{"id":5665,"date":"2024-04-15T02:16:59","date_gmt":"2024-04-15T02:16:59","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5665"},"modified":"2024-04-15T02:16:59","modified_gmt":"2024-04-15T02:16:59","slug":"a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/","title":{"rendered":"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;10 m&#8221; option2=&#8221;12 m&#8221; option3=&#8221;14 m&#8221; option4=&#8221;16 m&#8221; correct=&#8221;option2&#8243;]<!--more--><\/p>\n<p>The correct answer is B. 12 m.<\/p>\n<p>The maximum deflection of a simply supported beam is given by the following equation:<\/p>\n<p>$$\\delta_{max} = \\frac{5wL^4}{384EI}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\delta_{max}$ is the maximum deflection,<\/li>\n<li>$w$ is the uniformly distributed load,<\/li>\n<li>$L$ is the length of the beam,<\/li>\n<li>$E$ is the Young&#8217;s modulus of the material, and<\/li>\n<li>$I$ is the moment of inertia of the beam.<\/li>\n<\/ul>\n<p>The slope at the ends of a simply supported beam is given by the following equation:<\/p>\n<p>$$\\theta_{max} = \\frac{wL^3}{384EI}$$<\/p>\n<p>We can solve the equation for $L$ to get:<\/p>\n<p>$$L = \\sqrt{\\frac{384EI}{\\frac{5wL^4}{384EI} + \\theta_{max}}} = \\sqrt{\\frac{384EI}{\\theta_{max}}}$$<\/p>\n<p>We are given that $\\delta_{max} = 10$ mm, $\\theta_{max} = 0.002$ radian, $E = 200 \\times 10^9 \\text{ Pa}$, and $I = 1000 \\text{ mm}^4$. Substituting these values into the equation for $L$, we get:<\/p>\n<p>$$L = \\sqrt{\\frac{384 \\times 200 \\times 10^9 \\text{ Pa}}{0.002 \\text{ rad}}} = 12 \\text{ m}$$<\/p>\n<p>Therefore, the length of the joist is 12 m.<\/p>\n<p>Option A is incorrect because the maximum deflection of a simply supported beam is not equal to 10 mm. Option C is incorrect because the slope at the ends of a simply supported beam is not equal to 0.002 radian. Option D is incorrect because the length of the joist is not equal to 16 m.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;10 m&#8221; option2=&#8221;12 m&#8221; option3=&#8221;14 m&#8221; option4=&#8221;16 m&#8221; correct=&#8221;option2&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[639],"tags":[],"class_list":["post-5665","post","type-post","status-publish","format-standard","hentry","category-theory-of-structures","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;10 m&#8221; option2=&#8221;12 m&#8221; option3=&#8221;14 m&#8221; option4=&#8221;16 m&#8221; correct=&#8221;option2&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:16:59+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m","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:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/","og_locale":"en_US","og_type":"article","og_title":"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m","og_description":"[amp_mcq option1=&#8221;10 m&#8221; option2=&#8221;12 m&#8221; option3=&#8221;14 m&#8221; option4=&#8221;16 m&#8221; correct=&#8221;option2&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:16:59+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/","name":"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T02:16:59+00:00","dateModified":"2024-04-15T02:16:59+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-rolled-steel-joist-is-simply-supported-at-its-ends-and-carries-a-uniformly-distributed-load-which-causes-a-maximum-deflection-of-10-mm-and-slope-at-the-ends-of-0-002-radian-the-length-of-the-joist\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Civil engineering","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/"},{"@type":"ListItem","position":4,"name":"Theory of structures","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/theory-of-structures\/"},{"@type":"ListItem","position":5,"name":"A rolled steel joist is simply supported at its ends and carries a uniformly distributed load which causes a maximum deflection of 10 mm and slope at the ends of 0.002 radian. The length of the joist will be, A. 10 m B. 12 m C. 14 m D. 16 m"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/5665","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=5665"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/5665\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=5665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=5665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=5665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}