{"id":720,"date":"2020-12-07T14:40:03","date_gmt":"2020-12-07T14:40:03","guid":{"rendered":"https:\/\/pickedshares.com\/?p=720"},"modified":"2021-05-08T11:47:29","modified_gmt":"2021-05-08T11:47:29","slug":"engineering-mechanics-1-exercise-18-beam-with-joint-and-offset-load","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-18-beam-with-joint-and-offset-load\/","title":{"rendered":"Beam with joint and offset load"},"content":{"rendered":"\n<p>This exercise is about the following questions:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>How to calculate the forces in a joint?<\/li><li>How to calculate the bearing loads if a force acts with an offset?<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A force F acts with an offset on a beam. The beam is fixed on one side and connected to a floating bearing with a joint. Find the reaction forces in A, B and C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"554\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-1024x554.jpg\" alt=\"Beam with joint and an offset force\" class=\"wp-image-431\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-1024x554.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-300x162.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-768x416.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-400x217.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18-800x433.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-18.jpg 1110w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Beam with joint and an offset force<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The following video is in german language.<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Reaktionskr&auml;fte bestimmen - Technische Mechanik 1, &Uuml;bung 18\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_veRHEbA_pB8\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FveRHEbA_pB8%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/veRHEbA_pB8\" \/><meta itemprop=\"duration\" content=\"PT7M39S\" \/><meta itemprop=\"uploadDate\" content=\"2020-11-11T23:00:12Z\" \/><\/div><div id=\"lyte_veRHEbA_pB8\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FveRHEbA_pB8%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Reaktionskr\u00e4fte bestimmen - Technische Mechanik 1, \u00dcbung 18<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/veRHEbA_pB8\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FveRHEbA_pB8%2F0.jpg\" alt=\"Reaktionskr&auml;fte bestimmen - Technische Mechanik 1, &Uuml;bung 18\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Ein Tr\u00e4ger ist auf einer Seite auf einem Loslager gelagert und \u00fcber ein Gelenk mit einer festen Einspannung verbunden. An dem am Tr\u00e4ger befindlichen Kragarm mit der L\u00e4nge a greift die Kraft F in der dargestellten Weise an. Bestimmen Sie die Reaktionskr\u00e4fte in dem Loslager A, im Gelenk B und in der festen Einspannung C. In dieser \u00dcbung wird vorgerechnet, wie man die Kr\u00e4ftebilanzen und die Momentenbilanz aufstellt, um Lagerreaktionen zu ermitteln.\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>The beam is divided into two sections to determine the bearing reactions and the joint forces.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Section 1<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-1024x917.jpg\" alt=\"Free-cut area 1 of the beam\" class=\"wp-image-722\" width=\"512\" height=\"459\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-1024x917.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-300x269.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-768x688.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-400x358.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1-800x717.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-1.jpg 1036w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Free-cut section 1 of the beam<\/figcaption><\/figure>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\\[ \\require{cancel} \\]\n<p>The equilibrium of forces in the x-direction is<\/p>\n<p>\\[\\tag{1} \\sum F_x = 0 = F + F_{Bx} \\]<\/p>\n<p>\\[\\tag{2} F_{Bx} = -F \\]<\/p>\n\n<p>The equilibrium of forces in the y-direction is<\/p>\n<p>\\[\\tag{3} \\sum F_y = 0 = F_{Ay} + F_{By} \\]<\/p>\n\n<p>The equilibrium of moments around point A gives<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{4} \\sum M(A) = 0 = -F \\cdot a + F_{By} \\cdot 2 \\cdot a \\]<\/p>\n<\/div>\n\n<p>\\[\\tag{5} F_{By} = \\frac{F \\cdot \\bcancel{a}}{2 \\cdot \\bcancel{a}} \\]<\/p>\n\n<p>So the result from equation 3 is<\/p>\n<p>\\[\\tag{6} F_{Ay} = - \\frac{F}{2} \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Section 2<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"709\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-1024x709.jpg\" alt=\"Free-cut area 2 of the beam\" class=\"wp-image-724\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-1024x709.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-300x208.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-768x532.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-400x277.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2-800x554.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-18-2.jpg 1121w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Free-cut section 2 of the beam<\/figcaption><\/figure>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\\[ \\require{cancel} \\]\n<p>The equilibrium of forces in the x-direction is<\/p>\n<p>\\[\\tag{7} \\sum F_x = 0 = - F_{Bx} + F_{Cx} \\]<\/p>\n<p>\\[\\tag{8} F_{Cx} = -F \\]<\/p>\n<p>The equilibrium of forces in the y-direction is<\/p>\n<p>\\[\\tag{9} \\sum F_y = 0 = - F_{By} + F_{Cy} \\]<\/p>\n<p>\\[\\tag{10} F_{Cy} = \\frac{F}{2} \\]<\/p>\n\n<p>The equilibrium of moments around point C gives<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{11} \\sum M(C) = 0 = F_{By} \\cdot 2a + M_C \\]<\/p>\n<\/div>\n<p>\\[\\tag{12} M_C = - F \\cdot a \\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Beam with joint and offset load\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-18-beam-with-joint-and-offset-load\/\" aria-label=\"Read more about Beam with joint and offset load\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":431,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[30,45,46,29],"class_list":["post-720","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-beams","tag-bearing-loads","tag-reaction-forces","tag-statics","infinite-scroll-item","masonry-post","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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