{"id":100186,"date":"2026-02-15T20:25:41","date_gmt":"2026-02-15T20:25:41","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100186"},"modified":"2026-07-13T02:47:32","modified_gmt":"2026-07-13T02:47:32","slug":"pipe-support-spacing","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/zh\/calculators\/pipe-support-spacing\/","title":{"rendered":"Simply Supported Pipe-Section Beam Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Simply Supported Pipe-Section Beam Arithmetic\",\"description\":\"Calculates the ideal simply supported span that produces an entered midspan deflection under documented uniform mass loading, plus bending stress and reactions. It does not set allowable support spacing.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/pipe-support-spacing\/\",\"applicationCategory\":\"EngineeringApplication\",\"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\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Actual hollow-section inertia\",\"Documented uniform pipe\/fluid\/added mass\",\"Simply supported deflection inversion\",\"Bending stress and support reactions\",\"No automatic support-spacing acceptance\"],\"keywords\":\"simply supported pipe beam,uniform load deflection,hollow circular section inertia,pipe support preliminary arithmetic\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Is the calculated span a maximum allowable support spacing?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is the ideal span that produces the entered deflection in one simply supported Euler\u2013Bernoulli model; stress,code,dynamics,thermal and real support checks remain separate.\"}},{\"@type\":\"Question\",\"name\":\"Does this model a continuous multi-span pipe?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Continuous spans depend on span sequence, end conditions and support stiffness and cannot be replaced by a universal fixed-fixed coefficient.\"}},{\"@type\":\"Question\",\"name\":\"Are DN\/Schedule and material tables built in?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Enter actual controlled geometry,masses,density and temperature-dependent modulus.\"}},{\"@type\":\"Question\",\"name\":\"What loads are included?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Only gravity from entered pipe,contained-fluid and added uniform mass per length using conventional standard gravity.\"}}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#7a4b22;--al:#f9f0e8;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--f:'DM Sans',sans-serif;--m:'JetBrains Mono',monospace;--d:'Fraunces',serif}.vc-calculator{font-family:var(--f);font-size:15px;line-height:1.65;color:var(--i);max-width:960px;margin:auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 20px 40px;border-bottom:3px solid var(--a)}.vc-header-eyebrow{font:500 11px var(--m);letter-spacing:.15em;text-transform:uppercase;color:var(--a)}.vc-header-title{font:800 clamp(24px,4vw,36px)\/1.15 var(--d);margin:10px 0 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var(--bl);border-radius:6px;background:var(--sa);font-size:13px;color:var(--is)}.vc-check input{margin-top:4px}.vc-validation{min-height:22px;color:var(--r);font-size:13px;margin-top:10px}.vc-results{border-top:1px solid var(--bl);background:var(--sa);padding:0;max-height:0;overflow:hidden}.vc-results.vc-visible{max-height:1600px;padding:24px}.vc-result-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:12px}.vc-rcard{background:var(--s);border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--a);background:var(--al)}.vc-rcard-label{font:500 10px var(--m);letter-spacing:.1em;text-transform:uppercase;color:var(--im)}.vc-rcard-value{font:600 19px var(--m);overflow-wrap:anywhere}.vc-primary .vc-rcard-value{font-size:24px;color:var(--a)}.vc-status{grid-column:1\/-1;padding:12px;background:var(--yl);border-left:3px solid var(--y);font-size:13px;color:var(--is)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;padding:18px 24px;border:0;background:transparent;cursor:pointer;text-align:left}.vc-section-title{font:700 18px var(--d)}.vc-section-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-section-body{max-height:15000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--bl)}.vc-theory h3{font:700 17px var(--d);margin:24px 0 8px}.vc-theory p,.vc-theory li{font-size:14px;color:var(--is)}.vc-formula{padding:14px;border:2px solid var(--b);border-radius:6px;background:var(--sa);text-align:center;font:500 14px var(--m);margin:12px 0}.vc-warning{padding:14px;background:var(--yl);border-left:3px solid var(--y);color:var(--is)}.vc-faq-item{border:1px solid var(--bl);margin-top:8px}.vc-faq-q{width:100%;padding:14px;border:0;background:var(--sa);text-align:left;font-weight:600}.vc-faq-a{display:none;padding:14px;color:var(--is)}.vc-faq-item.vc-open .vc-faq-a{display:block}.vc-footer{text-align:center;padding:30px;color:var(--im);font-size:13px}@media(max-width:600px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-full,.vc-primary,.vc-status{grid-column:1}}<\/style>\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">One ideal beam span \u2014 not a support-spacing code check<\/p><h1 class=\"vc-header-title\">Simply Supported Pipe-Section Beam Arithmetic<\/h1><p class=\"vc-header-subtitle\">Invert one documented uniform-load deflection target for an ideal pin\u2013roller hollow circular beam,and report the associated bending stress and reactions.No continuous-span coefficient or allowable spacing is invented.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Actual geometry<\/span><span class=\"vc-badge\">Uniform load only<\/span><span class=\"vc-badge\">No maximum-span verdict<\/span><\/div><\/header><div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-od\">Actual outside diameter Do<\/label><input class=\"vc-input\" id=\"vc-od\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-wall\">Actual structural wall thickness t<\/label><input class=\"vc-input\" id=\"vc-wall\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-geom-unit\">Geometry\/deflection unit<\/label><select class=\"vc-select\" id=\"vc-geom-unit\"><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-deflection\">Documented target midspan deflection \u03b4<\/label><input class=\"vc-input\" id=\"vc-deflection\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-pipe-mass\">Actual pipe linear mass<\/label><input class=\"vc-input\" id=\"vc-pipe-mass\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mass-unit\">Linear-mass unit<\/label><select class=\"vc-select\" id=\"vc-mass-unit\"><option value=\"kgm\">kg\/m<\/option><option value=\"lbft\">lb\/ft<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-fluid-density\">Contained-fluid density <span class=\"vc-hint\">(zero allowed)<\/span><\/label><input class=\"vc-input\" id=\"vc-fluid-density\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-density-unit\">Density unit<\/label><select class=\"vc-select\" id=\"vc-density-unit\"><option value=\"kgm3\">kg\/m\u00b3<\/option><option value=\"lbft3\">lb\/ft\u00b3<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-added-mass\">Added uniform linear mass <span class=\"vc-hint\">(zero allowed)<\/span><\/label><input class=\"vc-input\" id=\"vc-added-mass\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-e\">Documented Young&#8217;s modulus E<\/label><input class=\"vc-input\" id=\"vc-e\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-e-unit\">Modulus unit<\/label><select class=\"vc-select\" id=\"vc-e-unit\"><option value=\"gpa\">GPa<\/option><option value=\"ksi\">ksi<\/option><\/select><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Geometry,mass,modulus,deflection and support-model source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"pipe\/component ID and condition;Do\/t\/mass sources;fluid state\/density;added mass;E at temperature;deflection basis;model revision\/date\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>The assessed member is idealized as one straight,prismatic,slender,small-deflection Euler\u2013Bernoulli hollow circular beam with one pin and one roller,constant E and only uniform vertical gravity load.The entered wall is structural\/effective;fluid fills the actual ID;added mass is uniform.Point loads,support stiffness\/gaps,continuity,dynamics,thermal\/seismic\/wind\/ice,pressure effects,local stresses,fatigue and code acceptance are checked separately.<\/span><\/label><\/div><\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form><div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Ideal span producing entered deflection<\/div><div class=\"vc-rcard-value\" id=\"vc-r-span\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Outer-fibre bending stress at that span<\/div><div class=\"vc-rcard-value\" id=\"vc-r-stress\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Vertical reaction at each ideal support<\/div><div class=\"vc-rcard-value\" id=\"vc-r-reaction\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Second moment of area I<\/div><div class=\"vc-rcard-value\" id=\"vc-r-i\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Uniform mass \/ force per length<\/div><div class=\"vc-rcard-value\" id=\"vc-r-load\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Ideal simply supported uniform-load arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equations and code boundary<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula\">Di=Do\u22122t;&nbsp; I=\u03c0(Do\u2074\u2212Di\u2074)\/64;&nbsp; w=mtotal\u00b7gn;&nbsp; \u03b4max=5wL\u2074\/(384EI)<\/div><div class=\"vc-formula\">L\u03b4=[384EI\u03b4target\/(5w)]<sup>1\/4<\/sup>;&nbsp; Mmax=wL\u03b4\u00b2\/8;&nbsp; \u03c3outer=Mmax(Do\/2)\/I;&nbsp; R=wL\u03b4\/2<\/div><p>gn=9.80665m\/s\u00b2 is conventional standard gravity.The span is the mathematical inversion of one ideal service-load deflection equation.It is not labelled allowable or maximum support spacing.The displayed stress is elastic bending stress from this uniform gravity load only and is not compared with a material\/code allowable.<\/p><h3>No continuous-span shortcut<\/h3><p>A continuous multi-span pipe is not universally fixed\u2013fixed.End spans,interior spans,unequal lengths,support settlement\/stiffness and piping continuity change moments and deflections.The former `1\/384` continuous coefficient and generic longer-span result are therefore not used.<\/p><h3>Current code scope<\/h3><p>ASME B31.1-2024 covers power-piping design through operation\/maintenance;ASME B31.3-2024 covers process-piping materials\/components,design,fabrication,assembly,erection,examination,inspection and testing.The public records do not establish universal2.5mm deflection or DN-based support-spacing tables.<\/p><div class=\"vc-warning\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> exact selected-code support\/load\/stress\/deflection rules and any project spacing table.No ASME compliance or final support-layout decision is emitted.<\/div><h3>Sources<\/h3><p><a href=\"https:\/\/www.egr.msu.edu\/~harichan\/classes\/ce405\/chap2.pdf\" target=\"_blank\" rel=\"noopener\">Michigan State simply supported UDL moment\/deflection example<\/a>; <a href=\"https:\/\/www.ceas.uc.edu\/research\/centers-labs\/siemens-simulation-technology-center\/courses---projects\/nx-nastran\/solid-mechanics-course\/solid-mechanics-examples\/simply-supported-beam-example.html\" target=\"_blank\" rel=\"noopener\">University of Cincinnati Euler\u2013Bernoulli scope<\/a>; <a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\/nist-guide-si-appendix-b8\" target=\"_blank\" rel=\"noopener\">NIST conventional standard gravity<\/a>; <a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/b31-1-power-piping\" target=\"_blank\" rel=\"noopener\">ASME B31.1-2024<\/a>; <a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/b31-3-process-piping\/2024\" target=\"_blank\" rel=\"noopener\">ASME B31.3-2024<\/a>.<\/p><\/div><\/div><\/div><div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 Vibromera \u2014 reviewed 13 July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function token(raw){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)?v:null}function pos(raw){var v=token(raw);return v!==null&&v>0?v:null}function nn(raw){var v=token(raw);return v!==null&&v>=0?v:null}function fmt(v){if(v===0)return'0';if(Math.abs(v)>=1e9||Math.abs(v)<1e-7)return v.toExponential(8);return Number(v.toPrecision(11)).toString()}function len(v,u){return v*(u==='in'?.0254:.001)}function mass(v,u){return v*(u==='lbft'?.45359237\/.3048:1)}function rho(v,u){return v*(u==='lbft3'?.45359237\/.028316846592:1)}function modulus(v,u){return v*(u==='ksi'?6894757.293168:1e9)}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){if(!$('vc-source').value.trim())return hide('Enter the controlled geometry,mass,modulus,deflection and model source.');if(!$('vc-gate').checked)return hide('Confirm the narrow simply supported Euler\u2013Bernoulli model boundaries.');var odr=pos($('vc-od').value),tr=pos($('vc-wall').value),deltaR=pos($('vc-deflection').value),pmr=pos($('vc-pipe-mass').value),fr=nn($('vc-fluid-density').value),ar=nn($('vc-added-mass').value),er=pos($('vc-e').value);if([odr,tr,deltaR,pmr,fr,ar,er].some(function(x){return x===null}))return hide('Enter positive Do,t,pipe mass,E,deflection and non-negative complete fluid\/added masses.');var gu=$('vc-geom-unit').value,Do=len(odr,gu),t=len(tr,gu),delta=len(deltaR,gu);if(!(2*t<Do))return hide('Wall thickness must be less than half the outside diameter.');var Di=Do-2*t,I=Math.PI*(Math.pow(Do,4)-Math.pow(Di,4))\/64,Af=Math.PI*Di*Di\/4,mp=mass(pmr,$('vc-mass-unit').value),mf=rho(fr,$('vc-density-unit').value)*Af,ma=mass(ar,$('vc-mass-unit').value),mt=mp+mf+ma,E=modulus(er,$('vc-e-unit').value),w=mt*9.80665,L=Math.pow(384*E*I*delta\/(5*w),.25),M=w*L*L\/8,stress=M*(Do\/2)\/I,R=w*L\/2;if(![Do,t,Di,I,Af,mp,mf,ma,mt,E,w,L,M,stress,R].every(function(x){return Number.isFinite(x)&&x>=0})||L<=0)return hide('The ideal-beam arithmetic did not produce finite positive geometry\/span.');$('vc-r-span').textContent=fmt(L)+' m | '+fmt(L\/.3048)+' ft';$('vc-r-stress').textContent=fmt(stress\/1e6)+' MPa | '+fmt(stress\/6894757.293168)+' ksi';$('vc-r-reaction').textContent=fmt(R)+' N | '+fmt(R\/4.4482216152605)+' lbf';$('vc-r-i').textContent=fmt(I)+' m\u2074 | '+fmt(I*1e12)+' mm\u2074';$('vc-r-load').textContent=fmt(mt)+' kg\/m | '+fmt(w)+' N\/m (pipe '+fmt(mp)+';fluid '+fmt(mf)+';added '+fmt(ma)+' kg\/m)';$('vc-r-note').textContent='This is the span that produces the entered deflection in one ideal pin\u2013roller uniform-load beam.It is not a maximum allowable support spacing;stress,dynamics,thermal,local,point-load,support and code checks remain open.';$('vc-validation').textContent='';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',String(s.classList.contains('vc-open')))})});var faq=[['Why is there no continuous-span result?','Continuity depends on the real sequence of spans,end conditions and support stiffness.A universal fixed-fixed coefficient is unsafe.'],['Why show bending stress without pass\/fail?','The stress covers only this ideal uniform gravity load.Code combinations,allowables,temperature and other stresses are separate.'],['Can fluid density be zero?','Yes.Use zero for an empty\/no-contained-fluid mass case when that state is the controlled case.'],['Can this place supports near a valve?','No.Valves and fittings are concentrated loads and require a model that includes their positions and actual support conditions.']];var l=$('vc-faq-list');faq.forEach(function(x){var w=document.createElement('div');w.className='vc-faq-item';var b=document.createElement('button');b.type='button';b.className='vc-faq-q';b.textContent=x[0];var a=document.createElement('div');a.className='vc-faq-a';a.textContent=x[1];w.appendChild(b);w.appendChild(a);l.appendChild(w)});l.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});hide('')})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the ideal simply supported span producing a documented uniform-load deflection,plus bending stress and reactions,without claiming allowable pipe-support spacing.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100186","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100186\/revisions"}],"predecessor-version":[{"id":102524,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100186\/revisions\/102524"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/media?parent=100186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/categories?post=100186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/tags?post=100186"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}