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Je dostupný v 51 jazykoch" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-51" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">51 jazykov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Young_se_modulus" title="Young se modulus – afrikánčina" lang="af" hreflang="af" data-title="Young se modulus" data-language-autonym="Afrikaans" data-language-local-name="afrikánčina" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%85%D9%84_%D9%8A%D9%88%D9%86%D8%BA" title="معامل يونغ – arabčina" lang="ar" hreflang="ar" data-title="معامل يونغ" data-language-autonym="العربية" data-language-local-name="arabčina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C_%D0%AE%D0%BD%D0%B3%D0%B0" title="Модуль Юнга – bieloruština" lang="be" hreflang="be" data-title="Модуль Юнга" data-language-autonym="Беларуская" data-language-local-name="bieloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%87%E0%A6%AF%E0%A6%BC%E0%A6%82-%E0%A6%8F%E0%A6%B0_%E0%A6%97%E0%A7%81%E0%A6%A3%E0%A6%BE%E0%A6%99%E0%A7%8D%E0%A6%95" title="ইয়ং-এর গুণাঙ্ক – bengálčina" lang="bn" hreflang="bn" data-title="ইয়ং-এর গুণাঙ্ক" data-language-autonym="বাংলা" data-language-local-name="bengálčina" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/M%C3%B2dul_d%27elasticitat" title="Mòdul d'elasticitat – katalánčina" lang="ca" hreflang="ca" data-title="Mòdul d'elasticitat" data-language-autonym="Català" data-language-local-name="katalánčina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Modul_pru%C5%BEnosti_v_tahu" title="Modul pružnosti v tahu – čeština" lang="cs" hreflang="cs" data-title="Modul pružnosti v tahu" data-language-autonym="Čeština" data-language-local-name="čeština" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AE%D0%BD%D0%B3_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%C4%95" title="Юнг модулĕ – čuvaština" lang="cv" hreflang="cv" data-title="Юнг модулĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Youngs_modul" title="Youngs modul – dánčina" lang="da" hreflang="da" data-title="Youngs modul" data-language-autonym="Dansk" data-language-local-name="dánčina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elastizit%C3%A4tsmodul" title="Elastizitätsmodul – nemčina" lang="de" hreflang="de" data-title="Elastizitätsmodul" data-language-autonym="Deutsch" data-language-local-name="nemčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Young%27s_modulus" title="Young's modulus – angličtina" lang="en" hreflang="en" data-title="Young's modulus" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Modulo_de_Young" title="Modulo de Young – esperanto" lang="eo" hreflang="eo" data-title="Modulo de Young" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/M%C3%B3dulo_de_Young" title="Módulo de Young – španielčina" lang="es" hreflang="es" data-title="Módulo de Young" data-language-autonym="Español" data-language-local-name="španielčina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Normaalelastsusmoodul" title="Normaalelastsusmoodul – estónčina" lang="et" hreflang="et" data-title="Normaalelastsusmoodul" data-language-autonym="Eesti" data-language-local-name="estónčina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Youngen_modulu" title="Youngen modulu – baskičtina" lang="eu" hreflang="eu" data-title="Youngen modulu" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%88%D9%84_%DB%8C%D8%A7%D9%86%DA%AF" title="مدول یانگ – perzština" lang="fa" hreflang="fa" data-title="مدول یانگ" data-language-autonym="فارسی" data-language-local-name="perzština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kimmokerroin" title="Kimmokerroin – fínčina" lang="fi" hreflang="fi" data-title="Kimmokerroin" data-language-autonym="Suomi" data-language-local-name="fínčina" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Module_d%27Young" title="Module d'Young – francúzština" lang="fr" hreflang="fr" data-title="Module d'Young" data-language-autonym="Français" data-language-local-name="francúzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Modal_Young" title="Modal Young – írčina" lang="ga" hreflang="ga" data-title="Modal Young" data-language-autonym="Gaeilge" data-language-local-name="írčina" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/M%C3%B3dulo_de_Young" title="Módulo de Young – galícijčina" lang="gl" hreflang="gl" data-title="Módulo de Young" data-language-autonym="Galego" data-language-local-name="galícijčina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%95%D7%93%D7%95%D7%9C_%D7%94%D7%90%D7%9C%D7%A1%D7%98%D7%99%D7%95%D7%AA" title="מודול האלסטיות – hebrejčina" lang="he" hreflang="he" data-title="מודול האלסטיות" data-language-autonym="עברית" data-language-local-name="hebrejčina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AF%E0%A4%82%E0%A4%97_%E0%A4%AE%E0%A4%BE%E0%A4%AA%E0%A4%BE%E0%A4%82%E0%A4%95" title="यंग मापांक – hindčina" lang="hi" hreflang="hi" data-title="यंग मापांक" data-language-autonym="हिन्दी" data-language-local-name="hindčina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Youngov_modul_elasti%C4%8Dnosti" title="Youngov modul elastičnosti – chorvátčina" lang="hr" hreflang="hr" data-title="Youngov modul elastičnosti" data-language-autonym="Hrvatski" data-language-local-name="chorvátčina" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Modulus_Young" title="Modulus Young – indonézština" lang="id" hreflang="id" data-title="Modulus Young" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A4%E3%83%B3%E3%82%B0%E7%8E%87" title="ヤング率 – japončina" lang="ja" hreflang="ja" data-title="ヤング率" data-language-autonym="日本語" data-language-local-name="japončina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AE%D0%BD%D0%B3_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%96" title="Юнг модулі – kazaština" lang="kk" hreflang="kk" data-title="Юнг модулі" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AF%E0%B2%82%E0%B2%97%E0%B3%8D_%E0%B2%AE%E0%B2%BE%E0%B2%AA%E0%B2%BE%E0%B2%82%E0%B2%95" title="ಯಂಗ್ ಮಾಪಾಂಕ – kannadčina" lang="kn" hreflang="kn" data-title="ಯಂಗ್ ಮಾಪಾಂಕ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannadčina" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%81%EB%A5%A0" title="영률 – kórejčina" lang="ko" hreflang="ko" data-title="영률" data-language-autonym="한국어" data-language-local-name="kórejčina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Jungo_modulis" title="Jungo modulis – litovčina" lang="lt" hreflang="lt" data-title="Jungo modulis" data-language-autonym="Lietuvių" data-language-local-name="litovčina" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Junga_modulis" title="Junga modulis – lotyština" lang="lv" hreflang="lv" data-title="Junga modulis" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%88%D1%83%D0%BD%D0%B3%D0%BE%D0%B2_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB" title="Јунгов модул – macedónčina" lang="mk" hreflang="mk" data-title="Јунгов модул" data-language-autonym="Македонски" data-language-local-name="macedónčina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AF%E0%B4%82%E0%B4%97%E0%B5%8D_%E0%B4%AE%E0%B4%BE%E0%B4%AA%E0%B4%A8%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%82" title="യംഗ് മാപനാങ്കം – malajálamčina" lang="ml" hreflang="ml" data-title="യംഗ് മാപനാങ്കം" data-language-autonym="മലയാളം" data-language-local-name="malajálamčina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Modulus_Young" title="Modulus Young – malajčina" lang="ms" hreflang="ms" data-title="Modulus Young" data-language-autonym="Bahasa Melayu" data-language-local-name="malajčina" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Youngs_modul" title="Youngs modul – nórčina (nynorsk)" lang="nn" hreflang="nn" data-title="Youngs modul" data-language-autonym="Norsk nynorsk" data-language-local-name="nórčina (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Elastisitetsmodul" title="Elastisitetsmodul – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Elastisitetsmodul" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Modu%C5%82_Younga" title="Moduł Younga – poľština" lang="pl" hreflang="pl" data-title="Moduł Younga" data-language-autonym="Polski" data-language-local-name="poľština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%B3dulo_de_Young" title="Módulo de Young – portugalčina" lang="pt" hreflang="pt" data-title="Módulo de Young" data-language-autonym="Português" data-language-local-name="portugalčina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modulul_lui_Young" title="Modulul lui Young – rumunčina" lang="ro" hreflang="ro" data-title="Modulul lui Young" data-language-autonym="Română" data-language-local-name="rumunčina" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C_%D0%AE%D0%BD%D0%B3%D0%B0" title="Модуль Юнга – ruština" lang="ru" hreflang="ru" data-title="Модуль Юнга" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Young%27s_modulus" title="Young's modulus – škótčina" lang="sco" hreflang="sco" data-title="Young's modulus" data-language-autonym="Scots" data-language-local-name="škótčina" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Youngov_modul_elasti%C4%8Dnosti" title="Youngov modul elastičnosti – srbochorvátčina" lang="sh" hreflang="sh" data-title="Youngov modul elastičnosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvátčina" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%BA%E0%B6%82_%E0%B6%B8%E0%B7%8F%E0%B6%B4%E0%B7%8F%E0%B6%82%E0%B6%9A%E0%B6%BA" title="යං මාපාංකය – sinhalčina" lang="si" hreflang="si" data-title="යං මාපාංකය" data-language-autonym="සිංහල" data-language-local-name="sinhalčina" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Young%27s_modulus" title="Young's modulus – Simple English" lang="en-simple" hreflang="en-simple" data-title="Young's modulus" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Jangov_modul" title="Jangov modul – srbčina" lang="sr" hreflang="sr" data-title="Jangov modul" data-language-autonym="Српски / srpski" data-language-local-name="srbčina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AF%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%AE%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81" title="யங்கின் மட்டு – tamilčina" lang="ta" hreflang="ta" data-title="யங்கின் மட்டு" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A1%E0%B8%AD%E0%B8%94%E0%B8%B8%E0%B8%A5%E0%B8%B1%E0%B8%AA%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A2%E0%B8%B1%E0%B8%87" title="มอดุลัสของยัง – thajčina" lang="th" hreflang="th" data-title="มอดุลัสของยัง" data-language-autonym="ไทย" data-language-local-name="thajčina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Young_mod%C3%BCl%C3%BC" title="Young modülü – turečtina" lang="tr" hreflang="tr" data-title="Young modülü" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AE%D0%BD%D0%B3_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D0%B5" title="Юнг модуле – tatárčina" lang="tt" hreflang="tt" data-title="Юнг модуле" data-language-autonym="Татарча / tatarça" data-language-local-name="tatárčina" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C_%D0%AE%D0%BD%D0%B3%D0%B0" title="Модуль Юнга – ukrajinčina" lang="uk" hreflang="uk" data-title="Модуль Юнга" data-language-autonym="Українська" data-language-local-name="ukrajinčina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yung_moduli" title="Yung moduli – uzbečtina" lang="uz" hreflang="uz" data-title="Yung moduli" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Su%E1%BA%A5t_Young" title="Suất Young – vietnamčina" lang="vi" hreflang="vi" data-title="Suất Young" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamčina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9D%A8%E6%B0%8F%E6%A8%A1%E9%87%8F" title="杨氏模量 – 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lang="sk" dir="ltr"><p><b>Youngov modul</b> alebo aj <b>modul pružnosti v ťahu</b> je číslo, ktoré charakterizuje správanie materiálu zaťaženého ťahovým <a href="/wiki/Mechanick%C3%A9_nap%C3%A4tie" title="Mechanické napätie">napätím</a>. Čím je Youngov modul vyšší tým treba väčšie napätie (pri rovnakom <a href="/wiki/Prierez" class="mw-disambig" title="Prierez">priereze</a> väčšiu <a href="/wiki/Sila" title="Sila">silu</a>) na dosiahnutie rovnakej <a href="/wiki/Deform%C3%A1cia" class="mw-disambig" title="Deformácia">deformácie</a> (predĺženia). </p><p>Youngov modul vystupuje ako konštanta v <a href="/wiki/Hookov_z%C3%A1kon" title="Hookov zákon">Hookovom zákone</a>. Označuje sa písmenom <b>E</b> a udáva sa v jednotkách napätia – v <a href="/wiki/Pascal" title="Pascal">pascaloch</a> [Pa]. Pre jeho vysoké hodnoty je praktickejšie používať násobnú jednotku gigapascal [GPa]. Modul je pre daný materiál závislý od <a href="/wiki/Teplota" title="Teplota">teploty</a>, s narastajúcou teplotou môže klesať. Je pomenovaný po <a href="/w/index.php?title=Thomas_Young&action=edit&redlink=1" class="new" title="Thomas Young (stránka neexistuje)">Thomasovi Youngovi</a>, britskom fyzikovi, lekárovi a egyptológovi. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Experimentálne_určovanie"><span id="Experiment.C3.A1lne_ur.C4.8Dovanie"></span>Experimentálne určovanie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Youngov_modul&veaction=edit&section=1" title="Upraviť sekciu: Experimentálne určovanie" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Youngov_modul&action=edit&section=1" title="Editovat zdrojový kód sekce Experimentálne určovanie"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Stress_v_strain_A36_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Stress_v_strain_A36_2.png/250px-Stress_v_strain_A36_2.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Stress_v_strain_A36_2.png/375px-Stress_v_strain_A36_2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/00/Stress_v_strain_A36_2.png 2x" data-file-width="400" data-file-height="400" /></a><figcaption>Závislosti napätia od predĺženia (ťahový diagram).<br /> vodorovná os predĺženie<br />zvislá os napätie.<br /> Medzi začiatkom súradnicovej sústavy a bodom 2 je oblasť platnosti Hookovho zákona.</figcaption></figure> <p>Modul je definovaný priamo z Hookovho zákona ako pomer napätia v ťahu a <a href="/w/index.php?title=Pomern%C3%A1_deform%C3%A1cia&action=edit&redlink=1" class="new" title="Pomerná deformácia (stránka neexistuje)">pomernej deformácie</a> v oblasti malých napätí. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {\sigma }{\varepsilon }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ</mi> <mi>ε</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {\sigma }{\varepsilon }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e550b558c0d862ab9e0367371e726a0793aeb44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.04ex; height:4.676ex;" alt="{\displaystyle E={\frac {\sigma }{\varepsilon }}}"></span> </p><p><b>ε</b> = <b>Δ l</b> / <b>l</b> </p> <ul><li><b>E</b> – Youngov modul [Pa]</li> <li><b>σ</b> – napätie v ťahu [Pa]</li> <li><b>ε</b> – pomerné predĺženie pod napätím [-]</li> <li><b>Δ l</b> – zmena dĺžky pri zaťažení</li> <li><b>l</b> – dĺžka pred zaťažením</li></ul> <p>Experimentálne sa dá zmerať z ťahového diagramu – závislosti napätia od predĺženia. Je úmerný <a href="/wiki/Smernica" class="mw-disambig" title="Smernica">smernici</a> (<a href="/wiki/Tangens" title="Tangens">tangens</a> uhla sklonu) <a href="/wiki/Line%C3%A1rny" class="mw-redirect mw-disambig" title="Lineárny">lineárnej</a> časti krivky od nulového napätia po <a href="/wiki/Medza_proporcionality" title="Medza proporcionality">medzu proporcionality</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Využitie"><span id="Vyu.C5.BEitie"></span>Využitie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Youngov_modul&veaction=edit&section=2" title="Upraviť sekciu: Využitie" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Youngov_modul&action=edit&section=2" title="Editovat zdrojový kód sekce Využitie"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Youngov modul sa používa na výpočet deformácií materiálov na základe ich zaťaženia. Napríklad na výpočet predĺženia oceľového lana žeriavu, ak je na ňom zavesené bremeno možno použiť vzťah: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta l={\frac {l}{S.E}}.F\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>l</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>l</mi> <mrow> <mi>S</mi> <mo>.</mo> <mi>E</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mi>F</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta l={\frac {l}{S.E}}.F\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/179de6d1f9186a7b7d8a72399c75d449d5c8bbe3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.228ex; height:5.509ex;" alt="{\displaystyle \Delta l={\frac {l}{S.E}}.F\ }"></span> </p><p>(Ide o úpravu predtým uvedeného vzťahu, kde napätie <b>σ</b> bolo vyjadrené silou <b>F</b> a prierezom lana <b>S</b>, pri čom <b>σ=F/S</b> ) </p> <ul><li><b>Δ l</b> – predĺženie lana [m]</li> <li><b>l</b> – dĺžka lana [m]</li> <li><b>S</b> – <a href="/wiki/Prierez" class="mw-disambig" title="Prierez">prierez</a> lana [m<sup>2</sup>]</li> <li><b>E</b> – Youngov modul [Pa]</li> <li><b>F</b> – <a href="/wiki/Sila" title="Sila">sila</a> = tiaž bremena [N]</li> <li><b>σ</b> – napätie v ťahu [Pa]</li></ul> <div class="mw-heading mw-heading2"><h2 id="Typy_materiálov"><span id="Typy_materi.C3.A1lov"></span>Typy materiálov</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Youngov_modul&veaction=edit&section=3" title="Upraviť sekciu: Typy materiálov" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Youngov_modul&action=edit&section=3" title="Editovat zdrojový kód sekce Typy materiálov"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pre mnoho materiálov je modul konštantný pre veľký rozsah napätí. Tieto materiály sa nazývajú <b>lineárne</b> a ich správanie zodpovedá Hookovmu zákonu. Do tejto skupiny patria napríklad <a href="/wiki/Oce%C4%BE" title="Oceľ">oceľ</a>, <a href="/wiki/Uhl%C3%ADkov%C3%A9_vl%C3%A1kno" title="Uhlíkové vlákno">uhlíkové vlákno</a>, <a href="/wiki/Sklo" title="Sklo">sklo</a>. </p><p>Pre iné materiály, napríklad <a href="/wiki/Guma" class="mw-disambig" title="Guma">guma</a> sa ich modul pružnosti mení v závislosti od zaťaženia, t. j. závislosť napätia od deformácie nie je lineárna. Preto sa nazývajú aj <b>nelineárne</b> materiály. </p><p>Niektoré materiály, najčastejšie <a href="/wiki/Kompozitn%C3%BD_materi%C3%A1l" title="Kompozitný materiál">kompozitné</a> ale aj iné, majú vnútornú štruktúru, ktorá ovplyvňuje ich <a href="/w/index.php?title=Mechanick%C3%A9_vlastnosti&action=edit&redlink=1" class="new" title="Mechanické vlastnosti (stránka neexistuje)">mechanické vlastnosti</a> podľa toho v ktorom smere sa vzhľadom na jej orientáciu zisťujú. Takéto materiály sa nazývajú <a href="/w/index.php?title=Anizotropn%C3%BD_materi%C3%A1l&action=edit&redlink=1" class="new" title="Anizotropný materiál (stránka neexistuje)">anizotropné</a> a majú rozdielny aj Youngov modul v rôznych smeroch. Napríklad kompozitný materiál s uhlíkovými vláknami má modul vyší v smere rovnobežnom s vláknami, ako v iných smeroch. </p><p><i>Youngov modul</i> je rádovo vyšší ako medza <a href="/wiki/Pevnos%C5%A5" class="mw-disambig" title="Pevnosť">pevnosti</a>, ktorá platí pre rozsahy mimo medzu proporcionality (pozri obrázok bod 3.). Materiály u ktorých je pomer Youngovho modulu k medzi pevnosti </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {E}{Rm}}<150}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <mi>R</mi> <mi>m</mi> </mrow> </mfrac> </mrow> <mo><</mo> <mn>150</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {E}{Rm}}<150}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6442493e380b5b6db9e2777461c5814bbb63c77f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.226ex; height:5.343ex;" alt="{\displaystyle {\frac {E}{Rm}}<150}"></span> sa nazývajú <b>vysokopevné</b>. </p> <div class="mw-heading mw-heading2"><h2 id="Približné_hodnoty"><span id="Pribli.C5.BEn.C3.A9_hodnoty"></span>Približné hodnoty</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Youngov_modul&veaction=edit&section=4" title="Upraviť sekciu: Približné hodnoty" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Youngov_modul&action=edit&section=4" title="Editovat zdrojový kód sekce Približné hodnoty"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Youngov modul závisí hlavne na presnom zložení materiálu. Napríklad pre <a href="/wiki/Kov" title="Kov">kovy</a> môže byť <a href="/wiki/Rozptyl" class="mw-disambig" title="Rozptyl">rozptyl</a> hodnôt až 5 % a viac v závislosti od presného zloženia <a href="/wiki/Zliatina" title="Zliatina">zliatiny</a> a <a href="/wiki/Tepeln%C3%A9_spracovanie" class="mw-redirect" title="Tepelné spracovanie">tepelného spracovania</a>. V tabuľke sú uvedené približné hodnoty pre vybrané materiály. </p> <table class="wikitable" cellpadding="4" cellspacing="0" border="1" style="border-collapse: collapse"> <caption style="font-size:larger;font-weight:bold;">Približná veľkosť Youngovho modulu tuhých telies </caption> <tbody><tr> <th>Materiál </th> <th>Youngov modul (E) V [GPa] </th></tr> <tr> <td><a href="/wiki/Guma" class="mw-disambig" title="Guma">guma</a> (malé namáhanie) </td> <td align="center">0,01 – 0,1 </td></tr> <tr> <td><a href="/wiki/Polyetyl%C3%A9n" title="Polyetylén">polyetylén</a> s nízkou <a href="/wiki/Hustota" class="mw-disambig" title="Hustota">hustotou</a> </td> <td align="center">0,2 </td></tr> <tr> <td><a href="/wiki/Polypropyl%C3%A9n" title="Polypropylén">polypropylén</a> </td> <td align="center">1,5 – 2 </td></tr> <tr> <td><a href="/wiki/Polystyr%C3%A9n" title="Polystyrén">polystyrén</a> </td> <td align="center">3 – 3,5 </td></tr> <tr> <td><a href="/w/index.php?title=Nylon&action=edit&redlink=1" class="new" title="Nylon (stránka neexistuje)">nylon</a> </td> <td align="center">2 – 4 </td></tr> <tr> <td>dubové <a href="/wiki/Drevo" title="Drevo">drevo</a> (pozdĺž vlákien) </td> <td align="center">11 </td></tr> <tr> <td>vysokopevnostný <a href="/wiki/Bet%C3%B3n" title="Betón">betón</a> </td> <td align="center">30 </td></tr> <tr> <td><a href="/wiki/Hor%C4%8D%C3%ADk" title="Horčík">horčík</a> </td> <td align="center">45 </td></tr> <tr> <td>zliatiny <a href="/wiki/Hlin%C3%ADk" title="Hliník">hliníka</a> </td> <td align="center">69 </td></tr> <tr> <td><a href="/wiki/Sklo" title="Sklo">sklo</a> </td> <td align="center">72 </td></tr> <tr> <td><a href="/wiki/Mosadz" title="Mosadz">mosadz</a> a <a href="/wiki/Bronz" title="Bronz">bronz</a> </td> <td align="center">103 – 124 </td></tr> <tr> <td><a href="/wiki/Tit%C3%A1n" class="mw-redirect mw-disambig" title="Titán">titán</a> </td> <td align="center">105 – 120 </td></tr> <tr> <td><a href="/wiki/Uhl%C3%ADkov%C3%A9_vl%C3%A1kno" title="Uhlíkové vlákno">uhlíkové vlákno</a> (pozdĺž vlákien) </td> <td align="center">150 </td></tr> <tr> <td><a href="/wiki/Oce%C4%BE" title="Oceľ">oceľ</a> </td> <td align="center">190 – 210 </td></tr> <tr> <td><a href="/wiki/Volfr%C3%A1m" title="Volfrám">volfrám</a> </td> <td align="center">400 – 410 </td></tr> <tr> <td><a href="/wiki/Karbid_kremi%C4%8Dit%C3%BD" title="Karbid kremičitý">karbid kremičitý</a> </td> <td align="center">450 </td></tr> <tr> <td><a href="/wiki/Karbid_volfr%C3%A1mu" title="Karbid volfrámu">karbid volfrámu</a> </td> <td align="center">450 – 650 </td></tr> <tr> <td><a href="/wiki/Uhl%C3%ADkov%C3%A1_nanor%C3%BArka" title="Uhlíková nanorúrka">uhlíkové nanotrubice</a> </td> <td align="center">1 000 a viac </td></tr> <tr> <td><a href="/wiki/Diamant" title="Diamant">diamant</a> (C) </td> <td align="center">1 050 – 1 200 </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Zdroj: „<a dir="ltr" href="https://sk.wikipedia.org/w/index.php?title=Youngov_modul&oldid=7752339">https://sk.wikipedia.org/w/index.php?title=Youngov_modul&oldid=7752339</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C5%A0peci%C3%A1lne:Kateg%C3%B3rie" title="Špeciálne:Kategórie">Kategórie</a>: <ul><li><a href="/wiki/Kateg%C3%B3ria:Mechanick%C3%A9_vlastnosti_materi%C3%A1lov" title="Kategória:Mechanické vlastnosti materiálov">Mechanické vlastnosti materiálov</a></li><li><a href="/wiki/Kateg%C3%B3ria:Materi%C3%A1lov%C3%A9_kon%C5%A1tanty" title="Kategória:Materiálové konštanty">Materiálové konštanty</a></li><li><a href="/wiki/Kateg%C3%B3ria:Eponymick%C3%A9_term%C3%ADny_vo_fyzike" title="Kategória:Eponymické termíny vo fyzike">Eponymické termíny vo fyzike</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Dátum a čas poslednej úpravy tejto stránky: 3. december 2023, 10:53.</li> <li id="footer-info-copyright">Text je dostupný za podmienok <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike License 4.0 Unported</a>; prípadne za ďalších podmienok. 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