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id="toc-Chemical_sensor_applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" 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mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B7%D0%BE%D0%BB%D0%B0" title="Конзола – Bulgarian" lang="bg" hreflang="bg" data-title="Конзола" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Volad%C3%ADs" title="Voladís – Catalan" lang="ca" hreflang="ca" data-title="Voladís" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kragtr%C3%A4ger" title="Kragträger – German" lang="de" hreflang="de" data-title="Kragträger" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Konsool_(tugevus%C3%B5petus)" title="Konsool (tugevusõpetus) – Estonian" lang="et" hreflang="et" data-title="Konsool (tugevusõpetus)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CF%8C%CE%B2%CE%BF%CE%BB%CE%BF%CF%82" title="Πρόβολος – Greek" lang="el" hreflang="el" data-title="Πρόβολος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Voladizo" title="Voladizo – Spanish" lang="es" hreflang="es" data-title="Voladizo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kantilevro" title="Kantilevro – Esperanto" lang="eo" hreflang="eo" data-title="Kantilevro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B7%D8%B1%D9%87" title="طره – Persian" lang="fa" hreflang="fa" data-title="طره" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Porte-%C3%A0-faux" title="Porte-à-faux – French" lang="fr" hreflang="fr" data-title="Porte-à-faux" data-language-autonym="Français" data-language-local-name="French" 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/Starrmhaide" title="Starrmhaide – Irish" lang="ga" hreflang="ga" data-title="Starrmhaide" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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/Beiril" title="Beiril – Galician" lang="gl" hreflang="gl" data-title="Beiril" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%99%B8%ED%8C%94%EB%B3%B4" title="외팔보 – Korean" lang="ko" hreflang="ko" data-title="외팔보" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BE%E0%A4%B9%E0%A5%81%E0%A4%A7%E0%A4%B0%E0%A4%A8" title="बाहुधरन – Hindi" lang="hi" hreflang="hi" data-title="बाहुधरन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Modiliono" title="Modiliono – Ido" lang="io" hreflang="io" data-title="Modiliono" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kantilever" title="Kantilever – Indonesian" lang="id" hreflang="id" data-title="Kantilever" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%96%D7%99%D7%96_(%D7%9E%D7%91%D7%A0%D7%94)" title="זיז (מבנה) – Hebrew" lang="he" hreflang="he" data-title="זיז (מבנה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D0%BE%D0%BB%D1%8C%D0%B4%D1%8B_(%D0%90%D1%80%D1%8B%D1%81%D1%82%D1%8B)_%D0%B0%D1%80%D2%9B%D0%B0%D0%BB%D1%8B%D2%9B" title="Консольды (Арысты) арқалық – Kazakh" lang="kk" hreflang="kk" data-title="Консольды (Арысты) арқалық" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Konsolsija" title="Konsolsija – Latvian" lang="lv" hreflang="lv" data-title="Konsolsija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Konzol_(befogott_tart%C3%B3)" title="Konzol (befogott tartó) – Hungarian" lang="hu" hreflang="hu" data-title="Konzol (befogott tartó)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AC%E0%A4%BE%E0%A4%B9%E0%A5%81" title="प्रबाहु – Marathi" lang="mr" hreflang="mr" data-title="प्रबाहु" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Uitkragende_ligger" title="Uitkragende ligger – Dutch" lang="nl" hreflang="nl" data-title="Uitkragende ligger" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AB%E3%83%B3%E3%83%81%E3%83%AC%E3%83%90%E3%83%BC" title="カンチレバー – Japanese" lang="ja" hreflang="ja" data-title="カンチレバー" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wspornik" title="Wspornik – Polish" lang="pl" hreflang="pl" data-title="Wspornik" data-language-autonym="Polski" data-language-local-name="Polish" 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/Estrutura_em_consola" title="Estrutura em consola – Portuguese" lang="pt" hreflang="pt" data-title="Estrutura em consola" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Consol%C4%83_(mecanic%C4%83)" title="Consolă (mecanică) – Romanian" lang="ro" hreflang="ro" data-title="Consolă (mecanică)" data-language-autonym="Română" data-language-local-name="Romanian" 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%9A%D0%BE%D0%BD%D1%81%D0%BE%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B1%D0%B0%D0%BB%D0%BA%D0%B0" title="Консольная балка – Russian" lang="ru" hreflang="ru" data-title="Консольная балка" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Konsol_kiri%C5%9F" title="Konsol kiriş – Turkish" lang="tr" hreflang="tr" data-title="Konsol kiriş" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%9A%D0%BE%D0%BD%D1%81%D0%BE%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B1%D0%B0%D0%BB%D0%BA%D0%B0" title="Консольна балка – Ukrainian" lang="uk" hreflang="uk" data-title="Консольна балка" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%82%AC%E8%87%82" title="悬臂 – Chinese" lang="zh" hreflang="zh" data-title="悬臂" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Beam anchored at only one end</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.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">For the figure skating element, see <a href="/wiki/Cantilever_(figure_skating)" title="Cantilever (figure skating)">Cantilever (figure skating)</a>.</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cantilever_examples.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Cantilever_examples.svg/200px-Cantilever_examples.svg.png" decoding="async" width="200" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Cantilever_examples.svg/300px-Cantilever_examples.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Cantilever_examples.svg/400px-Cantilever_examples.svg.png 2x" data-file-width="278" data-file-height="259" /></a><figcaption>A schematic image of three types of cantilever. The top example has a full moment connection (like a horizontal flagpole bolted to the side of a building). The middle example is created by an extension of a simple supported beam (such as the way a <a href="/wiki/Springboard" title="Springboard">diving board</a> is anchored and extends over the edge of a swimming pool). The bottom example is created by adding a <a href="/wiki/Robin_boundary_condition" title="Robin boundary condition">Robin boundary condition</a> to the beam element, which essentially adds an elastic spring to the end board. The top and bottom example may be considered structurally equivalent, depending on the effective stiffness of the spring and beam element.</figcaption></figure> <p>A <b>cantilever</b> is a rigid <a href="/wiki/Structural_element" title="Structural element">structural element</a> that extends horizontally and is unsupported at one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a <a href="/wiki/Beam_(structure)" title="Beam (structure)">beam</a>, plate, <a href="/wiki/Truss" title="Truss">truss</a>, or <a href="/wiki/Concrete_slab" title="Concrete slab">slab</a>. </p><p>When subjected to a <a href="/wiki/Structural_load" title="Structural load">structural load</a> at its far, unsupported end, the cantilever carries the load to the support where it applies a <a href="/wiki/Shear_stress" title="Shear stress">shear stress</a> and a <a href="/wiki/Bending_moment" title="Bending moment">bending moment</a>.<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><p>Cantilever construction allows overhanging structures without additional support. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="In_bridges,_towers,_and_buildings"><span id="In_bridges.2C_towers.2C_and_buildings"></span>In bridges, towers, and buildings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=1" title="Edit section: In bridges, towers, and buildings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cantilevers are widely found in construction, notably in <a href="/wiki/Cantilever_bridge" title="Cantilever bridge">cantilever bridges</a> and <a href="/wiki/Balcony" title="Balcony">balconies</a> (see <a href="/wiki/Corbel" title="Corbel">corbel</a>). In cantilever bridges, the cantilevers are usually built as pairs, with each cantilever used to support one end of a central section. The <a href="/wiki/Forth_Bridge" title="Forth Bridge">Forth Bridge</a> in <a href="/wiki/Scotland" title="Scotland">Scotland</a> is an example of a cantilever <a href="/wiki/Truss_bridge" title="Truss bridge">truss bridge</a>. A cantilever in a traditionally <a href="/wiki/Timber_framing" title="Timber framing">timber framed</a> building is called a <a href="/wiki/Jettying" title="Jettying">jetty</a> or <a href="/wiki/Pennsylvania_barn" title="Pennsylvania barn">forebay</a>. In the southern United States, a historic barn type is the cantilever barn of <a href="/wiki/Log_cabin" title="Log cabin">log construction</a>. </p><p>Temporary cantilevers are often used in construction. The partially constructed structure creates a cantilever, but the completed structure does not act as a cantilever. This is very helpful when temporary supports, or <a href="/wiki/Falsework" title="Falsework">falsework</a>, cannot be used to support the structure while it is being built (e.g., over a busy roadway or river, or in a deep valley). Therefore, some <a href="/wiki/Truss_arch_bridge" title="Truss arch bridge">truss arch bridges</a> (see <a href="/wiki/Navajo_Bridge" title="Navajo Bridge">Navajo Bridge</a>) are built from each side as cantilevers until the spans reach each other and are then jacked apart to stress them in compression before finally joining. Nearly all <a href="/wiki/Cable-stayed_bridges" class="mw-redirect" title="Cable-stayed bridges">cable-stayed bridges</a> are built using cantilevers as this is one of their chief advantages. Many box girder bridges are built <a href="/wiki/Segmental_bridge" title="Segmental bridge">segmentally</a>, or in short pieces. This type of construction lends itself well to balanced cantilever construction where the bridge is built in both directions from a single support. </p><p>These structures rely heavily on <a href="/wiki/Torque" title="Torque">torque</a> and rotational equilibrium for their stability. </p><p>In an architectural application, <a href="/wiki/Frank_Lloyd_Wright" title="Frank Lloyd Wright">Frank Lloyd Wright</a>'s <a href="/wiki/Fallingwater" title="Fallingwater">Fallingwater</a> used cantilevers to project large balconies. The East Stand at <a href="/wiki/Elland_Road" title="Elland Road">Elland Road</a> Stadium in Leeds was, when completed, the largest cantilever stand in the world<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> holding 17,000 spectators. The <a href="/wiki/Roof" title="Roof">roof</a> built over the stands at <a href="/wiki/Old_Trafford" title="Old Trafford">Old Trafford</a> uses a cantilever so that no supports will block views of the field. The old (now demolished) <a href="/wiki/Miami_Stadium" title="Miami Stadium">Miami Stadium</a> had a similar roof over the spectator area. The largest cantilevered roof in Europe is located at <a href="/wiki/St_James%27_Park" title="St James' Park">St James' Park</a> in <a href="/wiki/Newcastle-Upon-Tyne" class="mw-redirect" title="Newcastle-Upon-Tyne">Newcastle-Upon-Tyne</a>, the home stadium of <a href="/wiki/Newcastle_United_F.C." title="Newcastle United F.C.">Newcastle United F.C.</a><sup id="cite_ref-IStructE_3-0" class="reference"><a href="#cite_note-IStructE-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-highbeamdotcom_4-0" class="reference"><a href="#cite_note-highbeamdotcom-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Less obvious examples of cantilevers are free-standing (vertical) <a href="/wiki/Radio_masts_and_towers" title="Radio masts and towers">radio towers</a> without <a href="/wiki/Guy-wire" title="Guy-wire">guy-wires</a>, and <a href="/wiki/Chimneys" class="mw-redirect" title="Chimneys">chimneys</a>, which resist being blown over by the wind through cantilever action at their base. </p> <ul class="gallery mw-gallery-nolines"> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:ForthBridgeEdinburgh.jpg" class="mw-file-description" title="The Forth Bridge, a cantilever truss bridge"><img alt="The Forth Bridge, a cantilever truss bridge" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/ForthBridgeEdinburgh.jpg/120px-ForthBridgeEdinburgh.jpg" decoding="async" width="120" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/ForthBridgeEdinburgh.jpg/180px-ForthBridgeEdinburgh.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/ForthBridgeEdinburgh.jpg/240px-ForthBridgeEdinburgh.jpg 2x" data-file-width="538" data-file-height="358" /></a></span></div> <div class="gallerytext">The <a href="/wiki/Forth_Bridge" title="Forth Bridge">Forth Bridge</a>, a cantilever truss bridge</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Pierre_Pflimlin_Bridge_UC_Adjusted.jpg" class="mw-file-description" title="This concrete bridge temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support formwork."><img alt="This concrete bridge temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support formwork." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pierre_Pflimlin_Bridge_UC_Adjusted.jpg/120px-Pierre_Pflimlin_Bridge_UC_Adjusted.jpg" decoding="async" width="120" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pierre_Pflimlin_Bridge_UC_Adjusted.jpg/180px-Pierre_Pflimlin_Bridge_UC_Adjusted.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pierre_Pflimlin_Bridge_UC_Adjusted.jpg/240px-Pierre_Pflimlin_Bridge_UC_Adjusted.jpg 2x" data-file-width="1000" data-file-height="740" /></a></span></div> <div class="gallerytext">This <a href="/wiki/Pierre_Pflimlin_Bridge" title="Pierre Pflimlin Bridge">concrete bridge</a> temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support <a href="/wiki/Formwork" title="Formwork">formwork</a>.</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Howrah_Bridge.jpg" class="mw-file-description" title="Howrah Bridge in India, a cantilever bridge"><img alt="Howrah Bridge in India, a cantilever bridge" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Howrah_Bridge.jpg/120px-Howrah_Bridge.jpg" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Howrah_Bridge.jpg/180px-Howrah_Bridge.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Howrah_Bridge.jpg/240px-Howrah_Bridge.jpg 2x" data-file-width="1024" data-file-height="768" /></a></span></div> <div class="gallerytext"><a href="/wiki/Howrah_Bridge" title="Howrah Bridge">Howrah Bridge</a> in <a href="/wiki/India" title="India">India</a>, a cantilever bridge</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:FallingwaterCantilever570320cv.jpg" class="mw-file-description" title="A cantilevered balcony of the Fallingwater house, by Frank Lloyd Wright"><img alt="A cantilevered balcony of the Fallingwater house, by Frank Lloyd Wright" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/FallingwaterCantilever570320cv.jpg/120px-FallingwaterCantilever570320cv.jpg" decoding="async" width="120" height="84" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/FallingwaterCantilever570320cv.jpg/180px-FallingwaterCantilever570320cv.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/FallingwaterCantilever570320cv.jpg/240px-FallingwaterCantilever570320cv.jpg 2x" data-file-width="967" data-file-height="674" /></a></span></div> <div class="gallerytext">A cantilevered balcony of the <a href="/wiki/Fallingwater" title="Fallingwater">Fallingwater</a> house, by <a href="/wiki/Frank_Lloyd_Wright" title="Frank Lloyd Wright">Frank Lloyd Wright</a></div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Canton_Viaduct,_Southern_view,_west_side.JPG" class="mw-file-description" title="A cantilevered railroad deck and fence on the Canton Viaduct"><img alt="A cantilevered railroad deck and fence on the Canton Viaduct" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Canton_Viaduct%2C_Southern_view%2C_west_side.JPG/67px-Canton_Viaduct%2C_Southern_view%2C_west_side.JPG" decoding="async" width="67" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Canton_Viaduct%2C_Southern_view%2C_west_side.JPG/101px-Canton_Viaduct%2C_Southern_view%2C_west_side.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Canton_Viaduct%2C_Southern_view%2C_west_side.JPG/135px-Canton_Viaduct%2C_Southern_view%2C_west_side.JPG 2x" data-file-width="1024" data-file-height="1824" /></a></span></div> <div class="gallerytext">A cantilevered railroad deck and fence on the <a href="/wiki/Canton_Viaduct" title="Canton Viaduct">Canton Viaduct</a></div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Cantilever-barn-moa-tn1.jpg" class="mw-file-description" title="A cantilever barn in rural Tennessee"><img alt="A cantilever barn in rural Tennessee" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cantilever-barn-moa-tn1.jpg/120px-Cantilever-barn-moa-tn1.jpg" decoding="async" width="120" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cantilever-barn-moa-tn1.jpg/180px-Cantilever-barn-moa-tn1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cantilever-barn-moa-tn1.jpg/240px-Cantilever-barn-moa-tn1.jpg 2x" data-file-width="1989" data-file-height="1377" /></a></span></div> <div class="gallerytext">A cantilever barn in rural <a href="/wiki/Tennessee" title="Tennessee">Tennessee</a></div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:18-22-186-cades.jpg" class="mw-file-description" title="Cantilever barn at Cades Cove"><img alt="Cantilever barn at Cades Cove" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/18-22-186-cades.jpg/120px-18-22-186-cades.jpg" decoding="async" width="120" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/18-22-186-cades.jpg/180px-18-22-186-cades.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/18-22-186-cades.jpg/240px-18-22-186-cades.jpg 2x" data-file-width="2048" data-file-height="1366" /></a></span></div> <div class="gallerytext">Cantilever barn at <a href="/wiki/Cades_Cove" title="Cades Cove">Cades Cove</a></div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:DoubleJettiedBuilding.jpg" class="mw-file-description" title="A double jettied building in Cambridge, England"><img alt="A double jettied building in Cambridge, England" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/DoubleJettiedBuilding.jpg/87px-DoubleJettiedBuilding.jpg" decoding="async" width="87" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/DoubleJettiedBuilding.jpg/131px-DoubleJettiedBuilding.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/DoubleJettiedBuilding.jpg/175px-DoubleJettiedBuilding.jpg 2x" data-file-width="768" data-file-height="1054" /></a></span></div> <div class="gallerytext">A double jettied building in Cambridge, England</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Cantilever_Jenga.JPG" class="mw-file-description" title="Cantilever occurring in the game "Jenga""><img alt="Cantilever occurring in the game "Jenga"" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Cantilever_Jenga.JPG/120px-Cantilever_Jenga.JPG" decoding="async" width="120" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Cantilever_Jenga.JPG/180px-Cantilever_Jenga.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Cantilever_Jenga.JPG/240px-Cantilever_Jenga.JPG 2x" data-file-width="2543" data-file-height="2145" /></a></span></div> <div class="gallerytext">Cantilever occurring in the game "<a href="/wiki/Jenga" title="Jenga">Jenga</a>"</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Riverplace_Tower_in_Jacksonville.jpg" class="mw-file-description" title="Cantilever facade of Riverplace Tower in Jacksonville, Florida, by Welton Becket and KBJ Architects"><img alt="Cantilever facade of Riverplace Tower in Jacksonville, Florida, by Welton Becket and KBJ Architects" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Riverplace_Tower_in_Jacksonville.jpg/80px-Riverplace_Tower_in_Jacksonville.jpg" decoding="async" width="80" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Riverplace_Tower_in_Jacksonville.jpg/120px-Riverplace_Tower_in_Jacksonville.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Riverplace_Tower_in_Jacksonville.jpg/160px-Riverplace_Tower_in_Jacksonville.jpg 2x" data-file-width="2592" data-file-height="3872" /></a></span></div> <div class="gallerytext">Cantilever facade of <a href="/wiki/Riverplace_Tower" title="Riverplace Tower">Riverplace Tower</a> in <a href="/wiki/Jacksonville,_Florida" title="Jacksonville, Florida">Jacksonville, Florida</a>, by <a href="/wiki/Welton_Becket" title="Welton Becket">Welton Becket</a> and <a href="/wiki/KBJ_Architects" title="KBJ Architects">KBJ Architects</a></div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Cantilever_crown.png" class="mw-file-description" title="This radiograph of a "bridge" dental restoration features a cantilevered crown to the left."><img alt="This radiograph of a "bridge" dental restoration features a cantilevered crown to the left." src="//upload.wikimedia.org/wikipedia/en/thumb/6/6e/Cantilever_crown.png/93px-Cantilever_crown.png" decoding="async" width="93" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6e/Cantilever_crown.png/140px-Cantilever_crown.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6e/Cantilever_crown.png/187px-Cantilever_crown.png 2x" data-file-width="651" data-file-height="835" /></a></span></div> <div class="gallerytext">This <a href="/wiki/Radiograph" class="mw-redirect" title="Radiograph">radiograph</a> of a "bridge" dental restoration features a cantilevered crown to the left.</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Ronan_Point_collapse_closeup.jpg" class="mw-file-description" title="Ronan Point: Structural failure of part of floors cantilevered from a central shaft."><img alt="Ronan Point: Structural failure of part of floors cantilevered from a central shaft." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ronan_Point_collapse_closeup.jpg/81px-Ronan_Point_collapse_closeup.jpg" decoding="async" width="81" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ronan_Point_collapse_closeup.jpg/121px-Ronan_Point_collapse_closeup.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ronan_Point_collapse_closeup.jpg/161px-Ronan_Point_collapse_closeup.jpg 2x" data-file-width="538" data-file-height="800" /></a></span></div> <div class="gallerytext"><a href="/wiki/Ronan_Point" title="Ronan Point">Ronan Point</a>: Structural failure of part of floors cantilevered from a central shaft.</div> </li> <li class="gallerybox" style="width: 125px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Fiat_tagliero,_08.JPG" class="mw-file-description" title="Fiat Tagliero, a Futurist-style service station in Asmara, Eritrea, has a mirrored cantilevered roof."><img alt="Fiat Tagliero, a Futurist-style service station in Asmara, Eritrea, has a mirrored cantilevered roof." src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Fiat_tagliero%2C_08.JPG/120px-Fiat_tagliero%2C_08.JPG" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Fiat_tagliero%2C_08.JPG/180px-Fiat_tagliero%2C_08.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Fiat_tagliero%2C_08.JPG/240px-Fiat_tagliero%2C_08.JPG 2x" data-file-width="2648" data-file-height="1624" /></a></span></div> <div class="gallerytext"><a href="/wiki/Fiat_Tagliero" class="mw-redirect" title="Fiat Tagliero">Fiat Tagliero</a>, a <a href="/wiki/Futurist_architecture" title="Futurist architecture">Futurist-style</a> <a href="/wiki/Filling_station" title="Filling station">service station</a> in <a href="/wiki/Asmara" title="Asmara">Asmara</a>, <a href="/wiki/Eritrea" title="Eritrea">Eritrea</a>, has a mirrored cantilevered roof.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Aircraft">Aircraft</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=2" title="Edit section: Aircraft"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Junkers_J_1_at_D%C3%B6beritz_1915.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Junkers_J_1_at_D%C3%B6beritz_1915.jpg/200px-Junkers_J_1_at_D%C3%B6beritz_1915.jpg" decoding="async" width="200" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Junkers_J_1_at_D%C3%B6beritz_1915.jpg/300px-Junkers_J_1_at_D%C3%B6beritz_1915.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Junkers_J_1_at_D%C3%B6beritz_1915.jpg/400px-Junkers_J_1_at_D%C3%B6beritz_1915.jpg 2x" data-file-width="4348" data-file-height="1737" /></a><figcaption>The pioneering <a href="/wiki/Junkers_J_1" title="Junkers J 1">Junkers J 1</a> all-metal monoplane of 1915, the first aircraft to fly with cantilever wings</figcaption></figure> <p>The cantilever is commonly used in the wings of <a href="/wiki/Fixed-wing_aircraft" title="Fixed-wing aircraft">fixed-wing aircraft</a>. Early aircraft had light structures which were braced with <a href="/wiki/Flying_wires" class="mw-redirect" title="Flying wires">wires</a> and <a href="/wiki/Strut#Aircraft" title="Strut">struts</a>. However, these introduced aerodynamic drag which limited performance. While it is heavier, the cantilever avoids this issue and allows the plane to fly faster. </p><p><a href="/wiki/Hugo_Junkers" title="Hugo Junkers">Hugo Junkers</a> pioneered the cantilever wing in 1915. Only a dozen years after the <a href="/wiki/Wright_Brothers" class="mw-redirect" title="Wright Brothers">Wright Brothers</a>' initial flights, Junkers endeavored to eliminate virtually all major external bracing members in order to decrease airframe drag in flight. The result of this endeavor was the <a href="/wiki/Junkers_J_1" title="Junkers J 1">Junkers J 1</a> pioneering all-metal monoplane of late 1915, designed from the start with all-metal cantilever wing panels. About a year after the initial success of the Junkers J 1, <a href="/wiki/Reinhold_Platz" title="Reinhold Platz">Reinhold Platz</a> of <a href="/wiki/Fokker" title="Fokker">Fokker</a> also achieved success with a cantilever-winged <a href="/wiki/Sesquiplane" class="mw-redirect" title="Sesquiplane">sesquiplane</a> built instead with wooden materials, the <a href="/wiki/Fokker_V.1" title="Fokker V.1">Fokker V.1</a>. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:De_Havilland_DH88_Comet.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/De_Havilland_DH88_Comet.jpg/200px-De_Havilland_DH88_Comet.jpg" decoding="async" width="200" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/De_Havilland_DH88_Comet.jpg/300px-De_Havilland_DH88_Comet.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/De_Havilland_DH88_Comet.jpg/400px-De_Havilland_DH88_Comet.jpg 2x" data-file-width="3600" data-file-height="2400" /></a><figcaption><a href="/wiki/De_Havilland_DH.88_Comet" title="De Havilland DH.88 Comet">de Havilland DH.88 Comet</a> G-ACSS, winner of the <a href="/wiki/MacRobertson_Air_Race" title="MacRobertson Air Race">Great Air Race of 1934</a>, showing off its cantilever wing</figcaption></figure> <p>In the cantilever wing, one or more strong beams, called <i><a href="/wiki/Spar_(aviation)" class="mw-redirect" title="Spar (aviation)">spars</a></i>, run along the span of the wing. The end fixed rigidly to the central fuselage is known as the root and the far end as the tip. In flight, the wings generate <a href="/wiki/Lift_(force)" title="Lift (force)">lift</a> and the spars carry this load through to the fuselage. </p><p>To resist horizontal shear stress from either drag or engine thrust, the wing must also form a stiff cantilever in the horizontal plane. A single-spar design will usually be fitted with a second smaller drag-spar nearer the <a href="/wiki/Trailing_edge" title="Trailing edge">trailing edge</a>, braced to the main spar via additional internal members or a stressed skin. The wing must also resist twisting forces, achieved by cross-bracing or otherwise stiffening the main structure. </p><p>Cantilever wings require much stronger and heavier spars than would otherwise be needed in a wire-braced design. However, as the speed of the aircraft increases, the drag of the bracing increases sharply, while the wing structure must be strengthened, typically by increasing the strength of the spars and the thickness of the skinning. At speeds of around 200 miles per hour (320 km/h) the drag of the bracing becomes excessive and the wing strong enough to be made a cantilever without excess weight penalty. Increases in engine power through the late 1920s and early 1930s raised speeds through this zone and by the late 1930s cantilever wings had almost wholly superseded braced ones.<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> Other changes such as enclosed cockpits, retractable undercarriage, landing flaps and stressed-skin construction furthered the design revolution, with the pivotal moment widely acknowledged to be the <a href="/wiki/MacRobertson_Air_Race" title="MacRobertson Air Race">MacRobertson England-Australia air race</a> of 1934, which was won by a <a href="/wiki/De_Havilland_DH.88_Comet" title="De Havilland DH.88 Comet">de Havilland DH.88 Comet</a>.<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><p>Currently, cantilever wings are almost universal with bracing only being used for some slower aircraft where a lighter weight is prioritized over speed, such as in the <a href="/wiki/Ultralight_aircraft" class="mw-redirect" title="Ultralight aircraft">ultralight</a> class. </p> <div class="mw-heading mw-heading2"><h2 id="Cantilever_in_microelectromechanical_systems">Cantilever in microelectromechanical systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=3" title="Edit section: Cantilever in microelectromechanical systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:AFM_(used)_cantilever_in_Scanning_Electron_Microscope,_magnification_1000x.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF/220px-AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF/330px-AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF/440px-AFM_%28used%29_cantilever_in_Scanning_Electron_Microscope%2C_magnification_1000x.GIF 2x" data-file-width="1280" data-file-height="1024" /></a><figcaption><a href="/wiki/Scanning_electron_microscope" title="Scanning electron microscope">SEM</a> image of a used <a href="/wiki/Atomic_force_microscopy" title="Atomic force microscopy">AFM</a> cantilever</figcaption></figure> <p>Cantilevered beams are the most ubiquitous structures in the field of <a href="/wiki/Microelectromechanical_systems" class="mw-redirect" title="Microelectromechanical systems">microelectromechanical systems</a> (MEMS). An early example of a MEMS cantilever is the Resonistor,<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><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> an electromechanical monolithic resonator. MEMS cantilevers are commonly fabricated from <a href="/wiki/Silicon" title="Silicon">silicon</a> (Si), <a href="/wiki/Silicon_nitride" title="Silicon nitride">silicon nitride</a> (Si<sub>3</sub>N<sub>4</sub>), or <a href="/wiki/Polymer" title="Polymer">polymers</a>. The fabrication process typically involves undercutting the cantilever structure to <i>release</i> it, often with an anisotropic wet or <a href="/wiki/Reactive_ion_etching" class="mw-redirect" title="Reactive ion etching">dry</a> etching technique. Without cantilever transducers, <a href="/wiki/Atomic_force_microscopy" title="Atomic force microscopy">atomic force microscopy</a> would not be possible. A large number of research groups are attempting to develop cantilever arrays as <a href="/wiki/Biosensor" title="Biosensor">biosensors</a> for medical diagnostic applications. MEMS cantilevers are also finding application as <a href="/wiki/Radio_frequency" title="Radio frequency">radio frequency</a> <a href="/wiki/Mechanical_filter" title="Mechanical filter">filters</a> and <a href="/wiki/Resonator" title="Resonator">resonators</a>. The MEMS cantilevers are commonly made as <a href="/wiki/Unimorph" title="Unimorph">unimorphs</a> or <a href="/wiki/Bimorph" title="Bimorph">bimorphs</a>. </p><p>Two equations are key to understanding the behavior of MEMS cantilevers. The first is <i>Stoney's formula</i>, which relates cantilever end <a href="/wiki/Deflection_(engineering)" title="Deflection (engineering)">deflection</a> δ to applied stress σ: </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 ={\frac {3\sigma \left(1-\nu \right)}{E}}{\frac {L^{2}}{t^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>σ</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>ν</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mi>E</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta ={\frac {3\sigma \left(1-\nu \right)}{E}}{\frac {L^{2}}{t^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f332262d69ab7acba1cd8cf6e1b371ee9d34f140" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:18.38ex; height:6.009ex;" alt="{\displaystyle \delta ={\frac {3\sigma \left(1-\nu \right)}{E}}{\frac {L^{2}}{t^{2}}}}"></span></dd></dl> <p>where <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> is <a href="/wiki/Poisson%27s_ratio" title="Poisson's ratio">Poisson's ratio</a>, <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is <a href="/wiki/Young%27s_modulus" title="Young's modulus">Young's modulus</a>, <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> is the beam length and <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> is the cantilever thickness. Very sensitive optical and capacitive methods have been developed to measure changes in the static deflection of cantilever beams used in dc-coupled sensors. </p><p>The second is the formula relating the cantilever <a href="/wiki/Spring_constant" class="mw-redirect" title="Spring constant">spring constant</a> <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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> to the cantilever dimensions and material constants: </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 k={\frac {F}{\delta }}={\frac {Ewt^{3}}{4L^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>δ</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mi>w</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k={\frac {F}{\delta }}={\frac {Ewt^{3}}{4L^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa8503b9c83c1877027d684f4e2ab50dd4550ad3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.155ex; height:5.843ex;" alt="{\displaystyle k={\frac {F}{\delta }}={\frac {Ewt^{3}}{4L^{3}}}}"></span></dd></dl> <p>where <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 F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> is force and <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> is the cantilever width. The spring constant is related to the cantilever resonance frequency <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 \omega _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a713d16c489051d4f515e12b1f86061c6be799b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \omega _{0}}"></span> by the usual <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillator</a> formula <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 \omega _{0}={\sqrt {k/m_{\text{equivalent}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>equivalent</mtext> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}={\sqrt {k/m_{\text{equivalent}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07199e95b36800ab198d2e016b876937fbec3752" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.969ex; height:4.843ex;" alt="{\displaystyle \omega _{0}={\sqrt {k/m_{\text{equivalent}}}}}"></span>. A change in the force applied to a cantilever can shift the resonance frequency. The frequency shift can be measured with exquisite accuracy using <a href="/wiki/Heterodyne" title="Heterodyne">heterodyne</a> techniques and is the basis of ac-coupled cantilever sensors. </p><p>The principal advantage of MEMS cantilevers is their cheapness and ease of fabrication in large arrays. The challenge for their practical application lies in the square and cubic dependences of cantilever performance specifications on dimensions. These superlinear dependences mean that cantilevers are quite sensitive to variation in process parameters, particularly the thickness as this is generally difficult to accurately measure.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> However, it has been shown that microcantilever thicknesses can be precisely measured and that this variation can be quantified.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Controlling <a href="/wiki/Residual_stress" title="Residual stress">residual stress</a> can also be difficult. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MEMS_Microcantilever_in_Resonance.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/MEMS_Microcantilever_in_Resonance.png/220px-MEMS_Microcantilever_in_Resonance.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/MEMS_Microcantilever_in_Resonance.png/330px-MEMS_Microcantilever_in_Resonance.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/MEMS_Microcantilever_in_Resonance.png/440px-MEMS_Microcantilever_in_Resonance.png 2x" data-file-width="2048" data-file-height="1536" /></a><figcaption>MEMS cantilever in resonance<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Chemical_sensor_applications">Chemical sensor applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=4" title="Edit section: Chemical sensor applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Chemical_sensor" class="mw-redirect" title="Chemical sensor">chemical sensor</a> can be obtained by coating a recognition receptor layer over the upper side of a microcantilever beam.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> A typical application is the immunosensor based on an <a href="/wiki/Antibody" title="Antibody">antibody</a> layer that interacts selectively with a particular <a href="/wiki/Immunogen" title="Immunogen">immunogen</a> and reports about its content in a specimen. In the static mode of operation, the sensor response is represented by the beam bending with respect to a reference microcantilever. Alternatively, microcantilever sensors can be operated in the dynamic mode. In this case, the beam vibrates at its resonance frequency and a variation in this parameter indicates the concentration of the <a href="/wiki/Analyte" title="Analyte">analyte</a>. Recently, microcantilevers have been fabricated that are porous, allowing for a much larger surface area for <a href="/wiki/Analyte" title="Analyte">analyte</a> to bind to, increasing sensitivity by raising the ratio of the analyte mass to the device mass.<sup id="cite_ref-Noyce_Vanfleet_Craighead_Davis_1999_pp._1148–1154_13-0" class="reference"><a href="#cite_note-Noyce_Vanfleet_Craighead_Davis_1999_pp._1148–1154-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Surface stress on microcantilever, due to receptor-target binding, which produces cantilever deflection can be analyzed using optical methods like laser interferometry. Zhao et al., also showed that by changing the attachment protocol of the receptor on the microcantilever surface, the sensitivity can be further improved when the surface stress generated on the microcantilever is taken as the sensor signal.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 23em;"> <ul><li><a href="/wiki/Applied_mechanics" title="Applied mechanics">Applied mechanics</a></li> <li><a href="/wiki/Bicycle_brake#Cantilever_brakes" title="Bicycle brake">Cantilever bicycle brakes</a></li> <li><a href="/wiki/Bicycle_frame#Cantilever" title="Bicycle frame">Cantilever bicycle frame</a></li> <li><a href="/wiki/Cantilever_chair" title="Cantilever chair">Cantilever chair</a></li> <li><a href="/wiki/Cantilever_method" title="Cantilever method">Cantilever method</a></li> <li><a href="/wiki/Cantilevered_stairs" title="Cantilevered stairs">Cantilevered stairs</a></li> <li><a href="/wiki/Corbel_arch" title="Corbel arch">Corbel arch</a></li> <li><a href="/wiki/Euler%E2%80%93Bernoulli_beam_theory" title="Euler–Bernoulli beam theory">Euler–Bernoulli beam theory</a></li> <li><a href="/wiki/Grand_Canyon_Skywalk" title="Grand Canyon Skywalk">Grand Canyon Skywalk</a></li> <li><a href="/wiki/Knudsen_force" title="Knudsen force">Knudsen force</a> in the context of microcantilevers</li> <li><a href="/wiki/Orthodontics" title="Orthodontics">Orthodontics</a></li> <li><a href="/wiki/Statics" title="Statics">Statics</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.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 mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output 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Elliott: Rapid microcantilever-thickness determination by optical interferometry, Measurement Science and Technology 25, 015202 (2014)</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPatrick_C._FletcherY._XuP._GopinathJ._Williams2008" class="citation conference cs1">Patrick C. Fletcher; Y. Xu; P. Gopinath; J. Williams; B. W. Alphenaar; R. D. Bradshaw; Robert S. Keynton (2008). <i>Piezoresistive Geometry for Maximizing Microcantilever Array Sensitivity</i>. IEEE Sensors.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Piezoresistive+Geometry+for+Maximizing+Microcantilever+Array+Sensitivity&rft.date=2008&rft.au=Patrick+C.+Fletcher&rft.au=Y.+Xu&rft.au=P.+Gopinath&rft.au=J.+Williams&rft.au=B.+W.+Alphenaar&rft.au=R.+D.+Bradshaw&rft.au=Robert+S.+Keynton&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBănică2012" class="citation book cs1">Bănică, Florinel-Gabriel (2012). <i>Chemical Sensors and Biosensors:Fundamentals and Applications</i>. Chichester, UK: John Wiley & Sons. p. 576. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-118-35423-0" title="Special:BookSources/978-1-118-35423-0"><bdi>978-1-118-35423-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Sensors+and+Biosensors%3AFundamentals+and+Applications&rft.place=Chichester%2C+UK&rft.pages=576&rft.pub=John+Wiley+%26+Sons&rft.date=2012&rft.isbn=978-1-118-35423-0&rft.aulast=B%C4%83nic%C4%83&rft.aufirst=Florinel-Gabriel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></span> </li> <li id="cite_note-Noyce_Vanfleet_Craighead_Davis_1999_pp._1148–1154-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Noyce_Vanfleet_Craighead_Davis_1999_pp._1148–1154_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNoyceVanfleetCraigheadDavis1999" class="citation journal cs1">Noyce, Steven G.; Vanfleet, Richard R.; Craighead, Harold G.; Davis, Robert C. (1999-02-22). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9418787">"High surface-area carbon microcantilevers"</a>. <i>Nanoscale Advances</i>. <b>1</b> (3): 1148–1154. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC8NA00101D">10.1039/C8NA00101D</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9418787">9418787</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/36133213">36133213</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nanoscale+Advances&rft.atitle=High+surface-area+carbon+microcantilevers&rft.volume=1&rft.issue=3&rft.pages=1148-1154&rft.date=1999-02-22&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9418787%23id-name%3DPMC&rft_id=info%3Apmid%2F36133213&rft_id=info%3Adoi%2F10.1039%2FC8NA00101D&rft.aulast=Noyce&rft.aufirst=Steven+G.&rft.au=Vanfleet%2C+Richard+R.&rft.au=Craighead%2C+Harold+G.&rft.au=Davis%2C+Robert+C.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9418787&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhaoGosaiShrotriya2019" class="citation journal cs1">Zhao, Yue; Gosai, Agnivo; Shrotriya, Pranav (1 December 2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.snb.2019.126963">"Effect of Receptor Attachment on Sensitivity of Label Free Microcantilever Based Biosensor Using Malachite Green Aptamer"</a>. <i>Sensors and Actuators B: Chemical</i>. <b>300</b>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.snb.2019.126963">10.1016/j.snb.2019.126963</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Sensors+and+Actuators+B%3A+Chemical&rft.atitle=Effect+of+Receptor+Attachment+on+Sensitivity+of+Label+Free+Microcantilever+Based+Biosensor+Using+Malachite+Green+Aptamer&rft.volume=300&rft.date=2019-12-01&rft_id=info%3Adoi%2F10.1016%2Fj.snb.2019.126963&rft.aulast=Zhao&rft.aufirst=Yue&rft.au=Gosai%2C+Agnivo&rft.au=Shrotriya%2C+Pranav&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252Fj.snb.2019.126963&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=7" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Inglis, Simon: <i>Football Grounds of Britain</i>. CollinsWillow, 1996. page 206.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMadou2002" class="citation book cs1">Madou, Marc J (2002). <i>Fundamentals of Microfabrication</i>. Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-0826-7" title="Special:BookSources/0-8493-0826-7"><bdi>0-8493-0826-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Microfabrication&rft.pub=Taylor+%26+Francis&rft.date=2002&rft.isbn=0-8493-0826-7&rft.aulast=Madou&rft.aufirst=Marc+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoth1993" class="citation book cs1">Roth, Leland M (1993). <a rel="nofollow" class="external text" href="https://archive.org/details/understandingarc00roth/page/23"><i>Understanding Architecture: Its Elements History and Meaning</i></a>. Oxford, UK: Westview Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/understandingarc00roth/page/23">23–4</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-06-430158-3" title="Special:BookSources/0-06-430158-3"><bdi>0-06-430158-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+Architecture%3A+Its+Elements+History+and+Meaning&rft.place=Oxford%2C+UK&rft.pages=23-4&rft.pub=Westview+Press&rft.date=1993&rft.isbn=0-06-430158-3&rft.aulast=Roth&rft.aufirst=Leland+M&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Funderstandingarc00roth%2Fpage%2F23&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSarid1994" class="citation book cs1">Sarid, Dror (1994). <i>Scanning Force Microscopy</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-509204-X" title="Special:BookSources/0-19-509204-X"><bdi>0-19-509204-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scanning+Force+Microscopy&rft.pub=Oxford+University+Press&rft.date=1994&rft.isbn=0-19-509204-X&rft.aulast=Sarid&rft.aufirst=Dror&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACantilever" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cantilever&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" 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