{"id":5681,"date":"2024-04-15T02:17:12","date_gmt":"2024-04-15T02:17:12","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5681"},"modified":"2024-04-15T02:17:12","modified_gmt":"2024-04-15T02:17:12","slug":"a-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/","title":{"rendered":"A square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be A. $$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$ B. $$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$ C. $$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$ D. $$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$&#8221; option2=&#8221;$$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; option3=&#8221;$$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; option4=&#8221;$$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; correct=&#8221;option3&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$.<\/p>\n<p>The bending stress is calculated by the following formula:<\/p>\n<p>$$\\sigma = \\frac{M}{I}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\sigma$ is the bending stress<\/li>\n<li>$M$ is the bending moment<\/li>\n<li>$I$ is the moment of inertia<\/li>\n<\/ul>\n<p>The bending moment is calculated by the following formula:<\/p>\n<p>$$M = P\\cdot d$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$M$ is the bending moment<\/li>\n<li>$P$ is the load<\/li>\n<li>$d$ is the distance from the load to the centroid of the beam<\/li>\n<\/ul>\n<p>The moment of inertia of a square beam is calculated by the following formula:<\/p>\n<p>$$I = \\frac{1}{36}{\\text{a}^4}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$I$ is the moment of inertia<\/li>\n<li>$a$ is the side of the square<\/li>\n<\/ul>\n<p>Substituting the expressions for $M$ and $I$ into the expression for $\\sigma$, we get:<\/p>\n<p>$$\\sigma = \\frac{{P\\cdot d}}{{\\frac{1}{36}{\\text{a}^4}}}$$<\/p>\n<p>$$\\sigma = \\frac{{36{\\text{P}}}}{{{{\\text{a}}^4}}}\\cdot d$$<\/p>\n<p>In this case, the load is applied at the centroid of one of the quarters of the square. The distance from the load to the centroid of the beam is $\\frac{a}{2}$. Therefore, the bending stress is:<\/p>\n<p>$$\\sigma = \\frac{{36{\\text{P}}}}{{{{\\text{a}}^4}}}\\cdot \\frac{a}{2}$$<\/p>\n<p>$$\\sigma = \\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$&#8221; option2=&#8221;$$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; option3=&#8221;$$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; option4=&#8221;$$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$&#8221; correct=&#8221;option3&#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-5681","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 square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be A. $$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$ B. $$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$ C. $$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$ D. $$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$<\/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-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be A. $$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$ B. $$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$ C. $$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$ D. $$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;$$frac{{text{P}}}{{{{text{a}}^2}}}$$&#8221; option2=&#8221;$$frac{{2{text{P}}}}{{{{text{a}}^2}}}$$&#8221; option3=&#8221;$$frac{{3{text{P}}}}{{{{text{a}}^2}}}$$&#8221; option4=&#8221;$$frac{{4{text{P}}}}{{{{text{a}}^2}}}$$&#8221; correct=&#8221;option3&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:17:12+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 square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be A. $$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$ B. $$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$ C. $$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$ D. $$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$","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-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/","og_locale":"en_US","og_type":"article","og_title":"A square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be A. $$\\frac{{\\text{P}}}{{{{\\text{a}}^2}}}$$ B. $$\\frac{{2{\\text{P}}}}{{{{\\text{a}}^2}}}$$ C. $$\\frac{{3{\\text{P}}}}{{{{\\text{a}}^2}}}$$ D. $$\\frac{{4{\\text{P}}}}{{{{\\text{a}}^2}}}$$","og_description":"[amp_mcq option1=&#8221;$$frac{{text{P}}}{{{{text{a}}^2}}}$$&#8221; option2=&#8221;$$frac{{2{text{P}}}}{{{{text{a}}^2}}}$$&#8221; option3=&#8221;$$frac{{3{text{P}}}}{{{{text{a}}^2}}}$$&#8221; option4=&#8221;$$frac{{4{text{P}}}}{{{{text{a}}^2}}}$$&#8221; correct=&#8221;option3&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:17:12+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-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-square-column-carries-a-load-p-at-the-centroid-of-one-of-the-quarters-of-the-square-if-a-is-the-side-of-the-main-square-the-combined-bending-stress-will-be-a-fractextptexta2\/","name":"A square column carries a load P at the centroid of one of the quarters of the square. 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