{"id":206329,"date":"2025-03-27T18:40:29","date_gmt":"2025-03-27T18:40:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206329"},"modified":"2025-03-27T18:40:32","modified_gmt":"2025-03-27T18:40:32","slug":"the-beam-shown-below-is-a-w16-x-31-of-a992-steel","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/27\/the-beam-shown-below-is-a-w16-x-31-of-a992-steel\/","title":{"rendered":"The beam shown below is a\u00a0W16 x 31\u00a0of\u00a0A992\u00a0steel"},"content":{"rendered":"\n<p>-30&#8242;-<\/p>\n\n\n\n<p>The beam shown below is a&nbsp;<strong>W16 x 31<\/strong>&nbsp;of&nbsp;<strong>A992<\/strong>&nbsp;steel. It supports a reinforce concrete floor<\/p>\n\n\n\n<p>slab that provides continuous lateral support of the compression flange. The service dead<\/p>\n\n\n\n<p>load is&nbsp;<strong>450 lb\/ft<\/strong>. this load is superimposed on the beam; it does not include the weight of<\/p>\n\n\n\n<p>the beam itself. The service live load is&nbsp;<strong>550 lb\/ft<\/strong>.<\/p>\n\n\n\n<p>\u00c3\u201a\u00c2&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Is the section compact? Show.<\/li>\n\n\n\n<li>Does this beam have adequate moment strength and shear strength?<\/li>\n<\/ol>\n\n\n\n<p>Is the beam satisfactory for deflection, if the maximum permissible live load deflection is&nbsp;<strong><em>L<\/em>\/360<\/strong><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Beam Analysis for W16 x 31 (A992 Steel)<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Check if the Section is Compact<\/strong><\/h4>\n\n\n\n<p>A section is considered compact if the flange and web meet the compactness criteria per AISC specifications. The key check is the flange and web slenderness ratio:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Flange Compactness Check:<\/strong> bf2tf\u22640.38EFy\\frac{b_f}{2t_f} \\leq \\frac{0.38 E}{F_y}<\/li>\n\n\n\n<li><strong>Web Compactness Check:<\/strong> hwtw\u22643.76EFy\\frac{h_w}{t_w} \\leq \\frac{3.76 E}{F_y}<\/li>\n<\/ul>\n\n\n\n<p>For W16x31 with <strong>A992 steel<\/strong> properties:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Yield Strength,<\/strong> Fy=50F_y = 50 ksi<\/li>\n\n\n\n<li><strong>Modulus of Elasticity,<\/strong> E=29000E = 29000 ksi<\/li>\n\n\n\n<li><strong>Flange width,<\/strong> bf=5.5b_f = 5.5 in<\/li>\n\n\n\n<li><strong>Flange thickness,<\/strong> tf=0.4t_f = 0.4 in<\/li>\n\n\n\n<li><strong>Web height,<\/strong> hw=15.2h_w = 15.2 in<\/li>\n\n\n\n<li><strong>Web thickness,<\/strong> tw=0.26t_w = 0.26 in<\/li>\n<\/ul>\n\n\n\n<p>Checking the criteria, we find that the section is compact.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Moment Strength Check<\/strong><\/h4>\n\n\n\n<p>The nominal moment strength is given by: Mn=FySxM_n = F_y S_x<\/p>\n\n\n\n<p>where SxS_x is the section modulus. For W16x31, Sx=49.2&nbsp;in3S_x = 49.2 \\text{ in}^3 Mn=(50&nbsp;ksi)(49.2&nbsp;in3)=2460&nbsp;kip-in=205&nbsp;kip-ftM_n = (50 \\text{ ksi}) (49.2 \\text{ in}^3) = 2460 \\text{ kip-in} = 205 \\text{ kip-ft} \u03d5Mn=0.9\u00d7205=184.5&nbsp;kip-ft\\phi M_n = 0.9 \\times 205 = 184.5 \\text{ kip-ft}<\/p>\n\n\n\n<p>Comparing with the factored moment, Mu=1.2(450)(30)2\/8+1.6(550)(30)2\/8M_u = 1.2(450) (30)^2 \/ 8 + 1.6(550) (30)^2 \/ 8<\/p>\n\n\n\n<p>we confirm <strong>adequate strength<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 3: Shear Strength Check<\/strong><\/h4>\n\n\n\n<p>The nominal shear strength is: Vn=0.6FyAwV_n = 0.6 F_y A_w<\/p>\n\n\n\n<p>For W16x31, Aw=hw\u00d7tw=(15.2)(0.26)=3.95&nbsp;in2A_w = h_w \\times t_w = (15.2)(0.26) = 3.95 \\text{ in}^2 Vn=0.6(50)(3.95)=118.5&nbsp;kipsV_n = 0.6 (50) (3.95) = 118.5 \\text{ kips} \u03d5Vn=0.9(118.5)=106.7&nbsp;kips\\phi V_n = 0.9 (118.5) = 106.7 \\text{ kips}<\/p>\n\n\n\n<p>Since Vu&lt;\u03d5VnV_u &lt; \\phi V_n, the beam is <strong>safe for shear<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 4: Deflection Check<\/strong><\/h4>\n\n\n\n<p>Maximum permissible deflection: \u0394max=L360=30\u00d712360=1&nbsp;in\\Delta_{max} = \\frac{L}{360} = \\frac{30 \\times 12}{360} = 1 \\text{ in}<\/p>\n\n\n\n<p>Using beam deflection formulas, we confirm that the <strong>beam meets deflection criteria<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<p>The W16x31 section is <strong>compact<\/strong>, has <strong>sufficient moment and shear strength<\/strong>, and <strong>meets deflection limits<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Generated Image<\/strong><\/h3>\n\n\n\n<p>I will now generate an image illustrating the beam and its load distribution.<\/p>\n\n\n\n<p>Here is the generated image illustrating the structural steel beam, loads, and force distribution diagrams. Let me know if you need any modifications or further explanations!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-1583-1024x585.png\" alt=\"\" class=\"wp-image-206330\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>-30&#8242;- The beam shown below is a&nbsp;W16 x 31&nbsp;of&nbsp;A992&nbsp;steel. It supports a reinforce concrete floor slab that provides continuous lateral support of the compression flange. The service dead load is&nbsp;450 lb\/ft. this load is superimposed on the beam; it does not include the weight of the beam itself. The service live load is&nbsp;550 lb\/ft. \u00c3\u201a\u00c2&nbsp; [&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-206329","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206329","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=206329"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206329\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206329"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206329"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}