Ing. CIVIL
UNSCH
FISICA II
Índice: INTRODUCCIÓN .............................................................................................................................. 3 I.
PLANTEAMIENTO DEL PROBLEMA ................................................................................... 4
II.
OBJETIVOS .............................................................................................................................. 4 2.1.
OBJETIVOS GENERALES ............................................................................................. 4
2.2.
OBJETIVOS ESPECÍFICOS .......................................................................................... 4
III.
REVISIÓN BIBLIOGRÁFICA .............................................................................................. 5
3.1.
CONCEPTOS APLICADOS A LA FÍSICA .................................................................... 5
3.1.1.
ELASTICIDAD ........................................................................................................... 5
3.1.2. ESFUERZOS ................................................................................................................. 7 3.1.2.1. Tracción y compresión: ............................................................................................. 7 3.1.2.2. Esfuerzo de corte ..................................................................................................... 10 3.3.3. FLEXIÓN ....................................................................................................................... 11 3.2.
CONCEPTOS APLICADOS A LA INGENIERÍA ........................................................ 12
3.2.1.
PUENTE ................................................................................................................... 12
3.2.1.1.
Partes de un puente ........................................................................................... 12
3.2.1.2.
Taxonomía estructural y evolucionaría ........................................................... 13
3.2.1.3.
Comportamiento estructural de un puente ..................................................... 13
3.2.2.
PUENTE COLGANTE ............................................................................................ 16
3.2.2.1.
Contexto Histórico .............................................................................................. 16
3.2.2.2.
Concepto del puente colgante .......................................................................... 16
3.2.2.3.
Comportamiento Estructural de un Puente Colgante ................................... 17
3.2.2.4.
Partes y Elementos de un Puente Colgante .................................................. 19
3.2.2.5.
Materiales con el que están compuestas las partes de un puente colgante 20
3.2.2.6. 3.2.3.
Comparación con otros puentes ...................................................................... 23 CARGAS .................................................................................................................. 24
3.2.3.1.
Cargas Estructurales Concepto de Estructura ............................................... 25
3.2.3.2.
Tipos de Cargas .................................................................................................. 26
3.2.3.3.
Clasificación de las Cargas ........................................................................... 26
3.2.3.4. Cargas en las vigas ................................................................................................. 27 Ingeniería civil
1
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Ing. CIVIL
UNSCH
FISICA II Simétrica ..................................... 31
3.2.3.5.
Peso Propio de los Cables con Deflexión
3.2.3.6.
Carga Viva en los Puentes. .............................................................................. 34
3.2.3.7.
Cargas por Peso Propio y Peso Muerto en los Puentes .............................. 35
3.2.2.8. Líneas de Influencia en un Puente. ........................................................................ 36
IV.
DESARROLLO DE LOS OBJETIVOS ............................................................................ 37
Objetivo 1 ..................................................................................................................................... 37 Objetivo 2 ..................................................................................................................................... 38 Objetivo 3 ..................................................................................................................................... 40 V. IMPACTO AMBIENTAL ......................................................................................................... 41 VI.
OPINIÓN CRÍTICA ............................................................................................................. 43
VII.
CONCLUSIONES ............................................................................................................... 44
7.1.
CONCLUSIONES ........................................................................................................... 44
BIBLIOGRAFÍA ............................................................................................................................... 45
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Ing. CIVIL
UNSCH
FISICA II
INTRODUCCIÓN Se denomina puente colgante a una estructura que permite cruzar, a distinto nivel, un obstáculo y está compuesta por un tablero soportado mediante péndolas verticales o inclinadas de cables, que son la estructura portante, y que cuelgan apoyados en dos torres. La necesidad de cruzar obstáculos naturales, sean ríos o quebradas, ha hecho que desde muy antiguo el hombre desarrolle este tipo de puentes. En el Perú, en la época de los incas, se emplearon sistemas de sogas denominados oroyas, con un cable, o huaros, con dos cables, y puentes colgantes que empleaban cables formados por varias sogas hechas de fibras vegetales del maguey. Estos puentes no tenían vigas de rigidez. Uno de los más notables fue el puente sobre el río Apurímac, en la vecindad de Curahuasi.
Para tener un poco más de conocimientos acerca del puente colgante y así poder desarrollar los objetivos planteados tendremos que desarrollar lo siguiente: el funcionamiento puente colgante, como están distribuidas las cargas vivas y cargas muertas, como ayuda la forma del cable principal en el funcionamiento y a que que esfuerzos está sometida el puente colgante, elementos del puente colgante, los mecanismos de construcción, la elasticidad de los materiales, como la física física interviene en un puente colgante.
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Ing. CIVIL
UNSCH
I.
FISICA II
PLANTEAMIENTO DEL PROBLEMA
¿Cuál es el comportamiento estructural de un puente colgante sometido a fuerzas generales por cargas vivas y su propio peso?
II.
OBJETIVOS
2.1.
OBJETIVOS GENERALES
Evaluar la resistencia que ejercen partes de un puente colgante cuando están sometidas a fuerzas externas.
2.2.
OBJETIVOS ESPECÍFICOS
1. Conocer la elasticidad de los materiales que componen el puente colgante desde un aspecto físico, para saber cuan resistente pueden ser a los distintos esfuerzos que generan. 2. Analizar la forma de un puente colgante desde el punto de vista físico para comprender de qué manera aporta en la resistencia de los materiales que lo componen. 3. Analizar cómo están actuando las fuerzas internas en las diversas partes del puente colgante, mediante estudios físicos para comprender los efectos que produces y afectan a estas.
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III.
REVISIÓN BIBLIOGRÁFICA
3.1.
CONCEPTOS APLICADOS A LA FÍSICA
FISICA II
3.1.1. ELASTICIDAD Elasticidad es la propiedad que tiene los cuerpos de recuperar su forma y dimensiones originales cuando la fuerza aplicada cesa de actuar. Se dice que el cuerpo es perfectamente elástico (material elástico) si recobra su forma original de un modo completo al descárgalo, y que es parcialmente elástico (material no elástico) si la deformación producida por las fuerzas exteriores no desaparece por completo al descargarlo. En el caso de un cuerpo perfectamente elástico, el trabajo realizado por las fuerzas exteriores durante la deformación se transforma completamente en energía potencial de deformación. En el caso de un cuerpo parcialmente elástico, parte de aquel trabajo se transforma en calor desarrollado en el cuero durante la deformación no elástica. Experimentalmente, se ha visto que cuerpos tales como el acero, la madera y la piedra pueden considerarse como perfectamente elásticos por debajo de cierto límite que depende de las propiedades del material. Suponiendo que las fuerzas externas que actúan sobre una estructura son conocidas, es un problema fundamental para el proyectista dimensionar las partes de la estructura para que estén en condiciones perfectamente elásticas en todos los casos de carga. Solamente en tales condiciones la estructura tendrá una vida larga y segura y no presentara deformaciones permanentes en sus elementos.
CURVA DE ESFUERZO DE TENSIÓN Y DEFORMACIÓN UNITARIA
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Ing. CIVIL
UNSCH
FISICA II
Deformación elástica.- Ocurre desde el origen hasta el límite elástico o límite de elasticidad (b). En esta zona, denominada zona elástica, si el material es sometido a esfuerzo, y al reducir este, el material retorna a su forma original sin sufrir deformaciones permanentes. Al principio del estiramiento, que va desde el origen hasta el límite de proporcionalidad elástico (a), vemos que la deformación es proporcional al esfuerzo observándose en la gráfica un segmento rectilíneo. En esta zona es válida la ley de Hooke. Más allá del límite de proporcionalidad elástica (a), hasta el límite elástico (b); observamos en la gráfica que no se mantiene la línea recta, por tanto no existe una relación sencilla entre el esfuerzo y la deformación. Pero en esta zona la deformación es reversible, es decir el el material recupera su forma original.
Deformación plástica o flujo plástico.- Si el material se somete más allá del límite elástico (b), entra en la zona plástica, donde si quitamos el esfuerzo aplicado el material no vuelve a su estado original y queda permanentemente deformado. Si el esfuerzo continúa incrementándose, se llega al punto final de esta zona denominado punto de ruptura (c), donde se produce la fractura o ruptura del material. El esfuerzo necesario para causar la ruptura se denomina esfuerzo de rotura. Entre el límite elástico y el punto de ruptura, existe una zona de fluencia, donde el material se deforma fácilmente sin necesidad de aumentar el esfuerzo, el sólido se comporta como un líquido y fluye.
Cuerpos frágiles.- Se denomina así si la zona de fluencia es pequeña o inexistente.
Cuerpos dúctiles.- Se denomina así si la zona de fluencia es amplia.
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Ing. CIVIL
UNSCH
FISICA II
3.1.2. ESFUERZOS Cuando se aplica una o varias fuerzas a una estructura (un puente, un edificio, edificio, el cuerpo de una máquina, etc.) se dice que está sometido a esfuerzo. Si la soporta soporta sin deformaciones excesivamente o sin romperse, decimos que es una estructura resistente a este esfuerzo. Esfuerzos:
Tracción. Compresión. Cizalladura.
3.1.2.1. Tracción y compresión: Si se somete una barra a dos fuerzas opuestas que actúan perpendicularmente a sus secciones transversales, ocurrirán cambios longitudinales en la dirección de la fuerza.
Si las tensiones son hacia fuera y tienden a estirarlo, se llama tracción, la barra sufre un alargamiento.
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Ing. CIVIL
UNSCH
FISICA II
Esfuerzo de Tensión El esfuerzo es una consecuencia de las fuerzas internas de corto alcance que se producen por la aplicación de fuerzas exteriores. El esfuerzo se define como la relación entre la intensidad de la fuerza externa por unidad de área de la sección transversal. donde: A: área sobre el cual actúa la fuerza (m 2) F: fuerza (N) σ: esfuerzo (N/m2)
Deformación Longitudinal (Unitaria) El cambio de longitud que sufre la barra bajo esfuerzo de tensión axial, se conoce como deformación longitudinal ∆l ∆ l . La deformación unitaria se define como el cambio en la longitud por unidad de longitud. donde: ∆l : deformación l 0: longitud inicial
Módulo de Young (Y) El módulo de elasticidad o Young, mide la resistencia del solido a ser deformado, entre mayor sea el valor de Y, mayor es la rigidez del material. donde:
σ: esfuerzo (N/m 2)
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Ing. CIVIL
UNSCH
FISICA II
Ej emplo de es esf uerzo de tracción : Muchos puentes, como los puentes de tirantes y los puentes colgantes, utilizan gruesos cables de acero para sostener el tablero por donde circulan los vehículos. Estos cables se denominan tirantes y están sometidos a tracción. En la foto debajo, observamos el puente atirantado Vasco de Goma, en Portugal
Ej emplo de es esf uerzo de compr compr esi ón: Uno de los ejemplos más comunes de esfuerzo de compresión es el que resisten las columnas pilares y muros de carga de los edificios, como las columnas del templo griego que se ilustra. Estos componentes estructurales deben sostener el peso de la parte del edificio que está situado encima de ellos. Como consecuencia de la fuerza ejercida por el peso aparece una fuerza de reacción con sentido hacia arriba que proviene de los cimientos.
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Ing. CIVIL
UNSCH
FISICA II
3.1.2.2. Esfuerzo de corte Un cuerpo está sometido a un esfuerzo de corte (también llamado de cizallamiento, de cilladura, o esfuerzo cortante) cuando se le aplican fuerzas tangenciales o paralelas al área.
donde: σc: esfuerzo de corte (N/m 2) F: fuerza (N) A: área sobre sobre el cual actúa actúa la fuerza fuerza (m2)
Deformación de Corte ( λc): La deformación de corte o cizalladura o deformación angular, se define como la tangente del ángulo de deformación. donde: λc: deformación de corte θ: es tan pequeño que
Módulo de corte (G): El módulo de corte o también llamado coeficiente de rigidez, mide la resistencia al movimiento de los planos de un sólido al deslizar uno sobre otro.
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FISICA II
3.3.3. FLEXIÓN Curvatura, deformación que experimenta un sólido cuando se aplican fuerzas o soporta cargas que actúan en su plano de simetría o están dispuestas en pares simétricos con respecto a dicho plano. Una pieza experimenta flexión, cuando está sometida a fuerzas externas que se ejercen en sentido transversal a su longitud. Estas fuerzas se hallan generalmente en el mismo plano y son con frecuencia perpendiculares al eje de la pieza. Bajo su acción, la pieza cede y se deforma; si era recta (como es nuestro caso), adquiere cierta curvatura, acortándose las fibras situadas en la parte cóncava y alargándose las de la parte convexa.
En la parte superior la barra está sometida a esfuerzos de compresión y en la parte inferior la barra está sometida a esfuerzos de tracción, esta combinación de esfuerzos se denomina esfuerzo de flexión. Ej emplo de esf uerzo de f lexi ón Aunque no se pueda apreciar a simple vista, la plataforma p lataforma de un puente se comba cuando debe soportar el peso de un vehículo. La flexión de un puente es muy pequeña ya que están
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Ing. CIVIL
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3.2.
FISICA II
CONCEPTOS APLICADOS A LA INGENIERÍA
3.2.1. PUENTE Un puente es una construcción que permite salvar un accidente geográfico como un río, un río, un cañón, un cañón, un valle, un camino, un camino, una vía férrea, un cuerpo de agua o cualquier otro obstáculo físico. El diseño de cada puente varía dependiendo de su función y la naturaleza del terreno sobre el que se construye. Su proyecto y su cálculo pertenecen a la ingeniería estructural, siendo estructural, siendo numerosos los tipos de diseños que se han aplicado a lo largo de la historia, influidos por los materiales disponibles, las técnicas desarrolladas y las consideraciones económicas, entre otros factores. Al momento de analizar el diseño de un puente, la calidad del suelo o roca donde habrá de apoyarse y el régimen del río por encima del que cruza son de suma importancia para garantizar la vida del mismo. Por tanto el diseño de cada puente varía dependiendo de su función y la naturaleza del terreno donde se construye el puente. 3.2.1.1.
Partes de un puente
La superestructura: conjunto de tramos que salvan los vanos situados entre los
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Ing. CIVIL
UNSCH
3.2.1.2.
FISICA II
Taxonomía estructural y evolucionaría
Los puentes pueden ser clasificados por la forma en que las cuatro fuerzas de tensión, compresión, flexión y tensión cortante o cizalladura están distribuidas en toda su estructura. La mayor parte de los puentes emplea todas las fuerzas principales en cierto grado, pero sólo unas pocas predominan. La separación de fuerzas puede estar bastante clara. En un puente suspendido, suspendido, los elementos en tensión son distintos en forma y disposición. En otros casos las fuerzas pueden estar distribuidas entre un gran número de miembros, tal como en uno apuntalado, o no muy perceptibles a simple vista como en una caja de vigas. Los puentes también pueden ser clasificados por su linaje. Las armaduras de los puentes pueden trabajar a flexión (vigas), a tracción (cables), a flexión y compresión (arcos y armaduras), etc. En la construcción de los puentes una de las partes más delicadas es la cimentación bajo agua debido a la dificultad de encontrar un terreno que resista las presiones, siendo normal el empleo de pilotes de cimentación. Los puentes de grandes dimensiones descansan generalmente sobre cimientos de
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Ing. CIVIL
UNSCH
FISICA II
Se mencionara algunos tipos de puente y los principales esfuerzos que soportan
En viga.- Trabaja a tracción en la zona inferior de la estructura y compresión en la superior, es decir, soporta un esfuerzo de flexión. Están formados fundamentalmente por elementos horizontales que se apoyan en sus extremos sobre soportes o pilares. Mientras que la fuerza que se transmite a través de los pilares es vertical y hacia abajo y, por lo tanto, éstos se ven sometidos a esfuerzos de compresión, las vigas o elementos horizontales tienden a flexionarse como consecuencia de las cargas que soportan.
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Ing. CIVIL
UNSCH
FISICA II
En arco.- Trabaja a compresión en la mayor parte de la estructura. Están constituidos básicamente por una sección curvada hacia arriba que se apoya en unos soportes o estribos y que abarca una luz o espacio vacío. En ciertas ocasiones el arco es el que soporta el tablero (arco bajo tablero) tablero) del puente sobre el que se circula, mediante una serie de soportes auxiliares, mientras que en otras de él es del que pende el tablero (arco sobre tablero) mediante tablero) mediante la utilización de tirantes. La sección curvada del puente está siempre sometida a esfuerzos de compresión, igual que los soportes, tanto del arco como los auxiliares que sustentan el tablero. Los tirantes soportan esfuerzos de tracción.
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Ing. CIVIL
UNSCH
FISICA II
3.2.2. PUENTE COLGANTE 3.2.2.1.
Contexto Histórico
El diseño actual de los puentes colgantes fue desarrollado a principios del siglo XIX los primeros ejemplos incluyen el puente de Menai el de Conwy ambos puestos en funcionamiento en 1826 en el norte del país de Gales, y el primer puente Hammersmith (1827) en la zona oeste de Londres. Este tipo de puentes fue una revolución total, debido a que es prácticamente la única solución para salvar grandes luces (superiores a un kilómetro). Pero esto acarrea un gran análisis en el comportamiento estructural pues de por si es una estructura de poca rigidez, está claro que no posee el soporte adecuado ante distintas cargas pesadas en comparación con otros tipos de puentes, pero en otros aspectos es bastante conveniente. Durante el transcurso del tiempo se han estado innovando los materiales que compongan las partes del puente de tal manera que proporcionen la resistencia adecuada a los tipos de cargas que más le afectan. La mayoría de los puentes colgantes usan estructuras de acero reticuladas para soportar la carretera en consideración a los efectos desfavorables que muestran los puentes con placas
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Ing. CIVIL
UNSCH
FISICA II
a esfuerzos de compresión, los demás elementos del puente, es decir, cables y tirantes, están sometidos a esfuerzos de tracción. Desde la antigüedad este tipo de puentes han sido utilizados por la humanidad para salvar obstáculos. Con el paso de los siglos y la introducción y mejora de distintos materiales de construcción, este tipo de puentes son capaces en la actualidad de soportar el tráfico rodado e incluso líneas de ferrocarril ligeras.
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Ing. CIVIL
UNSCH
FISICA II
Para presentar los procedimientos de análisis de puentes colgantes es necesario indicar las hipótesis en que se basan:
El cable es perfectamente flexible, sólo puede resistir esfuerzos de tracción. tracción. Esto significa que los momentos de flexión son nulos en todos los puntos del cable. El cable es homogéneo y de sección constante. Las cargas que actúan en el cable hacen que en condiciones de servicio servicio su comportamiento sea elástico, siguiendo la ley de Hooke. El eje del cable se desplaza solo en el plano vertical. La carga externa es vertical y distribuida distribuida sobre la proyección horizontal del
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Ing. CIVIL
UNSCH
3.2.2.4.
FISICA II
Partes y Elementos de un Puente Colgante
Tramo lateral: segmento entre dos pilones situado en los extremos del puente. Con luces que varían entre 0.20 a 0.50 de la luz del tramo central. Tramo central: segmento entre dos pilones situado en la parte central del puente. Pilón lateral: construcción vertical similar a una torre situada en un costado, la cual sostiene generalmente los cables de un puente colgante o de un puente atirantado. Base del pilón: parte inferior del pilón es muy resistente a los esfuerzos de compresión, en esta se encuentra el diseño de una buena cimentación ya
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Ing. CIVIL
UNSCH
FISICA II
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Ing. CIVIL
UNSCH
FISICA II
Los cables principales que poseen la forma parabólica y son de gran flexibilidad llegan a tener un diámetro de aproximadamente un metro y son los encargados de soportar las cargas de los tirantes, a estos cables se los levanta hasta y por encima de las torres (pilón), al cual lo someten a compresión, luego continúan más allá de las torres hasta que alcanzan un punto de anclaje, estos puntos están ubicados en roca solida o cemento y ayudan a distribuir la carga de los cables. Por tanto también son importantes para aumentar la cantidad de peso que puede soportar un puente.
b) LAS PÉNDOLAS Son los elementos doblemente articulados que trasmiten las cargas del tablero del puente y de las vigas de rigidez a los cables. Pueden
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Ing. CIVIL
UNSCH
FISICA II
El hormigón o concreto es un material compuesto empleado en construcción formado esencialmente por un aglomerante, un aglomerante, que en la mayoría de los casos es cemento, al que se añade partículas o fragmentos de un agregado, agua agregado, agua y aditivos
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Ing. CIVIL
UNSCH
FISICA II
los agentes atmosféricos como de los gases y humos de las fábricas y ciudades lo que supone un mantenimiento caro.
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Ing. CIVIL
UNSCH
FISICA II
DESVENTAJAS o
Al faltar rigidez el puente se puede volver intransitable en condiciones de
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UNSCH
FISICA II
estructura similares. Con experiencia, se pueden también “estimar” la magnitud de
esas cargas.
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3.2.3.2.
FISICA II
Tipos de Cargas
Cargas muertas, cargas vivas, cargas accidentales o ambientales o dinámicas (de
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