{"id":100248,"date":"2026-02-15T20:29:37","date_gmt":"2026-02-15T20:29:37","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100248"},"modified":"2026-03-05T15:40:46","modified_gmt":"2026-03-05T15:40:46","slug":"stress-concentration-factor","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/sw\/calculators\/stress-concentration-factor\/","title":{"rendered":"Kikokotoo cha Sababu ya Mkusanyiko wa Msongo Kt | Vibromera"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Stress Concentration Factor Calculator\",\"description\":\"Kt calculator for common geometries: hole in plate, shoulder fillet, U-notch, V-notch.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/stress-concentration-factor\/\",\"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\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is stress concentration factor Kt?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Kt is the ratio of maximum local stress to nominal stress at a geometric discontinuity. Kt = \u03c3_max \/ \u03c3_nom. It depends only on geometry, not material. A circular hole in a wide plate under tension has Kt \u2248 3.0.\"}},\n{\"@type\":\"Question\",\"name\":\"What causes stress concentrations?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Any abrupt change in geometry: holes, notches, fillets, keyways, threads, grooves, changes in cross-section. The stress flow lines crowd together at these features, increasing local stress.\"}},\n{\"@type\":\"Question\",\"name\":\"How does Kt affect fatigue life?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Stress concentrations dramatically reduce fatigue life because fatigue cracks initiate at the point of highest stress. The fatigue notch factor Kf \u2264 Kt accounts for material sensitivity: Kf = 1 + q(Kt-1), where q is the notch sensitivity factor.\"}},\n{\"@type\":\"Question\",\"name\":\"How can stress concentrations be reduced?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use generous fillet radii, avoid sharp corners, use gradual transitions, add relief grooves near shoulders, polish surfaces at critical points, and use shot peening to introduce beneficial compressive residual stress.\"}},\n{\"@type\":\"Question\",\"name\":\"What is Peterson's Stress Concentration Factors?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Peterson's is the definitive reference book containing charts and equations for Kt values for hundreds of geometric configurations. It provides Kt as a function of geometric ratios (r\/d, D\/d, etc.) for tension, bending, and torsion loading.\"}}\n]}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@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\":\"Stress Concentration Factor\",\"item\":\"https:\/\/vibromera.eu\/calculators\/stress-concentration-factor\/\"}]}\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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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}@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-scf\">\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p>\n    <h1 class=\"vc-header-title\">Stress Concentration Factor Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Look up Kt for common geometries \u2014 hole in plate, shoulder fillet, U-notch \u2014 using simplified Peterson&#8217;s chart data.<\/p>\n    <div class=\"vc-badges\"><span class=\"vc-badge\">Peterson&#8217;s Charts<\/span><span class=\"vc-badge\">Kt Lookup<\/span><span class=\"vc-badge\">#173<\/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 vc-field-full\">\n                <label class=\"vc-label\" for=\"vc-geom\">Geometry<\/label>\n                <select class=\"vc-select\" id=\"vc-geom\">\n                    <option value=\"hole\" selected>Central Hole in Flat Plate (tension)<\/option>\n                    <option value=\"shoulder\">Shoulder Fillet \u2014 Stepped Round Bar (tension)<\/option>\n                    <option value=\"notch\">U-Notch in Flat Plate (tension)<\/option>\n                    <option value=\"groove\">Circumferential Groove in Round Bar (tension)<\/option>\n                <\/select>\n            <\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-W\">Width W or D_major <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-W\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 100\" value=\"100\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-d\" id=\"vc-d-label\">Hole dia d or d_minor <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-d\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 20\" value=\"20\"><\/div>\n            <div class=\"vc-field\" id=\"vc-field-r\"><label class=\"vc-label\" for=\"vc-r\">Fillet\/Notch Radius r <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-r\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 5\" value=\"5\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-snom\">Nominal Stress \u03c3_nom <span class=\"vc-label-hint\">(MPa, optional)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-snom\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 100\" value=\"100\"><\/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-geom=\"hole\" data-W=\"100\" data-d=\"10\" data-r=\"5\">Plate W=100, hole d=10<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-geom=\"shoulder\" data-W=\"50\" data-d=\"30\" data-r=\"3\">Shaft D=50\u2192d=30, r=3<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-geom=\"notch\" data-W=\"80\" data-d=\"60\" data-r=\"5\">Notch plate W=80, d=60, r=5<\/button>\n        <\/div>\n    <\/form>\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><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><\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Stress Concentration Factor Kt<\/div><div class=\"vc-rcard-value\" id=\"vc-r-Kt\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Max Local Stress \u03c3_max<\/div><div class=\"vc-rcard-value\" id=\"vc-r-smax\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Geometry Ratio<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div><\/div>\n        <\/div>\n        <div class=\"vc-viz\" id=\"vc-viz\" style=\"text-align:center;margin:16px 0 8px\"><\/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\"><div class=\"vc-section-inner vc-theory\">\n        <h3>Stress Concentration Factor<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n        <h3>Typical Kt Values<\/h3>\n        <table class=\"vc-table\">\n            <thead><tr><th>Geometry<\/th><th>Kt Range<\/th><\/tr><\/thead>\n            <tbody>\n                <tr><td>Central hole in wide plate<\/td><td>~3.0 (small d\/W)<\/td><\/tr>\n                <tr><td>Shoulder fillet (D\/d=2, r\/d=0.1)<\/td><td>~1.8\u20132.5<\/td><\/tr>\n                <tr><td>U-notch<\/td><td>~1.5\u20133.5<\/td><\/tr>\n                <tr><td>Circumferential groove<\/td><td>~1.5\u20133.0<\/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> These are approximate values from simplified curve-fit equations. For precise values, consult Peterson&#8217;s Stress Concentration Factors or perform FEA. Kt is for elastic analysis only.<\/p><\/div>\n    <\/div><\/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\/stress-calculator\/\">Stress Calculator<\/a><a class=\"vc-related-link\" href=\"\/calculators\/fatigue-life-calculator\/\">Fatigue Life<\/a><a class=\"vc-related-link\" href=\"\/calculators\/safety-factor-calculator\/\">Safety Factor<\/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. 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>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p><p style=\"font-size:12px;margin-top:4px;\">Peterson&#8217;s SCF simplified data. Last updated: February 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';var SLUG='stress-concentration-factor';\nfunction $(id){return document.getElementById(id)}\nfunction fmt(n,d){if(isNaN(n)||!isFinite(n))return'\u2014';var f=n.toFixed(d===undefined?2:d);return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\nfunction updateUI(){\n    var g=$('vc-geom').value;\n    $('vc-field-r').style.display=(g==='hole')?'none':'';\n    $('vc-d-label').innerHTML=g==='hole'?'Hole Diameter d <span class=\"vc-label-hint\">(mm)<\/span>':g==='shoulder'?'Minor Diameter d <span class=\"vc-label-hint\">(mm)<\/span>':'Net Width d <span class=\"vc-label-hint\">(mm)<\/span>';\n}\n\nfunction calculate(){\n    updateUI();\n    var g=$('vc-geom').value;\n    var W=parseFloat($('vc-W').value),d=parseFloat($('vc-d').value),r=parseFloat($('vc-r').value),snom=parseFloat($('vc-snom').value);\n    if(!W||W<=0||!d||d<=0||d>=W){$('vc-results').classList.remove('vc-visible');return}\n    var Kt,ratioLabel;\n    switch(g){\n        case'hole':\n            \/\/ Howland: Kt = 3.0 - 3.13(d\/W) + 3.66(d\/W)^2 - 1.53(d\/W)^3  (for \u03c3_nom on net section)\n            var dW=d\/W;\n            Kt=3.0-3.13*dW+3.66*dW*dW-1.53*dW*dW*dW;\n            \/\/ Correct for gross section nominal \u2192 net: Kt_net = Kt_gross * W\/(W-d)\n            \/\/ The above formula gives Kt on net section already for small d\/W\n            ratioLabel='d\/W = '+fmt(dW,3);\n            break;\n        case'shoulder':\n            if(!r||r<=0){$('vc-results').classList.remove('vc-visible');return}\n            var Dd=W\/d,rd=r\/d;\n            \/\/ Simplified: Kt \u2248 C1 + C2*(r\/d) + C3*(r\/d)^2 based on D\/d\n            \/\/ Neuber approx: Kt \u2248 1 + 1\/sqrt(A*r\/d) \u2014 simplified\n            Kt=1+2*Math.sqrt((W\/2-d\/2)\/(2*r));\/\/ Neuber simplified\n            if(Kt<1)Kt=1;\n            ratioLabel='D\/d = '+fmt(Dd,2)+', r\/d = '+fmt(rd,3);\n            break;\n        case'notch':\n            if(!r||r<=0){$('vc-results').classList.remove('vc-visible');return}\n            var t=(W-d)\/2;\/\/ notch depth\n            Kt=1+2*Math.sqrt(t\/r);\/\/ Neuber for U-notch\n            ratioLabel='t\/r = '+fmt(t\/r,2)+', depth t = '+fmt(t,1)+'mm';\n            break;\n        case'groove':\n            if(!r||r<=0){$('vc-results').classList.remove('vc-visible');return}\n            var tg=(W-d)\/2;\n            Kt=1+2*Math.sqrt(tg\/r);\n            ratioLabel='t\/r = '+fmt(tg\/r,2)+', depth = '+fmt(tg,1)+'mm';\n            break;\n    }\n\n    var smax=snom&&snom>0?Kt*snom:NaN;\n\n    $('vc-r-Kt').innerHTML=fmt(Kt,3);\n    $('vc-r-smax').innerHTML=isNaN(smax)?'\u2014':fmt(smax,1)+' <span class=\"vc-rcard-unit\">MPa<\/span>';\n    $('vc-r-ratio').innerHTML='<span style=\"font-size:14px\">'+ratioLabel+'<\/span>';\n    $('vc-results').classList.add('vc-visible');\n    drawViz(g,W,d,r,Kt);\n\n    saveHistory({geom:g,Kt:Kt,_summary:'Kt='+fmt(Kt,2)+', '+g});\n}\n\ndocument.querySelectorAll('.vc-preset-btn').forEach(function(btn){btn.addEventListener('click',function(e){e.preventDefault();\n    $('vc-geom').value=this.getAttribute('data-geom');$('vc-W').value=this.getAttribute('data-W');$('vc-d').value=this.getAttribute('data-d');\n    if(this.getAttribute('data-r'))$('vc-r').value=this.getAttribute('data-r');\n    calculate();\n})});\n\n$('vc-form').addEventListener('input',calculate);$('vc-form').addEventListener('change',calculate);\n\n$('vc-copy-btn').addEventListener('click',function(){var text='Stress Concentration\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nKt: '+$('vc-r-Kt').textContent+'\\n\u03c3_max: '+$('vc-r-smax').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu';if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('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\ndocument.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\nvar faqData=[\n    {q:'What is Kt?',a:'<p>Kt = \u03c3_max \/ \u03c3_nom. Ratio of max local stress to nominal stress at a geometric discontinuity. Depends only on geometry, not material.<\/p>'},\n    {q:'What causes stress concentrations?',a:'<p>Any abrupt geometry change: holes, notches, fillets, keyways, threads, grooves. Stress flow lines crowd together, increasing local stress.<\/p>'},\n    {q:'How does Kt affect fatigue?',a:'<p>Dramatically reduces fatigue life. Fatigue notch factor Kf = 1 + q(Kt\u22121), where q is notch sensitivity (0 to 1, material-dependent).<\/p>'},\n    {q:'How to reduce Kt?',a:'<p>Generous fillet radii, avoid sharp corners, gradual transitions, relief grooves, polished surfaces, shot peening for compressive residual stress.<\/p>'},\n    {q:'What is Peterson\\'s reference?',a:'<p>The definitive reference with Kt charts for hundreds of geometries. This calculator uses simplified curve-fit approximations.<\/p>'}\n];\nvar fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\nfl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(!b)return;b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\nfunction drawViz(geom,W,d,r,Kt){\n  var c=$('vc-viz'),SVW=380,SVH=200;\n  var svg='<svg width=\"'+SVW+'\" height=\"'+SVH+'\" viewBox=\"0 0 '+SVW+' '+SVH+'\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">';\n  svg+='<defs><marker id=\"sa\" markerWidth=\"6\" markerHeight=\"4\" refX=\"0\" refY=\"2\" orient=\"auto\"><path d=\"M0,0 L6,2 L0,4\" fill=\"#2a5c8c\"\/><\/marker>';\n  svg+='<marker id=\"sb\" markerWidth=\"6\" markerHeight=\"4\" refX=\"6\" refY=\"2\" orient=\"auto\"><path d=\"M6,0 L0,2 L6,4\" fill=\"#2a5c8c\"\/><\/marker><\/defs>';\n  var cx=SVW\/2,cy=SVH\/2;\n  var barH=60,barW=280,notchR=Math.max(6,Math.min(25,(r||5)*1.2));\n  var x0=cx-barW\/2,y0=cy-barH\/2;\n  \/\/ Main bar body\n  if(geom==='hole'){\n    var holeR=Math.max(8,Math.min(35,d*0.8));\n    svg+='<rect x=\"'+x0+'\" y=\"'+y0+'\" width=\"'+barW+'\" height=\"'+barH+'\" rx=\"2\" fill=\"#e0e7ef\" stroke=\"#7b8fa3\" stroke-width=\"1.5\"\/>';\n    svg+='<circle cx=\"'+cx+'\" cy=\"'+cy+'\" r=\"'+holeR+'\" fill=\"#f4f1ec\" stroke=\"#3578b2\" stroke-width=\"1.5\"\/>';\n    \/\/ stress lines curving around hole\n    for(var i=-2;i<=2;i++){\n      var ly=cy+i*12;\n      if(Math.abs(i)<=1){\n        var dx=holeR+4;\n        svg+='<path d=\"M'+x0+' '+ly+' L'+(cx-dx-15)+' '+ly+' Q'+(cx-dx)+' '+ly+' '+(cx-dx)+' '+(ly+i*3)+' Q'+(cx-dx)+' '+(ly+i*6)+' '+(cx-dx+10)+' '+(cy+i*(holeR+5))+'\" fill=\"none\" stroke=\"rgba(231,76,60,0.4)\" stroke-width=\"1\"\/>';\n        svg+='<path d=\"M'+(x0+barW)+' '+ly+' L'+(cx+dx+15)+' '+ly+' Q'+(cx+dx)+' '+ly+' '+(cx+dx)+' '+(ly+i*3)+' Q'+(cx+dx)+' '+(ly+i*6)+' '+(cx+dx-10)+' '+(cy+i*(holeR+5))+'\" fill=\"none\" stroke=\"rgba(231,76,60,0.4)\" stroke-width=\"1\"\/>';\n      } else {\n        svg+='<line x1=\"'+x0+'\" y1=\"'+ly+'\" x2=\"'+(x0+barW)+'\" y2=\"'+ly+'\" stroke=\"rgba(231,76,60,0.25)\" stroke-width=\"0.7\"\/>';\n      }\n    }\n    \/\/ Kt label at top of hole\n    svg+='<text x=\"'+cx+'\" y=\"'+(y0-6)+'\" text-anchor=\"middle\" fill=\"#e74c3c\" font-size=\"12\" font-weight=\"bold\">Kt = '+Kt.toFixed(2)+'<\/text>';\n  } else {\n    \/\/ Notched \/ shoulder \/ groove bar\n    var notchD=(W-d)\/2;var nVis=Math.max(8,Math.min(20,notchD*0.7));\n    svg+='<rect x=\"'+x0+'\" y=\"'+y0+'\" width=\"'+barW+'\" height=\"'+barH+'\" rx=\"2\" fill=\"#e0e7ef\" stroke=\"#7b8fa3\" stroke-width=\"1.5\"\/>';\n    \/\/ Top notch\n    svg+='<path d=\"M'+(cx-notchR)+' '+y0+' Q'+cx+' '+(y0+nVis)+' '+(cx+notchR)+' '+y0+'\" fill=\"#f4f1ec\" stroke=\"#3578b2\" stroke-width=\"1.5\"\/>';\n    \/\/ Bottom notch\n    svg+='<path d=\"M'+(cx-notchR)+' '+(y0+barH)+' Q'+cx+' '+(y0+barH-nVis)+' '+(cx+notchR)+' '+(y0+barH)+'\" fill=\"#f4f1ec\" stroke=\"#3578b2\" stroke-width=\"1.5\"\/>';\n    \/\/ Converging stress lines\n    var nLines=7;\n    for(var j=0;j<nLines;j++){\n      var frac=(j\/(nLines-1));\n      var ly1=y0+4+frac*(barH-8);\n      var ly2=y0+nVis+2+frac*(barH-2*nVis-4);\n      svg+='<line x1=\"'+x0+'\" y1=\"'+ly1+'\" x2=\"'+(cx-notchR-5)+'\" y2=\"'+ly2+'\" stroke=\"rgba(231,76,60,'+(0.25+frac*0.3)+')\" stroke-width=\"0.8\"\/>';\n      svg+='<line x1=\"'+(cx+notchR+5)+'\" y1=\"'+ly2+'\" x2=\"'+(x0+barW)+'\" y2=\"'+ly1+'\" stroke=\"rgba(231,76,60,'+(0.25+frac*0.3)+')\" stroke-width=\"0.8\"\/>';\n    }\n    svg+='<text x=\"'+cx+'\" y=\"'+(y0-6)+'\" text-anchor=\"middle\" fill=\"#e74c3c\" font-size=\"12\" font-weight=\"bold\">Kt = '+Kt.toFixed(2)+'<\/text>';\n    \/\/ radius label\n    svg+='<text x=\"'+(cx+notchR+8)+'\" y=\"'+(y0+12)+'\" fill=\"#3578b2\" font-size=\"10\">r<\/text>';\n  }\n  \/\/ Force arrows\n  svg+='<line x1=\"'+(x0-30)+'\" y1=\"'+cy+'\" x2=\"'+(x0-4)+'\" y2=\"'+cy+'\" stroke=\"#2a5c8c\" stroke-width=\"2\" marker-end=\"url(#sa)\"\/>';\n  svg+='<line x1=\"'+(x0+barW+30)+'\" y1=\"'+cy+'\" x2=\"'+(x0+barW+4)+'\" y2=\"'+cy+'\" stroke=\"#2a5c8c\" stroke-width=\"2\" marker-start=\"url(#sb)\"\/>';\n  svg+='<text x=\"'+(x0-32)+'\" y=\"'+(cy-6)+'\" fill=\"#2a5c8c\" font-size=\"11\" text-anchor=\"end\">\u03c3<\/text>';\n  svg+='<text x=\"'+(x0+barW+32)+'\" y=\"'+(cy-6)+'\" fill=\"#2a5c8c\" font-size=\"11\">\u03c3<\/text>';\n  svg+='<text x=\"'+cx+'\" y=\"'+(SVH-4)+'\" text-anchor=\"middle\" fill=\"#5a5650\" font-size=\"10\">'+geom.replace(\/-\/g,' ')+' \u2014 stress lines converge at notch<\/text>';\n  svg+='<\/svg>';\n  c.innerHTML=svg;\n}\n\nfunction 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\nfunction renderFormulas(){try{katex.render('K_t = \\\\frac{\\\\sigma_{max}}{\\\\sigma_{nom}}',$('vc-katex-1'),{displayMode:true,throwOnError:false})}catch(e){}}\n\nfunction init(){renderFormulas();calculate()}\nif(document.readyState==='loading'){document.addEventListener('DOMContentLoaded',init)}else{init()}\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Kikokotoo cha bure cha mgawo wa mkusanyiko wa msongo Kt. Data iliyorahisishwa ya chati ya Peterson kwa ajili ya hali za mwisho, tundu, pembe za mviringo na mabega. Ingiza vipimo ili kupata Kt.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100248","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100248","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100248\/revisions"}],"predecessor-version":[{"id":100764,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100248\/revisions\/100764"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/media?parent=100248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/categories?post=100248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/tags?post=100248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}