{"id":194339,"date":"2025-02-24T04:45:57","date_gmt":"2025-02-24T04:45:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194339"},"modified":"2025-02-24T04:45:59","modified_gmt":"2025-02-24T04:45:59","slug":"each-of-the-four-vertical-links-has-an-8-times-36-mm-uniform-rectangular-cross-section-and-each-of-the-four-pins-has-a-16-mm-diameter","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/24\/each-of-the-four-vertical-links-has-an-8-times-36-mm-uniform-rectangular-cross-section-and-each-of-the-four-pins-has-a-16-mm-diameter\/","title":{"rendered":"Each of the four vertical links has an 8 times 36-mm uniform rectangular cross section, and each of the four pins has a 16-mm diameter"},"content":{"rendered":"\n<p>Each of the four vertical links has an 8 times 36-mm uniform rectangular cross section, and each of the four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in the links connecting points B and D, points C and E.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1297.png\" alt=\"\" class=\"wp-image-194340\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the maximum average normal stress in the vertical links connecting points B and D, and points C and E, we analyze the forces acting on these links and their cross-sectional areas.<\/p>\n\n\n\n<p><strong>Given Data:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cross-sectional dimensions of each link: 8 mm (thickness) \u00d7 36 mm (width)<\/li>\n\n\n\n<li>Diameter of each pin: 16 mm<\/li>\n\n\n\n<li>Applied load, P: 20 kN<\/li>\n\n\n\n<li>Geometric distances: 0.4 m, 0.25 m, and 0.2 m (as per the provided diagram)<\/li>\n<\/ul>\n\n\n\n<p><strong>Analysis:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Free-Body Diagram (FBD):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Consider the member ABC as a free body.<\/li>\n\n\n\n<li>The applied load P = 20 kN acts vertically downward at point C.<\/li>\n\n\n\n<li>Reactions occur at points B and A due to the pins.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Moment Equations:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Taking moments about point A to find the force in link BD:\n<ul class=\"wp-block-list\">\n<li>Sum of moments about A: (0.4 m) \u00d7 F_BD &#8211; (0.25 m + 0.4 m) \u00d7 20 kN = 0<\/li>\n\n\n\n<li>Solving for F_BD: F_BD = (0.65 m \u00d7 20 kN) \/ 0.4 m = 32.5 kN<\/li>\n\n\n\n<li>This indicates that link BD is in tension.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Taking moments about point B to find the force in link CE:\n<ul class=\"wp-block-list\">\n<li>Sum of moments about B: (0.4 m) \u00d7 F_CE &#8211; (0.25 m) \u00d7 20 kN = 0<\/li>\n\n\n\n<li>Solving for F_CE: F_CE = (0.25 m \u00d7 20 kN) \/ 0.4 m = 12.5 kN<\/li>\n\n\n\n<li>This indicates that link CE is in compression.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Cross-Sectional Area Calculations:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Link BD:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Net area considering pin hole: (36 mm &#8211; 16 mm) \u00d7 8 mm = 20 mm \u00d7 8 mm = 160 mm\u00b2<\/li>\n\n\n\n<li>Since there are two parallel links, total net area = 2 \u00d7 160 mm\u00b2 = 320 mm\u00b2<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Link CE:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Gross area without considering pin hole: 36 mm \u00d7 8 mm = 288 mm\u00b2<\/li>\n\n\n\n<li>For two parallel links, total area = 2 \u00d7 288 mm\u00b2 = 576 mm\u00b2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Stress Calculations:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Link BD (Tension):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Average normal stress, \u03c3_BD = Force \/ Area = 32.5 kN \/ 320 mm\u00b2 = 32,500 N \/ 320 \u00d7 10\u207b\u2076 m\u00b2 = 101.56 MPa<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Link CE (Compression):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Average normal stress, \u03c3_CE = Force \/ Area = 12.5 kN \/ 576 mm\u00b2 = 12,500 N \/ 576 \u00d7 10\u207b\u2076 m\u00b2 = 21.7 MPa<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The maximum average normal stress occurs in the links connecting points B and D, with a value of approximately <strong>101.56 MPa<\/strong> in tension.<\/li>\n\n\n\n<li>The links connecting points C and E experience an average normal stress of approximately <strong>21.7 MPa<\/strong> in compression.<\/li>\n<\/ul>\n\n\n\n<p>These calculations are consistent with standard structural analysis methods, ensuring the links&#8217; design can withstand the applied loads without exceeding material stress limits.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Each of the four vertical links has an 8 times 36-mm uniform rectangular cross section, and each of the four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in the links connecting points B and D, points C and E. The Correct Answer and Explanation is : To determine [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-194339","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=194339"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194339\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}