{"id":137543,"date":"2015-10-28T03:00:00","date_gmt":"2015-10-28T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=5e0d408a300d581fe1a86c524de35c23"},"modified":"2015-10-28T03:00:00","modified_gmt":"2015-10-28T00:00:00","slug":"a-derivation-of-the-beam-equation","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=137543","title":{"rendered":"A derivation of the beam equation"},"content":{"rendered":"<p>The Euler\u2013Bernoulli equation describing the deflection of a beam is a vital tool in structural and<br \/>\nmechanical engineering. However, its derivation usually entails a number of intermediate steps that<br \/>\nmay confuse engineering or science students at the beginnig of their undergraduate studies. We<br \/>\nexplain how this equation may be deduced, beginning with an approximate expression for the energy,<br \/>\nfrom which the forces and finally the equation itself may be obtained. The description is begun at<br \/>\nthe level of small \u2018particles\u2019, and the continuum level is taken later on. However, when a<br \/>\ncomputational solution is sought, the description turns back to the discrete level again. We first<br \/>\nconsider the easier case of a string under tension, and then focus on the beam. Numerical solutions<br \/>\nfor several loads are obtained.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Euler\u2013Bernoulli equation describing the deflection of a beam is a vital tool in structural and<br \/>\nmechanical engineering. However, its derivation usually entails a number of intermediate steps that<br \/>\nmay confuse engineering or science students at th&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-137543","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/137543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=137543"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/137543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=137543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=137543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=137543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}