{"id":510,"date":"2020-11-30T08:44:17","date_gmt":"2020-11-30T08:44:17","guid":{"rendered":"https:\/\/pickedshares.com\/?p=510"},"modified":"2021-02-22T16:33:27","modified_gmt":"2021-02-22T16:33:27","slug":"engineering-mechanics-1-exercise-4-calculate-the-permissible-angle","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-4-calculate-the-permissible-angle\/","title":{"rendered":"Calculate the permissible angle"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This exercise shows how to calculate the permissible rope angle for a given load.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A load of G = 10 kN has to be attached to <a href=\"https:\/\/pickedshares.com\/en\/reaction-forces-in-bearings-joints-and-guidances\/\">two suspension<\/a> points with ropes. The maximum permissible tensile force of the rope is 20 kN. What value must the angle \u03b1 have so the rope doesn't break?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"743\" height=\"612\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E4.png\" alt=\"weight load hold by two ropes\" class=\"wp-image-394\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E4.png 743w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E4-300x247.png 300w\" sizes=\"auto, (max-width: 743px) 100vw, 743px\" \/><figcaption>Weight load hold by two ropes<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">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=\"Zul&auml;ssigen Winkel berechnen - Technische Mechanik 1, &Uuml;bung 4\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_GVJGQ1oj4GM\" 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%2FGVJGQ1oj4GM%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/GVJGQ1oj4GM\" \/><meta itemprop=\"duration\" content=\"PT5M30S\" \/><meta itemprop=\"uploadDate\" content=\"2020-02-21T19:59:24Z\" \/><\/div><div id=\"lyte_GVJGQ1oj4GM\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FGVJGQ1oj4GM%2Fhqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Zul\u00e4ssigen Winkel berechnen - Technische Mechanik 1, \u00dcbung 4<\/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\/GVJGQ1oj4GM\" 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%2FGVJGQ1oj4GM%2F0.jpg\" alt=\"Zul&auml;ssigen Winkel berechnen - Technische Mechanik 1, &Uuml;bung 4\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Eine Last von 10 kN soll mit einem Seil an zwei Aufh\u00e4ngepunkten befestigt werden. Die maximal zul\u00e4ssige Zugkraft des Seils betr\u00e4gt 20 kN. Wie gro\u00df muss der Winkel Alpha sein, damit das Seil nicht rei\u00dft? Diese \u00dcbung findet man auch auf https:\/\/pickedshares.com\/technische-mechanik-1-uebung-4-zulaessigen-winkel-berechnen\/ A load (G = 10 kN) shall be held by a rope that can bear a maximum tensile force of 20 kN. How big can the angle Alpha be without tearing the rope? This exercise can also be found at https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-4-calculate-the-permissible-angle\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p class=\"wp-block-paragraph\">Due to the symmetrical arrangement of the suspension, the look on one side is sufficient. It is a <a href=\"http:\/\/web.mit.edu\/4.441\/1_lectures\/1_lecture7\/1_lecture7.html#:~:text=A%20concurrent%20coplanar%20force%20system,contact%20with%20the%20common%20point.\" target=\"_blank\" rel=\"noreferrer noopener\">system of concurrent forces<\/a> in a plane.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"543\" height=\"664\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-4_solved.png\" alt=\"Rope forces for exercise 4 (only one side)\" class=\"wp-image-466\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-4_solved.png 543w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-4_solved-245x300.png 245w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/tm1-4_solved-400x489.png 400w\" sizes=\"auto, (max-width: 543px) 100vw, 543px\" \/><figcaption>Rope forces for exercise 4 (only one side)<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The vertical component of the rope force equals to the half of the load G:<\/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<p>\\[\\tag{1} {F_{\\mathit{1y}}}=\\frac{G}{2}\\]\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and the relationship to the rope force is<\/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<p>\\[\\tag{2} {F_1} \\sin{\\left( \\alpha \\right) }={F_{\\mathit{1y}}}\\]\n<\/p>\n<p>\\[\\tag{3} F_1 = \\frac{F_1y}{\\sin\\left( \\alpha \\right) }\\]\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The rope force shall not be greater than 20 kN, so the following applies<\/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<p>\\[\\tag{4} 20 kN \\geq \\frac{F_1y}{\\sin\\left( \\alpha \\right) }\\]\n<\/p>\n<p>\\[\\tag{5} \\alpha \\geq \\arcsin \\left( \\frac{5 kN}{20 kN } \\right) \\]\n<\/p>\n<p>\\[\\tag{6} \\alpha \\geq 14.48\u00b0 \\]\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So the angle \u03b1 must stay or be equal to 14.48\u00b0, or the rope will break. This was the way to calculate it for a symmetrical setup. We have another exercise, where an asymetrical layout is investigated, just take a look into the category Engineering Mechanics I in the menu at the side.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This was the exercise about how to calculate the permissible rope angle if you have a given load and maximum rope force. If you enjoyed it, please share it!<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Calculate the permissible angle\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-4-calculate-the-permissible-angle\/\" aria-label=\"Read more about Calculate the permissible angle\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":395,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[47,29],"class_list":["post-510","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-resultant-force","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 v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculate the permissible angle &#8226; Engineering Mechanics<\/title>\n<meta name=\"description\" content=\"A load hall be suspended symmetrically on two ropes. 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