{"id":704,"date":"2020-12-06T19:58:02","date_gmt":"2020-12-06T19:58:02","guid":{"rendered":"https:\/\/pickedshares.com\/?p=704"},"modified":"2021-05-08T11:39:56","modified_gmt":"2021-05-08T11:39:56","slug":"engineering-mechanics-1-exercise-13-cantilever-beam-bearing-reactions","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-13-cantilever-beam-bearing-reactions\/","title":{"rendered":"Cantilever beam bearing reactions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A beam fixed on one side at point A is loaded with forces F<sub>1<\/sub> and F<sub>2<\/sub>. Which bearing reactions occur in A?<\/p>\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\/11\/Screenshot_20201105-134015_Sketch.jpg\" alt=\"Beam with a fixation bearing and two external forces\" class=\"wp-image-417\" width=\"715\" height=\"460\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134015_Sketch.jpg 953w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134015_Sketch-300x193.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134015_Sketch-768x494.jpg 768w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><figcaption>Beam with a fixation bearing and two external forces<\/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. Please scroll down for the written solution.<\/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=\"Lagerreaktionen der festen Einspannung bestimmen - Technische Mechanik 1, &Uuml;bung 13\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_Eq7N_eZguaY\" 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%2FEq7N_eZguaY%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/Eq7N_eZguaY\" \/><meta itemprop=\"duration\" content=\"PT3M39S\" \/><meta itemprop=\"uploadDate\" content=\"2020-10-29T09:00:57Z\" \/><\/div><div id=\"lyte_Eq7N_eZguaY\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FEq7N_eZguaY%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Lagerreaktionen der festen Einspannung bestimmen - Technische Mechanik 1, \u00dcbung 13<\/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\/Eq7N_eZguaY\" 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%2FEq7N_eZguaY%2F0.jpg\" alt=\"Lagerreaktionen der festen Einspannung bestimmen - Technische Mechanik 1, &Uuml;bung 13\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Ein im Punkt A einseitig eingespannter Tr\u00e4ger wird mit den Kr\u00e4ften F1 und F2 belastet. Welche Lagerreaktionen treten in A auf?\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>See the free body diagram of the cantilever beam below. We consider <a href=\"https:\/\/web.ua.es\/docivis\/magnet\/righthand_rule.html#:~:text=The%20right%2Dhand%20rule%20imposes,the%20index%20finger%20represents%20b.\" target=\"_blank\" rel=\"noreferrer noopener\">left turning moments as positive<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-1024x576.jpg\" alt=\"Free cut of the beam\" class=\"wp-image-580\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-1024x576.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-300x169.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-768x432.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-400x225.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch-800x450.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-073922_Sketch.jpg 1303w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Free cut of the beam<\/figcaption><\/figure>\n\n\n\n<p>In this exercise the only bearing of the beam is the fixation in A. The <a href=\"https:\/\/pickedshares.com\/en\/reaction-forces-in-bearings-joints-and-guidances\/\">bearing loads<\/a> can be determined as follows:<\/p>\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\\[ \\newcommand{\\myvec}[1]{{\\begin{pmatrix}#1\\end{pmatrix}}} \\]\n\n\n<p>The equilibrium of forces in the x-direction is<\/p>\n<p>\\[\\tag{1} \\sum F_x = 0 = F_{Ax} \\]<\/p>\n\n<p>The equilibrium of forces in the y-direction is<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{2} \\sum F_y = 0 = F_1 - F_2 + F_{Ay} \\]<\/p>\n<\/div>\n<p>\\[\\tag{3} F_{Ay} = F_2 - F_1 \\]<\/p>\n\n<p>The equilibrium of moments around point A is<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{4} \\sum M(A) = 0 = -F_1 \\cdot (a+b) + F_2 \\cdot b + M_A \\]<\/p>\n<\/div>\n<p>\\[\\tag{5} M_A = F_1 \\cdot (a+b) - F_2 \\cdot b \\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Cantilever beam bearing reactions\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-13-cantilever-beam-bearing-reactions\/\" aria-label=\"Read more about Cantilever beam bearing reactions\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":411,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[30,45,46,29],"class_list":["post-704","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 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Cantilever beam bearing reactions &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"A beam is fixed on one side (cantilever beam) and loaded with two forces. 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