99 160.95 143.41 129.42 115.39 101.35 87.36 69.83 55.81 41.78 27.80

VC 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86

VU-VC 130.14 123.11 105.96 92.28 78.45 64.76 50.95 33.71 19.82 5.92 -8.06

E#3@ 5.84 6.18 7.18 8.24 9.69 11.74 14.92 22.56 38.36 128.38 -94.39

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 198.00 198.00 195.95 194.29 193.27 191.48 190.50 189.02 188.32 187.62 187.62

Vud/Mu <= 1.0 1.00 1.00 0.46 0.28 0.21 0.15 0.12 0.08 0.06 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86


f1.3 raiz(f́ c)bwd 92.82 92.82 91.87 91.09 90.61 89.77 89.31 88.61 88.29 87.96 87.96

VC considerado 92.82 92.82 85.71 56.66 45.57 36.60 36.41 36.13 35.99 35.86 35.86

VS = VU-VC 75.16 68.13 57.70 72.76 69.83 64.76 50.95 33.71 19.82 5.92 0.01






254



4.9.1.- CARGA VIVA




5 0.027 0.027

4

2.446 1.00

0.306

-0.066-0.066

0.213

0.120

Carga (P)

6

0.3062

3

Analisis

Excentricidad (m)

Factor de reduccion


1.00 6.00 1.50

Datos


1.000

0.400

0.213

0.120

S

e

n

in

n

PRi 1

2161

2



255



5 0.228 0.228

2.000

No. De vigas

6 0.158 0.158

Datos

AnalisisViga Ri

Carga (P)

1.506.000.92

Excentricidad (m)

0.439

Ri x FR

0.439

1.00

Factor de reduccion

4 0.298 0.298

1 0.509 0.509

3 0.368 0.368

2

2.00

Separacion (m)

S

e

n

in

n

PRi 1

2161

2



256


16.292T5 0.272 59.870

59.870

T1T2

26.318

DESCARGA DE CAMION


0.193

1.193

T6 0.188 59.870 11.280

0.607

40.800133.858

Analisis

T3 0.440




CARGA POR TRABE

DESCARGA TOTAL =


59.87059.8700.523

142.868

31.33036.343

T4 0.356 59.870 21.305

25

50

LI




257


30.35

59.87

40.50

0.00

33.90

20.51

7.87

0.31

12.48

40.50

253.57

0.10 0.15

59.87 58.05 56.20 51.59

31.1939.40

36.3 35.2 34.1 31.3 29.1 26.8

19.6938.31 35.57 33.38

22.424.6

47.90 44.21 40.52 36.83

29.00 26.81

288.2

325.59

28.52

1.2

8.1

25.31

20.0 16.8

23.75

10.1

0.35

12.00

13.6

0.25

23.2

10.00

122.4

0.30

9.6

CORTANTE

22.2

0.0 kL

332.2181.1 221.8

569.78

17.50

0.35

562.34524.66

370.18

112.4

16.0014.00

6.4

0.25 0.30

10.00

245.23

292.47

0.3

16.8 64.1

0.20

0.0 0.92 2.00 4.00

61.0 128.7

6.00 8.00 18.00

150.9 193.977.0

20.00

176.0 217.2 252.3 281.3 308.9

12.00

324.2 333.3 336.4

105.0 129.9

3.0

0.0 4.9

184.8

64.657.9

0.0 18.7

1.9 2.30.5

79.00.0 121.311.4

0.01

318.5

103.58 218.44

132.6

51.79

35.45

257.10.0

70.91

0.05 0.10 0.15 0.20

0.0 0.92 2.00 4.00

33.6 32.0 30.4 26.4

12.0

0.10.2 0.2 0.2 0.2

19.2 18.2 15.8 13.9

7.4 7.0 5.3 3.9

11.1 9.6 7.3

0.3

Reacción

22.20 14.05

5.0

20.65 18.71 17.15

3.2 0.0

0.45 0.50

8.00

0.1

6.1

18.00 20.00

2.2 1.54.6

15.1

0.0

12.8

32.22 24.83 21.14

19.6 17.3

24.07 21.88

20.1

7.7

0.3

0.7

6.00

1.9

0.3

3.1

0.1

6.1

345.9341.4

0.0

28.79 26.85 15.61

14.00 16.00

0.0

0.40

30.35 29.57

11.7

280.13

0.0 0.0

5.7 3.8

380.35378.19



LOSA + ZOCLO

CARPETA



CARGA VIVA TRABE


8.5

288.74155.75 191.38 220.37

x

PESO PROPIO






CARGA VIVA TRABE

x / L

0.01 53.39

2.9

365.31

91.8 102.3

547.31

26.70

0.01

0.0

x

PESO PROPIO

LOSA + ZOCLO

CARPETA 14.07.2

36.5

3.0

201.2199.4

298.28

286.65

74.4 76.570.9

118.0

474.85

168.2

356.33

113.46 269.18

29.5 40.4

1.1 2.5 2.81.6

77.2

0.40 0.45

0.0 31.3

0.05

MOMENTO

0.0 kL 0.50x / L


423.48

31.4 62.9

205.84150.13

12.2 3.5 2.3



258


kg/cm² H = m H = m

IX = m4IX = m4

A = m² A = m²Yi = m Yi = ma = m a = m

SI


ACERO fY = kg/cm²



% kg/cm² f y = 4,200 kg/cm2


0.02 L 0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L 0.45L 0.50L

0.02 L



0.02 L



kg/cm²

kg/cm²

kg/cm²

kg/cm²

0.39 3.68

20

0.71


ton/m 1.730.63

TRABE4200

BAJA RELAJACIÓN


1.66 ton/m

PESO PROPIO

1.01

LOSA

ton/m


40.00CLARO =

DATOS

LOSA

2,100,000

0.9000

COMPUESTA


17.31

ESFUERZO DEL

CONCRETO fCi EN LA


CONCRETO f´C = 450

ACERO DE


ton/m

GEOMETRÍA

320,319

MATERIALES

TRABE

SECCIONES

SIMPLE

250

20

140


HR = 55


ton/mton/m


EC =

CARGAS

7

6

5

6

2

-29.590

9

4

-22.131

211.603 -25.477

225.868 161.725 -26.825

4

4

186.924

181.07

1.00

257.07

0.75

341.36 345.87332.24

13

13

13

35.24

0

13

0

26.84

13

13

81.052 56.001

288.25

-8.332

8.316

12.91453.574 23.563

318.49

-0.263

13

221.76

13 13

13

11

0

09

13

13

166.151 -16.940

0 0

236.650

13

13

13

5.569

36.34

0

132.018

12.83

13 5

13

-4.825

00

0.01

9 0 0

005

31.44 132.60

0.0 L

-7.470113.729 82.971

4

122.482

138.242

153.675

22.034

19.5624.60 22.3634.12 31.32 29.08

13

13

0.40 L 16.00

0.45 L 18.00

14.00

A LA TRANSFERENCIA

EN SERVICIO


0.20 L 8.00

13

31.708

40.433 9.231 12.350

-2.2540 0 0

0

20.562

166.868

169.195

99.251

20 25

14.887

17.706

13.561

7

3


0.50 L 20.00

fSMAX =

fI MIN =

169.195

-29.590 PASA

fSMIN =

fI MAX =

-11.18

236.6

MCARGA VIVA

VCARGA VIVA

Distancia 0L

25

0.35 L

13

13

13

13

0.92

0.05 L

0.10 L

0.15 L

0.20 L

0

2.00

4.00

6.00

0.25 L

0.30 L

0.35 L

0.40 L

0.45 L

0.50 L

2.0300

0.4662

0.90161.1584

8.00

10.00

39.536 -10.193

15.07

62.88

20.00

1.8300

0.3038

0.69290.92600.9000

12.00

14.00

16.00

18.00

Distancia5 10 15 20


30

0.25 L 10.00

0.30 L 12.00

0 0 0

0 0 0

0.15 L 6.00


13 7 0

13 11 0

66

31.5

13 11 3 23.058

23.966

-26.979

235.72011 3

REACCIONES

0.92

0.05 L 2.00

0.10 L 4.00

7 0 0

13


FINALESINICIALES


0.0 L 0


5 10 15


Esfuerzos Servicio


24.49%4.32%

Esfuerzos Trans.

22

13 0

0 0

0

PASA POR MOMENTO

ULTIMO

Flexion

PASA POR MOMENTO



ULTIMO

31

Suma

5

9

13

59

63PASA POR MOMENTO


ULTIMO

37

46

52

PASA POR MOMENTO



ULTIMO

-11.182

A LA TRANSFERENCIA

PASA

PASA

PASA

EN SERVICIO

PASA POR MOMENTO


ULTIMO

PASA POR MOMENTO

ULTIMO

66



259










X TRABE EN METROS

0.05L 0.10L 0.15L 0.20L 0.25L 0.30L 0.35L 0.40L .45L 0.50L

2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

fs 2.38 95.65 136.94 197.94 222.33 257.61 292.72 311.19 323.50 332.58

f i 447.64 864.85 932.98 1078.22 1364.83 1536.42 1742.81 1862.37 1953.62 1944.32

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830 1.830

fcr (kg/cm²) 43.547 83.523 89.509 103.142 129.290 144.907 163.201 173.791 181.663 180.888

fs 16.155 29.757 46.513 51.019 66.790 74.462 81.780 85.819 88.241 89.053

f i -20.257 -35.277 -58.342 -60.920 -83.750 -93.368 -102.546 -107.610 -110.646 -111.666

ytorones 0.050 0.070 0.087 0.097 0.115 0.125 0.140 0.147 0.154 0.154

h 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030 2.030

fcd (kg/cm²) -19.360 -33.020 -53.843 -55.555 -75.205 -83.034 -89.849 -93.620 -95.579 -96.460

CC (kg/cm²) = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

CC = 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399 615.7399

% fPU = 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32 4.32

AE (kg/cm²) = 302.81027 580.79056 622.41701 717.21157 899.03656 1007.6316 1134.8379 1208.4837 1263.2188 1257.828231

CRC (kg/cm²) = 387.04598 771.14173 697.21115 848.81552 1025.0423 1157.6472 1329.4622 1430.1604 1510.9014 1495.430958

CRS (kg/cm²) = 271.42968 224.42686 223.96075 206.90107 179.90723 162.41748 141.1061 128.70662 119.19605 120.508634

AE + CRC + CRS 961.29 1576.36 1543.59 1772.93 2103.99 2327.70 2605.41 2767.35 2893.32 2873.77

% fPU = 6.75 11.06 10.83 12.44 14.76 16.33 18.28 19.42 20.30 20.17

% fPU TOTAL = 11.07 15.38 15.15 16.76 19.09 20.66 22.60 23.74 24.62 24.49

fPU = 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250 14,250

fSE = 12,673 12,058 12,091 11,861 11,530 11,307 11,029 10,867 10,741 10,760

(fPU - fSE)AS* = 20 48 66 87 124 152 188 211 229 228

X 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000



260


0 2 4 6 8 10 12 14 16 18 20

0

50

100

150

200

250



FU

ER

ZA

(e

n t

on

ela

da

s)



261



## ## 40 ## #### ## 54 ## #### ## 81 ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## #### ## ## ## ##



-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )


-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)




262




x0.00 0.000 31.707786 -33.94 247.50 -10.19311523

0.05 2.000 12.91360261 -33.94 247.50 23.56252132

0.10 4.000 -0.262990035 -33.94 247.50 56.00122372

0.15 6.000 -7.469785946 -33.94 247.50 82.97053987

0.20 8.000 -8.331860494 -33.94 247.50 99.25078201

0.25 10.000 -16.93983924 -33.94 247.50 122.482223

0.30 12.000 -22.13102411 -33.94 247.50 138.2421642

0.35 14.000 -25.47744212 -33.94 247.50 153.6747735

0.40 16.000 -26.82513331 -33.94 247.50 161.7250355

0.45 18.000 -26.97922378 -33.94 247.50 166.8678529

0.50 20.000 -29.59002659 -33.94 247.50 169.1950126

-50

0

50

100

150

200

250

300

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

E

N k

g/c

m²

LONGITUD (m)


-50.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

ES

FU

ER

ZOS

( k

g/cm

² )

LONGITUD ( m )




263




w

AL CENTRO DEL CLARO

40.00






H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 336.38 -1025.2 -1025.2 1000.9 1000.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 201.20 -613.2 1744.0 598.7 838.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -187.772 1.00 0.00 -677.0 1067.0 63.5 901.8 63.5 63.5 144.4 144.4 C

Asfal + Parapeto 0.00 0.00 202.60 -503.4 563.5 291.9 1193.7 291.9 355.4 378.8 523.2 O

Carga viva + I 0.00 0.00 345.87 -859.4 -295.9 498.3 1692.0 498.3 853.6 646.7 1169.9 M









264




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 65.34 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 333.33 -1016.0 -1016.0 991.8 991.8 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 199.37 -607.7 1758.8 593.2 823.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -189.05 1.00 0.00 -681.6 1077.2 63.9 887.7 63.9 63.9 145.4 145.4 C

Asfal + Parapeto 0.00 0.00 200.74 -498.8 578.4 289.2 1176.9 289.2 353.1 375.3 520.7 O

Carga viva + I 0.00 0.00 341.36 -848.2 -269.8 491.8 1668.7 491.8 844.9 638.2 1158.9 M









265




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 62.37 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 324.18 -988.1 -988.1 964.6 964.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 193.90 -591.0 1667.7 576.9 797.3 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -172.60 1.01 0.00 -625.3 1042.4 60.1 857.4 60.1 60.1 135.0 135.0 C

Asfal + Parapeto 0.00 0.00 195.23 -485.1 557.3 281.3 1138.6 281.3 341.3 365.0 500.0 O

Carga viva + I 0.00 0.00 332.24 -825.6 -268.3 478.6 1617.3 478.6 820.0 621.2 1121.2 M









266




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 58.41 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 308.92 -941.6 -941.6 919.2 919.2 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 184.77 -563.2 1552.9 549.8 755.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -152.18 1.02 0.00 -554.0 998.9 54.5 809.9 54.5 54.5 121.0 121.0 C

Asfal + Parapeto 0.00 0.00 186.05 -462.3 536.6 268.0 1077.9 268.0 322.5 347.8 468.9 O

Carga viva + I 0.00 0.00 318.49 -791.4 -254.8 458.8 1536.7 458.8 781.4 595.4 1064.3 M










267




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 51.48 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 281.28 -857.3 -857.3 836.9 836.9 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 168.24 -512.8 1356.5 500.6 677.7 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -119.83 1.03 0.00 -440.6 915.8 45.5 723.1 45.5 45.5 98.6 98.6 C

Asfal + Parapeto 0.00 0.00 169.39 -420.9 494.9 244.0 967.2 244.0 289.5 316.7 415.3 O

Carga viva + I 0.00 0.00 288.25 -716.3 -221.3 415.3 1382.4 415.3 704.8 538.9 954.2 M










268




269




w

40.00








H = 1.8300 m H = 2.0300 m As* = 45.54 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 252.29 -769.0 -769.0 750.7 750.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 150.90 -459.9 1201.6 449.0 597.9 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -95.82 1.04 0.00 -354.6 846.9 37.7 635.6 37.7 37.7 80.6 80.6 C

Asfal + Parapeto 0.00 0.00 151.95 -377.6 469.4 218.9 854.5 218.9 256.6 284.1 364.7 O

Carga viva + I 0.00 0.00 257.07 -638.8 -169.4 370.3 1224.8 370.3 627.0 480.6 845.3 M










270




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 36.63 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 217.21 -662.0 -662.0 646.3 646.3 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 129.92 -396.0 924.2 386.6 522.2 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -64.94 1.06 0.00 -243.3 680.9 27.2 549.4 27.2 27.2 56.8 56.8 C

Asfal + Parapeto 0.00 0.00 85.81 -213.2 467.7 123.6 673.0 123.6 150.9 160.4 217.2 O

Carga viva + I 0.00 0.00 221.76 -551.0 -83.3 319.5 992.5 319.5 470.3 414.6 631.8 M










271




w

40








H = 1.8300 m H = 2.0300 mts. As* = 30.69 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 13






Po.Po Viga 0.00 0.00 176.02 -536.5 -536.5 523.7 523.7 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 105.00 -320.0 817.3 312.4 395.6 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -47.37 1.07 0.00 -178.7 638.6 20.6 416.2 20.6 20.6 42.3 42.3 C

Asfal + Parapeto 0.00 0.00 106.00 -263.4 375.2 152.7 568.9 152.7 173.3 198.2 240.5 O

Carga viva + I 0.00 0.00 181.07 -449.9 -74.7 260.8 829.7 260.8 434.1 338.5 579.0 M










272




w

40








H = 1.8300 m H = 2.0300 mts. As* = 21.78 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 9






Po.Po Viga 0.00 0.00 128.74 -392.4 -392.4 383.1 383.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 77.00 -234.7 575.8 229.1 284.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -34.33 1.09 0.00 -130.9 444.9 15.7 300.5 15.7 15.7 31.8 31.8 C

Asfal + Parapeto 0.00 0.00 47.52 -118.1 326.9 68.5 369.0 68.5 84.2 88.8 120.6 O

Carga viva + I 0.00 0.00 132.60 -329.5 -2.6 191.0 560.0 191.0 275.2 247.9 368.5 M










273




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 12.87 cm² 5 13

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 61.03 -186.0 -186.0 181.6 181.6 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 36.50 -111.2 424.5 108.6 86.1 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -12.37 1.11 0.00 -47.8 376.7 6.0 92.1 6.0 6.0 11.9 11.9 C

Asfal + Parapeto 0.00 0.00 36.75 -91.3 285.4 52.9 145.0 52.9 59.0 68.7 80.6 O

Carga viva + I 0.00 0.00 62.88 -156.2 129.1 90.6 235.6 90.6 149.6 117.6 198.2 M










274




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 8.91 cm² 5 9

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 31.28 -95.3 -95.3 93.1 93.1 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 18.71 -57.0 347.3 55.7 7.4 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -25.61 1.11 0.00 -98.9 248.4 12.5 19.9 12.5 12.5 24.7 24.7 C

Asfal + Parapeto 0.00 0.00 18.82 -46.8 201.6 27.1 47.0 27.1 39.6 35.2 59.8 O

Carga viva + I 0.00 0.00 31.44 -78.1 123.5 45.3 92.3 45.3 84.9 58.8 118.6 M










275




w

40.00








H = 1.8300 m H = 2.0300 mts. As* = 7.05 cm² 5 5

Ix = 0.3038 m4Ix = 0.4662 m4

e losa = 20.00 cm 10 0






Po.Po Viga 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I


Losa 0.00 0.00 0.00 0.0 395.4 0.0 -111.8 0.0 0.0 0.0 0.0 P

100% Pd.Dif.1a. -20.26 1.11 0.00 -78.3 317.1 9.9 -101.9 9.9 9.9 19.5 19.5 C

Asfal + Parapeto 0.00 0.00 0.00 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 O

Carga viva + I 0.00 0.00 0.01 0.0 317.1 0.0 -101.9 0.0 9.9 0.0 19.5 M










276



x en metros 0.915 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

MCM 68.81 134.28 253.26 387.02 432.94 555.14 618.91 679.74 713.31 733.44 740.18

MCV 31.44 62.88 132.60 181.07 221.76 257.07 288.25 318.49 332.24 341.36 345.87

MU en ton-m 157.57 310.80 616.54 895.43 1043.30 1278.66 1429.12 1573.71 1647.15 1693.08 1711.63

VCM 70.49 66.95 58.12 51.09 44.04 36.97 29.94 21.12 14.08 7.02 0.00

VCV 35.24 34.12 31.32 29.08 26.84 24.60 22.36 19.56 17.31 15.07 12.83

VU en ton 167.99 160.95 143.41 129.42 115.39 101.35 87.36 69.83 55.81 41.78 27.80

VC 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86

VU-VC 130.14 123.11 105.96 92.28 78.45 64.76 50.95 33.71 19.82 5.92 -8.06

E#3@ 5.84 6.18 7.18 8.24 9.69 11.74 14.92 22.56 38.36 128.38 -94.39

bw de trabe 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

d trabe 198.00 198.00 195.95 194.29 193.27 191.48 190.50 189.02 188.32 187.62 187.62

Vud/Mu <= 1.0 1.00 1.00 0.46 0.28 0.21 0.15 0.12 0.08 0.06 0.05 0.03

Vc = f0.53*raiz(f́ c)bwd 37.84 37.84 37.45 37.13 36.94 36.60 36.41 36.13 35.99 35.86 35.86


f1.3 raiz(f́ c)bwd 92.82 92.82 91.87 91.09 90.61 89.77 89.31 88.61 88.29 87.96 87.96

VC considerado 92.82 92.82 85.71 56.66 45.57 36.60 36.41 36.13 35.99 35.86 35.86

VS = VU-VC 75.16 68.13 57.70 72.76 69.83 64.76 50.95 33.71 19.82 5.92 0.01






277


5.- ESTRUCTURACION DE LAS COLUMNAS

5.1- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA EL EJE 1

DATOSFyacer= 4200 kg/cm²Eacer= 2034000 kg/cm² No. De var. = 40 CENT PLAST = 75

RADIO INT= 0 cms SEP. VARS.= 10.68 cms ANG. Z. CONC.= 47.86235954 grados DIST= 24.6816 cmsRADIO EXT= 75 cms ANG. SUBT.= 9.000 grados COSENO= 0.670912467

ESPESOR= 75 cms recubrimiento = 7 cms SENO= 0.741536555DIAM. EXT= 150 cms No. DE CAPAS= 10.000023 TANG= 0.904766482

f'c= 250 kg/cm² RADIO ACERO= 68 cmsf*c= 212.5 kg/cm² AREA CONC= 17671.5 cm²ø = 1 75

POSIC DE EJE NEUTRO PROPUESTO PAXIAL PURA= 4564 ton 3651.087PORCENTAJE DE LA ALTURA = 0.193580902

C= 29.037 SUMA DE MOMENTOS= 492.986 m-t. % ACERO1.147610559 0.0114761

Porcen As = 0.0115 As= 202.8 PNORMAL= 0.000 TON

ACERO AREA di defsi defadm ESFi F Dcgeom M MCEP ANGULO

1 5.070 7.000 0.002 0.002 4068.000 20624.760 68.000 1402483.680 35.490 0.000 12 10.140 7.837 0.002 0.002 4068.000 41249.520 67.163 2770433.718 79.469 9.000 33 10.140 10.328 0.002 0.002 3931.596 39866.382 64.672 2578233.007 104.727 18.000 54 10.140 14.412 0.002 0.002 3073.495 31165.239 60.588 1888254.408 146.133 27.000 75 10.140 19.987 0.001 0.001 1901.883 19285.093 55.013 1060934.979 202.666 36.000 96 10.140 26.917 0.000 0.000 445.609 4518.471 48.083 217263.240 272.935 45.000 117 10.140 35.030 -0.001 -0.001 -1259.470 -12771.025 39.970 -510451.728 355.209 54.000 138 10.140 44.128 -0.002 -0.002 -3171.368 -32157.674 30.872 -992755.937 447.463 63.000 159 10.140 53.987 -0.003 -0.002 -4068.000 -41249.520 21.013 -866790.422 547.425 72.000 17

10 10.140 64.362 -0.004 -0.002 -4068.000 -41249.520 10.638 -438802.727 652.633 81.000 1911 10.140 75.000 -0.005 -0.002 -4068.000 -41249.520 0.000 -10.303 760.497 90.000 2112 10.140 85.637 -0.006 -0.002 -4068.000 -41249.520 -10.637 438782.374 868.362 99.000 2313 10.140 96.013 -0.007 -0.002 -4068.000 -41249.520 -21.013 866770.824 973.571 108.000 2514 10.140 105.871 -0.008 -0.002 -4068.000 -41249.520 -30.871 1273416.599 1073.533 117.000 2715 10.140 114.969 -0.009 -0.002 -4068.000 -41249.520 -39.969 1648706.778 1165.787 126.000 2916 10.140 123.083 -0.010 -0.002 -4068.000 -41249.520 -48.083 1983400.513 1248.062 135.000 3117 10.140 130.013 -0.010 -0.002 -4068.000 -41249.520 -55.013 2269256.573 1318.331 144.000 3318 10.140 135.588 -0.011 -0.002 -4068.000 -41249.520 -60.588 2499236.266 1374.865 153.000 3519 10.140 139.672 -0.011 -0.002 -4068.000 -41249.520 -64.672 2667676.755 1416.271 162.000 3720 10.140 142.163 -0.012 -0.002 -4068.000 -41249.520 -67.163 2770430.495 1441.530 171.000 3921 5.070 143.000 -0.012 -0.002 -4068.000 -20624.760 -68.000 1402483.680 725.010 180.000 40

DIAGRAMAS DE INTERACCION DE COLUMNAS CIRCULARES


A n á l i s i s d e l a s P i l a sCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

278


Pu = 210.930 ton f'c = 250 kg/cm2Mux = 15.090 ton-m fy = 4200 kg/cm2Muy = 124.290 ton-m

Vux = 32.940 ton-m 1550 cmVuy = 1.561 ton-m

excentricidad accidentalecx = 0.060 mecy = 0.060 m

150transversal longitudinal

Se revisa por relación de esbeltez M1 = 1 M1 = 1M2 = 1 M2 = 1 Rec: 7 cm

Se desprecian los efectos por relación de esbeltez si se cumple con lo siguiente:

klur PROPIEDADES

sentido transversal A = cm2 1.767 m2

klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m

sentido longitudinal Ec= kg/cm2 ########## ton/m2

klu 1.2 x Armado: 40 Varillas

r

Calculo del factor de amplificacion de momentos

ø = 0.7

Pu cm = 210.93

Pc = tPc = t

d sx= 1.018d sy = 1.018

Pu = 210.930 ton

Mux = 28.070 ton-m 142.05 <-- MOMENTO PARA DISEÑOMuy = 139.249 ton-m

MuR= 142.050 ton-m

Vux = 32.940 ton-m

Vuy = 1.561 ton-m

Revisión por flexión

si

si

< 34 - (12M1/M2)

CM+SISX+0.33SISY Q=2 Mu

17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=

37.500Se considera la relación de esbeltez

=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963

Se considera la relación de esbeltez

Elementos Amplificados

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



279


My si Pu> 0.1f'cAg 0.7 Fr a utilizar = 0.805

Mx si Pu< 0.1f'cAg 0.9 Fr = 0.805

0.1 f'c Ag = 441,786 > Pu= kg

Datos para la grafica de interacción

M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

142.050 210.930

899.17 1335.168

Línea de carga máxima0 2909.5

899.2 2909.5

Pu MR

210.93 880

Mux Muy 142.05ø Mrx ø Mry 707.97

Revisión por cortanteNo de ramas = 2

El cortante que toma el concreto es: vars # 4Area: 1.2668

Vu = 1.56 ton Vc = 125.87 ton Vc > Vu, o.k.

Vu-Vc = ton Vsmax= 88,014 ton

No es necesario el refuerzo por cortante s = acero minimo cm

Línea de proyeccion:

210,930

Ec No. 2:

DEL DIAGRAMA DE INTERACCIÓN:

0.201 < 1.00

-124.3

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)

Diagrama de interacción

bdfV cc'53.0 f



280


Pu = 211.032 ton

Mux = 15.320 ton-m f'c = 250 kg/cm2Muy = 413.900 ton-m fy = 4200 kg/cm2Vux = 109.710 ton-m

Vuy = 1.528 ton-m 1550 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 211.03

Pc = tPc = t

d sx= 1.018d sy = 1.018

Pu = 211.032 ton


MuR= 435.040 ton-m

Vux = 109.710 ton-m

Vuy = 1.528 ton-m


si

si

< 34 - (12M1/M2)

CM+0.33SISX+SISY Q=2 M

17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=


=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963



bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



281


FrMy si Pu> 0.1f'cAg 0.7 Fr a utilizar = 0.804

Mx si Pu< 0.1f'cAg 0.9 Fr = 0.804

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

435.040 211.032

899.17 436.171


899.2 2909.5

Pu MR

211.03 620


La ecuación No. 1 no aplica Mu PR PO Pmáx

435.04 1322 4564 2909

11 1 SE ACEPTA EL ARMADO

1063.502 3671.5 La sección trabaja a un : 14 %







211,032

Ec No. 2:

Ec No. 1:



0.872 < 1.00

-124.3

-

1497

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



282


Pu = 446.570 ton


Vuy = 3.450 ton-m 1550 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 446.57

Pc = tPc = t

d sx= 1.039d sy = 1.039

Pu = 446.570 ton


MuR= 70.296 ton-m

Vux = 0.000 ton-m

Vuy = 3.450 ton-m


si

si

< 34 - (12M1/M2)

1.3(CM + 5/3 CV + i ) Q=2 M

17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=


=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963



bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



283



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.700

0.1 f'c Ag = 441,786 < Pu= kg


M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

70.296 446.570

899.17 5712.109


899.2 2909.5

La ecuación No. 2 no aplicaPu MR

446.57 380


Revisión por cortante

No de ramas = 2El cortante que toma el concreto es: vars # 4

Area: 1.2668Vu = 3.45 ton Vc = 125.87 ton Vc > Vu, o.k.




446,570

Ec No. 2:


0.264 < 1.00

-122.4

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

7,000.0

-100 0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



284


5.2- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA LAS COLUMNAS DEL EJE 2



285


DATOS

Fyacer= 4200 kg/cm²

Eacer= 2034000 kg/cm² No. De var. = 86 CENT PLAST = 75

RADIO INT= 0 cms SEP. VARS.= 4.97 cms ANG. Z. CONC.= 56.85877946 grados DIST= 33.9973 cms

RADIO EXT= 75 cms ANG. SUBT.= 4.186 grados COSENO= 0.54670256ESPESOR= 75 cms recubrimiento = 7 cms SENO= 0.837326884

DIAM. EXT= 150 cms No. DE CAPAS= 21.5000503 TANG= 0.652919376

f'c= 250 kg/cm² RADIO ACERO= 68 cmsf*c= 212.5 kg/cm² AREA CONC= 17671.5 cm²

ø = 1 75POSIC DE EJE NEUTRO PROPUESTO PAXIAL PURA= 5494 ton 4395.0588PORCENTAJE DE LA ALTURA = 0.266645553




1 5.070 7.000 0.002 0.002 4068.000 20624.760 68.000 1402483.680 35.490 0.000 12 10.140 7.181 0.002 0.002 4068.000 41249.520 67.819 2797484.538 72.819 4.186 33 10.140 7.725 0.002 0.002 4068.000 41249.520 67.275 2775075.995 78.328 8.372 54 10.140 8.627 0.002 0.002 4068.000 41249.520 66.373 2737861.290 87.476 12.558 75 10.140 9.883 0.002 0.002 4068.000 41249.520 65.117 2686038.979 100.215 16.744 96 10.140 11.487 0.002 0.002 4068.000 41249.520 63.513 2619885.555 116.477 20.930 117 10.140 13.429 0.002 0.002 4053.169 41099.134 61.571 2530494.635 136.175 25.116 138 10.140 15.701 0.002 0.002 3706.684 37585.773 59.299 2228813.784 159.204 29.302 159 10.140 18.288 0.002 0.002 3311.930 33582.969 56.712 1904554.076 185.441 33.488 17

10 10.140 21.178 0.001 0.001 2871.014 29112.078 53.822 1566865.168 214.747 37.674 1911 10.140 24.355 0.001 0.001 2386.287 24196.954 50.645 1225444.724 246.964 41.860 2112 10.140 27.803 0.001 0.001 1860.337 18863.822 47.197 890318.385 281.921 46.046 2313 10.140 31.502 0.001 0.001 1295.970 13141.135 43.498 571611.427 319.432 50.232 2514 10.140 35.433 0.000 0.000 696.196 7059.427 39.567 279317.041 359.295 54.418 2715 10.140 39.576 0.000 0.000 64.216 651.147 35.424 23066.276 401.300 58.605 2916 10.140 43.907 0.000 0.000 -596.599 -6049.516 31.093 -188095.381 445.221 62.791 3117 10.140 48.405 -0.001 -0.001 -1282.723 -13006.810 26.595 -345919.914 490.824 66.977 3318 10.140 53.044 -0.001 -0.001 -1990.495 -20183.616 21.956 -443152.562 537.866 71.163 3519 10.140 57.800 -0.001 -0.001 -2716.138 -27541.641 17.200 -473707.202 586.095 75.349 3720 10.140 62.648 -0.002 -0.002 -3455.782 -35041.629 12.352 -432817.481 635.256 79.535 3921 10.140 67.563 -0.002 -0.002 -4068.000 -41249.520 7.437 -306792.196 685.084 83.721 4122 10.140 72.516 -0.002 -0.002 -4068.000 -41249.520 2.484 -102453.139 735.315 87.907 4323 10.140 77.483 -0.003 -0.002 -4068.000 -41249.520 -2.483 102432.547 785.680 92.093 4524 10.140 82.437 -0.003 -0.002 -4068.000 -41249.520 -7.437 306771.714 835.911 96.279 4725 10.140 87.351 -0.004 -0.002 -4068.000 -41249.520 -12.351 509474.128 885.739 100.465 4926 10.140 92.199 -0.004 -0.002 -4068.000 -41249.520 -17.199 709458.291 934.900 104.651 5127 10.140 96.956 -0.004 -0.002 -4068.000 -41249.520 -21.956 905657.204 983.130 108.837 5328 10.140 101.595 -0.005 -0.002 -4068.000 -41249.520 -26.595 1097024.067 1030.172 113.023 5529 10.140 106.092 -0.005 -0.002 -4068.000 -41249.520 -31.092 1282537.859 1075.775 117.209 5730 10.140 110.424 -0.005 -0.002 -4068.000 -41249.520 -35.424 1461208.789 1119.696 121.395 5931 10.140 114.566 -0.006 -0.002 -4068.000 -41249.520 -39.566 1632083.574 1161.700 125.581 6132 10.140 118.497 -0.006 -0.002 -4068.000 -41249.520 -43.497 1794250.528 1201.565 129.767 6333 10.140 122.197 -0.006 -0.002 -4068.000 -41249.520 -47.197 1946844.423 1239.075 133.953 6534 10.140 125.644 -0.006 -0.002 -4068.000 -41249.520 -50.644 2089051.110 1274.033 138.139 6735 10.140 128.822 -0.007 -0.002 -4068.000 -41249.520 -53.822 2220111.857 1306.250 142.325 6936 10.140 131.712 -0.007 -0.002 -4068.000 -41249.520 -56.712 2339327.403 1335.556 146.511 7137 10.140 134.299 -0.007 -0.002 -4068.000 -41249.520 -59.299 2446061.683 1361.793 150.697 7338 10.140 136.570 -0.007 -0.002 -4068.000 -41249.520 -61.570 2539745.226 1384.823 154.883 7539 10.140 138.513 -0.007 -0.002 -4068.000 -41249.520 -63.513 2619878.193 1404.521 159.069 7740 10.140 140.117 -0.008 -0.002 -4068.000 -41249.520 -65.117 2686033.042 1420.783 163.255 7941 10.140 141.373 -0.008 -0.002 -4068.000 -41249.520 -66.373 2737856.810 1433.523 167.441 8142 10.140 142.275 -0.008 -0.002 -4068.000 -41249.520 -67.275 2775072.994 1442.671 171.628 8343 10.140 142.819 -0.008 -0.002 -4068.000 -41249.520 -67.819 2797483.033 1448.180 175.814 8544 5.070 143.000 -0.008 -0.002 -4068.000 -20624.760 -68.000 1402483.680 725.010 180.000 86




286








klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 358.91

Pc = tPc = t

d sx= 1.031d sy = 1.031

Pu = 358.910 ton


MuR= 260.353 ton-m

Vux = 36.500 ton-m

Vuy = 3.300 ton-m


si

si

16,92616,926

( 1 )

( 2 )

37.500

238751.963




=1550.0

= 49.60 > 22.038

> 22.038

=1550.0

=

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76449.60

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



287



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.738

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

260.353 358.910

1269.16 1749.601


1269.2 3502.3

Pu MR

358.91 1260







0.280 < 1.00

-122.6

+ = =Ec No. 2:



358,910

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



288


Pu = 359.060 ton


Vuy = 3.360 ton-m 2150 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 359.06

Pc = tPc = t

d sx= 1.062d sy = 1.062

Pu = 359.060 ton


MuR= 821.687 ton-m

Vux = 121.260 ton-m

Vuy = 3.360 ton-m


si

si

8,7978,797

( 1 )

( 2 )

37.500

238751.963




=2150.0

= 68.80 > 22.038

> 22.038

=2150.0

=

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76468.80

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



289



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.737

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

821.687 359.060

1269.16 554.595


1269.2 3502.3

Pu MR

359.06 1120



821.69 1322 5494 3502








0.995 < 1.00

-122.5

-

1284

+ = =Ec No. 2:

Ec No. 1:




359,060

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



290


Pu = 808.398 ton


Vuy = 7.980 ton-m 2150 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 808.40

Pc = tPc = t

d sx= 1.151d sy = 1.151

Pu = 808.398 ton


MuR= 149.178 ton-m

Vux = 0.000 ton-m

Vuy = 7.980 ton-m


si

si

8,7978,797

( 1 )

( 2 )

37.500

238751.963




=2150.0

= 68.80 > 22.038

> 22.038

=2150.0

=

< 34 - (12M1/M2)

1.3(CM + 5/3 CV + i ) Q=2 M

17671.459

SECCION

24850488.764

24850488.76468.80

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



291



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.700

0.1 f'c Ag = 441,786 < Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

149.178 808.398

1269.16 6877.581


1269.2 3502.3


808.40 740







0.288 < 1.00

-117.9

+ = =Ec No. 2:



808,398

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

7,000.0

8,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



292


5.3- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA LAS COLUMNAS DEL EJE 3

DATOS

Fyacer= 4200 kg/cm²

Eacer= 2034000 kg/cm² No. De var. = 86 CENT PLAST = 75

RADIO INT= 0 cms SEP. VARS.= 4.97 cms ANG. Z. CONC.= 56.85877946 grados DIST= 33.9973 cms

RADIO EXT= 75 cms ANG. SUBT.= 4.186 grados COSENO= 0.54670256ESPESOR= 75 cms recubrimiento = 7 cms SENO= 0.837326884

DIAM. EXT= 150 cms No. DE CAPAS= 21.5000503 TANG= 0.652919376

f'c= 250 kg/cm² RADIO ACERO= 68 cmsf*c= 212.5 kg/cm² AREA CONC= 17671.5 cm²

ø = 1 75POSIC DE EJE NEUTRO PROPUESTO PAXIAL PURA= 5494 ton 4395.0588PORCENTAJE DE LA ALTURA = 0.266645553




1 5.070 7.000 0.002 0.002 4068.000 20624.760 68.000 1402483.680 35.490 0.000 12 10.140 7.181 0.002 0.002 4068.000 41249.520 67.819 2797484.538 72.819 4.186 33 10.140 7.725 0.002 0.002 4068.000 41249.520 67.275 2775075.995 78.328 8.372 54 10.140 8.627 0.002 0.002 4068.000 41249.520 66.373 2737861.290 87.476 12.558 75 10.140 9.883 0.002 0.002 4068.000 41249.520 65.117 2686038.979 100.215 16.744 96 10.140 11.487 0.002 0.002 4068.000 41249.520 63.513 2619885.555 116.477 20.930 117 10.140 13.429 0.002 0.002 4053.169 41099.134 61.571 2530494.635 136.175 25.116 138 10.140 15.701 0.002 0.002 3706.684 37585.773 59.299 2228813.784 159.204 29.302 159 10.140 18.288 0.002 0.002 3311.930 33582.969 56.712 1904554.076 185.441 33.488 17

10 10.140 21.178 0.001 0.001 2871.014 29112.078 53.822 1566865.168 214.747 37.674 1911 10.140 24.355 0.001 0.001 2386.287 24196.954 50.645 1225444.724 246.964 41.860 2112 10.140 27.803 0.001 0.001 1860.337 18863.822 47.197 890318.385 281.921 46.046 2313 10.140 31.502 0.001 0.001 1295.970 13141.135 43.498 571611.427 319.432 50.232 2514 10.140 35.433 0.000 0.000 696.196 7059.427 39.567 279317.041 359.295 54.418 2715 10.140 39.576 0.000 0.000 64.216 651.147 35.424 23066.276 401.300 58.605 2916 10.140 43.907 0.000 0.000 -596.599 -6049.516 31.093 -188095.381 445.221 62.791 3117 10.140 48.405 -0.001 -0.001 -1282.723 -13006.810 26.595 -345919.914 490.824 66.977 3318 10.140 53.044 -0.001 -0.001 -1990.495 -20183.616 21.956 -443152.562 537.866 71.163 3519 10.140 57.800 -0.001 -0.001 -2716.138 -27541.641 17.200 -473707.202 586.095 75.349 3720 10.140 62.648 -0.002 -0.002 -3455.782 -35041.629 12.352 -432817.481 635.256 79.535 3921 10.140 67.563 -0.002 -0.002 -4068.000 -41249.520 7.437 -306792.196 685.084 83.721 4122 10.140 72.516 -0.002 -0.002 -4068.000 -41249.520 2.484 -102453.139 735.315 87.907 4323 10.140 77.483 -0.003 -0.002 -4068.000 -41249.520 -2.483 102432.547 785.680 92.093 4524 10.140 82.437 -0.003 -0.002 -4068.000 -41249.520 -7.437 306771.714 835.911 96.279 4725 10.140 87.351 -0.004 -0.002 -4068.000 -41249.520 -12.351 509474.128 885.739 100.465 4926 10.140 92.199 -0.004 -0.002 -4068.000 -41249.520 -17.199 709458.291 934.900 104.651 5127 10.140 96.956 -0.004 -0.002 -4068.000 -41249.520 -21.956 905657.204 983.130 108.837 5328 10.140 101.595 -0.005 -0.002 -4068.000 -41249.520 -26.595 1097024.067 1030.172 113.023 5529 10.140 106.092 -0.005 -0.002 -4068.000 -41249.520 -31.092 1282537.859 1075.775 117.209 5730 10.140 110.424 -0.005 -0.002 -4068.000 -41249.520 -35.424 1461208.789 1119.696 121.395 5931 10.140 114.566 -0.006 -0.002 -4068.000 -41249.520 -39.566 1632083.574 1161.700 125.581 6132 10.140 118.497 -0.006 -0.002 -4068.000 -41249.520 -43.497 1794250.528 1201.565 129.767 6333 10.140 122.197 -0.006 -0.002 -4068.000 -41249.520 -47.197 1946844.423 1239.075 133.953 6534 10.140 125.644 -0.006 -0.002 -4068.000 -41249.520 -50.644 2089051.110 1274.033 138.139 6735 10.140 128.822 -0.007 -0.002 -4068.000 -41249.520 -53.822 2220111.857 1306.250 142.325 6936 10.140 131.712 -0.007 -0.002 -4068.000 -41249.520 -56.712 2339327.403 1335.556 146.511 7137 10.140 134.299 -0.007 -0.002 -4068.000 -41249.520 -59.299 2446061.683 1361.793 150.697 7338 10.140 136.570 -0.007 -0.002 -4068.000 -41249.520 -61.570 2539745.226 1384.823 154.883 7539 10.140 138.513 -0.007 -0.002 -4068.000 -41249.520 -63.513 2619878.193 1404.521 159.069 7740 10.140 140.117 -0.008 -0.002 -4068.000 -41249.520 -65.117 2686033.042 1420.783 163.255 7941 10.140 141.373 -0.008 -0.002 -4068.000 -41249.520 -66.373 2737856.810 1433.523 167.441 8142 10.140 142.275 -0.008 -0.002 -4068.000 -41249.520 -67.275 2775072.994 1442.671 171.628 8343 10.140 142.819 -0.008 -0.002 -4068.000 -41249.520 -67.819 2797483.033 1448.180 175.814 8544 5.070 143.000 -0.008 -0.002 -4068.000 -20624.760 -68.000 1402483.680 725.010 180.000 86




293








klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 358.91

Pc = tPc = t

d sx= 1.031d sy = 1.031

Pu = 358.910 ton


MuR= 260.353 ton-m

Vux = 36.500 ton-m

Vuy = 3.300 ton-m


si

si

16,92616,926

( 1 )

( 2 )

37.500

238751.963




=1550.0

= 49.60 > 22.038

> 22.038

=1550.0

=

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76449.60

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



294



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.738

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

260.353 358.910

1269.16 1749.601


1269.2 3502.3

Pu MR

358.91 1260







0.280 < 1.00

-122.6

+ = =Ec No. 2:



358,910

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



295


Pu = 359.060 ton


Vuy = 3.360 ton-m 2150 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 359.06

Pc = tPc = t

d sx= 1.062d sy = 1.062

Pu = 359.060 ton


MuR= 821.687 ton-m

Vux = 121.260 ton-m

Vuy = 3.360 ton-m


si

si

8,7978,797

( 1 )

( 2 )

37.500

238751.963




=2150.0

= 68.80 > 22.038

> 22.038

=2150.0

=

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76468.80

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



296




297



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.737

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

821.687 359.060

1269.16 554.595


1269.2 3502.3

Pu MR

359.06 1120



821.69 1322 5494 3502








0.995 < 1.00

-122.5

-

1284

+ = =Ec No. 2:

Ec No. 1:




359,060

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



298


Pu = 808.398 ton


Vuy = 7.980 ton-m 2150 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 808.40

Pc = tPc = t

d sx= 1.151d sy = 1.151

Pu = 808.398 ton


MuR= 149.178 ton-m

Vux = 0.000 ton-m

Vuy = 7.980 ton-m


si

si

8,7978,797

( 1 )

( 2 )

37.500

238751.963




=2150.0

= 68.80 > 22.038

> 22.038

=2150.0

=

< 34 - (12M1/M2)

1.3(CM + 5/3 CV + i ) Q=2 M

17671.459

SECCION

24850488.764

24850488.76468.80

bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



299



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.700

0.1 f'c Ag = 441,786 < Pu= kg


M, (t-m) P, (t)

425.236 -1120.120

798.591 -424.501

974.334 0.000

###### 212.181

1205.26 855.510

1269.16 1520.352

1204.26 2247.957

1064.52 2949.681

901.88 3560.065

715.963 4091.800

516.478 4543.762

0.000 5493.824

0.000 0.000

149.178 808.398

1269.16 6877.581


1269.2 3502.3


808.40 740







0.288 < 1.00

-117.9

+ = =Ec No. 2:



808,398

-2,000.0

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

7,000.0

8,000.0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



300


5.4- ESTRUCTURACION DE LAS COLUMNAS DE 1.5 MTS. PARA EL EJE 4

DATOSFyacer= 4200 kg/cm²Eacer= 2034000 kg/cm² No. De var. = 40 CENT PLAST = 75

RADIO INT= 0 cms SEP. VARS.= 10.68 cms ANG. Z. CONC.= 47.86235954 grados DIST= 24.6816 cmsRADIO EXT= 75 cms ANG. SUBT.= 9.000 grados COSENO= 0.670912467

ESPESOR= 75 cms recubrimiento = 7 cms SENO= 0.741536555DIAM. EXT= 150 cms No. DE CAPAS= 10.000023 TANG= 0.904766482

f'c= 250 kg/cm² RADIO ACERO= 68 cmsf*c= 212.5 kg/cm² AREA CONC= 17671.5 cm²ø = 1 75

POSIC DE EJE NEUTRO PROPUESTO PAXIAL PURA= 4564 ton 3651.087PORCENTAJE DE LA ALTURA = 0.193580902




1 5.070 7.000 0.002 0.002 4068.000 20624.760 68.000 1402483.680 35.490 0.000 12 10.140 7.837 0.002 0.002 4068.000 41249.520 67.163 2770433.718 79.469 9.000 33 10.140 10.328 0.002 0.002 3931.596 39866.382 64.672 2578233.007 104.727 18.000 54 10.140 14.412 0.002 0.002 3073.495 31165.239 60.588 1888254.408 146.133 27.000 75 10.140 19.987 0.001 0.001 1901.883 19285.093 55.013 1060934.979 202.666 36.000 96 10.140 26.917 0.000 0.000 445.609 4518.471 48.083 217263.240 272.935 45.000 117 10.140 35.030 -0.001 -0.001 -1259.470 -12771.025 39.970 -510451.728 355.209 54.000 138 10.140 44.128 -0.002 -0.002 -3171.368 -32157.674 30.872 -992755.937 447.463 63.000 159 10.140 53.987 -0.003 -0.002 -4068.000 -41249.520 21.013 -866790.422 547.425 72.000 17

10 10.140 64.362 -0.004 -0.002 -4068.000 -41249.520 10.638 -438802.727 652.633 81.000 1911 10.140 75.000 -0.005 -0.002 -4068.000 -41249.520 0.000 -10.303 760.497 90.000 2112 10.140 85.637 -0.006 -0.002 -4068.000 -41249.520 -10.637 438782.374 868.362 99.000 2313 10.140 96.013 -0.007 -0.002 -4068.000 -41249.520 -21.013 866770.824 973.571 108.000 2514 10.140 105.871 -0.008 -0.002 -4068.000 -41249.520 -30.871 1273416.599 1073.533 117.000 2715 10.140 114.969 -0.009 -0.002 -4068.000 -41249.520 -39.969 1648706.778 1165.787 126.000 2916 10.140 123.083 -0.010 -0.002 -4068.000 -41249.520 -48.083 1983400.513 1248.062 135.000 3117 10.140 130.013 -0.010 -0.002 -4068.000 -41249.520 -55.013 2269256.573 1318.331 144.000 3318 10.140 135.588 -0.011 -0.002 -4068.000 -41249.520 -60.588 2499236.266 1374.865 153.000 3519 10.140 139.672 -0.011 -0.002 -4068.000 -41249.520 -64.672 2667676.755 1416.271 162.000 3720 10.140 142.163 -0.012 -0.002 -4068.000 -41249.520 -67.163 2770430.495 1441.530 171.000 3921 5.070 143.000 -0.012 -0.002 -4068.000 -20624.760 -68.000 1402483.680 725.010 180.000 40




301








klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 210.93

Pc = tPc = t

d sx= 1.018d sy = 1.018

Pu = 210.930 ton


MuR= 142.050 ton-m

Vux = 32.940 ton-m

Vuy = 1.561 ton-m


si

si

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=


=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963



bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



302


My si Pu> 0.1f'cAg 0.7 Fr a utilizar = 0.805

Mx si Pu< 0.1f'cAg 0.9 Fr = 0.805

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

142.050 210.930

899.17 1335.168


899.2 2909.5

Pu MR

210.93 880








210,930

Ec No. 2:


0.201 < 1.00

-124.3

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



303


Pu = 211.032 ton


Vuy = 1.528 ton-m 1550 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 211.03

Pc = tPc = t

d sx= 1.018d sy = 1.018

Pu = 211.032 ton


MuR= 435.040 ton-m

Vux = 109.710 ton-m

Vuy = 1.528 ton-m


si

si

< 34 - (12M1/M2)


17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=


=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963



bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



304



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.804

0.1 f'c Ag = 441,786 > Pu= kg


M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

435.040 211.032

899.17 436.171


899.2 2909.5

Pu MR

211.03 620



435.04 1322 4564 2909









211,032

Ec No. 2:

Ec No. 1:



0.872 < 1.00

-124.3

-

1497

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



305


Pu = 446.570 ton


Vuy = 3.450 ton-m 1550 cm





klur PROPIEDADES


klu 1.2 x Ix = cm4 0.249 m4

r Iy = cm4 0.249 m4

rx = cm 0.375 m

ry = cm 0.375 m



r


ø = 0.7

Pu cm = 446.57

Pc = tPc = t

d sx= 1.039d sy = 1.039

Pu = 446.570 ton


MuR= 70.296 ton-m

Vux = 0.000 ton-m

Vuy = 3.450 ton-m


si

si

< 34 - (12M1/M2)

1.3(CM + 5/3 CV + i ) Q=2 M

17671.459

SECCION

24850488.764

24850488.76449.60 > 22.0

38=

1550.0=


=1550.0

= 49.60 > 22.038

16,92616,926

( 1 )

( 2 )

37.500

238751.963



bsc MM 2

0.11

1

c

us

P

P

f

2

2

u

ckl

EIP

gcu AfP '1.0

gcu AfP '1.0

0

1111

PPP

P

nynx

nxy

0.1ny

ny

nx

ux

M

M

M

M

ff



306



Mx si Pu< 0.1f'cAg 0.9 Fr = 0.700

0.1 f'c Ag = 441,786 < Pu= kg


M, (t-m) P, (t)

253.477 -438.303

492.986 0.000

507.285 29.786

698.797 501.352

832.68 1001.000

899.17 1520.350

879.54 2075.272

797.80 2618.104

678.99 3110.104

528.005 3552.146

356.618 3932.920

0.000 4563.859

0.000 0.000

70.296 446.570

899.17 5712.109


899.2 2909.5


446.57 380








446,570

Ec No. 2:


0.264 < 1.00

-122.4

+ = =

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

7,000.0

-100 0 100 200 300 400 500 600 700 800 900 1000

Ca

rga

ax

ial (

t)

Momento (t-m)


bdfV cc'53.0 f



307




308


6 - ESTRUCTURACION DE CABEZALES6.1 - ESTRUCTURACION DE CABEZAL PARA EL EJE 1


A n á l i s i s d e l a s C a b e z a l e sCALLE VALLE DEL TARIM # 131, COL. VALLE DE ARAGON 3A SECCION ECATEPEC, EDO. DE MEXICO TEL. 01 (442)3911131

309


t-m t-m

Acero mínimo

Barras del No @ se usará 23 cm

Momento resistente

> Mu, OK

f

0.90

As = cm2

Momento ultimo ton-m/m

80.56 94.10

Acero requerido por momento último

cm2

A min = cm2

6

2.651

170.00

127.731 153.277

7.916 0.002

36.741

4.160 0.001

19.133

19.133 Rige el acero mínimo

1.2Mcr =

t-m

6

95.822cm

Con barras del No.

Momento de agrietamiento y acero mínimo

170.00 120.00 7.50 112.50 250.00

h cm

r cm

d cm

f 'C

kg/cm²fy

kg/cm²

4200

Cortante ultimo ton/m

120.00

b cm

23

REVISIÓN DEL ACERO EN EL CABEZAL

As UNA BARRA

cm²

2.850

No de barras

8

As cm²

22.802

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



310


El cortante que toma el concreto: f =

Cortante que tomará el acero

Revisando el acero mínimo

VS = Vu - VC =

s = cm

Se proponen a cada

0.85

136.228

0.000

2.85

0.000

Requiere el mínimo: 80.48

64

REVISIÓN POR CORTANTE

t

t

0.142

30 cm

Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS

No ramas Barras del No AV

cm²

Menor que el mínimo

bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



311


t-m t-m

Acero mínimo

Barras del No @ 37 se usará 37 cm

Momento resistente

163.00 250.00




f b

cmh

cmr

cmd cm

f 'C

kg/cm²fy

kg/cm²

420011.66 9.85 0.90 120.00 170.00 7.00

0.406 0.000


7.567

170.00

120.00

0.002

A min = 35.893 cm2

180.952 1.2Mcr = 217.142

1.894 cm2

As = 1.894 cm2

Rige el acero mínimo

69.841 t-m

Con barras del No.

As UNA BARRA

cm²No de barras

As cm²

6 2.850 4 11.401


> Mu, OK

6

1.878 cm Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



312





VS = Vu - VC =

s = cm

Se proponen a cada

0.100

0.000 t


cm²

0.000 Menor que el mínimo

30 cm

4 6 2.85



0.85

139.326 t Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



313


6.2 - ESTRUCTURACION DE CABEZAL PARA EL EJE 2



314


t-m t-m

Acero mínimo


Momento resistente

> Mu, OK

23


As UNA BARRA

cm²

5.067

No de barras

8

As cm²

40.537

Con barras del No.


170.00 120.00 7.50 112.50 250.00

h cm

r cm

d cm

f 'C

kg/cm²fy

kg/cm²

4200


120.00

b cm

168.771cm

8

4.713

170.00

127.731 153.277

7.916 0.002

36.741

7.749 0.002

35.955


1.2Mcr =

t-m

8

f

0.90

As = cm2


150.06 177.80


cm2

A min = cm2

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



315





VS = Vu - VC =

s = cm

30 cm

Vu > Vc; NO CUMPLE, REQUIERE ESTRIBOS


cm²


Se proponen a cada

0.85

136.228

41.572

2.85

0.104


64


t

t

0.142

bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



316


t-m t-m

Acero mínimo


Momento resistente


> Mu, OK

6

2.347 cm


87.175 t-m

Con barras del No.

As UNA BARRA

cm²No de barras

As cm²

6 2.850 5 14.251

11.642 cm2

As = 11.642 cm2

120.00 170.00 7.00

2.485 0.001


7.567

170.00

120.00

0.002

A min = 35.893 cm2

180.952 1.2Mcr = 217.142

163.00 250.00




f b

cmh

cmr

cmd cm

f 'C

kg/cm²fy

kg/cm²

420071.31 60.98 0.90

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



317





VS = Vu - VC =

s = cm

4 6 2.85



0.85

139.326 t Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS

Se proponen a cada

0.100

0.000 t


cm²


30 cm

bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



318




319



t-m t-m

Acero mínimo


Momento resistente

> Mu, OK

23


As UNA BARRA

cm²

5.067

No de barras

8

As cm²

40.537

Con barras del No.


170.00 120.00 7.50 112.50 250.00

h cm

r cm

d cm

f 'C

kg/cm²fy

kg/cm²

4200


120.00

b cm

168.771cm

8

4.713

170.00

127.731 153.277

7.916 0.002

36.741

7.749 0.002

35.955


1.2Mcr =

t-m

8

f

0.90

As = cm2


150.06 177.80


cm2

A min = cm2

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



320





VS = Vu - VC =

s = cm

30 cm

Vu > Vc; NO CUMPLE, REQUIERE ESTRIBOS


cm²


Se proponen a cada

0.85

136.228

41.572

2.85

0.104


64


t

t

0.142

bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



321




322


t-m t-m

Acero mínimo


Momento resistente


> Mu, OK

6

2.347 cm


87.175 t-m

Con barras del No.

As UNA BARRA

cm²No de barras

As cm²

6 2.850 5 14.251

11.642 cm2

As = 11.642 cm2

120.00 170.00 7.00

2.485 0.001


7.567

170.00

120.00

0.002

A min = 35.893 cm2

180.952 1.2Mcr = 217.142

163.00 250.00




f b

cmh

cmr

cmd cm

f 'C

kg/cm²fy

kg/cm²

420071.31 60.98 0.90

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



323





VS = Vu - VC =

s = cm

4 6 2.85



0.85

139.326 t Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS

Se proponen a cada

0.100

0.000 t


cm²


30 cm

bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



324



t-m t-m

Acero mínimo


Momento resistente

> Mu, OK

f

0.90

As = cm2


80.56 94.10


cm2

A min = cm2

6

2.651

170.00

127.731 153.277

7.916 0.002

36.741

4.160 0.001

19.133


1.2Mcr =

t-m

6

95.822cm

Con barras del No.


170.00 120.00 7.50 112.50 250.00

h cm

r cm

d cm

f 'C

kg/cm²fy

kg/cm²

4200


120.00

b cm

23


As UNA BARRA

cm²

2.850

No de barras

8

As cm²

22.802

Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



325





VS = Vu - VC =

s = cm

Se proponen a cada

0.85

136.228

0.000

2.85

0.000


64


t

t

0.142

30 cm

Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS


cm²


bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



326




327


t-m t-m

Acero mínimo


Momento resistente

163.00 250.00




f b

cmh

cmr

cmd cm

f 'C

kg/cm²fy

kg/cm²

420011.66 9.85 0.90 120.00 170.00 7.00

0.406 0.000


7.567

170.00

120.00

0.002

A min = 35.893 cm2

180.952 1.2Mcr = 217.142

1.894 cm2

As = 1.894 cm2


69.841 t-m

Con barras del No.

As UNA BARRA

cm²No de barras

As cm²

6 2.850 4 11.401


> Mu, OK

6

1.878 cm Mr = Ø As fy ( d - a/2 ) =

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f

bdAS

bf

fAa

C

yS

'85.0

SA

2/

1298.1

3'

h

bhf

y

IfM

C

t

gtcr

2bd

MR u

n f

'

'

85.0

211

85.0

C

n

y

C

f

R

f

f



328





VS = Vu - VC =

s = cm

Se proponen a cada

0.100

0.000 t


cm²


30 cm

4 6 2.85



0.85

139.326 t Vu < Vc; SI CUMPLE, NO REQUIERE ESTRIBOS bdfV cc'53.0 f

df

Vs

s

A

y

v

f

y

wv

f

b

s

A 5.3min



Memoria Est. 2

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Transcript of Memoria Est. 2