{"id":189095,"date":"2025-02-08T18:39:39","date_gmt":"2025-02-08T18:39:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189095"},"modified":"2025-02-08T18:39:42","modified_gmt":"2025-02-08T18:39:42","slug":"a-c7-x-9-8-tension-member-is-connected-to-a-3%e2%81%848-in-thick-gusset-plate","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/08\/a-c7-x-9-8-tension-member-is-connected-to-a-3%e2%81%848-in-thick-gusset-plate\/","title":{"rendered":"A C7 \u00d7 9.8 tension member is connected to a 3\u20448-in.-thick gusset plate"},"content":{"rendered":"\n<p>A C7 \u00d7 9.8 tension member is connected to a 3\u20448-in.-thick gusset plate as shown in Figure P3.5-5. Both the member and the gusset plate are A36 steel.<\/p>\n\n\n\n<p>a. Compute the available block shear strength of the tension member for both LRFD and ASD.<\/p>\n\n\n\n<p>b. Compute the available block shear strength of the gusset plate for both LRFD and ASD.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-177.png\" alt=\"\" class=\"wp-image-189096\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To compute the available block shear strength of the tension member and the gusset plate, we will use the Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD) methods, as specified by the American Institute of Steel Construction (AISC) for A36 steel.<\/p>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tension Member:<\/strong> C7 \u00d7 9.8 channel section<\/li>\n\n\n\n<li><strong>Gusset Plate Thickness:<\/strong> 3\/8 inches<\/li>\n\n\n\n<li><strong>Material:<\/strong> A36 steel (Fy = 36 ksi, Fu = 58 ksi)<\/li>\n<\/ul>\n\n\n\n<p><strong>a. Available Block Shear Strength of the Tension Member<\/strong><\/p>\n\n\n\n<p><em>LRFD Method:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Gross Area in Shear (Agv):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Agv = 2 \u00d7 (height of the channel) \u00d7 (thickness of the flange)<\/li>\n\n\n\n<li>Agv = 2 \u00d7 (7 inches) \u00d7 (0.375 inches) = 5.25 in\u00b2<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Net Area in Shear (Anv):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Anv = Agv &#8211; (number of bolt holes \u00d7 area of one bolt hole)<\/li>\n\n\n\n<li>Assuming 2 bolt holes of 0.75 inches diameter:\n<ul class=\"wp-block-list\">\n<li>Area of one bolt hole = \u03c0 \u00d7 (0.75\/2)\u00b2 \u2248 0.4418 in\u00b2<\/li>\n\n\n\n<li>Anv = 5.25 in\u00b2 &#8211; 2 \u00d7 0.4418 in\u00b2 \u2248 4.3664 in\u00b2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Net Area in Tension (Ant):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ant = (width of the flange &#8211; (number of bolt holes \u00d7 diameter of bolt)) \u00d7 thickness of the flange<\/li>\n\n\n\n<li>Ant = (7 inches &#8211; 2 \u00d7 0.75 inches) \u00d7 0.375 inches = 4.5 inches \u00d7 0.375 inches = 1.6875 in\u00b2<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Nominal Block Shear Strength (Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 Fu \u00d7 Anv + Ubs \u00d7 Fu \u00d7 Ant<\/li>\n\n\n\n<li>Assuming Ubs = 1.0 for uniform tension stress:\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 58 ksi \u00d7 4.3664 in\u00b2 + 1.0 \u00d7 58 ksi \u00d7 1.6875 in\u00b2 \u2248 151.5 kips + 97.8 kips = 249.3 kips<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Design Strength (\u03c6Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03c6 = 0.75 (for tension members)<\/li>\n\n\n\n<li>\u03c6Rn = 0.75 \u00d7 249.3 kips \u2248 187 kips<\/li>\n<\/ul>\n\n\n\n<p><em>ASD Method:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Allowable Block Shear Strength (Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 Fy \u00d7 Anv + Ubs \u00d7 Fu \u00d7 Ant<\/li>\n\n\n\n<li>Rn = 0.6 \u00d7 36 ksi \u00d7 4.3664 in\u00b2 + 1.0 \u00d7 58 ksi \u00d7 1.6875 in\u00b2 \u2248 94.5 kips + 97.8 kips = 192.3 kips<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Allowable Strength (Rn\/\u03a9):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03a9 = 2.0 (for ASD)<\/li>\n\n\n\n<li>Rn\/\u03a9 = 192.3 kips \/ 2.0 \u2248 96.15 kips<\/li>\n<\/ul>\n\n\n\n<p><strong>b. Available Block Shear Strength of the Gusset Plate<\/strong><\/p>\n\n\n\n<p><em>LRFD Method:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Gross Area in Shear (Agv):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Agv = (number of bolt lines) \u00d7 (thickness of the gusset plate) \u00d7 (distance between bolt lines)<\/li>\n\n\n\n<li>Agv = 2 \u00d7 0.375 inches \u00d7 3 inches = 2.25 in\u00b2<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Net Area in Shear (Anv):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Anv = Agv &#8211; (number of bolt holes \u00d7 area of one bolt hole)<\/li>\n\n\n\n<li>Anv = 2.25 in\u00b2 &#8211; 2 \u00d7 0.4418 in\u00b2 \u2248 1.3664 in\u00b2<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Nominal Block Shear Strength (Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 Fu \u00d7 Anv + Ubs \u00d7 Fu \u00d7 Ant<\/li>\n\n\n\n<li>Assuming Ubs = 1.0 for uniform tension stress:\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 58 ksi \u00d7 1.3664 in\u00b2 + 1.0 \u00d7 58 ksi \u00d7 1.6875 in\u00b2 \u2248 47.6 kips + 97.8 kips = 145.4 kips<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Design Strength (\u03c6Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03c6 = 0.75 (for tension members)<\/li>\n\n\n\n<li>\u03c6Rn = 0.75 \u00d7 145.4 kips \u2248 109.05 kips<\/li>\n<\/ul>\n\n\n\n<p><em>ASD Method:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Allowable Block Shear Strength (Rn):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rn = 0.6 \u00d7 Fy \u00d7 Anv + Ubs \u00d7 Fu \u00d7 Ant<\/li>\n\n\n\n<li>Rn = 0.6 \u00d7 36 ksi \u00d7 1.3664 in\u00b2 + 1.0 \u00d7 58 ksi \u00d7 1.6875 in\u00b2 \u2248 29.5 kips + 97.8 kips = 127.3 kips<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculate the Allowable Strength (Rn\/\u03a9):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03a9 = 2.0 (for ASD)<\/li>\n\n\n\n<li>Rn\/\u03a9 = 127.3 kips \/ 2.0 \u2248 63.65 kips<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A C7 \u00d7 9.8 tension member is connected to a 3\u20448-in.-thick gusset plate as shown in Figure P3.5-5. Both the member and the gusset plate are A36 steel. a. Compute the available block shear strength of the tension member for both LRFD and ASD. b. Compute the available block shear strength of the gusset plate [&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-189095","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189095","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=189095"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189095\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189095"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189095"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189095"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}