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class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Primjena_naprezanja" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primjena_naprezanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Primjena naprezanja</span> </div> </a> <button aria-controls="toc-Primjena_naprezanja-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Sadržaj cjeline Primjena naprezanja</span> </button> <ul id="toc-Primjena_naprezanja-sublist" class="vector-toc-list"> <li id="toc-Normalno_naprezanje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Normalno_naprezanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Normalno naprezanje</span> </div> </a> <ul id="toc-Normalno_naprezanje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Posmično_naprezanje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Posmično_naprezanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Posmično naprezanje</span> </div> </a> <ul id="toc-Posmično_naprezanje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hookeov_zakon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hookeov_zakon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Hookeov zakon</span> </div> </a> <ul id="toc-Hookeov_zakon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deformacija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Deformacija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Deformacija</span> </div> </a> <ul id="toc-Deformacija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dopušteno_i_proračunsko_naprezanje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dopušteno_i_proračunsko_naprezanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Dopušteno i proračunsko naprezanje</span> </div> </a> <ul id="toc-Dopušteno_i_proračunsko_naprezanje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Toplinska_naprezanja" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Toplinska_naprezanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Toplinska naprezanja</span> </div> </a> <ul id="toc-Toplinska_naprezanja-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Dijagram_naprezanja" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dijagram_naprezanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Dijagram naprezanja</span> </div> </a> <ul id="toc-Dijagram_naprezanja-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaz sadržaja stranice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prikaz sadržaja stranice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Naprezanje</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Idi na druge jezične varijante članka. Dostupan je na 63 jezika" > <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-63" 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">63 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%AC%D9%87%D8%A7%D8%AF_(%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7)" title="إجهاد (ميكانيكا) – arapski" lang="ar" hreflang="ar" data-title="إجهاد (ميكانيكا)" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Tensi%C3%B3n_(mec%C3%A1nica)" title="Tensión (mecánica) – asturijski" lang="ast" hreflang="ast" data-title="Tensión (mecánica)" data-language-autonym="Asturianu" data-language-local-name="asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/G%C9%99rginlik_(mexanika)" title="Gərginlik (mexanika) – azerbajdžanski" lang="az" hreflang="az" data-title="Gərginlik (mexanika)" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Spaunnung" title="Spaunnung – Bavarian" lang="bar" hreflang="bar" data-title="Spaunnung" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Механічнае напружанне – bjeloruski" lang="be" hreflang="be" data-title="Механічнае напружанне" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D1%8D%D1%85%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Мэханічнае напружаньне – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Мэханічнае напружаньне" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D1%80%D0%B5%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0)" title="Напрежение (механика) – bugarski" lang="bg" hreflang="bg" data-title="Напрежение (механика)" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%80%E0%A6%A1%E0%A6%BC%E0%A6%A8" title="পীড়ন – bangla" lang="bn" hreflang="bn" data-title="পীড়ন" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Mehani%C4%8Dki_napon" title="Mehanički napon – bosanski" lang="bs" hreflang="bs" data-title="Mehanički napon" data-language-autonym="Bosanski" data-language-local-name="bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tensi%C3%B3_(mec%C3%A0nica)" title="Tensió (mecànica) – katalonski" lang="ca" hreflang="ca" data-title="Tensió (mecànica)" data-language-autonym="Català" data-language-local-name="katalonski" 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/Mechanick%C3%A9_nap%C4%9Bt%C3%AD" title="Mechanické napětí – češki" lang="cs" hreflang="cs" data-title="Mechanické napětí" data-language-autonym="Čeština" data-language-local-name="češki" 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%9C%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D1%85%D0%B8%D0%B2%D1%80%D0%B5%D0%BB%C4%95%D1%85" title="Механикăлла хиврелĕх – čuvaški" lang="cv" hreflang="cv" data-title="Механикăлла хиврелĕх" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" 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/Sp%C3%A6nding_(mekanik)" title="Spænding (mekanik) – danski" lang="da" hreflang="da" data-title="Spænding (mekanik)" data-language-autonym="Dansk" data-language-local-name="danski" 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/Mechanische_Spannung" title="Mechanische Spannung – njemački" lang="de" hreflang="de" data-title="Mechanische Spannung" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%AC%CF%83%CE%B7_(%CE%BC%CE%B7%CF%87%CE%B1%CE%BD%CE%B9%CE%BA%CE%AE)" title="Τάση (μηχανική) – grčki" lang="el" hreflang="el" data-title="Τάση (μηχανική)" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Stress_(mechanics)" title="Stress (mechanics) – engleski" lang="en" hreflang="en" data-title="Stress (mechanics)" data-language-autonym="English" data-language-local-name="engleski" 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/Stre%C4%89o_(mekaniko)" title="Streĉo (mekaniko) – esperanto" lang="eo" hreflang="eo" data-title="Streĉo (mekaniko)" 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/Tensi%C3%B3n_mec%C3%A1nica" title="Tensión mecánica – španjolski" lang="es" hreflang="es" data-title="Tensión mecánica" data-language-autonym="Español" data-language-local-name="španjolski" 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/Pinge_(mehaanika)" title="Pinge (mehaanika) – estonski" lang="et" hreflang="et" data-title="Pinge (mehaanika)" data-language-autonym="Eesti" data-language-local-name="estonski" 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/Tentsio_mekaniko" title="Tentsio mekaniko – baskijski" lang="eu" hreflang="eu" data-title="Tentsio mekaniko" data-language-autonym="Euskara" data-language-local-name="baskijski" 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/%D8%AA%D9%86%D8%B4_(%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9)" title="تنش (مکانیک) – perzijski" lang="fa" hreflang="fa" data-title="تنش (مکانیک)" data-language-autonym="فارسی" data-language-local-name="perzijski" 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/J%C3%A4nnitys" title="Jännitys – finski" lang="fi" hreflang="fi" data-title="Jännitys" data-language-autonym="Suomi" data-language-local-name="finski" 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/Contrainte_(m%C3%A9canique)" title="Contrainte (mécanique) – francuski" lang="fr" hreflang="fr" data-title="Contrainte (mécanique)" data-language-autonym="Français" data-language-local-name="francuski" 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/Strus_(fisic)" title="Strus (fisic) – irski" lang="ga" hreflang="ga" data-title="Strus (fisic)" data-language-autonym="Gaeilge" data-language-local-name="irski" 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/Tensi%C3%B3n_mec%C3%A1nica" title="Tensión mecánica – galicijski" lang="gl" hreflang="gl" data-title="Tensión mecánica" data-language-autonym="Galego" data-language-local-name="galicijski" 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%90%D7%9E%D7%A5_(%D7%94%D7%A0%D7%93%D7%A1%D7%94)" title="מאמץ (הנדסה) – hebrejski" lang="he" hreflang="he" data-title="מאמץ (הנדסה)" data-language-autonym="עברית" data-language-local-name="hebrejski" 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%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%AC%E0%A4%B2" title="प्रतिबल – hindski" lang="hi" hreflang="hi" data-title="प्रतिबल" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estr%C3%A8s" title="Estrès – haićanski kreolski" lang="ht" hreflang="ht" data-title="Estrès" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haićanski kreolski" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Mechanikai_fesz%C3%BClts%C3%A9g" title="Mechanikai feszültség – mađarski" lang="hu" hreflang="hu" data-title="Mechanikai feszültség" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A5%D5%AD%D5%A1%D5%B6%D5%AB%D5%AF%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AC%D5%A1%D6%80%D5%B8%D6%82%D5%B4" title="Մեխանիկական լարում – armenski" lang="hy" hreflang="hy" data-title="Մեխանիկական լարում" data-language-autonym="Հայերեն" data-language-local-name="armenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tegangan_(mekanika)" title="Tegangan (mekanika) – indonezijski" lang="id" hreflang="id" data-title="Tegangan (mekanika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tensione_interna" title="Tensione interna – talijanski" lang="it" hreflang="it" data-title="Tensione interna" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BF%9C%E5%8A%9B" title="応力 – japanski" lang="ja" hreflang="ja" data-title="応力" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AA%E0%B3%80%E0%B2%A1%E0%B2%A8" title="ಪೀಡನ – karnatački" lang="kn" hreflang="kn" data-title="ಪೀಡನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="karnatački" 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/%EB%B3%80%ED%98%95%EB%A0%A5" title="변형력 – korejski" lang="ko" hreflang="ko" data-title="변형력" data-language-autonym="한국어" data-language-local-name="korejski" 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/%C4%AEtempis" title="Įtempis – litavski" lang="lt" hreflang="lt" data-title="Įtempis" data-language-autonym="Lietuvių" data-language-local-name="litavski" 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/Meh%C4%81niskais_spriegums" title="Mehāniskais spriegums – latvijski" lang="lv" hreflang="lv" data-title="Mehāniskais spriegums" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B4%AF%E0%B4%BE%E0%B4%B8%E0%B4%82" title="ആയാസം – malajalamski" lang="ml" hreflang="ml" data-title="ആയാസം" data-language-autonym="മലയാളം" data-language-local-name="malajalamski" 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/Tegasan_(mekanik)" title="Tegasan (mekanik) – malajski" lang="ms" hreflang="ms" data-title="Tegasan (mekanik)" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Mechanische_spanning" title="Mechanische spanning – nizozemski" lang="nl" hreflang="nl" data-title="Mechanische spanning" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Mekanisk_spenning" title="Mekanisk spenning – norveški nynorsk" lang="nn" hreflang="nn" data-title="Mekanisk spenning" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški 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/Spenning_(mekanikk)" title="Spenning (mekanikk) – norveški bokmål" lang="nb" hreflang="nb" data-title="Spenning (mekanikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" 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/Napr%C4%99%C5%BCenie" title="Naprężenie – poljski" lang="pl" hreflang="pl" data-title="Naprężenie" data-language-autonym="Polski" data-language-local-name="poljski" 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/Tens%C3%A3o_(mec%C3%A2nica)" title="Tensão (mecânica) – portugalski" lang="pt" hreflang="pt" data-title="Tensão (mecânica)" data-language-autonym="Português" data-language-local-name="portugalski" 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/Tensiune_(mecanic%C4%83)" title="Tensiune (mecanică) – rumunjski" lang="ro" hreflang="ro" data-title="Tensiune (mecanică)" data-language-autonym="Română" data-language-local-name="rumunjski" 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%B5%D1%85%D0%B0%D0%BD%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%8F%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Механическое напряжение – ruski" lang="ru" hreflang="ru" data-title="Механическое напряжение" data-language-autonym="Русский" data-language-local-name="ruski" 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/Stress_(mechanics)" title="Stress (mechanics) – škotski" lang="sco" hreflang="sco" data-title="Stress (mechanics)" data-language-autonym="Scots" data-language-local-name="škotski" 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/Napor_(mehanika)" title="Napor (mehanika) – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Napor (mehanika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Stress_(mechanics)" title="Stress (mechanics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Stress (mechanics)" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Mechanick%C3%A9_nap%C3%A4tie" title="Mechanické napätie – slovački" lang="sk" hreflang="sk" data-title="Mechanické napätie" data-language-autonym="Slovenčina" data-language-local-name="slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Mehanska_napetost" title="Mehanska napetost – slovenski" lang="sl" hreflang="sl" data-title="Mehanska napetost" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D0%BE%D0%BD_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0)" title="Напон (механика) – srpski" lang="sr" hreflang="sr" data-title="Напон (механика)" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dragsp%C3%A4nning" title="Dragspänning – švedski" lang="sv" hreflang="sv" data-title="Dragspänning" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%95%E0%AF%88%E0%AE%B5%E0%AF%81" title="தகைவு – tamilski" lang="ta" hreflang="ta" data-title="தகைவு" data-language-autonym="தமிழ்" data-language-local-name="tamilski" 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%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%84%E0%B9%89%E0%B8%99" title="ความเค้น – tajlandski" lang="th" hreflang="th" data-title="ความเค้น" data-language-autonym="ไทย" data-language-local-name="tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Stress_(mekanika)" title="Stress (mekanika) – tagalog" lang="tl" hreflang="tl" data-title="Stress (mekanika)" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Gerilme" title="Gerilme – turski" lang="tr" hreflang="tr" data-title="Gerilme" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B5%D0%BD%D0%BD%D1%8F" title="Напруження – ukrajinski" lang="uk" hreflang="uk" data-title="Напруження" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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/Mexanik_kuchlanish" title="Mexanik kuchlanish – uzbečki" lang="uz" hreflang="uz" data-title="Mexanik kuchlanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" 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/%E1%BB%A8ng_su%E1%BA%A5t" title="Ứng suất – vijetnamski" lang="vi" hreflang="vi" data-title="Ứng suất" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BA%94%E5%8A%9B" title="应力 – wu kineski" lang="wuu" hreflang="wuu" data-title="应力" data-language-autonym="吴语" data-language-local-name="wu kineski" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%87%89%E5%8A%9B" title="應力 – kineski" lang="zh" hreflang="zh" data-title="應力" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%87%89%E5%8A%9B" title="應力 – kantonski" lang="yue" hreflang="yue" data-title="應力" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q206175#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Tensile_testing_on_a_coir_composite.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Tensile_testing_on_a_coir_composite.jpg/300px-Tensile_testing_on_a_coir_composite.jpg" decoding="async" width="300" height="401" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Tensile_testing_on_a_coir_composite.jpg/450px-Tensile_testing_on_a_coir_composite.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Tensile_testing_on_a_coir_composite.jpg/600px-Tensile_testing_on_a_coir_composite.jpg 2x" data-file-width="1712" data-file-height="2288" /></a><figcaption><a href="/wiki/Vla%C4%8Dno_ispitivanje" title="Vlačno ispitivanje">Vlačno ispitivanje</a> na <a href="/wiki/Kidalica" title="Kidalica">kidalici</a> za nestandardni ispitni uzorak.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Axial_stress_noavg.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Axial_stress_noavg.svg/300px-Axial_stress_noavg.svg.png" decoding="async" width="300" height="246" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Axial_stress_noavg.svg/450px-Axial_stress_noavg.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Axial_stress_noavg.svg/600px-Axial_stress_noavg.svg.png 2x" data-file-width="491" data-file-height="403" /></a><figcaption><a href="/wiki/Normala" title="Normala">Normalno</a> naprezanje <i>σ</i> djeluje jednoliko po poprečnom presjeku <a href="/wiki/Plo%C5%A1tina" class="mw-redirect" title="Ploština">ploštine</a> A, pa je ukupna <a href="/wiki/Sila" title="Sila">sila</a> <i>F</i> u presjeku <i>σ ∙ A</i>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Shear_stress.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Shear_stress.svg/300px-Shear_stress.svg.png" decoding="async" width="300" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Shear_stress.svg/450px-Shear_stress.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Shear_stress.svg/600px-Shear_stress.svg.png 2x" data-file-width="583" data-file-height="258" /></a><figcaption><a href="/wiki/Smicanje" title="Smicanje">Posmično</a> naprezanje u vodoravnoj šipki zbog djelovanja dvije okomite šipke čije su osi pomaknute (kao na primjer <a href="/wiki/%C5%A0kare" title="Škare">škare</a>).</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Stress_in_a_continuum.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Stress_in_a_continuum.svg/300px-Stress_in_a_continuum.svg.png" decoding="async" width="300" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Stress_in_a_continuum.svg/450px-Stress_in_a_continuum.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Stress_in_a_continuum.svg/600px-Stress_in_a_continuum.svg.png 2x" data-file-width="582" data-file-height="340" /></a><figcaption><a href="/wiki/Tenzor" title="Tenzor">Tenzor</a> naprezanja.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Normal_stress.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Normal_stress.svg/300px-Normal_stress.svg.png" decoding="async" width="300" height="277" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Normal_stress.svg/450px-Normal_stress.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Normal_stress.svg/600px-Normal_stress.svg.png 2x" data-file-width="477" data-file-height="441" /></a><figcaption> Naprezanje <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 \sigma =F/A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =F/A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f889dfaa80d2d7ebb35ee0dc03353460d196c57f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.074ex; height:2.843ex;" alt="{\displaystyle \sigma =F/A}"></span> uglavnom je prosječno naprezanje u presjeku. Naprezanje se često ne raspoređuje jednako u presjeku (<i>m</i>–<i>m</i>), posebno u blizini mjesta gdje djeluje vanjska sila u hvatištu (<i>n</i>–<i>n</i>).</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Metal_yield.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Metal_yield.svg/300px-Metal_yield.svg.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Metal_yield.svg/450px-Metal_yield.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Metal_yield.svg/600px-Metal_yield.svg.png 2x" data-file-width="331" data-file-height="248" /></a><figcaption><a href="/wiki/Dijagram_naprezanja" title="Dijagram naprezanja">Dijagram naprezanja</a> (<i>σ</i> - vlačnog naprezanja i <i>ε</i> - linijske vlačne deformacije) za tipični neželjezni materijal:<br /> 1: Stvarna granica elastičnosti<br /> 2: Granica proporcionalnosti<br /> 3: Granica elastičnosti<br /> 4: <a href="/wiki/Granica_razvla%C4%8Denja" title="Granica razvlačenja">Granica razvlačenja</a> ili σ<sub>0,2</sub> (<a class="mw-selflink selflink">naprezanje</a> pri kojem nastaje trajno produljenje od 0,2% prvobitne dužine šipke ili štapa)</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Stress_v_strain_A36_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Stress_v_strain_A36_2.svg/300px-Stress_v_strain_A36_2.svg.png" decoding="async" width="300" height="310" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Stress_v_strain_A36_2.svg/450px-Stress_v_strain_A36_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Stress_v_strain_A36_2.svg/600px-Stress_v_strain_A36_2.svg.png 2x" data-file-width="777" data-file-height="804" /></a><figcaption>Dijagram naprezanja za niskougljični ili meki čelik. Hookeov zakon vrijedi u početnom području od 0 do donje granice tečenja (2):<br /> 1. <a href="/wiki/Vla%C4%8Dna_%C4%8Dvrsto%C4%87a" title="Vlačna čvrstoća">Vlačna čvrstoća</a> materijala<br /> 2. <a href="/wiki/Granica_razvla%C4%8Denja" title="Granica razvlačenja">Granica razvlačenja</a> ili σ<sub>0,2</sub><br /> 3. <a href="/wiki/Lom_materijala" title="Lom materijala">Lom materijala</a><br /> 4. Područje plastičnih deformacija<br /> 5. Područje klonulosti<br /> A: Teoretski dijagram naprezanja (F/A<sub>0</sub>)<br /> B: Stvarni dijagram naprezanja (F/A)</figcaption></figure> <p><b>Naprezanje</b> je unutarnja <a href="/wiki/Sila" title="Sila">sila</a> raspodijeljena po jedinici <a href="/wiki/Povr%C5%A1ina" title="Površina">površine</a> nekoga čvrstog tijela koja se javlja kao reakcija na djelovanje vanjskih sila ili promjene <a href="/wiki/Temperatura" title="Temperatura">temperature</a> tijela, s jedinicom <a href="/wiki/Paskal" title="Paskal">paskal</a> (Pa = N/m<sup>2</sup>). Veličina naprezanja u nekoj točki tijela ovisi o orijentaciji presjeka tijela na kojem se naprezanje promatra. Takvo puno naprezanje je <a href="/wiki/Vektor" title="Vektor">vektor</a> općenito položen pod <a href="/wiki/Kut" title="Kut">kutom</a> prema <a href="/wiki/Normala" title="Normala">normali</a> na presjek i može se rastaviti na tri skalarne komponente vezane uz <a href="/wiki/Koordinatni_sustav" title="Koordinatni sustav">koordinatni sustav</a>: jednu u smjeru normale <i>x</i> na presjek (<i>σ<sub>x</sub></i>, normalno naprezanje) i dvije na nju okomite koje leže u površini presjeka u smjeru preostalih dviju osi (<i>τ<sub>xy</sub></i> i <i>τ<sub>xz</sub></i>, <a href="/wiki/Tangenta" title="Tangenta">tangencijalna</a> ili <a href="/wiki/Smicanje" title="Smicanje">posmična</a> naprezanja). Uzimajući svaku os kao normalu na odgovarajući presjek, proizlazi da u svakoj točki tijela postoji devet komponenata naprezanja vezanih uz jedan koordinatni sustav, koje djeluju na element <a href="/wiki/Volumen" class="mw-redirect" title="Volumen">volumena</a> i koje tvore takozvani <a href="/wiki/Tenzor" title="Tenzor">tenzor</a> naprezanja drugoga reda. Zbog <a href="/wiki/Simetrija" title="Simetrija">simetričnosti</a> toga tenzora, koja slijedi iz uvjeta ravnoteže elementa volumena, samo je 6 međusobno različitih komponenata, jer je <i>τ<sub>ij</sub></i> = <i>τ<sub>ji</sub></i> (na primjer <i>τ<sub>xy</sub></i> = <i>τ<sub>yx</sub></i>). Kako se u nekoj točki mijenja <a href="/wiki/Orijentacija" title="Orijentacija">orijentacija</a> koordinatnih osi, tako se mijenjaju i iznosi naprezanja. U svakoj točki tijela moguća je takva orijentacija osi prema kojima postoje samo normalna naprezanja, dok su posmična jednaka nuli. Ta tri naprezanja nazivaju se glavnim naprezanjima, od kojih su dva ekstremne vrijednosti <i>σ<sub>max</sub></i> i <i>σ<sub>min</sub></i> u toj točki. </p><p>Zbog unutarnjih silâ javljaju se u tijelu <a href="/wiki/Deformacija" title="Deformacija">deformacije</a> s kojima su naprezanja vezana preko <a href="/wiki/Hookeov_zakon" title="Hookeov zakon">Hookeova zakona</a>. <a href="/wiki/%C4%8Cvrsto%C4%87a" title="Čvrstoća">Čvrstoća</a> <a href="/wiki/Konstrukcija" title="Konstrukcija">konstruktivnih</a> elemenata procjenjuje se prema takozvanim hipotezama ili teorijama čvrstoće u kojima naprezanja imaju presudnu ulogu.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Primjena_naprezanja">Primjena naprezanja</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=1" title="Uredi odlomak: Primjena naprezanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=1" title="Uredi kôd odjeljka Primjena naprezanja"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ako na neko tijelo djeluju vanjske sile, one nastoje da razdvoje ili približe pojedine čestice tijela. Tome se tijelo suprotstavlja unutrašnjim silama koje djeluju među njegovim česticama. Unutrašnja sila podijeljena ploštinom (površinom) presjeka na kojem djeluje zove se naprezanje. Prema djelovanju razlikuju se normalno naprezanje i posmično naprezanje. Normalnim naprezanjem tijelo se opire međusobnom primicanju ili razmicanju svojih čestica. Posmičnim naprezanjem tijelo se opire klizanju jednog sloja čestica po drugom.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Normalno_naprezanje">Normalno naprezanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=2" title="Uredi odlomak: Normalno naprezanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=2" title="Uredi kôd odjeljka Normalno naprezanje"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Najjednostavniji prikaz naprezanja se dobije ako se promatra štap što ga rastežu dvije jednake i suprotno usmjerene sile. Zato što pravac djelovanja sila prolazi kroz os štapa kaže se da je osno opterećen. <a href="/wiki/Normala" title="Normala">Normalno</a> naprezanje <i>σ</i> djeluje jednoliko po poprečnom presjeku ploštine <i>A</i>, pa je ukupna sila u presjeku <i>σ ∙ A</i>. Iz ravnoteže odsječenog dijela slijedi <i>σ ∙ A = F</i>, odnosno: </p> <dl><dd><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 \sigma ={\frac {F}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ={\frac {F}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31def95c6a21e9623f365a856d09d467dfba3983" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.007ex; height:5.343ex;" alt="{\displaystyle \sigma ={\frac {F}{A}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Posmično_naprezanje"><span id="Posmi.C4.8Dno_naprezanje"></span>Posmično naprezanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=3" title="Uredi odlomak: Posmično naprezanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=3" title="Uredi kôd odjeljka Posmično naprezanje"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ako se promatra naprezanje u vodoravnoj šipki zbog djelovanja dvije okomite šipke čije su osi pomaknute (kao na primjer <a href="/wiki/%C5%A0kare" title="Škare">škare</a>), u presjeku vodoravne šipke pojavljuje se posmično ili tangencijalno naprezanje. Posmično naprezanje nije jednoliko raspodijeljeno po presjeku, ali je njegova prosječna vrijednost: </p> <dl><dd><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 \tau ={F \over A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau ={F \over A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a18f6989a7cc12295d9dd33979547b046adea3d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.88ex; height:5.343ex;" alt="{\displaystyle \tau ={F \over A}}"></span></dd></dl> <p>Unutrašnje sile u tijelu općenito ne djeluju okomito na presjek, u općem slučaju djeluje normalno i posmično opterećenje. </p> <div class="mw-heading mw-heading3"><h3 id="Hookeov_zakon">Hookeov zakon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=4" title="Uredi odlomak: Hookeov zakon" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=4" title="Uredi kôd odjeljka Hookeov zakon"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><style data-mw-deduplicate="TemplateStyles:r7016135">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Hookeov_zakon" title="Hookeov zakon">Hookeov zakon</a></div></i></div> <p><b>Hookeov zakon</b> je zakonitost koja opisuje ovisnost promjene oblika čvrstoga tijela u obliku štapa o djelovanju vanjske sile, što ju je utvrdio <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a>. Opterećenjem izazvano naprezanje <i>σ</i> razmjerno je <a href="/wiki/Deformacija" title="Deformacija">deformaciji</a> <i>ε</i>, odnosno: </p> <dl><dd><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 \sigma =E\cdot \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mi>E</mi> <mo>⋅</mo> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =E\cdot \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d703f44b1381590e63929e5042074df101cc6e3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.966ex; height:2.176ex;" alt="{\displaystyle \sigma =E\cdot \varepsilon }"></span></dd></dl> <p>Faktor razmjernosti <i>E</i> je <a href="/wiki/Youngov_modul_elasti%C4%8Dnosti" title="Youngov modul elastičnosti">modul elastičnosti</a> i karakterističan je za pojedini materijal. Do određene granice naprezanja Hookeov zakon može se primijeniti na većinu <a href="/wiki/Konstrukcijski_%C4%8Delik" title="Konstrukcijski čelik">konstrukcijskih materijala</a>. Za složenija opterećenja tijela različitih oblika rabi se Hookeov zakon u poopćenom obliku, koji se izražava s više skalarnih linearnih jednadžba.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Deformacija">Deformacija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=5" title="Uredi odlomak: Deformacija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=5" title="Uredi kôd odjeljka Deformacija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Deformacija" title="Deformacija">Deformacija</a></div></i></div> <p><b>Deformacija</b> (<a href="/wiki/Latinski_jezik" title="Latinski jezik">lat</a>. <i>deformatio</i>: izobličenje, nagrđivanje), u <a href="/wiki/Fizika" title="Fizika">fizici</a>, je promjena oblika tijela (rastezanje, svijanje, sukanje i drugo) pod utjecajem vanjskih ili unutarnjih sila. Može biti elastična, kada se nakon prestanka djelovanja sile tijelo vraća u prvobitni oblik, i neelastična, kada deformirani oblik ostaje i nakon prestanka djelovanja sile.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Dopušteno_i_proračunsko_naprezanje"><span id="Dopu.C5.A1teno_i_prora.C4.8Dunsko_naprezanje"></span>Dopušteno i proračunsko naprezanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=6" title="Uredi odlomak: Dopušteno i proračunsko naprezanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=6" title="Uredi kôd odjeljka Dopušteno i proračunsko naprezanje"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stvarno neprezanje je ono koje se u <a href="/wiki/Konstrukcija" title="Konstrukcija">konstrukciji</a> pojavljuje u toku rada konstrukcije, dok je proračunsko naprezanje ono koje se očekuje da će se pojaviti u konstrukciji na temelju predviđenog opterećenja i proračuna. Proračunsko naprezanje razlikuje se od stvarnog naprezanja. Za to postoji više razloga. Često je tome uzrok nedovoljno poznavanje opterećenja koje će djelovati na konstrukciju. Teško je, naime, računski odrediti sile koje djeluju, na primjer, na <a href="/wiki/Krilo_zrakoplova" title="Krilo zrakoplova">krilo zrakoplova</a>, oplatu <a href="/wiki/Brod" title="Brod">broda</a> koji plovi na uzburkanom moru ili na <a href="/wiki/Osovina" title="Osovina">osovinu</a> pri vožnji na neravnom putu. Drugi je uzrok u izboru načina proračuna, pri čemu se mnogi detalji zanemaruju. Treći je uzrok ograničena točnost izraza koji se upotrebljava u <a href="/wiki/Nauka_o_%C4%8Dvrsto%C4%87i" title="Nauka o čvrstoći">nauci o čvrstoći</a>. Osim toga, u konstrukciji mogu postojati početna, montažna ili toplinska naprezanja koja su najčešće nepoznata. Zbog toga je proračunsko naprezanje samo procjena stvarnog naprezanja. </p><p>Stvarno naprezanje očito mora biti manje od <a href="/wiki/%C4%8Cvrsto%C4%87a" title="Čvrstoća">čvrstoće</a> materijala, inače bi se konstrukcija slomila. Međutim, vrlo često se ne smije dopustiti pojava ni najmanje plastične deformacije. Budući da stvarno naprezanje može biti veće od proračunskog, treba osigurati da najveće proračunsko naprezanje bude manje od dopuštenog naprezanja <i>σ<sub>dop</sub></i>, odnosno <i>τ<sub>dop</sub></i>. </p> <dl><dd><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 \sigma _{dop}={\frac {\sigma _{0,2}}{S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>o</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mi>S</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{dop}={\frac {\sigma _{0,2}}{S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c532027c1f860740c777640b84f75bea9d9fd241" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.639ex; height:5.176ex;" alt="{\displaystyle \sigma _{dop}={\frac {\sigma _{0,2}}{S}}}"></span></dd></dl> <p>gdje je: <i>σ<sub>0,2</sub></i> - <a href="/wiki/Granica_razvla%C4%8Denja" title="Granica razvlačenja">granica razvlačenja</a> ili točnije naprezanje pri kojem nastaje trajno produljenje od 0,2% prvobitne dužine šipke ili štapa, <i>S</i> - koeficijent sigurnosti. Koeficijent sigurnosti uvijek je veći od jedinice, najčešće je od 1,5 do 2,5, ali može biti i veći od 10. Izbor koeficijenta sigurnosti ovisi o mnogim okolnostima, između ostalog o poznavanju opterećenja, o opasnoosti za ljudski život, o važnosti konstrukcije i drugom. </p> <div class="mw-heading mw-heading3"><h3 id="Toplinska_naprezanja">Toplinska naprezanja</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=7" title="Uredi odlomak: Toplinska naprezanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=7" title="Uredi kôd odjeljka Toplinska naprezanja"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Toplinsko_istezanje" title="Toplinsko istezanje">Toplinsko istezanje</a></div></i></div> <p>Toplinska naprezanja <i>σ<sub>T</sub></i> pojavljuju se pri zagrijavanju ili hlađenju čvrsto upetih predmeta: </p> <dl><dd><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 \sigma _{T}=E\cdot \varepsilon =E\cdot {\frac {\Delta l}{l}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>E</mi> <mo>⋅</mo> <mi>ε</mi> <mo>=</mo> <mi>E</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>l</mi> </mrow> <mi>l</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{T}=E\cdot \varepsilon =E\cdot {\frac {\Delta l}{l}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83d5aff730fe4bb4696337f0a3d9f90bc65c487f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.372ex; height:5.509ex;" alt="{\displaystyle \sigma _{T}=E\cdot \varepsilon =E\cdot {\frac {\Delta l}{l}}}"></span></dd></dl> <p>gdje je: <i>E</i> - <a href="/wiki/Youngov_modul_elasti%C4%8Dnosti" title="Youngov modul elastičnosti">Youngov modul elastičnosti</a>, <i>Δ l</i> - dužinsko ili linearno <a href="/wiki/Toplinsko_istezanje" title="Toplinsko istezanje">toplinsko istezanje</a> (ili skraćenje): </p> <dl><dd><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=\alpha _{1}\cdot l_{0}\cdot \Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>l</mi> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta l=\alpha _{1}\cdot l_{0}\cdot \Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96897d91144a482d70fecc2cd6b535ce1927d9db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.947ex; height:2.509ex;" alt="{\displaystyle \Delta l=\alpha _{1}\cdot l_{0}\cdot \Delta T}"></span></dd></dl> <p>gdje je: <i>l<sub>0</sub></i> - početna duljina, <i>ΔT</i> - temperaturna razlika, <i>α<sub>1</sub></i> - koeficijent toplinskog istezanja. Toplinska naprezanja upetog štapa proizlaze: </p> <dl><dd><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 \sigma _{T}=E\cdot \alpha _{1}\cdot \Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>E</mi> <mo>⋅</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{T}=E\cdot \alpha _{1}\cdot \Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31fe04be129a5fd6ba2f3f5e0c94596b77cdb959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.063ex; height:2.509ex;" alt="{\displaystyle \sigma _{T}=E\cdot \alpha _{1}\cdot \Delta T}"></span></dd></dl> <p>Toplinska naprezanja ne ovise o izmjerama predmeta i mogu biti katkada vrlo velika.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Dijagram_naprezanja">Dijagram naprezanja</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=8" title="Uredi odlomak: Dijagram naprezanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=8" title="Uredi kôd odjeljka Dijagram naprezanja"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Dijagram_naprezanja" title="Dijagram naprezanja">Dijagram naprezanja</a></div></i></div> <p><b>Dijagram naprezanja</b> prikazuje međusobnu ovisnost <i>σ</i> - <a href="/wiki/Vla%C4%8Dna_%C4%8Dvrsto%C4%87a" title="Vlačna čvrstoća">vlačnog naprezanja</a> i <i>ε</i> - relativnog produljenja ili linijske vlačne <a href="/wiki/Deformacija" title="Deformacija">deformacije</a>. U <a href="/wiki/Materijal" title="Materijal">materijalu</a> koji je opterećen nekom <a href="/wiki/Sila" title="Sila">silom</a> <i>F</i> nastaju naprezanja <i>σ</i> koja uzrokuju njegovo rastezanje. Naprezanje <i>σ</i> je omjer sile <i>F</i> i <a href="/wiki/Povr%C5%A1ina" title="Površina">ploštine</a> <i>A</i> presjeka štapa ili šipke (okomitog na smjer sile).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 \sigma ={\frac {F}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ={\frac {F}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31def95c6a21e9623f365a856d09d467dfba3983" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.007ex; height:5.343ex;" alt="{\displaystyle \sigma ={\frac {F}{A}}}"></span></dd></dl> <p>Zbog djelovanja sile <i>F</i> (a time nastalog naprezanja <i>σ</i>) štap ili šipka će se od početne duljine <i>L<sub>0</sub></i> rastegnuti na duljinu <i>L</i>. Tako je produljenje štapa ili šipke: </p> <dl><dd><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 \varepsilon ={\frac {\Delta L}{L_{0}}}={\frac {L-L_{0}}{L_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>L</mi> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>L</mi> <mo>−</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon ={\frac {\Delta L}{L_{0}}}={\frac {L-L_{0}}{L_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a806540a8975b4b920548d9b117fa9e91cf9bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.532ex; height:5.843ex;" alt="{\displaystyle \varepsilon ={\frac {\Delta L}{L_{0}}}={\frac {L-L_{0}}{L_{0}}}}"></span></dd></dl> <p><b>Relativno produljenje</b> <i>ε</i> (duljinska ili uzdužna deformacija) štapa ili šipke je produljenje s obzirom na početnu duljinu L<sub>o</sub>. Početno je naprezanje linearno (deformacija je izravno razmjerna naprezanju). U području linearnog rastezanja (<a href="/wiki/Hookeov_zakon" title="Hookeov zakon">Hookeov zakon</a>) materijal je elastičan i nakon prestanka djelovanja sile, odnosno naprezanja, on se vraća u početno stanje. <a href="/wiki/Youngov_modul_elasti%C4%8Dnosti" title="Youngov modul elastičnosti">Youngov modul elastičnosti</a> je omjer naprezanja i relativnog produljenja (u području elastičnosti).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Tehnička granica <a href="/wiki/Elasti%C4%8Dnost" title="Elastičnost">elastičnosti</a> je naprezanje pri kojem osjetljiva mjerila osjete prvo primjetno trajno produljenje materijala (pri još nepromijenjenom presjeku A<sub>o</sub>). Nakon te granice (obično na kraju linearnog rastezanja) materijal se rasteže plastično i nakon prestanka djelovanja sile ne vraća se više na početnu duljinu <i>L<sub>0</sub></i>, već ostaje određeno trajno produljenje, uz suženje presjeka, <i>A < A<sub>0</sub>)</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Naprezanje&veaction=edit&section=9" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Naprezanje&action=edit&section=9" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <b>naprezanje</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=42938">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> "Tehnička enciklopedija" (<b>Nauka o čvrstoći</b>), glavni urednik Hrvoje Požar, Grafički zavod Hrvatske, 1987.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> <b>Hookeov zakon</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=42938">[2]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"> <b>deformacija</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=42938">[3]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"> "Strojarski priručnik", Bojan Kraut, Tehnička knjiga Zagreb 2009.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.fesb.hr/~djelaska/documents/ES-skripta-760.pdf">[4]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120131031429/http://www.fesb.hr/~djelaska/documents/ES-skripta-760.pdf">Arhivirana inačica izvorne stranice</a> od 31. siječnja 2012. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Elementi strojeva", Fakultet elektrotehnike, strojarstva i brodogradnje Split, Prof. dr. sc. Damir Jelaska, 2011.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.riteh.uniri.hr/zav_katd_sluz/zvd_kons_stroj/katedre/konstruiranje/kolegiji/ke1/ke1_materijali_vj/1.UvodOsnove.pdf">[5]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170228170156/http://www.riteh.uniri.hr/zav_katd_sluz/zvd_kons_stroj/katedre/konstruiranje/kolegiji/ke1/ke1_materijali_vj/1.UvodOsnove.pdf">Arhivirana inačica izvorne stranice</a> od 28. veljače 2017. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Konstrukcijski elementi I", Tehnički fakultet Rijeka, Božidar Križan i Saša Zelenika, 2011.</span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Dobavljeno iz "<a dir="ltr" href="https://hr.wikipedia.org/w/index.php?title=Naprezanje&oldid=6396294">https://hr.wikipedia.org/w/index.php?title=Naprezanje&oldid=6396294</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:Klasi%C4%8Dna_mehanika" title="Kategorija:Klasična mehanika">Klasična mehanika</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"> Ova stranica posljednji je put uređivana 22. svibnja 2022. u 15:59.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencijom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hr">Creative Commons: Imenuj autora/Dijeli pod istim uvjetima</a>; mogu se primjenjivati i dodatni uvjeti. 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