{"id":35470,"date":"2024-09-09T09:02:22","date_gmt":"2024-09-09T07:02:22","guid":{"rendered":"https:\/\/biblus.accasoftware.com\/en\/?p=35470"},"modified":"2024-10-01T11:56:37","modified_gmt":"2024-10-01T09:56:37","slug":"benefits-and-applications-of-buttresses-in-construction","status":"publish","type":"post","link":"https:\/\/biblus.accasoftware.com\/en\/benefits-and-applications-of-buttresses-in-construction\/","title":{"rendered":"Benefits and applications of buttresses in construction"},"content":{"rendered":"<p class=\"sommario\">Buttresses are structural elements used to counteract lateral forces and ensure the safety and stability of buildings. Learn more<\/p>\n<p><!--more--><\/p>\n<p>Used since ancient times to allow the construction of robust and resistant structures, buttresses have always been an effective solution to reinforce load-bearing walls and provide essential support against horizontal forces. Discover in this article the multiple applications and benefits resulting from the use of these particular structural elements, essential to ensure the safety and durability of constructions.<\/p>\n<p>If you are involved in designing new structures or renovating existing buildings, why not revolutionize your way of working with a <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" target=\"_blank\" rel=\"noopener\">structural calculation software<\/a> based on the integration of BIM technology and FEM analysis? Try it now to explore all its features and discover the advantages of efficient, reliable, and cutting-edge design. Don&#8217;t miss the opportunity to optimize your work and improve your results with the help of technology.<\/p>\n<h2 id=\"what-are-buttresses\">What are buttresses?<\/h2>\n<p>Buttresses are <a href=\"https:\/\/biblus.accasoftware.com\/en\/structural-components-identification-and-verification\/\" target=\"_blank\" rel=\"noopener\">structural elements<\/a> used to <strong>reinforce the walls of a masonry structure<\/strong>, absorbing the <strong>horizontal and oblique forces<\/strong> acting on it. They can be positioned outside the structure or incorporated within the masonry itself to increase its resistance.<\/p>\n<p>Made of masonry or reinforced concrete, buttresses are designed with the main objective of <strong>stabilizing the walls of a building<\/strong> or <strong>retaining walls<\/strong> against overturning, counteracting the lateral forces generated by architectural elements such as arches, vaults, or domes, or by soil pressures or seismic action. These construction elements are characterized by their <strong>prismatic shape<\/strong>, with a quadrangular section that gradually inclines upwards, creating a sort of &#8220;shoe.&#8221;<\/p>\n<p>Frequently found in Gothic churches and other works of historical value, buttresses have played a fundamental role in the evolution of architecture, especially in <strong>structures of considerable height<\/strong> or <strong>with large openings<\/strong>. Originally conceived as protruding pillars arranged along the outer walls of buildings, over time they have undergone adaptations and modifications in response to the structural and stylistic needs of the period. In their most evolved form, buttresses appear as flying arches leaning against the external masonry of basilicas and cathedrals. Also known as flying buttresses and positioned at the bays, the purpose of these elements is to <strong>effectively intervene where lateral forces are unbalanced<\/strong>, providing support and stability in critical areas of the structure.<\/p>\n<p>In addition to their function of structural stabilization, these elements can also, in some cases, have an aesthetic value that contributes to defining the overall appearance of the work, giving a distinctive character and a sense of grandeur to the architectural structures that have them.<\/p>\n<h3>Difference between lesenes, pilasters, and buttresses<\/h3>\n<p>Due to their configuration, buttresses are often confused with other architectural elements, such as pilasters or piers, which are used for similar purposes but <strong>differ<\/strong> in their <strong>position<\/strong> and <strong>function<\/strong> within the building. Let&#8217;s examine the main differences between these elements:<\/p>\n<ul>\n<li><strong>lesenes<\/strong>: these are vertical architectural elements similar to pillars that can be found on the walls of a building and slightly protrude from the surface. Lesenes are set against the wall structure and do not have a load-bearing function but are used purely for decorative purposes;<\/li>\n<li><strong>pilasters<\/strong>: similar to pilasters but distinguished from them as they are like pillars embedded directly in the wall rather than simply resting on it. Piers protrude more from the surface of the masonry and can also have a load-bearing function in addition to a decorative one. They are used to provide structural support, especially in buildings with large openings or arches, while also assuming an ornamental role;<\/li>\n<li><strong>buttresses<\/strong>: are structural elements used to provide support and stability to architectural structures. They are commonly employed to counteract lateral forces or oblique stresses acting on the walls of a building. Unlike pilasters and piers, buttresses can be integrated or not into the masonry and protrude much more from the outer wall line. Their predominant function is structural rather than decorative.<\/li>\n<\/ul>\n<div id=\"attachment_27790\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-27790\" class=\"size-full wp-image-27790 lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/biblus.accasoftware.com\/en\/wp-content\/uploads\/sites\/2\/2024\/07\/Difference-between-lesenes-pilasters-and-buttresses.jpg\" alt=\"Difference between pilasters, piers, and buttresses\" width=\"800\" height=\"400\" \/><p id=\"caption-attachment-27790\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"size-full wp-image-27790 lazyload\" src=\"https:\/\/biblus.accasoftware.com\/en\/wp-content\/uploads\/sites\/2\/2024\/07\/Difference-between-lesenes-pilasters-and-buttresses.jpg\" alt=\"Difference between pilasters, piers, and buttresses\" width=\"800\" height=\"400\" \/><\/noscript> Difference between lesenes, pilasters, and buttresses<\/p><\/div>\n<h2 id=\"applications-of-buttresses-in-architecture-and-engineering\">Applications of buttresses in architecture and engineering<\/h2>\n<p>Buttresses have various applications in the field of engineering and architecture. Below are described some of their most common uses:<\/p>\n<ul>\n<li><strong>structural support of walls<\/strong>: one of the main purposes of buttresses is to provide support and stability to the vertical walls of buildings, especially when they are subjected to significant lateral forces. Positioned externally along the wall, these elements develop in height with a progressively decreasing thickness, effectively counteracting the pressure exerted on it. Their presence is essential to prevent overturning, collapse, or deformation of the masonry walls, thus ensuring the overall stability of the entire structure;<\/li>\n<li><strong>reinforcement of arches and vaults<\/strong>: arches and vaults are structural elements that, due to their load transmission methods, can generate thrust forces on the perimeter walls of buildings. To prevent these forces from causing the collapse of the walls, buttresses are used. These structural elements absorb and distribute the lateral forces coming from the elements above, reducing the pressures on the masonry and ensuring the structural stability of the entire system;<\/li>\n<li><strong>stabilization of historical buildings<\/strong>: buttresses can be used to prevent structural collapses and reinforce walls in existing buildings and historical buildings that may have stability issues. Commonly used in restoration projects, these elements help absorb the lateral forces that threaten the building&#8217;s stability, ensuring its long-term preservation;<\/li>\n<li><strong>support of retaining walls<\/strong>: buttresses can be used in retaining walls to support embankments and prevent overturning or collapse of the structure under the action of lateral forces. These elements are positioned on the opposite side of the wall compared to the pressure exerted by the ground, generating a counterforce that ensures the stability of the structure in its retaining role;<\/li>\n<li><strong>seismic reinforcement<\/strong>: in high seismic risk areas, buttresses are used to strengthen the walls of buildings and mitigate the risk of structural damage caused by earthquakes. These elements are designed to absorb and distribute the seismic forces acting on the structure, reducing the stresses on the load-bearing elements. The use of buttresses improves the building&#8217;s ability to withstand seismic events and ensure the safety of occupants.<\/li>\n<\/ul>\n<h2 id=\"what-are-the-advantages-of-buttresses\">What are the advantages of buttresses?<\/h2>\n<p>Buttresses have played a fundamental role in the <strong>preservation of countless architectures<\/strong> that have come down to us through the centuries thanks to their presence. These elements are able to ensure the stability and longevity of structures, offering support against forces that could threaten their integrity over time.<\/p>\n<p>Buttresses <strong>prevent the overturning of structural elements<\/strong>. Positioned strategically along the external walls of buildings, these elements absorb and distribute the <strong>lateral<\/strong> or <strong>oblique forces<\/strong> that could threaten the structure&#8217;s stability. This support mechanism prevents structural collapse and protects buildings from irreparable damage.<\/p>\n<p>Buttresses also play an essential role in geotechnical engineering. They can be used as <strong>reinforcement for retaining walls<\/strong>, counteracting the <strong>forces exerted by large embankments<\/strong>. This function not only improves the structure&#8217;s resistance but also contributes to ensuring the safety of the surrounding areas, avoiding potential landslides or ground collapses.<\/p>\n<div id=\"attachment_27791\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-27791\" class=\"size-full wp-image-27791 lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/biblus.accasoftware.com\/en\/wp-content\/uploads\/sites\/2\/2024\/07\/Advantages-of-buttresses.jpg\" alt=\"Advantages of buttresses\" width=\"800\" height=\"400\" \/><p id=\"caption-attachment-27791\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"size-full wp-image-27791 lazyload\" src=\"https:\/\/biblus.accasoftware.com\/en\/wp-content\/uploads\/sites\/2\/2024\/07\/Advantages-of-buttresses.jpg\" alt=\"Advantages of buttresses\" width=\"800\" height=\"400\" \/><\/noscript> Advantages of buttresses<\/p><\/div>\n<h2 id=\"factors-to-consider-in-the-design-of-buttresses-in-a-building\">Factors to consider in the design of buttresses in a building<\/h2>\n<p>When designing buttresses in a building, it is essential to consider several factors to ensure stability and structural safety. Among the main factors to take into account are:<\/p>\n<ol>\n<li><strong>prevention of the phenomenon of wall detachment<\/strong>: buttresses must be designed to prevent the phenomenon of wall detachment, which could cause wall rotations and vault enlargements, reducing deflections and increasing thrusts;<\/li>\n<li><strong>resistance to lateral and seismic actions<\/strong>: buttresses must be designed to resist lateral actions, such as those caused by wind or seismic events, which could cause the facade to rotate outwards;<\/li>\n<li><strong>intervention to maintain structural balance<\/strong>: buttresses must be designed to maintain the structure in balance, counteracting lateral thrusts and ensuring the overall stability of the building.<\/li>\n<\/ol>\n<p>The design of buttresses requires a deep understanding of the specific structural needs of each building. First and foremost, it is essential to carry out a <strong>detailed analysis of the forces and loads acting on the building<\/strong>. This includes the weight of the structure itself, loads due to wind, snow, and other environmental factors, as well as any concentrated loads such as those generated by mechanical or architectural systems. Then it is necessary to <strong>properly size the buttresses<\/strong> to ensure the structural stability of the building. This includes determining the dimensions, cross-sections, and most suitable materials for the buttresses based on the expected loads and soil properties. The <strong>placement of the buttresses along the wall line<\/strong> must be carefully studied to maximize effectiveness in distributing the loads.<\/p>\n<p>To assess the stresses to which your structures are subjected, whether in the design of new buildings or in the renovation of existing constructions, rely on the efficiency of a <a class=\"textualLink_edilus\" href=\"https:\/\/www.accasoftware.com\/en\/structural-engineering-analysis-software\" target=\"_blank\" rel=\"noopener\">BIM-based structural calculation software<\/a>, with integrated FEM solver. Model your structural elements with intelligent parametric objects and leverage computing power to perform advanced structural analyses quickly and with extremely reliable results. Let technology guide you to revolutionize your design approach. Take advantage of a free thirty-day trial and discover how this tool can simplify your work, increase the accuracy of your elaborations, and ensure optimal results for your projects.<\/p>\n<p>&nbsp;<\/p>\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\" width=\"728\" height=\"160\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto\/edilus-en.jpg\" alt=\"Edilus\" width=\"728\" height=\"160\" \/><\/noscript><\/a><\/div>\n<p>&nbsp;<\/p>\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\" width=\"600\" height=\"500\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"\/wp-content\/themes\/enfold-child\/img\/banner_prodotto_mobile\/edilus-en.jpg\" alt=\"Edilus\" width=\"600\" height=\"500\" \/><\/noscript><\/a><\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Buttresses are structural elements used to counteract lateral forces and ensure the safety and stability of buildings. Learn more<\/p>\n","protected":false},"author":54,"featured_media":35471,"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":"buttress","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=\"34\" \/><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;buttress&quot;}\">buttress<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:18100}\">18100<\/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;buttresses&quot;}\">buttresses<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:4400}\">4400<\/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;the buttress&quot;}\">the buttress<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:2900}\">2900<\/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;buttress definition&quot;}\">buttress definition<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1900}\">1900<\/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;buttressing&quot;}\">buttressing<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1300}\">1300<\/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;definition for buttress&quot;}\">definition for buttress<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1000}\">1000<\/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;buttresses meaning&quot;}\">buttresses meaning<\/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;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;what is a buttress&quot;}\">what is a buttress<\/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;EN&quot;}\">EN<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;buttress define&quot;}\">buttress define<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:590}\">590<\/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;definition of buttress&quot;}\">definition of buttress<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:590}\">590<\/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;what are buttresses&quot;}\">what are buttresses<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:480}\">480<\/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;buttress architecture&quot;}\">buttress architecture<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:390}\">390<\/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;architecture buttress&quot;}\">architecture buttress<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:260}\">260<\/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;what does buttress mean&quot;}\">what does buttress mean<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:260}\">260<\/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;define buttresses&quot;}\">define buttresses<\/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;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;contrefort&quot;}\">contrefort<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1600}\">1600<\/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;contrefort d\u00e9finition&quot;}\">contrefort d\u00e9finition<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:90}\">90<\/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;contrefort mur&quot;}\">contrefort mur<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:90}\">90<\/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;contrefort definition&quot;}\">contrefort definition<\/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;FR&quot;}\">FR<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;contrefort synonyme&quot;}\">contrefort synonyme<\/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;contraforte&quot;}\">contraforte<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1000}\">1000<\/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;contrafortes&quot;}\">contrafortes<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:320}\">320<\/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;contraforte arquitetura&quot;}\">contraforte arquitetura<\/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;PTB&quot;}\">PTB<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;contrafort&quot;}\">contrafort<\/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;muro com contraforte&quot;}\">muro com contraforte<\/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;muro contraforte&quot;}\">muro contraforte<\/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;o que \u00e9 contraforte&quot;}\">o que \u00e9 contraforte<\/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;contrafuerte&quot;}\">contrafuerte<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1900}\">1900<\/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;contrafuertes&quot;}\">contrafuertes<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:1600}\">1600<\/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;contrafuertes y arbotantes&quot;}\">contrafuertes y arbotantes<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:260}\">260<\/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;contrafuerte arquitectura&quot;}\">contrafuerte arquitectura<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:3,&quot;3&quot;:210}\">210<\/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;contrafuerte de un muro&quot;}\">contrafuerte de un muro<\/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;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;que es un contrafuerte&quot;}\">que es un contrafuerte<\/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;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;contrafuertes arquitectura&quot;}\">contrafuertes arquitectura<\/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;definicion de contrafuerte&quot;}\">definicion de contrafuerte<\/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;ES&quot;}\">ES<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;contrafuerte definicion&quot;}\">contrafuerte definicion<\/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;que son los contrafuertes&quot;}\">que son los contrafuertes<\/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;DE&quot;}\">DE<\/td>\r\n<td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;strebepfeiler&quot;}\">strebepfeiler<\/td>\r\n<td 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