{"id":156553,"date":"2023-08-31T14:59:11","date_gmt":"2023-08-31T09:29:11","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156553"},"modified":"2023-08-31T14:59:13","modified_gmt":"2023-08-31T09:29:13","slug":"consider-a-prismatic-straight-beam-of-length-%f0%9d%90%bf-%f0%9d%9c%8b-m-pinned-at-the-two-ends-as-shown-in-the-figure-the-beam-has-a-square-cross-section-of-side-p-6-mm","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-a-prismatic-straight-beam-of-length-%f0%9d%90%bf-%f0%9d%9c%8b-m-pinned-at-the-two-ends-as-shown-in-the-figure-the-beam-has-a-square-cross-section-of-side-p-6-mm\/","title":{"rendered":"Consider a prismatic straight beam of length \ud835\udc3f = \ud835\udf0b m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side p = 6 mm"},"content":{"rendered":"\n<p> Q. <span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt;\">Consider a prismatic straight beam of length <\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt; font-family: &quot;Cambria Math&quot;, serif;\">\ud835\udc3f = \ud835\udf0b <\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt;\">m, pinned at the two ends as shown in<span style=\"letter-spacing:.05pt\"> <\/span>the<span style=\"letter-spacing:.85pt\"> <\/span>figure.<span style=\"letter-spacing:.9pt\"> <\/span>The<span style=\"letter-spacing:.8pt\"> <\/span>beam<span style=\"letter-spacing:.95pt\"> <\/span>has<span style=\"letter-spacing:1.0pt\"> <\/span>a<span style=\"letter-spacing:.9pt\"> <\/span>square<span style=\"letter-spacing:.9pt\"> <\/span>cross-section<span style=\"letter-spacing:\n.9pt\"> <\/span>of<span style=\"letter-spacing:.9pt\"> <\/span>side<span style=\"letter-spacing:.95pt\"> <\/span><i>p<span style=\"letter-spacing:.95pt\"> <\/span><\/i>=<span style=\"letter-spacing:.85pt\"> <\/span>6<span style=\"letter-spacing:.9pt\"> <\/span>mm.<span style=\"letter-spacing:.85pt\"> <\/span>The<span style=\"letter-spacing:.95pt\"> <\/span>Young\u2019s<span style=\"letter-spacing:.85pt\"> <\/span>modulus<span style=\"letter-spacing:-2.85pt\"> <\/span><i>E <\/i>= 200 GPa, and the coefficient of thermal expansion <\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt; font-family: &quot;Cambria Math&quot;, serif;\">\ud835\udefc = 3 \u00d7 10<sup>\u22126<\/sup> K<sup>\u22121<\/sup><\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt;\">. The minimum<span style=\"letter-spacing:.05pt\"> <\/span>temperature<span style=\"letter-spacing:\n-.1pt\"> <\/span>rise<span style=\"letter-spacing:-.1pt\"> <\/span>required<span style=\"letter-spacing:.05pt\"> <\/span>to cause<span style=\"letter-spacing:-.1pt\"> <\/span>Euler<span style=\"letter-spacing:-.05pt\"> <\/span>buckling<span style=\"letter-spacing:-.05pt\"> <\/span>of<span style=\"letter-spacing:-.05pt\"> <\/span>the<span style=\"letter-spacing:-.15pt\"> <\/span>beam<span style=\"letter-spacing:-.05pt\"> <\/span>is<u>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/u><\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt; font-family: &quot;Cambria Math&quot;, serif;\">K<\/span><span style=\"text-align: justify; background-color: var(--base-3); color: var(--contrast); font-size: 12pt;\">.<\/span> <\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"477\" height=\"391\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-672.png\" alt=\"\" class=\"wp-image-156554\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-672.png 477w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-672-300x246.png 300w\" sizes=\"auto, (max-width: 477px) 100vw, 477px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. Consider a prismatic straight beam of length \ud835\udc3f = \ud835\udf0b m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side p = 6 mm. The Young\u2019s modulus E = 200 GPa, and the coefficient of thermal expansion \ud835\udefc = 3 \u00d7 10\u22126 K\u22121. The minimum [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156555,"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-156553","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\/156553","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=156553"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156553\/revisions"}],"predecessor-version":[{"id":156556,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156553\/revisions\/156556"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156555"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}