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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</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">(Top)</div> </a> </li> <li id="toc-Etymology" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Etymology"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Etymology</span> </div> </a> <ul id="toc-Etymology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Characteristics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Characteristics</span> </div> </a> <button aria-controls="toc-Characteristics-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>Toggle Characteristics subsection</span> </button> <ul id="toc-Characteristics-sublist" class="vector-toc-list"> <li id="toc-Simple_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simple_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Simple truss</span> </div> </a> <ul id="toc-Simple_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Planar_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Planar_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Planar truss</span> </div> </a> <ul id="toc-Planar_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Space_frame_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Space_frame_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Space frame truss</span> </div> </a> <ul id="toc-Space_frame_truss-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Types</span> </div> </a> <button aria-controls="toc-Types-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>Toggle Types subsection</span> </button> <ul id="toc-Types-sublist" class="vector-toc-list"> <li id="toc-Warren_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Warren_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Warren truss</span> </div> </a> <ul id="toc-Warren_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Octet_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Octet_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Octet truss</span> </div> </a> <ul id="toc-Octet_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pratt_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pratt_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Pratt truss</span> </div> </a> <ul id="toc-Pratt_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Town's_lattice_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Town's_lattice_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Town's lattice truss</span> </div> </a> <ul id="toc-Town's_lattice_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bowstring_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bowstring_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Bowstring truss</span> </div> </a> <ul id="toc-Bowstring_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-King_and_queen_post_trusses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#King_and_queen_post_trusses"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>King and queen post trusses</span> </div> </a> <ul id="toc-King_and_queen_post_trusses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lenticular_truss" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lenticular_truss"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Lenticular truss</span> </div> </a> <ul id="toc-Lenticular_truss-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vierendeel_structure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vierendeel_structure"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Vierendeel structure</span> </div> </a> <ul id="toc-Vierendeel_structure-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Statics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Statics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Statics</span> </div> </a> <ul id="toc-Statics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Analysis</span> </div> </a> <button aria-controls="toc-Analysis-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>Toggle Analysis subsection</span> </button> <ul id="toc-Analysis-sublist" class="vector-toc-list"> <li id="toc-Forces_in_members" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Forces_in_members"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Forces in members</span> </div> </a> <ul id="toc-Forces_in_members-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Design_of_members" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Design_of_members"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Design of members</span> </div> </a> <ul id="toc-Design_of_members-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Design_of_joints" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Design_of_joints"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Design of joints</span> </div> </a> <ul id="toc-Design_of_joints-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-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>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Post_frame_structures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Post_frame_structures"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Post frame structures</span> </div> </a> <ul id="toc-Post_frame_structures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gallery" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gallery"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Gallery</span> </div> </a> <ul id="toc-Gallery-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">8</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">9</span> <span>References</span> </div> </a> <ul id="toc-References-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <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="Toggle the table of contents" > <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">Toggle the table of contents</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">Truss</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="Go to an article in another language. Available in 38 languages" > <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-38" 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">38 languages</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%AC%D9%85%D8%A7%D9%84%D9%88%D9%86" title="جمالون – Arabic" lang="ar" hreflang="ar" data-title="جمالون" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D0%B5%D1%80%D0%BC%D0%B0_(%D0%BA%D0%B0%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%86%D1%8B%D1%8F)" title="Ферма (канструкцыя) – Belarusian" lang="be" hreflang="be" data-title="Ферма (канструкцыя)" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%B5%D1%80%D0%BC%D0%B0_(%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%86%D0%B8%D1%8F)" title="Ферма (конструкция) – Bulgarian" lang="bg" hreflang="bg" data-title="Ферма (конструкция)" 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/Gelosia_(estructura)" title="Gelosia (estructura) – Catalan" lang="ca" hreflang="ca" data-title="Gelosia (estructura)" data-language-autonym="Català" data-language-local-name="Catalan" 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/P%C5%99%C3%ADhradov%C3%A1_konstrukce" title="Příhradová konstrukce – Czech" lang="cs" hreflang="cs" data-title="Příhradová konstrukce" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fachwerk" title="Fachwerk – German" lang="de" hreflang="de" data-title="Fachwerk" 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/Kandes%C3%B5restik" title="Kandesõrestik – Estonian" lang="et" hreflang="et" data-title="Kandesõrestik" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Armadura_(estructura)" title="Armadura (estructura) – Spanish" lang="es" hreflang="es" data-title="Armadura (estructura)" 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/%C4%B4aluzio_(strukturo)" title="Ĵaluzio (strukturo) – Esperanto" lang="eo" hreflang="eo" data-title="Ĵaluzio (strukturo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Sareta_(ingeniaritza)" title="Sareta (ingeniaritza) – Basque" lang="eu" hreflang="eu" data-title="Sareta (ingeniaritza)" data-language-autonym="Euskara" data-language-local-name="Basque" 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%AE%D8%B1%D9%BE%D8%A7" title="خرپا – Persian" lang="fa" hreflang="fa" data-title="خرپا" 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/Treillis_(structure)" title="Treillis (structure) – French" lang="fr" hreflang="fr" data-title="Treillis (structure)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8A%B8%EB%9F%AC%EC%8A%A4" title="트러스 – Korean" lang="ko" hreflang="ko" data-title="트러스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%A5%D6%80%D5%B4%D5%A1_(%D5%AF%D5%B8%D5%B6%D5%BD%D5%BF%D6%80%D5%B8%D6%82%D5%AF%D6%81%D5%AB%D5%A1)" title="Ֆերմա (կոնստրուկցիա) – Armenian" lang="hy" hreflang="hy" data-title="Ֆերմա (կոնստրուկցիա)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A4%B8" title="ट्रस – Hindi" lang="hi" hreflang="hi" data-title="ट्रस" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rangka_batang" title="Rangka batang – Indonesian" lang="id" hreflang="id" data-title="Rangka batang" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Travatura_reticolare" title="Travatura reticolare – Italian" lang="it" hreflang="it" data-title="Travatura reticolare" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%91%D7%9A" title="מסבך – Hebrew" lang="he" hreflang="he" data-title="מסבך" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%86%E0%B2%B8%E0%B2%B0%E0%B3%86%E0%B2%95%E0%B2%9F%E0%B3%8D%E0%B2%9F%E0%B3%81_(%E0%B2%B8%E0%B2%B0%E0%B2%95%E0%B2%9F%E0%B3%8D%E0%B2%9F%E0%B3%81)" title="ಆಸರೆಕಟ್ಟು (ಸರಕಟ್ಟು) – Kannada" lang="kn" hreflang="kn" data-title="ಆಸರೆಕಟ್ಟು (ಸರಕಟ್ಟು)" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%90%E1%83%9B%E1%83%AC%E1%83%94" title="წამწე – Georgian" lang="ka" hreflang="ka" data-title="წამწე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Santvara" title="Santvara – Lithuanian" lang="lt" hreflang="lt" data-title="Santvara" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D1%83%D0%BB%D0%B3%D1%83%D1%83%D1%80%D1%8B%D0%BD_%D1%85%D0%B8%D0%B9%D1%86" title="Тулгуурын хийц – Mongolian" lang="mn" hreflang="mn" data-title="Тулгуурын хийц" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vakwerk_(ligger)" title="Vakwerk (ligger) – Dutch" lang="nl" hreflang="nl" data-title="Vakwerk (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%83%88%E3%83%A9%E3%82%B9" title="トラス – Japanese" lang="ja" hreflang="ja" data-title="トラス" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fagverk" title="Fagverk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Fagverk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ferma_(tizim)" title="Ferma (tizim) – Uzbek" lang="uz" hreflang="uz" data-title="Ferma (tizim)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kratownica" title="Kratownica – Polish" lang="pl" hreflang="pl" data-title="Kratownica" 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/Treli%C3%A7a" title="Treliça – Portuguese" lang="pt" hreflang="pt" data-title="Treliça" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B5%D1%80%D0%BC%D0%B0_(%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%86%D0%B8%D1%8F)" title="Ферма (конструкция) – Russian" lang="ru" hreflang="ru" data-title="Ферма (конструкция)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Truss" title="Truss – Simple English" lang="en-simple" hreflang="en-simple" data-title="Truss" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pali%C4%8Dje" title="Paličje – Slovenian" lang="sl" hreflang="sl" data-title="Paličje" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ristikkorakenne" title="Ristikkorakenne – Finnish" lang="fi" hreflang="fi" data-title="Ristikkorakenne" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a 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searchaux" style="display:none">Rigid structure that consists of two-force members only</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 other uses, see <a href="/wiki/Truss_(disambiguation)" class="mw-disambig" title="Truss (disambiguation)">Truss (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:RRTrussBridgeSideView.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/RRTrussBridgeSideView.jpg/220px-RRTrussBridgeSideView.jpg" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/RRTrussBridgeSideView.jpg/330px-RRTrussBridgeSideView.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/RRTrussBridgeSideView.jpg/440px-RRTrussBridgeSideView.jpg 2x" data-file-width="800" data-file-height="400" /></a><figcaption><a href="/wiki/Truss_bridge" title="Truss bridge">Truss bridge</a> for a single-track railway, converted to pedestrian use and pipeline support. In this example the truss is a group of triangular units supporting the bridge.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:SteelDetail(2D-Truss).pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/SteelDetail%282D-Truss%29.pdf/page1-220px-SteelDetail%282D-Truss%29.pdf.jpg" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/SteelDetail%282D-Truss%29.pdf/page1-330px-SteelDetail%282D-Truss%29.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/SteelDetail%282D-Truss%29.pdf/page1-440px-SteelDetail%282D-Truss%29.pdf.jpg 2x" data-file-width="1175" data-file-height="835" /></a><figcaption>Typical detail of a steel truss, which is considered as a <a href="/wiki/Revolute_joint" title="Revolute joint">revolute joint</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:TL020504.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/TL020504.jpg/220px-TL020504.jpg" decoding="async" width="220" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/TL020504.jpg/330px-TL020504.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/TL020504.jpg/440px-TL020504.jpg 2x" data-file-width="1533" data-file-height="978" /></a><figcaption>Historical detail of a steel truss with an actual revolute joint</figcaption></figure> <p>A <b>truss</b> is an assembly of <i>members</i> such as <a href="/wiki/Beam_(structure)" title="Beam (structure)">beams</a>, connected by <i>nodes</i>, that creates a rigid structure.<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>In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object".<sup id="cite_ref-PleshaGrayCostanzo_2-0" class="reference"><a href="#cite_note-PleshaGrayCostanzo-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A "two-force member" is a structural component where force is applied to only two points. Although this rigorous definition allows the members to have any shape connected in any stable configuration, architectural trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as <i><a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">nodes</a></i>. </p><p>In this typical context, external forces and reactions to those forces are considered to act only at the nodes and result in forces in the members that are either <a href="/wiki/Tension_(physics)" title="Tension (physics)">tensile</a> or <a href="/wiki/Compression_(physics)" title="Compression (physics)">compressive</a>. For straight members, moments (<a href="/wiki/Torque" title="Torque">torques</a>) are explicitly excluded because, and only because, all the joints in a truss are treated as <a href="/wiki/Revolute_joint" title="Revolute joint">revolutes</a>, as is necessary for the links to be two-force members. </p><p>A planar truss is one where all members and nodes lie within a two-dimensional plane, while a <a href="/wiki/Space_frame" title="Space frame">space frame</a> has members and nodes that extend into <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three dimensions</a>. The top beams in a truss are called 'top chords' and are typically in <a href="/wiki/Compression_(physics)" title="Compression (physics)">compression</a>, the bottom beams are called 'bottom chords', and are typically in <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a>. The interior beams are called <i>webs</i>, and the areas inside the webs are called <i>panels</i>,<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> or from <a href="/wiki/Graphic_statics" title="Graphic statics">graphic statics</a> (see <a href="/wiki/Cremona_diagram" title="Cremona diagram">Cremona diagram</a>) 'polygons'.<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> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Truss</i> derives from the <a href="/wiki/Old_French" title="Old French">Old French</a> word <i>trousse</i>, from around 1200 AD, which means "collection of things bound together".<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><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> The term <i>truss</i> has often been used to describe any assembly of members such as a <a href="/wiki/Cruck" title="Cruck">cruck</a> frame<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> or a couple of rafters.<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><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> </p> <div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=2" title="Edit section: Characteristics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wells_egyptian_ship_red_sea.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wells_egyptian_ship_red_sea.png/220px-Wells_egyptian_ship_red_sea.png" decoding="async" width="220" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wells_egyptian_ship_red_sea.png/330px-Wells_egyptian_ship_red_sea.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wells_egyptian_ship_red_sea.png/440px-Wells_egyptian_ship_red_sea.png 2x" data-file-width="1630" data-file-height="848" /></a><figcaption>An Egyptian ship with a rope truss, the oldest known use of trusses. Trusses did not come into common use until the Roman era.</figcaption></figure> <p>A truss consists of typically (but not necessarily) straight members connected at joints, traditionally termed <i>panel points</i>. Trusses are typically (but not necessarily<sup id="cite_ref-BeerJohnston_11-0" class="reference"><a href="#cite_note-BeerJohnston-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>) composed of triangles because of the structural stability of that shape and design. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed.<sup id="cite_ref-ricker_12-0" class="reference"><a href="#cite_note-ricker-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape. </p> <div class="mw-heading mw-heading3"><h3 id="Simple_truss">Simple truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=3" title="Edit section: Simple truss"><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:Trusses_008.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Trusses_008.jpg/220px-Trusses_008.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Trusses_008.jpg/330px-Trusses_008.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Trusses_008.jpg/440px-Trusses_008.jpg 2x" data-file-width="2272" data-file-height="1704" /></a><figcaption>Planar roof trusses</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Santa_croce,_navata,_capriate.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Santa_croce%2C_navata%2C_capriate.JPG/170px-Santa_croce%2C_navata%2C_capriate.JPG" decoding="async" width="170" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Santa_croce%2C_navata%2C_capriate.JPG/255px-Santa_croce%2C_navata%2C_capriate.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Santa_croce%2C_navata%2C_capriate.JPG/340px-Santa_croce%2C_navata%2C_capriate.JPG 2x" data-file-width="1536" data-file-height="2048" /></a><figcaption>The roof trusses of the <a href="/wiki/Basilica_di_Santa_Croce" class="mw-redirect" title="Basilica di Santa Croce">Basilica di Santa Croce</a> in Florence</figcaption></figure> <p>The simplest form of a truss is one single triangle. This type of truss is seen in a <a href="/wiki/Framing_(construction)" title="Framing (construction)">framed</a> roof consisting of <a href="/wiki/Rafter" title="Rafter">rafters</a> and a ceiling <a href="/wiki/Joist" title="Joist">joist</a>,<sup id="cite_ref-maginnis_13-0" class="reference"><a href="#cite_note-maginnis-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and in other mechanical structures such as <a href="/wiki/Bicycle_frame" title="Bicycle frame">bicycles</a> and aircraft. Because of the stability of this shape and the methods of analysis used to calculate the forces within it, a truss composed entirely of triangles is known as a simple truss.<sup id="cite_ref-hibbeler_14-0" class="reference"><a href="#cite_note-hibbeler-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> However, a simple truss is often defined more restrictively by demanding that it can be constructed through successive addition of pairs of members, each connected to two existing joints and to each other to form a new joint, and this definition does not require a simple truss to comprise only triangles.<sup id="cite_ref-BeerJohnston_11-1" class="reference"><a href="#cite_note-BeerJohnston-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The traditional diamond-shape bicycle frame, which utilizes two conjoined triangles, is an example of a simple truss.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Planar_truss">Planar truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=4" title="Edit section: Planar truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Roof_truss_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Roof_truss_2.jpg/220px-Roof_truss_2.jpg" decoding="async" width="220" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Roof_truss_2.jpg/330px-Roof_truss_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Roof_truss_2.jpg/440px-Roof_truss_2.jpg 2x" data-file-width="3913" data-file-height="1650" /></a><figcaption>Roof truss</figcaption></figure> <p>A planar truss lies in a single <a href="/wiki/Plane_(mathematics)" title="Plane (mathematics)">plane</a>.<sup id="cite_ref-hibbeler_14-1" class="reference"><a href="#cite_note-hibbeler-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Planar trusses are typically used in parallel to form roofs and bridges.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>The depth of a truss, or the height between the upper and lower chords, is what makes it an efficient structural form. A solid <a href="/wiki/Girder" title="Girder">girder</a> or <a href="/wiki/Beam_(structure)" title="Beam (structure)">beam</a> of equal strength would have substantial weight and material cost as compared to a truss. For a given <a href="/wiki/Span_(engineering)" title="Span (engineering)">span</a>, a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.<sup id="cite_ref-meriman_17-0" class="reference"><a href="#cite_note-meriman-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Space_frame_truss">Space frame truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=5" title="Edit section: Space frame truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Space_frame" title="Space frame">space frame</a> truss is a three-dimensional framework of members pinned at their ends. A <a href="/wiki/Tetrahedron" title="Tetrahedron">tetrahedron</a> shape is the simplest space truss, consisting of six members that meet at four joints.<sup id="cite_ref-hibbeler_14-2" class="reference"><a href="#cite_note-hibbeler-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Large planar structures may be composed from tetrahedrons with common edges, and they are also employed in the base structures of large free-standing power line pylons. </p> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 122px"> <div class="thumb" style="width: 120px;"><span typeof="mw:File"><a href="/wiki/File:Tetrahedron.png" class="mw-file-description" title="Simple tetrahedron"><img alt="Simple tetrahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/180px-Tetrahedron.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/270px-Tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/360px-Tetrahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span></div> <div class="gallerytext">Simple tetrahedron</div> </li> <li class="gallerybox" style="width: 228.66666666667px"> <div class="thumb" style="width: 226.66666666667px;"><span typeof="mw:File"><a href="/wiki/File:SpaceFrame02.png" class="mw-file-description" title="Diagram of a space frame such as used for a roof"><img alt="Diagram of a space frame such as used for a roof" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/SpaceFrame02.png/340px-SpaceFrame02.png" decoding="async" width="227" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/SpaceFrame02.png/510px-SpaceFrame02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/SpaceFrame02.png/679px-SpaceFrame02.png 2x" data-file-width="711" data-file-height="377" /></a></span></div> <div class="gallerytext">Diagram of a space frame such as used for a roof</div> </li> <li class="gallerybox" style="width: 91.333333333333px"> <div class="thumb" style="width: 89.333333333333px;"><span typeof="mw:File"><a href="/wiki/File:Pylon-gorai.jpg" class="mw-file-description" title="This electrical pylon is a three-dimensional truss structure"><img alt="This electrical pylon is a three-dimensional truss structure" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pylon-gorai.jpg/134px-Pylon-gorai.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pylon-gorai.jpg/201px-Pylon-gorai.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pylon-gorai.jpg/268px-Pylon-gorai.jpg 2x" data-file-width="400" data-file-height="538" /></a></span></div> <div class="gallerytext">This <a href="/wiki/Electricity_pylon" class="mw-redirect" title="Electricity pylon">electrical pylon</a> is a three-dimensional truss structure</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=6" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><i>For more truss types, see <a href="/wiki/Truss_bridge#Truss_types_used_in_bridges" title="Truss bridge">truss types used in bridges</a>.</i></dd></dl> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Large_Timber_Howe_Truss.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Large_Timber_Howe_Truss.jpg/170px-Large_Timber_Howe_Truss.jpg" decoding="async" width="170" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Large_Timber_Howe_Truss.jpg/255px-Large_Timber_Howe_Truss.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Large_Timber_Howe_Truss.jpg/340px-Large_Timber_Howe_Truss.jpg 2x" data-file-width="1099" data-file-height="1358" /></a><figcaption>A large timber <a href="/wiki/Howe_truss" title="Howe truss">Howe truss</a> in a commercial building</figcaption></figure> <p>There are two basic types of truss: </p> <ul><li>The pitched truss, or common truss, is characterized by its triangular shape. It is most often used for roof construction. Some common trusses are named according to their "web configuration". The chord size and web configuration are determined by span, load and spacing.</li> <li>The parallel chord truss, or flat truss, gets its name from its parallel top and bottom chords. It is often used for floor construction.</li></ul> <p>A combination of the two is a truncated truss, used in <a href="/wiki/Hip_(roofing)" class="mw-redirect" title="Hip (roofing)">hip</a> roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with <a href="/wiki/Truss_connector_plate" title="Truss connector plate">metal connector plates</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Warren_truss">Warren truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=7" title="Edit section: Warren truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Warren_truss" title="Warren truss">Warren truss</a></div> <p>Truss members form a series of equilateral triangles, alternating up and down. </p> <div class="mw-heading mw-heading3"><h3 id="Octet_truss">Octet truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=8" title="Edit section: Octet truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Truss members are made up of all equivalent equilateral triangles. The minimum composition is two regular tetrahedrons along with an octahedron. They fill up three dimensional space in a variety of configurations. </p> <div class="mw-heading mw-heading3"><h3 id="Pratt_truss">Pratt truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=9" title="Edit section: Pratt truss"><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:Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg/220px-Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg" decoding="async" width="220" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg/330px-Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg/440px-Tempe-Southern_Pacific_Railroad_Bridge-1912-2.jpg 2x" data-file-width="4204" data-file-height="3077" /></a><figcaption>Tempe Salt River Southern Pacific Railroad bridge</figcaption></figure> <p><span class="mw-valign-top" typeof="mw:File"><a href="/wiki/File:Pratt_truss.png" class="mw-file-description" title="Pratt truss"><img alt="Pratt truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Pratt_truss.png/100px-Pratt_truss.png" decoding="async" width="100" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Pratt_truss.png/150px-Pratt_truss.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Pratt_truss.png/200px-Pratt_truss.png 2x" data-file-width="320" data-file-height="100" /></a></span> The Pratt truss was patented in 1844 by two <a href="/wiki/Boston" title="Boston">Boston</a> railway engineers,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Caleb Pratt and his son <a href="/wiki/Thomas_Willis_Pratt" title="Thomas Willis Pratt">Thomas Willis Pratt</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The design uses vertical members for <a href="/wiki/Compression_(physics)" title="Compression (physics)">compression</a> and diagonal members to respond to <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a>. The Pratt truss design remained popular as bridge designers switched from wood to iron, and from iron to steel.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> This continued popularity of the Pratt truss is probably due to the fact that the configuration of the members means that longer diagonal members are only in tension for gravity load effects. This allows these members to be used more efficiently, as slenderness effects related to <a href="/wiki/Buckling" title="Buckling">buckling</a> under compression loads (which are compounded by the length of the member) will typically not control the design. Therefore, for given planar truss with a fixed depth, the Pratt configuration is usually the most efficient under static, vertical loading. </p><p>The <a href="/wiki/Southern_Pacific_Railroad" title="Southern Pacific Railroad">Southern Pacific Railroad</a> bridge in <a href="/wiki/Tempe,_Arizona" title="Tempe, Arizona">Tempe</a>, <a href="/wiki/Arizona" title="Arizona">Arizona</a> is a 393 meter (1,291 foot) long truss bridge built in 1912.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The structure, still in use today, consists of nine Pratt truss spans of varying lengths. </p><p>The <a href="/wiki/Wright_Flyer" title="Wright Flyer">Wright Flyer</a> used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower <a href="/wiki/Aerodynamic_drag" class="mw-redirect" title="Aerodynamic drag">aerodynamic drag</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Town's_lattice_truss"><span id="Town.27s_lattice_truss"></span>Town's lattice truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=10" title="Edit section: Town's lattice truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Lattice_truss_bridge" title="Lattice truss bridge">Lattice truss bridge</a></div> <figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:Lattice_truss.png" class="mw-file-description" title="Lattice Truss"><img alt="Lattice Truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Lattice_truss.png/100px-Lattice_truss.png" decoding="async" width="100" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Lattice_truss.png/150px-Lattice_truss.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Lattice_truss.png/200px-Lattice_truss.png 2x" data-file-width="320" data-file-height="100" /></a><figcaption>Lattice Truss</figcaption></figure> <p>American architect <a href="/wiki/Ithiel_Town" title="Ithiel Town">Ithiel Town</a> designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, <a href="/wiki/Patented" class="mw-redirect" title="Patented">patented</a> in 1820 and 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them, to form a <a href="/wiki/Latticework" title="Latticework">lattice</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Bowstring_truss">Bowstring truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=11" title="Edit section: Bowstring truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bowstring_Truss_Bridge.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bowstring_Truss_Bridge.JPG/220px-Bowstring_Truss_Bridge.JPG" decoding="async" width="220" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bowstring_Truss_Bridge.JPG/330px-Bowstring_Truss_Bridge.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bowstring_Truss_Bridge.JPG/440px-Bowstring_Truss_Bridge.JPG 2x" data-file-width="2963" data-file-height="1497" /></a><figcaption>A bowstring truss is used on the oldest metal bridge in Virginia</figcaption></figure> <p>Named for their shape, bowstring trusses were first used for arched <a href="/wiki/Truss_bridge" title="Truss bridge">truss bridges</a>, often confused with <a href="/wiki/Tied-arch_bridge" title="Tied-arch bridge">tied-arch bridges</a>. </p><p>Thousands of bowstring trusses were used during <a href="/wiki/World_War_II" title="World War II">World War II</a> for holding up the curved roofs of aircraft hangars and other military buildings. Many variations exist in the arrangements of the members connecting the nodes of the upper arc with those of the lower, straight sequence of members, from nearly isosceles triangles to a variant of the Pratt truss. </p> <div class="mw-heading mw-heading3"><h3 id="King_and_queen_post_trusses">King and queen post trusses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=12" title="Edit section: King and queen post trusses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/King_post" title="King post">King post</a></div> <figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:King_post_truss.png" class="mw-file-description" title="King Post Truss"><img alt="King Post Truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/King_post_truss.png/100px-King_post_truss.png" decoding="async" width="100" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/King_post_truss.png/150px-King_post_truss.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/King_post_truss.png/200px-King_post_truss.png 2x" data-file-width="320" data-file-height="100" /></a><figcaption>King Post Truss</figcaption></figure> <p>One of the simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support. </p> <figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:Queen_post_truss.png" class="mw-file-description" title="Queen Post Truss"><img alt="Queen Post Truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Queen_post_truss.png/100px-Queen_post_truss.png" decoding="async" width="100" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Queen_post_truss.png/150px-Queen_post_truss.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Queen_post_truss.png/200px-Queen_post_truss.png 2x" data-file-width="320" data-file-height="100" /></a><figcaption>Queen Post Truss</figcaption></figure> <p>The queen post truss, sometimes <i>queenpost</i> or <i>queenspost</i>, is similar to a king post truss in that the outer supports are angled towards the centre of the structure. The primary difference is the horizontal extension at the centre which relies on <a href="/wiki/Beam_(structure)" title="Beam (structure)">beam</a> action to provide mechanical stability. This truss style is only suitable for relatively short spans.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <p><span class="anchor" id="Railroad"></span> </p> <table class="wikitable floatright" border="1" style="width:60%; float:right; margin-left:1em; margin-right:3em; margin-bottom:2em"> <tbody><tr> <th colspan="1"><span style="font-size:120%">Queen post trusses on rail vehicles</span><br /> </th></tr> <tr> <td colspan="1">An application of the queen post truss, once common on freight and passenger railroad vehicles – especially ones with wooden bodies – is an inversion of the design applied to bridges. Originally deployed on cars with wood frames (and on some very early steel frame cars with shallow sills) to provide strength to resist vertical deflection, the truss made the car stronger and/or lighter than the alternatives available at the time. The design was superseded when stronger, cheaper steels became available and steel centre sills were incorporated.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_(NRM_RA14847).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg/600px-South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg" decoding="async" width="600" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg/900px-South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg/1200px-South_Australian_Railways_clerestory-roofed_suburban_end-and-centre-loading_car_no_440_%28NRM_RA14847%29.jpg 2x" data-file-width="2941" data-file-height="1165" /></a><figcaption>A <a href="/wiki/South_Australian_Railways" title="South Australian Railways">South Australian Railways</a> passenger car built in 1918 with queen post trusses. The queen posts are the two vertical components; the short horizontal tube at the mid-point of the truss rod is the turnbuckle, which is adjusted by rotating to achieve the desired support of the car's frame.</figcaption></figure> </td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Lenticular_truss">Lenticular truss</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=13" title="Edit section: Lenticular truss"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg/220px-Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg" decoding="async" width="220" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg/330px-Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg/440px-Waterville_Bridge_in_Swatara_State_Park_HAER_462-14.jpg 2x" data-file-width="4335" data-file-height="3395" /></a><figcaption>The <a href="/wiki/Waterville_Bridge" title="Waterville Bridge">Waterville Bridge</a> in <a href="/wiki/Swatara_State_Park" title="Swatara State Park">Swatara State Park</a> in Pennsylvania is a lenticular truss</figcaption></figure> <p>Lenticular trusses, patented in 1878 by William Douglas (although the <a href="/wiki/Gaunless_Bridge" title="Gaunless Bridge">Gaunless Bridge</a> of 1823 was the first of the type), have the top and bottom chords of the truss arched, forming a lens shape. A <a href="/wiki/Lenticular_pony_truss_bridge" class="mw-redirect" title="Lenticular pony truss bridge">lenticular pony truss bridge</a> is a bridge design that involves a lenticular truss extending above and below the roadbed. </p> <div class="mw-heading mw-heading3"><h3 id="Vierendeel_structure">Vierendeel structure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=14" title="Edit section: Vierendeel structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Vierendeel_Truss"></span> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Arthur_Vierendeel" title="Arthur Vierendeel">Arthur Vierendeel</a> and <a href="/wiki/Vierendeel_bridge" title="Vierendeel bridge">Vierendeel bridge</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Grammene-vierendeelbridge_20030618.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Grammene-vierendeelbridge_20030618.jpg/220px-Grammene-vierendeelbridge_20030618.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Grammene-vierendeelbridge_20030618.jpg/330px-Grammene-vierendeelbridge_20030618.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Grammene-vierendeelbridge_20030618.jpg/440px-Grammene-vierendeelbridge_20030618.jpg 2x" data-file-width="1024" data-file-height="768" /></a><figcaption>A <a href="/wiki/Vierendeel_bridge" title="Vierendeel bridge">Vierendeel bridge</a>, which lacks diagonal elements in the primary structure</figcaption></figure> <p>The members of a Vierendeel structure are not triangulated but form rectangular openings. The structure has a <a href="/wiki/Rigid_frame" title="Rigid frame">frame</a> with fixed joints that are capable of transferring and resisting <a href="/wiki/Bending_moment" title="Bending moment">bending moments</a>. As such, it does not fit the definition of a truss, since it contains non-two-force members: regular trusses comprise members that are commonly assumed to have pinned joints, with the implication that no moments exist at the jointed ends. This style of structure was named after the Belgian engineer <a href="/wiki/Arthur_Vierendeel" title="Arthur Vierendeel">Arthur Vierendeel</a>,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> who developed the design in 1896. It is rarely used for bridges because of higher costs compared to a triangulated truss, but in buildings it has the advantage that a large amount of the exterior envelope remains unobstructed and it can therefore be used for <a href="/wiki/Window" title="Window">windows</a> and door openings. In some applications this is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces. </p> <div class="mw-heading mw-heading2"><h2 id="Statics">Statics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=15" title="Edit section: Statics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Onufriyenko-Sofora-EVA.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Onufriyenko-Sofora-EVA.jpg/220px-Onufriyenko-Sofora-EVA.jpg" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Onufriyenko-Sofora-EVA.jpg/330px-Onufriyenko-Sofora-EVA.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Onufriyenko-Sofora-EVA.jpg/440px-Onufriyenko-Sofora-EVA.jpg 2x" data-file-width="4000" data-file-height="2626" /></a><figcaption><a href="/wiki/Aleksandr_Serebrov" title="Aleksandr Serebrov">Cosmonaut Alexander Serebrov</a> sets up an integrated truss structure "<a href="/wiki/Mir#Unpressurised_elements" title="Mir">Rapana</a>" at <a href="/wiki/Mir" title="Mir">Mir space station</a>, September 16, 1993</figcaption></figure> <p>A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints and rollers, is described as being <a href="/wiki/Statically_indeterminate#Statically_determinate" title="Statically indeterminate">statically determinate</a>. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all (horizontal and vertical) forces, as well as all moments acting about the node equal zero. Analysis of these conditions at each node yields the magnitude of the compression or tension forces. </p><p>Trusses that are supported at more than two positions are said to be <a href="/wiki/Statically_indeterminate" title="Statically indeterminate">statically indeterminate</a>, and the application of Newton's Laws alone is not sufficient to determine the member forces. </p><p>In order for a truss with pin-connected members to be stable, it does not need to be entirely composed of triangles.<sup id="cite_ref-BeerJohnston_11-2" class="reference"><a href="#cite_note-BeerJohnston-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In mathematical terms, the following necessary condition for <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">stability</a> of a simple truss exists: </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 m\geq 2j-r\qquad \qquad \mathrm {(a)} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>≥</mo> <mn>2</mn> <mi>j</mi> <mo>−</mo> <mi>r</mi> <mspace width="2em" /> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi mathvariant="normal">a</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\geq 2j-r\qquad \qquad \mathrm {(a)} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a564aad2f13bdc54e4257bfc701f843dcce77b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.411ex; height:2.843ex;" alt="{\displaystyle m\geq 2j-r\qquad \qquad \mathrm {(a)} }"></span></dd></dl> <p>where <i>m</i> is the total number of truss members, <i>j</i> is the total number of joints and <i>r</i> is the number of reactions (equal to 3 generally) in a 2-dimensional structure. </p><p>When <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 m=2j-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mi>j</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=2j-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f87a59c3b7853d8a466ba7bae6b5b5044af6992" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.262ex; height:2.509ex;" alt="{\displaystyle m=2j-3}"></span>, the truss is said to be <i>statically determinate</i>, because the (<i>m</i>+3) internal member forces and support reactions can then be completely determined by 2<i>j</i> <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">equilibrium</a> equations, once we know the external <a href="/wiki/Structural_load" title="Structural load">loads</a> and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members. </p><p>Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. Their member forces depend on the relative <a href="/wiki/Stiffness" title="Stiffness">stiffness</a> of the members, in addition to the equilibrium condition described. </p> <div class="mw-heading mw-heading2"><h2 id="Analysis">Analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=16" title="Edit section: Analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cremonadiagram.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cremonadiagram.jpg/170px-Cremonadiagram.jpg" decoding="async" width="170" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cremonadiagram.jpg/255px-Cremonadiagram.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cremonadiagram.jpg/340px-Cremonadiagram.jpg 2x" data-file-width="500" data-file-height="775" /></a><figcaption><a href="/wiki/Cremona_diagram" title="Cremona diagram">Cremona diagram</a> for a plane truss</figcaption></figure> <p>Because the forces in each of its two main girders are essentially planar, a truss is usually modeled as a two-dimensional plane frame. However if there are significant out-of-plane forces, the structure must be modeled as a three-dimensional space. </p><p>The analysis of trusses often assumes that loads are applied to joints only and not at intermediate points along the members. The weight of the members is often insignificant compared to the applied loads and so is often omitted; alternatively, half of the weight of each member may be applied to its two end joints. Provided that the members are long and slender, the <a href="/wiki/Moment_(physics)" title="Moment (physics)">moments</a> transmitted through the joints are negligible, and the junctions can be treated as "<a href="/wiki/Hinge" title="Hinge">hinges</a>" or "pin-joints". </p><p>Under these simplifying assumptions, every member of the truss is then subjected to pure <a href="/wiki/Compression_(physics)" title="Compression (physics)">compression</a> or pure <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a> forces – shear, bending moment, and other more-complex <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stresses</a> are all practically zero. Trusses are physically stronger than other ways of arranging structural elements, because nearly every material can resist a much larger load in tension or compression than in shear, bending, torsion, or other kinds of force. </p><p>These simplifications make trusses easier to analyze. <a href="/wiki/Structural_analysis" title="Structural analysis">Structural analysis</a> of trusses of any type can readily be carried out using a matrix method such as the <a href="/wiki/Direct_stiffness_method" title="Direct stiffness method">direct stiffness method</a>, the <a href="/wiki/Flexibility_method" title="Flexibility method">flexibility method</a>, or the <a href="/wiki/Finite_element" class="mw-redirect" title="Finite element">finite element</a> method. </p> <div class="mw-heading mw-heading3"><h3 id="Forces_in_members">Forces in members</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=17" title="Edit section: Forces in members"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Illustrated is a simple, <a href="/wiki/Statically_determinate" class="mw-redirect" title="Statically determinate">statically determinate</a> flat truss with 9 joints and (2 x 9) − 3 = 15 members. External loads are concentrated in the outer joints. Since this is a <a href="/wiki/Symmetry" title="Symmetry">symmetrical</a> truss with symmetrical vertical loads, the reactive forces at A and B are vertical, equal, and half the total load. </p><p>The internal <a href="/wiki/Force" title="Force">forces</a> in the members of the truss can be calculated in a variety of ways, including graphical methods: </p> <ul><li><a href="/wiki/Cremona_diagram" title="Cremona diagram">Cremona diagram</a></li> <li><a href="/wiki/Carl_Culmann" title="Carl Culmann">Culmann diagram</a></li> <li>Ritter analytical method (<a href="/wiki/Structural_analysis#Method_of_sections" title="Structural analysis">method of sections</a>)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Design_of_members">Design of members</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=18" title="Edit section: Design of members"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A truss can be thought of as a <a href="/wiki/Beam_(structure)" title="Beam (structure)">beam</a> where the web consists of a series of separate members instead of a continuous plate. In the truss, the lower horizontal member (the <i>bottom chord</i>) and the upper horizontal member (the <i>top chord</i>) carry <a href="/wiki/Tension_(mechanics)" class="mw-redirect" title="Tension (mechanics)">tension</a> and <a href="/wiki/Compression_(physics)" title="Compression (physics)">compression</a>, fulfilling the same function as the <a href="/wiki/Flange" title="Flange">flanges</a> of an <a href="/wiki/I-beam" title="I-beam">I-beam</a>. Which chord carries tension and which carries compression depends on the overall direction of <a href="/wiki/Bending" title="Bending">bending</a>. In the truss pictured above right, the bottom chord is in tension, and the top chord in compression. </p><p>The diagonal and vertical members form the <i>truss web</i>, and carry the <a href="/wiki/Shear_stress" title="Shear stress">shear stress</a>. Individually, they are also in tension and compression, the exact arrangement of forces is depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Shanghai_Shimao_Plaza_Construction.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Shanghai_Shimao_Plaza_Construction.jpg/170px-Shanghai_Shimao_Plaza_Construction.jpg" decoding="async" width="170" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Shanghai_Shimao_Plaza_Construction.jpg/255px-Shanghai_Shimao_Plaza_Construction.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Shanghai_Shimao_Plaza_Construction.jpg/340px-Shanghai_Shimao_Plaza_Construction.jpg 2x" data-file-width="1200" data-file-height="1600" /></a><figcaption>Truss sections stabilize this building under construction in <a href="/wiki/Shanghai" title="Shanghai">Shanghai</a> and will house <a href="/wiki/Mechanical_floor" title="Mechanical floor">mechanical floors</a></figcaption></figure> <p>In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing <a href="/wiki/Buckling" title="Buckling">buckling</a>. In the adjacent picture, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members. </p><p>The inclusion of the elements shown is largely an engineering decision based upon economics, being a balance between the costs of raw materials, off-site fabrication, component transportation, on-site erection, the availability of machinery and the cost of labor. In other cases the appearance of the structure may take on greater importance and so influence the design decisions beyond mere matters of economics. Modern materials such as <a href="/wiki/Prestressed_concrete" title="Prestressed concrete">prestressed concrete</a> and fabrication methods, such as automated <a href="/wiki/Welding" title="Welding">welding</a>, have significantly influenced the design of modern <a href="/wiki/Bridge" title="Bridge">bridges</a>. </p><p>Once the force on each member is known, the next step is to determine the <a href="/wiki/Cross_section_(geometry)" title="Cross section (geometry)">cross section</a> of the individual truss members. For members under tension the cross-sectional area <i>A</i> can be found using <i>A</i> = <i>F</i> × γ / σ<sub><i>y</i></sub>, where <i>F</i> is the force in the member, γ is a <a href="/wiki/Safety_factor" class="mw-redirect" title="Safety factor">safety factor</a> (typically 1.5 but depending on <a href="/wiki/Building_code" title="Building code">building codes</a>) and σ<sub>y</sub> is the yield <a href="/wiki/Tensile_strength" class="mw-redirect" title="Tensile strength">tensile strength</a> of the steel used. </p><p>The members under compression also have to be designed to be safe against buckling. </p><p>The weight of a truss member depends directly on its cross section—that weight partially determines how strong the other members of the truss need to be. Giving one member a larger cross section than on a previous iteration requires giving other members a larger cross section as well, to hold the greater weight of the first member—one needs to go through another iteration to find exactly how much greater the other members need to be. Sometimes the designer goes through several iterations of the design process to converge on the "right" cross section for each member. On the other hand, reducing the size of one member from the previous iteration merely makes the other members have a larger (and more expensive) safety factor than is technically necessary, but doesn't <i>require</i> another iteration to find a buildable truss. </p><p>The effect of the weight of the individual truss members in a large truss, such as a bridge, is usually insignificant compared to the force of the external loads. </p> <div class="mw-heading mw-heading3"><h3 id="Design_of_joints">Design of joints</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=19" title="Edit section: Design of joints"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the <a href="/wiki/Bolted_joint" title="Bolted joint">bolted joints</a>, e.g., involving shear stress of the bolt connections used in the joints. Based on the needs of the project, truss internal connections (joints) can be designed as rigid, semi rigid, or hinged. Rigid connections can allow transfer of bending moments leading to development of secondary bending moments in the members. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=20" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:A_type_of_truss_used_in_roofing.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/A_type_of_truss_used_in_roofing.jpg/220px-A_type_of_truss_used_in_roofing.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/A_type_of_truss_used_in_roofing.jpg/330px-A_type_of_truss_used_in_roofing.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/A_type_of_truss_used_in_roofing.jpg/440px-A_type_of_truss_used_in_roofing.jpg 2x" data-file-width="4032" data-file-height="3024" /></a><figcaption>A type of truss used in roofing</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Post_frame_structures">Post frame structures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=21" title="Edit section: Post frame structures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Truss_uplift" title="Truss uplift">Truss uplift</a></div> <p>Component connections are critical to the structural integrity of a framing system. In buildings with large, clearspan wood trusses, the most critical connections are those between the truss and its supports. In addition to gravity-induced forces (a.k.a. bearing loads), these connections must resist shear forces acting perpendicular to the plane of the truss and uplift forces due to wind. Depending upon overall building design, the connections may also be required to transfer bending moment. </p><p>Wood posts enable the fabrication of strong, direct, yet inexpensive connections between large trusses and walls. Exact details for post-to-truss connections vary from designer to designer, and may be influenced by post type. Solid-sawn timber and <a href="/wiki/Glulam" class="mw-redirect" title="Glulam">glulam</a> posts are generally notched to form a truss bearing surface. The truss is rested on the notches and bolted into place. A special plate/bracket may be added to increase connection load transfer capabilities. With mechanically-laminated posts, the truss may rest on a shortened outer-ply or on a shortened inner-ply. The later scenario places the bolts in double shear and is a very effective connection. </p> <div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truss&action=edit&section=22" title="Edit section: Gallery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 77.333333333333px"> <div class="thumb" style="width: 75.333333333333px;"><span typeof="mw:File"><a href="/wiki/File:Bank_of_china_night.jpg" class="mw-file-description" title="The Hong Kong Bank of China Tower has an externally visible truss structure"><img alt="The Hong Kong Bank of China Tower has an externally visible truss structure" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Bank_of_china_night.jpg/113px-Bank_of_china_night.jpg" decoding="async" width="76" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Bank_of_china_night.jpg/170px-Bank_of_china_night.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Bank_of_china_night.jpg/227px-Bank_of_china_night.jpg 2x" data-file-width="1001" data-file-height="1588" /></a></span></div> <div class="gallerytext">The <a href="/wiki/Bank_of_China_Tower,_Hong_Kong" class="mw-redirect" title="Bank of China Tower, Hong Kong">Hong Kong Bank of China Tower</a> has an externally visible truss structure</div> </li> <li class="gallerybox" style="width: 99.333333333333px"> <div class="thumb" style="width: 97.333333333333px;"><span typeof="mw:File"><a href="/wiki/File:HK_HSBC_Main_Building_2008.jpg" class="mw-file-description" title="The HSBC Main Building, Hong Kong has an externally visible truss structure"><img alt="The HSBC Main Building, Hong Kong has an externally visible truss structure" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/HK_HSBC_Main_Building_2008.jpg/146px-HK_HSBC_Main_Building_2008.jpg" decoding="async" width="98" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/HK_HSBC_Main_Building_2008.jpg/219px-HK_HSBC_Main_Building_2008.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/HK_HSBC_Main_Building_2008.jpg/292px-HK_HSBC_Main_Building_2008.jpg 2x" data-file-width="1177" data-file-height="1452" /></a></span></div> <div class="gallerytext">The <a href="/wiki/HSBC_Main_Building,_Hong_Kong" class="mw-redirect" title="HSBC Main Building, Hong Kong">HSBC Main Building, Hong Kong</a> has an externally visible truss structure</div> </li> <li class="gallerybox" style="width: 162px"> <div class="thumb" style="width: 160px;"><span typeof="mw:File"><a href="/wiki/File:Below_Auckland_Harbour_Bridge_Hossen27.jpg" class="mw-file-description" title="Support structure under the Auckland Harbour Bridge"><img alt="Support structure under the Auckland Harbour Bridge" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Below_Auckland_Harbour_Bridge_Hossen27.jpg/240px-Below_Auckland_Harbour_Bridge_Hossen27.jpg" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Below_Auckland_Harbour_Bridge_Hossen27.jpg/360px-Below_Auckland_Harbour_Bridge_Hossen27.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Below_Auckland_Harbour_Bridge_Hossen27.jpg/480px-Below_Auckland_Harbour_Bridge_Hossen27.jpg 2x" data-file-width="2592" data-file-height="1944" /></a></span></div> <div class="gallerytext">Support structure under the <a href="/wiki/Auckland_Harbour_Bridge" title="Auckland Harbour Bridge">Auckland Harbour Bridge</a></div> </li> <li class="gallerybox" style="width: 162px"> <div class="thumb" style="width: 160px;"><span typeof="mw:File"><a href="/wiki/File:Auckland_Harbour_Bridge_Watchman.jpg" class="mw-file-description" title="The Auckland Harbour Bridge seen from Watchman Island to its west"><img alt="The Auckland Harbour Bridge seen from Watchman Island to its west" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Auckland_Harbour_Bridge_Watchman.jpg/240px-Auckland_Harbour_Bridge_Watchman.jpg" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Auckland_Harbour_Bridge_Watchman.jpg/360px-Auckland_Harbour_Bridge_Watchman.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Auckland_Harbour_Bridge_Watchman.jpg/480px-Auckland_Harbour_Bridge_Watchman.jpg 2x" data-file-width="1600" data-file-height="1200" /></a></span></div> <div class="gallerytext">The <a href="/wiki/Auckland_Harbour_Bridge" title="Auckland Harbour Bridge">Auckland Harbour Bridge</a> seen from <a href="/wiki/Watchman_Island" title="Watchman Island">Watchman Island</a> to its west</div> </li> <li class="gallerybox" style="width: 182px"> <div class="thumb" style="width: 180px;"><span typeof="mw:File"><a href="/wiki/File:The_Little_Belt_Bridge_(1935).jpeg" class="mw-file-description" title="Little Belt Bridge: a truss bridge in Denmark"><img alt="Little Belt Bridge: a truss bridge in Denmark" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/The_Little_Belt_Bridge_%281935%29.jpeg/270px-The_Little_Belt_Bridge_%281935%29.jpeg" decoding="async" width="180" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/The_Little_Belt_Bridge_%281935%29.jpeg/405px-The_Little_Belt_Bridge_%281935%29.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/The_Little_Belt_Bridge_%281935%29.jpeg/540px-The_Little_Belt_Bridge_%281935%29.jpeg 2x" data-file-width="1350" data-file-height="900" /></a></span></div> <div class="gallerytext"><i><a href="/wiki/Little_Belt_Bridge" title="Little Belt Bridge">Little Belt Bridge</a></i>: a truss <a href="/wiki/Bridge" title="Bridge">bridge</a> in Denmark</div> </li> <li class="gallerybox" style="width: 218.66666666667px"> <div class="thumb" style="width: 216.66666666667px;"><span typeof="mw:File"><a href="/wiki/File:Bow-string-truss.jpg" class="mw-file-description" title="Pre-fabricated steel bow string roof trusses built in 1942 for war department properties in Northern Australia"><img alt="Pre-fabricated steel bow string roof trusses built in 1942 for war department properties in Northern Australia" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Bow-string-truss.jpg/325px-Bow-string-truss.jpg" decoding="async" width="217" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Bow-string-truss.jpg/488px-Bow-string-truss.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Bow-string-truss.jpg/650px-Bow-string-truss.jpg 2x" data-file-width="1184" data-file-height="656" /></a></span></div> <div class="gallerytext"><a href="/wiki/Pre-fabricated" class="mw-redirect" title="Pre-fabricated">Pre-fabricated</a> steel bow string roof trusses built in 1942 for war department properties in Northern Australia</div> </li> <li class="gallerybox" style="width: 167.33333333333px"> <div class="thumb" style="width: 165.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Truss_Dachstuhl.jpg" class="mw-file-description" title="Roof truss in a side building of Cluny Abbey, France"><img alt="Roof truss in a side building of Cluny Abbey, France" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Truss_Dachstuhl.jpg/248px-Truss_Dachstuhl.jpg" decoding="async" width="166" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Truss_Dachstuhl.jpg/371px-Truss_Dachstuhl.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Truss_Dachstuhl.jpg/495px-Truss_Dachstuhl.jpg 2x" data-file-width="1391" data-file-height="1012" /></a></span></div> <div class="gallerytext">Roof truss in a side building of <a href="/wiki/Cluny_Abbey" title="Cluny Abbey">Cluny Abbey</a>, France</div> </li> <li class="gallerybox" style="width: 239.33333333333px"> <div class="thumb" style="width: 237.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Queen-post-truss.png" class="mw-file-description" title="A section through a queen post timber roof truss"><img alt="A section through a queen post timber roof truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Queen-post-truss.png/356px-Queen-post-truss.png" decoding="async" width="238" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/25/Queen-post-truss.png 1.5x" data-file-width="504" data-file-height="255" /></a></span></div> <div class="gallerytext">A section through a queen post <a href="/wiki/Timber_roof_truss" title="Timber roof truss">timber roof truss</a></div> </li> <li class="gallerybox" style="width: 162px"> <div class="thumb" style="width: 160px;"><span typeof="mw:File"><a href="/wiki/File:Woodlands_mall3_texas.jpg" class="mw-file-description" title="A space truss carrying a floor in The Woodlands Mall"><img alt="A space truss carrying a floor in The Woodlands Mall" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Woodlands_mall3_texas.jpg/240px-Woodlands_mall3_texas.jpg" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Woodlands_mall3_texas.jpg/360px-Woodlands_mall3_texas.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Woodlands_mall3_texas.jpg/480px-Woodlands_mall3_texas.jpg 2x" data-file-width="2592" data-file-height="1944" /></a></span></div> <div class="gallerytext">A space truss carrying a floor in <a href="/wiki/The_Woodlands_Mall" title="The Woodlands Mall">The Woodlands Mall</a></div> </li> <li class="gallerybox" style="width: 92px"> <div class="thumb" style="width: 90px;"><span typeof="mw:File"><a href="/wiki/File:Elledningsstolpe2_lund.jpg" class="mw-file-description" title="Electricity pylon"><img alt="Electricity pylon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Elledningsstolpe2_lund.jpg/135px-Elledningsstolpe2_lund.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Elledningsstolpe2_lund.jpg/202px-Elledningsstolpe2_lund.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Elledningsstolpe2_lund.jpg/270px-Elledningsstolpe2_lund.jpg 2x" data-file-width="1944" data-file-height="2592" /></a></span></div> <div class="gallerytext"><a href="/wiki/Electricity_pylon" class="mw-redirect" title="Electricity pylon">Electricity pylon</a></div> </li> <li class="gallerybox" style="width: 121.33333333333px"> <div class="thumb" style="width: 119.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Inside_wboylston_old_stone_church.jpg" class="mw-file-description" title="Timber roof truss"><img alt="Timber roof truss" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Inside_wboylston_old_stone_church.jpg/179px-Inside_wboylston_old_stone_church.jpg" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Inside_wboylston_old_stone_church.jpg/269px-Inside_wboylston_old_stone_church.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Inside_wboylston_old_stone_church.jpg/359px-Inside_wboylston_old_stone_church.jpg 2x" data-file-width="1980" data-file-height="1986" /></a></span></div> <div class="gallerytext"><a href="/wiki/Timber_roof_truss" title="Timber roof truss">Timber roof truss</a></div> </li> <li class="gallerybox" style="width: 162px"> <div class="thumb" style="width: 160px;"><span typeof="mw:File"><a href="/wiki/File:Temporary_bridge_made_of_Truss.jpg" class="mw-file-description" title="Modern temporary bridge made of Bailey bridge truss panels in Montreal Québec"><img alt="Modern temporary bridge made of Bailey bridge truss panels in Montreal Québec" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Temporary_bridge_made_of_Truss.jpg/240px-Temporary_bridge_made_of_Truss.jpg" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Temporary_bridge_made_of_Truss.jpg/360px-Temporary_bridge_made_of_Truss.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Temporary_bridge_made_of_Truss.jpg/480px-Temporary_bridge_made_of_Truss.jpg 2x" data-file-width="3264" data-file-height="2448" /></a></span></div> <div class="gallerytext">Modern temporary bridge made of <a href="/wiki/Bailey_bridge" title="Bailey bridge">Bailey bridge</a> truss panels in <a href="/wiki/Montreal" title="Montreal">Montreal</a> <a href="/wiki/Qu%C3%A9bec" class="mw-redirect" title="Québec">Québec</a></div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg" class="mw-file-description" title="Three dimensional truss construction"><img alt="Three dimensional truss construction" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg/320px-Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg" decoding="async" width="214" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg/480px-Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg/640px-Three_dimensional_truss_construction_Unic_Rotarex%C2%AE.jpg 2x" data-file-width="1241" data-file-height="698" /></a></span></div> <div class="gallerytext">Three dimensional truss construction</div> </li> <li class="gallerybox" style="width: 217.33333333333px"> <div class="thumb" style="width: 215.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg" class="mw-file-description" title="Example of calculation truss forces made by program that use matrix Gauss solving method"><img alt="Example of calculation truss forces made by program that use matrix Gauss solving method" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg/323px-Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg.png" decoding="async" width="216" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg/485px-Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg/646px-Kratownica_statycznie_wyznaczalna_-_obci%C4%85%C5%BCenia.svg.png 2x" data-file-width="1394" data-file-height="777" /></a></span></div> <div class="gallerytext">Example of calculation truss forces made by program that use matrix Gauss solving method</div> </li> </ul> <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=Truss&action=edit&section=23" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Brown_truss" title="Brown truss">Brown truss</a></li> <li><a href="/wiki/Convex_uniform_honeycomb" title="Convex uniform honeycomb">Convex uniform honeycomb</a></li> <li><a href="/wiki/Geodesic_dome" title="Geodesic dome">Geodesic dome</a></li> <li><a href="/wiki/Lattice_tower" title="Lattice tower">Lattice tower</a></li> <li><a href="/wiki/Serrurier_truss" title="Serrurier truss">Serrurier truss</a></li> <li>Stress: <ul><li><a href="/wiki/Compressive_stress" title="Compressive stress">Compressive stress</a></li> <li><a href="/wiki/Tensile_stress" class="mw-redirect" title="Tensile stress">Tensile stress</a></li></ul></li> <li><a href="/wiki/Structural_mechanics" title="Structural mechanics">Structural mechanics</a></li> <li><a href="/wiki/Structural_steel" title="Structural steel">Structural steel</a></li> <li><a href="/wiki/Tensegrity" title="Tensegrity">Tensegrity</a></li> <li><a href="/wiki/Truss_rod" title="Truss rod">Truss rod</a></li></ul> <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=Truss&action=edit&section=24" 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 .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.merriam-webster.com/dictionary/truss">"Definition of TRUSS"</a>. 7 March 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Definition+of+TRUSS&rft.date=2024-03-07&rft_id=https%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2Ftruss&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-PleshaGrayCostanzo-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-PleshaGrayCostanzo_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPleshaGrayCostanzo2013" class="citation book cs1">Plesha, Michael E.; Gray, Gary L.; Costanzo, Francesco (2013). <i>Engineering Mechanics: Statics</i> (2nd ed.). New York: McGraw-Hill Companies Inc. pp. <span class="nowrap">364–</span>407. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-338029-2" title="Special:BookSources/978-0-07-338029-2"><bdi>978-0-07-338029-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+Mechanics%3A+Statics&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E364-%3C%2Fspan%3E407&rft.edition=2nd&rft.pub=McGraw-Hill+Companies+Inc.&rft.date=2013&rft.isbn=978-0-07-338029-2&rft.aulast=Plesha&rft.aufirst=Michael+E.&rft.au=Gray%2C+Gary+L.&rft.au=Costanzo%2C+Francesco&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Ching, Frank. <i>A Visual Dictionary of Architecture</i>. 2nd ed. Hoboken, N.J.: Wiley, 2012. 277. Print. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780470648858" title="Special:BookSources/9780470648858">9780470648858</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Bow R. H., Economics of construction in relation to framed structures. Spon, London, 1873</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Reif, F., <a rel="nofollow" class="external text" href="http://www.etymonline.com/index.php?term=truss">etymonline.com</a> (1965).</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Oxford English Dictionary</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Noble, Allen George. Traditional buildings a global survey of structural forms and cultural functions. London: I.B. Tauris; 2007. 115. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1845113055" title="Special:BookSources/1845113055">1845113055</a></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Davies, Nikolas, and Erkki Jokiniemi. Dictionary of architecture and building construction. Amsterdam: Elsevier/Architectural Press, 2008. 394. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0750685026" title="Special:BookSources/0750685026">0750685026</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Davies, Nikolas, and Erkki Jokiniemi. Architect's illustrated pocket dictionary. Oxford: Architectural Press, 2011. 121. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0080965377" title="Special:BookSources/0080965377">0080965377</a></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Crabb, George. Universal Technological Dictionary Or Familiar Explanation of the Terms used in All Arts and Sciences...", Volume 1 London: 1823. Couples.</span> </li> <li id="cite_note-BeerJohnston-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-BeerJohnston_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-BeerJohnston_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-BeerJohnston_11-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="BeerJohnston" class="citation book cs1">Beer, Ferd; Johnston, Russ (2013). <i>Vector Mechanics for Engineers: Statics</i> (10th ed.). New York, NY: McGraw-Hill. pp. <span class="nowrap">285–</span>313. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-740228-0" title="Special:BookSources/978-0-07-740228-0"><bdi>978-0-07-740228-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vector+Mechanics+for+Engineers%3A+Statics&rft.place=New+York%2C+NY&rft.pages=%3Cspan+class%3D%22nowrap%22%3E285-%3C%2Fspan%3E313&rft.edition=10th&rft.pub=McGraw-Hill&rft.date=2013&rft.isbn=978-0-07-740228-0&rft.aulast=Beer&rft.aufirst=Ferd&rft.au=Johnston%2C+Russ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-ricker-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-ricker_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRicker1912" class="citation book cs1">Ricker, Nathan Clifford (1912) [1912]. <a rel="nofollow" class="external text" href="https://archive.org/details/atreatiseondesi00rickgoog"><i>A Treat on Design and Construction of Roofs</i></a>. New York: J. Wiley & Sons. p. <a rel="nofollow" class="external text" href="https://archive.org/details/atreatiseondesi00rickgoog/page/n34">12</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-08-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treat+on+Design+and+Construction+of+Roofs&rft.place=New+York&rft.pages=12&rft.pub=J.+Wiley+%26+Sons&rft.date=1912&rft.aulast=Ricker&rft.aufirst=Nathan+Clifford&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fatreatiseondesi00rickgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-maginnis-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-maginnis_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaginnis1903" class="citation book cs1">Maginnis, Owen Bernard (1903). <a rel="nofollow" class="external text" href="https://archive.org/details/roframingmadeea01magigoog"><i>Roof Framing Made Easy</i></a> (2nd ed.). New York: The Industrial Publication Company. p. <a rel="nofollow" class="external text" href="https://archive.org/details/roframingmadeea01magigoog/page/n13">9</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-08-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Roof+Framing+Made+Easy&rft.place=New+York&rft.pages=9&rft.edition=2nd&rft.pub=The+Industrial+Publication+Company&rft.date=1903&rft.aulast=Maginnis&rft.aufirst=Owen+Bernard&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Froframingmadeea01magigoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-hibbeler-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-hibbeler_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hibbeler_14-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-hibbeler_14-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHibbeler1983" class="citation book cs1">Hibbeler, Russell Charles (1983) [1974]. <i>Engineering Mechanics-Statics</i> (3rd ed.). New York: Macmillan Publishing Co., Inc. pp. <span class="nowrap">199–</span>224. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-02-354310-8" title="Special:BookSources/0-02-354310-8"><bdi>0-02-354310-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+Mechanics-Statics&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E199-%3C%2Fspan%3E224&rft.edition=3rd&rft.pub=Macmillan+Publishing+Co.%2C+Inc.&rft.date=1983&rft.isbn=0-02-354310-8&rft.aulast=Hibbeler&rft.aufirst=Russell+Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Wingerter, R., and Labossiere, P., <i>ME 354, Mechanics of Materials Laboratory: Structures</i>, University of Washington (February 2004), p.1</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLublinerPapadopoulos2016" class="citation book cs1">Lubliner, Jacob; Papadopoulos, Panayiotis (2016-10-23). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fhJADQAAQBAJ&q=Planar+trusses+are+typically+used+in+parallel+to+form+roofs+and+bridges&pg=PA128"><i>Introduction to Solid Mechanics: An Integrated Approach</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319188782" title="Special:BookSources/9783319188782"><bdi>9783319188782</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Solid+Mechanics%3A+An+Integrated+Approach&rft.pub=Springer&rft.date=2016-10-23&rft.isbn=9783319188782&rft.aulast=Lubliner&rft.aufirst=Jacob&rft.au=Papadopoulos%2C+Panayiotis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfhJADQAAQBAJ%26q%3DPlanar%2Btrusses%2Bare%2Btypically%2Bused%2Bin%2Bparallel%2Bto%2Bform%2Broofs%2Band%2Bbridges%26pg%3DPA128&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-meriman-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-meriman_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMerriman1912" class="citation book cs1">Merriman, Mansfield (1912) [192]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=AUVIAAAAIAAJ"><i>American Civil Engineers' Pocket Book</i></a>. New York: J. Wiley & Sons. p. 785<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-08-16</span></span>. <q>The Economic Depth of a Truss is that which makes the material in a bridge a minimum.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=American+Civil+Engineers%27+Pocket+Book&rft.place=New+York&rft.pages=785&rft.pub=J.+Wiley+%26+Sons&rft.date=1912&rft.aulast=Merriman&rft.aufirst=Mansfield&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DAUVIAAAAIAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://www.heritage.nsw.gov.au/07_subnav_01_2.cfm?itemid=5056556">Bethanga Bridge</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110609175557/http://www.heritage.nsw.gov.au/07_subnav_01_2.cfm?itemid=5056556">Archived</a> 2011-06-09 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> at the <a rel="nofollow" class="external text" href="http://www.heritage.nsw.gov.au">NSW Heritage Office</a>; retrieved 2008-Feb-06</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://www.tdot.state.tn.us/bridges/historybridges.htm">A Brief History of Covered Bridges in Tennessee</a></i> at the <a rel="nofollow" class="external text" href="http://www.tdot.state.tn.us">Tennessee Department of Transportation</a>; retrieved 2008-Feb-06</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://www.sha.state.md.us/keepingcurrent/maintainRoadsBridges/bridges/OPPE/historicBridges/V-Pratt.pdf">The Pratt Truss</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080528131942/http://www.sha.state.md.us/keepingcurrent/maintainRoadsBridges/bridges/OPPE/historicBridges/V-Pratt.pdf">Archived</a> 2008-05-28 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> courtesy of the <a rel="nofollow" class="external text" href="http://www.sha.state.md.us">Maryland Department of Transportation</a>; retrieved 2008-Feb-6</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.loc.gov/resource/hhh.az0240.photos">"1. Southern Pacific Railroad Bridge, Ash Avenue Bridge and Mill Avenue Bridge from Tempe Butte looking northwest. - Arizona Eastern Railroad Bridge, Spanning Salt River, Tempe, Maricopa County, AZ"</a>. <i>Library of Congress</i><span class="reference-accessdate">. Retrieved <span class="nowrap">26 March</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Library+of+Congress&rft.atitle=1.+Southern+Pacific+Railroad+Bridge%2C+Ash+Avenue+Bridge+and+Mill+Avenue+Bridge+from+Tempe+Butte+looking+northwest.+-+Arizona+Eastern+Railroad+Bridge%2C+Spanning+Salt+River%2C+Tempe%2C+Maricopa+County%2C+AZ&rft_id=https%3A%2F%2Fwww.loc.gov%2Fresource%2Fhhh.az0240.photos&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://www.tempe.gov/museum/Tempe_history/properties/hps228.htm">Tempe Historic Property Survey</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071110232206/http://www.tempe.gov/museum/Tempe_history/properties/hps228.htm">Archived</a> 2007-11-10 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> at the <a rel="nofollow" class="external text" href="http://www.tempe.gov/museum/">Tempe Historical Museum</a>; retrieved 2008-Feb-06</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Dario Gasparini, Case Western Reserve University. <a rel="nofollow" class="external text" href="http://www.woodcenter.org/docs/dayton-conference/Gasparini__WrightBrothersPrattTruss.pdf">The Wright Brothers and the Pratt Truss</a>, presentation slides</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080512012401/http://www.dot.state.oh.us/se/coveredbridges/truss_types.htm">"Truss types"</a>. <a href="/wiki/Ohio_Department_of_Transportation" title="Ohio Department of Transportation">Ohio Department of Transportation</a>. Archived from <a rel="nofollow" class="external text" href="http://www.dot.state.oh.us/se/coveredbridges/truss_types.htm">the original</a> on 2008-05-12<span class="reference-accessdate">. Retrieved <span class="nowrap">15 December</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Truss+types&rft.pub=Ohio+Department+of+Transportation&rft_id=http%3A%2F%2Fwww.dot.state.oh.us%2Fse%2Fcoveredbridges%2Ftruss_types.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTomikawa2005" class="citation web cs1">Tomikawa, T.T. (2005). <a rel="nofollow" class="external text" href="https://cs.trains.com/mrr/f/13/t/261922.aspx">"Truss rod"</a>. <i>Model Railroader</i>. <a href="/wiki/Kalmbach_Media" title="Kalmbach Media">Kalmbach Media</a><span class="reference-accessdate">. Retrieved <span class="nowrap">16 December</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Model+Railroader&rft.atitle=Truss+rod&rft.date=2005&rft.aulast=Tomikawa&rft.aufirst=T.T.&rft_id=https%3A%2F%2Fcs.trains.com%2Fmrr%2Ff%2F13%2Ft%2F261922.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruss" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://users.telenet.be/karel.roose/vierendeel/vierendeel.html">Vierendeel bruggen</a></span> </li> </ol></div></div> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid 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