{"id":59386,"date":"2016-03-17T16:21:58","date_gmt":"2016-03-17T14:21:58","guid":{"rendered":"http:\/\/wpcalc.com\/?p=59386"},"modified":"2025-05-09T10:15:36","modified_gmt":"2025-05-09T07:15:36","slug":"cantilever-beam-with-couple-moment","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/cantilever-beam-with-couple-moment\/","title":{"rendered":"Cantilever Beam with Couple Moment Calculator"},"content":{"rendered":"\n<p><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Cantilever Beam with Couple Moment Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\text{Slope at free end} = \\frac{M \\cdot L}{E \\cdot I}\n\\text{Deflection at any section} = \\frac{M \\cdot x^2}{2 \\cdot E \\cdot I}\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$M$$: Couple moment (Nm)<\/li>\n<li>$$L$$: Length of beam (m)<\/li>\n<li>$$x$$: Distance from fixed end (m)<\/li>\n<li>$$E$$: Young\u2019s modulus (Pa)<\/li>\n<li>$$I$$: Moment of inertia (m\u2074)<\/li>\n<\/ul>\n<p>\r\n<\/section><br \/>\nThis calculator determines how a cantilever beam bends when a pure moment is applied at its free end. It helps assess deflection at any point and angular displacement, essential for design safety and compliance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the slope at the free end and deflection at any section of a cantilever beam subjected to a couple moment. Ideal for structural analysis and educational purposes in civil and mechanical engineering.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[19],"class_list":["post-59386","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-civil"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59386","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=59386"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59386\/revisions"}],"predecessor-version":[{"id":63979,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59386\/revisions\/63979"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59386"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}