{"id":5697,"date":"2026-10-14T10:08:02","date_gmt":"2026-10-14T07:08:02","guid":{"rendered":"https:\/\/wpcalc.com\/fr\/ingenierie\/module-de-flexion\/"},"modified":"2026-10-14T10:08:02","modified_gmt":"2026-10-14T07:08:02","slug":"module-de-flexion","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/fr\/ingenierie\/module-de-flexion\/","title":{"rendered":"Module de flexion d'une section de poutre"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Calculer les caract\u00e9ristiques de section pour la flexion d&#039;une poutre<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"5697\" data-favorite-title=\"Module de flexion\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/ingenierie\/module-de-flexion\/\" data-favorite-excerpt=\"Calculez le module de flexion \u00e9lastique et le moment quadratique d&#039;une section rectangulaire, circulaire, tubulaire ou en I\/H. Saisissez les dimensions, choisissez une forme et obtenez les caract\u00e9ristiques par rapport \u00e0 l&#039;axe fort de flexion.\" aria-label=\"Ajouter aux favoris\" data-favorite-icon=\"icon icon-civil\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/fr\/ingenierie\/module-de-flexion\/\" method=\"POST\" class=\"calculator\" id=\"calculator-5697\" data-post=\"5697\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Forme de la section<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"forme_de_la_section\"><option value=\"rect\" selected>Rectangle<\/option><option value=\"circle\">Cercle plein<\/option><option value=\"tube\">Tube circulaire creux<\/option><option value=\"isec\">Profil\u00e9 en I \/ H<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Largeur (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"largeur_b\" id=\"field-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-4\">Hauteur (h)<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"hauteur_h\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"200\" min=\"0.01\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-4\">Hauteur mesur\u00e9e parall\u00e8lement \u00e0 l&#039;axe de flexion<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Diam\u00e8tre (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"diamtre_d\" id=\"field-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"50\" min=\"0.01\" value=\"50\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-8\">Diam\u00e8tre ext\u00e9rieur (D)<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"diamtre_extrieur_d\" id=\"field-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-10\">Diam\u00e8tre int\u00e9rieur (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"diamtre_intrieur_d\" id=\"field-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"80\" min=\"0.01\" value=\"80\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-12\">Hauteur totale (h)<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"hauteur_totale_h\" id=\"field-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"200\" min=\"0.01\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-13\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-14\">Largeur de semelle (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"largeur_de_semelle_b\" id=\"field-14\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"100\" min=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-15\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-16\">\u00c9paisseur de semelle (tf)<\/label><div class=\"term\">tf<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"paisseur_de_semelle_tf\" id=\"field-16\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0.01\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-17\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><div class=\"field has-term\" id=\"input-10\" hidden><label for=\"field-18\">\u00c9paisseur d&#039;\u00e2me (tw)<\/label><div class=\"term\">tw<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"paisseur_dme_tw\" id=\"field-18\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"0.01\" value=\"6\"\/><div class=\"grid grid-cols-1\"><select id=\"field-19\" name=\"unit\" aria-label=\"Unit\u00e9\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"5697\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Caract\u00e9ristiques de la section<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Moment quadratique<\/span><span class=\"result-term\">Ixx<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Module de flexion \u00e9lastique<\/span><span class=\"result-term\">Sxx<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Formule et remarques<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copier le lien vers ce calcul<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Laisser un commentaire<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"5697\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">J\u2019aime <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Utile <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confus <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">D\u00e9\u00e7u <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inexact <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Module de flexion<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formule<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ S_{xx} = \\frac{I_{xx}}{c} \\qquad \\sigma_{max} = \\frac{M}{S_{xx}} \\\\\\ I_{xx} = \\frac{b h^{3}}{12} \\ \\text{(rectangle)} \\qquad I_{xx} = \\frac{\\pi d^{4}}{64} \\ \\text{(cercle plein)} \\\\\\ I_{xx} = \\frac{\\pi \\left(D^{4} - d^{4}\\right)}{64} \\ \\text{(tube creux)} \\qquad I_{xx} = \\frac{b h^{3} - \\left(b - t_{w}\\right)\\left(h - 2 t_{f}\\right)^{3}}{12} \\ \\text{(profil\u00e9 I \/ H)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>O\u00f9\\u00a0:<\/strong><\/p>\n<ul>\n<li>\\(S_{xx}\\) \u2014 module de flexion \u00e9lastique par rapport \u00e0 l'axe horizontal passant par le centre de gravit\u00e9 (axe x\u2013x) (mm\u00b3 ou in\u00b3)<\/li>\n<li>\\(I_{xx}\\) \u2014 moment quadratique par rapport au m\u00eame axe (mm\u2074 ou in\u2074)<\/li>\n<li>\\(c\\) \u2014 distance de l'axe neutre \u00e0 la fibre extr\u00eame\\u00a0: \\(c = h\/2\\) ou \\(c = D\/2\\)<\/li>\n<li>\\(b\\) \u2014 largeur (ou largeur d'aile pour un profil\u00e9 en I)<\/li>\n<li>\\(h\\) \u2014 hauteur totale de la section<\/li>\n<li>\\(d\\) \u2014 diam\u00e8tre (cercle plein) ou diam\u00e8tre int\u00e9rieur (tube)<\/li>\n<li>\\(D\\) \u2014 diam\u00e8tre ext\u00e9rieur d'un tube<\/li>\n<li>\\(t_{f},\\ t_{w}\\) \u2014 \u00e9paisseurs d'aile et d'\u00e2me d'un profil\u00e9 I \/ H<\/li>\n<li>\\(M\\) \u2014 moment fl\u00e9chissant appliqu\u00e9\\u00a0; \\(\\sigma_{max}\\) \u2014 contrainte maximale de flexion<\/li>\n<\/ul>\n<p>Le module de flexion traduit l'efficacit\u00e9 avec laquelle une section r\u00e9siste \u00e0 la flexion\\u00a0: plus \\(S_{xx}\\) est grand, plus la contrainte de flexion produite par un moment donn\u00e9 est faible.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Module de flexion \u2013 Exemple de calcul<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemple\\u00a0:<\/strong> une poutre en bois de section rectangulaire, large de 100 mm et haute de 200 mm, charg\u00e9e de fa\u00e7on \u00e0 fl\u00e9chir autour de son axe fort.<\/p>\n<p>\\[ I_{xx} = \\frac{b h^{3}}{12} = \\frac{100 \\times 200^{3}}{12} = 66{,}666{,}667 \\ \\text{mm}^{4} \\approx 160.2 \\ \\text{in}^{4} \\]<\/p>\n<p>\\[ S_{xx} = \\frac{I_{xx}}{h\/2} = \\frac{66{,}666{,}667}{100} = 666{,}667 \\ \\text{mm}^{3} \\approx 40.68 \\ \\text{in}^{3} \\]<\/p>\n<p><strong>R\u00e9sultat\\u00a0:<\/strong> \\(I_{xx} \\approx 6{,}67 \\times 10^{7}\\) mm\u2074 et \\(S_{xx} \\approx 6{,}67 \\times 10^{5}\\) mm\u00b3 (40,68 in\u00b3). Un moment fl\u00e9chissant de 10 kN\u00b7m produirait donc une contrainte maximale de \\(\\sigma = 10^{7} \/ 666{,}667 \\approx 15.0\\) N\/mm\u00b2 (MPa), soit 15,0 MPa.<\/p>\n<p>\n\r\n<\/section>\n<h2>Comment utiliser le calculateur<\/h2>\n<ol>\n<li>S\u00e9lectionnez la <strong>forme de la section<\/strong>\\u00a0: rectangle, cercle plein, tube circulaire creux ou profil\u00e9 I \/ H. Seuls les champs de dimensions utiles pour cette forme s'affichent.<\/li>\n<li>Saisissez les dimensions dans les champs visibles \u2014 par exemple <strong>Largeur (b)<\/strong> et <strong>Hauteur (h)<\/strong> pour un rectangle, ou <strong>Diam\u00e8tre ext\u00e9rieur (D)<\/strong> et <strong>Diam\u00e8tre int\u00e9rieur (d)<\/strong> pour un tube.<\/li>\n<li>Choisissez l'unit\u00e9 (mm, cm, m ou in) de chaque dimension. Les r\u00e9sultats suivent le syst\u00e8me d'unit\u00e9s de votre saisie, avec une conversion vers l'autre syst\u00e8me affich\u00e9e entre crochets.<\/li>\n<li>Lisez le <strong>moment quadratique<\/strong> et le <strong>module de flexion \u00e9lastique<\/strong> dans le panneau de r\u00e9sultats, accompagn\u00e9s de la formule exacte utilis\u00e9e pour votre forme.<\/li>\n<\/ol>\n<h2>Qu'est-ce que le module de flexion\\u00a0?<\/h2>\n<p>Lorsqu'une poutre fl\u00e9chit, la mati\u00e8re la plus \u00e9loign\u00e9e de l'axe neutre est la plus sollicit\u00e9e, tandis que celle qui se trouve au niveau de l'axe neutre ne supporte presque aucune contrainte de flexion. Le <strong>module de flexion \u00e9lastique<\/strong> \\(S\\) traduit la quantit\u00e9 de mati\u00e8re \u00ab\\u00a0utile\\u00a0\u00bb qu'une section place loin de cet axe. Il est d\u00e9fini comme le moment quadratique divis\u00e9 par la distance \u00e0 la fibre extr\u00eame, \\(S = I\/c\\), et relie le moment fl\u00e9chissant \u00e0 la contrainte par la formule de flexion \\(\\sigma = M\/S\\).<\/p>\n<p>La cons\u00e9quence pratique est simple\\u00a0: \u00e0 moment appliqu\u00e9 \u00e9gal, un module de flexion plus grand signifie une contrainte maximale de flexion plus faible. C'est pourquoi les poutres en I et les profil\u00e9s H sont si r\u00e9pandus\\u00a0: en concentrant la mati\u00e8re dans les ailes, loin de l'axe neutre, ils atteignent un \\(S\\) \u00e9lev\u00e9 avec relativement peu de mati\u00e8re. Doubler la hauteur d'une poutre rectangulaire, par exemple, multiplie son module de flexion par environ quatre.<\/p>\n<p>Toutes les propri\u00e9t\u00e9s sont ici calcul\u00e9es par rapport \u00e0 l'<strong>axe fort x\u2013x<\/strong> (l'axe horizontal passant par le centre de gravit\u00e9), qui correspond \u00e0 l'orientation habituelle des poutres dans les planchers et les toitures. Une section peut aussi \u00eatre sollicit\u00e9e autour de son axe faible y\u2013y\\u00a0; dans ce cas, le module de flexion est nettement plus petit \u2014 pour un rectangle, \\(S_{yy} = h b^{2}\/6\\).<\/p>\n<p>Pour transformer ce r\u00e9sultat en v\u00e9rification de dimensionnement, combinez-le avec le moment fl\u00e9chissant de votre cas de charge. Si vous connaissez la charge appliqu\u00e9e \u00e0 la poutre, nos calculateurs de <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-uniform-load\/\">poutre sur deux appuis avec charge uniform\u00e9ment r\u00e9partie<\/a> ou de <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-center-point-load\/\">poutre sur deux appuis avec charge ponctuelle centrale<\/a> vous donneront le moment maximal\\u00a0; divisez-le par \\(S_{xx}\\) pour obtenir la contrainte maximale et comparez-la \u00e0 la contrainte admissible de votre mat\u00e9riau.<\/p>\n<h2>Hypoth\u00e8ses, limites et conseils pratiques<\/h2>\n<ul>\n<li><strong>Comportement \u00e9lastique uniquement.<\/strong> Les r\u00e9sultats supposent que le mat\u00e9riau reste en dessous de sa limite d'\u00e9lasticit\u00e9. Pour un calcul plastique, il faut utiliser le module de flexion plastique (sup\u00e9rieur au module \u00e9lastique).<\/li>\n<li><strong>Sections homog\u00e8nes et sym\u00e9triques.<\/strong> Les formules supposent un seul mat\u00e9riau et une forme \u00e0 double sym\u00e9trie, de sorte que l'axe neutre passe par le centre de gravit\u00e9. Les poutres composites (b\u00e9ton\u2013acier, par exemple) exigent une analyse en section homog\u00e9n\u00e9is\u00e9e.<\/li>\n<li><strong>Cong\u00e9s et d\u00e9tails n\u00e9glig\u00e9s.<\/strong> Les profil\u00e9s lamin\u00e9s r\u00e9els pr\u00e9sentent des cong\u00e9s \u00e0 la jonction \u00e2me-aile et des ailes \u00e0 \u00e9paisseur variable\\u00a0: les valeurs des catalogues diff\u00e8rent donc de quelques pour cent du calcul id\u00e9alis\u00e9.<\/li>\n<li><strong>L'orientation compte.<\/strong> Saisissez la hauteur mesur\u00e9e parall\u00e8lement \u00e0 la direction de flexion. Un rectangle de 100 \u00d7 200 pos\u00e9 \u00e0 plat (flexion autour de l'axe faible) n'offre que le quart du module de flexion de la m\u00eame section mise debout.<\/li>\n<li><strong>V\u00e9rification des tubes.<\/strong> Pour un tube creux, le diam\u00e8tre int\u00e9rieur doit \u00eatre inf\u00e9rieur au diam\u00e8tre ext\u00e9rieur\\u00a0; les parois tr\u00e8s minces peuvent par ailleurs \u00eatre r\u00e9gies par le voilement local plut\u00f4t que par la contrainte de flexion.<\/li>\n<li><strong>La flexion ne fait pas tout.<\/strong> Une poutre peut aussi rompre par cisaillement, fl\u00e8che excessive ou d\u00e9versement. Les \u00e9l\u00e9ments comprim\u00e9s \u00e9lanc\u00e9s doivent \u00e9galement \u00eatre v\u00e9rifi\u00e9s \u00e0 l'aide du <a href=\"https:\/\/wpcalc.com\/en\/engineering\/euler-buckling-load\/\">calculateur de charge critique d'Euler<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculez le module de flexion \u00e9lastique et le moment quadratique d'une section rectangulaire, circulaire, tubulaire ou en I\/H. Saisissez les dimensions, choisissez une forme et obtenez les caract\u00e9ristiques par rapport \u00e0 l'axe fort de flexion.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[82],"class_list":["post-5697","post","type-post","status-publish","format-standard","hentry","category-ingenierie","tag-poutres"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/5697","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/comments?post=5697"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/5697\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/media?parent=5697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/categories?post=5697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/tags?post=5697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}