{"id":256860,"date":"2025-07-16T14:01:44","date_gmt":"2025-07-16T14:01:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256860"},"modified":"2025-07-16T14:01:46","modified_gmt":"2025-07-16T14:01:46","slug":"determine-the-force-in-members-bc-hc-and-hg-using-the-method-of-sections","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/determine-the-force-in-members-bc-hc-and-hg-using-the-method-of-sections\/","title":{"rendered":"Determine the force in members BC, HC, and HG using the method of sections"},"content":{"rendered":"\n<p>Determine the force in members BC, HC, and HG using the method of sections. State if these members are in tension or compression. 5 kN 4 kN 4 kN 3 kN 2 kN B C D A E 3 m H F + 2 m G 5 m 5 m 5m5m<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-482.png\" alt=\"\" class=\"wp-image-256864\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here are the final answers and a detailed explanation of the solution.<\/p>\n\n\n\n<p><strong>Final Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The force in member\u00a0<strong>BC<\/strong>\u00a0is\u00a0<strong>20.5 kN in compression<\/strong>.<\/li>\n\n\n\n<li>The force in member\u00a0<strong>HC<\/strong>\u00a0is\u00a0<strong>12.0 kN in tension<\/strong>.<\/li>\n\n\n\n<li>The force in member\u00a0<strong>HG<\/strong>\u00a0is\u00a0<strong>29.0 kN in tension<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>This problem is solved using the Method of Sections, which allows us to find the forces in specific members without analyzing the entire truss joint by joint.<\/p>\n\n\n\n<p><strong>1. Calculate Support Reactions<\/strong><\/p>\n\n\n\n<p>First, we must determine the external support reactions at points A and E by treating the entire truss as a rigid body. The support at A is a roller, providing a vertical reaction (Ay). The support at E is a pin, providing both vertical (Ey) and horizontal (Ex) reactions.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sum of Horizontal Forces (\u03a3Fx = 0):<\/strong>\u00a0Since there are no external horizontal loads, the horizontal reaction at E is zero.\n<ul class=\"wp-block-list\">\n<li>Ex = 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Sum of Moments about Point E (\u03a3ME = 0):<\/strong>\u00a0We sum the moments about pin E to find the reaction at A. We will consider counter-clockwise moments as positive.\n<ul class=\"wp-block-list\">\n<li>(Ay * 12 m) &#8211; (12 kN * 9 m) &#8211; (14 kN * 6 m) &#8211; (18 kN * 3 m) = 0<\/li>\n\n\n\n<li>12Ay &#8211; 108 kNm &#8211; 84 kNm &#8211; 54 kNm = 0<\/li>\n\n\n\n<li>12Ay = 246 kNm<\/li>\n\n\n\n<li><strong>Ay = 20.5 kN<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Make a Section Cut<\/strong><\/p>\n\n\n\n<p>To find the forces in members BC, HC, and HG, we make a vertical cut through these three members. This separates the truss into a left and a right section. We will analyze the left section for equilibrium.<\/p>\n\n\n\n<p><strong>3. Analyze the Left Section<\/strong><\/p>\n\n\n\n<p>We draw a free-body diagram of the left section, which includes joints A, B, and H. The forces acting on this section are the upward reaction Ay (20.5 kN), the downward load at B (12 kN), and the internal forces from the cut members: F_BC, F_HC, and F_HG. We assume all unknown forces are in tension (pulling away from the section).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Find Force in HG (F_HG):<\/strong>\u00a0To find F_HG, we sum the moments about point C. This point is chosen because the lines of action for F_BC and F_HC pass through it, so their moments are zero.\n<ul class=\"wp-block-list\">\n<li>\u03a3MC = 0<\/li>\n\n\n\n<li>(20.5 kN * 6 m) &#8211; (12 kN * 3 m) &#8211; (F_HG * 3 m) = 0<\/li>\n\n\n\n<li>123 kNm &#8211; 36 kNm = 3*F_HG<\/li>\n\n\n\n<li>87 kNm = 3*F_HG<\/li>\n\n\n\n<li><strong>F_HG = 29.0 kN<\/strong>. The positive result means our assumption of tension was correct.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Find Force in BC (F_BC):<\/strong>\u00a0To find F_BC, we can sum moments about point H. The forces F_HG and F_HC pass through H.\n<ul class=\"wp-block-list\">\n<li>\u03a3MH = 0<\/li>\n\n\n\n<li>(20.5 kN * 3 m) + (F_BC * 3 m) = 0<\/li>\n\n\n\n<li>61.5 kNm = -3*F_BC<\/li>\n\n\n\n<li><strong>F_BC = -20.5 kN<\/strong>. The negative sign indicates the force is opposite to our tension assumption, so the member is in\u00a0<strong>compression<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Find Force in HC (F_HC):<\/strong>\u00a0We can now find F_HC by summing the vertical forces. The angle of member HC with the vertical is 45 degrees, as the panel height and width are both 3 m.\n<ul class=\"wp-block-list\">\n<li>\u03a3Fy = 0<\/li>\n\n\n\n<li>20.5 kN &#8211; 12 kN &#8211; F_HC * sin(45\u00b0) = 0<\/li>\n\n\n\n<li>8.5 kN = F_HC * sin(45\u00b0)<\/li>\n\n\n\n<li>F_HC = 8.5 \/ sin(45\u00b0) = 8.5 \/ 0.7071<\/li>\n\n\n\n<li><strong>F_HC = 12.02 kN<\/strong>, which we round to\u00a0<strong>12.0 kN<\/strong>. The positive result confirms it is in\u00a0<strong>tension<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-183.jpeg\" alt=\"\" class=\"wp-image-256868\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Determine the force in members BC, HC, and HG using the method of sections. State if these members are in tension or compression. 5 kN 4 kN 4 kN 3 kN 2 kN B C D A E 3 m H F + 2 m G 5 m 5 m 5m5m The Correct Answer and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-256860","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256860","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=256860"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256860\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}