{"id":1396,"date":"2024-09-23T14:58:52","date_gmt":"2024-09-23T12:58:52","guid":{"rendered":"https:\/\/solveredu.com\/?p=1396"},"modified":"2026-01-27T23:39:20","modified_gmt":"2026-01-27T22:39:20","slug":"teorema-de-steiner","status":"publish","type":"post","link":"https:\/\/solveredu.com\/es\/post\/twierdzenie-steinera\/","title":{"rendered":"Teorema de Steiner"},"content":{"rendered":"<p class=\"wp-block-paragraph\" id=\"foo\">En este art\u00edculo aprender\u00e1s qu\u00e9 es el Teorema de Steiner y c\u00f3mo aplicarlo en la pr\u00e1ctica.<\/p>\n\n\n\n<ol id=\"91wpyzoaaa5swa1375982\" class=\"wp-block-list\">\n<li><a href=\"#1qctj\">Teorema de Steiner - definici\u00f3n<\/a><\/li>\n\n\n\n<li><a href=\"#fehhb35357\">Teorema de Steiner - ejemplo de aplicaci\u00f3n<\/a><\/li>\n<\/ol>\n\n\n\n<h1 id=\"1qctj\" class=\"wp-block-heading has-large-font-size\">Teorema de Steiner - definici\u00f3n<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>El teorema de Steiner permite calcular el momento de inercia de una figura plana con respecto a un eje paralelo a un eje central dado, es decir, que pasa por el centro de gravedad de la figura.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"547\" data-attachment-id=\"1400\" data-permalink=\"https:\/\/solveredu.com\/es\/post\/twierdzenie-steinera\/steiner3-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?fit=1088%2C581&amp;ssl=1\" data-orig-size=\"1088,581\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Steiner3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?fit=1024%2C547&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?resize=1024%2C547&#038;ssl=1\" alt=\"Teorema de Stainer, SolverEdu\" class=\"wp-image-1400\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?resize=1024%2C547&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?resize=300%2C160&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?resize=768%2C410&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3-1.jpg?w=1088&amp;ssl=1 1088w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"xjpzr30153\">Como se ilustra m\u00e1s arriba, <strong>Teorema de Steiner<\/strong> nos permite calcular el momento de inercia alrededor de cualquier eje paralelo alejado del eje central de nuestra figura. Conocemos el valor del momento respecto al eje central si le sumamos el \u00e1rea de la figura \"A\" multiplicada por la distancia del eje al cuadrado.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"b0q6f33254\">El momento de desviaci\u00f3n seg\u00fan el Teorema de Steiner se calcula sumando el producto del \u00e1rea y la distancia de los ejes \"a\" y \"b\" al valor del momento de desviaci\u00f3n de la figura respecto a los ejes centrales.<\/p>\n\n\n\n<h2 id=\"fehhb35357\" class=\"wp-block-heading has-medium-font-size\">Teorema de Steiner - ejemplo de aplicaci\u00f3n<\/h2>\n\n\n\n<figure style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\" class=\"wp-block-table\"><table class=\"has-theme-5-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#ffffff\"><tbody><tr><td>Puedes encontrar m\u00e1s ejemplos de uso y c\u00e1lculo de momentos de carga utilizando el Teorema de Steiner en mi calculadora <a href=\"https:\/\/solveredu.com\/es\/calculadora-momento-de-inercia\/\" target=\"_blank\" rel=\"noreferrer noopener\"><u>Momento de inercia<\/u><\/a>. No dude en utilizar<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"du0jt36071\">Como ejemplo de aplicaci\u00f3n del Teorema de Steiner, analicemos el rect\u00e1ngulo de lados b1 y h1 que se muestra en la figura siguiente. Las f\u00f3rmulas de los momentos de orden de figuras sencillas como un rect\u00e1ngulo se pueden encontrar en <a href=\"https:\/\/solveredu.com\/es\/post\/momentos-de-inercia-de-figuras-planas\/\">entrada<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"553\" height=\"585\" data-attachment-id=\"1401\" data-permalink=\"https:\/\/solveredu.com\/es\/post\/twierdzenie-steinera\/steiner4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner4.jpg?fit=553%2C585&amp;ssl=1\" data-orig-size=\"553,585\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Steiner4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner4.jpg?fit=553%2C585&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner4.jpg?resize=553%2C585&#038;ssl=1\" alt=\"C\u00e1lculo del momento de inercia para los ejes x e y utilizando el teorema de Steiner - soluci\u00f3n de ejemplo, SolverEdu\" class=\"wp-image-1401\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner4.jpg?w=553&amp;ssl=1 553w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner4.jpg?resize=284%2C300&amp;ssl=1 284w\" sizes=\"auto, (max-width: 553px) 100vw, 553px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"343\" data-attachment-id=\"1402\" data-permalink=\"https:\/\/solveredu.com\/es\/post\/twierdzenie-steinera\/steiner5\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?fit=1118%2C375&amp;ssl=1\" data-orig-size=\"1118,375\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Steiner5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?fit=1024%2C343&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?resize=1024%2C343&#038;ssl=1\" alt=\"centro de gravedad del rect\u00e1ngulo, SolverEdu\" class=\"wp-image-1402\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?resize=1024%2C343&amp;ssl=1 1024w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?resize=300%2C101&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?resize=768%2C258&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner5.jpg?w=1118&amp;ssl=1 1118w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>","protected":false},"excerpt":{"rendered":"<p>W tym artykule dowiesz si\u0119 co to jest Twierdzenie Steinera oraz jak je zastosowa\u0107 w praktyce. Twierdzenie Steinera &#8211; definicja Twierdzenie Steinera umo\u017cliwia wyliczenie momentu bezw\u0142adno\u015bci p\u0142askiej figury wzgl\u0119dem osi, kt\u00f3ra jest r\u00f3wnoleg\u0142a do danej osi centralnej, czyli przechodz\u0105cej przez \u015brodek ci\u0119\u017cko\u015bci figury. Zgodnie z rysunkiem powy\u017cej, Twierdzenie Steinera pozwala nam obliczy\u0107 moment bezw\u0142adno\u015bci wzgl\u0119dem [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1398,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[14815],"tags":[14867,14853,14866,14852],"class_list":["post-1396","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-moment-bezwladnosci","tag-moment-statyczny","tag-twierdzenie-stainera","tag-srodek-ciezkosci"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/Steiner3.jpg?fit=1088%2C581&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-mw","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/posts\/1396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/comments?post=1396"}],"version-history":[{"count":8,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/posts\/1396\/revisions"}],"predecessor-version":[{"id":3069,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/posts\/1396\/revisions\/3069"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/media\/1398"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/media?parent=1396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/categories?post=1396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/es\/wp-json\/wp\/v2\/tags?post=1396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}