{"id":5708,"date":"2024-04-15T02:17:35","date_gmt":"2024-04-15T02:17:35","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5708"},"modified":"2024-04-15T02:17:35","modified_gmt":"2024-04-15T02:17:35","slug":"a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/","title":{"rendered":"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$&#8221; option2=&#8221;$$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$&#8221; option3=&#8221;$$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$&#8221; option4=&#8221;$$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}}$.<\/p>\n<p>The maximum dip $h$ of a pre-stressed rectangular beam which carries two concentrated loads $W$ at $\\frac{{\\text{L}}}{3}$ from either end, is provided with a bent tendon with tension $P$ such that central one-third portion of the tendon remains parallel to the longitudinal axis, can be calculated using the following formula:<\/p>\n<p>$$h = \\frac{{3{\\text{WL}}}}{{4{\\text{P}}}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$h$ is the maximum dip of the beam,<\/li>\n<li>$W$ is the concentrated load,<\/li>\n<li>$L$ is the length of the beam, and<\/li>\n<li>$P$ is the tension in the tendon.<\/li>\n<\/ul>\n<p>The formula can be derived by considering the equilibrium of the beam. The beam is subjected to two concentrated loads $W$ at $\\frac{{\\text{L}}}{3}$ from either end, and a tensile force $P$ in the tendon. The beam is also supported by two reactions at the ends. The reactions at the ends must be equal and opposite in order to maintain equilibrium.<\/p>\n<p>The bending moment at any point along the beam can be calculated using the following formula:<\/p>\n<p>$$M = \\frac{{W{\\text{L}}}}{{6}} &#8211; \\frac{{P{\\text{x}}}}{{2}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$M$ is the bending moment,<\/li>\n<li>$W$ is the concentrated load,<\/li>\n<li>$L$ is the length of the beam,<\/li>\n<li>$x$ is the distance from the left end of the beam, and<\/li>\n<li>$P$ is the tension in the tendon.<\/li>\n<\/ul>\n<p>The maximum bending moment occurs at the center of the beam, where $x = \\frac{{L}}{2}$. The maximum bending moment is then:<\/p>\n<p>$$M_{\\max} = \\frac{{W{\\text{L}}}}{{12}} &#8211; \\frac{{P{\\text{L}}}}{{4}}$$<\/p>\n<p>The maximum deflection of the beam can be calculated using the following formula:<\/p>\n<p>$$\\delta = \\frac{{M_{\\max}{\\text{L}}^{3}}}{{3EI}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\delta$ is the maximum deflection,<\/li>\n<li>$M_{\\max}$ is the maximum bending moment,<\/li>\n<li>$L$ is the length of the beam,<\/li>\n<li>$E$ is the Young&#8217;s modulus of the beam, and<\/li>\n<li>$I$ is the moment of inertia of the beam.<\/li>\n<\/ul>\n<p>The moment of inertia of a rectangular beam can be calculated using the following formula:<\/p>\n<p>$$I = \\frac{{\\text{bh}^{3}}}{{12}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$I$ is the moment of inertia,<\/li>\n<li>$b$ is the width of the beam,<\/li>\n<li>$h$ is the height of the beam.<\/li>\n<\/ul>\n<p>Substituting the formula for $M_{\\max}$ into the formula for $\\delta$, we get:<\/p>\n<p>$$\\delta = \\frac{{\\frac{{W{\\text{L}}}}{{12}} &#8211; \\frac{{P{\\text{L}}}}{{4}}{\\text{L}}^{3}}}{{3EI}}$$<\/p>\n<p>$$\\delta = \\frac{{WL^{4}}}{{144EI}} &#8211; \\frac{{PL^{3}}}{{36EI}}$$<\/p>\n<p>$$\\delta = \\frac{{WL^{4}}}{{144EI}} &#8211; \\frac{{2PL^{3}}}{{36EI}}$$<\/p>\n<p>$$\\delta = \\frac{{WL^{4}}}{{144EI}} &#8211; \\frac{{WL^{3}}}{{18EI}}$$<\/p>\n<p>$$\\delta = \\frac{{WL^{3}}}{{18EI}}$$<\/p>\n<p>The maximum dip $h$ is equal to the maximum deflection $\\delta$ divided by two. Therefore, the maximum dip $h$ is:<\/p>\n<p>$$h = \\frac{{\\delta}}{2} = \\frac{{\\frac{{WL^{3}}}{{18EI}}}}{2} = \\frac{{WL^{3}}}{{36EI}}$$<\/p>\n<p>$$h = \\frac{{3{\\text{WL}}}}{{4{\\text{P}}}}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$&#8221; option2=&#8221;$$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$&#8221; option3=&#8221;$$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$&#8221; option4=&#8221;$$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[640],"tags":[],"class_list":["post-5708","post","type-post","status-publish","format-standard","hentry","category-rcc-structures-design","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 pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$<\/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-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;$$frac{{{text{WL}}}}{{text{P}}}$$&#8221; option2=&#8221;$$frac{{{text{WL}}}}{{2{text{P}}}}$$&#8221; option3=&#8221;$$frac{{{text{WL}}}}{{3{text{P}}}}$$&#8221; option4=&#8221;$$frac{{{text{WL}}}}{{4{text{P}}}}$$&#8221; correct=&#8221;option1&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:17:35+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$","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-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/","og_locale":"en_US","og_type":"article","og_title":"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$","og_description":"[amp_mcq option1=&#8221;$$frac{{{text{WL}}}}{{text{P}}}$$&#8221; option2=&#8221;$$frac{{{text{WL}}}}{{2{text{P}}}}$$&#8221; option3=&#8221;$$frac{{{text{WL}}}}{{3{text{P}}}}$$&#8221; option4=&#8221;$$frac{{{text{WL}}}}{{4{text{P}}}}$$&#8221; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:17:35+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/","name":"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T02:17:35+00:00","dateModified":"2024-04-15T02:17:35+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-pre-stressed-rectangular-beam-which-carries-two-concentrated-loads-w-at-fractextl3-from-either-end-is-provided-with-a-bent-tendon-with-tension-p-such-that-central-one-third-portion\/#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":"Rcc structures design","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/rcc-structures-design\/"},{"@type":"ListItem","position":5,"name":"A pre-stressed rectangular beam which carries two concentrated loads W at $$\\frac{{\\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is A. $$\\frac{{{\\text{WL}}}}{{\\text{P}}}$$ B. $$\\frac{{{\\text{WL}}}}{{2{\\text{P}}}}$$ C. $$\\frac{{{\\text{WL}}}}{{3{\\text{P}}}}$$ D. $$\\frac{{{\\text{WL}}}}{{4{\\text{P}}}}$$"}]},{"@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\/5708","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=5708"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/5708\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=5708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=5708"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=5708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}