{"id":100223,"date":"2026-02-15T20:28:12","date_gmt":"2026-02-15T20:28:12","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100223"},"modified":"2026-03-05T15:43:12","modified_gmt":"2026-03-05T15:43:12","slug":"shaft-diameter-torsion","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/tl\/calculators\/shaft-diameter-torsion\/","title":{"rendered":"Shaft Diameter for Torsion Calculator | Libreng Tool"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Shaft Diameter for Torsion Calculator\",\"alternateName\":[\"Torsion Shaft Calculator\",\"Shaft Sizing Calculator\"],\"description\":\"Calculate minimum shaft diameter for pure torsion loading. Enter torque and allowable shear stress.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/shaft-diameter-torsion\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-06-01\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Solid and hollow shaft\",\"Multiple material presets\",\"Safety factor display\",\"Auto-calculation\"],\"keywords\":\"shaft diameter, torsion, shear stress, torque, shaft design\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is the formula for minimum shaft diameter under torsion?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For a solid circular shaft: d = \u221b(16T\/(\u03c0\u03c4_all)), where T is the applied torque and \u03c4_all is the allowable shear stress. This comes from the torsion formula \u03c4 = Tc\/J = 16T\/(\u03c0d\u00b3) for a solid shaft.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I choose the allowable shear stress?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The allowable shear stress is typically 50-60% of the tensile yield strength: \u03c4_all = 0.577 \u00d7 \u03c3_y (von Mises criterion). For steel AISI 1045: \u03c4_all \u2248 180 MPa. Apply a safety factor of 1.5-3.0 depending on application criticality and loading type.\"}},\n{\"@type\":\"Question\",\"name\":\"How does a hollow shaft compare to a solid shaft?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A hollow shaft with the same outer diameter has slightly less torsional strength but much less weight. The strength ratio is (1-k\u2074) where k = d_i\/d_o. For k = 0.5 (ID = half OD), you retain 93.75% of strength at about 75% of the weight.\"}},\n{\"@type\":\"Question\",\"name\":\"Should I account for keyways and stress concentrations?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Yes. Keyways reduce shaft strength by 25-50% depending on type. Apply a stress concentration factor Kt (typically 1.6-3.0 for keyways). The effective stress becomes \u03c4_eff = Kt \u00d7 \u03c4. Size the shaft for the concentrated stress or reduce the allowable stress accordingly.\"}},\n{\"@type\":\"Question\",\"name\":\"What about combined bending and torsion?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"When both bending moment M and torque T act, use the equivalent torque: T_eq = \u221a(M\u00b2 + T\u00b2) for maximum shear stress theory, or T_eq = \u221a(M\u00b2 + 0.75T\u00b2) for von Mises criterion. Then size the shaft using T_eq in place of T.\"}}\n]}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[\n{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},\n{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},\n{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Shaft Diameter for Torsion\",\"item\":\"https:\/\/vibromera.eu\/calculators\/shaft-diameter-torsion\/\"}\n]}\n<\/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 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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;white-space:nowrap;transition:background .15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}\n.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 a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\n@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-shaft-torsion\">\n\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool #071<\/p>\n    <h1 class=\"vc-header-title\">Shaft Diameter for Torsion Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate the minimum shaft diameter required to transmit a given torque. Enter torque, allowable shear stress, and material to get the required diameter with safety factor.<\/p>\n    <div class=\"vc-badges\"><span class=\"vc-badge\">Shafts &amp; Rotors<\/span><span class=\"vc-badge\">Solid &amp; Hollow<\/span><span class=\"vc-badge\">Auto-Calc<\/span><\/div>\n<\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-T\">Torque T <span class=\"vc-label-hint\">(N\u00b7m)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-T\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 500\" value=\"500\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-tau\">Allowable Shear Stress \u03c4<sub>all<\/sub> <span class=\"vc-label-hint\">(MPa)<\/span><\/label>\n                <select class=\"vc-select\" id=\"vc-tau\">\n                    <option value=\"40\">Mild Steel (AISI 1020) \u2014 40 MPa<\/option>\n                    <option value=\"80\" selected>Med Carbon (AISI 1045) \u2014 80 MPa<\/option>\n                    <option value=\"110\">Alloy Steel (4140) \u2014 110 MPa<\/option>\n                    <option value=\"140\">High-Strength (4340) \u2014 140 MPa<\/option>\n                    <option value=\"25\">Stainless 304 \u2014 25 MPa<\/option>\n                    <option value=\"custom\">Custom value&#8230;<\/option>\n                <\/select>\n            <\/div>\n            <div class=\"vc-field\" id=\"vc-custom-tau-field\" style=\"display:none\">\n                <label class=\"vc-label\" for=\"vc-tau-custom\">Custom \u03c4<sub>all<\/sub> <span class=\"vc-label-hint\">(MPa)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-tau-custom\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 60\" value=\"60\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-sf\">Safety Factor<\/label>\n                <select class=\"vc-select\" id=\"vc-sf\">\n                    <option value=\"1.5\">1.5 \u2014 Steady load, known conditions<\/option>\n                    <option value=\"2.0\" selected>2.0 \u2014 Normal service<\/option>\n                    <option value=\"2.5\">2.5 \u2014 Shock\/impact possible<\/option>\n                    <option value=\"3.0\">3.0 \u2014 Heavy shock, uncertain loads<\/option>\n                <\/select>\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-hollow\">Shaft Type<\/label>\n                <select class=\"vc-select\" id=\"vc-hollow\">\n                    <option value=\"0\" selected>Solid shaft<\/option>\n                    <option value=\"0.3\">Hollow \u2014 k = 0.3 (d_i\/d_o)<\/option>\n                    <option value=\"0.5\">Hollow \u2014 k = 0.5<\/option>\n                    <option value=\"0.7\">Hollow \u2014 k = 0.7<\/option>\n                <\/select>\n            <\/div>\n        <\/div>\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-T=\"100\" data-tau=\"80\" data-sf=\"2.0\" data-k=\"0\">Small motor 100 N\u00b7m<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-T=\"500\" data-tau=\"80\" data-sf=\"2.0\" data-k=\"0\">Pump drive 500 N\u00b7m<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-T=\"5000\" data-tau=\"110\" data-sf=\"2.5\" data-k=\"0\">Industrial 5 kN\u00b7m<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Minimum Shaft Diameter<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-d\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Actual Shear Stress<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-tau\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Safety Factor Applied<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-sf\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Polar Moment J<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-J\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Angle of Twist (per m)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-theta\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/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\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Minimum Diameter (Solid Shaft)<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <h3>Hollow Shaft<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <h3>Angle of Twist<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <table class=\"vc-table\">\n                <thead><tr><th>Material<\/th><th>\u03c3_y (MPa)<\/th><th>\u03c4_all (MPa)<\/th><th>G (GPa)<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>AISI 1020 (mild)<\/td><td>210<\/td><td>40<\/td><td>79<\/td><\/tr>\n                    <tr><td>AISI 1045 (medium)<\/td><td>310<\/td><td>80<\/td><td>79<\/td><\/tr>\n                    <tr><td>AISI 4140 (alloy)<\/td><td>415<\/td><td>110<\/td><td>80<\/td><\/tr>\n                    <tr><td>AISI 4340 (high-str)<\/td><td>470<\/td><td>140<\/td><td>80<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n            <div class=\"vc-warning-box\"><p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary);\"><strong>\u26a0\ufe0f Note:<\/strong> This calculator sizes for pure torsion only. For combined bending + torsion, use the equivalent torque method. Always account for keyways and stress concentrations.<\/p><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/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-deflection-calculator\/\">Shaft Deflection<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/keyway-calculator\/\">Keyway Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/press-fit-calculator\/\">Press-Fit Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/rotor-moment-of-inertia\/\">Rotor Moment of Inertia<\/a>\n    <\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/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>\n<\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional field balancing instruments and software.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p><p style=\"font-size:12px;margin-top:4px;\">Shaft diameter for torsion. Last updated: June 2025<\/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\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n    'use strict';\n    var SLUG='shaft-diameter-torsion';\n    function $(id){return document.getElementById(id)}\n    function fmt(n,d){if(isNaN(n)||!isFinite(n))return '\u2014';var f=n.toFixed(d===undefined?2:d);return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\n    \/\/ G values in GPa by tau\n    var Gmap={'40':79,'80':79,'110':80,'140':80,'25':77,'custom':79};\n\n    $('vc-tau').addEventListener('change',function(){\n        $('vc-custom-tau-field').style.display=this.value==='custom'?'flex':'none';\n    });\n\n    function calculate(){\n        var T=parseFloat($('vc-T').value); \/\/ N\u00b7m\n        var tauSel=$('vc-tau').value;\n        var tauAll=tauSel==='custom'?parseFloat($('vc-tau-custom').value):parseFloat(tauSel);\n        var sf=parseFloat($('vc-sf').value);\n        var k=parseFloat($('vc-hollow').value);\n        if(!T||T<=0||!tauAll||tauAll<=0){$('vc-results').classList.remove('vc-visible');return}\n\n        var tauDesign=tauAll\/sf; \/\/ MPa\n        var Tmm=T*1000; \/\/ N\u00b7mm\n\n        var dMin;\n        if(k===0){\n            dMin=Math.pow(16*Tmm\/(Math.PI*tauDesign),1\/3);\n        } else {\n            dMin=Math.pow(16*Tmm\/(Math.PI*tauDesign*(1-Math.pow(k,4))),1\/3);\n        }\n\n        \/\/ Round up to nearest mm\n        var dRound=Math.ceil(dMin);\n\n        \/\/ Actual stress with rounded diameter\n        var J;\n        if(k===0){\n            J=Math.PI*Math.pow(dRound,4)\/32;\n        } else {\n            var di=k*dRound;\n            J=Math.PI*(Math.pow(dRound,4)-Math.pow(di,4))\/32;\n        }\n        var tauActual=Tmm*dRound\/2\/J; \/\/ MPa\n\n        \/\/ Angle of twist per meter\n        var G=(Gmap[tauSel]||79)*1000; \/\/ MPa\n        var thetaRad=Tmm*1000\/(G*J); \/\/ rad\/m (T in N\u00b7mm, L=1000mm)\n        var thetaDeg=thetaRad*180\/Math.PI;\n\n        $('vc-r-d').innerHTML=fmt(dMin,1)+' <span class=\"vc-rcard-unit\">mm<\/span> <span class=\"vc-rcard-unit\">(round up: '+dRound+' mm)<\/span>';\n        $('vc-r-tau').innerHTML=fmt(tauActual,1)+' <span class=\"vc-rcard-unit\">MPa<\/span> <span class=\"vc-rcard-unit\">(allow: '+fmt(tauAll,0)+' MPa)<\/span>';\n        $('vc-r-sf').innerHTML=fmt(sf,1)+' <span class=\"vc-rcard-unit\">(design \u03c4 = '+fmt(tauDesign,1)+' MPa)<\/span>';\n        $('vc-r-J').innerHTML=fmt(J,0)+' <span class=\"vc-rcard-unit\">mm\u2074<\/span>';\n        $('vc-r-theta').innerHTML=fmt(thetaDeg,3)+' <span class=\"vc-rcard-unit\">\u00b0\/m<\/span>';\n        $('vc-results').classList.add('vc-visible');\n\n        saveHistory({T:T,tau:tauAll,sf:sf,d:fmt(dMin,1),_summary:'T='+T+' N\u00b7m \u2192 d='+fmt(dMin,1)+' mm'});\n    }\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn){btn.addEventListener('click',function(e){e.preventDefault();$('vc-T').value=this.getAttribute('data-T');$('vc-tau').value=this.getAttribute('data-tau');$('vc-sf').value=this.getAttribute('data-sf');$('vc-hollow').value=this.getAttribute('data-k');$('vc-custom-tau-field').style.display='none';calculate()})});\n\n    $('vc-form').addEventListener('input',calculate);\n    $('vc-form').addEventListener('change',calculate);\n\n    $('vc-copy-btn').addEventListener('click',function(){\n        var text='Shaft Diameter (Torsion)\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nTorque: '+$('vc-T').value+' N\u00b7m\\nMin Diameter: '+$('vc-r-d').textContent+'\\nShear Stress: '+$('vc-r-tau').textContent+'\\nSafety Factor: '+$('vc-r-sf').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu';\n        if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'},2000)})}\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\n    var faqData=[\n        {q:'What is the formula for minimum shaft diameter under torsion?',a:'<p>For a solid shaft: d = \u221b(16T\/(\u03c0\u03c4_all)). This comes from the torsion formula \u03c4 = 16T\/(\u03c0d\u00b3). Apply a safety factor by using \u03c4_design = \u03c4_all \/ SF.<\/p>'},\n        {q:'How do I choose the allowable shear stress?',a:'<p>Allowable shear stress is typically 50\u201360% of tensile yield: \u03c4_all \u2248 0.577 \u00d7 \u03c3_y (von Mises). Apply safety factor 1.5\u20133.0 depending on application.<\/p>'},\n        {q:'How does a hollow shaft compare to solid?',a:'<p>A hollow shaft with k = d_i\/d_o = 0.5 retains 93.75% of torsional strength at about 75% of the weight. The diameter increases by factor 1\/(1\u2212k\u2074)^(1\/3).<\/p>'},\n        {q:'Should I account for keyways?',a:'<p>Yes. Keyways reduce shaft strength by 25\u201350%. Apply stress concentration factor Kt (typically 1.6\u20133.0). Size the shaft accordingly or reduce allowable stress.<\/p>'},\n        {q:'What about combined bending and torsion?',a:'<p>Use equivalent torque: T_eq = \u221a(M\u00b2 + T\u00b2) for max shear stress theory, or T_eq = \u221a(M\u00b2 + 0.75T\u00b2) for von Mises. Then size using T_eq.<\/p>'}\n    ];\n    var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\n    fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(!b)return;b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\n    function saveHistory(entry){var key='vc_history_'+SLUG;var arr=[];try{arr=JSON.parse(localStorage.getItem(key))||[]}catch(e){}entry._ts=new Date().toISOString();arr.unshift(entry);if(arr.length>10)arr=arr.slice(0,10);try{localStorage.setItem(key,JSON.stringify(arr))}catch(e){}}\n\n    function renderFormulas(){\n        try{\n            katex.render('d = \\\\sqrt[3]{\\\\frac{16T}{\\\\pi \\\\tau_{all}\/SF}}',$('vc-katex-1'),{displayMode:true,throwOnError:false});\n            katex.render('d_o = \\\\sqrt[3]{\\\\frac{16T}{\\\\pi \\\\tau_{design}(1-k^4)}}, \\\\quad k = \\\\frac{d_i}{d_o}',$('vc-katex-2'),{displayMode:true,throwOnError:false});\n            katex.render('\\\\theta = \\\\frac{TL}{GJ} \\\\quad [\\\\text{rad}]',$('vc-katex-3'),{displayMode:true,throwOnError:false});\n        }catch(e){}\n    }\n\n    function init(){renderFormulas();calculate()}\n    if(document.readyState==='loading'){document.addEventListener('DOMContentLoaded',init)}else{init()}\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Libreng online na kalkulador para sa minimum na diameter ng shaft sa ilalim ng torsion. Maglagay ng torque at pinapayagang shear stress upang makalkula ang kinakailangang diameter. Nagpapakita ng safety factor at polar moment of inertia.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100223","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/calculator\/100223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/calculator\/100223\/revisions"}],"predecessor-version":[{"id":100775,"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/calculator\/100223\/revisions\/100775"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/media?parent=100223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/categories?post=100223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/tl\/wp-json\/wp\/v2\/tags?post=100223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}