{"id":100249,"date":"2026-02-15T20:29:40","date_gmt":"2026-02-15T20:29:40","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100249"},"modified":"2026-07-15T17:33:37","modified_gmt":"2026-07-15T17:33:37","slug":"stud-bolt-torque","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/stud-bolt-torque\/","title":{"rendered":"Controlled Empirical Stud Torque Worksheet"},"content":{"rendered":"<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Controlled Empirical Stud Torque Worksheet\",\"description\":\"Apply a documented joint-specific torque coefficient to a controlled per-stud target preload and diameter, with optional coefficient-bound sensitivity and explicit source limits.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/stud-bolt-torque\/\",\"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 select stud size, material class or preload?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Diameter, target preload and torque coefficient must come from the controlled joint design, assembly procedure and matching torque-clamp evidence.\"}},{\"@type\":\"Question\",\"name\":\"Can one dry or lubricated nut factor be used for every joint?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Torque-preload behavior depends strongly on the exact threads, nut, washer or bearing surface, material, coating, lubricant, cleanliness, reuse, running torque and test method.\"}},{\"@type\":\"Question\",\"name\":\"Does T=KDP establish ASME, ISO, ASTM or VDI compliance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is an empirical point relationship. Applicable standards and the approved assembly procedure control design, test, tightening sequence, tooling, scatter and acceptance.\"}}]}<\/script><\/p>\n<style>\n#st-tool{--st-ink:#17212b;--st-muted:#53616f;--st-line:#cbd5df;--st-soft:#f3f7fa;--st-blue:#075985;--st-blue2:#e0f2fe;--st-red:#991b1b;--st-green:#166534;max-width:1120px;margin:24px auto;font-family:Inter,system-ui,-apple-system,\"Segoe UI\",sans-serif;color:var(--st-ink);line-height:1.55}#st-tool *{box-sizing:border-box}#st-tool h1,#st-tool h2,#st-tool h3{line-height:1.2;color:var(--st-ink)}#st-tool h1{font-size:clamp(28px,4vw,44px);margin:0 0 12px}#st-tool h2{font-size:24px;margin:0 0 14px}#st-tool h3{font-size:17px;margin:0 0 10px}\n.st-hero{padding:30px;border:1px solid var(--st-line);border-radius:16px;background:linear-gradient(135deg,#fff,var(--st-soft))}.st-kicker{font-weight:800;letter-spacing:.08em;text-transform:uppercase;color:var(--st-blue);font-size:12px}.st-lead{font-size:17px;color:var(--st-muted);max-width:900px;margin:0}.st-badges{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px}.st-badge{border:1px solid #7dd3fc;background:var(--st-blue2);color:#0c4a6e;border-radius:999px;padding:5px 10px;font-size:12px;font-weight:700}.st-alert{margin-top:18px;padding:14px 16px;border-left:4px solid #b45309;background:#fff7ed}.st-alert strong{color:#7c2d12}\n.st-card{margin-top:20px;padding:24px;border:1px solid var(--st-line);border-radius:14px;background:#fff}.st-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:16px}.st-field{display:flex;flex-direction:column;gap:6px}.st-field label{font-weight:750;font-size:13px}.st-required{color:var(--st-red)}.st-input,.st-select,.st-textarea{width:100%;border:1px solid #94a3b8;border-radius:8px;background:#fff;color:var(--st-ink);padding:10px 11px;font:inherit}.st-input:focus,.st-select:focus,.st-textarea:focus{outline:3px solid rgba(14,165,233,.2);border-color:#0284c7}.st-textarea{min-height:82px;resize:vertical}.st-help{font-size:12px;color:var(--st-muted)}.st-checks{display:grid;gap:10px;margin-top:16px}.st-check{display:grid;grid-template-columns:22px 1fr;gap:9px;align-items:start;padding:10px;border:1px solid var(--st-line);border-radius:8px;background:var(--st-soft)}.st-check input{margin-top:4px;width:17px;height:17px}.st-actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:18px}.st-btn{border:0;border-radius:8px;padding:11px 18px;font:inherit;font-weight:800;cursor:pointer}.st-primary{background:var(--st-blue);color:#fff}.st-secondary{background:#e2e8f0;color:var(--st-ink)}.st-btn:focus{outline:3px solid rgba(14,165,233,.35);outline-offset:2px}.st-status{min-height:28px;margin-top:14px;font-weight:750}.st-status[data-kind=\"error\"]{color:var(--st-red)}.st-status[data-kind=\"ok\"]{color:var(--st-green)}\n.st-output{display:none}.st-output[data-visible=\"true\"]{display:block}.st-summary{padding:14px 16px;border:1px solid #7dd3fc;border-radius:9px;background:var(--st-blue2);font-weight:750}.st-result-grid{display:grid;grid-template-columns:repeat(4,minmax(0,1fr));gap:10px;margin-top:14px}.st-result{border:1px solid var(--st-line);border-radius:9px;padding:12px;background:var(--st-soft)}.st-result span{display:block;color:var(--st-muted);font-size:12px}.st-result output{display:block;margin-top:4px;font-weight:800;font-variant-numeric:tabular-nums;overflow-wrap:anywhere}.st-formula{font-family:ui-monospace,SFMono-Regular,Consolas,monospace;padding:12px 14px;border:1px solid var(--st-line);background:var(--st-soft);border-radius:8px;overflow-x:auto}.st-boundary{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:12px}.st-boundary>div{padding:14px;border:1px solid var(--st-line);border-radius:9px}.st-boundary ul{margin:8px 0 0;padding-left:20px}.st-note{font-size:13px;color:var(--st-muted)}.st-source-list{padding-left:20px}.st-source-list li{margin:8px 0}.st-source-list a{color:var(--st-blue)}\n@media(max-width:760px){.st-grid,.st-boundary{grid-template-columns:1fr}.st-card,.st-hero{padding:18px}.st-result-grid{grid-template-columns:1fr 1fr}}@media(max-width:430px){.st-result-grid{grid-template-columns:1fr}.st-actions{display:grid}.st-btn{width:100%}}\n<\/style>\n<p><main id=\"st-tool\"><\/p>\n<section class=\"st-hero\" aria-labelledby=\"st-title\">\n<div class=\"st-kicker\">Controlled empirical assembly worksheet<\/div>\n<h1 id=\"st-title\">Documented stud torque from target preload<\/h1>\n<p class=\"st-lead\">Apply one controlled torque coefficient K to one per-stud target preload P and the matching nominal diameter D. The worksheet performs the empirical arithmetic T = KDP; it does not select a stud, strength, preload, lubricant or assembly procedure.<\/p>\n<div class=\"st-badges\"><span class=\"st-badge\">No material presets<\/span><span class=\"st-badge\">No generic dry\/lubricated K<\/span><span class=\"st-badge\">Exact SI\/imperial units<\/span><span class=\"st-badge\">No compliance verdict<\/span><\/div>\n<div class=\"st-alert\"><strong>Critical boundary:<\/strong> torque is an indirect and friction-sensitive way to target clamp force. A point value of K cannot predict achieved preload or its distribution. Use only data and a procedure matching the exact fastener, nut, bearing surface, coating, lubricant, cleanliness, reuse\/cycle condition and tool process.<\/div>\n<\/section>\n<form id=\"st-form\" novalidate>\n<section class=\"st-card\" aria-labelledby=\"st-input-heading\">\n<h2 id=\"st-input-heading\">1. Controlled empirical inputs<\/h2>\n<div class=\"st-grid\">\n<div class=\"st-field\"><label for=\"st-k\">Documented torque coefficient K <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-k\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Positive plain decimal\"><\/p>\n<div class=\"st-help\">Dimensionless point value from the exact controlled configuration; not a generic lubricant label.<\/div>\n<\/div>\n<div class=\"st-field\"><label for=\"st-method\">K evidence method <span class=\"st-required\">*<\/span><\/label><select class=\"st-select\" id=\"st-method\"><option value=\"\">Select controlled evidence<\/option><option value=\"iso16047\">ISO 16047 torque\/clamp-force test report<\/option><option value=\"joint-test\">Project joint-specific torque-tension test<\/option><option value=\"procedure\">Approved assembly procedure with traceable test basis<\/option><option value=\"manufacturer\">Manufacturer test report for exact configuration<\/option><\/select><\/div>\n<div class=\"st-field\"><label for=\"st-k-low\">Optional controlled lower K bound<\/label><input class=\"st-input\" id=\"st-k-low\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Supply both bounds or neither\"><\/p>\n<div class=\"st-help\">Used only for arithmetic preload sensitivity at the nominal torque; it is not a confidence interval unless the source says so.<\/div>\n<\/div>\n<div class=\"st-field\"><label for=\"st-k-high\">Optional controlled upper K bound<\/label><input class=\"st-input\" id=\"st-k-high\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Supply both bounds or neither\"><\/div>\n<div class=\"st-field\"><label for=\"st-diameter\">Matching nominal diameter D <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-diameter\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Positive plain decimal\"><\/div>\n<div class=\"st-field\"><label for=\"st-diameter-unit\">Diameter unit <span class=\"st-required\">*<\/span><\/label><select class=\"st-select\" id=\"st-diameter-unit\"><option value=\"\">Select<\/option><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div>\n<div class=\"st-field\"><label for=\"st-preload\">Controlled target preload P per stud <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-preload\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"Nonnegative plain decimal\"><\/div>\n<div class=\"st-field\"><label for=\"st-preload-unit\">Preload unit <span class=\"st-required\">*<\/span><\/label><select class=\"st-select\" id=\"st-preload-unit\"><option value=\"\">Select<\/option><option value=\"N\">N<\/option><option value=\"kN\">kN<\/option><option value=\"lbf\">lbf<\/option><\/select><\/div>\n<\/div>\n<\/section>\n<section class=\"st-card\" aria-labelledby=\"st-record-heading\">\n<h2 id=\"st-record-heading\">2. Joint, source and assembly record<\/h2>\n<div class=\"st-grid\">\n<div class=\"st-field\"><label for=\"st-record\">Record \/ joint ID <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-record\" type=\"text\" maxlength=\"120\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-joint\">Exact stud, nut, washer and joint identities <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-joint\" type=\"text\" maxlength=\"400\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-drawing\">Drawing \/ specification revision <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-drawing\" type=\"text\" maxlength=\"240\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-preload-source\">Target-preload source, edition and location <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-preload-source\" type=\"text\" maxlength=\"400\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-preload-basis\">Per-stud load case and preload basis <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-preload-basis\" type=\"text\" maxlength=\"400\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-k-source\">K test\/report source, revision and sample statistics <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-k-source\" type=\"text\" maxlength=\"500\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-k-config\">K configuration: threads, materials, coating, lubricant and surfaces <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-k-config\" type=\"text\" maxlength=\"500\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-diameter-basis\">Diameter definition used by the K source <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-diameter-basis\" type=\"text\" maxlength=\"240\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-interface\">Rotating nut\/end and bearing interface <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-interface\" type=\"text\" maxlength=\"300\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-procedure\">Assembly sequence, passes and running-torque treatment <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-procedure\" type=\"text\" maxlength=\"500\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-wrench\">Tool ID, calibration date, range and accuracy <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-wrench\" type=\"text\" maxlength=\"400\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-conditions\">Temperature, cleanliness, reuse\/cycles and service condition <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-conditions\" type=\"text\" maxlength=\"500\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-analyst\">Analyst \/ checker <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-analyst\" type=\"text\" maxlength=\"120\" autocomplete=\"off\"><\/div>\n<div class=\"st-field\"><label for=\"st-date\">Record date <span class=\"st-required\">*<\/span><\/label><input class=\"st-input\" id=\"st-date\" type=\"date\"><\/div>\n<\/div>\n<div class=\"st-field\" style=\"margin-top:16px\"><label for=\"st-notes\">Notes<\/label><textarea class=\"st-textarea\" id=\"st-notes\" maxlength=\"1600\" placeholder=\"Optional exclusions, statistical interpretation and follow-up verification. No data is stored.\"><\/textarea><\/div>\n<\/section>\n<section class=\"st-card\" aria-labelledby=\"st-confirm-heading\">\n<h2 id=\"st-confirm-heading\">3. Confirmations<\/h2>\n<div class=\"st-checks\"><label class=\"st-check\" for=\"st-c1\"><input id=\"st-c1\" type=\"checkbox\"><span>I verified that the target preload is a per-stud value from the controlled joint design and governing load\/assembly procedure\u2014not a generic percentage of a property-class value.<\/span><\/label><label class=\"st-check\" for=\"st-c2\"><input id=\"st-c2\" type=\"checkbox\"><span>I verified that K and any bounds match the exact threads, nut, washer\/bearing surface, material, coating, lubricant, application quantity, cleanliness, reuse\/cycles, temperature and running-torque treatment.<\/span><\/label><label class=\"st-check\" for=\"st-c3\"><input id=\"st-c3\" type=\"checkbox\"><span>I verified that D is the same nominal-diameter definition used by the K evidence and that the entered units refer to one tightened stud\/nut interface.<\/span><\/label><label class=\"st-check\" for=\"st-c4\"><input id=\"st-c4\" type=\"checkbox\"><span>I will use the result only inside the approved procedure that controls preload scatter, tool calibration\/range, tightening sequence\/passes, gasket or joint behavior and verification; it is not an ISO\/ASME\/ASTM\/VDI compliance verdict.<\/span><\/label><\/div>\n<div class=\"st-actions\"><button class=\"st-btn st-primary\" type=\"submit\">Calculate documented nominal torque<\/button><button class=\"st-btn st-secondary\" id=\"st-reset\" type=\"button\">Clear worksheet<\/button><\/div>\n<div class=\"st-status\" id=\"st-status\" role=\"alert\" aria-live=\"polite\"><\/div>\n<\/section><\/form>\n<section class=\"st-card st-output\" id=\"st-output\" data-visible=\"false\" aria-labelledby=\"st-output-heading\">\n<h2 id=\"st-output-heading\">4. Empirical point result<\/h2>\n<div class=\"st-summary\" id=\"st-summary\"><\/div>\n<div class=\"st-result-grid\">\n<div class=\"st-result\"><span>Nominal torque<\/span><output id=\"st-r-nm\">\u2014<\/output><\/div>\n<div class=\"st-result\"><span>Nominal torque<\/span><output id=\"st-r-lbfft\">\u2014<\/output><\/div>\n<div class=\"st-result\"><span>Nominal torque<\/span><output id=\"st-r-lbfin\">\u2014<\/output><\/div>\n<div class=\"st-result\"><span>Normalized target preload<\/span><output id=\"st-r-preload\">\u2014<\/output><\/div>\n<\/div>\n<p class=\"st-note\" id=\"st-r-sensitivity\">\n<p class=\"st-note\" id=\"st-r-boundary\">\n<\/section>\n<section class=\"st-card\" aria-labelledby=\"st-method-heading\">\n<h2 id=\"st-method-heading\">Method and applicability<\/h2>\n<div class=\"st-formula\">T<sub>nom<\/sub> = K \u00d7 D \u00d7 P<sub>target<\/sub><br \/>If controlled K bounds are supplied and T<sub>nom<\/sub> is applied: P<sub>sens,low<\/sub> = T<sub>nom<\/sub>\/(K<sub>high<\/sub>D); P<sub>sens,high<\/sub> = T<sub>nom<\/sub>\/(K<sub>low<\/sub>D)<\/div>\n<div class=\"st-boundary\" style=\"margin-top:14px\">\n<div>\n<h3>What is calculated<\/h3>\n<ul>\n<li>One empirical nominal torque for one target preload.<\/li>\n<li>Exact N, kN, lbf, mm, inch, N\u00b7m and lbf conversions.<\/li>\n<li>Optional arithmetic K-bound preload sensitivity only.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>What must be controlled<\/h3>\n<ul>\n<li>Target preload from the complete joint design.<\/li>\n<li>Configuration-specific K evidence and statistics.<\/li>\n<li>Assembly sequence, tool and verification procedure.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>What is not calculated<\/h3>\n<ul>\n<li>Stud strength, stress area, yield\/proof utilization or thread stripping.<\/li>\n<li>Flange\/gasket load distribution, relaxation, thermal or external loads.<\/li>\n<li>Achieved-preload probability, acceptance or code compliance.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p class=\"st-note\">The optional sensitivity interval is not a guaranteed preload interval and not a statistical confidence\/tolerance bound unless the controlled source explicitly defines it that way. A point K by itself provides no scatter estimate.<\/p>\n<\/section>\n<section class=\"st-card\" aria-labelledby=\"st-source-heading\">\n<h2 id=\"st-source-heading\">Sources and standards boundary<\/h2>\n<ul class=\"st-source-list\">\n<li><a href=\"https:\/\/ntrs.nasa.gov\/citations\/20140008863\" rel=\"noopener\" target=\"_blank\">NASA Goddard \u2014 <em>Torque Tension Testing of Fasteners Used for NASA Flight Hardware Applications<\/em><\/a>: gives T = KDP, documents test determination of K, strong dependence on friction\/lubrication\/configuration and wide scatter; its reported coefficients are specific to tested hardware and are not presets here.<\/li>\n<li><a href=\"https:\/\/ntrs.nasa.gov\/citations\/19900009424\" rel=\"noopener\" target=\"_blank\">NASA RP-1228, <em>Fastener Design Manual<\/em>, March 1990<\/a>, printed page 17: presents T = KFd as a quick empirical formula and explicitly warns that an assumed K = 0.2 must not be used blindly.<\/li>\n<li><a href=\"https:\/\/www.iso.org\/standard\/27788.html\" rel=\"noopener\" target=\"_blank\">ISO 16047:2005 with Amendment 1:2012<\/a>: published and confirmed torque\/clamp-force test conditions for applicable fasteners; it is a test standard, not a universal K table.<\/li>\n<li><a href=\"https:\/\/www.iso.org\/standard\/60610.html\" rel=\"noopener\" target=\"_blank\">ISO 898-1:2013 with Cor 1:2013<\/a>: published mechanical-property scope for specified carbon\/alloy-steel metric fasteners; its official scope explicitly excludes torque\/clamp-force performance and points to ISO 16047 for testing.<\/li>\n<li><a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/pressure-boundary-bolted-flange-joint-assembly\" rel=\"noopener\" target=\"_blank\">ASME PCC-1\u20142022<\/a>: current official scope is pressure-boundary flanged joints with specified ring-type gasket geometry\u2014not every stud application and not a generic K value.<\/li>\n<li><a href=\"https:\/\/www.vdi.de\/en\/home\/vdi-standards\/details\/vdi-2230-blatt-1-systematic-calculation-of-highly-stressed-bolted-joints-joints-with-one-cylindrical-bolt\" rel=\"noopener\" target=\"_blank\">VDI 2230 Part 1:2015-11<\/a>: controlled calculation method for highly stressed single-bolt joints; the licensed method is not reproduced by this point worksheet.<\/li>\n<li><a href=\"https:\/\/store.astm.org\/a0193_a0193m-26.html\" rel=\"noopener\" target=\"_blank\">ASTM A193\/A193M-26<\/a>: active bolting-material specification for high-temperature\/high-pressure and special-purpose applications. It does not justify one universal B7 preload or K value; exact material\/design criteria remain controlled project inputs.<\/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>: exact inch and pound-force basis used for unit normalization.<\/li>\n<\/ul>\n<p><strong>Classification:<\/strong> T = KDP is an empirical general-engineering relationship, not an ISO torque formula. The former metric stress-area table, B7\/L7\/property-class strengths, 70\u201375% utilization presets, generic dry\/oiled\/MoS\u2082\/anti-seize coefficients, universal \u00b125% statement and assembly advice are withheld as <strong>NEEDS_LICENSED_SOURCE<\/strong> or exact project-test\/procedure data.<\/p>\n<\/section>\n<p><\/main><\/p>\n<p><script>\n(function(){\n  'use strict';\n  var N_PER_LBF=4.4482216152605,M_PER_IN=0.0254,NM_PER_LBFIN=N_PER_LBF*M_PER_IN,NM_PER_LBFFT=N_PER_LBF*12*M_PER_IN;\n  var diameterFactors={mm:0.001,in:M_PER_IN},preloadFactors={N:1,kN:1000,lbf:N_PER_LBF};\n  var required=['st-record','st-joint','st-drawing','st-preload-source','st-preload-basis','st-k-source','st-k-config','st-diameter-basis','st-interface','st-procedure','st-wrench','st-conditions','st-analyst','st-date'];\n  function byId(id){return document.getElementById(id);}\n  function parseDecimal(raw,allowZero){var s=String(raw).trim(),re=\/^(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/;if(!re.test(s))return null;var n=Number(s.replace(',','.'));if(!Number.isFinite(n)||n<0||(!allowZero&&n===0))return null;return n;}\n  function compute(k,d,dUnit,preload,pUnit,kLow,kHigh){if(!Number.isFinite(k)||k<=0||k>10)throw new Error('k range');if(!Number.isFinite(d)||d<=0||d>1e9||!diameterFactors[dUnit])throw new Error('diameter');if(!Number.isFinite(preload)||preload<0||preload>1e12||!preloadFactors[pUnit])throw new Error('preload');var bounded=kLow!==null||kHigh!==null;if(bounded&&(!Number.isFinite(kLow)||!Number.isFinite(kHigh)||kLow<=0||kHigh<=0||kLow>k||kHigh<k||kHigh>10))throw new Error('bounds');var dM=d*diameterFactors[dUnit],pN=preload*preloadFactors[pUnit],torqueNm=k*dM*pN;if(!Number.isFinite(torqueNm)||torqueNm>1e15)throw new Error('torque range');var out={k:k,dM:dM,preloadN:pN,torqueNm:torqueNm,torqueLbfFt:torqueNm\/NM_PER_LBFFT,torqueLbfIn:torqueNm\/NM_PER_LBFIN,bounded:bounded,preloadLowN:null,preloadHighN:null};if(bounded){out.preloadLowN=torqueNm\/(kHigh*dM);out.preloadHighN=torqueNm\/(kLow*dM);}return out;}\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('st-output').dataset.visible='false';byId('st-summary').textContent='';['nm','lbfft','lbfin','preload'].forEach(function(x){byId('st-r-'+x).textContent='\u2014';});byId('st-r-sensitivity').textContent='';byId('st-r-boundary').textContent='';}\n  function fail(message,field){clearResults();var s=byId('st-status');s.dataset.kind='error';s.textContent=message;if(field)field.focus();}\n  byId('st-form').addEventListener('submit',function(ev){ev.preventDefault();var k=parseDecimal(byId('st-k').value,false);if(k===null||k>10){fail('K must be a positive plain decimal not greater than the computational bound 10.',byId('st-k'));return;}var method=byId('st-method').value;if(!\/^(iso16047|joint-test|procedure|manufacturer)$\/.test(method)){fail('Select the controlled K evidence method.',byId('st-method'));return;}var loRaw=byId('st-k-low').value.trim(),hiRaw=byId('st-k-high').value.trim(),kLow=null,kHigh=null;if(loRaw||hiRaw){if(!loRaw||!hiRaw){fail('Supply both controlled K bounds or leave both blank.',loRaw?byId('st-k-high'):byId('st-k-low'));return;}kLow=parseDecimal(loRaw,false);kHigh=parseDecimal(hiRaw,false);if(kLow===null||kHigh===null||kLow>k||kHigh<k||kHigh>10){fail('K bounds must be positive plain decimals with lower \u2264 K \u2264 upper \u2264 10.',byId('st-k-low'));return;}}var d=parseDecimal(byId('st-diameter').value,false);if(d===null){fail('Diameter must be a positive plain decimal.',byId('st-diameter'));return;}var dUnit=byId('st-diameter-unit').value;if(!diameterFactors[dUnit]){fail('Select the diameter unit.',byId('st-diameter-unit'));return;}var preload=parseDecimal(byId('st-preload').value,true);if(preload===null){fail('Target preload must be a nonnegative plain decimal.',byId('st-preload'));return;}var pUnit=byId('st-preload-unit').value;if(!preloadFactors[pUnit]){fail('Select the preload unit.',byId('st-preload-unit'));return;}for(var i=0;i<required.length;i++){var f=byId(required[i]);if(!f.value.trim()){fail('Complete every required joint, source and assembly-record field.',f);return;}}for(var c=1;c<=4;c++)if(!byId('st-c'+c).checked){fail('Complete all four source-match and decision-boundary confirmations.',byId('st-c'+c));return;}var r;try{r=compute(k,d,dUnit,preload,pUnit,kLow,kHigh);}catch(e){fail('Normalized input, coefficient bounds or result is outside the controlled finite range.',byId('st-k'));return;}byId('st-summary').textContent='Empirical point calculation: Tnom = K \u00d7 D \u00d7 Ptarget = '+fmt(r.torqueNm)+' N\u00b7m.';byId('st-r-nm').textContent=fmt(r.torqueNm)+' N\u00b7m';byId('st-r-lbfft').textContent=fmt(r.torqueLbfFt)+' lbf\u00b7ft';byId('st-r-lbfin').textContent=fmt(r.torqueLbfIn)+' lbf\u00b7in';byId('st-r-preload').textContent=fmt(r.preloadN\/1000)+' kN';byId('st-r-sensitivity').textContent=r.bounded?'At the nominal torque, arithmetic sensitivity for the supplied K bounds is '+fmt(r.preloadLowN\/1000)+' to '+fmt(r.preloadHighN\/1000)+' kN. This is not a guaranteed or statistical preload interval.':'No controlled K bounds were supplied; no achieved-preload sensitivity interval is reported.';byId('st-r-boundary').textContent='Nominal empirical torque only. The approved joint design, test evidence and assembly procedure control actual setpoint, scatter, sequence, tooling and acceptance.';byId('st-output').dataset.visible='true';var s=byId('st-status');s.dataset.kind='ok';s.textContent='Documented empirical torque calculation completed.';byId('st-output').scrollIntoView({behavior:'smooth',block:'start'});\n  });\n  byId('st-reset').addEventListener('click',function(){byId('st-form').reset();clearResults();var s=byId('st-status');s.textContent='';s.dataset.kind='';byId('st-k').focus();});clearResults();\n})();\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Apply a documented joint-specific torque coefficient to a controlled per-stud target preload and diameter, with optional coefficient-bound sensitivity.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100249","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100249","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100249\/revisions"}],"predecessor-version":[{"id":102594,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100249\/revisions\/102594"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}