REQUERIMIENTOS PARA CIMENTACIÓN DE TUBERÍAS EN REDES DE ACUEDUCTO Y ALCANTARILLADO
Código: Estado: Versión: Origen: Tipo Doc.:
NS-035 Vigente 3.1 EAAB-Norma Técnica Norma Téc. de Servicio Elaborada
INFORMACION GENERAL Tema: Comité: Antecedentes: Vigente desde:
GEOTECNIA Subcomité de Diseño - Alcantarillado; Subcomité Diseño - Acueducto 20/05/2004
Contenido del Documento :
TABLA DE CONTENIDO 1 2 3 4 4.1 4.2 4.2 4.3 4.4 4.5 4.6 4.6 4.7 4.8 4.9 4.9
ALCANCE DOCUMENTOS RELACIONADOS TERMINOLOGÍA REQUISITOS GENERALIDADES PROC PROCES ESO O DE SEL SELECC ECCIÓN IÓN DEL DEL TIPO TIPO DE CIME CIMENT NTAC ACIÓ IÓN N SELECCIÓN DEL TIPO DE TUBERÍA RIGIDEZ DE LA TUBERÍA CONDICIONES DE INSTALACIÓN DETE DETERM RMIN INA ACIÓ CIÓN DE LAS CO COND NDIC ICIO IONE NES S DE CAR CARGA SELECCIÓN DE DEL TI TIPO DE DE CI CIMENTACIÓN DET DETERMI ERMINA NACI CIÓ ÓN DE CO COND NDIC ICIO ION NES LIMIT IMITE E REQU REQUIS ISIT ITOS OS PARA PARA PRES PRESEN ENTA TACI CIÓN ÓN Y APR APROB OBAC ACIÓ IÓN N DE DE LOS LOS DISE DISEÑO ÑOS S
ANEXOS Anexo A. Anexo B. Anexo C. Anexo D.
Condiciones de de instalación de tuberías Determinación Determinación de cargas vivas vivas Tipos de cimentación cimentación de tuberías tuberías Anchos máximos máximos de excavación.
Documento controlado, su reproducción está sujeta a previo permiso por escrito de la E.A.A.B.
Impreso el día: 04/11/2004 Pag 1
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
1. ALCANCE Esta norma establece los requisitos para dimensionamiento de cimentación de tuberías en los sistemas de acueducto y alcantarillado, para los diferentes tipos de tubería aprobados por la E.A.AB-E.S.P y para las diferentes condiciones de instalación utilizando métodos de estado límite de servicio y resistencia última. 2. DOCUMENTOS RELACIONADOS AMERICAN SOCIETY FOR TESTING AND MATERIALS. Standard specification for type PSM Poly(vinyl chloride) (PVC) sewer pipe and fittings. (ASTM D3034). 1998 AMERICAN WATER WORKS ASSOCIATION. Undergraund Undergraund instalation of polyvinyl chloride (PVC) pressure pipe and fittings for water (C605). First edition. --------. Steel pipe. A guide for design and instalation instalati on (M 11). Third edition. --------. --------. PVC pipe. Design and Instalation. Instalation. (M 23). --------. Fiberglass pipe design. (M 45). Fisrts edition. --------. --------. Ductile iron pipe and fitting fitting (M 41). First edition. --------. Concrete pressure pipe (M 9). Second edition. ETERNIT. Cálculo de Tubería de fibrocemento. ICONTEC Práctica normalizada para instalación instalación subterránea subterránea de tubos termoplásticos termoplásticos alcantarillado y otras aplicaciones de flujo por gravedad (NTC 2795)
para
--------. --------. Guía para selección, diseño e instalación de de tubería termoplástica.(GTC termoplástica.(GTC 16) 16) --------. Instalación Instalac ión de tuberías para conducción de aguas sin presión (NTC 1259) MANUFACTURAS DE CEMENTO S.A. Estudios para instalación de tuberías de concreto en condición zanja y condición terraplén. . Febrero de 1994. MINISTERIO DE DESARROLLO DESARROLLO ECONÓMICO. Reglamento Reglamento técnico del sector agua agua potabla y saneamiento básico. Mayo de 1998. MINISTERIO DE DESARROLLO ECONÓMICO. Resolución 1096 de 2000. TUBOS MOORE. Manual de tubería de gres.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
3. TERMINOLOGÍA Los términos no indicados indicados en este ítem deben ser consultados en las normas normas técnicas de la EAAB-ESP NT-002 Terminología de acueducto y NT-003 Terminología de alcantaril alcantarillado. lado. 3.1 ANCHO DE CIMENTACIÓN (Bd) Ancho de zanja zanja en la clave de la tubería. 3.2 DIÁMETRO NOMINAL (DN) Número con el cual se conoce comunmente el diámetro de una tubería, aunque su valor no coincida con el diámetro real interno 3.3 DIÁMETRO REAL (DI) Diámetro interno de una tubería determinado con elementos apropiados. 3.4 DIÁMETRO EXTERNO (Bc) Diámetro externo de una tubería determinado con elementos apropiados. 3.5 DIÁMETRO MEDIO (D) Corresponde al promedio entre el diámetro real y el diámetro externo. 3.6 ESTADOS LÍMITE Condición bajo la cual se evalúan las condiciones predominantes mas críticas que puedan presentarse durante durante la construcción y la vida útil de una una estructura teniendo teniendo en cuenta el estado límite de falla y el estado límite de servicio. 3.7 ESTADO LÍMITE DE FALLA FALLA Desarrollo de un mecanismo de falla y ocurrencia de deformaciones causantes de la pérdida del equilibrio estático o de rotura de la estructura. 3.8 ESTADO LÍMITE DE SERVICIO Condición límite bajo la cual no se garantiza el comportamiento comportamiento adecuado de la estructura bajo las cargas de servicio, debido a deformaciones. 3.9 FACTOR DE CARGA Relación entre la carga que produce la falla en las condiciones de cada una de las cimentaciones
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
3.10 MÉTODO DE LA RESISTENCIA Método de diseño para estados límites que considera las solicitaciones últimas de una estructura o sistema estructural. 3.11 MÓDULO DE ELASTICIDAD Pendiente de la curva esfuerzo-deformación de un material. 3.12 RESISTENCIA ÚLTIMA Capacidad de una estructura o un elemento para soportar cargas de trabajo antes de la falla. 3.13 TUBO FLEXIBLE Es un conducto, cuyos cuyos cambios por por efecto de las las cargas externas, externas, pueden hacer variar su dimensión vertical u horizontal horizontal en mas de 3.0% 3.0% sin causar al material material grietas o roturas. roturas. Dependen exclusivamente exclusivamente de su resistencia para soportar soportar las cargas externas. externas. Al deformarse bajo las cargas, el diámetro horizontal aumenta comprimiendo el terreno adyacente a los lados y crea, por lo tanto, una resistencia pasiva, que ayuda a soportar las cargas verticales sobre la tubería. Hacen parte de esta categoría las tuberías fabricadas en PVC, acero, GRP y polietileno. 3.14 TUBO RÍGIDO Conducto cuyos cambios por efecto de cargas cargas externas en cualquier sección transversal, no pueden hacer hacer varias su dimensión vertical u horizontal horizontal por mas mas de 0.1% sin causar causar al material grietas o roturas. Hacen parte de esta categoría las tuberías fabricadas en concreto y gres. 3.15 TUBO SEMIRÍGIDO Conducto cuyos cuyos cambios por efecto efecto de cargas cargas externas externas en cualquier cualquier sección transversal, transversal, puede puede hacer varias su dimensión dimensión vertical u horizontal horizontal hasta un un 3% sin causar al material grietas grietas o roturas. Hacen parte de esta categoría las tuberías fabricadas en hierro dúctil con recubrimiento interno en mortero y las denominadas CCP. 4. REQUISITOS 4.1 GENERALIDADES La selección selección del del tipo de cimentación cimentación debe determinarse determinarse de acuerdo con los los métodos métodos de resistencia última o estados límite de servicio, según sea el caso. Cualquier otro método o combinación combinaci ón de métodos de diseño diferente al indicado en esta norma puede ser permitido siempre y cuando a juicio de la EAAB-ESP el diseñador diseñador presente presente evidencia que la alternativa alternativa indicada cumple con los propósitos de seguridad, durabilidad, resistencia y economía requeridos por la empresa.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Se debe evaluar y presentar el diseño de la cimentación con su respectivo análisis de costos. Del trabajo de diseño debe presentarse presentars e una memoria de cálculo que contenga sin excepción todas las consideraciones exigidas en la presente norma. La responsabilidad responsabilidad de los diseños para las cimentaciones cimentaciones de tuberías así como la adopción de todas las medidas necesarias para el cumplimiento de ellos corre por cuenta del diseñador o ejecutor de la obra. Todos los sistemas de tuberías para acueductos y alcantarillados alcantarillados deben resistir los sismos de diseño. En el diseño sísmico deben deben utilizarse todas todas las disposiciones aplicables en las Normas Normas Colombianas de diseño y construcción sismoresistente NSR-98, Ley 400 de 1997 y 1997 y decreto decreto 33 de 1998, 1998, o los decretos que lo reemplacen o complementen. Las normas de la EAAB-ESP que deben ser consultadas y utilizadas de forma paralela a esta norma son NS-010 Requisitos para la elaboración elaboración y presentación presentación de estudios geotécnicos, geotécnicos, NS-123 Criterios para selección de materiales de tuberías para redes de acueducto y alcantarillado y NS-090 Protección de tuberías en redes de acueducto y alcantarillado alcantarillado
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.2 PROCESO DE SELECCIÓN SELECCIÓN DEL TIPO DE CIMENTACIÓN CIMENTACIÓN Para seleccionar seleccionar adecuadamente adecuadamente el el tipo de cimentación siguiente proceso.
debe realizarse realizarse como mínimo el
(1) Selecció Selección n del tipo tipo de tuberí tubería a (Numeral 4.3)
Determinación Determinación de la
(2)
condició condición n de instala instalación ción de la tubería
(Numeral 4.4)
Selecció Selección n del tipo de
(3)
Cimentación (Numeral 4.6)
(4)
Cálculo de cargas (Numeral 4.5)
(5) Verificación de las condiciones condiciones Límite
Si cumple cumple
6
(Numeral 4.7)
No cumple (4)
Selecció Selección n del tipo de Cimentación * (Numeral 4.6
No cumple
(5) Determinación de las condiciones condiciones Límite (Numeral 4.7)
* En los casos casos en los que se requie requiera ra deben deben prever preverse se las diferentes diferentes alternativas alternativas de protección protección de la tubería tubería (ver NS-090)
Si cumple cumple (6)
Presentar diseño co con el análisis análisis de costos
(NS-123) (NS-123)
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.3 SELECCIÓN DEL DEL TIPO DE TUBERÍA La selección del tipo de tubería debe realizarse de acuerdo con las condiciones del proyecto de acuerdo con las consideraciones de la norma de la EAAB-ESP NS-123 Criterios para selección de materiales de tuberías para redes de acueducto y alcantarillado y debe estar sujeta a revisión por parte de la EAAB-ESP Para la selección deben tenerse en cuenta los materiales de tubería aprobados por la EAAB-ESP e indicados en las siguientes normas: NP-027 Tuberías para alcantarillado NP-032 Tuberías para acueducto De la selección del tipo de tubería depende depende el tipo de cimentación a utilizar y la evaluación de las condiciones límite. 4.4 RIGIDEZ DE LA TUBERÍA Existen varias expresiones matemáticas para definir la rigidez de la tubería (Tabla 1) para fines de la presente norma se emplea la expresión de rigidez específica del anillo (Sp).
Tabla 1. Comparación de las diferentes expresiones y denominaciones de rigidez Expresión [Unidades]· ⋅ I E ⋅ D 3
F
∆ y
=
STISS
[F / L]
ISO 10639.2 “Specific Ring Stiffness” o “Rigidez Específica del Anillo”
[F / L]
NTC 4764-2 “Ring Stiffness” o “Rigidez Anular”
E ⋅ ⋅ I R 3
Normas
STISS
E ⋅ I 0.149 ⋅ R 3
PS
[F / L]
ASTM D2412 y AWWA M45 “Pipe Stiffness” o “Rigidez de la Tubería”
Las dimensiones de las variables anteriores usualmente se dividen otra vez por unidad de longitud resultando en [F / L2]. Esto se debe a que la inercia de la tubería, I, se expresa en [L4 / L], o sea [¨L3].
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
A continuación aparecen las equivalencias entre las diferentes ecuaciones y las expresiones de acuerdo con las dimensiones geométricas conocidas del tubo: Sp =
Sp =
Sp
=
E ⋅ I D 3 1 E ⋅ t 3 12 D 3 1
E
12 Bc
t
Sp = Sp
1
− 1
3
E
12 ( RDE − 1)3
Esta expresión es general. general. D es el diámetro medio medio de la tubería y la inercia, I, es la de la pared del tubo, observando que cuando el espesor no es constante puede derivarse de ecuaciones especiales. Para CCP la inercia a usar es el 25% de la del tubo. Esta expresión funciona para tuberías con espesor de pared constante porque I=t3/12 . D es el diámetro diámetro medio medio de la tubería, se obtiene como el diámetro interno (DN) más el espesor (t) o como el diámetro externo (Bc) menos el espesor (t). Esta expresión es función del diámetro externo, Bc, y del espesor de la pared, t. Es muy útil en tuberías tuberías rígidas y semi-rígidas semi-rígidas para las que ambas variables son conocidas. El valor RDE, relación diámetro-espesor, es el reportado en tuberías plásticas a presión.
= 0 .018625 ⋅ PS El valor de PS es el reportado en las tuberías con espesor de pared variable o también llamadas estructurales.
4.5 CONDICIONES DE INSTALACIÓN Para la selección del tipo de cimentación deben tenerse tenerse en cuenta las condiciones de instalación de las tuberías que se indican en este numeral 4.5.1 Condiciones de de Instalación en Terraplén Condiciones de instalación de tuberías en las cuales la tubería se cubre por encima de la superficie natural del terreno o cuando se abre una zanja en suelo natural lo suficientemente ancha para que la fricción lateral de la pared de la zanja no afecte la carga actuante sobre la tubería. Se consideran dos situaciones que son la instalación en terraplenes con proyección positiva y la instalación en terraplenes con proyección negativa. 4.5.1.1 Tuberías instaladas en proyección proyección positiva Las tuberías son instaladas sobre una cama panda, con el extremo superior por encima de la rasante natural natural y luego cubiertos cubiertos con material material de relleno. Un esquema esquema de esta condición de instalación se observa en el Anexo Anexo A 4.5.1.2 Tuberías instaladas en proyección proyección negativa
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.6 DETERMINACIÓN DE LAS CONDICIONES DE CARGA Para la selección de la cimentación se deben deben evaluar como mínimo mínimo las cargas indicadas indicadas en este numeral; se deben deben considerar las las combinaciones de carga carga mas adecuadas de acuerdo acuerdo con las hipótesis de calculo calculo empleadas empleadas según cada caso. La nomenclatura utilizada en este capítulo debe ser consultada en el Anexo A de la presente norma. 4.6.1 Cargas Muertas en Tuberías Flexibles y Semirígidas Las cargas en tuberías causadas por el peso del suelo deben calcularse considerando el peso del prisma del suelo directamente sobre sobre la tubería, más o menos las fuerzas cortantes de fricción que se transfieren a este prisma por los suelos adyacentes. Para la determinación de las cargas muertas debe utilizarse la ecuación de la teoría de Marston 4.6.1.1. Tubería enterrada en zanja angosta (Bd menor que 2 Bc) La carga muerta debe ser calculada como: W d = C d γ Bd
2
Bc Bd
Donde Wd = Carg Carga a muer muerta ta sobr sobre e la tube tuberí ría a (kN/ (kN/m) m) Cd = Coeficien Coeficiente te adimen adimensiona sionall de carga carga basado basado en Hc/Bd Hc/Bd donde donde Hc es es la altura altura del rellen relleno o sobre la clave de la tubería 3 γ = Peso unitario unitario del del mater material ial de de relleno relleno (kN/m ) Bd = Anch Ancho o de de la la zan zanja ja en la clav clave e de de la tube tuberí ría a (m) (m) Bc = Diám Diámet etro ro exte extern rno o de de la la tub tuber ería ía (m) (m) El coeficiente adimensional de carga Cd se determina de acuerdo con la siguiente fórmula
Cd =
1- e
- 2k µ
Hc Bd
2 k µ
Donde: k = relación relación entre entre la presión presión lateral lateral unitaria unitaria y la presión presión vertical vertical unitaria unitaria los lados de la zanja y el material del relleno relleno (tan (tan φ µ = coeficiente de fricción deslizante entre los )
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.6.1.2 Tubería enterrada en una una zanja ancha (Bd mayor que 2 Bc) La carga muerta debe ser calculada como W d = C cγ Bc Donde: Wd = Carg Carga a muer muerta ta sobre sobre la tube tuberí ría a (kN/ (kN/m) m) Cc = Coefic Coeficien iente te que que es es funci función ón de las propi propied edade adess de los suelos suelos H/Bc H/Bc par para a tuber tuberías ías flexib flexibles les y semirígidas al considerar únicamente únicamente deflexiones iniciales. γ = Peso unitario del material de relleno (kN/m3) Bc = Diámetro ex externo de de la la tu tubería (m (m) 2
El porcentaje de asentamiento puede ser asumido como cero en cuyo caso H C c = c Bc 4.6.2 Cargas Muertas en Tuberías Rígidas 4.6.2.1 Instalación en zanja La carga sobre tuberías tuberías rígidas en condiciones condiciones de instalación en zanja se puede calcular con la siguiente fórmula : W d = C d γ Bd Donde: Wd = carg carga a muer muerta ta sobr sobre e la tube tuberí ría a (kN/ (kN/m) m) 3 γ = peso peso unita unitario rio del del mate materia riall del del rellen relleno o en en (kN/ (kN/m m) Bd = anch ancho o hor horiz izon onta tall de de la la zan zanja ja en la clav clave e de de la la tub tuber ería ía (m) (m) Cd = Coefic Coeficien iente te adim adimens ension ional al de de carga carga basad basado o en Hc/Bd Hc/Bd don donde de Hc Hc es la la altur altura a del del relle relleno no sobre la clave de la tubería (Se calcula de acuerdo con la expresión del numeral 4.5.1.1 de esta norma). 2
4.6.2.2 Instalación en terraplenes con proyección positiva La carga producida por el peso propio del suelo de relleno en una tubería instalada en relleno con proyección positiva debe ser calculada como el peso del prisma interior del suelo directamente por encima de la estructura, más o menos las fuerzas cortantes verticales que actúan en planos verticales que se extienden hacia arriba en el relleno desde los bordes de la tubería. Para la determinación de la carga muerta debe utilizarse la siguiente ecuación:
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
C c
C c
=
=
e
2 k µ ( H c / Bc )
−1
2k µ
(
e 2 k µ H e / Bc 2k µ
si Hc <= He.
)
− 1 H c H e 2k µ ( H / B ) + − e B B c c e
c
si Hc > He
Donde Cc = Coeficien Coeficiente te adimen adimensiona sionall de carga carga estimad estimado o para para tuberí tuberías as en condicion condiciones es de de instalac instalación ión en terraplén en condición positiva. Bc = Diám Diámet etro ro exte extern rno o de de la la tub tuber ería ía (m) (m) k = Relaci Relación ón entre entre la presió presión n late latera rall unit unitar aria ia y la la pres presión ión vertic vertical al unita unitaria ria µ = Coeficiente de fricción fricción deslizante entre los lados lados de la columna columna de relleno encima del tubo y el material adyacente e = Base de de lo los lo logaritmos na naturales Hc = Altura Altura del material material de relleno relleno sobre sobre la clave del conducto conducto.. He = Altura Altura del del plano plano de igual igual asentami asentamiento ento por encima encima de de la clave de la la tuberí tubería. a. 2
1 H c H e r sd p e 2k µ ( H / B ) − 1 1 H e + + − + 3 2k µ 2 B c 2k µ B c Bc r p H H H 1 H e H c H e + sd c − e e 2 k µ ( H / B ) − − = r sd p c 3 B c B c 2k µ B c B c B c B c e
e
c
c
p: Fracción del del diámetro externo externo por encima encima del nivel de atraque (ver (ver Anexo A) rsd : Relación de asentamientos. asentamient os. Los valores recomendados aparecen en la siguiente tabla.
Ma terial terial de s ubrasante ubrasante
r sd
Roca
1.0 1. 0
Suelo no comp resible resible Suelo co mpresible mpresible
0.7 0. 7 0.3 0. 3
4.6.2.3 Instalación en terraplenes con proyección negativa negativa
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Donde: Wd = carg carga a mue muert rta a sobr sobre e la la tub tuber ería ía (kN/ (kN/m) m) 3 γ = peso unitario unitario del del materia materiall del relleno relleno en (kN/m ) Cn = coeficien coeficiente te adimen adimensiona sionall de carga carga estimad estimado o para para tuberí tuberías as en condicion condiciones es de instalació instalación n en terraplén en condición negativa. Cn se define como C n
=
e −2 k µ ´( He / Bd )
Donde: k = µ = e = Bd = Hc = He =
− 1 Hc He −2k µ ´( He / Bd ) + − e − 2k µ ´ Bd Bd
Relación Relación entre entre la presión presión lateral lateral unitaria unitaria y la presión presión vertical vertical unitaria unitaria Coeficien Coeficiente te de fricci fricción ón deslizante deslizante entre entre los los lados lados de la la zanja zanja y el material material del relleno relleno Base de los logaritmos naturales Anch Ancho o hor horiz izon onta tall de de la la zan zanja ja en la clav clave e de de la la tub tuber ería ía (m) (m) Altu Altura ra del del mat mater eria iall de de rell rellen eno o sob sobre re la clav clave e del del con condu duct cto. o. Altur Altura a del del plano plano de igual igual asenta asentamie miento nto por por enci encima ma de la clave clave de de la la tube tubería ría..
1 H ´e H ´ H ´e 1 H ´e 1 − 1 H ´ H ´e − − − − + − B B 2k µ ´ B B B 2 B 2k µ ´ = − 2k µ ´ d d d d d d e− 2k µ ´( H ´ / B ) − 1 H ´ H ´e − 2 k µ ´( H ´ / B ) 2 e r + − sd p´ − 3 2 k µ ´ B B d d
e
−2 k µ ´( H ´e / Bd )
e
d
e
d
rsd : Relación de asentamientos. asentamient os. Los valores recomendados aparecen en la siguiente tabla.
p'
r sd
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Cargas vivas de aviones Cargas vivas de construcción
Para la determinación determinación de las cargas cargas vivas en vías debe tenerse en en cuenta las indicaciones del del Código Colombiano Colombiano del Diseño Sísmico de Puentes Puentes del Ministerio de transporte transporte donde se indica que el camión de diseño es el C4095 el cual aplica una carga de 7500 kg en una área de (0.50 m *0.25 m). El área de aplicación de la carga se observa en el Anexo B b) Factor de impacto (If) El factor de impacto depende de la profundidad de la tubería. El cuadro 1 indica algunos factores de impacto que deben ser tenidos en cuenta para la determinación de las cargas vivas sobre la tubería en vías pavimentadas pavimentadas Cuadro 1. Factor de impacto para vías pavimentadas de acuerdo a cuerdo con la profundidad Profundidad (m) 0.00-0.30 0.31-0.60 0.61-0.90 0.91 en adelante
Factor 1.3 1.2 1.1 1.0
El cuadro 2 indica algunos factores de impacto que deben ser tenidos en cuenta para la determinación de las cargas vivas sobre la tubería en vías en las que no existe estructura de pavimento. Cuadro 2. Factor de impacto para vías sin pavimentar de acuerdo con la profundidad
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Le
3 B = L + 1.75 c 4
Donde: L = Long ongitu itud de ALL, paralelo al eje longitudinal de la tubería (m) Bc = Diám Diámet etro ro exte extern rno o de de la la tub tuber ería ía (m) (m) 4.6.4 Otras Cargas Adicionalmente Adicionalmente deben ser evaluadas evaluadas
Cargas producidas por el peso del agua.
Cargas transientes
Y cualquier otra carga que el diseñador considere adecuada para cada caso en particular. 4.7 SELECCIÓN DEL TIPO DE CIMENTACIÓN 4.7.1 Consideraciones Generales La cimentación cimentaci ón de la tubería está conformada por el apoyo considerado desde el fondo de la excavación hasta la clave de la tubería tubería instalada y el relleno que se ubica desde la cota clave de la tubería instalada hasta la rasante del terreno natural. Cualquier condición especial que exija un tipo de apoyo o material de relleno que sea requerido y que no esté indicado dentro de esta norma debe ser consultada consultad a en el estudio geotécnico correspondiente, en el caso de no existir dichos estudios el responsable del diseño de la cimentación deberá proponer proponer y justificar debidamente la cimentación a utilizar. El material material de apoyo y relleno de la cimentación debe seleccionarse de acuerdo acuerdo con los materiales de rellenos aprobados por la EAAB-ESP e indicados en la norma de la EAAB-ESP
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.7.2 Zonificación de las Cimentaciones Los rellenos para la instalación de redes de acueducto y alcantarillado se deben seleccionar de acuerdo con las zonas indicadas a continuación:
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.7.5 Distancias Mínimas entre las Tuberías de Agua Potable y las otras Redes de Servicios Las distancias mínimas mínimas que conforman conforman la red de distribución distribución de agua agua potable y las tuberías de alcantarillado y las redes de teléfonos, energía y gas domiciliario deben definirse de acuerdo con las indicaciones del artículo 90 de la Resolución 1096 de noviembre de 2000. Las tuberías de acueducto no pueden estar ubicadas en la misma zanja de una tubería de alcantarillado de de aguas residuales o pluvial, pluvial, y su cota de batea debe estar por encima encima de la cota clave de alcantarillado. En general las tuberías de acueducto deben colocarse hacia uno de los costados de las vías, preferiblemente preferiblemente los costados norte y este, este, opuesto a aquel donde donde se coloquen las tuberías de alcantarillado de aguas residuales. 4.7.6 Profundidades de de Excavación para instalación de tuberías 4.7.6.1 Profundidad mínima mínima de instalación a clave de tuberías de distribución La profundidad profundidad mínima a clave a la cual deben instalarse las tuberías de la red de distribución distribución no debe ser menor de 1.00 m para calzada y 0.80 m para zona verde medidos desde la clave de la tubería hasta la superficie del terreno. Para los casos donde sea necesario colocar la tubería por encima de las profundidades antes mencionadas, mencionadas, debe efectuarse un análisis que tenga tenga en cuenta las cargas exteriores debidas debidas al peso de tierras, tierras, cargas vivas, impacto y otras que puedan puedan presentarse presentarse durante el el proceso de instalación. Se exceptúan las zonas zonas en donde se garantice que no habrá flujo vehicular. vehicular. previa aprobación por parte de la EAAB-ESP. 4.7.6.2 Profundidad máxima de de instalación a clave de las tuberías de de distribución La profundidad profundidad de instalación de las las tuberías que conforman la red de distribución, distribución, no debe exceder de 1.50 m medidos desde la clave de la tubería hasta la superficie del terreno. Los casos especiales deben ser aprobados por la EAAB-ESP.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.7.6.4 Profundidad máxima máxima de instalación a clave en alcantarillados sanitarios En general la máxima profundidad profundidad de instalación de los los colectores, con relación a la rasante rasante definitiva, es del orden de 5.00 m, aunque puede ser mayor siempre y cuando se garanticen los requerimientos requerimientos geotécnicos geotécnicos de las cimentaciones cimentaciones y estructurales de los materiales y colectores durante y después después de su construcción. Los cruces subterráneos subterráneos de lagos, lagos, ríos y corrientes corrientes superficiales deberán deberán acompañarse de un diseño diseño apropiado que justifique las dimensiones, dimensiones, los atraques y las profundidades empleadas y deberán proveerse de medios para impedir su destrucción por efectos efectos de la socavación de la corriente atravesada. atravesada. 4.7.6.5 Profundidad mínima mínima de instalación a clave en alcantarillados pluviales Como norma general se recomienda una profundidad mínima de recubrimiento de 1,00 metro, medido a partir de la clave del colector con respecto al nivel de la rasante final de la vía. No obstante dependiendo de el tipo de tubería a utilizar y las recomendaciones de los fabricantes de tubería, previo cumplimiento cumplimiento de los especificado anteriormente, anteriormente, el diseñador diseñador podrá podrá adoptar coberturas menores, siempre y cuando el diseñador lo justifique mediante los cálculos respectivos. Las conexiones domiciliarias y los colectores de aguas lluvias deben ser localizadas por debajo de las tuberías tuberías de acueducto. acueducto. Los colectores colectores de aguas lluvias deben localizarse a una una profundidad profundidad que no interfiera con las conexiones conexiones domiciliarias de aguas aguas residuales al sistema de recolección y evacuación de aguas residuales. Deben además considerarse las interferencias con
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.8.1.1 Deflexiones La deflexión horizontal que ocurre en una sección transversal de una tubería flexible al estar sometida a una carga vertical por unidad de longitud debe ser menor a la citada en este numeral (de acuerdo con el tipo de material) y puede estimarse mediante la siguiente ecuación : ∆ y D L KW = *100 8 EI Bc + 0.061E ´ 3 Bc Donde
∆y/Bc y/Bc Bc ∆y DL K W EI E I
= = = = = =
Porc Porcen enta taje je de defl deflex exió ión n de de la la tub tuber ería ía Diámetro exterior (mm) Deflexión (m) Factor Factor de de retar retardo do de de la defl deflexi exión ón Fact Factor or de sopo soport rte e Carga por unidad de longitud de la tubería (N/m de tubería). (Carga muerta + carga viva) = Rigidez de la pared de la tubería = Mód Módulo de elast lastiicid cidad del mate materi rial al de la tub tubería ría (MPa MPa) 4 = Mome Moment nto o de iner inerci cia a pola polarr de la secc secció ión n tran transv sver ersa sall de la pare pared d del del tubo tubo (m /m)
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Donde P = Carga total aplicada sobre el suelo (psi). (Carga viva+ Carga muerta) La carga total determinada en el numeral 4.5 debe ser afectada por la longitud efectiva de soporte de la tubería determinada en el numeral 4.5.3 de la presente norma. y/Bc ∆y/Bc DL K E E´ RDE RDE
= = = = = =
Porc Porcen enta taje je de defl deflex exió ión n de la tube tuberí ría a Facto Factorr de de reta retardo rdo de la defle deflexió xión n Fact Factor or de sopo soport rte e Módulo ulo de elas elasti tici cida dad d del mater terial ial de la tub tubería ría (psi) psi) Módulo de reacción de la subrasante (psi) Rela Relaci ción ón diam diamet etro ro espe espeso sor r
a) Factor de retardo retardo de la deflexión, DL El factor de retardo de la deflexión está relacionado con la deflexión adicional que ocurre a medida que el suelo que circunda la tubería t ubería se compacta o consolida, varía entre 1.0 y 1.5. Cuadro 3. valores del parámetro DL M at e r i a l
S ig la
DL
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
E´b = Módulo de de elasticidad elasticidad de los materiales materiales de la cimentación cimentación (MPa). (MPa). El módulo módulo de elasticidad del terreno natural mínimo para cada uno de los tipos de cimentación aprobados por la EAAB-ESP corresponde a aquel indicado en los esquemas anexos a la presente norma. E´n = Módulo Módulo de elasticid elasticidad ad del del terreno terreno natur natural al (MPa) (MPa) Bd = Ancho Ancho de la zanja zanja en la clave de la tubería tubería (m) D = Diá Diámetr etro nom nominal inal de la tub tubería (m) Los valores de Sc deben ser calculados del cuadro 4 Cuadro 4. Valores del factor combinado de soporte del suelo E´n /E´b
Bd /D 1.5
Bd /D 2 .0
Bd /D 2 .5
Bd /D 3 .0
Bd /D 4. 0
Bd /D 5.0
0.1 0.2 0.4 0.6 0.8 1.0 1.5 20
0.15 0.30 0.50 0.70 0.85 1.00 1.30 1 50
0.30 0.45 0.60 0.80 0.90 1.00 1.15 1 30
0.60 0.70 0.80 0.90 0.95 1.00 1.10 1 15
0.80 0.85 0.90 0.95 0.98 1.00 1.05 1 10
0.90 0.92 0.95 1.00 1.00 1.00 1.00 1 05
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 00
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Material CCP Concreto cilíndrico de acero DIP Hierro dúctil PVC Cloruro de polivinilo SP Acero PE Polietileno
E(KN/m2) 27,579,029 170,000,000 2,757,903 206,842,719 882,599
E (psi) 4,000,000 24,656,415 400,000 30,000,000 128,054
Deflexiones máximas admisibles El porcentaje de deflexión máxima admisible a largo plazo ( ∆y/Bc adm) para cada tipo de tubería se indica a continuación Tubería de PVC (ASTM D-3034) Tubería de hierro dúctil (AWWA M41) Tubería de polietileno (ASTM F-894) 7.5% Tubería de GRP (AWWA M45) Tubería de acero con recubrimiento recubrimient o en mortero (AWWA M11) 2.0% Tubería de acero con recubrimiento recubrimiento en mortero y revestimiento flexible (AWWA M11) Tubería de acero con revestimiento flexible (AWWA M11) 5.0%
7.5% 3.0% 5.0% 3.0%
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
b) Factor de flotación del agua Rw: Factor de flotación del agua Rw = 1 − 0.33 ⋅ (hw H ) si 0 ≤ hw
≤ H
Rw = 1 si hw > H en que: hw: Altura de la superficie de agua por encima de la parte superior de la tubería [m].
c) Coeficiente de soporte
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
4.8.1.4
Esfuerzo de flexión en el anillo (Bending Stress)
El chequeo de esta condición es utilizado en el diseño de tuberías de fundición dúctil, para las cuales el esfuerzo de flexión en el anillo ( f ) fue definido como 331000kN/m² , valor que involucra un amplio factor de seguridad seguridad con respecto respecto a la resistencia del material. material. Este límite no debe ser excedido por el esfuerzo de flexión generado en una cimentación ( f T) para cuyo cálculo se utiliza la siguiente expresión:
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
EH: Modulo Modulo de tensión tensión circunfe circunferenc rencial ial [kN/m²] [kN/m²] HDB:Base hidrostática de diseño eb: Máxima Máxima deform deformación ación del anillo anillo debid debido o a la deflexi deflexión ón [m/m] [m/m] ε b = D f
δ d t Bc Bc
en que: Df: Factor de deformada
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Factor de carga El factor de carga es el indicado en los esquemas anexos a la presente norma técnica para los diferentes tipos de cimentación aprobados por la Empresa. Factor de seguridad El factor de seguridad se debe calcular de acuerdo con la expresión indicada en este numeral y debe obtenerse un valor superior a mayor de 1.0 para concreto reforzado y de 1.5 para concreto simple, en caso de no obtenerse dicho valor debe cambiarse el tipo de cimentación seleccionado.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
FORMATO RESUMEN CIMENTACIÓN TUBERÍAS FT-01
NS-035 Ver
Título del Proyecto :_______________________________________________________________________________________________
PARA REDES: Número de tramos:________________________________ Condición de instalación promedio:___________________ Profundidad de cimentación: (m)_____________________ Longitud promedio de cada tramo:(m)_________________
2.0
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.