{"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\/bn\/jib-crane-cantilever-bending-moment-calculator\/","title":{"rendered":"\u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09c7\u09a8\u09cd\u09a1\u09bf\u0982 \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0"},"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\">\u099c\u09bf-\u09ac\u09bf\u09ae: \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u0993\u099c\u09a8 (N)<\/label>\n      <input id=\"calculator-Garm\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Garm\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L1\">\u098f\u09b2<sub>1<\/sub>\u09ae\u09cb\u099f \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af (\u09ae\u09bf\u09ae\u09bf)<\/label>\n      <input id=\"calculator-L1\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L1\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Ghoist\">\u099c\u09bf-\u09b9\u09cb\u0987\u09b8\u09cd\u099f: \u09b9\u09cb\u0987\u09b8\u09cd\u099f\u09c7\u09b0 \u0993\u099c\u09a8 (N)<\/label>\n      <input id=\"calculator-Ghoist\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Ghoist\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcap\">G: \u09a7\u09be\u09b0\u09a3\u0995\u09cd\u09b7\u09ae\u09a4\u09be (N)<\/label>\n      <input id=\"calculator-Gcap\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcap\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L3\">\u098f\u09b2<sub>3<\/sub>\u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 (\u09ae\u09bf\u09ae\u09bf)<\/label>\n      <input id=\"calculator-L3\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L3\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L2\">\u098f\u09b2<sub>2<\/sub>\u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0\u09c7\u09b0 \u09b8\u09be\u09ae\u09a8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af (\u09ae\u09bf\u09ae\u09bf)<\/label>\n      <input id=\"calculator-L2\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L2\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-Gcw\">\u099c\u09bf-\u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f: \u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f \u09ac\u09b2 (N)<\/label>\n      <input id=\"calculator-Gcw\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-Gcw\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n\n    <div class=\"calc-row\">\n      <label for=\"calculator-L4\">\u098f\u09b2<sub>4<\/sub>\u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f \u09a5\u09c7\u0995\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac (\u09ae\u09bf\u09ae\u09bf)<\/label>\n      <input id=\"calculator-L4\" type=\"number\" step=\"any\" autocomplete=\"off\">\n      <div class=\"error-msg\" id=\"error-L4\">\u0985\u09a8\u09c1\u0997\u09cd\u09b0\u09b9 \u0995\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c8\u09a7 \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09be\u09a8\u0964<\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"btn-group\">\n    <button id=\"calc-submit\" type=\"button\">\u0997\u09a3\u09a8\u09be \u0995\u09b0\u09c1\u09a8<\/button>\n    <button id=\"calc-reset\" type=\"button\">\u09b8\u09ac \u09b0\u09bf\u09b8\u09c7\u099f \u0995\u09b0\u09c1\u09a8<\/button>\n  <\/div>\n\n  <div class=\"result-wrap\">\n    <div class=\"result-label\">\u09ae\u09cb\u099f \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f M (N\u00b7mm)<\/div>\n    <div class=\"calc-result\" id=\"calc-result-Nmm\">&#8212;<\/div>\n\n    <div class=\"result-label\">\u09ae\u09cb\u099f \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f 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\">\u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09c7\u09a8\u09cd\u09a1\u09bf\u0982 \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0<\/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    \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8<sub>1<\/sub> =\n    <table class=\"jib-frac\">\n      <tr>\n        <td>\u099c\u09bf<sub>\u09ae\u09b0\u09c0\u099a\u09bf<\/sub><\/td>\n      <\/tr>\n      <tr>\n        <td class=\"jib-frac-line\"><\/td>\n      <\/tr>\n      <tr>\n        <td>\u098f\u09b2<sub>1<\/sub><\/td>\n      <\/tr>\n    <\/table>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    \u09ae<sub>1<\/sub> = (\u099c\u09bf)<sub>\u0989\u09a4\u09cd\u09a4\u09cb\u09b2\u09a8<\/sub> + \u099c\u09bf) \u00d7 \u098f\u09b2<sub>3<\/sub>\n  <\/div>\n\n  <div class=\"jib-formula-line\">\n    \u09ae<sub>2<\/sub> = q<sub>1<\/sub> \u00d7 L<sub>2<\/sub> \u00d7\n    <table class=\"jib-frac\">\n      <tr>\n        <td>\u098f\u09b2<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 \u098f\u09b2<sub>2<\/sub>) \u00d7\n    <table class=\"jib-frac\">\n      <tr>\n        <td>(\u098f\u09b2)<sub>1<\/sub> \u2212 \u098f\u09b2<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    \u09ae<sub>3<\/sub> = \u099c\u09bf<sub>\u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f<\/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>\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8<sub>1<\/sub>\u09b8\u09c1\u09b7\u09ae\u09ad\u09be\u09ac\u09c7 \u09ac\u09a3\u09cd\u099f\u09bf\u09a4 \u09ad\u09be\u09b0 (\u098f\u0995\u0995: N\/mm)<\/li>\n\n\n\n<li>\u099c\u09bf-\u09ac\u09bf\u09ae: \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u0993\u099c\u09a8 (\u098f\u0995\u0995: \u09a8\u09bf\u0989\u099f\u09a8)<\/li>\n\n\n\n<li>\u098f\u09b2<sub>1<\/sub>\u09ae\u09cb\u099f \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af (\u098f\u0995\u0995: \u09ae\u09bf\u09ae\u09bf)&nbsp;<\/li>\n\n\n\n<li>\u099c\u09bf-\u09b9\u09cb\u0987\u09b8\u09cd\u099f: \u0989\u09a4\u09cd\u09a4\u09cb\u09b2\u09a8 \u0993\u099c\u09a8 (\u098f\u0995\u0995: \u09a8\u09bf\u0989\u099f\u09a8)<\/li>\n\n\n\n<li>G: \u09a7\u09be\u09b0\u09a3\u0995\u09cd\u09b7\u09ae\u09a4\u09be (\u098f\u0995\u0995: N)<\/li>\n\n\n\n<li>\u098f\u09b2<sub>3<\/sub>\u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 (\u098f\u0995\u0995: \u09ae\u09bf\u09ae\u09bf)<\/li>\n\n\n\n<li>\u098f\u09b2<sub>2<\/sub>\u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0\u09c7\u09b0 \u09b8\u09be\u09ae\u09a8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af (\u098f\u0995\u0995: \u09ae\u09bf\u09ae\u09bf)<\/li>\n\n\n\n<li>\u099c\u09bf-\u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f: \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae \u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f (\u098f\u0995\u0995: \u09a8\u09bf\u0989\u099f\u09a8)<\/li>\n\n\n\n<li>\u098f\u09b2<sub>4<\/sub>\u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f \u09a5\u09c7\u0995\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac (\u098f\u0995\u0995: \u09ae\u09bf\u09ae\u09bf)<\/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> + \u098f\u09ae<sub>2<\/sub> \u2212 \u098f\u09ae<sub>3<\/sub>\n  <\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M: \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0\u09c7\u09b0 \u09ae\u09cb\u099f \u09a8\u09ae\u09a8 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 (\u098f\u0995\u0995: N\/mm)<\/li>\n\n\n\n<li>\u09ae<sub>1<\/sub>\u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7 (\u09b8\u09b8\u09c0\u09ae \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7) \u0989\u09a4\u09cd\u09a4\u09cb\u09b2\u09a8 \u09af\u09a8\u09cd\u09a4\u09cd\u09b0 \u098f\u09ac\u0982 \u09ad\u09be\u09b0\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/li>\n\n\n\n<li>\u09ae<sub>2<\/sub>\u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u0993\u099c\u09a8\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u09b8\u09c3\u09b7\u09cd\u099f \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/li>\n\n\n\n<li>\u09ae<sub>3<\/sub>\u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae \u0995\u09be\u0989\u09a8\u09cd\u099f\u09be\u09b0\u0993\u09af\u09bc\u09c7\u099f \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c3\u09b7\u09cd\u099f \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af<\/h2>\n\n\n\n<p>\u0997\u09a3\u09a8\u09be \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc, \u0995\u09bf\u099b\u09c1 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0997\u09a4 \u09a7\u09b0\u09a8 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u0964 \u09a4\u09be\u0987, \u098f\u0987 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09c7\u09a8\u09cd\u09a1\u09bf\u0982 \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u09c7 L \u09a8\u09be\u09ae\u0995 \u09a6\u09c1\u099f\u09bf \u09ad\u09c7\u09b0\u09bf\u09af\u09bc\u09c7\u09ac\u09b2 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964<sub>1<\/sub> \u098f\u09ac\u0982 \u098f\u09b2<sub>2<\/sub>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u098f\u09b2<sub>1<\/sub> = \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09ac\u09bf\u09ae\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/li>\n\n\n\n<li>\u098f\u09b2<sub>2<\/sub> = \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u09b8\u09be\u09ae\u09a8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/li>\n<\/ul>\n\n\n\n<p>\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09af\u09a6\u09bf \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8\u09c7\u09b0 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7 \u098f\u0995\u099f\u09bf \u0993\u09ad\u09be\u09b0\u09b9\u09cd\u09af\u09be\u0982 \u09a5\u09be\u0995\u09c7, \u09a4\u09be\u09b9\u09b2\u09c7 L<sub>\u09aa\u09bf\u099b\u09a8\u09c7\u09b0<\/sub> = \u098f\u09b2<sub>1<\/sub> \u2013 \u098f\u09b2<sub>2<\/sub>\u0995\u09c7\u09ac\u09b2 \u09a4\u0996\u09a8\u0987 \u09ac\u09c1\u09ae\u09c7\u09b0 \u09b8\u09cd\u09ac-\u0993\u099c\u09a8\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u09b8\u09c3\u09b7\u09cd\u099f \u09ad\u09cd\u09b0\u09be\u09ae\u0995 M2 \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09be\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u09ab\u09cd\u09b0\u09bf \u09b8\u09cd\u099f\u09cd\u09af\u09be\u09a8\u09cd\u09a1\u09bf\u0982 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8<\/li>\n\n\n\n<li>\u0993\u09af\u09bc\u09be\u09b2 \u09ae\u09be\u0989\u09a8\u09cd\u099f \u0995\u09b0\u09be \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8<\/li>\n\n\n\n<li>\u0993\u09af\u09bc\u09be\u09b2 \u099f\u09cd\u09b0\u09be\u09ad\u09c7\u09b2\u09bf\u0982 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8<\/li>\n\n\n\n<li>FEM \u09b8\u09cd\u099f\u09cd\u09af\u09be\u09a8\u09cd\u09a1\u09be\u09b0\u09cd\u09a1 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8\u09b8<\/li>\n\n\n\n<li>\u0993\u09af\u09bc\u09be\u09b0\u09cd\u0995\u09b8\u09cd\u099f\u09c7\u09b6\u09a8 \u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8\u09b8<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"\u099c\u09bf\u09ac \u0995\u09cd\u09b0\u09c7\u09a8 \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09c7\u09a8\u09cd\u09a1\u09bf\u0982 \u09ae\u09cb\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u099f\u09bf \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af, \u09a7\u09be\u09b0\u09a3\u0995\u09cd\u09b7\u09ae\u09a4\u09be, \u0995\u09cd\u09af\u09be\u09a8\u09cd\u099f\u09bf\u09b2\u09bf\u09ad\u09be\u09b0 \u09ac\u09bf\u09ae\u09c7\u09b0 \u09a8\u09bf\u099c\u09b8\u09cd\u09ac \u0993\u099c\u09a8 \u098f\u09ac\u0982 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09ae\u09a4\u09cb \u09ae\u09c2\u09b2 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