{"id":13880,"date":"2024-06-05T08:23:47","date_gmt":"2024-06-05T12:23:47","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me323\/?page_id=13880"},"modified":"2024-07-01T09:48:59","modified_gmt":"2024-07-01T13:48:59","slug":"h16-discussion-su24","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me323\/homework-discussion-su24-2\/h16-discussion-su24\/","title":{"rendered":"H16 Discussion &#8211; Su24"},"content":{"rendered":"<p><a href=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2024\/07\/H16.pdf\"><em><strong><span style=\"font-size: 14pt\">PROBLEM STATEMENT<\/span><\/strong><\/em><\/a><\/p>\n<p><em><strong><span style=\"font-size: 14pt\">DISCUSSION THREAD<\/span><\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wpa-warning wpa-image-missing-alt wp-image-13882\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2024\/06\/Screenshot-2024-06-05-at-8.24.15\u202fAM-300x140.jpg\" alt=\"\" width=\"381\" height=\"178\" data-warning=\"Missing alt text\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2024\/06\/Screenshot-2024-06-05-at-8.24.15\u202fAM-300x140.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2024\/06\/Screenshot-2024-06-05-at-8.24.15\u202fAM.jpg 370w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<p><em><strong>Hints<\/strong><\/em>:<br \/>\nSince this is a determinate beam, you are able to determine the reactions on the beam at B and C straight away from equilibrium considerations. It is recommended that you use the second-order approach for the integration process for finding rotations and displacements. For this, consider the two sections of the beam BC and CD.<\/p>\n<ul>\n<li>Make a mathematical cut through the beam between B and C, and from equilibrium considerations, determine the bending moment M(x). Integrate once and twice to get the rotation \u03b8(x) and displacement v(x):<br \/>\n\u03b8(x) = \u03b8(0)\u00a0+ (1\/EI) \u222bM(x)dx<br \/>\nv(x) = v(0) + \u00a0\u222b\u03b8(x)dx<br \/>\nwhere \u03b8(0) and v(0) are integration constants.<\/li>\n<li>Make a mathematical cut through the beam between C and D, and from equilibrium considerations, determine the bending moment M(x). Integrate once and twice to get the rotation \u03b8(x) and displacement v(x):<br \/>\n\u03b8(x) = \u03b8(a) + (1\/EI) \u222bM(x)dx<br \/>\nv(x) = v(a) + \u00a0\u222b\u03b8(x)dx<br \/>\nwhere \u03b8(a) and v(a) are integration constants. \u03b8(a) and v(a) are found from the results of integrating from B to C.<\/li>\n<li>Enforce the displacement boundary condition at x = a to determine the unknown integration constant.<\/li>\n<\/ul>\n<p>Any questions? Ask (and answer) questions here.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>PROBLEM STATEMENT DISCUSSION THREAD Hints: Since this is a determinate beam, you are able to determine the reactions on the beam at B and C straight away from equilibrium considerations. It is recommended that you use the second-order approach for the integration process for finding rotations and displacements. For this, consider the two sections of &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me323\/homework-discussion-su24-2\/h16-discussion-su24\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">H16 Discussion &#8211; Su24<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":13775,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-13880","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/13880","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/comments?post=13880"}],"version-history":[{"count":6,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/13880\/revisions"}],"predecessor-version":[{"id":14283,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/13880\/revisions\/14283"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/13775"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/media?parent=13880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}