{"id":1266,"date":"2020-12-02T16:58:31","date_gmt":"2020-12-02T16:58:31","guid":{"rendered":"https:\/\/pickedshares.com\/?p=1266"},"modified":"2021-05-08T11:35:43","modified_gmt":"2021-05-08T11:35:43","slug":"engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/","title":{"rendered":"Internal forces and moments of a beam"},"content":{"rendered":"\n<p>This exercise is about the following questions:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>How to determine the internal forces of a beam?<\/li><li>How to visualize the gradient of internal forces of a beam?<\/li><li>How to calculate the bending moment of a beam?<\/li><li>How to calculate the shear force and the normal force of a beam?<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A bent cantilever beam is fixed in A and under load of two forces F in different directions. The internal forces and moments of the beam have to be determined and visualized!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"515\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-1024x515.png\" alt=\"Bent cantilever beam with fixed support\" class=\"wp-image-1251\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-1024x515.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-300x151.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-768x386.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-400x201.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1-800x402.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1.png 1505w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Bent cantilever beam with fixed support<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The beam will be divided into two section because the functions (and gradients) for the bending moments in these two sections are different. This is caused by the bent shape of the beam.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"598\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-1024x598.png\" alt=\"The two sections of the bent beam\" class=\"wp-image-1255\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-1024x598.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-300x175.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-768x449.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-400x234.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2-800x467.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_2.png 1505w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>The two sections of the bent beam<\/figcaption><\/figure>\n\n\n\n<p>The sections will be referred to as I and II.<\/p>\n\n\n\n<p>In this solution the internal forces will be represented as F<sub>x<\/sub> and F<sub>y<\/sub>. These forces (this means the directions x and z, not the index I or II) stand both once for the normal force and the shear force in both sections, due to the bent shape of the beam. (The normal force and the shear force may be referred to as N and S in other exercises.) The bending moment is called M<sub>b<\/sub> here.<\/p>\n\n\n\n<p>The free body diagrams in the sections I and II are carried out without the need for the determination of the bearing reaction of the fixation A.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Section I<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"516\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-1024x516.png\" alt=\"Free body diagram of section I\" class=\"wp-image-1257\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-1024x516.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-300x151.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-768x387.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-400x201.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3-800x403.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_3.png 1515w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Free body diagram of section I<\/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\n<p>Establishing the equilibrium conditions for forces in the x and z directions as well as for the moments in section I:<\/p>\n\n<p>\\[ \\tag{1} \\sum F_x = 0 = -F_{xI} - F\\]<\/p>\n\n<p>\\[ \\tag{2} \\sum F_z = 0 = F_{zI} - F\\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[ \\tag{3} \\sum M_b(x) = 0 = - M_{bI} - F \\cdot (2a - x) + F \\cdot a \\]<\/p>\n<\/div>\n\n<p>The two forces in the x and z directions are constant over the entire range I. The bending moment in section I is a function of x.<\/p>\n<p>\\[ \\tag{4} F_{xI} = - F\\]<\/p>\n<p>\\[ \\tag{5} F_{zI} = F\\]<\/p>\n<p>\\[ \\tag{6} M_{bI} = F \\cdot (x-a) \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Section II<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"910\" height=\"1024\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-910x1024.png\" alt=\"Free body diagram of section II\" class=\"wp-image-1259\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-910x1024.png 910w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-267x300.png 267w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-768x865.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-400x450.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4-800x901.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_4.png 939w\" sizes=\"auto, (max-width: 910px) 100vw, 910px\" \/><figcaption>Free body diagram of section II<\/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\n<p>Establishing the equilibrium conditions for forces in the x and z directions as well as for the moments in section II:<\/p>\n\n<p>\\[ \\tag{7} \\sum F_x = 0 = F_{xII} - F\\]<\/p>\n\n<p>\\[ \\tag{8} \\sum F_z = 0 = -F_{zII} - F\\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[ \\tag{9} \\sum M_b(x) = 0 = M_{bII} + F \\cdot (a - z) \\]<\/p>\n<\/div>\n\n<p>The two forces in the x and z directions are constant over the entire range II. The bending moment in section II is a function of z.<\/p>\n\n<p>\\[ \\tag{10} F_{xII} = F\\]<\/p>\n<p>\\[ \\tag{11} F_{zII} = - F\\]<\/p>\n<p>\\[ \\tag{12} M_{bII} = F \\cdot (z-a) \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Graphic representation of the internal forces<\/h3>\n\n\n\n<p>With the functions determined above, the following representation of the gradients of shear force, normal force and bending moment results. The diagrams are rotated 90 \u00b0 for the upward part of the beam.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"849\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-1024x849.png\" alt=\"Visualization of the forces and bending moments\" class=\"wp-image-1261\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-1024x849.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-300x249.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-768x637.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-400x332.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5-800x663.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_5.png 1157w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Visualization of the forces and bending moments<\/figcaption><\/figure>\n\n\n\n<p>This means that all internal forces of the beam are determined and visualized.<\/p>\n\n\n\n<p>Here we have a <a href=\"https:\/\/pickedshares.com\/en\/category\/engineering-mechanics-ii\/\">collection of more exercises and solutions regarding the strength of material\/Engineering Mechanics II<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Internal forces and moments of a beam\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/\" aria-label=\"Read more about Internal forces and moments of a beam\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":1253,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52,60],"tags":[],"class_list":["post-1266","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-ii","category-exercises","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>Internal forces and moments of a beam<\/title>\n<meta name=\"description\" content=\"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Internal forces and moments of a beam\" \/>\n<meta property=\"og:description\" content=\"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/\" \/>\n<meta property=\"og:site_name\" content=\"pickedshares\" \/>\n<meta property=\"article:published_time\" content=\"2020-12-02T16:58:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-05-08T11:35:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1505\" \/>\n\t<meta property=\"og:image:height\" content=\"757\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1.png\" \/>\n<meta name=\"twitter:creator\" content=\"@pickedshares\" \/>\n<meta name=\"twitter:site\" content=\"@pickedshares\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/person\\\/6c617a6a61de9623da53f74a56810033\"},\"headline\":\"Internal forces and moments of a beam\",\"datePublished\":\"2020-12-02T16:58:31+00:00\",\"dateModified\":\"2021-05-08T11:35:43+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/\"},\"wordCount\":526,\"publisher\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm2-2_1preview.png\",\"articleSection\":[\"Engineering Mechanics II\",\"Exercises\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/\",\"name\":\"Internal forces and moments of a beam\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm2-2_1preview.png\",\"datePublished\":\"2020-12-02T16:58:31+00:00\",\"dateModified\":\"2021-05-08T11:35:43+00:00\",\"description\":\"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#primaryimage\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm2-2_1preview.png\",\"contentUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm2-2_1preview.png\",\"width\":705,\"height\":354,\"caption\":\"Bent cantilever beam with fixed support\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Start\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Exercises\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/category\\\/exercises\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Engineering Mechanics II\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/category\\\/exercises\\\/engineering-mechanics-ii\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Internal forces and moments of a beam\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\",\"name\":\"pickedshares\",\"description\":\"Engineering Design, Project Management, Tools and Exercises\",\"publisher\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\",\"name\":\"pickedshares.com\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"\",\"contentUrl\":\"\",\"caption\":\"pickedshares.com\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/x.com\\\/pickedshares\",\"https:\\\/\\\/www.instagram.com\\\/pickedshares\\\/\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UCSh8qo2-6dhtbZqSLStt3Rg\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/person\\\/6c617a6a61de9623da53f74a56810033\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"caption\":\"admin\"},\"sameAs\":[\"https:\\\/\\\/pickedshares.com\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Internal forces and moments of a beam","description":"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/","og_locale":"en_US","og_type":"article","og_title":"Internal forces and moments of a beam","og_description":"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.","og_url":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/","og_site_name":"pickedshares","article_published_time":"2020-12-02T16:58:31+00:00","article_modified_time":"2021-05-08T11:35:43+00:00","og_image":[{"width":1505,"height":757,"url":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1.png","type":"image\/png"}],"author":"admin","twitter_card":"summary_large_image","twitter_image":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1.png","twitter_creator":"@pickedshares","twitter_site":"@pickedshares","twitter_misc":{"Written by":"admin","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#article","isPartOf":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/"},"author":{"name":"admin","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/person\/6c617a6a61de9623da53f74a56810033"},"headline":"Internal forces and moments of a beam","datePublished":"2020-12-02T16:58:31+00:00","dateModified":"2021-05-08T11:35:43+00:00","mainEntityOfPage":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/"},"wordCount":526,"publisher":{"@id":"https:\/\/pickedshares.com\/en\/#organization"},"image":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#primaryimage"},"thumbnailUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1preview.png","articleSection":["Engineering Mechanics II","Exercises"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/","url":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/","name":"Internal forces and moments of a beam","isPartOf":{"@id":"https:\/\/pickedshares.com\/en\/#website"},"primaryImageOfPage":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#primaryimage"},"image":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#primaryimage"},"thumbnailUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1preview.png","datePublished":"2020-12-02T16:58:31+00:00","dateModified":"2021-05-08T11:35:43+00:00","description":"In this exercise the inner forces and the bending moment of a bent beam are calculated and visualized in diagrams.","breadcrumb":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#primaryimage","url":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1preview.png","contentUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm2-2_1preview.png","width":705,"height":354,"caption":"Bent cantilever beam with fixed support"},{"@type":"BreadcrumbList","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-2-exercise-2-inner-forces-and-moments-of-a-beam\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Start","item":"https:\/\/pickedshares.com\/en\/"},{"@type":"ListItem","position":2,"name":"Exercises","item":"https:\/\/pickedshares.com\/en\/category\/exercises\/"},{"@type":"ListItem","position":3,"name":"Engineering Mechanics II","item":"https:\/\/pickedshares.com\/en\/category\/exercises\/engineering-mechanics-ii\/"},{"@type":"ListItem","position":4,"name":"Internal forces and moments of a beam"}]},{"@type":"WebSite","@id":"https:\/\/pickedshares.com\/en\/#website","url":"https:\/\/pickedshares.com\/en\/","name":"pickedshares","description":"Engineering Design, Project Management, Tools and Exercises","publisher":{"@id":"https:\/\/pickedshares.com\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/pickedshares.com\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/pickedshares.com\/en\/#organization","name":"pickedshares.com","url":"https:\/\/pickedshares.com\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/logo\/image\/","url":"","contentUrl":"","caption":"pickedshares.com"},"image":{"@id":"https:\/\/pickedshares.com\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/x.com\/pickedshares","https:\/\/www.instagram.com\/pickedshares\/","https:\/\/www.youtube.com\/channel\/UCSh8qo2-6dhtbZqSLStt3Rg"]},{"@type":"Person","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/person\/6c617a6a61de9623da53f74a56810033","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","caption":"admin"},"sameAs":["https:\/\/pickedshares.com"]}]}},"_links":{"self":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/1266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/comments?post=1266"}],"version-history":[{"count":5,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/1266\/revisions"}],"predecessor-version":[{"id":5054,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/1266\/revisions\/5054"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/media\/1253"}],"wp:attachment":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/media?parent=1266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/categories?post=1266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/tags?post=1266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}