{"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\/pl\/jib-crane-cantilever-bending-moment-calculator\/","title":{"rendered":"Kalkulator momentu zginaj\u0105cego wspornika \u017curawia"},"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\">Belka G: ci\u0119\u017car belki wspornikowej (N)<\/label>\n      <input id=\"calculator-Garm\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Garm\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L1\">L<sub>1<\/sub>:Ca\u0142kowita d\u0142ugo\u015b\u0107 belki wspornikowej (mm)<\/label>\n      <input id=\"calculator-L1\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L1\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Ghoist\">G-hoist: Masa podno\u015bnika (N)<\/label>\n      <input id=\"calculator-Ghoist\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Ghoist\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcap\">G: Pojemno\u015b\u0107 (N)<\/label>\n      <input id=\"calculator-Gcap\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcap\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L3\">L<sub>3<\/sub>:Maksymalny promie\u0144 obrotu (mm)<\/label>\n      <input id=\"calculator-L3\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L3\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L2\">L<sub>2<\/sub>: D\u0142ugo\u015b\u0107 od \u015brodka obrotu do przedniego ko\u0144ca wspornika (mm)<\/label>\n      <input id=\"calculator-L2\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L2\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcw\">Przeciwwaga G: Si\u0142a przeciwwagi (N)<\/label>\n      <input id=\"calculator-Gcw\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcw\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L4\">L<sub>4<\/sub>: Odleg\u0142o\u015b\u0107 od przeciwwagi do \u015brodka obrotu (mm)<\/label>\n      <input id=\"calculator-L4\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L4\">Prosz\u0119 wpisa\u0107 prawid\u0142owy numer<\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"btn-group\">\n    <button id=\"calc-submit\" type=\"button\">Oblicza\u0107<\/button>\n    <button id=\"calc-reset\" type=\"button\">Zresetuj wszystko<\/button>\n  <\/div>\n\n  <div class=\"result-wrap\">\n    <div class=\"result-label\">Ca\u0142kowity moment M (N\u00b7mm)<\/div>\n    <div class=\"calc-result\" id=\"calc-result-Nmm\">&#8212;<\/div>\n\n    <div class=\"result-label\">Ca\u0142kowity moment 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\">Wz\u00f3r na kalkulator momentu zginaj\u0105cego wspornika \u017curawia<\/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>belka<\/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>wci\u0105gnik<\/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 (D\u0142.<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>przeciwwaga<\/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>: obci\u0105\u017cenie r\u00f3wnomiernie roz\u0142o\u017cone (jednostka: N\/mm)<\/li>\n\n\n\n<li>Belka G: ci\u0119\u017car belki wspornikowej (jednostka: N)<\/li>\n\n\n\n<li>L<sub>1<\/sub>: ca\u0142kowita d\u0142ugo\u015b\u0107 belki wspornikowej (jednostka: mm)&nbsp;<\/li>\n\n\n\n<li>G-hoist: ci\u0119\u017car podno\u015bnika (jednostka: N)<\/li>\n\n\n\n<li>G: pojemno\u015b\u0107 (jednostka: N)<\/li>\n\n\n\n<li>L<sub>3<\/sub>: maksymalny promie\u0144 obrotu (jednostka: mm)<\/li>\n\n\n\n<li>L<sub>2<\/sub>: d\u0142ugo\u015b\u0107 od \u015brodka obrotu do przedniego ko\u0144ca wspornika (jednostka: mm)<\/li>\n\n\n\n<li>Przeciwwaga G: przeciwwaga belki wspornikowej (jednostka: N)<\/li>\n\n\n\n<li>L<sub>4<\/sub>: odleg\u0142o\u015b\u0107 od przeciwwagi do \u015brodka obrotu (jednostka: 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: ca\u0142kowity moment zginaj\u0105cy wspornika \u017curawia wysi\u0119gnikowego (jednostka: N\/mm)<\/li>\n\n\n\n<li>M<sub>1<\/sub>: moment podnoszenia i \u0142adunku przy maksymalnym promieniu bezw\u0142adno\u015bci (promie\u0144 sko\u0144czony)<\/li>\n\n\n\n<li>M<sub>2<\/sub>:moment wywo\u0142any ci\u0119\u017carem belki wspornikowej<\/li>\n\n\n\n<li>M<sub>3<\/sub>:moment wywo\u0142any przez przeciwwag\u0119 belki wspornikowej<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Notatki<\/h2>\n\n\n\n<p>Podczas oblicze\u0144 konieczne jest uwzgl\u0119dnienie r\u00f3\u017cnych typ\u00f3w konstrukcyjnych niekt\u00f3rych \u017curawi wysi\u0119gnikowych. Dlatego ten kalkulator momentu zginaj\u0105cego wspornik \u017curawia wysi\u0119gnikowego uwzgl\u0119dnia dwie zmienne: L.<sub>1<\/sub> i L<sub>2<\/sub>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L<sub>1<\/sub> = Ca\u0142kowita d\u0142ugo\u015b\u0107 ca\u0142ej belki<\/li>\n\n\n\n<li>L<sub>2<\/sub> = D\u0142ugo\u015b\u0107 od \u015brodka obrotu do przedniego ko\u0144ca<\/li>\n<\/ul>\n\n\n\n<p>Dlatego je\u015bli belka wspornikowa \u017curawia ma wysi\u0119gnik, w\u00f3wczas L<sub>ty\u0142<\/sub> = L<sub>1<\/sub> \u2013 L<sub>2<\/sub>Dopiero wtedy mo\u017cna zastosowa\u0107 wz\u00f3r na obliczenie momentu M2 wywo\u0142anego ci\u0119\u017carem w\u0142asnym wysi\u0119gnika.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Odpowiednie \u017curawie wysi\u0119gnikowe<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u017burawie wolnostoj\u0105ce<\/li>\n\n\n\n<li>\u017burawie przy\u015bcienne<\/li>\n\n\n\n<li>\u017burawie przy\u015bcienne<\/li>\n\n\n\n<li>Standardowe \u017curawie FEM<\/li>\n\n\n\n<li>\u017burawie s\u0142upowe stanowiskowe<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"Kalkulator momentu zginaj\u0105cego wspornika \u017curawia wysi\u0119gnikowego oblicza si\u0142y dzia\u0142aj\u0105ce na belk\u0119 wspornikow\u0105 \u017curawia wysi\u0119gnikowego, wykorzystuj\u0105c kluczowe parametry, takie jak d\u0142ugo\u015b\u0107 belki wspornikowej, ud\u017awig, ci\u0119\u017car w\u0142asny belki wspornikowej i maksymalny promie\u0144 obrotu. Obliczenie momentu zginaj\u0105cego wspornika pomaga unikn\u0105\u0107 ryzyka p\u0119kni\u0119cia. U\u0142atwia r\u00f3wnie\u017c por\u00f3wnanie wp\u0142ywu r\u00f3\u017cnych ud\u017awig\u00f3w i promieni roboczych na konstrukcj\u0119 belki wspornikowej \u017curawi wysi\u0119gnikowych. Ponadto kalkulator momentu zginaj\u0105cego wspornika \u017curawia wysi\u0119gnikowego weryfikuje, czy przekroje poprzeczne belki wspornikowej i kolumny spe\u0142niaj\u0105 wymagania dotycz\u0105ce wytrzyma\u0142o\u015bci roboczej, ocenia racjonalno\u015b\u0107 schemat\u00f3w projektowych i dostarcza odniesienia do p\u00f3\u017aniejszego projektowania \u017curawia wysi\u0119gnikowego.","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\/pl\/wp-json\/wp\/v2\/posts\/17334"}],"collection":[{"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/comments?post=17334"}],"version-history":[{"count":8,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/posts\/17334\/revisions"}],"predecessor-version":[{"id":17344,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/posts\/17334\/revisions\/17344"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/media\/17337"}],"wp:attachment":[{"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/media?parent=17334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/categories?post=17334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dgcrane.com\/pl\/wp-json\/wp\/v2\/tags?post=17334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}