{"id":17213,"date":"2026-07-07T02:18:44","date_gmt":"2026-07-07T02:18:44","guid":{"rendered":"https:\/\/www.dgcrane.com\/?p=17213"},"modified":"2026-07-07T02:18:48","modified_gmt":"2026-07-07T02:18:48","slug":"overhead-and-gantry-crane-deflection-calculator","status":"publish","type":"post","link":"https:\/\/www.dgcrane.com\/de\/overhead-and-gantry-crane-deflection-calculator\/","title":{"rendered":"Durchbiegungsrechner f\u00fcr Br\u00fccken- und Portalkrane"},"content":{"rendered":"<!-- WordPress \u53ef\u76f4\u63a5\u7c98\u8d34\u5b8c\u6574\u4ee3\u7801\u5757 -->\n<div id=\"calculator\">\n    <style>\n        \/* \u4ec5\u4f5c\u7528\u4e8e #calculator \u5185\u90e8\uff0c\u65e0\u5168\u5c40\u6837\u5f0f\u6c61\u67d3 *\/\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-color: var(--bg-color);\n            color: var(--text-color);\n            box-sizing: border-box;\n        }\n        #calculator .calc-title {\n            font-size: 18px;\n            margin: 0 0 24px 0;\n            font-weight: 600;\n        }\n        #calculator .field-wrap {\n            margin-bottom: 18px;\n        }\n        #calculator label {\n            display: block;\n            font-size: 14px;\n            margin-bottom: 6px;\n        }\n        #calculator input {\n            width: 100%;\n            box-sizing: border-box;\n            height: 36px;\n            font-size: 16px;\n            border: 1px solid #ccc;\n            border-radius: 0;\n            padding: 0 10px;\n            transition: 0.2s ease;\n        }\n        #calculator input:focus {\n            border: 2px solid var(--primary-color);\n            outline: none;\n        }\n        #calculator input.error {\n            border: 2px solid var(--error-color);\n        }\n        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.result-label {\n            font-size: 14px;\n        }\n        #calculator .result-value {\n            font-size: 40px;\n            font-weight: bold;\n            margin-top: 4px;\n            word-break: break-all;\n        }\n        \/* \u79fb\u52a8\u7aef\u9002\u914d max-width:768px *\/\n        @media (max-width: 768px) {\n            #calculator input,\n            #calculator button {\n                height: 0.7rem;\n            }\n            #calculator label,\n            #calculator button,\n            #calculator .result-label {\n                font-size: 0.28rem;\n            }\n            #calculator .btn-group {\n                flex-direction: column;\n            }\n            #calculator button {\n                width: 100%;\n            }\n            #calculator .result-value {\n                font-size: 0.8rem;\n            }\n        }\n    <\/style>\n\n    <div class=\"field-wrap\">\n        <label for=\"calculator-P\">Konzentrierte Last P (N)<\/label>\n        <input type=\"number\" id=\"calculator-P\" placeholder=\"Eingangslastwert\">\n        <span class=\"error-msg\"><\/span>\n    <\/div>\n    <div class=\"field-wrap\">\n        <label for=\"calculator-L\">Spannweite L (m)<\/label>\n        <input type=\"number\" id=\"calculator-L\" placeholder=\"Eingabespanne\">\n        <span class=\"error-msg\"><\/span>\n    <\/div>\n    <div class=\"field-wrap\">\n        <label for=\"calculator-I\">Tr\u00e4gheitsmoment I (cm\u2074)<\/label>\n        <input type=\"number\" id=\"calculator-I\" placeholder=\"Eingangstr\u00e4gheitswert\">\n        <span class=\"error-msg\"><\/span>\n    <\/div>\n\n    <div class=\"btn-group\">\n        <button id=\"calculator-calcBtn\" class=\"calc-btn\">Berechnen<\/button>\n        <button id=\"calculator-resetBtn\" class=\"reset-btn\">Zur\u00fccksetzen<\/button>\n    <\/div>\n\n    <div class=\"result-wrap\">\n        <div class=\"result-label\">Durchbiegung (m)<\/div>\n        <div id=\"calculator-result\" class=\"result-value\">&#8212;<\/div>\n    <\/div>\n\n    <script>\n        (function() {\n            const fieldIds = ['P', 'L', 'I'];\n            const inputEls = {};\n            const errorMsgEls = {};\n            const resultEl = document.getElementById('calculator-result');\n            const calcBtn = document.getElementById('calculator-calcBtn');\n            const resetBtn = document.getElementById('calculator-resetBtn');\n            \/\/ \u94a2\u6750\u6807\u51c6\u5f39\u6027\u6a21\u91cf\u56fa\u5b9a\u503c 2.06\u00d710\u00b9\u00b9 Pa\n            const STEEL_E = 2.06e11;\n\n            \/\/ \u521d\u59cb\u5316DOM\u6620\u5c04\n            function initDomRefs() {\n                fieldIds.forEach(key => {\n                    inputEls[key] = document.getElementById(`calculator-${key}`);\n                    errorMsgEls[key] = inputEls[key].nextElementSibling;\n                    \/\/ \u8f93\u5165\u65f6\u6e05\u9664\u9519\u8bef\n                    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m\u2074\uff1a1 cm\u2074 = 1e-8 m\u2074\n            \/\/ f = (P * L^3) \/ (48 * E * I_m4)\n            function runCalculation() {\n                if(!validateAllFields()) {\n                    resultEl.textContent = '--';\n                    return;\n                }\n                const P = parseFloat(inputEls.P.value);\n                const L = parseFloat(inputEls.L.value);\n                const I_cm4 = parseFloat(inputEls.I.value);\n                \/\/ cm\u2074 \u8f6c m\u2074\n                const I_m4 = I_cm4 * Math.pow(10, -8);\n\n                const numerator = P * Math.pow(L, 3);\n                const denominator = 48 * STEEL_E * I_m4;\n                const deflection = numerator \/ denominator;\n                \/\/ \u7ed3\u679c\u4fdd\u75592\u4f4d\u5c0f\u6570\n                resultEl.textContent = deflection.toFixed(2);\n            }\n\n            \/\/ \u91cd\u7f6e\u5168\u90e8\n            function resetAll() {\n                fieldIds.forEach(key => {\n                    inputEls[key].value = '';\n                    clearError(inputEls[key], errorMsgEls[key]);\n                });\n                resultEl.textContent = '--';\n            }\n\n            \/\/ \u7ed1\u5b9a\u4e8b\u4ef6\n            function bindEvents() {\n                calcBtn.addEventListener('click', runCalculation);\n                resetBtn.addEventListener('click', resetAll);\n            }\n\n            \/\/ \u521d\u59cb\u5316\u5165\u53e3\n            function init() {\n                initDomRefs();\n                bindEvents();\n            }\n\n            window.BeamDeflectionCalc = {\n                init: init\n            };\n        })();\n\n        \/\/ \u9875\u9762\u52a0\u8f7d\u5b8c\u6210\u521d\u59cb\u5316\u8ba1\u7b97\u5668\n        document.addEventListener('DOMContentLoaded', function() {\n            BeamDeflectionCalc.init();\n        });\n    <\/script>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Formel zur Berechnung der Durchbiegung von Br\u00fccken- und Portalkranen<\/h2>\n\n\n\n<style>\n    .formula {\n        font-family: \"Microsoft YaHei\", sans-serif;\n        font-size: 1.2em;\n        margin: 20px 0;\n        padding: 15px;\n        background: #ffffff;\n        border-radius: 8px;\n        text-align: left;\n    }\n    .math-frac {\n        display: inline-block;\n        vertical-align: middle;\n        text-align: center;\n        margin: 0 6px;\n    }\n    .frac-numerator {\n        display: block;\n        padding: 0 10px;\n        border-bottom: 2px solid #222;\n    }\n    .frac-denominator {\n        display: block;\n        padding: 0 10px;\n    }\n    .sup-pow {\n        font-size: 0.6em;\n        line-height: 0;\n        position: relative;\n        top: -0.6em;\n    }\n<\/style>\n<div class=\"formula\">\n    f = <span class=\"math-frac\">\n        <span class=\"frac-numerator\">PL<span class=\"sup-pow\">3<\/span><\/span>\n        <span class=\"frac-denominator\">48EI<\/span>\n    <\/span>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>f: Maximale Auslenkung (Einheit: m)<\/li>\n\n\n\n<li>P: Radlast (Einheit: N)<\/li>\n\n\n\n<li>L: Spannweite des Haupttr\u00e4gers (Einheit: m)<\/li>\n\n\n\n<li>E: Elastizit\u00e4tsmodul (Einheit: Pa, typischerweise angenommen als 2,06 \u00d7 10\u00b9\u00b9 Pa)<\/li>\n\n\n\n<li>I: Tr\u00e4gheitsmoment (Einheit: m)<sup>4<\/sup>) <\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Hinweise<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bei internationalen Standardberechnungen wird die Einheit f\u00fcr den Elastizit\u00e4tsmodul von Stahl automatisch in Pa umgerechnet.<\/li>\n\n\n\n<li>Die Berechnungsergebnisse von <a href=\"https:\/\/www.dgcrane.com\/de\/crane-main-girder-section-moment-of-inertia-calculator\/\">Tr\u00e4gheitsmomentrechner f\u00fcr Kran-Haupttr\u00e4gerabschnitte<\/a> Die Werte sind in cm\u2074 angegeben, werden aber w\u00e4hrend des Berechnungsprozesses automatisch in die SI-Einheit m\u2074 umgerechnet.<\/li>\n\n\n\n<li>Dieser Rechner f\u00fcr die Durchbiegung von Br\u00fccken- und Portalkranen ist in erster Linie f\u00fcr Haupttr\u00e4ger mit rechteckigen Hohlprofilen anwendbar.<\/li>\n\n\n\n<li>Die in diesem Rechner f\u00fcr die Durchbiegung von Br\u00fccken- und Portalkranen verwendete Last ist eine konzentrierte Last in der Feldmitte (wobei sich der Laufkatze an der ung\u00fcnstigsten Stelle befindet).<\/li>\n\n\n\n<li>Es wird lediglich die vertikale statische Durchbiegung berechnet, der dynamische Lastkoeffizient wird nicht ber\u00fccksichtigt.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Anwendbare Krane<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Br\u00fcckenkr\u00e4ne (Spannweite \u2264 30 m)<\/li>\n\n\n\n<li>Portalkrane (Spannweite \u2264 30 m und kein Ausleger oder Auslegerl\u00e4nge \u2264 0,15L)<\/li>\n\n\n\n<li>Halbportalkrane (Spannweite \u2264 30 m und kein Ausleger oder Auslegerl\u00e4nge \u2264 0,15L)<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"Der Durchbiegungsrechner f\u00fcr Br\u00fccken- und Portalkrane gew\u00e4hrleistet Betriebssicherheit, reduziert Materialerm\u00fcdung und verl\u00e4ngert die Lebensdauer. Er berechnet pr\u00e4zise die vertikale Durchbiegung belasteter Tr\u00e4ger, bewertet deren Steifigkeit und Tragf\u00e4higkeit anhand von Tragf\u00e4higkeit, Spannweite, Laufkatzengewicht und Querschnittsparametern. Zudem beugt er Schienenverschlei\u00df, bleibenden Verformungen und instabilem Betrieb vor und optimiert die Konstruktion und das Gewicht. Abschlie\u00dfend \u00fcberpr\u00fcft er, ob die Durchbiegungswerte den Grenzwerten der ISO- und FEM-Normen entsprechen.","protected":false},"author":8,"featured_media":17216,"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-17213","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\/17213"}],"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=17213"}],"version-history":[{"count":4,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/posts\/17213\/revisions"}],"predecessor-version":[{"id":17219,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/posts\/17213\/revisions\/17219"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/media\/17216"}],"wp:attachment":[{"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/media?parent=17213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/categories?post=17213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dgcrane.com\/de\/wp-json\/wp\/v2\/tags?post=17213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}