{"id":9167,"date":"2021-08-14T23:36:42","date_gmt":"2021-08-15T03:36:42","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me323\/?page_id=9167"},"modified":"2022-09-09T11:58:30","modified_gmt":"2022-09-09T15:58:30","slug":"determinate-and-indeterminate-rods","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me323\/animations-and-demonstrations\/determinate-and-indeterminate-rods\/","title":{"rendered":"Determinate and indeterminate rods"},"content":{"rendered":"<p><span style=\"font-size: 14pt\"><em><strong>Determinate rod<\/strong><\/em><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-9170 aligncenter\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.37.33-PM-300x97.jpg\" alt=\"\" width=\"399\" height=\"129\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.37.33-PM-300x97.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.37.33-PM-768x247.jpg 768w, https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.37.33-PM.jpg 891w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>The rod system shown above is DETERMINATE.<\/p>\n<ul>\n<li>\n<div>Member loads depend on only equilibrium relations. For this problem, F<sub>1<\/sub> = F<sub>2<\/sub>.<\/div>\n<\/li>\n<li>\n<div>Due to the different cross-sectional areas, the stress in (2) is twice that of (1).<\/div>\n<\/li>\n<li>\n<div>Material properties, cross-sectional areas and member lengths do not factor in on the member loads.<\/div>\n<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/rod01_01b.gif\" width=\"613\" height=\"212\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt\"><em><strong>Indeterminate rod<\/strong><\/em><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-9173\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.44.03-PM-300x91.jpg\" alt=\"\" width=\"452\" height=\"137\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.44.03-PM-300x91.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/Screen-Shot-2021-08-14-at-11.44.03-PM.jpg 769w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>The rod system shown above is INDETERMINATE.<\/p>\n<ul>\n<li>\n<div>Both equilibrium and deformation must be included in the member load analysis.<\/div>\n<\/li>\n<li>\n<div>For this indeterminate rod, the compatibility equation relating the two member elongations is: \u00a0e<sub>1<\/sub> = -e<sub>2<\/sub> .<\/div>\n<\/li>\n<li>Solving for member loads gives: F<sub>1<\/sub> = -2F<sub>2<\/sub> (member(1) carries twice the load of (2) since (1) because it is twice as stiff). The &#8220;minus&#8221; sign says that (2) will be in compression where (1) is in tension.<\/li>\n<li>The magnitudes of the stress in (1) and (2) will be the same.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2022\/09\/rod02_01b.gif\" width=\"687\" height=\"239\" \/><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determinate rod The rod system shown above is DETERMINATE. Member loads depend on only equilibrium relations. For this problem, F1 = F2. Due to the different cross-sectional areas, the stress in (2) is twice that of (1). Material properties, cross-sectional areas and member lengths do not factor in on the member loads. &nbsp; Indeterminate rod &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me323\/animations-and-demonstrations\/determinate-and-indeterminate-rods\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Determinate and indeterminate rods<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":5074,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-9167","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9167","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=9167"}],"version-history":[{"count":8,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9167\/revisions"}],"predecessor-version":[{"id":10955,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9167\/revisions\/10955"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/5074"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/media?parent=9167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}