{"id":25187,"date":"2024-04-29T16:49:26","date_gmt":"2024-04-29T14:49:26","guid":{"rendered":"https:\/\/biblus.accasoftware.com\/es\/?p=25187"},"modified":"2024-05-10T11:25:53","modified_gmt":"2024-05-10T09:25:53","slug":"vigas-de-hormigon-armado-tipos-y-metodo-de-diseno","status":"publish","type":"post","link":"https:\/\/biblus.accasoftware.com\/es\/vigas-de-hormigon-armado-tipos-y-metodo-de-diseno\/","title":{"rendered":"Vigas de hormig\u00f3n armado: tipos y m\u00e9todo de dise\u00f1o"},"content":{"rendered":"<p class=\"sommario\">Las vigas de hormig\u00f3n armado son elementos estructurales horizontales compuestos por una combinaci\u00f3n de hormig\u00f3n y acero. Descubre m\u00e1s sobre ellas en este art\u00edculo<\/p>\n<p><!--more--><\/p>\n<p>Las vigas de hormig\u00f3n armado son elementos estructurales de vital importancia en la construcci\u00f3n moderna. Se destacan por su capacidad de resistir las solicitaciones de tracci\u00f3n, gracias al uso de armaduras de acero incorporadas en el conglomerado de hormig\u00f3n.<\/p>\n<p>En este art\u00edculo exploraremos las diferentes tipolog\u00edas de vigas de hormig\u00f3n armado utilizadas en la industria de la construcci\u00f3n. Analizaremos las caracter\u00edsticas de cada una de ellas, examinando sus aplicaciones espec\u00edficas en diversos contextos estructurales.<\/p>\n<p>Si eres un profesional involucrado en el dise\u00f1o estructural, debes saber que puedes contar con la ayuda de herramientas avanzadas para mejorar la eficiencia y la fiabilidad de tus procesos. Explora ahora las potencialidades de una soluci\u00f3n espec\u00edfica <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/es\/programa-calculo-estructuras\" target=\"_blank\" rel=\"noopener\">para el modelado y el an\u00e1lisis de estructuras de hormig\u00f3n armado<\/a>. Utilizando estos sistemas, tendr\u00e1s la posibilidad de importar el modelo arquitect\u00f3nico IFC de tu edificio en un entorno BIM y modelar tu estructura con objetos param\u00e9tricos inteligentes. Adem\u00e1s, podr\u00e1s aprovechar la potencia del solucionador FEM integrado para realizar an\u00e1lisis avanzados en tiempos muy r\u00e1pidos y evaluar de manera fiable la respuesta estructural de tus edificios.<\/p>\n<p>Ahora exploremos todos los beneficios de las vigas de hormig\u00f3n armado y comprendamos c\u00f3mo estos elementos estructurales pueden contribuir a la resistencia, seguridad y estabilidad de las construcciones.<\/p>\n<h2 id=\"vigas-de-hormigon-armado\">Vigas de hormig\u00f3n armado<\/h2>\n<p>Las vigas de hormig\u00f3n armado son elementos estructurales utilizados en la construcci\u00f3n de edificios e infraestructuras. Constituyen, en particular, los <strong>componentes horizontales de las estructuras portantes \u00abtipo p\u00f3rtico\u00bb<\/strong> realizadas mediante el uso de hormig\u00f3n armado.<\/p>\n<p>Este tipo de material deriva de la combinaci\u00f3n del hormig\u00f3n, que proporciona resistencia a la compresi\u00f3n, con el acero, que ofrece una alta resistencia a la tracci\u00f3n. Por lo tanto, el uso del hormig\u00f3n armado permite aprovechar las propiedades complementarias de ambos materiales, y crear <strong>estructuras muy resistentes<\/strong>, capaces de soportar esfuerzos de tracci\u00f3n y de compresi\u00f3n.<\/p>\n<p>Sin embargo, en el contexto de la construcci\u00f3n, existen diferentes tipolog\u00edas de vigas de hormig\u00f3n armado. Cada tipo de viga se dise\u00f1a para satisfacer necesidades espec\u00edficas. Ahora exploraremos juntos algunas de las tipolog\u00edas m\u00e1s comunes, con el objetivo de resaltar sus caracter\u00edsticas distintivas.<\/p>\n<div id=\"attachment_205718\" class=\"wp-caption aligncenter\" style=\"width: 1210px;\">\n<div id=\"attachment_205718\" style=\"width: 1210px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-205718\" class=\"wp-image-205718 size-full lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/biblus.accasoftware.com\/es\/wp-content\/uploads\/sites\/3\/2024\/04\/travi-ca.webp\" alt=\"Vigas de hormig\u00f3n armado\" width=\"1200\" height=\"800\" aria-describedby=\"caption-attachment-205718\" \/><p id=\"caption-attachment-205718\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"wp-image-205718 size-full lazyload\" src=\"https:\/\/biblus.accasoftware.com\/es\/wp-content\/uploads\/sites\/3\/2024\/04\/travi-ca.webp\" alt=\"Vigas de hormig\u00f3n armado\" width=\"1200\" height=\"800\" aria-describedby=\"caption-attachment-205718\" \/><\/noscript> Vigas de hormig\u00f3n armado<\/p><\/div>\n<\/div>\n<h2 id=\"tipologias-de-vigas-de-hormigon-armado\">Tipolog\u00edas de vigas de hormig\u00f3n armado<\/h2>\n<p>La versatilidad del hormig\u00f3n armado permite la realizaci\u00f3n de vigas en diversas formas, tipolog\u00edas y dimensiones, adaptables a las necesidades espec\u00edficas de dise\u00f1o. De todos modos, la elecci\u00f3n del tipo de viga a adoptar depende de las <strong>necesidades estructurales y funcionales del proyecto<\/strong>. Es importante considerar cuidadosamente las caracter\u00edsticas de la carga, la distribuci\u00f3n de las solicitaciones y las deformaciones previstas, con el fin de determinar la configuraci\u00f3n m\u00e1s adecuada para lograr una estructura estable y segura. Un ingeniero estructural evaluar\u00e1 cuidadosamente estas variables para identificar el tipo de viga m\u00e1s adecuado para el contexto espec\u00edfico.<\/p>\n<h3>Tipos de vigas seg\u00fan modalidades constructivas<\/h3>\n<p>Una primera clasificaci\u00f3n de estos elementos puede hacerse en funci\u00f3n de las <strong>modalidades constructivas<\/strong>, distinguiendo entre:<\/p>\n<ol>\n<li><strong>Vigas de hormig\u00f3n armado ordinario (CA):<\/strong> Se realizan mediante un vertido de hormig\u00f3n en encofrados especiales, preparados para conferir a la viga la forma deseada, y dentro de los cuales se coloca previamente la armadura met\u00e1lica. Esta \u00faltima est\u00e1 constituida por barras de acero de adherencia mejorada que tienen como objetivo garantizar la m\u00e1xima adherencia entre los dos materiales (hormig\u00f3n y acero), evitando fen\u00f3menos de deslizamiento. Las vigas de hormig\u00f3n armado ordinario se utilizan ampliamente en diversos contextos estructurales, como edificios residenciales, comerciales e industriales. Son adecuadas para forjados, cubiertas, vigas de soporte y vigas de borde. Su versatilidad y facilidad de realizaci\u00f3n las convierten en una elecci\u00f3n com\u00fan en la mayor\u00eda de las aplicaciones constructivas;<\/li>\n<li><strong>Vigas de hormig\u00f3n armado pretensado (CAP):<\/strong> Difieren de las ordinarias en el hecho de que la armadura se tensa antes del vertido de hormig\u00f3n. Este proceso permite mejorar a\u00fan m\u00e1s la resistencia de la viga, ya que la tensi\u00f3n preexistente contrarresta las solicitaciones de tracci\u00f3n durante la carga en servicio. Las vigas pretensadas pueden, por lo tanto, soportar cargas m\u00e1s altas que las vigas de hormig\u00f3n armado ordinario. La pretensi\u00f3n permite reducir la secci\u00f3n transversal de la viga, optimizando la eficiencia estructural y abriendo la posibilidad de crear luces m\u00e1s grandes sin necesidad de soportes intermedios. Las vigas de CAP se utilizan com\u00fanmente en grandes estructuras, como puentes, viaductos, edificios industriales, etc. Son ideales para proyectos que requieren una mayor capacidad de carga y una reducci\u00f3n de las deformaciones.<\/li>\n<\/ol>\n<h3>Tipos de vigas seg\u00fan condiciones de apoyo<\/h3>\n<p>Una subdivisi\u00f3n adicional de las vigas de hormig\u00f3n armado concierne a las <strong>condiciones de apoyo<\/strong>. Esta clasificaci\u00f3n tiene en cuenta las formas en que los extremos de las vigas est\u00e1n apoyados o restringidos. Aqu\u00ed algunas de las principales categor\u00edas:<\/p>\n<ol>\n<li><strong>vigas simplemente apoyadas<\/strong>: en este tipo de viga, los extremos descansan sobre soportes laterales que permiten la rotaci\u00f3n. Se trata de un tipo de restricci\u00f3n que simplifica el an\u00e1lisis estructural, ya que la viga puede moverse libremente sin transmitir momentos flectores a los apoyos. Esta configuraci\u00f3n se utiliza a menudo cuando se desea una distribuci\u00f3n uniforme de la carga a lo largo de la viga, garantizando al mismo tiempo una soluci\u00f3n estructural relativamente simple;<\/li>\n<li><strong>vigas empotradas<\/strong>: est\u00e1n sujetas a restricciones r\u00edgidas en los extremos, que impiden tanto la traslaci\u00f3n como la rotaci\u00f3n. Este tipo de viga se utiliza en situaciones donde es necesario resistir cargas y solicitaciones particularmente altas, como en cimentaciones o estructuras s\u00edsmicas;<\/li>\n<li><strong>vigas continuas<\/strong>: las vigas continuas son soportadas por varios puntos intermedios, como columnas o pilares. Estos puntos intermedios permiten una distribuci\u00f3n m\u00e1s uniforme de las cargas a lo largo de la viga. Las vigas continuas se utilizan para cubrir luces mayores y reducir la deformaci\u00f3n de la viga;<\/li>\n<li><strong>vigas voladizas<\/strong>: se caracterizan por un extremo que sobresale m\u00e1s all\u00e1 del punto de apoyo. Esta configuraci\u00f3n permite crear espacios abiertos amplios sin necesidad de soportes intermedios. Las vigas voladizas son comunes en las fachadas de los edificios o en estructuras suspendidas como puentes.<\/li>\n<\/ol>\n<h3>Tipos de vigas seg\u00fan sus caracter\u00edsticas formales<\/h3>\n<p>Considerando el aspecto geom\u00e9trico, es posible realizar una clasificaci\u00f3n adicional de las vigas de hormig\u00f3n armado, distingui\u00e9ndolas por sus <strong>caracter\u00edsticas formales<\/strong> entre:<\/p>\n<ol>\n<li><strong>vigas de secci\u00f3n rectangular<\/strong>: son las formas m\u00e1s comunes de vigas de hormig\u00f3n armado. Tienen una secci\u00f3n transversal rectangular, con un ancho generalmente menor que la altura. Esta forma es f\u00e1cil de realizar y ofrece una buena resistencia a la flexi\u00f3n;<\/li>\n<li><strong>vigas en T<\/strong>: tienen una secci\u00f3n transversal que recuerda a la letra \u00abT\u00bb. Est\u00e1n formadas por una parte central llamada \u00abalma\u00bb y por dos partes laterales colocadas en la parte superior del extremo de la viga, llamadas \u00abala\u00bb. Las vigas en T se utilizan a menudo en situaciones donde se necesita proporcionar una mayor resistencia al corte;<\/li>\n<li><strong>vigas en doble T<\/strong>: son similares a las vigas en T, pero tienen alas tanto en la parte superior como en la inferior del alma. Esta configuraci\u00f3n ofrece una mayor resistencia a la flexi\u00f3n y a la torsi\u00f3n que las vigas rectangulares o en T. Las vigas en doble T se utilizan com\u00fanmente en puentes y estructuras de gran tama\u00f1o;<\/li>\n<li><strong>vigas de secci\u00f3n compuesta<\/strong>: est\u00e1n formadas por dos o m\u00e1s materiales diferentes combinados para aprovechar las caracter\u00edsticas ventajosas de cada material. Por ejemplo, una viga puede estar compuesta por partes de acero para estructuras met\u00e1licas y partes de hormig\u00f3n armado, colaborando entre s\u00ed mediante un sistema de conexi\u00f3n especial. Este tipo de viga ofrece una mayor resistencia y rigidez que las vigas de hormig\u00f3n armado tradicionales;<\/li>\n<li><strong>vigas de secci\u00f3n variable<\/strong>: tienen una secci\u00f3n transversal que cambia a lo largo de su longitud. Esto se puede hacer para adaptarse a las diferentes solicitaciones y requisitos estructurales a lo largo de la viga. Las vigas de secci\u00f3n variable se utilizan a menudo en estructuras complejas o en situaciones donde se requiere una distribuci\u00f3n no uniforme de las cargas.<\/li>\n<\/ol>\n<div id=\"attachment_205716\" class=\"wp-caption aligncenter\" style=\"width: 810px;\">\n<div id=\"attachment_205716\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-205716\" class=\"wp-image-205716 size-full lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/biblus.accasoftware.com\/es\/wp-content\/uploads\/sites\/3\/2024\/04\/Classification-of-reinforced-concrete-beams.jpg\" alt=\"Classification of reinforced concrete beams\" width=\"800\" height=\"600\" aria-describedby=\"caption-attachment-205716\" \/><p id=\"caption-attachment-205716\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"wp-image-205716 size-full lazyload\" src=\"https:\/\/biblus.accasoftware.com\/es\/wp-content\/uploads\/sites\/3\/2024\/04\/Classification-of-reinforced-concrete-beams.jpg\" alt=\"Classification of reinforced concrete beams\" width=\"800\" height=\"600\" aria-describedby=\"caption-attachment-205716\" \/><\/noscript> Classification of reinforced concrete beams<\/p><\/div>\n<\/div>\n<h2 id=\"como-disenar-las-vigas-de-hormigon-armado\">C\u00f3mo dise\u00f1ar las vigas de hormig\u00f3n armado<\/h2>\n<p>El dise\u00f1o y la verificaci\u00f3n de las vigas de hormig\u00f3n armado requieren una serie de pasos y evaluaciones que siguen los principios de la ingenier\u00eda estructural.<\/p>\n<p>A continuaci\u00f3n, se presentan los aspectos fundamentales que deber\u00e1s considerar durante el dise\u00f1o:<\/p>\n<ul>\n<li><strong>an\u00e1lisis estructural<\/strong>: realiza un an\u00e1lisis estructural del edificio para determinar las acciones (cargas) que act\u00faan sobre las vigas;<\/li>\n<li><strong>an\u00e1lisis de las solicitaciones<\/strong>: determina las solicitaciones internas que act\u00faan sobre la viga. Este an\u00e1lisis se puede realizar utilizando m\u00e9todos anal\u00edticos o <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/es\/programa-calculo-estructuras\" target=\"_blank\" rel=\"noopener\">software de c\u00e1lculo estructural<\/a>;<\/li>\n<li><strong>verificaci\u00f3n de la resistencia<\/strong>: compara las solicitaciones internas con las capacidades de resistencia del hormig\u00f3n y del acero. Aseg\u00farate de cumplir con los requisitos de resistencia, <a href=\"https:\/\/biblus.accasoftware.com\/es\/ductilidad-estructural\/\" target=\"_blank\" rel=\"noopener\">ductilidad<\/a> y estabilidad definidos por la normativa;<\/li>\n<li><strong>dimensionamiento de las secciones transversales<\/strong>: determina las dimensiones de las secciones transversales de las vigas en funci\u00f3n de las solicitaciones calculadas y los requisitos de resistencia. Considera tambi\u00e9n aspectos de durabilidad, evaluando el recubrimiento m\u00ednimo del hormig\u00f3n (cubierta) para proteger la armadura de agentes agresivos;<\/li>\n<li><strong>c\u00e1lculo de la armadura<\/strong>: dise\u00f1a la armadura necesaria para resistir las solicitaciones de flexi\u00f3n, tracci\u00f3n, torsi\u00f3n y corte. Calcula la cantidad de armadura requerida, la disposici\u00f3n de las barras y el espesor del recubrimiento. Aseg\u00farate de cumplir con los requisitos de distancia m\u00ednima entre barras y las condiciones de anclaje;<\/li>\n<li><strong>definici\u00f3n de los detalles constructivos<\/strong>: define los detalles constructivos de las vigas, como las conexiones entre las barras de armadura, los nudos con los pilares, etc. Aseg\u00farate de que los detalles cumplan con los requisitos de resistencia, durabilidad y facilidad de construcci\u00f3n;<\/li>\n<li><strong>verificaci\u00f3n de la deformabilidad<\/strong>: verifica la deformabilidad de la viga, controlando las fisuras y la deformaci\u00f3n el\u00e1stica.<\/li>\n<li><strong>verificaci\u00f3n de la estabilidad<\/strong>: eval\u00faa la estabilidad global de la viga, teniendo en cuenta los efectos de inestabilidad, como el pandeo lateral o el colapso. Aseg\u00farate de que la viga est\u00e9 adecuadamente anclada y que se prevengan o corrijan las condiciones de inestabilidad.<\/li>\n<\/ul>\n<h2 id=\"herramientas-software-para-el-diseno-y-verificacion-de-vigas-de-hormigon-armado\">Herramientas software para el dise\u00f1o y verificaci\u00f3n de vigas de hormig\u00f3n armado<\/h2>\n<p>El proceso de dise\u00f1o y verificaci\u00f3n de las vigas de hormig\u00f3n armado puede simplificarse considerablemente, acelerarse y hacerse m\u00e1s fiable gracias a un <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/es\/programa-calculo-estructuras\" target=\"_blank\" rel=\"noopener\">software de c\u00e1lculo estructural espec\u00edfico para estructuras de hormig\u00f3n armado<\/a>. Experimenta ahora esta innovadora soluci\u00f3n para el c\u00e1lculo estructural de edificios de hormig\u00f3n armado y descubre las numerosas ventajas que puede ofrecerte.<\/p>\n<p>Utilizando este sistema podr\u00e1s modelar tu estructura <strong>en entorno BIM<\/strong> y aprovechar la potencia del <strong>solucionador FEM integrado<\/strong> para realizar an\u00e1lisis estructurales avanzados. Tendr\u00e1s la posibilidad de visualizar los resultados de forma gr\u00e1fica, dise\u00f1ar las armaduras y producir los documentos del proyecto dentro de un \u00fanico entorno. El software tambi\u00e9n ofrece la posibilidad de integrar m\u00f3dulos opcionales para el dise\u00f1o y el <strong>c\u00e1lculo de estructuras de hormig\u00f3n armado <\/strong>con elementos de mamposter\u00eda, madera y acero. Podr\u00e1s abordar la adaptaci\u00f3n de edificios existentes y el an\u00e1lisis no lineal, todo dentro del mismo entorno intuitivo y potente.<\/p>\n<div class='avia-iframe-wrap'><iframe title=\"Tutorial de EdiLus - Realizaci\u00f3n de rejillas complejas - ACCA software\" width=\"1500\" height=\"844\" src=\"https:\/\/www.youtube.com\/embed\/MgUionAtkEI?feature=oembed&#038;enablejsapi=1\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<div class=\"international-product-banner-desktop\" style=\"text-align: center;\"><a class=\"product-banner-link\" href=\"https:\/\/www.accasoftware.com\/es\/programa-calculo-estructuras\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto\/edilus-es.jpg\" alt=\"edilus\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto\/edilus-es.jpg\" alt=\"edilus\" \/><\/noscript><\/a><\/div>\n<div class=\"international-product-banner-mobile\" style=\"text-align: center;\"><a class=\"product-banner-link\" href=\"https:\/\/www.accasoftware.com\/es\/programa-calculo-estructuras\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto_mobile\/edilus-es.jpg\" alt=\"edilus\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto_mobile\/edilus-es.jpg\" alt=\"edilus\" \/><\/noscript><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Las vigas de hormig\u00f3n armado son elementos estructurales horizontales compuestos por una combinaci\u00f3n de hormig\u00f3n y acero. Descubre m\u00e1s sobre ellas en este art\u00edculo<\/p>\n","protected":false},"author":54,"featured_media":25188,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_data_scadenza_evento":"","_evento_nome":"","_evento_data":"","_evento_luogo":"","_evento_cta":"","keyword_en":"","keyword_es":"vigas de hormigon armado","keyword_fr":"","keyword_de":"","keyword_ptb":"","_note_content":"<table dir=\"ltr\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\" data-sheets-root=\"1\"><colgroup><col width=\"33\" \/><col width=\"580\" \/><col width=\"332\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam&quot;}\">reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:170}\">170<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;concrete beam reinforcement&quot;}\">concrete beam reinforcement<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:50}\">50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;doubly reinforced concrete beam&quot;}\">doubly reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:30}\">30<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;concrete beam reinforcement design&quot;}\">concrete beam reinforcement design<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;cross section of reinforced concrete beam&quot;}\">cross section of reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;cross section reinforced concrete beam&quot;}\">cross section reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;design a reinforced concrete beam example&quot;}\">design a reinforced concrete beam example<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;design of doubly reinforced concrete beam&quot;}\">design of doubly reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;design of t beams reinforced concrete&quot;}\">design of t beams reinforced concrete<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;flexural analysis of reinforced concrete beams&quot;}\">flexural analysis of reinforced concrete beams<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;flexural design of reinforced concrete beams&quot;}\">flexural design of reinforced concrete beams<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;how to design reinforced concrete beam&quot;}\">how to design reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;moment of inertia reinforced concrete beam&quot;}\">moment of inertia reinforced concrete beam<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam design&quot;}\">reinforced concrete beam design<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam design example&quot;}\">reinforced concrete beam design example<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam detailing&quot;}\">reinforced concrete beam detailing<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam details&quot;}\">reinforced concrete beam details<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam example&quot;}\">reinforced concrete beam example<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;reinforced concrete beam section&quot;}\">reinforced concrete beam section<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;types of reinforced concrete beams&quot;}\">types of reinforced concrete beams<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;design beams reinforced concrete&quot;}\">design beams reinforced concrete<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre en b\u00e9ton arm\u00e9&quot;}\">poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:170}\">170<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calcul d'une poutre en b\u00e9ton arm\u00e9&quot;}\">calcul d'une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calcul de poutre en b\u00e9ton arm\u00e9&quot;}\">calcul de poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;chemisage des poutres en b\u00e9ton arm\u00e9&quot;}\">chemisage des poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;comment calculer une poutre en b\u00e9ton arm\u00e9&quot;}\">comment calculer une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;comment dimensionner une poutre en b\u00e9ton arm\u00e9&quot;}\">comment dimensionner une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;comment faire une poutre en b\u00e9ton arm\u00e9&quot;}\">comment faire une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionnement d'une poutre en b\u00e9ton arm\u00e9&quot;}\">dimensionnement d'une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;d\u00e9finition poutre en b\u00e9ton arm\u00e9&quot;}\">d\u00e9finition poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ferraillage d'une poutre en b\u00e9ton arm\u00e9&quot;}\">ferraillage d'une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;les poutres en b\u00e9ton arm\u00e9&quot;}\">les poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;les types de poutres en b\u00e9ton arm\u00e9&quot;}\">les types de poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre en b\u00e9ton arm\u00e9 calcul&quot;}\">poutre en b\u00e9ton arm\u00e9 calcul<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre en b\u00e9ton arm\u00e9 d\u00e9finition&quot;}\">poutre en b\u00e9ton arm\u00e9 d\u00e9finition<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre en t b\u00e9ton arm\u00e9&quot;}\">poutre en t b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre en t\u00e9 b\u00e9ton arm\u00e9&quot;}\">poutre en t\u00e9 b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutre pr\u00e9fabriqu\u00e9e en b\u00e9ton arm\u00e9&quot;}\">poutre pr\u00e9fabriqu\u00e9e en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;poutres en b\u00e9ton arm\u00e9&quot;}\">poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;renforcement des poutres en b\u00e9ton arm\u00e9&quot;}\">renforcement des poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;r\u00e9aliser une poutre en b\u00e9ton arm\u00e9&quot;}\">r\u00e9aliser une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;type de poutre en b\u00e9ton arm\u00e9&quot;}\">type de poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;types de poutres en b\u00e9ton arm\u00e9&quot;}\">types de poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;une poutre en b\u00e9ton arm\u00e9&quot;}\">une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calcul des poutres en b\u00e9ton arm\u00e9&quot;}\">calcul des poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calcul des poutres en b\u00e9ton arm\u00e9 pdf&quot;}\">calcul des poutres en b\u00e9ton arm\u00e9 pdf<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionnement des poutres en b\u00e9ton arm\u00e9&quot;}\">dimensionnement des poutres en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionnement poutre en b\u00e9ton arm\u00e9&quot;}\">dimensionnement poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;d\u00e9finition d une poutre en b\u00e9ton arm\u00e9&quot;}\">d\u00e9finition d une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;d\u00e9finition d'une poutre en b\u00e9ton arm\u00e9&quot;}\">d\u00e9finition d'une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;fabriquer une poutre en b\u00e9ton arm\u00e9&quot;}\">fabriquer une poutre en b\u00e9ton arm\u00e9<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;vigas de concreto armado&quot;}\">vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:720}\">720<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;viga de concreto armado&quot;}\">viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:170}\">170<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;tabela de dimensionamento de vigas de concreto armado&quot;}\">tabela de dimensionamento de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:110}\">110<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionamento de vigas de concreto armado&quot;}\">dimensionamento de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:70}\">70<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;detalhamento de vigas de concreto armado&quot;}\">detalhamento de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:40}\">40<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo de vigas concreto armado&quot;}\">calculo de vigas concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo de vigas de concreto armado&quot;}\">calculo de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo de vigas de concreto armado gratis&quot;}\">calculo de vigas de concreto armado gratis<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo estrutural de vigas concreto armado&quot;}\">calculo estrutural de vigas concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo viga de concreto armado&quot;}\">calculo viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo vigas de concreto armado&quot;}\">calculo vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;como calcular viga de concreto armado&quot;}\">como calcular viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;como dimensionar vigas de concreto armado&quot;}\">como dimensionar vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;como fazer viga de concreto armado&quot;}\">como fazer viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;como fazer vigas de concreto armado&quot;}\">como fazer vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;concreto armado dimensionamento de vigas&quot;}\">concreto armado dimensionamento de vigas<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;c\u00e1lculo de vigas de concreto armado&quot;}\">c\u00e1lculo de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionamento de viga concreto armado&quot;}\">dimensionamento de viga concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionamento de vigas concreto armado&quot;}\">dimensionamento de vigas concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionamento vigas de concreto armado&quot;}\">dimensionamento vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;pilar e viga de concreto armado&quot;}\">pilar e viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;pilares e vigas de concreto armado&quot;}\">pilares e vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;tipos de vigas de concreto armado&quot;}\">tipos de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo de uma viga de concreto armado&quot;}\">calculo de uma viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;concreto armado calculo de vigas&quot;}\">concreto armado calculo de vigas<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;detalhamento de viga de concreto armado&quot;}\">detalhamento de viga de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;projeto de vigas de concreto armado&quot;}\">projeto de vigas de concreto armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;vigas de concreto armado defini\u00e7\u00e3o&quot;}\">vigas de concreto armado defini\u00e7\u00e3o<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:10}\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;vigas de hormigon armado&quot;}\">vigas de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:170}\">170<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;viga de hormigon armado&quot;}\">viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:70}\">70<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;armado de vigas de hormigon&quot;}\">armado de vigas de hormigon<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:40}\">40<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;largo maximo de una viga de hormigon armado&quot;}\">largo maximo de una viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:30}\">30<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;armadura de vigas hormigon armado&quot;}\">armadura de vigas hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calcular viga de hormigon armado&quot;}\">calcular viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo de vigas de hormigon armado&quot;}\">calculo de vigas de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculo viga de hormigon armado&quot;}\">calculo viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;calculos de vigas de hormigon armado&quot;}\">calculos de vigas de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;como dimensionar una viga de hormigon armado&quot;}\">como dimensionar una viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;detalle constructivo viga de hormigon armado&quot;}\">detalle constructivo viga de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensionado de vigas de hormigon armado&quot;}\">dimensionado de vigas de hormigon armado<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;dimensiones de vigas de hormigon armado&quot;}\">dimensiones de vigas de hormigon 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