{"id":706,"date":"2020-12-06T20:15:54","date_gmt":"2020-12-06T20:15:54","guid":{"rendered":"https:\/\/pickedshares.com\/?p=706"},"modified":"2021-05-08T11:41:27","modified_gmt":"2021-05-08T11:41:27","slug":"engineering-mechanics-1-exercise-14-determine-bearing-reactions","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-14-determine-bearing-reactions\/","title":{"rendered":"Bearing reactions under sloping load"},"content":{"rendered":"\n<p>This exercise shows how to calculate the bearing reactions under sloping load.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A bridge on a <a href=\"https:\/\/pickedshares.com\/en\/reaction-forces-in-bearings-joints-and-guidances\/\">floating bearing and a fixed bearing<\/a> is loaded by a braking car as shown. Determine the bearing reactions in A and B!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"518\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-1024x518.png\" alt=\"Beam on two supports with sloping load\" class=\"wp-image-3340\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-1024x518.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-300x152.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-768x388.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-400x202.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1-800x404.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-1.png 1157w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Beam on two supports with sloping load<\/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 bestimmen - Technische Mechanik 1, &Uuml;bung 14\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_QRozCPYjCVA\" 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%2FQRozCPYjCVA%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/QRozCPYjCVA\" \/><meta itemprop=\"duration\" content=\"PT5M52S\" \/><meta itemprop=\"uploadDate\" content=\"2020-11-01T09:00:04Z\" \/><\/div><div id=\"lyte_QRozCPYjCVA\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FQRozCPYjCVA%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Lagerreaktionen bestimmen - Technische Mechanik 1, \u00dcbung 14<\/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\/QRozCPYjCVA\" 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%2FQRozCPYjCVA%2F0.jpg\" alt=\"Lagerreaktionen bestimmen - Technische Mechanik 1, &Uuml;bung 14\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Eine Br\u00fccke wird durch ein bremsendes Auto wie abgebildet belastet. Welche Lagerreaktionen treten in A und B auf?\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"511\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-1024x511.png\" alt=\"Free body diagram of the beam\" class=\"wp-image-3346\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-1024x511.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-300x150.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-768x383.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-400x199.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2-800x399.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-14-2.png 1173w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Free body diagram 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\\[ \\newcommand{\\myvec}[1]{{\\begin{pmatrix}#1\\end{pmatrix}}} \\]\n\n\n<p>The equilibrium of forces in the x-direction is<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{1} \\sum F_x = 0 = F \\cdot \\sin \\alpha + F_{Bx} \\]<\/p>\n<\/div>\n<p>\\[\\tag{2}  F_{Bx} = - F \\cdot \\sin \\alpha\\]<\/p>\n\n\n<p>The equilibrium of forces in the y-direction is<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{3} \\sum F_y = 0 = F_{Ay} - F \\cdot \\cos \\alpha + F_{By} \\]<\/p>\n<\/div>\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 \\cdot \\cos \\alpha \\cdot a + F_{By} \\cdot (a+b) \\]<\/p>\n<\/div>\n<p>\\[\\tag{5} F_{By} = \\frac{F \\cdot \\cos \\alpha \\cdot a}{a+b} \\]<\/p>\n\n\n<p>From equation 3 follows<\/p>\n<p>\\[\\tag{6} F_{Ay} = F \\cdot \\cos \\alpha -  F_{By} \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{7} F_{Ay} = F \\cdot \\cos \\alpha -  \\frac{F \\cdot \\cos \\alpha \\cdot a}{a+b} \\]<\/p>\n<p>\\[\\tag{8} F_{Ay} = F \\cdot \\cos \\alpha \\cdot \\left(1 -  \\frac{a}{a+b} \\right) \\]<\/p>\n<\/div>\n\n\n\n<p>This was the basic exercise \"bearing reactions under sloping load\", used to show the appliance of fixed and floating bearings. Don't miss the other interesting exercises!<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Bearing reactions under sloping load\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-14-determine-bearing-reactions\/\" aria-label=\"Read more about Bearing reactions under sloping load\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":3342,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[30,45,46,29],"class_list":["post-706","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>Bearing reactions under sloping load &#8226; 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