{"id":740,"date":"2024-08-31T11:08:52","date_gmt":"2024-08-31T14:08:52","guid":{"rendered":"https:\/\/www.zuloaga.online\/ignacio\/?p=740"},"modified":"2024-08-31T11:24:40","modified_gmt":"2024-08-31T14:24:40","slug":"impacto-de-las-dimensiones-de-la-zapata-en-la-capacidad-de-carga-analisis-con-la-formula-de-terzaghi","status":"publish","type":"post","link":"https:\/\/www.zuloaga.online\/ignacio\/impacto-de-las-dimensiones-de-la-zapata-en-la-capacidad-de-carga-analisis-con-la-formula-de-terzaghi\/","title":{"rendered":"Impacto de las Dimensiones de la Zapata en la Capacidad de Carga: An\u00e1lisis con la F\u00f3rmula de Terzaghi"},"content":{"rendered":"<hr \/>\n<p>La capacidad portante de las cimentaciones es un tema fundamental en la ingenier\u00eda civil, especialmente cuando se dise\u00f1an estructuras que deben soportar cargas pesadas. Una pregunta com\u00fan es: <strong>\u00bfc\u00f3mo afecta el tama\u00f1o de una zapata a su capacidad de carga y tensi\u00f3n admisible?<\/strong> En este art\u00edculo, exploraremos esta pregunta en detalle utilizando la f\u00f3rmula de Terzaghi, una herramienta cl\u00e1sica para calcular la capacidad portante de zapatas.<\/p>\n<h3><strong>Teor\u00eda de la Capacidad de Carga de Terzaghi<\/strong><\/h3>\n<p>La capacidad portante de una cimentaci\u00f3n est\u00e1 influenciada por varios factores, incluidos el tipo de suelo, la cohesi\u00f3n, el peso unitario del suelo, la profundidad de cimentaci\u00f3n, y las dimensiones de la zapata. La f\u00f3rmula de Terzaghi es una de las m\u00e1s utilizadas para calcular la capacidad portante \u00faltima (<span class=\"katex\"><span class=\"katex-mathml\">qultq_{ult}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\">lt<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) de una zapata. Para una zapata cuadrada, la f\u00f3rmula es:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-display\"><span class=\"katex\"><strong><span class=\"katex-mathml\">q<sub>ult<\/sub>=cN<sub>c<\/sub>+\u03b3D<sub>f<\/sub>N<sub>q<\/sub>+0.5\u03b3BN<sub>\u03b3<\/sub><\/span><\/strong><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>Donde:<\/strong><\/p>\n<ul>\n<li><span class=\"katex\"><span class=\"katex-mathml\">q<sub>ul<\/sub><\/span><sub><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\">t<span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/sub><\/span> = Capacidad de carga \u00faltima del suelo (kPa).<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">c<\/span><\/span> = Cohesi\u00f3n del suelo (kPa).<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">\u03b3<\/span><\/span> = Peso unitario del suelo (kN\/m\u00b3).<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">D<sub>f<\/sub><\/span><sub><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/sub><\/span> = Profundidad de cimentaci\u00f3n (m).<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">B<\/span><\/span> = Ancho de la zapata (m).<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">N<sub>c<\/sub>,N<sub>q<\/sub>,N<sub>\u03b3<\/sub><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = Factores de capacidad portante, que dependen del \u00e1ngulo de fricci\u00f3n (<span class=\"katex\"><span class=\"katex-mathml\">\u03d5<\/span><\/span>) del suelo.<\/li>\n<\/ul>\n<h3><strong>Ejemplo de C\u00e1lculo: Comparando Dos Zapatas<\/strong><\/h3>\n<p>Para ilustrar c\u00f3mo el tama\u00f1o de la zapata afecta su capacidad de carga y tensi\u00f3n admisible, consideremos dos zapatas cuadradas de diferentes tama\u00f1os sometidas a las mismas condiciones de suelo:<\/p>\n<p><strong>Supuestos:<\/strong><\/p>\n<ul>\n<li>Cohesi\u00f3n del suelo (<span class=\"katex\"><span class=\"katex-mathml\">c<\/span><\/span>) = 0 kPa (suelo arenoso).<\/li>\n<li>Peso unitario del suelo (<span class=\"katex\"><span class=\"katex-mathml\">\u03b3<\/span><\/span>) = 18 kN\/m\u00b3.<\/li>\n<li>Profundidad de cimentaci\u00f3n (<span class=\"katex\"><span class=\"katex-mathml\">D<sub>f<\/sub><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) = 1 m.<\/li>\n<li>\u00c1ngulo de fricci\u00f3n interna del suelo (<span class=\"katex\"><span class=\"katex-mathml\">\u03d5<\/span><\/span>) = 30\u00b0, con factores <span class=\"katex\"><span class=\"katex-mathml\">N<sub>c<\/sub>=30.14<\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">N<sub>q<\/sub>=18.4<\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">N<sub>\u03b3<\/sub>=15.1<br \/>\n<\/span><\/span><\/li>\n<li>Factor de seguridad (<span class=\"katex\"><span class=\"katex-mathml\">FS<\/span><\/span>) = 3.<\/li>\n<\/ul>\n<h4><strong>C\u00e1lculo de Capacidad de Carga \u00daltima y Tensi\u00f3n Admisible<\/strong><\/h4>\n<ol>\n<li><strong>Zapata de 2&#215;2 m:<\/strong>\n<ul>\n<li>Ancho (<span class=\"katex\"><span class=\"katex-mathml\">B<\/span><\/span>) = 2 m.<\/li>\n<li>\u00c1rea = <span class=\"katex\"><span class=\"katex-mathml\">4\u2009m<sup>2<\/sup>.<br \/>\n<\/span><\/span><\/li>\n<li>Capacidad de carga \u00faltima (<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">q<sub>ult<\/sub>)<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">q<sub>ult1<\/sub>=18\u00d71\u00d718.4+0.5\u00d718\u00d72\u00d715.1=331.2+271.8=603\u2009kPa<\/span><\/span><\/span><\/strong><\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><strong>Tensi\u00f3n admisible (<span class=\"katex\"><span class=\"katex-mathml\">q<sub>adm1<\/sub><\/span><\/span>) = <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">603\/3=201\u2009kPa<\/span><\/span><\/span><\/strong><\/li>\n<\/ul>\n<\/li>\n<li><strong>Zapata de 4&#215;4 m:<\/strong>\n<ul>\n<li>Ancho (<span class=\"katex\"><span class=\"katex-mathml\">B<\/span><\/span>) = 4 m.<\/li>\n<li>\u00c1rea = <span class=\"katex\"><span class=\"katex-mathml\">16\u2009m<sup>2<\/sup><\/span><\/span>.<\/li>\n<li style=\"text-align: left;\">Capacidad de carga \u00faltima<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">qult<sub>2<\/sub>=18\u00d71\u00d718.4+0.5\u00d718\u00d74\u00d715.1=331.2+543.6=874.8\u2009kPaq<\/span><\/span><\/span><\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><strong>Tensi\u00f3n admisible (<span class=\"katex\"><span class=\"katex-mathml\">qadm<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) = <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">874.8\/3=291.6\u2009kPa<\/span><\/span><\/span><\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><strong>Resultados Comparativos<\/strong><\/h3>\n<p>La tabla a continuaci\u00f3n resume los resultados obtenidos para ambas zapatas:<\/p>\n<table>\n<thead>\n<tr>\n<th><strong>Par\u00e1metro<\/strong><\/th>\n<th><strong>Zapata 2&#215;2 m<\/strong><\/th>\n<th><strong>Zapata 4&#215;4 m<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ancho (<span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span>)<\/td>\n<td style=\"text-align: center;\">2 m<\/td>\n<td style=\"text-align: center;\">4 m<\/td>\n<\/tr>\n<tr>\n<td>\u00c1rea (<span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span>)<\/td>\n<td style=\"text-align: center;\">4 m\u00b2<\/td>\n<td style=\"text-align: center;\">16 m\u00b2<\/td>\n<\/tr>\n<tr>\n<td>Capacidad de Carga \u00daltima (<span class=\"katex\"><span class=\"katex-mathml\">qultq_{ult}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\">lt<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<td style=\"text-align: center;\">603 kPa<\/td>\n<td style=\"text-align: center;\">874.8 kPa<\/td>\n<\/tr>\n<tr>\n<td>Tensi\u00f3n Admisible (<span class=\"katex\"><span class=\"katex-mathml\">qadmq_{adm}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<td style=\"text-align: center;\">201 kPa<\/td>\n<td style=\"text-align: center;\">291.6 kPa<\/td>\n<\/tr>\n<tr>\n<td>Factor de Seguridad (<span class=\"katex\"><span class=\"katex-mathml\">FSFS<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">FS<\/span><\/span><\/span><\/span>)<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><strong>Conclusi\u00f3n<\/strong><\/h3>\n<p>Este an\u00e1lisis muestra que al aumentar las dimensiones de una zapata, la capacidad de carga \u00faltima del suelo aumenta significativamente. Esto se debe principalmente al t\u00e9rmino <span class=\"katex\"><span class=\"katex-mathml\">0.5\u03b3BN<sub>\u03b3<\/sub><\/span><\/span>, que incrementa proporcionalmente con el ancho de la zapata. Como resultado, la tensi\u00f3n admisible tambi\u00e9n aumenta, lo que permite soportar mayores cargas con zapatas m\u00e1s grandes.<\/p>\n<p><strong>Implicaci\u00f3n pr\u00e1ctica<\/strong>: Al dise\u00f1ar cimentaciones, aumentar el tama\u00f1o de la zapata no solo mejora la distribuci\u00f3n de la carga, sino que tambi\u00e9n permite utilizar suelos con menor capacidad portante o aumentar la carga soportada sin comprometer la seguridad estructural.<\/p>\n<p>Espero que este art\u00edculo te ayude a comprender mejor c\u00f3mo el tama\u00f1o de una zapata afecta su capacidad de carga y tensi\u00f3n admisible. Si necesitas m\u00e1s informaci\u00f3n sobre este tema o deseas asesor\u00eda espec\u00edfica para tu proyecto, no dudes en <strong><a href=\"https:\/\/ayuda.zuloaga.online\/\" target=\"_blank\" rel=\"noopener\">contactarme.<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>La capacidad portante de las cimentaciones es un tema fundamental en la ingenier\u00eda civil, especialmente cuando se dise\u00f1an estructuras que deben soportar cargas pesadas. Una pregunta com\u00fan es: \u00bfc\u00f3mo afecta el tama\u00f1o de una zapata a su capacidad de carga y tensi\u00f3n admisible? En este art\u00edculo, exploraremos esta pregunta en detalle utilizando la f\u00f3rmula de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":746,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[48,13,7],"tags":[],"class_list":["post-740","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-analisis-geotecnico","category-cimentaciones","category-geotecnia"],"_links":{"self":[{"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/posts\/740","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/comments?post=740"}],"version-history":[{"count":5,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/posts\/740\/revisions"}],"predecessor-version":[{"id":745,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/posts\/740\/revisions\/745"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/media\/746"}],"wp:attachment":[{"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/media?parent=740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/categories?post=740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zuloaga.online\/ignacio\/wp-json\/wp\/v2\/tags?post=740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}