{"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":"2026-07-15T17:13:44","modified_gmt":"2026-07-15T17:13:44","slug":"stress-concentration-factor","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bg\/calculators\/stress-concentration-factor\/","title":{"rendered":"Controlled Stress-Concentration Application Worksheet"},"content":{"rendered":"<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Controlled Stress-Concentration Application Worksheet\",\"description\":\"Apply a separately verified elastic stress-concentration factor to a matching nominal stress with explicit provenance, scope and units.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/stress-concentration-factor\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"isAccessibleForFree\":true,\"dateModified\":\"2026-07-15\",\"publisher\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"}}<\/script><br \/>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this worksheet calculate Kt from dimensions?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It only applies a theoretical elastic stress-concentration factor that the user has obtained from a controlled source matching the exact geometry, loading and nominal-stress definition.\"}},{\"@type\":\"Question\",\"name\":\"Is Kt the same as fatigue Kf or fracture-mechanics K?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. The theoretical elastic stress-concentration factor Kt is distinct from a fatigue notch factor and from the dimensional stress-intensity factor used in fracture mechanics.\"}},{\"@type\":\"Question\",\"name\":\"Does the reported local elastic stress prove safety?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. The multiplication does not assess plasticity, fatigue, fracture, multiaxial state, residual stress, code compliance or acceptance.\"}}]}<\/script><\/p>\n<style>\n#sc-tool{--sc-ink:#17212b;--sc-muted:#53616f;--sc-line:#cbd5df;--sc-soft:#f3f7fa;--sc-blue:#075985;--sc-blue2:#e0f2fe;--sc-red:#991b1b;--sc-green:#166534;max-width:1120px;margin:24px auto;font-family:Inter,system-ui,-apple-system,\"Segoe UI\",sans-serif;color:var(--sc-ink);line-height:1.55}#sc-tool *{box-sizing:border-box}#sc-tool h1,#sc-tool h2,#sc-tool h3{line-height:1.2;color:var(--sc-ink)}#sc-tool h1{font-size:clamp(28px,4vw,44px);margin:0 0 12px}#sc-tool h2{font-size:24px;margin:0 0 14px}#sc-tool h3{font-size:17px;margin:0 0 10px}\n.sc-hero{padding:30px;border:1px solid var(--sc-line);border-radius:16px;background:linear-gradient(135deg,#fff,var(--sc-soft))}.sc-kicker{font-weight:800;letter-spacing:.08em;text-transform:uppercase;color:var(--sc-blue);font-size:12px}.sc-lead{font-size:17px;color:var(--sc-muted);max-width:900px;margin:0}.sc-badges{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px}.sc-badge{border:1px solid #7dd3fc;background:var(--sc-blue2);color:#0c4a6e;border-radius:999px;padding:5px 10px;font-size:12px;font-weight:700}.sc-alert{margin-top:18px;padding:14px 16px;border-left:4px solid #b45309;background:#fff7ed}.sc-alert strong{color:#7c2d12}\n.sc-card{margin-top:20px;padding:24px;border:1px solid var(--sc-line);border-radius:14px;background:#fff}.sc-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:16px}.sc-field{display:flex;flex-direction:column;gap:6px}.sc-field 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var(--sc-line);background:var(--sc-soft);border-radius:8px;overflow-x:auto}.sc-boundary{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:12px}.sc-boundary>div{padding:14px;border:1px solid var(--sc-line);border-radius:9px}.sc-boundary ul{margin:8px 0 0;padding-left:20px}.sc-note{font-size:13px;color:var(--sc-muted)}.sc-source-list{padding-left:20px}.sc-source-list li{margin:8px 0}.sc-source-list a{color:var(--sc-blue)}\n@media(max-width:760px){.sc-grid,.sc-boundary{grid-template-columns:1fr}.sc-card,.sc-hero{padding:18px}.sc-result-grid{grid-template-columns:1fr 1fr}}@media(max-width:430px){.sc-result-grid{grid-template-columns:1fr}.sc-actions{display:grid}.sc-btn{width:100%}}\n<\/style>\n<p><main id=\"sc-tool\"><\/p>\n<section class=\"sc-hero\" aria-labelledby=\"sc-title\">\n<div class=\"sc-kicker\">Controlled elastic-stress worksheet<\/div>\n<h1 id=\"sc-title\">Apply a verified stress-concentration factor<\/h1>\n<p class=\"sc-lead\">Multiply a documented nominal stress by a separately established theoretical elastic factor K<sub>t<\/sub>. This worksheet deliberately does not infer K<sub>t<\/sub> from a few dimensions or a generic shape name.<\/p>\n<div class=\"sc-badges\"><span class=\"sc-badge\">No geometry lookup<\/span><span class=\"sc-badge\">Signed nominal stress<\/span><span class=\"sc-badge\">Exact MPa\/ksi conversion<\/span><span class=\"sc-badge\">No material allowable<\/span><\/div>\n<div class=\"sc-alert\"><strong>Boundary:<\/strong> the result is a theoretical local elastic stress estimate only when the factor and nominal-stress definition come from the same controlled case. It is not K<sub>f<\/sub>, K<sub>I<\/sub>, a fatigue result, a plastic notch analysis or design acceptance.<\/div>\n<\/section>\n<form id=\"sc-form\" novalidate>\n<section class=\"sc-card\" aria-labelledby=\"sc-input-heading\">\n<h2 id=\"sc-input-heading\">1. Controlled inputs<\/h2>\n<div class=\"sc-grid\">\n<div class=\"sc-field\"><label for=\"sc-kt\">Verified theoretical factor K<sub>t<\/sub> <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-kt\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"1 to 1000\"><\/p>\n<div class=\"sc-help\">Dimensionless. Obtain it from a controlled matching chart, handbook, validated FEA, experiment or approved project analysis.<\/div>\n<\/div>\n<div class=\"sc-field\"><label for=\"sc-method\">K<sub>t<\/sub> source method <span class=\"sc-required\">*<\/span><\/label><select class=\"sc-select\" id=\"sc-method\"><option value=\"\">Select the controlled method<\/option><option value=\"licensed\">Licensed chart or handbook<\/option><option value=\"fea\">Validated finite-element analysis<\/option><option value=\"test\">Experiment or test correlation<\/option><option value=\"project\">Approved project calculation or record<\/option><\/select><\/div>\n<div class=\"sc-field\"><label for=\"sc-nominal\">Matching nominal stress \u03c3<sub>nom<\/sub> <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-nominal\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Signed plain decimal\"><\/p>\n<div class=\"sc-help\">Preserve the documented sign convention. Enter the exact gross, net, remote or other nominal basis specified by the Kt source.<\/div>\n<\/div>\n<div class=\"sc-field\"><label for=\"sc-unit\">Nominal-stress unit <span class=\"sc-required\">*<\/span><\/label><select class=\"sc-select\" id=\"sc-unit\"><option value=\"\">Select<\/option><option value=\"MPa\">MPa<\/option><option value=\"ksi\">ksi<\/option><\/select><\/div>\n<\/div>\n<\/section>\n<section class=\"sc-card\" aria-labelledby=\"sc-record-heading\">\n<h2 id=\"sc-record-heading\">2. Geometry, loading and source record<\/h2>\n<div class=\"sc-grid\">\n<div class=\"sc-field\"><label for=\"sc-record\">Record \/ item ID <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-record\" type=\"text\" maxlength=\"120\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-geometry\">Exact geometry and drawing revision <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-geometry\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-loading\">Loading mode, direction and location <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-loading\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-nominal-basis\">Nominal-stress definition and section basis <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-nominal-basis\" type=\"text\" maxlength=\"300\" autocomplete=\"off\" placeholder=\"Remote, gross, net, bending nominal, etc.\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-source\">Source document and edition \/ revision <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-source\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-location\">Figure, table, equation or case location <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-location\" type=\"text\" maxlength=\"240\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-ratios\">Dimensional ratios and source domain <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-ratios\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-interpolation\">Interpolation \/ extrapolation statement <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-interpolation\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-validation\">Validation record or FEA\/test details <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-validation\" type=\"text\" maxlength=\"400\" autocomplete=\"off\" placeholder=\"For FEA: mesh, convergence, elements and boundary conditions\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-analyst\">Analyst \/ checker <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-analyst\" type=\"text\" maxlength=\"120\" autocomplete=\"off\"><\/div>\n<div class=\"sc-field\"><label for=\"sc-date\">Record date <span class=\"sc-required\">*<\/span><\/label><input class=\"sc-input\" id=\"sc-date\" type=\"date\"><\/div>\n<\/div>\n<div class=\"sc-field\" style=\"margin-top:16px\"><label for=\"sc-notes\">Notes<\/label><textarea class=\"sc-textarea\" id=\"sc-notes\" maxlength=\"1400\" placeholder=\"Optional uncertainty, exclusions and follow-up analyses. No data is stored.\"><\/textarea><\/div>\n<\/section>\n<section class=\"sc-card\" aria-labelledby=\"sc-confirm-heading\">\n<h2 id=\"sc-confirm-heading\">3. Confirmations<\/h2>\n<div class=\"sc-checks\"><label class=\"sc-check\" for=\"sc-c1\"><input id=\"sc-c1\" type=\"checkbox\"><span>I verified that the exact geometry, dimensional ratios, loading mode and direction match the controlled K<sub>t<\/sub> source and are within its stated domain; any extrapolation is explicitly documented.<\/span><\/label><label class=\"sc-check\" for=\"sc-c2\"><input id=\"sc-c2\" type=\"checkbox\"><span>I verified that the entered nominal stress uses exactly the same gross, net, remote or other basis as the K<sub>t<\/sub> definition.<\/span><\/label><label class=\"sc-check\" for=\"sc-c3\"><input id=\"sc-c3\" type=\"checkbox\"><span>I verified that the input is the theoretical elastic stress-concentration factor K<sub>t<\/sub>, not fatigue K<sub>f<\/sub>, fracture-mechanics K\/K<sub>I<\/sub>, a material factor or a safety factor.<\/span><\/label><label class=\"sc-check\" for=\"sc-c4\"><input id=\"sc-c4\" type=\"checkbox\"><span>I will not treat the scalar result as fatigue, plasticity, fracture, multiaxial, residual-stress, code or acceptance evidence.<\/span><\/label><\/div>\n<div class=\"sc-actions\"><button class=\"sc-btn sc-primary\" type=\"submit\">Apply documented Kt<\/button><button class=\"sc-btn sc-secondary\" id=\"sc-reset\" type=\"button\">Clear worksheet<\/button><\/div>\n<div class=\"sc-status\" id=\"sc-status\" role=\"alert\" aria-live=\"polite\"><\/div>\n<\/section><\/form>\n<section class=\"sc-card sc-output\" id=\"sc-output\" data-visible=\"false\" aria-labelledby=\"sc-output-heading\">\n<h2 id=\"sc-output-heading\">4. Result<\/h2>\n<div class=\"sc-summary\" id=\"sc-summary\"><\/div>\n<div class=\"sc-result-grid\">\n<div class=\"sc-result\"><span>Signed local elastic estimate<\/span><output id=\"sc-r-mpa\">\u2014<\/output><\/div>\n<div class=\"sc-result\"><span>Signed local elastic estimate<\/span><output id=\"sc-r-ksi\">\u2014<\/output><\/div>\n<div class=\"sc-result\"><span>Magnitude<\/span><output id=\"sc-r-abs\">\u2014<\/output><\/div>\n<div class=\"sc-result\"><span>Applied factor<\/span><output id=\"sc-r-kt\">\u2014<\/output><\/div>\n<\/div>\n<p class=\"sc-note\" id=\"sc-r-boundary\">\n<\/section>\n<section class=\"sc-card\" aria-labelledby=\"sc-method-heading\">\n<h2 id=\"sc-method-heading\">Method and applicability<\/h2>\n<div class=\"sc-formula\">K<sub>t<\/sub> = \u03c3<sub>local,max,elastic<\/sub> \/ \u03c3<sub>nom<\/sub><br \/>\u03c3<sub>local,max,elastic<\/sub> = K<sub>t<\/sub> \u00d7 \u03c3<sub>nom<\/sub><\/div>\n<div class=\"sc-boundary\" style=\"margin-top:14px\">\n<div>\n<h3>What the multiplication does<\/h3>\n<ul>\n<li>Preserves the nominal-stress sign convention.<\/li>\n<li>Normalizes MPa and ksi using exact SI definitions.<\/li>\n<li>Reports magnitude separately from the signed value.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>What must already be known<\/h3>\n<ul>\n<li>Exact geometry and all governing ratios.<\/li>\n<li>Loading direction and nominal-stress basis.<\/li>\n<li>A controlled factor and its interpolation\/domain record.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>What it does not assess<\/h3>\n<ul>\n<li>Yielding or redistribution at the notch.<\/li>\n<li>Fatigue sensitivity, K<sub>f<\/sub>, fracture K or K<sub>I<\/sub>.<\/li>\n<li>Multiaxial criteria, residual stress or safety.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p class=\"sc-note\">K<sub>t<\/sub> is dimensionless. MPa is preserved by multiplication. For ksi input the exact conversion used is 1 ksi = 6.894757293168361 MPa.<\/p>\n<\/section>\n<section class=\"sc-card\" aria-labelledby=\"sc-source-heading\">\n<h2 id=\"sc-source-heading\">Sources, status and withheld lookups<\/h2>\n<ul class=\"sc-source-list\">\n<li><a href=\"https:\/\/mechref.engr.illinois.edu\/sol\/axial.html#stressConcentration\" rel=\"noopener\" target=\"_blank\">University of Illinois Mechanics Reference \u2014 Axial Loading, Stress Concentration<\/a>: defines the factor as maximum stress divided by average stress and states that it is geometry based and found experimentally.<\/li>\n<li><a href=\"https:\/\/ntrs.nasa.gov\/citations\/19920021173\" rel=\"noopener\" target=\"_blank\">NASA TM-103591, C. D. Wilson, <em>Linear Elastic Fracture Mechanics Primer<\/em>, July 1992<\/a>, section 7.1, page 50: defines the dimensionless factor by \u03c3<sub>max<\/sub> = k<sub>t<\/sub>\u03c3, notes geometry dependence and distinguishes k<sub>t<\/sub> from fracture-mechanics K<sub>I<\/sub>.<\/li>\n<li><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" rel=\"noopener\" target=\"_blank\">NIST SP 811 Appendix B<\/a>: inch\/pound-force basis and stress conversion factors.<\/li>\n<\/ul>\n<p><strong>Classification:<\/strong> the multiplication is a bounded general-mechanics relationship, not an ISO\/ASME\/ASTM\/EN design rule. The previous generic hole, shoulder, U-notch and groove equations and range table are withheld as <strong>NEEDS_LICENSED_SOURCE<\/strong>: no controlled edition, figure, nominal-stress definition or validity domain was available to verify them. This worksheet therefore accepts only a separately verified K<sub>t<\/sub>.<\/p>\n<\/section>\n<p><\/main><\/p>\n<p><script>\n(function(){\n  'use strict';\n  var MPA_PER_KSI=6.894757293168361;\n  var required=['sc-record','sc-geometry','sc-loading','sc-nominal-basis','sc-source','sc-location','sc-ratios','sc-interpolation','sc-validation','sc-analyst','sc-date'];\n  function byId(id){return document.getElementById(id);}\n  function parseDecimal(raw,signed){var s=String(raw).trim(),re=signed?\/^-?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/:\/^(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/;if(!re.test(s))return null;var n=Number(s.replace(',','.'));return Number.isFinite(n)?n:null;}\n  function compute(kt,nominal,unit){if(!Number.isFinite(kt)||kt<1||kt>1000)throw new Error('kt range');if(!Number.isFinite(nominal)||Math.abs(nominal)>1e12)throw new Error('nominal range');if(unit!=='MPa'&&unit!=='ksi')throw new Error('unit');var nominalMPa=unit==='MPa'?nominal:nominal*MPA_PER_KSI,localMPa=kt*nominalMPa;if(!Number.isFinite(localMPa)||Math.abs(localMPa)>1e15)throw new Error('result range');return{kt:kt,nominalMPa:nominalMPa,localMPa:localMPa,localKsi:localMPa\/MPA_PER_KSI,magnitude:Math.abs(localMPa)};}\n  function fmt(n){if(Object.is(n,-0))n=0;if(!Number.isFinite(n))return'\u2014';var a=Math.abs(n);if(a!==0&&(a>=1e9||a<1e-6))return n.toExponential(10).replace(\/\\.?0+e\/,'e');return new Intl.NumberFormat('en-US',{maximumSignificantDigits:12,useGrouping:true}).format(n);}\n  function clearResults(){byId('sc-output').dataset.visible='false';byId('sc-summary').textContent='';['mpa','ksi','abs','kt'].forEach(function(x){byId('sc-r-'+x).textContent='\u2014';});byId('sc-r-boundary').textContent='';}\n  function fail(message,field){clearResults();var s=byId('sc-status');s.dataset.kind='error';s.textContent=message;if(field)field.focus();}\n  byId('sc-form').addEventListener('submit',function(ev){ev.preventDefault();var kt=parseDecimal(byId('sc-kt').value,false);if(kt===null||kt<1||kt>1000){fail('Kt must be a plain finite decimal from 1 through 1000.',byId('sc-kt'));return;}var method=byId('sc-method').value;if(!\/^(licensed|fea|test|project)$\/.test(method)){fail('Select the controlled Kt source method.',byId('sc-method'));return;}var nominal=parseDecimal(byId('sc-nominal').value,true);if(nominal===null){fail('Enter the matching signed nominal stress as a plain finite decimal.',byId('sc-nominal'));return;}var unit=byId('sc-unit').value;if(unit!=='MPa'&&unit!=='ksi'){fail('Select the nominal-stress unit.',byId('sc-unit'));return;}for(var i=0;i<required.length;i++){var f=byId(required[i]);if(!f.value.trim()){fail('Complete every required geometry and source-record field.',f);return;}}for(var c=1;c<=4;c++)if(!byId('sc-c'+c).checked){fail('Complete all four source-match and decision-boundary confirmations.',byId('sc-c'+c));return;}var r;try{r=compute(kt,nominal,unit);}catch(e){fail('Normalized input or result is outside the controlled finite range.',byId('sc-nominal'));return;}byId('sc-summary').textContent='Documented elastic application: \u03c3local = Kt \u00d7 \u03c3nom = '+fmt(r.localMPa)+' MPa.';byId('sc-r-mpa').textContent=fmt(r.localMPa)+' MPa';byId('sc-r-ksi').textContent=fmt(r.localKsi)+' ksi';byId('sc-r-abs').textContent=fmt(r.magnitude)+' MPa';byId('sc-r-kt').textContent=fmt(r.kt)+' (dimensionless)';byId('sc-r-boundary').textContent='This is a scalar theoretical elastic estimate for the documented source match\u2014not a fatigue, plasticity, fracture or acceptance result.';byId('sc-output').dataset.visible='true';var s=byId('sc-status');s.dataset.kind='ok';s.textContent='Documented stress-concentration application completed.';byId('sc-output').scrollIntoView({behavior:'smooth',block:'start'});\n  });\n  byId('sc-reset').addEventListener('click',function(){byId('sc-form').reset();clearResults();var s=byId('sc-status');s.textContent='';s.dataset.kind='';byId('sc-kt').focus();});clearResults();\n})();\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Apply a separately verified theoretical elastic stress-concentration factor to a matching nominal stress with explicit provenance, scope and 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