{"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\/de\/jib-crane-cantilever-bending-moment-calculator\/","title":{"rendered":"Biegemomentrechner f\u00fcr Auslegerkrane"},"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\">G-Tr\u00e4ger: Gewicht des Kragarmtr\u00e4gers (N)<\/label>\n      <input id=\"calculator-Garm\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Garm\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L1\">M<sub>1<\/sub>Gesamtl\u00e4nge des Kragarmtr\u00e4gers (mm)<\/label>\n      <input id=\"calculator-L1\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L1\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Ghoist\">G-Hebezeug: Hebegewicht (N)<\/label>\n      <input id=\"calculator-Ghoist\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Ghoist\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcap\">G: Kapazit\u00e4t (N)<\/label>\n      <input id=\"calculator-Gcap\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcap\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L3\">M<sub>3<\/sub>Maximaler Schwenkradius (mm)<\/label>\n      <input id=\"calculator-L3\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L3\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L2\">M<sub>2<\/sub>: L\u00e4nge vom Drehzentrum bis zum vorderen Ende des Auslegers (mm)<\/label>\n      <input id=\"calculator-L2\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L2\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcw\">G-Gegengewicht: Gegengewichtskraft (N)<\/label>\n      <input id=\"calculator-Gcw\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcw\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L4\">M<sub>4<\/sub>Abstand vom Gegengewicht zum Drehzentrum (mm)<\/label>\n      <input id=\"calculator-L4\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L4\">Bitte geben Sie eine g\u00fcltige Nummer ein.<\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"btn-group\">\n    <button id=\"calc-submit\" type=\"button\">Berechnen<\/button>\n    <button id=\"calc-reset\" type=\"button\">Alles zur\u00fccksetzen<\/button>\n  <\/div>\n\n  <div class=\"result-wrap\">\n    <div class=\"result-label\">Gesamtmoment M (N\u00b7mm)<\/div>\n    <div class=\"calc-result\" id=\"calc-result-Nmm\">&#8212;<\/div>\n\n    <div class=\"result-label\">Gesamtmoment 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\">Formel zur Berechnung des Biegemoments bei Auslegerkranen<\/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>Strahl<\/sub><\/td>\n      <\/tr>\n      <tr>\n        <td class=\"jib-frac-line\"><\/td>\n      <\/tr>\n      <tr>\n        <td>M<sub>1<\/sub><\/td>\n      <\/tr>\n    <\/table>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    M<sub>1<\/sub> = (G<sub>Hebezeug<\/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>M<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>Gegengewicht<\/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>: gleichm\u00e4\u00dfig verteilte Last (Einheit: N\/mm)<\/li>\n\n\n\n<li>G-Tr\u00e4ger: Gewicht eines Kragtr\u00e4gers (Einheit: N)<\/li>\n\n\n\n<li>M<sub>1<\/sub>Gesamtl\u00e4nge des Kragarmtr\u00e4gers (Einheit: mm)&nbsp;<\/li>\n\n\n\n<li>G-Hebezeug: Hebegewicht (Einheit: N)<\/li>\n\n\n\n<li>G: Kapazit\u00e4t (Einheit: N)<\/li>\n\n\n\n<li>M<sub>3<\/sub>: maximaler Schwenkradius (Einheit: mm)<\/li>\n\n\n\n<li>M<sub>2<\/sub>: L\u00e4nge vom Drehzentrum bis zum vorderen Ende des Auslegers (Einheit: mm)<\/li>\n\n\n\n<li>G-Gegengewicht: Kragarm-Gegengewicht (Einheit: N)<\/li>\n\n\n\n<li>M<sub>4<\/sub>Abstand vom Gegengewicht zum Drehzentrum (Einheit: 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: das gesamte Biegemoment des Auslegerkrans (Einheit: N\/mm)<\/li>\n\n\n\n<li>M<sub>1<\/sub>: das Moment der Hebevorrichtung und der Last beim maximalen Tr\u00e4gheitsradius (endlicher Radius)<\/li>\n\n\n\n<li>M<sub>2<\/sub>: das durch das Gewicht des Kragtr\u00e4gers verursachte Moment<\/li>\n\n\n\n<li>M<sub>3<\/sub>: das durch das Gegengewicht des Kragarmtr\u00e4gers verursachte Moment<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Hinweise<\/h2>\n\n\n\n<p>Bei der Berechnung m\u00fcssen die unterschiedlichen Bauarten von Auslegerkranen ber\u00fccksichtigt werden. Daher enth\u00e4lt dieser Rechner f\u00fcr das Biegemoment eines Auslegerkrans zwei Variablen, L.<sub>1<\/sub> und L<sub>2<\/sub>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M<sub>1<\/sub> = Gesamtl\u00e4nge des gesamten Balkens<\/li>\n\n\n\n<li>M<sub>2<\/sub> = L\u00e4nge vom Drehzentrum bis zum vorderen Ende<\/li>\n<\/ul>\n\n\n\n<p>Wenn der Kragarm des Auslegerkrans also einen \u00dcberhang aufweist, dann ist L<sub>hinteren<\/sub> = L<sub>1<\/sub> \u2013 L<sub>2<\/sub>Nur dann kann die Formel zur Berechnung des durch das Eigengewicht des Auslegers verursachten Moments M2 verwendet werden.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Anwendbare Auslegerkrane<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Freistehende Auslegerkrane<\/li>\n\n\n\n<li>Wandmontierte Schwenkkr\u00e4ne<\/li>\n\n\n\n<li>Wandschwenkkr\u00e4ne<\/li>\n\n\n\n<li>FEM Standard-Schwenkkrane<\/li>\n\n\n\n<li>Arbeitsplatz-Schwenkkrane<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"Der Biegemomentenrechner f\u00fcr Auslegerkrane berechnet die auf den Ausleger wirkenden Kr\u00e4fte anhand wichtiger Parameter wie Auslegerl\u00e4nge, Tragf\u00e4higkeit, Eigengewicht und maximaler Schwenkradius. Die Berechnung des Biegemoments hilft, Bruchrisiken zu vermeiden. Sie erm\u00f6glicht zudem einen einfachen Vergleich der Auswirkungen unterschiedlicher Tragf\u00e4higkeiten und Arbeitsradien auf die Auslegerkonstruktion. Dar\u00fcber hinaus \u00fcberpr\u00fcft der Rechner, ob die Querschnitte von Ausleger und St\u00fctze die Anforderungen an die Tragf\u00e4higkeit erf\u00fcllen, bewertet die Plausibilit\u00e4t von Konstruktionskonzepten und liefert Referenzwerte f\u00fcr die weitere Auslegerkrankonstruktion.","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\/de\/wp-json\/wp\/v2\/posts\/17334"}],"collection":[{"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/comments?post=17334"}],"version-history":[{"count":8,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/posts\/17334\/revisions"}],"predecessor-version":[{"id":17344,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/posts\/17334\/revisions\/17344"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/media\/17337"}],"wp:attachment":[{"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/media?parent=17334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/categories?post=17334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/tags?post=17334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}