{"id":100222,"date":"2026-02-15T20:28:09","date_gmt":"2026-02-15T20:28:09","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100222"},"modified":"2026-07-15T10:27:59","modified_gmt":"2026-07-15T10:27:59","slug":"shaft-deflection-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/vi\/calculators\/shaft-deflection-calculator\/","title":{"rendered":"C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n \u0111\u1ed9 v\u00f5ng tr\u1ee5c | C\u00f4ng c\u1ee5 mi\u1ec5n ph\u00ed #072"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Shaft Deflection Calculator\",\"description\":\"Calculate shaft deflection under various loads.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/shaft-deflection-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"Which load type should I choose?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Center point for symmetric loading, offset for asymmetric, distributed for self-weight, cantilever for overhung loads.\"}},\n{\"@type\":\"Question\",\"name\":\"What is acceptable shaft deflection?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"General L\/3000, gear shafts L\/5000, precision L\/10000.\"}},\n{\"@type\":\"Question\",\"name\":\"How does diameter affect deflection?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Deflection scales as 1\/d^4 via I. Doubling diameter reduces deflection 16x.\"}},\n{\"@type\":\"Question\",\"name\":\"What about stepped shafts?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use Castigliano theorem, transfer matrix, or FEA for stepped shafts.\"}},\n{\"@type\":\"Question\",\"name\":\"How to find critical speed from deflection?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"First critical speed Ncr = 946\/sqrt(delta_mm) RPM (Rayleigh approximation).\"}}\n]}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Shaft Deflection\",\"item\":\"https:\/\/vibromera.eu\/calculators\/shaft-deflection-calculator\/\"}]}<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" rel=\"stylesheet\">\n\n<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.css\">\n\n<style>:root{--vc-bg:#f4f1ec;--vc-surface:#fff;--vc-surface-alt:#f8f6f2;--vc-ink:#1a1a1a;--vc-ink-secondary:#5a5650;--vc-ink-muted:#8a857e;--vc-accent:#c85a2a;--vc-accent-hover:#b04d22;--vc-accent-light:#fdf0ea;--vc-blue:#2a5c8c;--vc-blue-light:#eaf1f8;--vc-green:#2a7a4b;--vc-green-light:#eaf8ef;--vc-yellow:#a67c00;--vc-yellow-light:#fef9e8;--vc-border:#d9d4cc;--vc-border-light:#e8e4dd;--vc-shadow:0 1px 3px rgba(26,26,26,.06),0 4px 12px rgba(26,26,26,.04);--vc-radius:8px;--vc-radius-lg:12px;--vc-font:'DM Sans',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif;--vc-mono:'JetBrains Mono',Consolas,Monaco,monospace;--vc-display:'Fraunces',Georgia,serif}.vc-calculator{font-family:var(--vc-font);font-size:15px;line-height:1.65;color:var(--vc-ink);max-width:960px;margin:0 auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 24px 40px;position:relative}.vc-header::after{content:'';position:absolute;bottom:0;left:50%;transform:translateX(-50%);width:80px;height:3px;background:var(--vc-accent);border-radius:2px}.vc-header-eyebrow{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:.15em;text-transform:uppercase;color:var(--vc-accent);margin:0 0 12px}.vc-header-title{font-family:var(--vc-display);font-size:clamp(24px,4vw,36px);font-weight:800;line-height:1.15;color:var(--vc-ink);margin:0 0 16px}.vc-header-subtitle{font-size:15px;color:var(--vc-ink-secondary);margin:0 auto 20px;max-width:600px}.vc-badges{display:inline-flex;gap:8px;flex-wrap:wrap;justify-content:center}.vc-badge{font-family:var(--vc-mono);font-size:11px;font-weight:500;padding:4px 10px;border-radius:4px;background:var(--vc-surface);border:1px solid var(--vc-border);color:var(--vc-ink-secondary)}.vc-card{background:var(--vc-surface);border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);box-shadow:var(--vc-shadow);overflow:hidden;margin-top:32px}.vc-unit-bar{display:flex;border-bottom:1px solid var(--vc-border-light);background:var(--vc-surface-alt)}.vc-unit-btn{flex:1;padding:12px;border:none;background:transparent;font-family:var(--vc-font);font-size:13px;font-weight:600;color:var(--vc-ink-muted);cursor:pointer;position:relative}.vc-unit-btn.vc-active{color:var(--vc-accent);background:var(--vc-surface)}.vc-unit-btn.vc-active::after{content:'';position:absolute;bottom:-1px;left:16px;right:16px;height:2px;background:var(--vc-accent)}.vc-form{padding:24px}.vc-form-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px}@media(max-width:600px){.vc-form-grid{grid-template-columns:1fr}}.vc-field{display:flex;flex-direction:column}.vc-label{font-size:12px;font-weight:600;letter-spacing:.04em;text-transform:uppercase;color:var(--vc-ink-secondary);margin-bottom:6px}.vc-label-hint{font-weight:400;text-transform:none;color:var(--vc-ink-muted);font-size:11px}.vc-select,.vc-input{width:100%;padding:10px 12px;border:1.5px solid var(--vc-border);border-radius:6px;font-family:var(--vc-font);font-size:14px;color:var(--vc-ink);background:var(--vc-surface)}.vc-select{padding-right:36px;appearance:none;cursor:pointer;background-image:url(\"data:image\/svg+xml,%3Csvg xmlns='http:\/\/www.w3.org\/2000\/svg' width='16' height='16' fill='none' stroke='%235a5650' stroke-width='2'%3E%3Cpath d='M4 6l4 4 4-4'\/%3E%3C\/svg%3E\");background-repeat:no-repeat;background-position:right 10px center}.vc-select:focus,.vc-input:focus{outline:none;border-color:var(--vc-accent);box-shadow:0 0 0 3px rgba(200,90,42,.12)}.vc-presets{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px;padding-top:18px;border-top:1px solid var(--vc-border-light)}.vc-presets-label{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:.1em;text-transform:uppercase;color:var(--vc-ink-muted);width:100%;margin-bottom:2px}.vc-preset-btn{padding:5px 12px;font-family:var(--vc-font);font-size:12px;font-weight:500;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);cursor:pointer}.vc-preset-btn:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}.vc-results{border-top:1px solid var(--vc-border-light);background:var(--vc-surface-alt);padding:0;max-height:0;overflow:hidden;transition:max-height .5s cubic-bezier(.4,0,.2,1),padding .3s}.vc-results.vc-visible{max-height:2000px;padding:24px}.vc-results-head{display:flex;align-items:center;justify-content:space-between;margin-bottom:18px}.vc-results-title{font-family:var(--vc-display);font-size:20px;font-weight:700;margin:0}.vc-copy-btn{display:inline-flex;align-items:center;gap:5px;padding:6px 12px;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface);font-size:12px;font-weight:500;color:var(--vc-ink-secondary);cursor:pointer}.vc-copy-btn.vc-copied{background:var(--vc-green-light);border-color:var(--vc-green);color:var(--vc-green)}.vc-result-grid{display:grid;grid-template-columns:1fr 1fr;gap:12px}@media(max-width:500px){.vc-result-grid{grid-template-columns:1fr}}.vc-rcard{background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px}.vc-rcard-primary{border-color:var(--vc-accent);border-width:2px;background:linear-gradient(135deg,#fdf6f2,var(--vc-surface));grid-column:1\/-1}.vc-rcard-label{font-family:var(--vc-mono);font-size:10px;font-weight:500;letter-spacing:.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:4px}.vc-rcard-value{font-family:var(--vc-mono);font-size:22px;font-weight:600;color:var(--vc-ink)}.vc-rcard-primary .vc-rcard-value{font-size:30px;color:var(--vc-accent)}.vc-rcard-unit{font-size:14px;font-weight:400;color:var(--vc-ink-secondary)}.vc-section{margin-top:24px;border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);background:var(--vc-surface);box-shadow:var(--vc-shadow);overflow:hidden}.vc-section-toggle{width:100%;display:flex;align-items:center;justify-content:space-between;padding:18px 24px;border:none;background:transparent;cursor:pointer;font-family:var(--vc-font);text-align:left}.vc-section-toggle:hover{background:var(--vc-surface-alt)}.vc-section-toggle-text{display:flex;align-items:center;gap:10px}.vc-section-icon{font-size:20px}.vc-section-title{font-family:var(--vc-display);font-size:18px;font-weight:700;margin:0}.vc-section-chevron{width:20px;height:20px;color:var(--vc-ink-muted);transition:transform .3s}.vc-section.vc-open .vc-section-chevron{transform:rotate(180deg)}.vc-section-body{max-height:0;overflow:hidden;transition:max-height .4s}.vc-section.vc-open .vc-section-body{max-height:20000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--vc-border-light)}.vc-theory h3{font-family:var(--vc-display);font-size:17px;font-weight:700;margin:28px 0 10px}.vc-theory h3:first-child{margin-top:20px}.vc-theory p{font-size:14px;color:var(--vc-ink-secondary);margin:0 0 10px}.vc-formula-box{background:var(--vc-surface-alt);border:2px solid var(--vc-border);border-radius:6px;padding:14px 20px;text-align:center;margin:14px 0;overflow-x:auto}.vc-warning-box{background:var(--vc-yellow-light);border-left:3px solid var(--vc-yellow);padding:14px 16px;border-radius:0 6px 6px 0;margin:14px 0}.vc-faq-list{display:flex;flex-direction:column;gap:8px;margin-top:20px}.vc-faq-item{border:1px solid var(--vc-border-light);border-radius:6px;overflow:hidden}.vc-faq-q{width:100%;display:flex;align-items:center;justify-content:space-between;gap:12px;padding:14px 16px;border:none;background:var(--vc-surface-alt);cursor:pointer;font-family:var(--vc-font);font-size:15px;font-weight:600;color:var(--vc-ink);text-align:left}.vc-faq-q:hover{background:#ede9e3}.vc-faq-chevron{width:16px;height:16px;color:var(--vc-ink-muted);transition:transform .25s}.vc-faq-item.vc-open .vc-faq-chevron{transform:rotate(180deg)}.vc-faq-a{max-height:0;overflow:hidden;transition:max-height .35s}.vc-faq-item.vc-open .vc-faq-a{max-height:1200px}.vc-faq-a-inner{padding:14px 16px;border-top:1px solid var(--vc-border-light);font-size:14px;color:var(--vc-ink-secondary)}.vc-faq-a-inner p{margin:0 0 8px}.vc-faq-a-inner p:last-child{margin-bottom:0}.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.vc-related-link{display:inline-block;padding:8px 16px;font-size:13px;font-weight:600;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);border:1px solid var(--vc-border);border-radius:var(--vc-radius);text-decoration:none}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none}.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}@media print{.vc-section-body{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-presets,.vc-promo{display:none!important}}<\/style>\n\n<div class=\"vc-calculator\">\n<header class=\"vc-header\">\n<p class=\"vc-header-eyebrow\">Free Engineering Tool #072<\/p>\n<h1 class=\"vc-header-title\">Shaft Deflection Calculator<\/h1>\n<p class=\"vc-header-subtitle\">Calculate shaft deflection under various loading conditions: center point, offset point, distributed, or cantilever.<\/p>\n<div class=\"vc-badges\"><span class=\"vc-badge\">Beam Formulas<\/span><span class=\"vc-badge\">4 Load Types<\/span><span class=\"vc-badge\">Auto-Calc<\/span><\/div>\n<\/header>\n<div class=\"vc-card\">\n<div class=\"vc-unit-bar\"><button type=\"button\" class=\"vc-unit-btn vc-active\" data-system=\"metric\">Metric (mm, N, GPa)<\/button><button type=\"button\" class=\"vc-unit-btn\" data-system=\"imperial\">Imperial (in, lbf, Mpsi)<\/button><\/div>\n<form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\">\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-len\">Shaft Length L <span class=\"vc-label-hint\" id=\"vc-lu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-len\" step=\"any\" min=\"1\" value=\"500\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-dia\">Shaft Diameter d <span class=\"vc-label-hint\" id=\"vc-du\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-dia\" step=\"any\" min=\"1\" value=\"40\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-E\">Young&#8217;s Modulus E <span class=\"vc-label-hint\" id=\"vc-eu\">(GPa)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-E\" step=\"any\" min=\"1\" value=\"210\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-load\">Load F or w <span class=\"vc-label-hint\" id=\"vc-flu\">(N or N\/mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-load\" step=\"any\" min=\"0\" value=\"5000\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-type\">Load Type<\/label><select class=\"vc-select\" id=\"vc-type\"><option value=\"center\" selected>Point at Center<\/option><option value=\"offset\">Point at Position a<\/option><option value=\"distributed\">Uniform Distributed<\/option><option value=\"cantilever\">Cantilever End Load<\/option><\/select><\/div>\n<div class=\"vc-field\" id=\"vc-f-a\" style=\"display:none\"><label class=\"vc-label\" for=\"vc-apos\">Position a <span class=\"vc-label-hint\" id=\"vc-au\">(mm from left)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-apos\" step=\"any\" min=\"0\" value=\"200\"><\/div>\n<\/div>\n<div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div>\n<button type=\"button\" class=\"vc-preset-btn\" data-l=\"500\" data-d=\"40\" data-f=\"5000\" data-t=\"center\">Center 5kN L500 d40<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-l=\"300\" data-d=\"30\" data-f=\"1000\" data-t=\"cantilever\">Cantilever 1kN L300 d30<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-l=\"600\" data-d=\"50\" data-f=\"10\" data-t=\"distributed\">Distrib 10N\/mm L600 d50<\/button>\n<\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div>\n<div class=\"vc-result-grid\">\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Maximum Deflection<\/div><div class=\"vc-rcard-value\" id=\"vc-r-def\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Max Slope<\/div><div class=\"vc-rcard-value\" id=\"vc-r-slope\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Moment of Inertia I<\/div><div class=\"vc-rcard-value\" id=\"vc-r-I\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Max Bending Moment<\/div><div class=\"vc-rcard-value\" id=\"vc-r-M\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Max Bending Stress<\/div><div class=\"vc-rcard-value\" id=\"vc-r-sig\">&mdash;<\/div><\/div>\n<\/div><\/div><\/div>\n\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x1F4D8;<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\n<h3>Simply Supported &#8211; Center Load<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n<h3>Simply Supported &#8211; Distributed<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n<h3>Cantilever &#8211; End Load<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n<h3>Moment of Inertia<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-4\"><\/div>\n<div class=\"vc-warning-box\"><p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary)\">Critical speed: N<sub>cr<\/sub> = 946\/&radic;&delta;<sub>mm<\/sub> RPM. Assumes uniform shaft and simply supported.<\/p><\/div>\n<\/div><\/div><\/div>\n\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x1F517;<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\">\n<a class=\"vc-related-link\" href=\"\/calculators\/shaft-diameter-torsion\/\">Shaft Diameter<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/rotor-moment-of-inertia\/\">Moment of Inertia<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/keyway-calculator\/\">Keyway Calculator<\/a>\n<a class=\"vc-related-link\" href=\"\/calculators\/ball-screw-calculator\/\">Ball Screw<\/a>\n<\/div><\/div><\/div><\/div>\n\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">&#x2753;<\/span><span class=\"vc-section-title\">FAQ<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera<\/strong> &mdash; Portable Balancing &amp; Vibration Analysis. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n<footer class=\"vc-footer\"><p>&copy; 2024&ndash;2025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n<\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n'use strict';\nvar SLUG='shaft-deflection-calculator',uS='metric';\nfunction $(id){return document.getElementById(id)}\nfunction fmt(n,d){if(isNaN(n)||!isFinite(n))return'\\u2014';return n.toFixed(d==null?2:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\n$('vc-type').addEventListener('change',function(){$('vc-f-a').style.display=this.value==='offset'?'flex':'none';calc()});\n\nfunction calc(){\n  var L=parseFloat($('vc-len').value),d=parseFloat($('vc-dia').value),E=parseFloat($('vc-E').value),F=parseFloat($('vc-load').value),type=$('vc-type').value,a=parseFloat($('vc-apos').value)||0;\n  if(!L||L<=0||!d||d<=0||!E||E<=0||!F||F<=0){$('vc-results').classList.remove('vc-visible');return}\n  var Lmm=uS==='imperial'?L*25.4:L,dmm=uS==='imperial'?d*25.4:d,Empa=uS==='imperial'?E*6894.76:E*1000,Fn=uS==='imperial'?F*4.44822:F,amm=uS==='imperial'?a*25.4:a;\n  var I=Math.PI*Math.pow(dmm,4)\/64,def,Mmax,slope;\n  if(type==='center'){def=Fn*Math.pow(Lmm,3)\/(48*Empa*I);Mmax=Fn*Lmm\/4;slope=Fn*Lmm*Lmm\/(16*Empa*I)}\n  else if(type==='offset'){var b=Lmm-amm;if(amm<=0||amm>=Lmm){$('vc-results').classList.remove('vc-visible');return}def=Fn*amm*amm*b*b\/(3*Empa*I*Lmm);Mmax=Fn*amm*b\/Lmm;slope=Fn*amm*b*(Lmm+Math.max(amm,b))\/(6*Empa*I*Lmm)}\n  else if(type==='distributed'){if(uS==='imperial'){Fn=Fn\/25.4}def=5*Fn*Math.pow(Lmm,4)\/(384*Empa*I);Mmax=Fn*Lmm*Lmm\/8;slope=Fn*Math.pow(Lmm,3)\/(24*Empa*I)}\n  else{def=Fn*Math.pow(Lmm,3)\/(3*Empa*I);Mmax=Fn*Lmm;slope=Fn*Lmm*Lmm\/(2*Empa*I)}\n  var sigma=Mmax*(dmm\/2)\/I;\n  if(uS==='imperial'){$('vc-r-def').innerHTML=fmt(def\/25.4,4)+' <span class=\"vc-rcard-unit\">in<\/span>';$('vc-r-I').innerHTML=fmt(I\/Math.pow(25.4,4),4)+' <span class=\"vc-rcard-unit\">in\\u2074<\/span>';$('vc-r-M').innerHTML=fmt(Mmax*0.000738,2)+' <span class=\"vc-rcard-unit\">lbf\\u00B7ft<\/span>';$('vc-r-sig').innerHTML=fmt(sigma*145.038,0)+' <span class=\"vc-rcard-unit\">psi<\/span>'}\n  else{$('vc-r-def').innerHTML=fmt(def,4)+' <span class=\"vc-rcard-unit\">mm<\/span>';$('vc-r-I').innerHTML=fmt(I,0)+' <span class=\"vc-rcard-unit\">mm\\u2074<\/span>';$('vc-r-M').innerHTML=fmt(Mmax\/1e3,1)+' <span class=\"vc-rcard-unit\">N\\u00B7m<\/span>';$('vc-r-sig').innerHTML=fmt(sigma,1)+' <span class=\"vc-rcard-unit\">MPa<\/span>'}\n  $('vc-r-slope').innerHTML=fmt(slope*1000,3)+' <span class=\"vc-rcard-unit\">mrad<\/span>';\n  $('vc-results').classList.add('vc-visible');\n  sH({L:L,d:d,F:F,type:type,_summary:type+' F='+F+' L='+L+' d='+d});\n}\n\nvar uB=document.querySelectorAll('.vc-unit-btn');uB.forEach(function(b){b.addEventListener('click',function(){uB.forEach(function(x){x.classList.remove('vc-active')});this.classList.add('vc-active');uS=this.getAttribute('data-system');$('vc-lu').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-du').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-eu').textContent=uS==='imperial'?'(Mpsi)':'(GPa)';$('vc-flu').textContent=uS==='imperial'?'(lbf or lbf\/in)':'(N or N\/mm)';$('vc-au').textContent=uS==='imperial'?'(in)':'(mm)';calc()})});\ndocument.querySelectorAll('.vc-preset-btn').forEach(function(b){b.addEventListener('click',function(e){e.preventDefault();$('vc-len').value=this.getAttribute('data-l');$('vc-dia').value=this.getAttribute('data-d');$('vc-load').value=this.getAttribute('data-f');$('vc-type').value=this.getAttribute('data-t');$('vc-f-a').style.display=this.getAttribute('data-t')==='offset'?'flex':'none';calc()})});\n$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);\n$('vc-copy-btn').addEventListener('click',function(){var t='Shaft Deflection\\nDeflection: '+$('vc-r-def').textContent+'\\nStress: '+$('vc-r-sig').textContent+'\\nMoment: '+$('vc-r-M').textContent;if(navigator.clipboard){navigator.clipboard.writeText(t).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.textContent='Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.textContent='Copy'},2000)})}});\ndocument.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\nvar fD=[{q:'Which load type to choose?',a:'<p>Center: symmetric. Offset: asymmetric. Distributed: self-weight. Cantilever: overhung.<\/p>'},{q:'Acceptable deflection?',a:'<p>General: L\/3000. Gear shafts: L\/5000. Precision: L\/10000.<\/p>'},{q:'How does diameter affect deflection?',a:'<p>1\/d\\u2074 via I. Doubling d reduces deflection 16x.<\/p>'},{q:'Stepped shafts?',a:'<p>Use Castigliano, transfer matrix, or FEA.<\/p>'},{q:'Critical speed from deflection?',a:'<p>N<sub>cr<\/sub>=946\/\\u221A\\u03B4<sub>mm<\/sub> RPM.<\/p>'}];\nvar fL=$('vc-faq-list');fD.forEach(function(f){fL.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\nfL.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\nfunction sH(e){var k='vc_history_'+SLUG,a=[];try{a=JSON.parse(localStorage.getItem(k))||[]}catch(x){}e._ts=new Date().toISOString();a.unshift(e);if(a.length>10)a=a.slice(0,10);try{localStorage.setItem(k,JSON.stringify(a))}catch(x){}}\n\nfunction rF(){try{\nkatex.render('\\\\delta_{max}=\\\\frac{FL^3}{48EI}',$('vc-katex-1'),{displayMode:true,throwOnError:false});\nkatex.render('\\\\delta_{max}=\\\\frac{5wL^4}{384EI}',$('vc-katex-2'),{displayMode:true,throwOnError:false});\nkatex.render('\\\\delta_{max}=\\\\frac{FL^3}{3EI}',$('vc-katex-3'),{displayMode:true,throwOnError:false});\nkatex.render('I=\\\\frac{\\\\pi d^4}{64}',$('vc-katex-4'),{displayMode:true,throwOnError:false});\n}catch(e){}}\nrF();calc();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>T\u00ednh to\u00e1n \u0111\u1ed9 v\u00f5ng c\u1ee7a tr\u1ee5c d\u01b0\u1edbi t\u00e1c d\u1ee5ng c\u1ee7a t\u1ea3i tr\u1ecdng t\u1eadp trung, t\u1ea3i tr\u1ecdng l\u1ec7ch t\u00e2m, t\u1ea3i tr\u1ecdng ph\u00e2n b\u1ed1 ho\u1eb7c t\u1ea3i tr\u1ecdng d\u1ea7m \u043a\u043e\u043d\u0441\u043e\u043b\u044c. Nh\u1eadp chi\u1ec1u d\u00e0i, \u0111\u01b0\u1eddng k\u00ednh, E v\u00e0 t\u1ea3i tr\u1ecdng.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100222","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100222\/revisions"}],"predecessor-version":[{"id":102567,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100222\/revisions\/102567"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/media?parent=100222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/categories?post=100222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/tags?post=100222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}