{"id":153826,"date":"2023-08-01T11:35:53","date_gmt":"2023-08-01T06:05:53","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=153826"},"modified":"2023-08-01T11:35:57","modified_gmt":"2023-08-01T06:05:57","slug":"a-plane-frame-shown-in-the-figure-not-to-scale-has-linear-elastic-springs-at-node-h-the-spring-constants-are-kx-ky-5-x-105-kn-m-and-kq-3-x-105-knm-rad","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-plane-frame-shown-in-the-figure-not-to-scale-has-linear-elastic-springs-at-node-h-the-spring-constants-are-kx-ky-5-x-105-kn-m-and-kq-3-x-105-knm-rad\/","title":{"rendered":"A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 \u00d7 105 kN\/m and kq\u00a0= 3 \u00d7 105 kNm\/rad"},"content":{"rendered":"\n<p>Q. A plane frame shown in the figure (<em>not to scale<\/em>) has linear elastic springs at node H. The spring constants are <em>kx <\/em>= <em>ky <\/em>= 5 \u00d7 10<sup>5<\/sup> <em>kN\/m <\/em>and <em>k<\/em>q\u00a0= 3 \u00d7 10<sup>5<\/sup> <em>kNm\/rad<\/em>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-462.png\" alt=\"\" class=\"wp-image-153827\" width=\"334\" height=\"334\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-462.png 459w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-462-300x300.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-462-150x150.png 150w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/figure>\n\n\n\n<p>For the externally applied moment of 30 <em>kNm <\/em>at node F, the rotation (in <strong><em>degrees<\/em><\/strong><em>, round off to 3 decimals<\/em>) observed in the rotational spring at node H is <\/p>\n\n\n\n<p>\u00a0Solution:<\/p>\n\n\n\n<p>Since horizontal reaction at E = Hc = 0 <\/p>\n\n\n\n<p>Bending moment at F for member FE = MFE = 0 <\/p>\n\n\n\n<p>Member FH behaves like propped cantilever beam\u00a0\u00a0\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"81\" height=\"25\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-463.png\" alt=\"\" class=\"wp-image-153828\"\/><\/figure>\n\n\n\n<p>30 kNm = 3 \u00d7 10<sup>5<\/sup> kNm\/rad \u00d7 \u03b8 <\/p>\n\n\n\n<p>\u21d2 \u03b8 = 1 \u00d7 10<sup>-4<\/sup> radians = 0.0057\u00b0<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 \u00d7 105 kN\/m and kq\u00a0= 3 \u00d7 105 kNm\/rad. For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":153829,"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-153826","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\/153826","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=153826"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153826\/revisions"}],"predecessor-version":[{"id":153830,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153826\/revisions\/153830"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/153829"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=153826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=153826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=153826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}