{"id":850,"date":"2026-10-03T15:50:32","date_gmt":"2026-10-03T14:50:32","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/young-modulu-hesaplama\/"},"modified":"2026-10-03T15:50:32","modified_gmt":"2026-10-03T14:50:32","slug":"young-modulu-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/fizik\/young-modulu-hesaplama\/","title":{"rendered":"Young Mod\u00fcl\u00fc Hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Gerilme ve Gerinimden Young Mod\u00fcl\u00fc Hesaplama<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"850\" data-favorite-title=\"Young Mod\u00fcl\u00fc\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/fizik\/young-modulu-hesaplama\/\" data-favorite-excerpt=\"Gerilme ve birim uzamadan ya da kuvvet, kesit alan\u0131 ve uzunluk de\u011fi\u015fiminden Young mod\u00fcl\u00fcn\u00fc (elastisite mod\u00fcl\u00fcn\u00fc) hesaplay\u0131n. Sonu\u00e7lar GPa, MPa, Pa ve psi cinsinden.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/fizik\/young-modulu-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-850\" data-post=\"850\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Hesaplama y\u00f6ntemi<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"hesaplama_yntemi\"><option value=\"ss\" selected>Gerilme ve gerinimden<\/option><option value=\"fal\">Kuvvet, alan ve uzunluklardan<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Gerilme (\u03c3)<\/label><div class=\"term\">\u03c3<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"gerilme_\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 200\" min=\"0\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"birim\" aria-label=\"Birim\"><option value=\"Pa\">Pa<\/option><option value=\"kPa\">kPa<\/option><option value=\"MPa\" selected>MPa<\/option><option value=\"GPa\">GPa<\/option><option value=\"psi\">psi<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Birim alan ba\u015f\u0131na kuvvet (\u03c3 = F\/A). A\u015fa\u011f\u0131daki kuvvet y\u00f6ntemini kullanmak istiyorsan\u0131z bo\u015f b\u0131rak\u0131n.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-4\">Gerinim (\u03b5)<\/label><div class=\"term\">\u03b5<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"gerinim_\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.001\" min=\"0\" value=\"0.001\"\/><small id=\"calc-info-4\">G\u00f6reli \u015fekil de\u011fi\u015ftirme \u03b5 = \u0394L\/L\u2080 (boyutsuz). 0,001 = %0,1 uzama.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-4\" hidden><label for=\"field-5\">Kuvvet (F)<\/label><div class=\"term\">F<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"kuvvet_f\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2000\" min=\"0\" value=\"2000\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"birim\" aria-label=\"Birim\"><option value=\"N\" selected>N<\/option><option value=\"kN\">kN<\/option><option value=\"lbf\">lbf<\/option><option value=\"kgf\">kgf<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Numuneye uygulanan \u00e7ekme veya basma kuvveti.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-5\" hidden><label for=\"field-7\">Kesit alan\u0131 (A)<\/label><div class=\"term\">A<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"kesit_alan_a\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm2\" selected>mm\u00b2<\/option><option value=\"cm2\">cm\u00b2<\/option><option value=\"m2\">m\u00b2<\/option><option value=\"in2\">in\u00b2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Kuvvete dik, numunenin ba\u015flang\u0131\u00e7 kesiti. 10 mm \u00d7 10 mm&#039;lik bir \u00e7ubu\u011fun kesit alan\u0131 A = 100 mm\u00b2&#039;dir.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-6\" hidden><label for=\"field-9\">Ba\u015flang\u0131\u00e7 uzunlu\u011fu (L\u2080)<\/label><div class=\"term\">L\u2080<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"balang_uzunluu_l\" id=\"field-9\" aria-describedby=\"calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1000\" min=\"0\" value=\"1000\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-9\">Kuvvet uygulanmadan \u00f6nceki numune uzunlu\u011fu (\u00f6l\u00e7\u00fcm uzunlu\u011fu).<\/small><\/div><div class=\"field is-single has-term\" id=\"input-7\" hidden><label for=\"field-11\">Uzunluk de\u011fi\u015fimi (\u0394L)<\/label><div class=\"term\">\u0394L<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"uzunluk_deiimi_l\" id=\"field-11\" aria-describedby=\"calc-info-11\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.1\" min=\"0\" value=\"0.1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-12\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-11\">Kuvvet etkisi alt\u0131nda numunenin uzamas\u0131 (pozitif) veya s\u0131k\u0131\u015fmas\u0131. S\u0131f\u0131r olmamal\u0131d\u0131r.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"850\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Young Mod\u00fcl\u00fc Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Young elastisite mod\u00fcl\u00fc<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Form\u00fcl, gerilme\u2013gerinim \u00f6zeti ve notlar<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"850\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Young Mod\u00fcl\u00fc Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ E = \\frac{\\sigma}{\\varepsilon} = \\frac{F \/ A}{\\Delta L \/ L_0} = \\frac{F \\, L_0}{A \\, \\Delta L} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(E\\) \u2014 Young mod\u00fcl\u00fc, elastisite mod\u00fcl\u00fc (Pa)<\/li>\n<li>\\(\\sigma\\) \u2014 gerilme, birim alana d\u00fc\u015fen kuvvet \\(\\sigma = F\/A\\) (Pa)<\/li>\n<li>\\(\\varepsilon\\) \u2014 birim uzama, ba\u011f\u0131l \u015fekil de\u011fi\u015ftirme \\(\\varepsilon = \\Delta L \/ L_0\\) (boyutsuz)<\/li>\n<li>\\(F\\) \u2014 uygulanan \u00e7ekme veya basma kuvveti (N)<\/li>\n<li>\\(A\\) \u2014 numunenin ba\u015flang\u0131\u00e7 kesit alan\u0131 (m\u00b2)<\/li>\n<li>\\(L_0\\) \u2014 numunenin ba\u015flang\u0131\u00e7 uzunlu\u011fu (m)<\/li>\n<li>\\(\\Delta L\\) \u2014 y\u00fck alt\u0131ndaki uzunluk de\u011fi\u015fimi (m)<\/li>\n<\/ul>\n<p>Form\u00fcl, Hooke yasas\u0131n\u0131n oran bi\u00e7imini ifade eder: Young mod\u00fcl\u00fc, elastik b\u00f6lgede gerilme ile birim uzama aras\u0131ndaki sabit orand\u0131r; yani gerilme\u2013birim uzama e\u011frisinin d\u00fcz do\u011fru k\u0131sm\u0131n\u0131n e\u011fimidir.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Young Mod\u00fcl\u00fc \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \u00e7elik bir \u00e7ubu\u011fa, i\u00e7inde 200 MPa gerilme olu\u015fturan ve orijinal uzunlu\u011funun %0,1'i kadar uzamas\u0131na neden olan bir y\u00fck uygulan\u0131yor.<\/p>\n<p>\\[ \\varepsilon = 0.1\\% = 0.001 \\]<\/p>\n<p>\\[ E = \\frac{\\sigma}{\\varepsilon} = \\frac{200\\,000\\,000\\ \\text{Pa}}{0.001} = 200\\,000\\,000\\,000\\ \\text{Pa} \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(E = 200\\ \\text{GPa}\\) \u2014 yap\u0131sal \u00e7elik i\u00e7in tipik bir de\u011fer.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Hesaplama y\u00f6ntemi<\/strong> a\u00e7\u0131l\u0131r men\u00fcs\u00fcn\u00fc a\u00e7\u0131n ve bu iki de\u011feri zaten biliyorsan\u0131z <em>Gerilme ve birim uzamadan<\/em>, gerilme ile birim uzamay\u0131 hesaplay\u0131c\u0131n\u0131n bulmas\u0131n\u0131 istiyorsan\u0131z <em>Kuvvet, alan ve uzunluklardan<\/em> se\u00e7ene\u011fini se\u00e7in.<\/li>\n<li>\u0130lk y\u00f6ntem i\u00e7in <strong>Gerilme (\u03c3)<\/strong> de\u011ferini birimiyle birlikte (Pa, kPa, MPa, GPa veya psi) ve <strong>Birim uzama (\u03b5)<\/strong> de\u011ferini ondal\u0131k kesir olarak girin \u2014 0,001, %0,1 uzama anlam\u0131na gelir.<\/li>\n<li>\u0130kinci y\u00f6ntem i\u00e7in <strong>Kuvvet (F)<\/strong> (N, kN, lbf veya kgf), <strong>Kesit alan\u0131 (A)<\/strong> (mm\u00b2, cm\u00b2, m\u00b2 veya in\u00b2), <strong>Ba\u015flang\u0131\u00e7 uzunlu\u011fu (L\u2080)<\/strong> ve <strong>Uzunluk de\u011fi\u015fimi (\u0394L)<\/strong> de\u011ferlerini uyumlu uzunluk birimleriyle girin.<\/li>\n<li>Sonucu okuyun: Young mod\u00fcl\u00fc, hesaplamada kullan\u0131lan gerilme ve birim uzama \u00f6zetiyle birlikte GPa, MPa, Pa, psi, ksi ve psf cinsinden g\u00f6sterilir.<\/li>\n<li>Sonucunuzu \u00e7elik, al\u00fcminyum, beton ve kau\u00e7uk gibi yayg\u0131n malzemelerin tipik de\u011ferleriyle kar\u015f\u0131la\u015ft\u0131ran yorum notunu inceleyin.<\/li>\n<\/ol>\n<h2>Young Mod\u00fcl\u00fc Nedir?<\/h2>\n<p>Young mod\u00fcl\u00fc (elastisite mod\u00fcl\u00fc olarak da adland\u0131r\u0131l\u0131r), bir malzemenin ne kadar kat\u0131 oldu\u011funu \u2014 gerilmeye veya s\u0131k\u0131\u015ft\u0131rmaya ne kadar direndi\u011fini \u2014 tan\u0131mlayan bir malzeme \u00f6zelli\u011fidir. Malzemenin y\u00fck kalkt\u0131ktan sonra \u00f6zg\u00fcn \u015fekline d\u00f6nd\u00fc\u011f\u00fc, \u015fekil de\u011fi\u015ftirmenin elastik b\u00f6lgesindeki gerilmenin birim uzamaya oran\u0131 olarak tan\u0131mlan\u0131r. Mod\u00fcl ne kadar y\u00fcksekse, ayn\u0131 miktarda \u015fekil de\u011fi\u015ftirmeyi olu\u015fturmak i\u00e7in o kadar fazla kuvvet gerekir.<\/p>\n<p>Gerilme \\(\\sigma = F\/A\\) y\u00fck\u00fcn \u015fiddetini \u2014 kesit alan\u0131na yay\u0131lan kuvveti \u2014 \u00f6l\u00e7er; birim uzama \\(\\varepsilon = \\Delta L \/ L_0\\) ise tepkiyi \u2014 orijinal uzunlu\u011fa g\u00f6re uzama veya k\u0131salma miktar\u0131n\u0131 \u2014 \u00f6l\u00e7er. Birim uzama boyutsuz oldu\u011fundan, Young mod\u00fcl\u00fc de gerilmeyle ayn\u0131 birimlere sahiptir; metrik uygulamada genellikle gigapaskal (GPa), emperyal birimlerde ise in\u00e7 kare ba\u015f\u0131na libre (psi) kullan\u0131l\u0131r.<\/p>\n<p>Sonu\u00e7, gerilme\u2013birim uzama e\u011frisinin do\u011frusal k\u0131sm\u0131n\u0131n e\u011fimini verir. 200 GPa de\u011fer, malzemeden yap\u0131lan 1 metrelik bir \u00e7ubu\u011fun, uygulanan her megapaskal gerilme i\u00e7in yaln\u0131zca 5 mikrometre uzayaca\u011f\u0131 anlam\u0131na gelir. Tipik de\u011ferler yumu\u015fak kau\u00e7uk i\u00e7in yakla\u015f\u0131k 0,01 GPa'dan elmas i\u00e7in yakla\u015f\u0131k 1100 GPa'ya kadar uzan\u0131r; yap\u0131sal \u00e7elik 200 GPa civar\u0131nda, al\u00fcminyum ala\u015f\u0131mlar\u0131 70 GPa civar\u0131nda, beton ise 30 GPa civar\u0131ndad\u0131r. Bir malzemenin mod\u00fcl\u00fcn\u00fc bilmek, yap\u0131 m\u00fchendisli\u011finde sehimleri \u00f6ng\u00f6rmek, malzeme biliminde yeni malzemeleri karakterize etmek ve elastik \u015fekil de\u011fi\u015ftirmenin \u00f6nemli oldu\u011fu k\u00f6pr\u00fclerden yaylara kadar her durumda gereklidir.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve Pratik \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca do\u011frusal elastik aral\u0131k.<\/strong> \\(E = \\sigma\/\\varepsilon\\) form\u00fcl\u00fc yaln\u0131zca, gerilme ile birim uzaman\u0131n orant\u0131l\u0131 oldu\u011fu orant\u0131l\u0131l\u0131k s\u0131n\u0131r\u0131n\u0131n alt\u0131nda ge\u00e7erlidir. Bu s\u0131n\u0131r\u0131n \u00f6tesinde malzeme akar veya do\u011frusal olmayan bi\u00e7imde \u015fekil de\u011fi\u015ftirir ve tek bir mod\u00fcl art\u0131k davran\u0131\u015f\u0131n\u0131 tan\u0131mlamaz.<\/li>\n<li><strong>Homojen ve izotrop malzeme.<\/strong> Hesaplama, kat\u0131nl\u0131\u011f\u0131n her yerde ve her y\u00f6nde ayn\u0131 oldu\u011funu varsayar. Ah\u015fap, kompozitler ve elyaf takviyeli malzemeler anizotropiktir \u2014 doku boyunca mod\u00fclleri, doku dik y\u00f6n\u00fcndekinin birka\u00e7 kat\u0131 olabilir.<\/li>\n<li><strong>K\u00fc\u00e7\u00fck \u015fekil de\u011fi\u015ftirmeler.<\/strong> Y\u00fck alt\u0131nda \u00f6l\u00e7\u00fclen de\u011ferleri de\u011fil, ba\u015flang\u0131\u00e7 kesit alan\u0131n\u0131 \\(A\\) ve ba\u015flang\u0131\u00e7 uzunlu\u011funu \\(L_0\\) kullan\u0131n. B\u00fcy\u00fck birim uzamalarda m\u00fchendislik gerilme\u2013birim uzama tan\u0131m\u0131 do\u011fru olmaktan \u00e7\u0131kar.<\/li>\n<li><strong>Pozitif b\u00fcy\u00fckl\u00fckler.<\/strong> Uzama veya k\u0131salmay\u0131 b\u00fcy\u00fckl\u00fck olarak girin; hesaplay\u0131c\u0131 s\u0131f\u0131r ve negatif de\u011ferleri kabul etmez. Uygulamada ayn\u0131 malzemenin \u00e7ekme ve basma mod\u00fclleri genellikle birbirine yak\u0131nd\u0131r, ancak baz\u0131 malzemeler (\u00f6r. beton) basma ve \u00e7ekmede \u00e7ok farkl\u0131 davran\u0131r.<\/li>\n<li><strong>S\u0131cakl\u0131k ve h\u0131z etkileri.<\/strong> Young mod\u00fcl\u00fc s\u0131cakl\u0131kla azal\u0131r ve y\u00fck\u00fcn uygulanma h\u0131z\u0131na ba\u011fl\u0131 olabilir; \u00f6zellikle polimerlerde b\u00f6yledir. Ba\u015fvuru tablolar\u0131ndaki de\u011ferler genellikle oda s\u0131cakl\u0131\u011f\u0131nda ve yava\u015f y\u00fckleme alt\u0131nda \u00f6l\u00e7\u00fclm\u00fc\u015ft\u00fcr.<\/li>\n<\/ul>\n<h2>Tipik Young Mod\u00fcl\u00fc De\u011ferleri<\/h2>\n<table>\n<thead>\n<tr>\n<th>Malzeme<\/th>\n<th>Young mod\u00fcl\u00fc (GPa)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Kau\u00e7uk (do\u011fal)<\/td>\n<td>0.01 \u2013 0.1<\/td>\n<\/tr>\n<tr>\n<td>Naylon<\/td>\n<td>2 \u2013 4<\/td>\n<\/tr>\n<tr>\n<td>Ah\u015fap (doku boyunca)<\/td>\n<td>9 \u2013 16<\/td>\n<\/tr>\n<tr>\n<td>Beton<\/td>\n<td>30 \u2013 40<\/td>\n<\/tr>\n<tr>\n<td>Al\u00fcminyum ala\u015f\u0131m\u0131<\/td>\n<td>69 \u2013 79<\/td>\n<\/tr>\n<tr>\n<td>Pirin\u00e7<\/td>\n<td>100 \u2013 110<\/td>\n<\/tr>\n<tr>\n<td>Bak\u0131r<\/td>\n<td>110 \u2013 130<\/td>\n<\/tr>\n<tr>\n<td>\u00c7elik (yap\u0131sal)<\/td>\n<td>190 \u2013 210<\/td>\n<\/tr>\n<tr>\n<td>Tungsten<\/td>\n<td>400 \u2013 411<\/td>\n<\/tr>\n<tr>\n<td>Elmas<\/td>\n<td>1050 \u2013 1200<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Y\u00fckl\u00fc bir yap\u0131daki kuvvetleri analiz ediyorsan\u0131z, <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/halat-gerilmesi-hesaplama\/\">halatlardaki gerilme hesaplay\u0131c\u0131m\u0131z<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/surtunme-kuvveti-hesaplayici\/\">s\u00fcrt\u00fcnme kuvveti hesaplay\u0131c\u0131m\u0131z<\/a> da i\u015finize yarayabilir. \u015eekil de\u011fi\u015ftirmi\u015f elastik bir cisimde depolanan enerji i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/esneklik-potansiyel-enerjisi-hesaplayici\/\">elastik potansiyel enerji hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gerilme ve birim uzamadan ya da kuvvet, kesit alan\u0131 ve uzunluk de\u011fi\u015fiminden Young mod\u00fcl\u00fcn\u00fc (elastisite mod\u00fcl\u00fcn\u00fc) hesaplay\u0131n. Sonu\u00e7lar GPa, MPa, Pa ve psi cinsinden.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[55],"class_list":["post-850","post","type-post","status-publish","format-standard","hentry","category-fizik","tag-mekanik"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=850"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/850\/revisions"}],"predecessor-version":[{"id":3520,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/850\/revisions\/3520"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}