tag:blogger.com,1999:blog-20921669218320518502024-03-14T08:28:29.294-07:00INGENIERIA PARA TORPES<i><b> Curiosidades, consejos y una visión particular sobre la Ingeniería civil </b> </i>Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.comBlogger65125tag:blogger.com,1999:blog-2092166921832051850.post-30778489822205752232016-02-06T08:14:00.000-08:002016-02-06T08:16:35.619-08:00An introduction to fatigue testing and design<b>Fatigue failure</b> occurs when an structure is subjected to cyclic loading, like wind, waves or traffic.<br />
Even if the load is below the yield stress of the material, the constant loading and unloading of the structure can make cracks to open and propagate until failure is reached.<br />
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These cracks usually appear at points of stress concentration, like welds, holes and sharp edges. <br />
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Fatigue testing allows us to characterized the resistance of materials under differents loads amplitudes and number of cycles. <br />
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An introduction to <b>fatigue testing</b>, <b>S-N diagrams</b> and <b>fatigue design</b> is shown the next videos:<br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-29789342760703786812015-06-05T10:17:00.001-07:002015-06-05T10:17:06.763-07:00TED TALKS Abe Davis: Extraer sonido de las imagenes"<b>Computer Vision</b>" es un campo de la ciencia dedicado al estudio y análisis de la imagen, con el fin de emular al ojo humano y ser capaz de extraer y procesar todo tipo de información de las mismas.<br />
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Un ejemplo de las aplicaciones que ofrece esta rama es la creación de<b> modelos 3D</b> mediante pares estereoscopicos de imagenes. Mediante algoritmos de busqueda es posible detectar pixeles hermanos en dos imagenes diferentes y deducir su posición en el espacio mediante reglas geométricas. <br />
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<b>123D CATCH! </b>de Autodesk es una herramienta muy popular que permite crear modelos 3D a partir de un grupo de imagenes tomadas desde diferentes angulos de forma muy facil, aquí podeis ver un modelo 3D de la fachada del <b>Hospital del Real (Granada)</b> que yo mismo hice hace algún tiempo:<br />
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<tr><td class="tr-caption" style="text-align: center;">Modelo 3D de la fachada del Hospital del Real (Granada)</td></tr>
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En este otro video podeis ver como con la ayuda de un dron y 123D CATCH! es posible mapear la topografía del terreno y obtener modelos 3D:<br />
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Lo que me gustaría mostrar ahora es algo que me parece mucho más impresionante y que creo puede tener un sinfín de aplicaciones dentro de la ingeniería de estructuras. <br />
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Se trata de una tecnología presentada recientemente, capaz de extraer <b>información acústica</b> a partir de movimientos en los objetos imperceptibles para el ojo humano.<br />
<b>A partir de una imagen de video</b>, sin sonido, es posible detectar las <b>minisculas vibraciones</b> que las ondas sonoras producen sobre los objetos e interpretar esta información para <b>recuperar el sonido de la imagen.</b><br />
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Lo más interesante de esta tecnología es que no solo se limita a la extracción de sonido, también permite extraer información sobre el <b>comportamiento dinámico</b> de los objetos. <br />
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Con esta nueva tecnología es posible obtener los <b>modos de vibración</b> de una estructura a partir de una grabación en video de 1 minuto, sin ningún tipo de información adicional.<br />
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Pero no solo eso, si no que<b> únicamente con la información extraida de ese minuto de video resulta posible crear una simulación de la estructura</b> donde someterla a diferentes cargas y poder estudiar su comportamiento. En la charla de <b>TED TALKS</b> podeis ver un ejemplo de esto último, unicamente con 5 segundos de video y dando un golpe en una mesa es capaz de crear un modelo virtual de un muñeco de alambre, que se mueve y deforma con la misma rigidez y modos de frecuencia que en la realidad.<br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com1tag:blogger.com,1999:blog-2092166921832051850.post-11869165594039631642015-01-26T14:16:00.000-08:002015-01-26T14:19:03.184-08:00Pandeo lateral según eurocodigo EC3 (HOJA DE CÁLCULO EXCEL!)Cada vez que leo la norma de acero española (<b>EAE</b> eaaa eeh!) y llego al capítulo de<b> pandeo lateral</b> me entran unos sudores fríos por el cuerpo , mi mente empieza a divagar sobre los grandes enigmas del ser humano. ¿De dónde venimos?¿a dónde vamos?¿cuantos coeficientes hacen falta para calcular un momento resistente?¿ Cmy, CMz, C11, Kxy? Más! necesito más!.<br />
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Seguro que no soy el único al que le pasa esto, por eso he hecho esta hoja de cálculo para comprobar el <b>pandeo lateral en perfiles metálicos</b> basandome en el <b>Eurocodigo EC3</b>.<br />
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Esta <b>hoja de cálculo</b> sirve para perfiles simétricos en I y H y te permite calcular el momento último resistente y por pandeo lateral de forma automática en secciones de clase 1,2,3 y 4. También te permite comprobar la resistencia frente a Axil y frente a pandeo por flexión (introduciendo el coeficiente de pandeo X de forma manual) y comprobar la interacción entre el momento y el axil de forma conservadora.<br />
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La forma de utilizarla es muy sencilla, simplemente tienes que introducir los parámetros geométricos de la sección, los coeficientes de pandeo ayudandote de las tablas, los esfuerzos de cálculo (Med, Ned ) y pulsar "Comprobar". La hoja te devuelve los esfuerzos últimos resistentes y te indica si cumple o si falla la sección, y si falla porque lo está haciendo. ¿No está mal verdad?.<br />
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<b><u>Podeis descargar la hoja de cálculo en el siguiente enlace:</u></b><br />
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<a href="https://mega.co.nz/#!l5JwRa4B!K7zH7-bH01dat2TrC3Q3Ce6ZIuuC8xnAklexeEVqq3Y" target="_blank">Hoja de Cálculo Pandeo Lateral segun eurocodigo EC3 (EXCEL)</a>Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com2tag:blogger.com,1999:blog-2092166921832051850.post-28455464210424747482015-01-05T15:12:00.002-08:002015-01-05T15:12:33.413-08:00Se hunde puente en Palermo una semana tras su inauguraciónEl pasado 23 de diciembre de 2014 se inauguró un <b>viaducto</b> en la autovía que une las
ciudades sicilianas de Palermo y Agrigento. El coste de la obra ascendió a 13 millones de euros, siendo la misma finalizada 3 meses antes del plazo acordado.<br />
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Hasta aquí todo bien, si no fuera porque justo una semana después de su inaguración parte de la obra se hunde. Por suerte no circulaba ningún vehiculo en el momento del<b> hundimiento</b>, asi que no hay que lamentar heridos.<br />
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Un viaducto no se cae todos los días, y aunque es una faena, la verdad es que resulta muy interesante pararse a analizar las posibles causas del fallo.<br />
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Buceando por la prensa no he encontrado demasiada información tecnica sobre el caso, pero he leido lo siguiente que me ha llamado la atención, y cito:<br />
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<i>En el momento del suceso no circulaba ningún vehículo ya que el
presidente del ANAS, Pietro Ciucci, decretó su cierre de manera cautelar
porque los técnicos ya habían detectado un día antes, el 30 de diciembre, un <b>"anómalo hundimiento" </b>del terreno.</i><br />
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Lo primero que se me ha venido a la cabeza ha sido "<i>Encuentros en la tercera fase</i>" , ¿qué será ese misterioso hundimiento? intrigado por esta curiosa reseña me dispongo a analizar las imagenes del desastre:<br />
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Pues resulta que el hundimiento tiene poco de misterioso, ya que se trata de un <b>deslizamiento</b> de libro. Incluso se pude apreciar perfectamente el reflejo de la cabeza del deslizamiento sobre el asfalto, el cual parece tratarse de un <b>deslizamiento local</b> en el interior de la obra de tierra.<br />
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Se puede ver también que hay presencia de nieve y que el terraplén parece estar empapado.<br />
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Presentadas las pruebas, parece probable que el deslizamiento se haya desencadenado por un exceso de presión intersticial en el interior del terraplén debido a la lluvia. También es posible que la causa del hundimiento haya sido un asiento diferencial de la cimentación del terraplén respecto al estribo de hormigón (elemento más riígido), aunque apuesto más por lo primero o una combinación de ambas situaciones.<br />
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Supongamos que la causa ha sido un incremento de pesión de poro. La pregunta que cabe hacerse ahora es si lo que ha fallado ha sido el sistema de drenaje, la resistencia del terraplén o ambas cosas. Mi teoría es que el fallo se ha producido por falta de resistencia debido a una <b>mala compactación </b>del terraplén, ya que además la zona del deslizamiento es justo en el entronque con los estribos de la obra de hormigón, siendo esta una zona donde la compactación requiere especial cuidado.<br />
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La mala compactación del material hace que el ángulo de rozamiento y la cohesión del mismo no alcancen los valores de diseño estipulados en proyecto, reduciendo por tanto el factor de seguriad al deslizamiento del <b>terraplen</b> y provocando el fallo en este caso.<br />
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Diseñar un terraplen para que no falle por deslizamiento local no tiene ningún misterio, asi que me parece poco probable que el fallo venga de un mal diseño en proyecto del mismo.<br />
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Por otro lado, no puedo evitar pensar mal y preguntarme de dónde han recortado esos 3 meses. ¿Habrán dado menos pasadas con las compactadoras de las indicadas en proyecto? y en el caso de que la contrata haya hecho eso, ¿la autoridad competente haría la vista gorda durante las mediciones de densidad a cambio de una mordida?.<br />
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Lo que es evidente es que alguien ha metido la pata, autoridad o la contrata, ya que este tipo de situaciones no son imprevistos ni anomal<span style="color: #0000ee;"><u>í</u></span>as y más habiendose producido justo al lado del estribo un viaducto, ya que esta es una zona donde se tiene especial cuidado durante diseño y donde (en teoría) se debe conocer bien el terreno donde se está cimentando.Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-3088136611203255312014-10-12T09:45:00.000-07:002014-10-12T09:45:02.905-07:00Momentos negativos en viga bi-apoyada, ¿nos hemos vuelto locos?La forma más común de “<b>apoyar</b>” una viga es dejarla en reposo
sobre una base o punto de apoyo, normalmente apoyos de neopreno o algún otro sistema similar. Parece lógico pensar, y es lo que uno piensa de forma instantanea cuando lee "<b>viga bi-apoyada</b>", que en las zonas de apoyo no van a aparecer <b>momentos negativos</b>. Pero, ¿podemos estar seguros de esto?.<br />
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<tr><td class="tr-caption" style="text-align: center;">Apoyos de neopreno</td></tr>
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La viga apoyada que se estudia en
<b>resistencia de materiales</b> y que se emplea para realizar cualquier tipo de
análisis estructural, no se corresponde de forma exacta con la idea que
tenemos de una viga apoyada en la realidad. En la viga “<b>ideal</b>”, que solemos emplear por inercia (mal hecho, porque siempre hay que pensar bien que es lo que se está haciendo y cuales son las <b>hipótesis</b> de los modelos que estamos empleando), se considera que las restricciones de los apoyos se aplican en
el<b> centro de gravedad</b> de la sección, en lugar de en la <b>cara inferior</b> como
ocurre en la realidad.</div>
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El <b>punto de apoyo</b> influye de forma crítica en la solución y
hay que tener cuidado con esto. La teoría de vigas, de forma general, parte de
una serie de simplificaciones. Una de ella es suponer que la viga se puede
considerar como una línea, el centro de gravedad, de forma que
supone que todas las cargas y restricciones actuan sobre el mismo.</div>
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En la vida real una <b>viga apoyada</b>, se encuentra
apoyada sobre la <b>cara inferior</b> de su sección. Es decir, la restricción al
desplazamiento se encuentra en la <b>fibra inferior</b> de la sección y no en el
centro de gravedad de la misma. (De forma similar ocurre con las cargas).</div>
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Uno puede pensar que cuando el canto de una viga es
relativamente pequeño, la influencia del punto de introducción de los apoyos es
irrelevante. Pero, ¿cómo de irrelevante resulta despreciar este efecto y
cuando podemos despreciarlo? La respuesta es que siempre que no aparezcan
<b>reacciones horizontales</b> en los apoyos (en el caso de emplear apoyo+carrito, por ejemplo), podemos despreciar este
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwJjS1XtN7H6qOO_dKV1jsUitl7a7_XhJ7i42H46walTHYOyTvMvR6et27jdtPbSlZc-vA7hR0oU1gf34noh2VfV8_aQrgc5di-R-Kzj3UGww5uQ57NR6qRheNivcyvLfbBmX2jwtmteGT/s1600/homeer.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwJjS1XtN7H6qOO_dKV1jsUitl7a7_XhJ7i42H46walTHYOyTvMvR6et27jdtPbSlZc-vA7hR0oU1gf34noh2VfV8_aQrgc5di-R-Kzj3UGww5uQ57NR6qRheNivcyvLfbBmX2jwtmteGT/s1600/homeer.gif" /></a>La confusión, y<b> aquí es donde podemos meter la pata de forma
bochornosa</b>, es cuando las reacciones horizontales de los apoyos no son nulas,
ya sea porque aparece<b> rozamiento</b> en los apoyos o porque ambos apoyos están diseñados para
absorber <b>componente horizontal</b>.<br />
<br />
El problema en este caso es que el punto de
aplicación de los apoyos no solo no resulta irrelevante en el análisis, sino que podemos
estar cometiendo <b>errores en las flechas y esfuerzos del orden del 50%</b> si no los tenemos
en cuenta de forma adecuada.<br />
<br />
<br />
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Para ilustrar esto, consideremos una viga <span style="mso-spacerun: yes;"> </span>bi-apoyada (apoyo+apoyo) de 6 metros de luz y
sección 10mmx1000mm, con una carga de 100N aplicada en centro de vano. Esta viga la hemos modelado con el programa de elementos finitos <b>SAP2000</b> empleando elementos lineales tipo “<b>frame</b>”(izquierda) y
elementos área tipo “<b>plane</b>" con tensión plana (derecha):</div>
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<br /></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXy8LcIFm_YIM3UbB56oejzDB_hS7yCzZJuxq8c8HChVDb5eALqBCCueQpAvS6_HtWRUAt3lLn_IFdpeAQ-VspcUyImuDUk8PBYHgVBiTcRf7w1xUH3M4rsvrkgaqRmex-Fl8y1wMknBMl/s1600/modelovigas.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXy8LcIFm_YIM3UbB56oejzDB_hS7yCzZJuxq8c8HChVDb5eALqBCCueQpAvS6_HtWRUAt3lLn_IFdpeAQ-VspcUyImuDUk8PBYHgVBiTcRf7w1xUH3M4rsvrkgaqRmex-Fl8y1wMknBMl/s1600/modelovigas.jpg" height="213" width="640" /></a></div>
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En el modelo con elementos área "plane" hemos aplicado los apoyos en la cara inferior de la viga, del mismo modo que se aplicarían en la realidad.<br />
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</xml><![endif]-->Como resultado del análisis estático se obtiene en el modelo
“frame” una flecha máxima de 21’74mm mientras que en el modelo “plane” la
flecha máxima es de 9’58mm, aproximadamente la mitad. <b>¿Por qué no coinciden las flechas?¿Qúe está pasando aquí?. </b></div>
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Si exageramos la deformada, podemos intuir mejor lo que está
ocurriendo:</div>
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Se puede ver que en la zona de los apoyos la sección del modelo "plane" no se
está deformando de la misma forma que en el caso de una viga bi-apoyada, sino
que aparece un <b>punto de inflexión</b> en la curvatura de la viga.<span style="mso-fareast-language: ES; mso-no-proof: yes;"> <span style="mso-spacerun: yes;"> </span>Si observamos las <b>tensiones normales</b> S11 en los
elementos “plane”, vemos como en la zona del apoyo la cara superior se
encuentra traccionada y la inferior comprimida (momento negativo), mientras que
en el centro de vano ocurre a la inversa (momento positivo), es decir se produce una <b>inversión en el signo del momento</b> como se puede apreciar:</span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0tw3Xfqg4iLb5JxdNlWzsm2CtgTBQcE3erjCJeZx2NAPXURzRXk8kv2f-eQ9yZWRmsFgN6ARkyFTW98rv5TLbkpJKem2bM9CrlNFJiCmf5DVc-xv7qvNy7DDOk6ZtuWWWquG0Eq5wzxjc/s1600/s11.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0tw3Xfqg4iLb5JxdNlWzsm2CtgTBQcE3erjCJeZx2NAPXURzRXk8kv2f-eQ9yZWRmsFgN6ARkyFTW98rv5TLbkpJKem2bM9CrlNFJiCmf5DVc-xv7qvNy7DDOk6ZtuWWWquG0Eq5wzxjc/s1600/s11.jpg" height="360" width="640" /></a></div>
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<br /></div>
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En el caso de emplear elementos “frame”, o de resolver el
problema de la viga de forma analítica, estamos considerando que los apoyos se
encuentran aplicados en el centro de gravedad de la sección, en lugar de en la cara
inferior de la misma, como habiamos modelado en el caso de elementos “plane”.</div>
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<br /></div>
<div class="MsoNormal">
Si cambiamos la restricción de apoyo<span style="mso-spacerun: yes;"> en el modelo "plane" </span>y la situamos en la<b> fibra central</b> de la
sección, vemos como la deformada coincide con lo esperado para el caso de viga
apoyada, arrojando una flecha máxima de 21’73mm frente a los 21’74mm del modelo
“frame”, esta vez muy similar:</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaXZp_45vHq8-GxZJsU3xdRCHaqwzjcgc_VCvvgaBqPE60Z3N4Tcdv2G2lPEPfmjkbBHNyNm-WDriFqu-N69JkjoUP3A7EaG-a3wxX84KzU8UixkcvXQYvspeMyo2O4le2G1YEjdia55WZ/s1600/modelovigas4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaXZp_45vHq8-GxZJsU3xdRCHaqwzjcgc_VCvvgaBqPE60Z3N4Tcdv2G2lPEPfmjkbBHNyNm-WDriFqu-N69JkjoUP3A7EaG-a3wxX84KzU8UixkcvXQYvspeMyo2O4le2G1YEjdia55WZ/s1600/modelovigas4.jpg" height="248" width="640" /></a></div>
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<br /></div>
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<div class="MsoNormal">
Vemos también que en este caso la distribución de <b>tensiones normales</b> de modelo "plane" se
corresponde con la de la viga biapoyada, estando la cara superior comprimida y la inferior traccionada en todos los puntos (sin puntos de inflexión
en el momento):</div>
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<br />
De forma análoga también podiamos haber cambiado el punto de inserción de
las cargas/reacciones en el modelo “frame”, y en lugar de considerar el centro de
gravedad, considerar la<b> cara inferior</b> de la sección.<br />
En este caso aparece de nuevo una inflexión
en la curvatura (como si estuviera parcialmente empotrada) que se traduce en un
<b>momento negativo</b> en la zona de apoyo. Obtenemos una flecha máxima en el modelo
"frame" de 9.52mm, frente a los 9.58mm del modelo “plane” con los apoyos en las
esquinas inferiores.</div>
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Por tanto se comprueba que el <b>punto de introducción de los
apoyos</b> en el modelo es crucial cuando aparecen reacciones horizontales. En la
mayoría de los casos una viga biapoyada se encuentra apoyada sobre su<b> cara inferior</b>, no en su centro de gravedad, además de que siempre existe una
cierta reacción horizontal en los apoyos debida al rozamiento y a la propia rigidez
de los mismos (<b>no existe el apoyo ideal</b>). Por este motivo si realizaramos el estudio
de esta viga (en la que aprecen reacciones horizontales) empleando la formula clásica de resistencia de materiales para la
viga biapoyada sin considerar la excentricidad de los apoyos estaríamos
cometiendo un error en la estimación de la flecha y otro error de similar
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Lo que más <span style="mso-spacerun: yes;"> </span>puede
chocar de todo esto es que una viga con restricciones de apoyo presente un
<b>momento negativo</b> en sus extremos. ¿Cómo es posible que equilibre este momento negativo
si en los apoyos no existe reacción de momento? </div>
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<br /></div>
<div class="MsoNormal">
Es posible, porque no es del todo cierto que no exista una
reacción de momento.<span style="mso-spacerun: yes;"> </span>Si nos paramos a
pensar por un segundo, nos daremos cuenta<span style="mso-spacerun: yes;">
</span>que al situar los apoyos en la cara inferior estamos situando la
<b>reacción horizontal</b><span style="mso-spacerun: yes;"> </span>“Rh” con una
<b>excentricidad</b><span style="mso-spacerun: yes;"> </span>“e” respecto del centro de
gravedad. Esto es la causa de<span style="mso-spacerun: yes;"> </span>que el
apoyo pueda absorber un momento M=Rh*e, siempre que Rh no sea nulo, ( ya que los
momentos flectores de una viga están calculados tomando como centro el centro
de gravedad de la sección).</div>
<div class="separator" style="clear: both; text-align: center;">
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Cuanto menor sea la componente “Rh” (menor sea el rozamiento
o la rigidez horizontal del apoyo), más se aproximará el comportamiento de la
viga a la de una <b>viga apoyada</b> ideal.</div>
<div class="MsoNormal">
Si colocamos en uno de los extremos un apoyo en carrito,
la<span style="mso-spacerun: yes;"> </span>componente "Rh" será nula y podemos ver como en este caso la
viga si se comporta como si estuviera apoyada, a pesar de incorporar los apoyos en su cara inferior (ya que Rh=0, M=Rh*e=0*e=0, por lo que pierde la capacidad para absorber momento en sus extremos).</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
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Como conclusión podemos afirmar (aunque nos duela en el corazón) que en el mundo real una viga <b>bi-apoyada </b>(en su cara inferior), en la que
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-4724129225739835342014-09-26T06:23:00.000-07:002014-10-12T09:50:09.639-07:00English for Engineers: Nociones de mecánica de suelos (II)Un saludo y bienvenidos a esta nueva sección dedicada a aprender<b> inglés técnico</b> de utilidad para <b>ingenieros civiles</b>
(English for engineers) en donde veremos vocabulario y expresiones de
utilidad al mismo tiempo que refrescamos algunos conceptos de la
ingeniería civil.<br />
<br />
Durante está serie de entradas dedicadas a la <b>mecánica de suelos, </b>subtitularé una serié de videos en inglés muy interesantes sobre dicho tema al español y al inglés. El objetivo es que trateis de entender el dialogo empleando los subtitulos en inglés, para así asociar cada a cada palabra su sonido de forma natural. <br />
<br />
Este segundo video se titula "<b>The particle nature of soil</b>" y en el se tratan algunos conceptos básicos que definen el comportamiento del suelo: de que está hecho y como resiste la carga.<br />
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<span style="font-size: large;"> <u><b>The particle nature of soil</b><b> (Video)</b></u></span></div>
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<span style="font-size: large;"><u><b>Vocabulary for civil engineers</b></u></span></div>
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<ul>
<li><b>Soil:</b> suelo</li>
<li><b>Particles</b>: partículas</li>
<li><b>Gravel: </b>grava</li>
<li><b>Sand: </b>arena</li>
<li><b>Silt: </b>limo</li>
<li><b>Clay:</b> arcilla<a name='more'></a></li>
<li><b>Limestone: </b>caliza</li>
<li><b>Challenge: </b>reto</li>
<li><b>Fundation: </b>cimentación</li>
<li><b>Skyscraper: </b>rascacielos</li>
<li><b>Tunnel:</b> tunel</li>
<li><b>Excavation: </b>excavación</li>
<li><b>The behaviour (of a material): </b>el comportamiento (de un material)</li>
<li><b>Stiff: </b>rigido, duro<b><br /></b></li>
<li><b>Stiffness:</b> rigidez</li>
<li><b>Load: </b>carga</li>
<li><b>Scale model:</b> modelo a escala</li>
<li><b>Shearing resistance:</b> resistencia al corte</li>
</ul>
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<span style="font-size: large;"><u><b>Expressions for civil engineers</b></u></span></div>
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<u><span id="goog_725298028"><b><b>To design:</b></b> diseñar</span></u><span id="goog_725298028"><u> </u></span></div>
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<span id="goog_725298028"><span id="goog_725298028"></span>When<b> designing</b> a tunnel, one of the big challenges that an engineer has to face is the high uncertainty in the materials that form the different layers of the soil </span><span id="goog_725298028"><span id="goog_725298028">and its behaviour</span>. Drilling through damp clay is completely different from blasting through hard limestone, thus the </span><span id="goog_725298028"><span id="goog_725298028">necessary </span>equipment to do so. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn5BVBPrCbWdxLPetjqc2iTOr7QemOqyc9ehPUbVntpXGMEMIYO3Rpb5zE-7RH2Dt5BYiB8vTpirXbTleFPcnftxVEIAn5XJBx-2VEU-rec_xXVvhInu6Mm-ay9sr12naPzXNvd3x4lRo_/s1600/2_3_1_jumbo_slide1_01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn5BVBPrCbWdxLPetjqc2iTOr7QemOqyc9ehPUbVntpXGMEMIYO3Rpb5zE-7RH2Dt5BYiB8vTpirXbTleFPcnftxVEIAn5XJBx-2VEU-rec_xXVvhInu6Mm-ay9sr12naPzXNvd3x4lRo_/s1600/2_3_1_jumbo_slide1_01.jpg" height="150" width="400" /></a></div>
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<i>Al <b>diseñar</b> un tunel, uno de los mayores retos al que se enfrenta un ingeniero es el alto grado de incertidumbre en los materiales que forman las distintas capas del suelo y su comportamiento. Excavar a traves de arcilla húmeda es completamente diferente a atravesar caliza dura, y por consiguiente también es diferente el equipo necesario para hacerlo.</i></div>
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<u><b>To resist/ to bear:</b> resistir, soportar</u><br />
<span id="goog_725298028"></span>The engineers built a scale model of the bridge to test it in the lab. The model was a perfect replica of how the real one would be. Not only the geometry was scaled down but also the stiffness of its elements, this way the engineers were able to predict accurately its behaviour againts the wind load and check whether it could <b>resist</b> it or not.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSXQs_yRmexX3hz2mJA3i8OYi9HaoYuSG0WJylFCZ4UA70nIUwbHkd1JCX7ThG1GlHtntQDRON4NmJNYs3W88RswG_mJPxGYniGAD6jLTveN9XhA3ZyFl_lQUwbGdWz6EP5t-35VXC0mPQ/s1600/Akashi+Kaiky%C5%8D+Bridge48.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSXQs_yRmexX3hz2mJA3i8OYi9HaoYuSG0WJylFCZ4UA70nIUwbHkd1JCX7ThG1GlHtntQDRON4NmJNYs3W88RswG_mJPxGYniGAD6jLTveN9XhA3ZyFl_lQUwbGdWz6EP5t-35VXC0mPQ/s1600/Akashi+Kaiky%C5%8D+Bridge48.JPG" height="180" width="320" /></a></div>
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<i>Los ingenieros construyeron un modelo a escala reducida del puente para experimentar en el laboratorio. El modelo era una replica perfecta de como seria el puente real. No solo la geometría estaba a escala si no también la rigidez de sus elementos, de esta forma los ingenieros fueron capaces de predecir con precisión su comportamiento frente a la acción del viento y comprobar si la podría <b>resistir</b> o no.</i><br />
<br />
<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-79419947439200709612014-09-23T12:18:00.001-07:002014-09-26T06:40:03.888-07:00English for Engineers: Nociones de mecánica de suelos (I)Un saludo y bienvenidos a esta nueva sección dedicada a aprender<b> inglés técnico</b> de utilidad para <b>ingenieros civiles</b> (English for engineers) en donde veremos vocabulario y expresiones de utilidad al mismo tiempo que refrescamos algunos conceptos de la ingeniería civil.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8a36SyNycct3k5_VPNIY0q6b0eMXJg9MZtoKP7oDZbqs6qBP7edHKmIXYw2Jg2A_QzRc52VNDLO11SbirTKgXZzseUkG-8CR8ntacLGqgiqUHZExI92q_XpYNxU3_LuPWwwpkGKm3k7zk/s1600/article-2169586-13F32DDC000005DC-141_634x425.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8a36SyNycct3k5_VPNIY0q6b0eMXJg9MZtoKP7oDZbqs6qBP7edHKmIXYw2Jg2A_QzRc52VNDLO11SbirTKgXZzseUkG-8CR8ntacLGqgiqUHZExI92q_XpYNxU3_LuPWwwpkGKm3k7zk/s1600/article-2169586-13F32DDC000005DC-141_634x425.jpg" height="267" width="400" /> </a></div>
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Durante estas primeras entradas subtitularé en inglés y en español una serie de videos cortos muy interesantes relacionados con la<b> mecánica de suelos</b>, añadiendo vocabulario y expresiones junto a ejemplos que aperecen en los mismos.<br />
<br />
El primer video se trata de una introducción muy somera a la <b>mecánica de suelos</b> y la <b>geotécnica</b>, en que consisten y de que problemas se ocupan. Mi recomendación es que lo veais en primer lugar con los subtitulos
en inglés y trateis de comprender todo lo que podais para despues
comparar con los subtitulos en español activados. (Si los subtitulos no aparecen, clickad en el video para verlo desde youtube)<br />
<br />
<div style="text-align: center;">
<span style="font-size: large;"> <u><b>An introduction to Soil mechanics</b><b> (Video)</b></u></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='426' height='240' src='https://www.youtube.com/embed/EkNY9DHJ8bs?feature=player_embedded' frameborder='0'></iframe> </div>
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<span style="font-size: large;"><u><b>Vocabulary for civil engineers</b></u></span></div>
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<ul style="text-align: justify;">
<li><span id="goog_725298028"><b>Civil engineering:</b> ingeniería civil</span></li>
<li><span id="goog_725298028"><b>Geotechnical engeenering</b>: geotécnia</span></li>
<li><span id="goog_725298028"><b>Soil mechanics:</b> mecánica del suelo </span></li>
<li><span id="goog_725298028"><b>Infrastructure:</b> infraestructura</span></li>
<li><span id="goog_725298028"><b>Structure:</b> estructura</span><span id="goog_725298028"><a name='more'></a> </span></li>
<li><span id="goog_725298028"><b>Project:</b> proyecto</span></li>
<li><span id="goog_725298028"><b>Road:</b> carretera</span></li>
<li><span id="goog_725298028"><b>Railway:</b> via de ferrocarril </span></li>
<li><span id="goog_725298028"><b>Tunnel:</b> tunel</span></li>
<li><span id="goog_725298028"><b>Canal: </b>canal de agua</span></li>
<li><span id="goog_725298028"><b>Damn:</b> presa</span></li>
<li><span id="goog_725298028"><b>Airport:</b> aeropuerto</span></li>
<li><span id="goog_725298028"><b>Bridge:</b> puente</span></li>
<li><span id="goog_725298028"><b>Building:</b> edificio</span></li>
</ul>
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<u><span id="goog_725298028"><b>To fall in/ to collapse</b>: colapsar (sobre si mismo)</span></u><span id="goog_725298028"><u> </u></span></div>
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<span id="goog_725298028"><span id="goog_725298028">No one were surprised when a section of the tunnel<b> fell in</b> during construction, not only because the </span>soil was poorer than expected in the project but also because the contractor was using really cheap materials to cut costs.</span></div>
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<i><span id="goog_725298028">Nadie se sorprendió cuando una sección del tunel <b>colapsó</b>
durante su construcción, no solo porque el suelo era de peor calidad
que lo esperado en proyecto, si no también porque el contratista estaba
utilizando materiales de mala calidad para reducir costes. </span></i></div>
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<span id="goog_725298028"><span id="goog_725298028"><u><b>To sink down:</b> hundirse en el terreno </u></span></span></div>
<span id="goog_725298028">It had been pouring non stop the entire week, so </span>when<span id="goog_725298028"> the eartquake stroke the city some of the oldest buildings, which were founded in sand, <b>sank down</b> due to liquefaction of the soil.</span><br />
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<span id="goog_725298028"><i>Habia
estado lloviendo a cantaros sin parar toda la semana, asi que cuando el
terremoto golpeo la ciudad algunos de los edificios más viejos,
cimentados en arenas, se <b>hundieron</b> debido a la liquefacción del terreno.</i></span></div>
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-72794798825573751512014-09-15T06:00:00.001-07:002014-09-18T08:32:24.166-07:00Vortex Shedding. Algunos comentarios. (Parte II)<!--[if gte mso 9]><xml>
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<![endif]-->Continuamos con la introducción que vimos en la <a href="http://ingenieriaparatorpes.blogspot.com.es/2014/08/vortex-shedding-y-la-nina-fantasma-del.html#more">(Parte I</a>) al fenómeno conocido como <b>Vortex Induced Vibrations (VIV). </b>En esta segunda parte vamós a realizar algunos comentarios sobre las características principales de la acción que este fenómeno induce sobre la estructura.<br />
<br />
En el caso de un <b>cuerpo cilíndrico</b>
de superficie lisa sumergido en un flujo, se puede observar que a partir de valores de Re
comprendidos entre 5 y 15 se forma una pareja de vórtices fijos aguas abajo del cilindro. Estos vórtices, qué llevan asociados zonas de baja presiones, se desprenden (<b>vortex shedding</b>) de forma<span style="mso-spacerun: yes;"> </span>alternativa y periódica a partir de cierto valor
de Re, formando lo que se
conoce como <b>calle vórtices de Von Karman</b>.<br />
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La frecuencia de desprendimiento de estos vórtices <span style="mso-spacerun: yes;"> </span>para un flujo uniforme viene caracterizada en función del
<b>número de Strouhal (St)</b>. Este número adimensional relaciona la frecuencia de desprendimiento
de vortices con la velocidad del flujo <span style="mso-spacerun: yes;"> </span>y
con la geometría del cuerpo:</div>
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Para cuerpos con secciones con esquinas como pueden ser
secciones rectangulares, perfiles en I, en T o en L<span style="mso-spacerun: yes;">
</span>el número de Strouhal toma un valor constante e independiente del <b>número de Reynolds
(Re)</b> , el cual se encuentra tabulado en diferentes normativas.<br />
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<tr><td class="tr-caption" style="text-align: center;">Nº de Strouhal VS Nº de Reynolds</td></tr>
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Para secciones cilíndricas el número de Strouhal varía en función del
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considerar constante de valor 0.22</div>
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De esta forma se puede considerar que por lo
general la frecuencia de desprendimiento de vórtices se relaciona de forma
lineal con la <b>velocidad del flujo</b>.<span style="mso-fareast-language: ES; mso-no-proof: yes;"> </span></div>
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El<b> desprendimiento de vórtices</b> origina unas<b> presiones de
arrastre</b> sobre el cuerpo sumergido que varian con el tiempo de forma
periódica. En la siguiente figura se puede ver, para el caso de un cilindro sumergido en un flujo, la distribución de las presiones según la coordenada angular. Cada color representa un intervalo de tiempo diferente. </div>
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Estas presiones integradas en toda la superficie se
traducen en una <b>fuerza resultante</b> que puede descomponerse en dos fuerzas de
<b>carácter sinusoidal</b>. Una de ellas paralela a la dirección del flujo FD cuya
frecuencia<span style="mso-spacerun: yes;"> es </span>el doble que la frecuencia de desprendimiento de los
vórtices, la cual oscila respecto a un valor medio. Y otra fuerza transversal<span style="mso-spacerun: yes;"> </span>al flujo FL <span style="mso-spacerun: yes;"></span> de igual frecuencia que la frecuencia de desprendimiento de los
vórtices, la cual oscila respecto a un valor nulo.<span style="mso-spacerun: yes;">
</span></div>
<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg8lPfeBjF7VN1hyDeQlgy4kRDv8HHN2zQHLS0i9oeSXuY4mXwrjw-zAX_mXDaQ33ZEnLTZ806J3rtNXhBayg0aHIHPny54urIk-tvTTrnlpyT_xoZKvr1ZCmgtyq095R4NpxBlFDrm-dx/s1600/presiones.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg8lPfeBjF7VN1hyDeQlgy4kRDv8HHN2zQHLS0i9oeSXuY4mXwrjw-zAX_mXDaQ33ZEnLTZ806J3rtNXhBayg0aHIHPny54urIk-tvTTrnlpyT_xoZKvr1ZCmgtyq095R4NpxBlFDrm-dx/s1600/presiones.jpg" height="376" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Presiones inducidas por desprendimiento de vortices. En rojo fuerza resultante de las presiones.</td></tr>
</tbody></table>
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</xml><![endif]-->La naturaleza periódica de estas dos fuerzas es la causa del
fenómeno conocido como<b> vortex induced vibrations (VIV).</b> <span style="mso-spacerun: yes;"> </span>Cuando <span style="mso-spacerun: yes;"> </span>el periodo de alguna de estas dos fuerzas se
acerca al periodo natural de algun modo de oscilación de la
estructura se producirá la resonancia, viendose las deformaciones amplificadas y pudiendo ocasionar el fallo de la estructura. Debido a que la frecuencia de estas dos fuerzas depende de forma lineal
con la velocidad del flujo según el <b>número de Strouhal (St)</b>, van a existir dos
<b>velocidades criticas</b> del flujo (Ucr) durante las cuales puede ocurrir la resonancia.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOTJPDaoL06bYSq1c3TLtoY2H8M1ghYhTPBuDjRq2cmRcvYLGSGMKP3-T9eOM0IkajvTvdSIFfPJc4wMbYCv_9JV-4wn5uOyVeQoCvN2Zag6luA-DnBhNr7Bh3bQ-BE9QgH0EmgDr6o8_L/s1600/fig2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOTJPDaoL06bYSq1c3TLtoY2H8M1ghYhTPBuDjRq2cmRcvYLGSGMKP3-T9eOM0IkajvTvdSIFfPJc4wMbYCv_9JV-4wn5uOyVeQoCvN2Zag6luA-DnBhNr7Bh3bQ-BE9QgH0EmgDr6o8_L/s1600/fig2.jpg" height="253" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Velocidades de flujo en las que puede ocurrer la resonancia</td></tr>
</tbody></table>
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Cuando la estructura entra en <b>resonancia</b> y
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de los vórtices. Cuando esto sucede la relación lineal entre velocidad y frecuencia
de desprendimiento de vórtices que venia dada por el<b> número de Strouhal (St)</b> deja de cumplirse. Los vórtices se comienzan a desprender con la misma frecuencia natural a la que la estructura oscila, de forma independiente a la velocidad del flujo. Este fenómeno se conoce como <b>lock-in.</b> </div>
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<br /></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5OaqEBhplzdTYNySAZbIbAQdF4ZNbVyRb3DJq3OtP0e4O8WRN_vF36r1dveQdfTvlBWYG_QgHbj_CGXsIDDFdKiq9eU1lpaDDiOFpieS0WFwysAqpz8iQCuBDgFLYeaTeCLKkIdxVFQTG/s1600/fig3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5OaqEBhplzdTYNySAZbIbAQdF4ZNbVyRb3DJq3OtP0e4O8WRN_vF36r1dveQdfTvlBWYG_QgHbj_CGXsIDDFdKiq9eU1lpaDDiOFpieS0WFwysAqpz8iQCuBDgFLYeaTeCLKkIdxVFQTG/s1600/fig3.jpg" height="640" width="516" /></a></div>
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En la figura superior se puede ver como
la relación lineal entre velocidad y frecuencia de desprendimiento de los
vórtices se rompe en el momento en el que la amplitud de la vibración de la estructura comienza a ser apreciable.</div>
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<br /></div>
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Para evitar los problemas inducidos por el desprendimiento de vortices, la tecnica más simple consiste en diseñar la estructura para que sus <b>modos naturales</b> de oscilación se encuentren fuera del rango en el que se pueda dar este fenómeno, esto es rodear el problema. También podemos dotar a la superficie de la estructura de elementos especiales que "confundan" al flujo de aire, tales como <b>alerones o helicoides</b>, evitando el desprendimiento periodico de vórtices.</div>
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<br /></div>
<div class="MsoNormal">
Si quereis saber más sobre diseño de estructuras frente a <b>vortex shedding</b> os recomiendo que le echeis un vistazo al capítulo 9 (Vortex induced oscillations) de la <b>DNV-RP-C205</b>:</div>
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<br /></div>
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<a href="https://www.google.es/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCYQFjAA&url=https%3A%2F%2Fexchange.dnv.com%2Fpublishing%2Fcodes%2Fdownload.asp%3Furl%3D2010-10%2Frp-c205.pdf&ei=XNsWVIGKCtLhatO9gpgM&usg=AFQjCNFwmP6S2467M2WkA8BZcjx1_dvgUw&sig2=-awdW0Zkw2xxsLkGXmxyNw&bvm=bv.75097201,d.d2s&cad=rja">DNV-RP-C205: Environmental conditions and environmental loads</a></div>
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<a href="http://www.vibrationdata.com/tutorials/VIV.pdf">Fundamentals of vortex induced vibrations by charles dalton</a></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/blZsWlIH-Fk?feature=player_embedded' frameborder='0'></iframe></div>
<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-79297100781420846962014-09-04T06:10:00.000-07:002014-09-08T04:42:48.121-07:00¿Cuándo aplicar la hipótesis de pequeñas deformaciones? (Parte III)En esta última entrada dedicada al <b>cálculo de estructuras</b> daremos finalmente respuesta a la pregunta "<i>¿Cuándo podemos aplicar la hipótesis de pequeñas deformaciones?</i>", y por si alguien se esta ponieno nervioso ya con tanta ecuación, voy a empezar la casa por el tejado y os voy a dar directamente <b>la receta:</b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDyYR2zqiySP8uBePcxYOVMKmCPCBLtomvKee3RB7S558tlpeUx_n73uoXMpMR4B1eVUa58KA9gYWCKxe4v6OTYxoCdbaNIb1uRwqSP9ql9HCkgc6f9VE0ISpFRClpioA1_j1rK9irerVn/s1600/CudroLimite_de_AplicacionPeque%C3%B1asDeformaciones.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDyYR2zqiySP8uBePcxYOVMKmCPCBLtomvKee3RB7S558tlpeUx_n73uoXMpMR4B1eVUa58KA9gYWCKxe4v6OTYxoCdbaNIb1uRwqSP9ql9HCkgc6f9VE0ISpFRClpioA1_j1rK9irerVn/s1600/CudroLimite_de_AplicacionPeque%C3%B1asDeformaciones.jpg" height="394" width="640" /></a></div>
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Esta pequeña tabla que he confecionado es todo lo que necesitas para saber si con la<b> hipótesis de las pequeñas deformaciones</b> los resultados obtenidos en tu cálculo serán o no lo suficiente precisos.<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span><br />
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">La tabla está diseñada a partir del caso de viga empotrada en voladizo con una
carga<span style="mso-spacerun: yes;"> </span>puntual en su extremo y sus
resultados se pueden considerar del lado de la seguridad respecto a otros
sistemas estructurales, obteniendo en cualquier caso un error menor.</span><br />
<br />
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Pero si no me crees, puedes seguir leyendo y comprobar por ti mismo de donde ha salido esta bonita tabla. </span><br />
<a name='more'></a><br />
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF5vqQ5EbANzcTW_vhejmyNM9ydivpfTwiQ446T60rhS8En12EXSAn4MLU9l3_7aHf47rAw4qZ-7pjtjdfRRY-IXsCeXrLS7nOsckf9W3I5LeL_Mnw4LWyT7e9XKIOgHJJyK6BKT2yyhPq/s1600/1216698031.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF5vqQ5EbANzcTW_vhejmyNM9ydivpfTwiQ446T60rhS8En12EXSAn4MLU9l3_7aHf47rAw4qZ-7pjtjdfRRY-IXsCeXrLS7nOsckf9W3I5LeL_Mnw4LWyT7e9XKIOgHJJyK6BKT2yyhPq/s1600/1216698031.jpg" height="240" width="320" /></a>Recapitulando un poco, en la entrada anterior <a href="http://ingenieriaparatorpes.blogspot.com.es/2014/08/cuando-aplicar-la-hipotesis-de-pequenas_29.html">(Parte II)</a> habiamos
establecido <b>EDO</b> y las condiciones de contorno que definen la deformada
de una viga sin considerar la hipótesis de pequeñas deformaciones. Sin
embargo, por su complejidad, no la habiamos llegado a resolver.<br />
<br />
Antes de ponernos a resolver la ecuación (numérica o analíticamente) como locos sería conveniente tener una idea de que forma puede tener esta, la cual deduciremos con ayuda del <b>Teorema Pi de Buckingham. </b><br />
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Para ello tendremos que definir el número de <b>variables</b> que pensamos van a influir en el problema y el número de <b>dimensiones.</b> En nuestro caso, nos encontramos con 5 variables {E, I, L, P, Ymax}, (que se pueden descomponer en dimensiones de Longitud y Fuerza) y 3 dimensiones básias {Longitud, Masa, Tiempo}.<br />
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Según el Teorema Pi de Buckingham podremos formar 5-3=2 <b>monomios adimensionales</b> (A y B), los cuales estarán relacionados según una formula del tipo A=f(B). En nuestro caso, hemos formado los siguientes monomios:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB46_DMbOMXgUK7mc9HQgjxRRWW0gLrEzBo2bwNN-AVp66Q7zct4lu2vd3HxaZpzXMcVQ76S6TiTqSXnf4YsHJeniiI-zJhUlAbFTT6rpvY8kHOTyoC2xKRZpw-WICbquTTV-a7d8hgbet/s1600/13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB46_DMbOMXgUK7mc9HQgjxRRWW0gLrEzBo2bwNN-AVp66Q7zct4lu2vd3HxaZpzXMcVQ76S6TiTqSXnf4YsHJeniiI-zJhUlAbFTT6rpvY8kHOTyoC2xKRZpw-WICbquTTV-a7d8hgbet/s1600/13.jpg" /></a></div>
De forma que la solución de nuestro problema es de la forma:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvwqLOKYrQVzKRPUwMVBwV4DomW1TpL8mm12kJ1RWX7C79n1JQNnpLNsDr301AwTYLmDDEjTFQpJJKViSJC_SLRXAe1KpywmKicFgAfZ9FRnMpzjAKpvgwqIpX-X5QuzuNPA-R9vtsfLab/s1600/14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvwqLOKYrQVzKRPUwMVBwV4DomW1TpL8mm12kJ1RWX7C79n1JQNnpLNsDr301AwTYLmDDEjTFQpJJKViSJC_SLRXAe1KpywmKicFgAfZ9FRnMpzjAKpvgwqIpX-X5QuzuNPA-R9vtsfLab/s1600/14.jpg" /></a></div>
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Lo interesante de este resultado es que
hemos demostrado que existe un único <b>parámetro</b> que nos permite generalizar el
comportamiento de la viga para grandes deformaciones. Este parámetro, al que
llamaremos "<b>alfa</b>"</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; position: relative; top: 4.5pt;"></span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">, nos permitirá definir
la frontera de validez de la hipótesis de pequeñas deformaciones:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_RDr7dC9iSYBjo_LNzJ8C79_P22YQj2M5nEvpVIqrej-KKec-gtIKQj2nicPjuTTEgmKx7-rvxL294tBV87UfzJnqaGxQf2evwTOtZhNrgXNzfv5kMKvtvkwlbqUKxgeGIj-1wT7NM6KO/s1600/15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_RDr7dC9iSYBjo_LNzJ8C79_P22YQj2M5nEvpVIqrej-KKec-gtIKQj2nicPjuTTEgmKx7-rvxL294tBV87UfzJnqaGxQf2evwTOtZhNrgXNzfv5kMKvtvkwlbqUKxgeGIj-1wT7NM6KO/s1600/15.jpg" /></a></div>
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<![endif]--><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Para el caso de pequeñas deformaciones se puede observar como
la<b> flecha máxima</b> de la viga en voladizo sigue una expresión equivalente<span style="mso-spacerun: yes;">,
</span>ya que en dicho problema participan las mismas magnitudes y dimensiones:</span><br />
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Ya que ambas expresiones <span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><span style="mso-spacerun: yes;"></span></span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> dependen del mismo parámetro </span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; position: relative; top: 4.5pt;"></span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">"alfa", podremos compararlas
y estudiar el valor de dicho parámetro</span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> a partir del cual las
diferencias en los resultados comienzan a ser apreciables.</span> Como ya comentamos anteriormente, la resolución simbólica de la flecha para el caso de grandes
deformaciones puede resultar algo compleja y, aunque se puede hacer, yo he preferido
resolver el problema de forma numérica con ayuda del programa <b>Wolfram
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"></span>El procedimiento que he seguido ha sido realizar un cambio de variable para dejar la EDO de la deformada en función de "L" y "alfa", para después fijar un valor de "L" y calcular su solución para distintos valores de "alfa", ya que esta solo depende de dicho parámetro.<br />
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Tras resolver esta ecuación para los
distintos valores de "<b>alfa</b></span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; position: relative; top: 4.5pt;"></span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">”, he calculado la
flecha máxima <b>Ymax</b> en el extremo del voladizo por simple integración numérica de la expresión:</span></div>
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{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
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mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
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mso-pagination:widow-orphan;
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mso-hansi-theme-font:minor-latin;
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<![endif]-->
</span></div>
<div class="MsoNormal">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">El código que he empleado para la
resolución es el siguiente y como siempre lo podéis descargar desde este<a href="https://mega.co.nz/#!N9hWlAZL"> enlace</a>:</span></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFv6P1NJZTOmQrd7amKHWtR9G1346AhPuatDkmzCE81UdtGFdBRx0w4bHqfVm4xJ_IxSN5r4V_S3UDm0EfCgcK5vufUD2LaEkhvpYZq6QTKE_y5bCxxOaLId1dnAlADiM1oVnafluA8kd_/s1600/19.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFv6P1NJZTOmQrd7amKHWtR9G1346AhPuatDkmzCE81UdtGFdBRx0w4bHqfVm4xJ_IxSN5r4V_S3UDm0EfCgcK5vufUD2LaEkhvpYZq6QTKE_y5bCxxOaLId1dnAlADiM1oVnafluA8kd_/s1600/19.jpg" height="217" width="640" /></a> </div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"></span><!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
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<![endif]--><br />
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UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
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<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]-->
</div>
<div class="MsoNormal">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">De esta forma he podido obtener los pares
de puntos {alfa</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; position: relative; top: 4.5pt;"></span><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><span style="mso-spacerun: yes;"> </span>, Ymax/L} que definen la curva para el caso
de grandes deformaciones (en naranja punteado) y compararla con el caso de pequeñas deformaciones (en azul).</span></div>
<div class="MsoNormal">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></div>
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"></span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW-XMREunVeFYxwUG2JnwqqocaWEemGZ6HVhTXn2IUPrR32LAcaIR4jpb8G1lt-jHrebBwAOD2PWForX14dKeue9l4QH807CF7yRyIIMmJwgMz7Ls4lmEz0fdfn2i5yZXKJjfG1Jn4aD57/s1600/20.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW-XMREunVeFYxwUG2JnwqqocaWEemGZ6HVhTXn2IUPrR32LAcaIR4jpb8G1lt-jHrebBwAOD2PWForX14dKeue9l4QH807CF7yRyIIMmJwgMz7Ls4lmEz0fdfn2i5yZXKJjfG1Jn4aD57/s1600/20.jpg" height="440" width="640" /></a></span></div>
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">
</span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></div>
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">
</span>
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"></span><!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><br />
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<w:View>Normal</w:View>
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<w:PunctuationKerning/>
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<w:LidThemeOther>ES</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
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<m:mathPr>
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<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
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<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
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<w:LsdException Locked="false" Priority="34" SemiHidden="false"
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Como se puede observar en el caso de <b>pequeñas
deformaciones</b> el error incurrido es por exceso, es decir, las
deformaciones obtenidas son mayores que si consideráramos<b> grandes deformaciones</b>, por lo que en cualquier caso estamos
trabajando del lado de la seguridad siempre que consideremos la hipótesis de pequeñas deformaciones. <span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">El
error cometido al emplear la hipótesis de pequeñas deformaciones se puede
calcular como la diferencia entre la flecha obtenida con la hipótesis de
pequeñas deformaciones y la obtenida sin considerar dicha hipótesis, dividido
entre esta última. </span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span>El valor del parámetro "alfa<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.5pt; position: relative; top: 4.5pt;"></span>” que límita la frontera
entre pequeñas y grandes deformaciones dependerá del margen de error que
estemos dispuestos a admitir. El procedimiento a seguir, y que queda reflejado en la tabla resumen proporcionada al principio, será establecer un margen de error absoluto admisible. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6G20MjrAGSWTGsGposjzsPWKDN_lUUASh_cr1sUiQdemcaVEYUdqx8IBJwM6pgyp4385SlxxDAaDkYSBISAbeJOzeaMVK3VRGWrElzvsmhspSLD7hKu-Ef6F4PxDF3aa1-M5APRChYSsu/s1600/cute-cats-cups-large-msg-128926455737.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6G20MjrAGSWTGsGposjzsPWKDN_lUUASh_cr1sUiQdemcaVEYUdqx8IBJwM6pgyp4385SlxxDAaDkYSBISAbeJOzeaMVK3VRGWrElzvsmhspSLD7hKu-Ef6F4PxDF3aa1-M5APRChYSsu/s1600/cute-cats-cups-large-msg-128926455737.jpg" height="212" width="320" /></a></div>
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Con este error absoluto y una estimación de la flecha máxima podemos calcular el error relativo en % y entrando en la gráfica obtener el valor de "alfa" correspondiente.</div>
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Y así es como podemos saber como de pequeñas tienen que ser las deformaciones para poder ser consideradas "pequeñas". Aunque algunas cosas, las mires como las mires,siempre van a ser pequeñas.<br />
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<div style="text-align: right;">
<a href="http://ingenieriaparatorpes.blogspot.com.es/2014/08/cuando-aplicar-la-hipotesis-de-pequenas_29.html">Parte II</a></div>
<div style="text-align: right;">
<a href="http://ingenieriaparatorpes.blogspot.com.es/2014/08/cuando-aplicar-la-hipotesis-de-pequenas.html#more">Parte I</a></div>
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-36432990955853199742014-08-29T04:00:00.000-07:002014-10-04T09:21:53.005-07:00¿Cuándo aplicar la hipótesis de pequeñas deformaciones? (Parte II)<!--[if gte mso 9]><xml>
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<![endif]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="font-size: large;"><u><b>La ecuación de la viga para grandes deformaciones</b></u></span></span></div>
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNOFxal_LfXSyWc2bL7INnz5eD43xJfClSdlnUmwbUjXZK4qgB1mOH-vgprkVLVN7xBqgSI4S-NaZbc4P8mZn_lxflhZnJAY2Q2tARlUCj7B8LvUmG_Gm1Z4R78_6bpEvi64AYKGLTc40b/s1600/tumblr_ljqsyfUCt21qcrrq7o1_400.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNOFxal_LfXSyWc2bL7INnz5eD43xJfClSdlnUmwbUjXZK4qgB1mOH-vgprkVLVN7xBqgSI4S-NaZbc4P8mZn_lxflhZnJAY2Q2tARlUCj7B8LvUmG_Gm1Z4R78_6bpEvi64AYKGLTc40b/s1600/tumblr_ljqsyfUCt21qcrrq7o1_400.jpg" height="192" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">¿Soy lo suficiente pequeño? Yo creo que sí</td></tr>
</tbody></table>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> A lo largo de esta seríe de entradas dedicadas al <b>cálculo de estructuras</b> vamos a tratar de encontrar cual es el límite de aplicación de la <b>"hipótesis de pequeñas deformaciones</b>", es decir, cuando podemos y cuando no podemos considerar pequeñas las mismas.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> En la entrada anterior <a href="http://ingenieriaparatorpes.blogspot.com.es/2014/08/cuando-aplicar-la-hipotesis-de-pequenas.html">(Parte I)</a> comentamos como podríamos definir dicho límite o frontera entre lo que es "pequeño" y lo que no, llegando a la conclusión de que todo depende del error que estemos dispuestos a asumir.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Para
conocer de forma precisa el<b> </b>error en el que se incurre al realizar la "hipótesis de pequeñas deformaciones" y poder definir una frontera
entre las pequeñas y las grandes deformaciones estudiaremos la <b>expresión general de la deformada</b> (sin considerar pequeñas deformaciones!).</span><br />
<br />
<a name='more'></a><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">En nuestro caso, vamos a estudiar el
comportamiento de una viga empotrada en voladizo, sobre la que actúa una carga puntual “P” en su extremo. Como simplificación despreciaremos la deformación por
cortante y solo consideraremos las deformaciones debidas a los esfuerzos
flectores M(x).</span><br />
<br />
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<style>
/* Style Definitions */
table.MsoNormalTable
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mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
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<![endif]-->
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<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
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<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
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<w:PunctuationKerning/>
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<w:DoNotPromoteQF/>
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<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
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<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
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<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
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<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
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<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
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<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="22" SemiHidden="false"
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UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
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<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
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<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
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<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="69" SemiHidden="false"
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<w:LsdException Locked="false" Priority="19" SemiHidden="false"
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UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
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<w:LsdException Locked="false" Priority="32" SemiHidden="false"
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<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]-->El comportamiento de dicha viga,<span style="mso-spacerun: yes;"> </span>en el caso de prescindir de la simplificación
de pequeñas deformaciones, viene dado por la<b> Ley de Navier</b>:<br />
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcyh0qZ2B4Mwe3EEL3a5FBlPNjUlMTWlaU2hQMrzbEVPWNVuswsIJrzjPgieXiN73es4XFqIt6Q-aKWgAxCsi4KQ1vRj0eeVnxju01hSuQsEfAXQra-lqjoDE9t_iNTJdbtqWPPw4m3gbw/s1600/3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcyh0qZ2B4Mwe3EEL3a5FBlPNjUlMTWlaU2hQMrzbEVPWNVuswsIJrzjPgieXiN73es4XFqIt6Q-aKWgAxCsi4KQ1vRj0eeVnxju01hSuQsEfAXQra-lqjoDE9t_iNTJdbtqWPPw4m3gbw/s1600/3.jpg" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
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<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
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<br />
<div class="separator" style="clear: both; text-align: center;">
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<w:WordDocument>
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<w:ValidateAgainstSchemas/>
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<w:LidThemeOther>ES</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
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<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
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<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
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<w:OverrideTableStyleHps/>
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<div class="MsoNormal" style="text-align: left;">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Donde E e I son el módulo de Young del
material y la inercia de la sección, respectivamente.</span></div>
<div class="MsoNormal" style="text-align: left;">
<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">“K” es la curvatura de la deformada, es
decir, la inversa del radio de curvatura “p”. De forma general esta se puede
expresar como:</span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilDSPNSqT-DbJKNURE1uUuhjaLHpRLqnetxNIbw0G8MzxXj8TnbNqX2FpwwEM1tXjUm_AZB_qkpwJw24jyDiAf6npJIchWAtTgP9AypHGn1yOVPEGjwCXchlw-hkGNtJqgwW8EFKR0ckgD/s1600/4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilDSPNSqT-DbJKNURE1uUuhjaLHpRLqnetxNIbw0G8MzxXj8TnbNqX2FpwwEM1tXjUm_AZB_qkpwJw24jyDiAf6npJIchWAtTgP9AypHGn1yOVPEGjwCXchlw-hkGNtJqgwW8EFKR0ckgD/s1600/4.jpg" /></a></div>
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<div class="MsoNormal">
En el caso de una viga empotrada de longitud “L” sometida
únicamente a una carga puntual “P” en su extremo situado a una distancia “xf”,
la ley de esfuerzos flectores sigue una expresión lineal:</div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5pr1GNqd9-w-caZqafesGo0e7iLdXgEjiHifyBK18k4KekYcBSxZb4LMK142aS92eDAoEMsJSo8g2CzJzlpzpDGNgOuudoNbP970MtdOCE3lZI8lkRpB_lOEOFh11rAn-rZUC6uKHkDso/s1600/6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5pr1GNqd9-w-caZqafesGo0e7iLdXgEjiHifyBK18k4KekYcBSxZb4LMK142aS92eDAoEMsJSo8g2CzJzlpzpDGNgOuudoNbP970MtdOCE3lZI8lkRpB_lOEOFh11rAn-rZUC6uKHkDso/s1600/6.jpg" /></a></div>
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/* Style Definitions */
table.MsoNormalTable
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mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]-->Remarcar que aunque el extremo de la viga se encuentre en la
coordenada x=xf, esta distanccia será menor que la propia longitud “L” de la viga debido a
que<span style="mso-spacerun: yes;"> </span>no estamos considerando que los
desplazamientos sean pequeños.
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<div class="separator" style="clear: both; text-align: center;">
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<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
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<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
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<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
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Teniendo en cuenta todo lo dicho hasta ahora y derivando respecto de “s”, la <b>Ley de Navier</b> queda como:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAwctv345IDaNx4823vbL9ZShQDifitDLXD-1fyw7AXUVCSla2n6k51bkdMSKHtHpLFXe73AN1a4Fms59sqHRoJc_7GtSXZXtvuHPZPvD6ZPBCt5zmXx_uo_mq8j9clhsLqkVeA2VeUUGk/s1600/8.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>Esta ecuación diferencial, de resolución algo compleja, nos
permitirá conocer la <b>deformación angular</b> <span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -5.5pt; position: relative; top: 5.5pt;"></span><span style="mso-spacerun: yes;"> </span>en función de la coordenada arco “s”. Las dos
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">La primera condición significa que el giro en s=0 es nulo, ya que la viga se encuentra
empotrada.</span></div>
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">La segunda condición significa que en s=L, el extremo libre de la viga, el momento flector es nulo, M(L)=0.</span></div>
<br />
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Una vez conocida la expresión de la deformación angular<span style="mso-spacerun: yes;"></span>, podremos calcular la<b> flecha vertical</b> "y(s)"que
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La <b>flecha máxima</b> se dará en el extremo del voladizo, por
tanto:</div>
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<br /></div>
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En resumen, y para no perder el norte de lo que
estamos buscando tras esta pequeña aventura “diferencial”, hemos conseguido definir una función (aunque no la hemos resuelto!) <span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><span style="mso-spacerun: yes;"></span>que nos define la deformación de nuestra viga en voladizo para el caso de grandes deformaciones y queremos conocer la <b>flecha máxima "Ymax"</b>
para poder así compararla con la flecha que obtendríamos si hubiéramos considerado
como pequeñas las deformaciones. </span></div>
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Además queremos sacar algo de provecho de
todo esto. Alguna regla que podamos generalizar para distintos problemas estructurales y que
nos permita decidir si con la <b>hipótesis<span style="mso-spacerun: yes;"> </span>de pequeñas deformaciones</b> es suficiente o no de forma rápida, para consumir el menor tiempo posible y trabajar de forma más eficiente. Lo ideal de todo este embrollo matemático-existencial en el que nos hemos metido es que existiera un <b>parámetro</b>, fácil de calcular, que relacionara todas
las variables del problema y el cual definiera la frontera entre
pequeñas y grandes deformaciones.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBK-qHmFycXESUu7nKgbs131odPlts-sxhnKGjIZvoG2mjHR6XABknpPadl2Wl1x5E5BITEv-UpC3NFxdpDJQmf5nP3i5bk_KcSh2Of8xSe_eOSMF-beu0y0NKZ9fWmSLRAK3FG4OJ5-hW/s1600/small-white-sleeping-cute-puppy-dog.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBK-qHmFycXESUu7nKgbs131odPlts-sxhnKGjIZvoG2mjHR6XABknpPadl2Wl1x5E5BITEv-UpC3NFxdpDJQmf5nP3i5bk_KcSh2Of8xSe_eOSMF-beu0y0NKZ9fWmSLRAK3FG4OJ5-hW/s1600/small-white-sleeping-cute-puppy-dog.jpg" height="131" width="200" /></a></td></tr>
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<span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Ya que a priori no sabemos que forma puede adoptar la expresión de la deformada, desconocemos si este parámetro existe siquiera. No obstante, hay una forma de averiguar su existencia sin tener que resolver analíticamente la EDO de la deformada, empleando el <b>Teorema Pi de Buckingham</b>, que veremos en la siguiente entrada (<a href="http://ingenieriaparatorpes.blogspot.com.es/2014/09/cuando-aplicar-la-hipotesis-de-pequenas.html">Parte III</a>).</span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: ES; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: ES; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-no-proof: yes;"> </span>Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-88916383942343214302014-08-28T11:28:00.001-07:002014-10-04T09:23:07.745-07:00¿Cuándo aplicar la hipótesis de pequeñas deformaciones? (Parte I)<h2 style="text-align: center;">
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<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS2dwWCBkr67Qdt5pc2QxxZPr7KXT0cV5ScGvCRQsSYPtOw8MbGl3fPfaX_RmW6YjERT0xVEILG_FQbukqEbdaQphDYZi-bi7dCfpzbX3a9_VAcV-y-qLI_bqDBpm442QxYVcrzsFKh_0l/s1600/30.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS2dwWCBkr67Qdt5pc2QxxZPr7KXT0cV5ScGvCRQsSYPtOw8MbGl3fPfaX_RmW6YjERT0xVEILG_FQbukqEbdaQphDYZi-bi7dCfpzbX3a9_VAcV-y-qLI_bqDBpm442QxYVcrzsFKh_0l/s1600/30.jpg" height="170" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">¡Así de pequeño!</td></tr>
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Una de las hipótesis que se utiliza en el cálculo
de estructuras es considerar pequeñas las <b>deformaciones</b>. Es decir, suponer que los desplazamientos que las cargas producen son muy pequeños en comparación con las dimensiones de la propia estructura y como las deformaciones suelen ser del orden de los <b>milímetros</b>, tiene sentido pensar esto.</div>
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<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Considerar pequeñas las deformaciones implica que podemos
realizar una serie de simplificaciones sobre las ecuaciones que gobiernan el
comportamiento de la estructura, facilitando la resolución del problema en gran
medida. Una de las consecuencias directas de que las deformaciones sean
pequeñas es que podemos simplificar la expresión de la <b>curvatura “k”</b> de una
viga y pasar de este bicho: </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1bh7OCqf38OaVt4omla8x2wtNsWscWFoqMqfR894_ZOjKk_dRRGfm_1r4AYmA_mMXVQ1tWNeYjeeqGxpvCb8xk7M26b9pDodS7bbaCMinjM-oTovHVUqm16tQ_2GdYed9zZjQy0VtJbJQ/s1600/1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1bh7OCqf38OaVt4omla8x2wtNsWscWFoqMqfR894_ZOjKk_dRRGfm_1r4AYmA_mMXVQ1tWNeYjeeqGxpvCb8xk7M26b9pDodS7bbaCMinjM-oTovHVUqm16tQ_2GdYed9zZjQy0VtJbJQ/s1600/1.jpg" /></a></div>
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<![endif]-->A este otro, mucho más agradable a la vista y sencillo de
resolver:<br />
<br />
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Pero además el emplear la <b>hipótesis de pequeñas
deformaciones</b> nos permite considerar que el material se va a comportar de forma<b>
lineal</b>, facilitándonos aún más el cálculo ya que esto nos permite emplear la
<b>superposición</b> de cargas. De esta forma podemos calcular las deformaciones y los
esfuerzos que varias acciones originan sobre una estructura por separado y únicamente
sumar los resultados para obtener el efecto de su combinación.</div>
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<br /></div>
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En el caso de que las deformaciones no sean pequeñas, las
ecuaciones a resolver serán más complejas y además la respuesta de la
estructura a las cargas no será lineal como en el caso anterior. Hoy en día la mayoría de los programas de<b> cálculo
estructural</b> incorporan la opción de emplear la hipótesis de pequeñas
deformaciones o de grandes deformaciones, por lo que en principio la dificultad
añadida en las ecuaciones no nos va a suponer ningún problema. </div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpwwYexIw67yc4FWQTop7nqBFKXKJAEXngK66PYHOTtLR4arJiQ3eNid0Qi1gAbZbkmUUuTWWKq6K0VHTM_tjmnstQFvWp04lKmgi8aG4DQo5_8ej90d1r4fyGwO6PGXwxkjMZfTA1Neu/s1600/SAP2000.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpwwYexIw67yc4FWQTop7nqBFKXKJAEXngK66PYHOTtLR4arJiQ3eNid0Qi1gAbZbkmUUuTWWKq6K0VHTM_tjmnstQFvWp04lKmgi8aG4DQo5_8ej90d1r4fyGwO6PGXwxkjMZfTA1Neu/s1600/SAP2000.jpg" height="225" width="400" /></a></div>
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<br /></div>
<div class="MsoNormal" style="text-align: left;">
La linealidad en la respuesta de la estructura, en cambio,
si que nos va a facilitar bastante el trabajo ya que de esta forma podremos incorporar
combinaciones de cargas sin importar su orden de aplicación, ya que el resultado final será el mismo independientemente de este.</div>
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Por tanto, siempre que podamos utilizaremos la hipótesis de
pequeñas deformaciones. Llegados a este punto la pregunta que cabe hacerse es <b>¿Cuándo
podemos considerar pequeños las deformaciones?</b>,<span style="mso-spacerun: yes;"> </span>¿cómo de pequeño tiene que ser algo para
poder considerarlo pequeño?.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi41GaGqh_P5kFXlnp7p9ClCB-1L6z70_4wMkSGrJHETnEQoLYjeFhwW_qxu_lsqQlSM7XZRdciSVw2VpBGEJxgjhZpAv6OE5j1U7pCf1M_u0ACFKLWL3RyD1SsEvokTs828JKKmE0G0Sk/s1600/el-tama%C3%B1o-importa.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi41GaGqh_P5kFXlnp7p9ClCB-1L6z70_4wMkSGrJHETnEQoLYjeFhwW_qxu_lsqQlSM7XZRdciSVw2VpBGEJxgjhZpAv6OE5j1U7pCf1M_u0ACFKLWL3RyD1SsEvokTs828JKKmE0G0Sk/s1600/el-tama%C3%B1o-importa.jpg" height="130" width="200" /></a></div>
<div class="MsoNormal" style="text-align: left;">
La respuesta a esta pregunta es <b>“tan pequeño como para que
no se note<span style="mso-spacerun: yes;"> </span>la diferencia”</b>, es decir, tan
pequeño como para que el error cometido con la simplificación sea admisible.</div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
Si las deformaciones estimadas son del orden de 100 mm, un error de
1 mm podría considerarse pequeño. En cambio si las deformaciones fuesen del
orden de 1mm, un error de 1 mm podría considerarse grande.</div>
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<br /></div>
<div class="MsoNormal" style="text-align: left;">
Considerar que un error es o no admisible depende también de la magnitud del problema que estemos estudiando y del esfuerzo (tiempo y dinero) que estemos dispuestos a invertir en él, en resumen,<b> "no mates moscas a cañonazos" .</b></div>
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<br /></div>
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<br /></div>
<br />
<br />
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<br /></div>
Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com2tag:blogger.com,1999:blog-2092166921832051850.post-60748829588691082152014-08-16T10:05:00.002-07:002014-09-15T04:35:34.669-07:00Vortex Shedding y la niña fantasma del parque (Parte I)<!--[if gte mso 9]><xml>
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Muchos de vosotros habrá oido alguna vez la historia de la niña fantasma del parque o sobre algún parque infantil embrujado en el que los columpios se movian solos de forma misteriosa.</div>
<div class="MsoNormal">
Hace ya algún tiempo apareció un video en internet en el que un columpio se comenzaba a mover por si solo y del que varios programas de sucesos paranormales se hicieron eco sin poder dar explicación al columpio fantasma.</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/hFzOxOATKEs?feature=player_embedded' frameborder='0'></iframe></div>
<br />
<br />
<div class="MsoNormal">
Cuando un flujo, ya sea de agua o de aire, se ve
interrumpido por un cuerpo sólido o una estructura se produce una perturbación
en la corriente. En el caso de <b>estructuras de relativa esbeltez <span style="mso-spacerun: yes;"></span></b>sumergidas en un flujo, se puede provocar un
desprendimiento periódico de vórtices (<b>vortex shedding</b>) aguas abajo del flujo formandose la famosa <b>calle de Von Kárman</b>.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/Otg-0DsvkLE?feature=player_embedded' frameborder='0'></iframe></div>
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<a name='more'></a></div>
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Este desprendimiento de vórtices lleva asociado unas<b> fuerzas
de arrastre de carácter periódico y naturaleza dinámica</b>, las cuales pueden <span style="mso-spacerun: yes;"> </span>llegar a ocasionar fuertes vibraciones en la
estructura al coincidir la frecuencia de dichas fuerzas con la frecuencia
natural de la estructura y causar la resonancia. Este tipo de vibraciones, que ocurren incluso con velocidades bajas del
flujo, se conocen como vibraciones inducidas por<span style="mso-spacerun: yes;"> </span>desprendimiento de vórtices o<b> vortex induced vibracions (VIV)</b> y son, efectivamente, la causa de que el columpio fantasma entre en movimiento.</div>
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<br /></div>
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<![endif]-->Dentro de la<b> obra civil</b>, son susceptibles a
sufrir este tipo de fallo estructuras tales como aerogeneradores off-shore
pilotados en el fondo marino, rascacielos, chimeneas de gran altura, puentes
esbeltos, tirantes de puentes atirantados, farolas, etc. </div>
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<![endif]--><span style="mso-bidi-font-weight: normal;">Un caso bastante conocido de este fenómeno se dio hace unos años,
durante la construcción del puente "<b>Arcos de Alconétar</b>" sobre el río Tajo, en el Embalse de Alcántara. Los dos arcos metálicos gemelos de 220 m de luz</span><span style="mso-bidi-font-weight: normal;"><span style="mso-bidi-font-weight: normal;"> </span>comenzarón a vibrar de forma súbita </span><span style="mso-bidi-font-weight: normal;"><span style="mso-bidi-font-weight: normal;"> </span><span style="mso-bidi-font-weight: normal;"><span style="mso-bidi-font-weight: normal;">cuando se registraba un viento de a penas 20km/h, </span></span>según su <b>2º modo de oscilación, </b>con un periodo de 1'4 segundos.</span><br />
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La causa de estas repetinas oscilaciones fue el desprendimiento de vórtices de forma periódica debido al viento, ya que para la velocidad a la que soplaba el viento los vortices se desprendian con el mismo periodo (1'4 segundos) que el periodo natural del 2º modo de oscilación de la estructura metálica, lo que causó la entrada en resonancia de la misma.<br />
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<![endif]-->Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-35445133787662864472014-07-04T04:25:00.000-07:002014-07-04T04:25:15.410-07:00Fotos del Tower Bridge en construcciónEl <b>Tower Bridge</b> (puente de la torre) es un famoso puente levadizo del siglo XIX situado en Londres, abriendo paso sobre el Támesis. Se trata de un puente metálico que funciona a modo de puente colgante cuyos cables se han sustituido por celosias metálicas. El tablero transmite su peso a las pendolas verticales, las cuales lo transmiten al arco de celosía que trabaja a tracción, transmitiendo los esfuerzos a los anclajes laterales.<br />
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Como curiosidad, las torres tienen apariencia de ser monolitos de piedra, sin embargo este aspecto es simplemente estetico. En realidad son<b> torres metálicas</b> que se recubrieron con obra de fábrica y darle una apariencia más robusta, ya que en la época la gente tenia cierto pánico a los puentes metálicos.<br />
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-73025682671095323742014-06-25T07:37:00.000-07:002014-08-28T13:50:11.647-07:00Rehabilitación de una vía de ferrocarril<div class="separator" style="clear: both; text-align: center;">
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¿Te has preguntado alguna vez cómo se renueva una vía de ferrocarril? En estos dos videos podeis ver como es el proceso automatizado de retirada de las vías antiguas y el montaje de las nuevas:<br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-2389906974250518942014-06-19T11:10:00.001-07:002014-08-28T13:52:11.202-07:00Diseño y optimización de muros de gravedad (Descarga programa)<br />
<span class="export-link-gray-txt file-key"> Quiero compartir con vosotros un programa que he hecho con<b> Mathematica</b> para diseñar <b>muros de gravedad con el trasdos inclinado</b> en terrenos granulares (cohesion nula). Este programa te permite calcular la<b> geometría óptima</b> (mínimo peso), teniendo en cuenta las acciones del nivel freático, la altura de las tierras en el trasdos, una sobrecarga distribuida constante y el propio peso del muro.</span><br />
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<span class="export-link-gray-txt file-key">El programa realiza las comprobaciones de <b>estabilidad (vuelco y</b> <b>deslizamiento</b>) y comprueba <b>que no se alcanza la tensión de rotura a tracción</b> <b>en ninguna sección del muro.</b> Todas estas comprobaciones las realiza en función del<b> ancho de coronación (a) </b>y de la<b> pendiente (b)</b> del muro, de forma que como resultado se obtiene una <b>región de valores admisibles (a,b)</b> para los que se verifican todas las comprobaciones anteriores. </span><br />
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<tr><td class="tr-caption" style="text-align: center;">Peso del muro (lineas de nivel) y soluciones admisibles (región azul)</td></tr>
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<span class="export-link-gray-txt file-key">Junto a dicha region de valores de ancho de coronacion (a) y pendiente (b), el programa evalua el peso total del muro </span><span class="export-link-gray-txt file-key"><span class="export-link-gray-txt file-key">W(a,b) </span>en función de dichas variables y calcula la <b>solución para la cual el peso es mínimo</b>. </span><br />
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<span class="export-link-gray-txt file-key">El resultado se presenta también de forma gráfica, por lo que puedes comprobar visualmente el campo de soluciones al completo y manipular las variables (Ht, Ha y q) del problema para ver como afectan al resultado en tiempo real.</span><br />
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<span class="export-link-gray-txt file-key"><b>El programa es gratuito y de código abierto</b>. Solo necesitais tener instalado el programa Mathematica para poder ejecutarlo.</span><br />
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<span class="export-link-gray-txt file-key"><a href="https://mega.co.nz/#!Mk4X2YQS!dIeRTi6GlbW80h8E-EqtYoRqOqnF9SLbqmCzhh_lCPc" target="_blank">Descargar programa diseño muros V2</a></span><br />
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<span style="color: red;">(enlace de descarga actualizado)</span><br />
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<b><span style="color: red;">ACTUALIZACION: He detectado un error en el codigo del programa que he corregido en la V2.0, ademas de añadirle el cálculo de carga de hundimiento de la cimentación como comprobacion adicional asi que ahora tambien te comprueba que la cimentacion del muro no falle por hundimiento (segun terzaghi).</span></b><br />
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<b><span style="color: red;">Si tienes la version anterior eliminala y cambiala por la V2.0. Perdón por las molestias.</span></b><br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-28619844243827492162014-05-12T13:19:00.003-07:002014-08-28T13:54:23.685-07:00¿Es este año el mejor momento para comprar una vivienda?Estoy seguro que a lo largo de estos años has oido por la televisión a algún experto de dudosa procedencia y moral decir que<b> ahora es el mejor momento para comprar</b>, que el precio de la vivienda ha tocado fondo y que se las estan quitando de las manos.<br />
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Esto lo vienen diciendo, profetizando e incluso deseando en voz alta varias veces cada año desde que empezó la crisis y obviamente ninguna de esas<b> profecías</b> se ha cumplido hasta ahora (¿el poder del pensamiento positivo?).<br />
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Pero este tipo de comportamientos no debe sorprendernos a estas alturas. De hecho es comprensible ya que hay unos intereses detrás (poderoso caballero es dondinero) y todo el <b>sainete</b> esta metido en el ajo, o más bien en el <b>ladrillo</b>.<br />
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Este año todo apunta a que es <b>el año de la recuperación</b>, o al menos eso nos cuentan nuestros "hamijos" de <b>Bankinter</b> en uno de sus ultimos informes: <a href="http://blog.bankinter.com/cfs-file.ashx/__key/CommunityServer.Blogs.Components.WeblogFiles/bankinter/7610.vivienda_2D00_2014.pdf" target="_blank"><b><span style="font-family: mceinline;"> informe completo vivienda 2014 (pdf)</span></b></a><br />
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Como se puede apreciar en sus estimaciones, el repunte en el precio de la vivienta es evidente. Solo teneis que fijaros en la prognosis que hacen para 2015, donde se sacan de la manga <b>una curva que va "to parriba!"</b>, como debe ser, ya que el precio de la vivienda es capaz de desafiar cualquier tipo de correlación.<br />
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<tr><td class="tr-caption" style="text-align: center;">Lee "estimaciones" con la voz del Doctor Maligno y todo cobrará sentido, claaaaaro.</td></tr>
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El ajuste lineal por mínimos cuadrados es cosa del pasado, hoy en dia lo que se usa es el ajuste por bola de cristal. Lo único que les ha faltado es poner en un indice "Señora! que me las quitan de las manos!" y hacer referencia al<b> teorema del punto gordo y la circunferencia peluda.</b><br />
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Asi que,<b> ¿cuando va a empezar el precio de la vivienda?</b> Siendo sincero, no tengo ni idea y no creo que nadie la tenga. Lo que si podemos hacer es mirar al pasado y aprender de los errores, pero no a nuestro pasado sino al de nuestros hermanos de<b> burbuja</b>: los japoneses.<br />
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Japon, durante los años 80 vivió un boom inmobiliaro, " 価格が上昇しないことが " se repetian entre ellos sin parar, ¿te resulta familiar? nosotros hicimos lo mismo. Y pasó lo que tenia que pasar, como todas las burbujas, estas se pinchan. Y el pinchazo de la<b> burbuja japonesa </b>duró 15 años, con una bajada total de precios del 64%.<br />
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Nuestra burbuja pinchó en 2008, y desde entonces los precios han bajado un 40% en 6 años. Los japoneses son famosos por su disciplina, su industria y sus avances en tecnología punta y aun así tardarón 15 años en recuperarse. La pregunta que a cualquiera se le debe escapar es:<b> </b><br />
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<b>¿Podremos superar su marca con una economía basada unicamente en el "sol y playa"?¿Estamos ante un nuevo milagro de La Roja? Esto, amigos, solo el tiempo lo dirá.</b><br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com1tag:blogger.com,1999:blog-2092166921832051850.post-63282006801684679092014-05-05T06:37:00.000-07:002014-10-04T09:19:09.764-07:00Tuneles de viento y Simuladores de TornadosLa<b> ingeniería del viento</b>
se encarga de estudiar el efecto del viento sobre las estructuras
terrestres, como los edificios o los puentes. El viento es muy puñetero, porque parece que no hace nada pero hace, ya que induce <b>efectos dinámicos </b>sobre la estructura que pueden llevar al colapso de la misma, incluso cuando la velocidad con la que sopla es pequeña (el famoso puente de Tacoma Narrows).<br />
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<tr><td class="tr-caption" style="text-align: center;">modelo a escala en tunel de
viento del puente de Akash Kaikyo </td></tr>
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El viento esta gobernado por las ecuaciones de <b>Navier-Stokes</b>,
comportandose como un fluido con altas turbulencias y fluctuaciones en
el espacio y el tiempo.<br />
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Estas ecuaciones se pueden resolver de forma
numérica y crear modelos en ordenador, pero la gran herramienta para
estudiar el efecto del viento sobre las estructuras civiles son los <b>tuneles de viento de capa limite</b> y los
modelos a escala donde no solo se construye a escala la geometría de
los edificios, puentes, etc, sino que también se escala la realidad
física que le influye (rugosidad,viscosidad, comportamiento del fluido,fuerzas, etc).<br />
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Dentro de los túneles de viento, una de las tipologias más modernas es la de <b>simuladores de tornados y huracanes.</b> En el siguiente video podeis ver uno de los pocos simuladores de tornados que hay en todo el mundo, disfruten:<b><br /></b><br />
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-6948835363284781952014-04-29T13:03:00.002-07:002014-08-28T13:55:31.956-07:00Time Lapse de una tuneladora (must see)En este increible<b> time lapse</b> podeis ver como algunas de las operaciones que ocurren en un día de trabajo dentro de un tunel y como son los últimos momentos de una tuneladora. <br />
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Se trata de la excavación de un<b> tunel bi-tubo</b> de carretera sostenido mediante anillos de hormigón armado, situado dentro del "Airport Link highway" en Brisbane (Australia). <br />
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<a name='more'></a>Para la ejecución de esta obra de ingeniería se emplearon dos<b> tuneladoras</b> gemelas de tipo <b>EPB (Earth Pressure Balance)</b>, con una longitud total de 195m (escudos
de 15m y 180m de back-up), con cabezas de corte de 12.48m de
diametro armadas cada una con 80 discos de corte de 17 pulgadas.<br />
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<tr><td class="tr-caption" style="text-align: center;">En verde el tramo ejecutado con las EPB's. En azul el tramo ejecutado con rozadora donde se encuentran.</td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
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Estas dos <b>tuneladoras</b> trabajaron de forma paralela, avanzando durante 2.5km de trazado y atravesando desde zonas
rocosas hasta tramos arcillosos (se desgastaron un total de 900 discos de
corte en todo el trayecto).<br />
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El viaje de estas dos tuneladoras finaliza a 50 m bajo la superficie de una zona residencial, donde ambas secciones del tunel bi-tubo se encontran en una cámara subterreanea de entronque con otro tunel de menor diametro
ejecutado previamente mediante<b> rozadora</b>. <br />
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Para evitar tener que hacer un pozo de 50m y perturbarturbaciones en la zona urbana se decidió enterrar las cabezas de corte y los escudos
en unas fosas de 16.5m de profundidad y rellenando todo con hormigón.<br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-63102309154678478112014-04-10T05:43:00.001-07:002014-04-10T05:43:07.166-07:00Puente atirantado de la Ronda del Tajo<div class="separator" style="clear: both; text-align: center;">
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Situado en la Ronda del Tajo en Talavera de la Reina, este <b>puente atirantado </b>se contruyó para salvar el río Tajo. Este puente tiene 729 m de longitud con un tramo atirantado de 318 m de luz suspendido de un pilono central inclinado de 180 metros de altura. El tablero con una anchura de 36,00 metros está suspendido de dos parejas de 38 cables que se anclan en el pilono, el cual queda estabilizado lateralmente mediante otras tantas parejas de cables de retenida.<br />
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En este <b>video</b> podeis ver paso a paso el <b>proceso de construcción</b> de este puente atirantado:<br />
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-21486929348863617262014-04-05T07:00:00.000-07:002014-04-05T07:28:18.304-07:00Video Tutorial ArcGIS: Modelo 3D fotorrealista<br />
<a href="http://sia1.subirimagenes.net/img/2014/04/03/140403115449861354.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://sia1.subirimagenes.net/img/2014/04/03/140403115449861354.jpg" height="215" width="400" /></a><b>ArcGIS 10</b> es un programa de tratamiento y análisis de información cartográfica. <br />
En este tutorial os enseño como podemos descargar cartografía digital de cualquier zona de España.También veremos algunas<b> funciones básicas de ArcGIS</b> (cortar, pegar y manipular capas vectoriales, raster, mdt y ortofotos).<br />
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Además vereis como podeis crear vuestro propio <b>modelo 3D fotorrealista del terreno</b> con edificios incluidos de forma muy fácil y sencilla.<br />
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El modelo 3D que he hecho es de la Sierra del Torcal (Antequera) y en el video tutorial os explico paso a paso todo lo que he hecho para crearlo.<br />
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Podeis <b>descargaros</b> el tutorial en formato PDF desde este enlace:<br />
<a href="https://mega.co.nz/#!gpZUkCxC!4efGAYwzvvw-mWd4usLONGs5QgzjRbC0XGt7nhTgB5A" target="_blank">Descargar tutorial ArcGIS en pdf</a><br />
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Os dejo a continuación el <b>tutorial en formato video</b>. En la introducción de este video tutorial de ArcGIS podeis ver un vuelo virtual sobre el modelo 3D fotorrealista:<br />
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En la Parte 1 vemos como bajarnos la cartografía del IGN y como visualizarla en ArcGIS:<br />
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En la Parte 2 vemos como crear y editar una capa shape y como cortar y pegar capas raster MDT:<br />
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com10tag:blogger.com,1999:blog-2092166921832051850.post-84243199057541966662014-04-02T06:22:00.001-07:002014-04-02T06:22:11.791-07:00Proceso de construcción del puente "Mersey Gateway"
El puente "<b>Mersey Gateway</b>" se situa al noroeste de Inglaterra, cruzando el rio Mersey el canal de buques de Manchester. Las obras del mismo comenzarán en primavera de 2014 y se planea abrir al público en 2017.<br />
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Se trata de un<b> puente atirantado</b> con tres torres que se elevan hasta 135m sobre el rio, una luz maxima de entorno a 150m, 1km de longitud y 3 carriles en cada sentido.<br />
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En este video podeis dar un paseo virtual del proyecto completo y ver como es el <b>proceso constructivo</b> paso a paso de este puente atirantado:<br />
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Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-51375513292567384532014-03-27T14:22:00.001-07:002014-08-28T13:57:30.501-07:00Deslizamiento de ladera de Oso, Washington<div class="separator" style="clear: both; text-align: left;">
Coleccíón de imagenes del<b> deslizamiento de ladera</b> que ha ocurrido de forma repentina este sabado en la pequeña comunidad de Oso en Washington, EEUU y que ha arrasado con 49 casas. Se trata de un movimiento de tierras de grandes dimensiones donde se ha movilizado un volumen de más de 11.468.322 m3, combinación de<b> flujo de tierras </b>(mudslide) y<b> deslizamiento circular</b> (landslide).</div>
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<tr><td class="tr-caption" style="text-align: center;">A la izquierda antes del deslizamiento, a la derecha después del deslizamiento</td></tr>
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En dicha area ya se habían registrando movimientos de tierra desde 1950. En 1967 un gran deslizamiento incluso cambió el curso del río. En 1999 el <b>U.S Army Corps of Engineers</b> avisó del potencial peligro de que ocurriera otro gran deslizamiento. En 2006 ocurrió de nuevo otro gran deslizamiento, tras el cual se siguieron construyendo casas en la zona.</div>
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El 10 de Marzo se registró un pequeño terremoto de magnitud 1.1 a 100 metros del lugar del deslizamiento.</div>
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Esto, unido al hecho de que en este mes se han registrado fuertes lluvias, se baraja como la posible causa del deslizamiento.</div>
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<br />Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0tag:blogger.com,1999:blog-2092166921832051850.post-60612965417722596422014-03-17T06:05:00.003-07:002014-03-17T06:05:23.088-07:00Ampliación Norte del Puerto de ValenciaHoy os traigo un video del <b>proceso constructivo</b> de la <b>Ampliación Norte del Puerto de Valencia</b>.<br />
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Esta ampliación consiste en la realización de un nuevo <b>dique de abrigo</b> de 3385 m, cuya traza esta compuesta por un <b>dique en talud</b> de bloques cúbicos de hormigón (1120 m), un <b>dique vertical</b> (1841 m) y un <b>dique mixto</b> vertical con talud de bloques cúbicos de hormigón (366 m).
Además la obra se complementacon un <b>contradique</b> en talud de longitud aproximada 1095 m. Juan Maria http://www.blogger.com/profile/17437124621500431399noreply@blogger.com0