{"id":9209,"date":"2026-03-04T10:11:09","date_gmt":"2026-03-04T08:11:09","guid":{"rendered":"https:\/\/info.formfedern.com\/calculer-le-moment-dinertie-de-la-surface\/"},"modified":"2026-03-04T16:36:22","modified_gmt":"2026-03-04T14:36:22","slug":"calculer-le-moment-dinertie-de-la-surface","status":"publish","type":"post","link":"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/","title":{"rendered":"Calculer le moment d&rsquo;inertie de la surface"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-765\" src=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/\/Federklammer_2-300x196.jpg\" alt=\"Pi\u00e8ce estamp\u00e9e et pli\u00e9e comme un ressort fa\u00e7onn\u00e9 de Gutekunst\" width=\"401\" height=\"261\" data-wp-pid=\"765\" srcset=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/Federklammer_2-300x196.jpg 300w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Federklammer_2-200x130.jpg 200w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Federklammer_2.jpg 600w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Federklammer_2-307x200.jpg 307w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/>Lors de la conception de <a href=\"https:\/\/info.formfedern.com\/fr\/ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">ressorts plats<\/a>, de ressorts <a href=\"https:\/\/info.formfedern.com\/fr\/ressorts-de-forme-individuelle-et-ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">de forme<\/a> et <a href=\"https:\/\/info.formfedern.com\/flachformfeder_auslegen\/\" target=\"_blank\" rel=\"noopener noreferrer\">de ressorts de forme plats<\/a>, on calcule souvent, en plus de la <a href=\"https:\/\/info.formfedern.com\/biegespannung-berechnen\/\" target=\"_blank\" rel=\"noopener noreferrer\">contrainte de flexion<\/a>, le moment d&rsquo;inertie de la surface. Le moment d&rsquo;inertie de surface est une grandeur g\u00e9om\u00e9trique utilis\u00e9e dans la th\u00e9orie de la r\u00e9sistance. Elle est utilis\u00e9e pour calculer les d\u00e9formations et les contraintes en cas de flexion et de torsion des ressorts et <a href=\"https:\/\/info.formfedern.com\/stanzteile-kleinserien\/\" target=\"_blank\" rel=\"noopener noreferrer\">des pi\u00e8ces m\u00e9talliques moul\u00e9es<\/a>. Le moment d&rsquo;inertie de surface est d\u00e9duit de la section transversale des pi\u00e8ces m\u00e9talliques moul\u00e9es. Le moment d&rsquo;inertie de la surface est exprim\u00e9 en <sup>mm4<\/sup>. En fonction de la charge, on peut distinguer deux types diff\u00e9rents de moment d&rsquo;inertie de surface.<del><\/del><\/p>\n<p>Les graphiques suivants repr\u00e9sentent les sections sym\u00e9triques et asym\u00e9triques d&rsquo;un <a href=\"https:\/\/info.formfedern.com\/fr\/formez-des-ressorts-des-ressorts-a-lames-et-des-ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">ressort plat<\/a>, d&rsquo;un ressort de <a href=\"https:\/\/info.formfedern.com\/fr\/formez-des-ressorts-des-ressorts-a-lames-et-des-ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">forme<\/a> ou <a href=\"https:\/\/info.formfedern.com\/flachformfeder-berechnung\/\" target=\"_blank\" rel=\"noopener noreferrer\">d&rsquo;un ressort de forme plat<\/a> soumis \u00e0 diff\u00e9rentes charges. Les illustrations montrent un ressort plat encastr\u00e9 d&rsquo;un c\u00f4t\u00e9<strong>(1<\/strong> et <strong>2<\/strong>) ainsi que la sollicitation en flexion d&rsquo;un ressort de forme ou d&rsquo;une pi\u00e8ce m\u00e9tallique moul\u00e9e<strong>(3<\/strong>).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3592 size-medium\" src=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/\/Flaechentraegheit_Axial_1-300x115.jpg\" alt=\"Moment d'inertie de la surface axiale\" width=\"300\" height=\"115\" data-wp-pid=\"3592\" srcset=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-300x115.jpg 300w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-768x294.jpg 768w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-1024x392.jpg 1024w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-600x230.jpg 600w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-150x57.jpg 150w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-522x200.jpg 522w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1-200x77.jpg 200w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_1.jpg 1287w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3593 size-medium\" src=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/\/Flaechentraegheit_Axial_2-300x101.jpg\" alt=\"Moment d'inertie de la surface axiale\" width=\"300\" height=\"101\" data-wp-pid=\"3593\" srcset=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-300x101.jpg 300w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-768x258.jpg 768w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-1024x344.jpg 1024w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-600x201.jpg 600w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-150x50.jpg 150w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-596x200.jpg 596w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2-200x67.jpg 200w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Axial_2.jpg 1287w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3594 size-medium\" src=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/\/Flaechentraegheit_Torsion-300x99.jpg\" alt=\"Moment d'inertie \u00e0 plat Torsion\" width=\"300\" height=\"99\" data-wp-pid=\"3594\" srcset=\"https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-300x99.jpg 300w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-768x254.jpg 768w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-1024x338.jpg 1024w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-600x198.jpg 600w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-150x50.jpg 150w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-606x200.jpg 606w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-200x66.jpg 200w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion-800x264.jpg 800w, https:\/\/info.formfedern.com\/wp-content\/uploads\/Flaechentraegheit_Torsion.jpg 1093w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/#Moment_dinertie_axial_de_la_surface\" >Moment d&rsquo;inertie axial de la surface<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/#Moment_dinertie_de_surface_biaxial\" >Moment d&rsquo;inertie de surface biaxial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/#Grandeurs_derivees\" >Grandeurs d\u00e9riv\u00e9es<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/#Couple_de_resistance\" >Couple de r\u00e9sistance<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/info.formfedern.com\/fr\/calculer-le-moment-dinertie-de-la-surface\/#Rayon_dinertie_de_la_surface\" >Rayon d&rsquo;inertie de la surface<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Moment_dinertie_axial_de_la_surface\"><\/span>Moment d&rsquo;inertie axial de la surface<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Le moment d&rsquo;inertie axial de surface <em>Ia<\/em> d\u00e9crit la relation entre la section transversale du ressort plat et la courbure d&rsquo;un ressort plat sous charge. La r\u00e8gle est la suivante : plus <em>Ia<\/em> est grand, plus la courbure et les <a href=\"https:\/\/info.formfedern.com\/biegespannung-berechnen\/\" target=\"_blank\" rel=\"noopener noreferrer\">tensions<\/a> internes g\u00e9n\u00e9r\u00e9es dans la section sont faibles. L&rsquo;essentiel est ici la dilatation dans la direction de la force d&rsquo;attaque. Le graphique illustre le fait qu&rsquo;une force verticale d\u00e9forme moins un ressort plat lorsque celui-ci est serr\u00e9 de chant plut\u00f4t qu&rsquo;\u00e0 plat<strong>(1<\/strong> et <strong>2<\/strong>). Le syst\u00e8me axial<\/p>\n<p>Le moment d&rsquo;inertie de la surface est calcul\u00e9 \u00e0 l&rsquo;aide des formules suivantes :<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large Iy=\\int_{} z^{2} dA<\/span>\n<ul>\n<li>z = distance perpendiculaire de l&rsquo;axe y \u00e0 l&rsquo;\u00e9l\u00e9ment dA<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large Iz=\\int_{} y^{2} dA<\/span>\n<ul>\n<li>y = distance perpendiculaire de l&rsquo;axe z \u00e0 l&rsquo;\u00e9l\u00e9ment dA<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Moment_dinertie_de_surface_biaxial\"><\/span>Moment d&rsquo;inertie de surface biaxial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Le moment d&rsquo;inertie biaxial de surface <em>Iyz<\/em> est \u00e9galement appel\u00e9 moment de d\u00e9formation de surface ou moment centrifuge de surface. <em>Iyz<\/em> est utilis\u00e9 pour <a href=\"https:\/\/info.formfedern.com\/flachformfeder-berechnung\/\" target=\"_blank\" rel=\"noopener noreferrer\">calculer<\/a> la <a href=\"https:\/\/info.formfedern.com\/biegeverfahren-metallumformung\/\" target=\"_blank\" rel=\"noopener noreferrer\">d\u00e9formation<\/a> et les contraintes des ressorts de forme charg\u00e9s, des ressorts de forme plats et des pi\u00e8ces m\u00e9talliques moul\u00e9es asym\u00e9triques<strong>(3<\/strong>).<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large Iyz=Izy=\\int_{} yz dA <\/span>\n<p>Cette grandeur est \u00e9galement connue sous le nom de moment de d\u00e9viation ou de moment centrifuge. Elle est \u00e9gale \u00e0 z\u00e9ro si l&rsquo;axe y ou l&rsquo;axe z est un axe de sym\u00e9trie de la section.<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large Iyz = 0 <\/span>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Grandeurs_derivees\"><\/span>Grandeurs d\u00e9riv\u00e9es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Plusieurs autres grandeurs peuvent \u00eatre d\u00e9duites du moment d&rsquo;inertie de la surface, comme le moment de r\u00e9sistance et le rayon d&rsquo;inertie de la surface.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Couple_de_resistance\"><\/span>Couple de r\u00e9sistance<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Le moment de r\u00e9sistance est utilis\u00e9 dans la th\u00e9orie de l&rsquo;\u00e9lasticit\u00e9 lin\u00e9aire. On d\u00e9termine ainsi la contrainte la plus importante apparaissant au bord de la section, la contrainte m\u00e9canique. Il s&rsquo;agit du quotient du moment d&rsquo;inertie de la surface par la distance entre le bord et la fibre neutre :<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large W:=\\frac{I}{\\alpha max}<\/span>\n<p>&nbsp;<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Rayon_dinertie_de_la_surface\"><\/span>Rayon d&rsquo;inertie de la surface<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Pour les \u00e9l\u00e9ments de construction g\u00e9om\u00e9triquement similaires, tels que les rectangles ayant le m\u00eame rapport largeur\/hauteur, il est \u00e9galement possible de d\u00e9finir le rayon d&rsquo;inertie de la surface avec la dimension longueur. On peut ainsi comparer des corps dont la flexion et la rigidit\u00e9 sont similaires. Le rayon d&rsquo;inertie de la surface est inclus dans l&rsquo;\u00e9lancement.<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large iy:=\\sqrt{frac{Iy}{A}}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large iz:=\\sqrt{frac{Iz}{A}}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large ip:=\\sqrt{frac{Ip}{A}}<\/span>\n<p>&nbsp;<\/p>\n<p>Consultez ici plus d&rsquo;informations sur le <a href=\"https:\/\/info.formfedern.com\/flachformfeder-berechnung\/\" target=\"_blank\" rel=\"noopener noreferrer\">calcul<\/a> des <a href=\"https:\/\/info.formfedern.com\/fr\/ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">ressorts plats<\/a>, des ressorts <a href=\"https:\/\/info.formfedern.com\/fr\/ressorts-de-forme-individuelle-et-ressorts-plats\/\" target=\"_blank\" rel=\"noopener noreferrer\">de forme<\/a> et <a href=\"https:\/\/info.formfedern.com\/flachformfeder_auslegen\/\" target=\"_blank\" rel=\"noopener noreferrer\">des ressorts de forme plats<\/a>. Si vous recherchez un ressort technique pour votre application sp\u00e9cifique, il vous suffit de nous envoyer les donn\u00e9es du ressort souhait\u00e9 en cliquant sur le bouton de demande suivant \u00ab\u00a0<a href=\"https:\/\/info.formfedern.com\/fr\/demande-de-ressorts\/\" target=\"_blank\" rel=\"noopener noreferrer\">Demande de ressort<\/a>\u00a0\u00bb ou par e-mail <a href=\"mailto:info@gutekunst-formfedern.de\">info@gutekunst-formfedern.de<\/a> en indiquant la quantit\u00e9 n\u00e9cessaire et le dessin ou les donn\u00e9es CAO. Nous vous ferons une offre sans engagement dans un bref d\u00e9lai.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left;\"><a class=\"maxbutton-7 maxbutton maxbutton-federnanfrage\" target=\"_blank\" rel=\"noopener\" href=\"\/federnanfrage\/\"><span class='mb-text'>Federnanfrage<\/span><\/a><\/p>\n<p>&nbsp;<\/p>\n<p><em>Information additionnelle:<\/em><\/p>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/fr\/formez-des-ressorts-des-ressorts-a-lames-et-des-ressorts-plats\/\">Forme des ressorts, des ressorts plats et des ressorts \u00e0 lames<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/fr\/diagramme-contrainte-deformation-acier-a-ressorts\/\" target=\"_blank\" rel=\"noopener noreferrer\">Diagramme contrainte-d\u00e9formation acier \u00e0 ressorts<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/flachformfeder-berechnung\/\">Calcul du ressort de forme plate<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/flachformfeder_auslegen\/\">Disposez un ressort plat<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/fr\/rayon-de-courbure-dans-le-formage-des-metaux\/\" target=\"_blank\" rel=\"noopener noreferrer\">Rayon de courbure dans le formage des m\u00e9taux<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/info.formfedern.com\/fr\/important-lors-du-formage-de-toles-dacier-a-ressorts\/\" target=\"_blank\" rel=\"noopener noreferrer\">Important lors du formage de t\u00f4les d&rsquo;acier \u00e0 ressorts<\/a><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Lors de la conception de ressorts plats, de ressorts de forme et de ressorts de forme plats, on calcule souvent, en plus de la contrainte de flexion, le moment d&rsquo;inertie de la surface. Le moment d&rsquo;inertie de surface est une<\/p>\n","protected":false},"author":6,"featured_media":9213,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[718,725],"tags":[2965,2966,2964,2968,2962,2963,854,852,857,853,2967],"class_list":["post-9209","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-connaissance","category-ressorts-a-lames","tag-calcul-de-la-deformation","tag-calcul-des-contraintes","tag-charge","tag-contrainte-de-torsion","tag-couple-de-resistance","tag-moment-dinertie-de-la-surface","tag-ressorts-a-lames","tag-ressorts-de-forme","tag-ressorts-de-forme-fr","tag-ressorts-plats","tag-sollicitation-a-la-flexion"],"_links":{"self":[{"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/posts\/9209","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/comments?post=9209"}],"version-history":[{"count":6,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/posts\/9209\/revisions"}],"predecessor-version":[{"id":12096,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/posts\/9209\/revisions\/12096"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/media\/9213"}],"wp:attachment":[{"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/media?parent=9209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/categories?post=9209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/info.formfedern.com\/fr\/wp-json\/wp\/v2\/tags?post=9209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}