{"id":157887,"date":"2023-09-07T14:42:23","date_gmt":"2023-09-07T09:12:23","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157887"},"modified":"2023-09-07T14:42:27","modified_gmt":"2023-09-07T09:12:27","slug":"a-uniform-cantilever-beam-abc-of-length-l-is-subjected-to-a-point-load-p-at-point-b-and-a-concentrated-moment-m-at-point-c","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-uniform-cantilever-beam-abc-of-length-l-is-subjected-to-a-point-load-p-at-point-b-and-a-concentrated-moment-m-at-point-c\/","title":{"rendered":"A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a concentrated moment M at point C"},"content":{"rendered":"\n<p>Q. A uniform cantilever beam <em>ABC <\/em>of length <em>L <\/em>is subjected to a point load <em>P <\/em>at point <em>B <\/em>and a concentrated moment <em>M <\/em>at point <em>C <\/em>(as shown in figure). Let <em>E <\/em>be the Young\u2019s modulus of the beam material and <em>I <\/em>be the area moment of inertia of the beam\u2019s cross-section. Assuming the validity of the Euler-Bernoulli theory of slender beams, the downward deflection at point <em>C <\/em>is<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-832.png\" alt=\"\" class=\"wp-image-157888\" style=\"width:375px;height:189px\" width=\"375\" height=\"189\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-832.png 493w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-832-300x152.png 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"815\" height=\"83\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-833.png\" alt=\"\" class=\"wp-image-157889\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-833.png 815w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-833-300x31.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-833-768x78.png 768w\" sizes=\"auto, (max-width: 815px) 100vw, 815px\" \/><\/figure>\n\n\n\n<p>Ans: Option D<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Now, the deflection at C = deflection at C due to load P + deflection at C due to moment M \u21d2\u00a0deflection at B due to load P\u00a0+ slope at B due to load P\u00a0\u00d7 length between B and C + deflection at C due to moment M<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"386\" height=\"121\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-834.png\" alt=\"\" class=\"wp-image-157899\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-834.png 386w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-834-300x94.png 300w\" sizes=\"auto, (max-width: 386px) 100vw, 386px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a concentrated moment M at point C (as shown in figure). Let E be the Young\u2019s modulus of the beam material and I be the area moment of inertia of the beam\u2019s cross-section. Assuming the [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":157900,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-157887","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157887","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=157887"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157887\/revisions"}],"predecessor-version":[{"id":157904,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157887\/revisions\/157904"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157900"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}