{"id":991984,"date":"2022-09-22T14:28:09","date_gmt":"2022-09-22T12:28:09","guid":{"rendered":"https:\/\/dev.calter.doko.studio\/2022\/09\/22\/precision-del-calculo-de-flechas-cuando-el-momento-es-cercano-al-de-fisuracion\/"},"modified":"2026-06-16T10:40:08","modified_gmt":"2026-06-16T08:40:08","slug":"precision-del-calculo-de-flechas-cuando-el-momento-es-cercano-al-de-fisuracion","status":"publish","type":"post","link":"https:\/\/dev.calter.doko.studio\/en\/2022\/09\/22\/precision-del-calculo-de-flechas-cuando-el-momento-es-cercano-al-de-fisuracion\/","title":{"rendered":"Precisi\u00f3n del c\u00e1lculo de flechas cuando el momento es cercano al de fisuraci\u00f3n"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/sede_gamesa_calter-e1663831720241.jpg\" alt=\"sede_gamesa_calter\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hace un tiempo nos encontramos en una obra con un elemento estructural ornamental, muy repetido, donde se median unas flechas instant\u00e1neas mucho mayores (m\u00e1s del doble) de las que predice la vigente instrucci\u00f3n EHE-08.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ante la sorpresa de tales mediciones no soportadas por la formulaci\u00f3n normativa llegamos a las conclusiones que se exponen en la presente nota t\u00e9cnica y que esperamos puedan seros de utilidad.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong><\/strong><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\"><strong><\/strong><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Consideraciones previas<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><\/strong><strong>EHE-08: <\/strong>Las flechas instant\u00e1neas se calculan utilizando una inercia interpolada entre la bruta y la totalmente fisurada. Dicha interpolaci\u00f3n se realiza en funci\u00f3n de la relaci\u00f3n existente entre el momento de fisuraci\u00f3n de la pieza y el m\u00e1ximo momento actuante de la historia anterior de la pieza:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f1.png\" alt=\"f1\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Euroc\u00f3digo 2:<\/strong> M\u00e9todo general<br \/>Las flechas instant\u00e1neas se calculan utilizando una interpolaci\u00f3n similar pero, en este caso se interpolan no las inercias si no cualquier par\u00e1metro deformacional <span class=\"s1\">a <\/span>(enti\u00e9ndase I como bruto y II como fisurado):<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f2.png\" alt=\"f2\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para el c\u00e1lculo de flechas, es \u00fatil interpolar las curvaturas.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f3.png\" alt=\"f3\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Conocida la curvatura equivalente en cada secci\u00f3n, se puede proceder a realizar la integraci\u00f3n de las curvaturas para la obtenci\u00f3n de la flecha.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El par\u00e1metro <em>\u03b2 <\/em>que interpola es:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f4.png\" alt=\"f4\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">donde <em>\u03b2<\/em><span class=\"s1\">\u00a0<\/span>es el coeficiente que tiene en cuenta la duraci\u00f3n de la carga (1,0 para cargas de corta duraci\u00f3n y 0,50 para cargas de larga duraci\u00f3n o de muchos ciclos).<br \/><em>El cociente de momentos es pr\u00e1cticamente id\u00e9ntico al cociente de tensiones del acero en secci\u00f3n fisurada.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Euroc\u00f3digo 2:<\/strong> M\u00e9todo simplificado<br \/>Si no se dispone de una herramienta inform\u00e1tica (muy sencilla) para calcular la flecha mediante la integral de las curvaturas, el EC2 permite interpolar las flechas, es decir:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f5.png\" alt=\"f5\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Desarrollo<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><p class=\"p1\">Se desarrolla un ejemplo en el que se observa la gran diferencia de estos tres m\u00e9todos, sobre todo, cuando el momento actuante es muy cercano, aunque mayor, al momento de fisuraci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sea una placa biapoyada:<br \/>Luz=L=5.10 m<br \/>Ancho. B=1,00 m<br \/>Canto. C=0.14 m<br \/>Hormig\u00f3n HA-35<br \/>Armadura 5\u03c612 (en ambas caras)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se han calculado las flechas para diferentes valores de carga lineal sobre la viga q[kN\/m]. Los resultados pueden observarse en el gr\u00e1fico siguiente:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f6.png\" alt=\"f6\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se observar que los diferentes m\u00e9todos quedan entre los dos valores extremos Estado I y Estado II (Curvas (1) y (2)).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los valores de flecha obtenidos para momentos pr\u00f3ximos al de fisuraci\u00f3n son muy diferentes seg\u00fan la normativa que se utilice. A modo de ejemplo, para el valor de peso propio=3.5 kN\/m la EHE predice un valor de 5.60mm, (curva (3)), mientras que la de Euroc\u00f3digo 2 ,(curva (4)), estima este valor en 13.1 mm. (la diferencia de una a otra (7.50mm), porcentualmente es del orden de 130 %). O dicho de otro modo, la flecha seg\u00fan el euroc\u00f3digo es 2.3 veces la estimada seg\u00fan la EHE.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Con valores mayores de la carga, las predicciones de flecha son m\u00e1s parecidas. Para q=8 kN\/m, seg\u00fan la EHE la flecha es de 59 mm, mientras que el euroc\u00f3digo da un valor 68 mm (diferencia porcentual de 13 %).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Conclusi\u00f3n<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">La diferencia entre las f\u00f3rmulas de flecha del EC2 y de la EHE son muy significativas sobre todo para valores del momento cercano a la fisuraci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Esto puede ocurrir, por ejemplo, en elementos ornamentales en los que la carga pr\u00e1cticamente es la de peso propio y, por tanto, se proyectan elementos con muy poca armadura.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En este caso, las predicciones han sido contrastadas con mediciones y la medici\u00f3n que m\u00e1s se ajusta a la realidad es la del m\u00e9todo general del EC2.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ANEJO<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los datos num\u00e9ricos del gr\u00e1fico anterior se muestran a continuaci\u00f3n:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/odoo12.calter.es\/wp-content\/uploads\/2022\/09\/f7.png\" alt=\"f7\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Autor de la nota: Mart\u00edn Gamband\u00e9. Con la colaboraci\u00f3n de Carlos R\u00edos, Alberto Costaguta y Juan Carlos Arroyo.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hace un tiempo nos encontramos en una obra con un elemento estructural ornamental, muy repetido, donde se median unas flechas instant\u00e1neas mucho mayores (m\u00e1s del doble) de las que predice la vigente instrucci\u00f3n EHE-08. Ante la sorpresa de tales mediciones no soportadas por la formulaci\u00f3n normativa llegamos a las conclusiones que se exponen en la [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":991830,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[117,101,113],"tags":[],"class_list":["post-991984","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-news","category-technical-notes"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Precisi\u00f3n del c\u00e1lculo de flechas cuando el momento es cercano al de fisuraci\u00f3n | Calter Ingenier\u00eda<\/title>\n<meta name=\"description\" content=\"Nota t\u00e9cnica sobre la precisi\u00f3n del c\u00e1lculo de flechas cuando el momento es cercano al de fisuraci\u00f3n. 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