{"id":5670,"date":"2024-04-15T02:17:03","date_gmt":"2024-04-15T02:17:03","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5670"},"modified":"2024-04-15T02:17:03","modified_gmt":"2024-04-15T02:17:03","slug":"the-maximum-deflection-due-to-a-load-w-at-the-free-end-of-a-cantilever-of-length-l-and-having-flexural-rigidity-ei-is-a-fractextwtextl22textei-b-frac","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-maximum-deflection-due-to-a-load-w-at-the-free-end-of-a-cantilever-of-length-l-and-having-flexural-rigidity-ei-is-a-fractextwtextl22textei-b-frac\/","title":{"rendered":"The maximum deflection due to a load W at the free end of a cantilever of length L and having flexural rigidity E$$I$$, is A. $$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{2{\\text{E}}I}}$$ B. $$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{3{\\text{E}}I}}$$ C. $$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{2{\\text{E}}I}}$$ D. $$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{2{\\text{E}}I}}$$&#8221; option2=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{3{\\text{E}}I}}$$&#8221; option3=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{2{\\text{E}}I}}$$&#8221; option4=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$.<\/p>\n<p>The maximum deflection due to a load $W$ at the free end of a cantilever of length $L$ and having flexural rigidity $EI$ is given by the following equation:<\/p>\n<p>$$\\delta = \\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\delta$ is the maximum deflection,<\/li>\n<li>$W$ is the load,<\/li>\n<li>$L$ is the length of the cantilever,<\/li>\n<li>$E$ is the Young&#8217;s modulus, and<\/li>\n<li>$I$ is the moment of inertia.<\/li>\n<\/ul>\n<p>The equation can be derived using the following steps:<\/p>\n<ol>\n<li>Assume that the cantilever is a uniform beam with a constant cross-section.<\/li>\n<li>Apply the principle of superposition to find the deflection of the beam due to the load $W$.<\/li>\n<li>The deflection of the beam due to the load $W$ is given by the following equation:<\/li>\n<\/ol>\n<p>$$\\delta = \\frac{{M}}{{EI}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$M$ is the bending moment at the free end of the beam,<\/li>\n<li>$E$ is the Young&#8217;s modulus, and<\/li>\n<li>\n<p>$I$ is the moment of inertia.<\/p>\n<\/li>\n<li>\n<p>The bending moment at the free end of the beam is given by the following equation:<\/p>\n<\/li>\n<\/ul>\n<p>$$M = WL$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$W$ is the load, and<\/li>\n<li>\n<p>$L$ is the length of the cantilever.<\/p>\n<\/li>\n<li>\n<p>Substituting equation (2) into equation (3) gives the following equation:<\/p>\n<\/li>\n<\/ul>\n<p>$$\\delta = \\frac{{WL}}{{EI}}$$<\/p>\n<ol>\n<li>The maximum deflection occurs at the free end of the beam, where the bending moment is maximum.<\/li>\n<li>The maximum deflection is given by the following equation:<\/li>\n<\/ol>\n<p>$$\\delta = \\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{2{\\text{E}}I}}$$&#8221; option2=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{3{\\text{E}}I}}$$&#8221; option3=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{2{\\text{E}}I}}$$&#8221; option4=&#8221;$$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$&#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":[639],"tags":[],"class_list":["post-5670","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>The maximum deflection due to a load W at the free end of a cantilever of length L and having flexural rigidity E$$I$$, is A. $$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{2{\\text{E}}I}}$$ B. $$\\frac{{{\\text{W}}{{\\text{L}}^2}}}{{3{\\text{E}}I}}$$ C. $$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{2{\\text{E}}I}}$$ D. $$\\frac{{{\\text{W}}{{\\text{L}}^3}}}{{3{\\text{E}}I}}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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