{"id":17334,"date":"2026-09-04T02:10:12","date_gmt":"2026-09-04T02:10:12","guid":{"rendered":"https:\/\/www.dgcrane.com\/?p=17334"},"modified":"2026-09-04T02:10:15","modified_gmt":"2026-09-04T02:10:15","slug":"jib-crane-cantilever-bending-moment-calculator","status":"publish","type":"post","link":"https:\/\/www.dgcrane.com\/fr\/jib-crane-cantilever-bending-moment-calculator\/","title":{"rendered":"Calculateur de moment de flexion en porte-\u00e0-faux pour grue \u00e0 fl\u00e8che"},"content":{"rendered":"<div id=\"calculator\">\n  <style>\n    #calculator {\n      --primary-color: #0a3487;\n      --primary-hover: #f58423;\n      --error-color: #e53935;\n      --bg-color: #eaEEF7;\n      --text-color: #4a4a4a;\n      max-width: 545px;\n      padding: 30px;\n      background: var(--bg-color);\n      color: var(--text-color);\n      box-sizing: border-box;\n      transition: all 0.2s ease;\n    }\n\n    #calculator .input-grid {\n      display: grid;\n      grid-template-columns: repeat(2, minmax(0, 1fr));\n      gap: 0 16px;\n    }\n\n    #calculator .calc-row {\n      margin-bottom: 18px;\n    }\n\n    #calculator label {\n      display: block;\n      font-size: 14px;\n      margin-bottom: 6px;\n    }\n\n    #calculator input {\n      width: 100%;\n      height: 36px;\n      font-size: 16px;\n      border: 1px solid #ccc;\n      border-radius: 0;\n      padding: 0 10px;\n      box-sizing: border-box;\n    }\n\n    #calculator input:focus {\n      border: 2px solid var(--primary-color);\n      outline: none;\n    }\n\n    #calculator input.error {\n      border: 2px solid var(--error-color);\n    }\n\n    #calculator .error-msg {\n      color: var(--error-color);\n      font-size: 12px;\n      margin-top: 4px;\n      display: none;\n    }\n\n    #calculator .btn-group {\n      display: flex;\n      gap: 12px;\n      margin-top: 24px;\n    }\n\n    #calculator button {\n      flex: 1;\n      height: 34px;\n      font-size: 14px;\n      border-radius: 0;\n      border: none;\n      cursor: pointer;\n    }\n\n    #calculator #calc-submit {\n      background: var(--primary-color);\n      color: #fff;\n    }\n\n    #calculator #calc-submit:hover {\n      background: var(--primary-hover);\n    }\n\n    #calculator #calc-reset {\n      background: #fff;\n      color: var(--primary-color);\n      border: 1px solid var(--primary-color);\n    }\n\n    #calculator .result-wrap {\n      margin-top: 24px;\n      text-align: center;\n    }\n\n    #calculator .result-label {\n      margin-top: 14px;\n      font-size: 14px;\n    }\n\n    #calculator .calc-result {\n      font-size: 28px;\n      font-weight: bold;\n      color: var(--primary-color);\n    }\n\n    #calculator sup {\n      font-size: 0.7em;\n    }\n\n    @media (max-width: 768px) {\n      #calculator label,\n      #calculator button {\n        font-size: 0.28rem;\n      }\n\n      #calculator input {\n        height: 0.7rem;\n        font-size: 0.28rem;\n      }\n\n      #calculator button {\n        height: 0.7rem;\n        width: 100%;\n      }\n\n      #calculator .btn-group {\n        flex-direction: column;\n      }\n\n      #calculator .input-grid {\n        grid-template-columns: 1fr;\n      }\n    }\n  <\/style>\n\n  <div class=\"input-grid\">\n    <div class=\"calc-row\">\n      <label for=\"calculator-Garm\">Poutre en G : Poids de la poutre en porte-\u00e0-faux (N)<\/label>\n      <input id=\"calculator-Garm\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Garm\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L1\">L<sub>1<\/sub>: Longueur totale de la poutre en porte-\u00e0-faux (mm)<\/label>\n      <input id=\"calculator-L1\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L1\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Ghoist\">G-hoist : Poids du palan (N)<\/label>\n      <input id=\"calculator-Ghoist\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Ghoist\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcap\">G : Capacit\u00e9 (N)<\/label>\n      <input id=\"calculator-Gcap\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcap\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L3\">L<sub>3<\/sub>: Rayon de rotation maximal (mm)<\/label>\n      <input id=\"calculator-L3\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L3\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L2\">L<sub>2<\/sub>: Longueur du centre de rotation \u00e0 l&#39;extr\u00e9mit\u00e9 avant du porte-\u00e0-faux (mm)<\/label>\n      <input id=\"calculator-L2\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L2\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcw\">Contrepoids G : Force du contrepoids (N)<\/label>\n      <input id=\"calculator-Gcw\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcw\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L4\">L<sub>4<\/sub>: Distance entre le contrepoids et le centre de rotation (mm)<\/label>\n      <input id=\"calculator-L4\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L4\">Veuillez saisir un num\u00e9ro valide<\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"btn-group\">\n    <button id=\"calc-submit\" type=\"button\">Calculer<\/button>\n    <button id=\"calc-reset\" type=\"button\">R\u00e9initialiser tout<\/button>\n  <\/div>\n\n  <div class=\"result-wrap\">\n    <div class=\"result-label\">Moment total M (N\u00b7mm)<\/div>\n    <div class=\"calc-result\" id=\"calc-result-Nmm\">&#8212;<\/div>\n\n    <div class=\"result-label\">Moment total M (N\/m)<\/div>\n    <div class=\"calc-result\" id=\"calc-result-Nm\">&#8212;<\/div>\n  <\/div>\n\n  <script>\n    const JibMomentCalc = {\n      fields: [\"Garm\", \"L1\", \"Ghoist\", \"Gcap\", \"L3\", \"L2\", \"Gcw\", \"L4\"],\n\n      input(field) {\n        return document.getElementById(\"calculator-\" + field);\n      },\n\n      setError(field, message) {\n        this.input(field).classList.add(\"error\");\n        const error = document.getElementById(\"error-\" + field);\n        error.textContent = message || \"Please enter a valid number\";\n        error.style.display = \"block\";\n      },\n\n      clearError(field) {\n        this.input(field).classList.remove(\"error\");\n        document.getElementById(\"error-\" + field).style.display = \"none\";\n      },\n\n      value(field) {\n        const raw = this.input(field).value.trim();\n        const number = parseFloat(raw);\n\n        this.clearError(field);\n\n        if (raw === \"\" || !Number.isFinite(number)) {\n          this.setError(\n            field,\n            raw === \"\" ? \"Value cannot be empty\" : \"Please enter a valid number\"\n          );\n          return null;\n        }\n\n        return number;\n      },\n\n      formatPowerTen(number) {\n        if (number === 0) return \"0\";\n\n        const exponent = Math.floor(Math.log10(Math.abs(number)));\n        const base = number \/ Math.pow(10, exponent);\n\n        return base.toFixed(4) + \" \u00d7 10<sup>\" + exponent + \"<\/sup>\";\n      },\n\n      calculate() {\n        const values = {};\n\n        this.fields.forEach(field => {\n          values[field] = this.value(field);\n        });\n\n        if (this.fields.some(field => values[field] === null)) return;\n\n        if (values.L1 === 0) {\n          this.setError(\"L1\", \"L1 cannot be zero\");\n          return;\n        }\n\n        const q1 = values.Garm \/ values.L1;\n        const m1 = (values.Ghoist + values.Gcap) * values.L3;\n\n        \/* M2 = q1 \u00d7 L2 \u00d7 (L2 \u00f7 2)\n              \u2212 q1 \u00d7 (L1 \u2212 L2) \u00d7 ((L1 \u2212 L2) \u00f7 2) *\/\n        const m2 =\n          q1 * values.L2 * (values.L2 \/ 2) -\n          q1 * (values.L1 - values.L2) *\n            ((values.L1 - values.L2) \/ 2);\n\n        const m3 = values.Gcw * values.L4;\n        const total = m1 + m2 - m3;\n\n        document.getElementById(\"calc-result-Nmm\").innerHTML =\n          this.formatPowerTen(total);\n\n        document.getElementById(\"calc-result-Nm\").innerHTML =\n          this.formatPowerTen(total \/ 1000);\n      },\n\n      resetAll() {\n        this.fields.forEach(field => {\n          this.input(field).value = \"\";\n          this.clearError(field);\n        });\n\n        document.getElementById(\"calc-result-Nmm\").textContent = \"--\";\n        document.getElementById(\"calc-result-Nm\").textContent = \"--\";\n      },\n\n      init() {\n        document\n          .getElementById(\"calc-submit\")\n          .addEventListener(\"click\", () => this.calculate());\n\n        document\n          .getElementById(\"calc-reset\")\n          .addEventListener(\"click\", () => this.resetAll());\n\n        this.fields.forEach(field => {\n          this.input(field).addEventListener(\"input\", () => this.clearError(field));\n        });\n      }\n    };\n\n    JibMomentCalc.init();\n  <\/script>\n<\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Formule de calcul du moment de flexion en porte-\u00e0-faux d&#39;une grue \u00e0 fl\u00e8che<\/h2>\n\n\n\n<style>\n  .jib-formula-wrap {\n    width: 100%;\n    display: flex;\n    flex-direction: column;\n    align-items: center;\n    font-family: Arial, sans-serif;\n    font-size: 18px;\n    line-height: 2.2;\n    text-align: center;\n  }\n\n  .jib-formula-line {\n    width: 100%;\n  }\n\n  .jib-formula-wrap sub {\n    font-size: 0.72em;\n    vertical-align: -0.3em;\n  }\n\n  .jib-formula-wrap sup {\n    font-size: 0.72em;\n    vertical-align: 0.2em;\n  }\n\n  .jib-frac {\n    display: inline-table;\n    vertical-align: middle;\n    border-collapse: collapse;\n    margin: 0 3px;\n  }\n\n  .jib-frac td {\n    padding: 0 5px;\n    text-align: center;\n  }\n\n  .jib-frac .jib-frac-line {\n    height: 1px;\n    padding: 0;\n    border-bottom: 1px solid #222;\n  }\n<\/style>\n\n<div class=\"jib-formula-wrap\">\n  <div class=\"jib-formula-line\">\n    q<sub>1<\/sub> =\n    <table class=\"jib-frac\">\n      <tr>\n        <td>g<sub>faisceau<\/sub><\/td>\n      <\/tr>\n      <tr>\n        <td class=\"jib-frac-line\"><\/td>\n      <\/tr>\n      <tr>\n        <td>L<sub>1<\/sub><\/td>\n      <\/tr>\n    <\/table>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    M<sub>1<\/sub> = (G<sub>palan<\/sub> + G) \u00d7 L<sub>3<\/sub>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    M<sub>2<\/sub> = q<sub>1<\/sub> \u00d7 L<sub>2<\/sub> \u00d7\n    <table class=\"jib-frac\">\n      <tr>\n        <td>L<sub>2<\/sub><\/td>\n      <\/tr>\n      <tr>\n        <td class=\"jib-frac-line\"><\/td>\n      <\/tr>\n      <tr>\n        <td>2<\/td>\n      <\/tr>\n    <\/table>\n\n    \u2212 q<sub>1<\/sub> \u00d7 (L<sub>1<\/sub> \u2212 L<sub>2<\/sub>) \u00d7\n    <table class=\"jib-frac\">\n      <tr>\n        <td>(L<sub>1<\/sub> \u2212 L<sub>2<\/sub>)<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"jib-frac-line\"><\/td>\n      <\/tr>\n      <tr>\n        <td>2<\/td>\n      <\/tr>\n    <\/table>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    M<sub>3<\/sub> = G<sub>contrepoids<\/sub> \u00d7 L<sub>4<\/sub>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n  <\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>q<sub>1<\/sub>: charge uniform\u00e9ment r\u00e9partie (unit\u00e9 : N\/mm)<\/li>\n\n\n\n<li>Poutre G : poids de la poutre en porte-\u00e0-faux (unit\u00e9 : N)<\/li>\n\n\n\n<li>L<sub>1<\/sub>: longueur totale de la poutre en porte-\u00e0-faux (unit\u00e9 : mm)&nbsp;<\/li>\n\n\n\n<li>G-hoist : poids du palan (unit\u00e9 : N)<\/li>\n\n\n\n<li>G : capacit\u00e9 (unit\u00e9 : N)<\/li>\n\n\n\n<li>L<sub>3<\/sub>: rayon de rotation maximal (unit\u00e9 : mm)<\/li>\n\n\n\n<li>L<sub>2<\/sub>: longueur du centre de rotation \u00e0 l&#39;extr\u00e9mit\u00e9 avant du porte-\u00e0-faux (unit\u00e9 : mm)<\/li>\n\n\n\n<li>Contrepoids G\u00a0: contrepoids de poutre en porte-\u00e0-faux (unit\u00e9\u00a0: N)<\/li>\n\n\n\n<li>L<sub>4<\/sub>: distance entre le contrepoids et le centre de rotation (unit\u00e9 : mm)<\/li>\n<\/ul>\n\n\n\n<style>\n  .formula-wrap {\n    width: 100%;\n    display: flex;\n    justify-content: center;\n    align-items: center;\n    font-family: Arial, sans-serif;\n    font-size: 18px;\n    line-height: 2.2;\n    text-align: center;\n  }\n\n  .formula-wrap sub {\n    font-size: 0.72em;\n    vertical-align: -0.3em;\n  }\n\n  .formula-wrap sup {\n    font-size: 0.72em;\n    vertical-align: 0.2em;\n  }\n\n  .formula-wrap .formula-content {\n    display: inline-block;\n  }\n\n  .frac-table {\n    display: inline-table;\n    vertical-align: middle;\n    border-collapse: collapse;\n  }\n\n  .frac-table td {\n    text-align: center;\n    padding: 0 4px;\n  }\n\n  .frac-line td {\n    border-bottom: 1px solid #222;\n    height: 1px;\n    padding: 0;\n  }\n<\/style>\n\n<div class=\"formula-wrap\">\n  <div class=\"formula-content\">\n    M = M<sub>1<\/sub> + M<sub>2<\/sub> \u2212 M<sub>3<\/sub>\n  <\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M : le moment de flexion total du porte-\u00e0-faux de la grue \u00e0 fl\u00e8che (unit\u00e9 : N\/mm)<\/li>\n\n\n\n<li>M<sub>1<\/sub>: le moment du levage et de la charge au rayon de giration maximal (rayon fini)<\/li>\n\n\n\n<li>M<sub>2<\/sub>: le moment caus\u00e9 par le poids de la poutre en porte-\u00e0-faux<\/li>\n\n\n\n<li>M<sub>3<\/sub>: le moment caus\u00e9 par le contrepoids de la poutre en porte-\u00e0-faux<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Notes<\/h2>\n\n\n\n<p>Lors des calculs, il est n\u00e9cessaire de prendre en compte les diff\u00e9rents types de structures de certaines grues \u00e0 fl\u00e8che. Par cons\u00e9quent, ce calculateur de moment de flexion en porte-\u00e0-faux pour grue \u00e0 fl\u00e8che inclut deux variables, L.<sub>1<\/sub> et L<sub>2<\/sub>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L<sub>1<\/sub> = Longueur totale de la poutre<\/li>\n\n\n\n<li>L<sub>2<\/sub> = Longueur du centre de rotation \u00e0 l&#39;extr\u00e9mit\u00e9 avant<\/li>\n<\/ul>\n\n\n\n<p>Par cons\u00e9quent, si la poutre en porte-\u00e0-faux de la grue \u00e0 fl\u00e8che pr\u00e9sente un surplomb, alors L<sub>arri\u00e8re<\/sub> = L<sub>1<\/sub> \u2013 L<sub>2<\/sub>. Ce n&#39;est qu&#39;alors que la formule de calcul du moment M2 caus\u00e9 par le poids propre de la fl\u00e8che peut \u00eatre utilis\u00e9e.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Grues \u00e0 fl\u00e8che applicables<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Potence Sur F\u00fbt<\/li>\n\n\n\n<li>Potence Murale<\/li>\n\n\n\n<li>Grue V\u00e9locip\u00e8de Monopoutre<\/li>\n\n\n\n<li>Potences standard FEM<\/li>\n\n\n\n<li>Potences de poste de travail<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"Le calculateur de moment de flexion en porte-\u00e0-faux des grues \u00e0 fl\u00e8che calcule les forces agissant sur la poutre en porte-\u00e0-faux d&#39;une grue \u00e0 fl\u00e8che, \u00e0 partir de param\u00e8tres cl\u00e9s tels que la longueur de la poutre, sa capacit\u00e9, son poids propre et son rayon de rotation maximal. Le calcul du moment de flexion en porte-\u00e0-faux permet de pr\u00e9venir les risques de rupture. Il facilite \u00e9galement la comparaison de l&#39;influence des diff\u00e9rentes capacit\u00e9s de levage et rayons d&#39;action sur la structure de la poutre en porte-\u00e0-faux. De plus, ce calculateur v\u00e9rifie la conformit\u00e9 des sections transversales de la poutre et du poteau aux exigences de r\u00e9sistance, \u00e9value la pertinence des sch\u00e9mas de conception et fournit des r\u00e9f\u00e9rences pour la conception ult\u00e9rieure de grues \u00e0 fl\u00e8che.","protected":false},"author":8,"featured_media":17337,"parent":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"single-onlinetools.php","format":"standard","meta":{"_acf_changed":false,"rank_math_lock_modified_date":false,"pgc_sgb_lightbox_settings":"","footnotes":""},"categories":[1059],"tags":[],"class_list":["post-17334","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-online-tools"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/posts\/17334"}],"collection":[{"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/comments?post=17334"}],"version-history":[{"count":8,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/posts\/17334\/revisions"}],"predecessor-version":[{"id":17344,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/posts\/17334\/revisions\/17344"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/media\/17337"}],"wp:attachment":[{"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/media?parent=17334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/categories?post=17334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dgcrane.com\/fr\/wp-json\/wp\/v2\/tags?post=17334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}