{"id":194336,"date":"2025-02-24T04:44:18","date_gmt":"2025-02-24T04:44:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194336"},"modified":"2025-02-24T04:44:21","modified_gmt":"2025-02-24T04:44:21","slug":"each-of-the-four-vertical-links-has-an-8-x-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-x-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 X 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 X 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 (a) points B and D, (b) points C and E.<\/p>\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 value of the <strong>average normal stress<\/strong> in the links connecting points <strong>B and D<\/strong> and <strong>C and E<\/strong>, we use the formula:<\/p>\n\n\n\n<p>[<br>\\sigma = \\frac{P}{A}<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\sigma ) = Average normal stress (MPa),<\/li>\n\n\n\n<li>( P ) = Load carried by the link (N),<\/li>\n\n\n\n<li>( A ) = Cross-sectional area of the link ((\\text{mm}^2)).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given Data:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rectangular link dimensions<\/strong>: ( 8 \\times 36 ) mm<\/li>\n\n\n\n<li><strong>Pin diameter<\/strong>: ( 16 ) mm<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Calculate the Cross-Sectional Area of Each Link<\/strong><\/h4>\n\n\n\n<p>[<br>A = \\text{width} \\times \\text{thickness} = 36 \\times 8 = 288 \\text{ mm}^2<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Load Distribution<\/strong><\/h4>\n\n\n\n<p>Each link carries a portion of the total force ( P ). Assuming symmetric loading, each pair of links at <strong>B-D<\/strong> and <strong>C-E<\/strong> carries <strong>half of the applied load<\/strong>.<\/p>\n\n\n\n<p>Thus, force per link:<\/p>\n\n\n\n<p>[<br>P_{\\text{link}} = \\frac{P}{2}<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 3: Compute Normal Stress<\/strong><\/h4>\n\n\n\n<p>[<br>\\sigma = \\frac{P_{\\text{link}}}{A} = \\frac{P\/2}{288}<br>]<\/p>\n\n\n\n<p>To obtain the numerical value, we need the <strong>applied load ( P )<\/strong>. However, the formula provides a straightforward approach to solving for <strong>( \\sigma )<\/strong> given any applied force.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The normal stress depends on the applied force ( P ).<\/li>\n\n\n\n<li>Each link carries <strong>half of ( P )<\/strong>.<\/li>\n\n\n\n<li><strong>Formula to compute normal stress in links BD and CE<\/strong>: [<br>\\sigma = \\frac{P}{576}<br>]<\/li>\n<\/ul>\n\n\n\n<p>where ( P ) is in Newtons and ( \\sigma ) will be in MPa.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Generated Image<\/strong><\/h3>\n\n\n\n<p>I will now generate an image illustrating the structural system with forces, links, and stress distribution.<\/p>\n\n\n\n<p>Here is the generated image illustrating the mechanical structure with vertical links, pins, force distribution, and stress annotations. Let me know if you need any modifications or additional details!<\/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-1296.png\" alt=\"\" class=\"wp-image-194337\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Each of the four vertical links has an 8 X 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 (a) points B and D, (b) points C and E. The Correct Answer and Explanation is : [&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-194336","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194336","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=194336"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194336\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194336"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194336"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}