{"id":33177,"date":"2024-04-29T15:25:20","date_gmt":"2024-04-29T13:25:20","guid":{"rendered":"https:\/\/biblus.accasoftware.com\/en\/?p=33177"},"modified":"2024-10-01T12:30:57","modified_gmt":"2024-10-01T10:30:57","slug":"reinforced-concrete-beam-analysis","status":"publish","type":"post","link":"https:\/\/biblus.accasoftware.com\/en\/reinforced-concrete-beam-analysis\/","title":{"rendered":"Reinforced concrete beam analysis"},"content":{"rendered":"<p class=\"sommario\">Reinforced concrete beams are horizontal structural elements made of a combination of concrete and steel. Discover how to design them<\/p>\n<p><!--more--><\/p>\n<p>Reinforced concrete beams are fundamental structural elements in modern construction. They stand out for their ability to withstand tensile stresses, thanks to the use of steel reinforcement incorporated into the concrete mix.<\/p>\n<p>In this article, we will explore the different types of reinforced concrete beams used in the construction industry. We will analyze the characteristics of each type, examining their specific applications in various structural contexts.<\/p>\n<p>If you are involved in structural design, you should know that you can rely on advanced tools to improve the efficiency and reliability of your processes. Explore the potential of a specific solution <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" target=\"_blank\" rel=\"noopener\">for modeling and analyzing reinforced concrete structures<\/a>. By using these systems, you will be able to import the IFC architectural model of your building into a BIM environment and model your structure with intelligent parametric objects. You will also be able to leverage the power of the integrated FEM solver to perform advanced analyses quickly and reliably evaluate the structural response of your buildings.<\/p>\n<p>Let&#8217;s now explore all the advantages of reinforced concrete beams and understand how these structural elements can contribute to the strength, safety, and stability of constructions.<\/p>\n<h2 id=\"reinforced-concrete-beams\">Reinforced Concrete Beams<\/h2>\n<p>Reinforced concrete beams are structural elements used in the construction of buildings and infrastructure. Specifically, they constitute the <strong>horizontal components of &#8220;frame&#8221; load-bearing structures<\/strong> made using reinforced concrete.<\/p>\n<p>This material results from the combination of concrete, which provides compressive strength, with steel, which offers high tensile strength. The use of reinforced concrete allows for harnessing the complementary properties of the two materials and creating <strong>very strong structures<\/strong> capable of withstanding both tensile and compressive forces.<\/p>\n<p>In the context of construction, there are different types of reinforced concrete beams, each designed to meet specific needs. Let&#8217;s now explore together some of the most common types, aiming to highlight their distinctive features.<\/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\/en\/wp-content\/uploads\/sites\/2\/2024\/04\/travi-ca.jpg\" alt=\"Reinforced Concrete Beams\" 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\/en\/wp-content\/uploads\/sites\/2\/2024\/04\/travi-ca.jpg\" alt=\"Reinforced Concrete Beams\" width=\"1200\" height=\"800\" aria-describedby=\"caption-attachment-205718\" \/><\/noscript> Reinforced Concrete Beams<\/p><\/div>\n<\/div>\n<h2 id=\"types-of-reinforced-concrete-beams\">Types of Reinforced Concrete Beams<\/h2>\n<p>The versatility of reinforced concrete allows for the creation of beams in various shapes, types, and sizes, adaptable to specific design requirements. A first classification of these elements can be made based on the <strong>construction methods<\/strong>, distinguishing between:<\/p>\n<ol>\n<li><strong>ordinary reinforced concrete beams (RC)<\/strong>: made by pouring concrete into formworks, prepared to give the beam the desired shape, and inside which the steel reinforcement is previously positioned. The reinforcement consists of high bond steel bars aimed at ensuring maximum adhesion between the two materials (concrete and steel), avoiding slippage phenomena. Ordinary reinforced concrete beams are widely used in various structural contexts, such as residential, commercial, and industrial buildings. They are suitable for slabs, roofs, support beams, and eaves beams. Their versatility and ease of construction make them a common choice in most construction applications;<\/li>\n<li><strong>prestressed reinforced concrete beams (PC)<\/strong>: differ from ordinary beams in that the reinforcement is tensioned before pouring the concrete. This process further enhances the beam&#8217;s strength, as the pre-existing tension counteracts tensile stresses during service loads. Prestressed beams can, therefore, withstand higher loads compared to ordinary reinforced concrete beams. Prestressing allows for reducing the beam&#8217;s cross-section, optimizing structural efficiency and enabling the creation of larger spans without the need for intermediate supports. PC beams are commonly used in large structures such as bridges, viaducts, industrial buildings, etc. They are ideal for projects requiring higher load capacity and reduced deformations.<\/li>\n<\/ol>\n<p>Another subdivision of reinforced concrete beams concerns the <strong>boundary conditions<\/strong>. This classification takes into account how the beam ends are constrained or supported. Here are some of the main categories:<\/p>\n<ol>\n<li><strong>simply supported beams<\/strong>: in this type of beam, the ends are supported on lateral supports that allow rotation. This type of constraint simplifies structural analysis, as the beam can move freely without transmitting bending moments to the supports. This configuration is often used when a uniform load distribution along the beam is desired, ensuring a relatively simple structural solution;<\/li>\n<li><strong>fixed-end beams<\/strong>: are subject to rigid constraints at the ends, preventing both translation and rotation. This type of beam is used in situations where resistance to particularly high loads and stresses is required, such as in foundations or seismic structures;<\/li>\n<li><strong>continuous beams<\/strong>: continuous beams are supported by multiple intermediate points, such as columns or pillars. These intermediate points allow for a more uniform load distribution along the beam. Continuous beams are used to cover larger spans and reduce beam deformation;<\/li>\n<li><strong>cantilever beams<\/strong>: are characterized by one end protruding beyond the support point. This configuration allows for creating large open spaces without the need for intermediate supports. Cantilever beams are common in building facades or suspended structures like bridges.<\/li>\n<\/ol>\n<p>Considering the geometric aspect, a further classification of reinforced concrete beams can be made based on their <strong>formal characteristics<\/strong>, distinguishing them based on:<\/p>\n<ol>\n<li><strong>rectangular section beams<\/strong>: are the most common forms of reinforced concrete beams. They have a rectangular cross-section, with a width generally smaller than the height. This shape is simple to construct and offers good resistance to bending;<\/li>\n<li><strong>T-section beams<\/strong>: have a cross-section resembling the letter &#8220;T&#8221;. They consist of a central part called the &#8220;web&#8221; and two lateral parts located at the upper end of the beam, called &#8220;flanges&#8221;. T-section beams are often used in situations where greater resistance to shear forces is required;<\/li>\n<li><strong>double T-section beams<\/strong>: are similar to T-section beams but have flanges at both the upper and lower ends of the web. This configuration offers greater resistance to bending and torsion compared to rectangular or T-section beams. Double T-section beams are commonly used in bridges and large structures;<\/li>\n<li><strong>composite section beams<\/strong>: are made up of two or more different materials combined to exploit the advantageous characteristics of each material. For example, a beam can be made of parts in structural steel and parts in reinforced concrete, made to work together through a specific connection system. This type of beam offers greater strength and rigidity compared to traditional reinforced concrete beams;<\/li>\n<li><strong>variable section beams<\/strong>: have a cross-section that changes along their length. This can be done to adapt to different stresses and structural requirements along the beam. Variable section beams are often used in complex structures or situations where a non-uniform load distribution is required.<\/li>\n<\/ol>\n<p>The choice of the beam type to adopt depends on the <strong>structural and functional needs of the project<\/strong>. It is important to carefully consider the load characteristics, stress distribution, and expected deformations to determine the most appropriate configuration for achieving a stable and safe structure. A structural engineer will carefully evaluate these variables to identify the most suitable beam type for the specific context.<\/p>\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\/en\/wp-content\/uploads\/sites\/2\/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\/en\/wp-content\/uploads\/sites\/2\/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=\"how-to-design-reinforced-concrete-beams\">How to Design Reinforced Concrete Beams<\/h2>\n<p>The design and verification of reinforced concrete beams require a series of steps and evaluations following the principles of structural engineering.<\/p>\n<p>Below are the fundamental aspects you should consider during the design process:<\/p>\n<ul>\n<li><strong>structural analysis<\/strong>: perform a structural analysis of the building to determine the actions (loads) acting on the beams;<\/li>\n<li><strong>stress analysis<\/strong>: determine the internal stresses acting on the beam. This analysis can be carried out using analytical methods or <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" target=\"_blank\" rel=\"noopener\">structural calculation software<\/a>;<\/li>\n<li><strong>strength verification<\/strong>: compare the internal stresses with the strength capacities of concrete and steel. Make sure to meet the requirements for strength, <a href=\"https:\/\/biblus.accasoftware.com\/en\/ductile-design-of-steel-structures\/\" target=\"_blank\" rel=\"noopener\">ductility<\/a>, and stability defined by regulations;<\/li>\n<li><strong>sizing of cross-sections<\/strong>: determine the dimensions of the beam&#8217;s cross-sections based on calculated stresses and strength requirements. Also, consider durability aspects, evaluating the minimum concrete cover (concrete protection) to protect the reinforcement from aggressive agents;<\/li>\n<li><strong>reinforcement calculation<\/strong>: design the necessary reinforcement to withstand bending, tension, torsion, and shear stresses. Calculate the required amount of reinforcement, the arrangement of bars, and the thickness of the concrete cover. Make sure to meet the requirements for minimum bar spacing and anchoring conditions;<\/li>\n<li><strong>definition of construction details<\/strong>: define the construction details of the beams, such as connections between reinforcement bars, nodes with pillars, etc. Ensure that the details meet the requirements for strength, durability, and ease of construction;<\/li>\n<li><strong>deformability verification<\/strong>: verify the beam&#8217;s deformability, checking for cracks and elastic deformation;<\/li>\n<li><strong>stability verification<\/strong>: evaluate the overall stability of the beam, considering instability effects such as lateral deflection or collapse. Ensure that the beam is adequately supported and that instability conditions are prevented or corrected.<\/li>\n<\/ul>\n<p>The design and verification process of reinforced concrete beams can be significantly simplified, accelerated, and made more reliable through the use of <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" target=\"_blank\" rel=\"noopener\">specific structural calculation software for reinforced concrete structures<\/a>. Experience this innovative solution for the structural calculation of reinforced concrete buildings and discover the numerous advantages it can offer.<\/p>\n<p>By using this system, you can model your structure <strong>in a BIM environment<\/strong> and leverage the power of the <strong>integrated FEM solver<\/strong> to perform advanced structural analyses. You will have the opportunity to visualize results graphically, design reinforcements, and produce project documents within a single environment. The software also offers the possibility to integrate optional modules for the design and <strong>calculation of reinforced concrete structures<\/strong> with elements in masonry, wood, and steel. You can address the retrofitting of existing buildings and nonlinear analysis, all within the same intuitive and powerful environment.<\/p>\n<div class='avia-iframe-wrap'><iframe title=\"EdiLus Tutorial - Creating Complex grids - ACCA software\" width=\"1500\" height=\"844\" src=\"https:\/\/www.youtube.com\/embed\/Qb9yRfsvF7w?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 href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" 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-en.jpg\" alt=\"edilus\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto\/edilus-en.jpg\" alt=\"edilus\" \/><\/noscript><\/a><\/div>\n<div class=\"international-product-banner-mobile\" style=\"text-align: center\"><a href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" 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-en.jpg\" alt=\"edilus\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto_mobile\/edilus-en.jpg\" alt=\"edilus\" \/><\/noscript><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reinforced concrete beams are horizontal structural elements made of a combination of concrete and steel. Discover how to design them<\/p>\n","protected":false},"author":54,"featured_media":33178,"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":"reinforced concrete beam","keyword_es":"","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 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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 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;partes de una viga de hormigon armado&quot;}\">partes de 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;tipos de vigas de hormigon armado&quot;}\">tipos 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;tipos de vigas hormigon armado&quot;}\">tipos 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;vigas de hormigon armado medidas&quot;}\">vigas de hormigon armado medidas<\/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;vigas de hormig\u00f3n armado caracter\u00edsticas&quot;}\">vigas de hormig\u00f3n armado caracter\u00edsticas<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;stahlbetonbalken&quot;}\">stahlbetonbalken<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:140}\">140<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;bemessung stahlbetonbalken&quot;}\">bemessung stahlbetonbalken<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;bemessung stahlbetonbalken beispiel&quot;}\">bemessung stahlbetonbalken beispiel<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;bewehrung stahlbetonbalken&quot;}\">bewehrung stahlbetonbalken<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;konstruieren eines stahlbetonbalkens&quot;}\">konstruieren eines stahlbetonbalkens<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;stahlbetonbalken bemessung&quot;}\">stahlbetonbalken bemessung<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;stahlbetonbalken berechnen&quot;}\">stahlbetonbalken berechnen<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;stahlbetonbalken berechnung&quot;}\">stahlbetonbalken berechnung<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;stahlbetonbalken bewehrung berechnen&quot;}\">stahlbetonbalken bewehrung berechnen<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:20}\">20<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","footnotes":""},"categories":[5080],"tags":[5150],"class_list":["post-33177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bim-structural-calculation","tag-newsletter-340"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.8 (Yoast SEO v28.8) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Reinforced concrete beam analysis - BibLus<\/title>\n<meta name=\"description\" content=\"Reinforced concrete beams are horizontal structural elements consisting of a combination of concrete and steel. 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