{"id":100255,"date":"2026-02-15T20:29:55","date_gmt":"2026-02-15T20:29:55","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100255"},"modified":"2026-07-15T19:03:33","modified_gmt":"2026-07-15T19:03:33","slug":"thermal-expansion-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/vi\/calculators\/thermal-expansion-calculator\/","title":{"rendered":"M\u00e1y t\u00ednh gi\u00e3n n\u1edf nhi\u1ec7t \u2014 Tuy\u1ebfn t\u00ednh, th\u1ec3 t\u00edch v\u00e0 \u1ee9ng su\u1ea5t"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Thermal Expansion Calculator\",\"description\":\"Calculate linear and volumetric thermal expansion with 20+ materials. Pipe expansion, expansion loop sizing, thermal stress when constrained.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/thermal-expansion-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-06-01\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is the coefficient of thermal expansion (CTE)?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"CTE (\u03b1) is the fractional change in length per degree of temperature change. Units: \u00b5m\/(m\u00b7\u00b0C) or 10\u207b\u2076\/\u00b0C. Example: steel \u03b1 \u2248 12 \u00b5m\/(m\u00b7\u00b0C) means a 1m bar grows 12 \u00b5m per 1\u00b0C rise.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I calculate thermal stress in a constrained member?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"When expansion is fully restrained: \u03c3 = E \u00d7 \u03b1 \u00d7 \u0394T. For steel at \u0394T = 100\u00b0C: \u03c3 = 200,000 \u00d7 12e-6 \u00d7 100 = 240 MPa \u2014 nearly yield stress!\"}},\n{\"@type\":\"Question\",\"name\":\"What is volumetric expansion?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For isotropic materials, volumetric CTE \u2248 3 \u00d7 linear CTE. Volume change: \u0394V = V\u2080 \u00d7 3\u03b1 \u00d7 \u0394T. Important for tanks, pipes, and enclosed fluid systems.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I size an expansion loop for piping?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Guided-cantilever formula: loop leg length L = \u221a(3 \u00d7 E \u00d7 D \u00d7 \u0394 \/ S\u2090), where E = elastic modulus (MPa), D = pipe OD (mm), \u0394 = expansion (mm), S\u2090 = allowable stress range (MPa); L in mm. Rule of thumb for carbon steel (E \u2248 200 GPa, S\u2090 \u2248 138 MPa): L \u2248 66 \u00d7 \u221a(D \u00d7 \u0394) in mm.\"}},\n{\"@type\":\"Question\",\"name\":\"Does CTE vary with temperature?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Yes. CTE generally increases slightly with temperature. Values given are mean values over a range (typically 20\u2013100\u00b0C). For cryogenic or high-temp work, use specific data for the actual temperature range.\"}}\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 href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" rel=\"stylesheet\">\n\n<link rel=\"stylesheet\" 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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-therm-exp\">\n<header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p><h1 class=\"vc-header-title\">Thermal Expansion Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate linear and volumetric thermal expansion for 20+ materials. Pipe expansion between anchors, expansion loop sizing, and thermal stress when constrained (\u03c3 = E\u00b7\u03b1\u00b7\u0394T).<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Linear &amp; Volumetric<\/span><span class=\"vc-badge\">20+ Materials<\/span><span class=\"vc-badge\">Thermal Stress<\/span><span class=\"vc-badge\">Pipe Expansion<\/span><\/div><\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-unit-bar\" id=\"vc-unit-bar\"><button type=\"button\" class=\"vc-unit-btn vc-active\" data-u=\"metric\">Metric (mm, \u00b0C)<\/button><button type=\"button\" class=\"vc-unit-btn\" data-u=\"imperial\">Imperial (in, \u00b0F)<\/button><\/div>\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mat\">Material<\/label><select class=\"vc-select\" id=\"vc-mat\">\n                <optgroup label=\"Carbon &#038; Alloy Steels\">\n                    <option value=\"cs\" selected>Carbon steel (SA-516 \/ P265GH)<\/option>\n                    <option value=\"las\">Low-alloy steel (SA-387 \/ 16Mo3)<\/option>\n                    <option value=\"crmo\">Cr-Mo steel (2.25Cr-1Mo)<\/option>\n                <\/optgroup>\n                <optgroup label=\"Stainless Steels\">\n                    <option value=\"ss304\">Stainless 304 \/ 1.4301<\/option>\n                    <option value=\"ss316\">Stainless 316 \/ 1.4401<\/option>\n                    <option value=\"ss321\">Stainless 321 \/ 1.4541<\/option>\n                    <option value=\"duplex\">Duplex 2205<\/option>\n                <\/optgroup>\n                <optgroup label=\"Non-Ferrous Metals\">\n                    <option value=\"al\">Aluminium 6061<\/option>\n                    <option value=\"cu\">Copper (pure)<\/option>\n                    <option value=\"brass\">Brass (CuZn30)<\/option>\n                    <option value=\"bronze\">Bronze (CuSn8)<\/option>\n                    <option value=\"ti\">Titanium Grade 2<\/option>\n                    <option value=\"ni\">Nickel 200<\/option>\n                    <option value=\"inc625\">Inconel 625<\/option>\n                    <option value=\"inc718\">Inconel 718<\/option>\n                <\/optgroup>\n                <optgroup label=\"Cast Iron\">\n                    <option value=\"gci\">Grey cast iron<\/option>\n                    <option value=\"dci\">Ductile cast iron<\/option>\n                <\/optgroup>\n                <optgroup label=\"Non-Metals\">\n                    <option value=\"concrete\">Concrete<\/option>\n                    <option value=\"glass\">Glass (soda-lime)<\/option>\n                    <option value=\"ptfe\">PTFE (Teflon)<\/option>\n                    <option value=\"pe\">Polyethylene (HDPE)<\/option>\n                    <option value=\"pvc\">PVC<\/option>\n                    <option value=\"invar\">Invar 36 (low CTE)<\/option>\n                <\/optgroup>\n                <option value=\"custom\">\u2014 Custom CTE \u2014<\/option>\n            <\/select><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-cte\">CTE \u03b1 <span class=\"vc-label-hint\">(\u00d710\u207b\u2076 \/\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-cte\" step=\"any\" value=\"12.0\" placeholder=\"e.g. 12\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-len\">Original Length <span class=\"vc-label-hint\" id=\"vc-len-unit\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-len\" step=\"any\" value=\"1000\" placeholder=\"e.g. 1000\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-dt\">Temperature Change \u0394T <span class=\"vc-label-hint\" id=\"vc-dt-unit\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-dt\" step=\"any\" value=\"100\" placeholder=\"e.g. 100\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-vol\">Original Volume <span class=\"vc-label-hint\" id=\"vc-vol-unit\">(cm\u00b3 \u2014 optional, for volumetric)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-vol\" step=\"any\" value=\"\" placeholder=\"optional\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-emod\">Elastic Modulus E <span class=\"vc-label-hint\">(GPa \u2014 for stress calc)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-emod\" step=\"any\" value=\"200\" placeholder=\"e.g. 200\"><\/div>\n        <\/div>\n        <div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-mat=\"cs\" data-len=\"6000\" data-dt=\"80\">6m steel pipe, \u0394T=80\u00b0C<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-mat=\"ss304\" data-len=\"3000\" data-dt=\"200\">3m SS304 pipe, \u0394T=200\u00b0C<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-mat=\"al\" data-len=\"2000\" data-dt=\"50\">2m aluminium, \u0394T=50\u00b0C<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-mat=\"cu\" data-len=\"500\" data-dt=\"150\">0.5m copper, \u0394T=150\u00b0C<\/button>\n        <\/div>\n    <\/form>\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Expansion 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\">Linear Expansion \u0394L<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dl\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Expansion in mm<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mm\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Expansion in \u00b5m<\/div><div class=\"vc-rcard-value\" id=\"vc-r-um\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Expansion in mils<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mils\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">New Length<\/div><div class=\"vc-rcard-value\" id=\"vc-r-newlen\" style=\"font-size:18px\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Strain \u03b5<\/div><div class=\"vc-rcard-value\" id=\"vc-r-strain\" style=\"font-size:18px\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Thermal Stress (if constrained)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-stress\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Thermal Force (per cm\u00b2 area)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-force\" style=\"font-size:18px\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Volumetric Expansion \u0394V<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dv\" style=\"font-size:18px\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Expansion Loop (steel pipe, rule of thumb)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-loop\" style=\"font-size:16px\">\u2014<\/div><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Theory, Formulas &amp; CTE Database<\/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>Linear Expansion<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n        <p>Where \u03b1 is the coefficient of thermal expansion (CTE) in 1\/\u00b0C, L\u2080 is the original length, and \u0394T is the temperature change.<\/p>\n        <h3>Volumetric Expansion<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n        <p>For isotropic materials, the volumetric CTE is approximately 3\u00d7 the linear CTE.<\/p>\n        <h3>Thermal Stress (Constrained Member)<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n        <p>When expansion is completely prevented (e.g., pipe between two rigid anchors), the resulting stress can be very high. This is compressive for heating and tensile for cooling.<\/p>\n        <h3>Expansion Loop Sizing (Rule of Thumb)<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-4\"><\/div>\n        <p>Where D is the pipe outer diameter (mm) and \u0394 is the expansion (mm); the result L is in mm. The factor 66 comes from the guided-cantilever formula L = \u221a(3 \u00b7 E \u00b7 D \u00b7 \u0394 \/ S\u2090) evaluated for carbon steel (E = 200 GPa, S\u2090 = 138 MPa). For other materials or allowable stresses use the full formula (L scales as \u221a(E\/S\u2090)). This is a screening estimate, not a full code flexibility analysis.<\/p>\n        <h3>Practical Example<\/h3>\n        <div class=\"vc-example-box\"><div class=\"vc-example-title\">Example \u2014 6m Carbon Steel Pipe, \u0394T = 80\u00b0C<\/div>\n            <p><strong>Given:<\/strong> L\u2080 = 6000 mm, \u03b1 = 12 \u00d7 10\u207b\u2076 \/\u00b0C, \u0394T = 80\u00b0C, E = 200 GPa<\/p>\n            <p>\u0394L = 12e-6 \u00d7 6000 \u00d7 80 = <strong>5.76 mm<\/strong><\/p>\n            <p>Thermal stress if constrained: \u03c3 = 200,000 \u00d7 12e-6 \u00d7 80 = <strong>192 MPa<\/strong><\/p>\n            <p>Expansion loop (DN100\/OD 114 mm): L \u2248 66 \u00d7 \u221a(114 \u00d7 5.76) \u2248 <strong>1,690 mm \u2248 1.7 m<\/strong><\/p>\n        <\/div>\n        <h3>Material CTE Database<\/h3>\n        <table class=\"vc-table\"><thead><tr><th>Material<\/th><th>\u03b1 (\u00d710\u207b\u2076 \/\u00b0C)<\/th><th>E (GPa)<\/th><th>Notes<\/th><\/tr><\/thead><tbody>\n            <tr><td>Carbon steel<\/td><td>12.0<\/td><td>200<\/td><td>SA-516, P265GH<\/td><\/tr>\n            <tr><td>Low-alloy steel<\/td><td>12.5<\/td><td>200<\/td><td>16Mo3, SA-387<\/td><\/tr>\n            <tr><td>Cr-Mo steel (2.25Cr)<\/td><td>12.0<\/td><td>205<\/td><td>SA-335 P22<\/td><\/tr>\n            <tr><td>Stainless 304<\/td><td>17.3<\/td><td>193<\/td><td>1.4301, 18Cr-8Ni<\/td><\/tr>\n            <tr><td>Stainless 316<\/td><td>16.0<\/td><td>193<\/td><td>1.4401, 16Cr-10Ni-2Mo<\/td><\/tr>\n            <tr><td>Stainless 321<\/td><td>17.0<\/td><td>193<\/td><td>1.4541, Ti-stabilized<\/td><\/tr>\n            <tr><td>Duplex 2205<\/td><td>13.0<\/td><td>200<\/td><td>1.4462<\/td><\/tr>\n            <tr><td>Aluminium 6061<\/td><td>23.6<\/td><td>69<\/td><td>T6 temper<\/td><\/tr>\n            <tr><td>Copper<\/td><td>17.0<\/td><td>117<\/td><td>Pure, annealed<\/td><\/tr>\n            <tr><td>Brass (CuZn30)<\/td><td>20.0<\/td><td>110<\/td><td>Cartridge brass<\/td><\/tr>\n            <tr><td>Bronze (CuSn8)<\/td><td>18.0<\/td><td>110<\/td><td>Phosphor bronze<\/td><\/tr>\n            <tr><td>Titanium Gr.2<\/td><td>8.6<\/td><td>103<\/td><td>Commercially pure<\/td><\/tr>\n            <tr><td>Nickel 200<\/td><td>13.3<\/td><td>207<\/td><td>Pure nickel<\/td><\/tr>\n            <tr><td>Inconel 625<\/td><td>12.8<\/td><td>207<\/td><td>Ni-Cr-Mo<\/td><\/tr>\n            <tr><td>Inconel 718<\/td><td>13.0<\/td><td>211<\/td><td>Ni-Cr-Fe<\/td><\/tr>\n            <tr><td>Grey cast iron<\/td><td>10.5<\/td><td>110<\/td><td>GG25<\/td><\/tr>\n            <tr><td>Ductile cast iron<\/td><td>11.0<\/td><td>170<\/td><td>GGG40<\/td><\/tr>\n            <tr><td>Concrete<\/td><td>12.0<\/td><td>30<\/td><td>Varies with mix<\/td><\/tr>\n            <tr><td>Glass (soda-lime)<\/td><td>9.0<\/td><td>72<\/td><td>Window glass<\/td><\/tr>\n            <tr><td>PTFE (Teflon)<\/td><td>120.0<\/td><td>0.5<\/td><td>Very high CTE<\/td><\/tr>\n            <tr><td>HDPE<\/td><td>150.0<\/td><td>1.0<\/td><td>Polyethylene<\/td><\/tr>\n            <tr><td>PVC<\/td><td>80.0<\/td><td>3.0<\/td><td>Rigid PVC<\/td><\/tr>\n            <tr><td>Invar 36<\/td><td>1.2<\/td><td>145<\/td><td>Ultra-low CTE alloy<\/td><\/tr>\n        <\/tbody><\/table>\n        <div class=\"vc-info-box\"><p><strong>\ud83d\udca1 Note:<\/strong> CTE values are mean values for 20\u2013100\u00b0C. For high-temperature or cryogenic applications, use specific data from material standards.<\/p><\/div>\n    <\/div><\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-related\"><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><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/allowable-stress-by-material\/\">Allowable Stress<\/a><a class=\"vc-related-link\" href=\"\/calculators\/strength-unit-converter\/\">Strength Unit Converter<\/a><a class=\"vc-related-link\" href=\"\/calculators\/density-mass-volume\/\">Density Calculator<\/a><\/div><\/div><\/div><\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-faq\"><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><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera<\/strong> \u2014 Portable Balancing &amp; 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Units: \u00b5m\/(m\u00b7\u00b0C) or equivalently 10\u207b\u2076\/\u00b0C.<\/p><p>Example: Steel \u03b1 \u2248 12 means a 1-meter bar grows 12 \u00b5m (0.012 mm) for each 1\u00b0C rise. Over 100\u00b0C, that\\'s 1.2 mm \u2014 significant for precision machinery and piping.<\/p>'},\n        {q:'How do I calculate thermal stress in a constrained member?',a:'<p>When a member is fully restrained (can\\'t expand freely), the thermal stress is:<\/p><p><strong>\u03c3 = E \u00d7 \u03b1 \u00d7 \u0394T<\/strong><\/p><p>For carbon steel at \u0394T = 100\u00b0C: \u03c3 = 200,000 MPa \u00d7 12\u00d710\u207b\u2076 \u00d7 100 = <strong>240 MPa<\/strong>. This is close to the yield strength! Always check that constrained thermal stresses don\\'t exceed allowable values.<\/p>'},\n        {q:'What is volumetric vs linear expansion?',a:'<p><strong>Linear:<\/strong> Change in one dimension. \u0394L = \u03b1 \u00d7 L\u2080 \u00d7 \u0394T<\/p><p><strong>Volumetric:<\/strong> Change in volume. \u0394V \u2248 3\u03b1 \u00d7 V\u2080 \u00d7 \u0394T (for isotropic materials).<\/p><p>Volumetric expansion matters for enclosed fluids (tanks, pipes), sealed containers, and precision assemblies.<\/p>'},\n        {q:'How do I size an expansion loop for piping?',a:'<p>Guided-cantilever formula: <strong>L = \u221a(3 \u00d7 E \u00d7 D \u00d7 \u0394 \/ S\u2090)<\/strong> with E in MPa, D and \u0394 in mm, S\u2090 in MPa (L in mm). Rule of thumb for carbon steel (E \u2248 200 GPa, S\u2090 \u2248 138 MPa): <strong>L \u2248 66 \u00d7 \u221a(D \u00d7 \u0394)<\/strong> where D = pipe OD (mm) and \u0394 = expansion (mm).<\/p><p>For DN100 pipe (OD 114 mm) with 6 mm expansion: L \u2248 66 \u00d7 \u221a(114 \u00d7 6) \u2248 1,700 mm \u2248 1.7 m.<\/p><p>Alternatives to loops: bellows expansion joints, sliding supports, changes of direction in routing.<\/p>'},\n        {q:'Does CTE vary with temperature?',a:'<p>Yes. CTE generally <strong>increases with temperature<\/strong>. The values in our database are mean values for the 20\u2013100\u00b0C range.<\/p><ul><li>Cryogenic: CTE is lower (sometimes much lower)<\/li><li>High-temp (>500\u00b0C): CTE increases 10\u201330% above room-temp values<\/li><li>Near phase changes: CTE can change dramatically<\/li><\/ul><p>For critical applications, use specific material data from standards (ASME II-D, EN 13480) for your exact temperature range.<\/p>'}\n    ];\n    var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\n    fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(!b)return;b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\n    function renderFormulas(){try{\n        katex.render('\\\\Delta L = \\\\alpha \\\\cdot L_0 \\\\cdot \\\\Delta T',$('vc-katex-1'),{displayMode:true,throwOnError:false});\n        katex.render('\\\\Delta V \\\\approx 3\\\\alpha \\\\cdot V_0 \\\\cdot \\\\Delta T',$('vc-katex-2'),{displayMode:true,throwOnError:false});\n        katex.render('\\\\sigma = E \\\\cdot \\\\alpha \\\\cdot \\\\Delta T',$('vc-katex-3'),{displayMode:true,throwOnError:false});\n        katex.render('L_{\\\\text{loop}} \\\\approx 66\\\\sqrt{D_{\\\\text{OD}} \\\\cdot \\\\Delta L} \\\\quad [\\\\text{mm}]',$('vc-katex-4'),{displayMode:true,throwOnError:false});\n    }catch(e){}}\n    function init(){\n        try{var su=localStorage.getItem('vc_unit_'+SLUG);if(su)setUnit(su)}catch(e){}\n        loadURL();renderFormulas();calculate();\n    }\n    if(document.readyState==='loading')document.addEventListener('DOMContentLoaded',init);else init();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n gi\u00e3n n\u1edf nhi\u1ec7t mi\u1ec5n ph\u00ed: gi\u00e3n n\u1edf tuy\u1ebfn t\u00ednh v\u00e0 th\u1ec3 t\u00edch v\u1edbi h\u01a1n 20 lo\u1ea1i v\u1eadt li\u1ec7u. Gi\u00e3n n\u1edf \u1ed1ng gi\u1eefa c\u00e1c \u0111i\u1ec3m neo, t\u00ednh to\u00e1n k\u00edch th\u01b0\u1edbc v\u00f2ng gi\u00e3n n\u1edf. \u1ee8ng su\u1ea5t nhi\u1ec7t \u03c3=E\u03b1\u0394T khi b\u1ecb h\u1ea1n ch\u1ebf.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100255","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":4,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100255\/revisions"}],"predecessor-version":[{"id":102599,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100255\/revisions\/102599"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/media?parent=100255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/categories?post=100255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/tags?post=100255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}