{"id":223111,"date":"2025-06-01T08:51:57","date_gmt":"2025-06-01T08:51:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223111"},"modified":"2025-06-01T08:52:00","modified_gmt":"2025-06-01T08:52:00","slug":"a-cantilever-wood-beam-consists-of-eight-2-in","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/a-cantilever-wood-beam-consists-of-eight-2-in\/","title":{"rendered":"A cantilever wood beam consists of eight 2 in"},"content":{"rendered":"\n<p>A cantilever wood beam consists of eight 2 in. thick planks glued together to form a cross section that is 16 in. deep. Each plank has a width of<br>in. The cantilever beam has a length of<br>ft and it supports a concentrated load of<br>lb. (a) Calculate the magnitude of the horizontal shear stress at points A, B, C, and D. (b) From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. Answer:<br>i psi<br>i psi<br>i psi<br>i psi<br>A cantilever wood beam consists of eight 2 in. thick planks glued together to form a cross section that is 16 in. deep. Each plank has a width of<br>in. The cantilever beam has a length of<br>ft and it supports a concentrated load of<br>lb. (a) Calculate the magnitude of the horizontal shear stress at points A, B, C, and D. (b) From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. Answer:<br>i psi<br>i psi<br>i psi<br>i psi<\/p>\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>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Width<\/strong> of each plank (in inches)<\/li>\n\n\n\n<li><strong>Length<\/strong> of the beam (in feet)<\/li>\n\n\n\n<li><strong>Magnitude of the concentrated load<\/strong> (in pounds)<\/li>\n\n\n\n<li>Clarification of the locations of points <strong>A, B, C, and D<\/strong> (typically they are taken at different heights in the cross-section, such as center of each plank)<\/li>\n<\/ul>\n\n\n\n<p>However, I can proceed with a <strong>general explanation and solution method<\/strong>, assuming:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8 planks, each 2 in. thick \u2192 total height = 16 in.<\/li>\n\n\n\n<li>Width of each plank = <strong>w<\/strong> in (you need to provide this)<\/li>\n\n\n\n<li>Load <strong>P<\/strong> applied at the free end of the cantilever beam of length <strong>L<\/strong><\/li>\n\n\n\n<li>Shear stress is highest at the neutral axis and zero at top\/bottom surfaces.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>General Procedure to Calculate Shear Stress<\/strong><\/h3>\n\n\n\n<p>Shear stress at a horizontal plane is calculated as: \u03c4=VQIb\\tau = \\frac{VQ}{Ib}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>VV: Shear force at the section<\/li>\n\n\n\n<li>QQ: First moment of area above\/below the point where stress is calculated<\/li>\n\n\n\n<li>II: Moment of inertia of the entire cross-section<\/li>\n\n\n\n<li>bb: Width at the point where the shear stress is being calculated<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step-by-Step Outline<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Cross Section Properties<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Height h=16\u2009inh = 16 \\, \\text{in}<\/li>\n\n\n\n<li>Each plank: 2\u2009in2 \\, \\text{in} high<\/li>\n\n\n\n<li>Moment of inertia I=112wh3I = \\frac{1}{12} w h^3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Shear Force (V)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>At the fixed end: V=PV = P<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>First Moment of Area (Q)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>For point A (top): zero<\/li>\n\n\n\n<li>For point B: compute QQ for area above mid-height of plank 2<\/li>\n\n\n\n<li>For C: include more area, centered around mid-height of plank 4<\/li>\n\n\n\n<li>For D: near neutral axis, QQ is largest<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Distribution of Shear Stress<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Shear stress is parabolic<\/strong>, maximum at mid-height (point D), zero at top and bottom.<\/li>\n\n\n\n<li>Numerical values depend on the input <strong>w, P, L<\/strong>, etc.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<p>To <strong>compute exact values in psi<\/strong> at A, B, C, D and plot the graph, I need:<\/p>\n\n\n\n<p>\u2705 Width of each plank<br>\u2705 Beam length<br>\u2705 Load magnitude<br>\u2705 Exact location of points A\u2013D<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-37.jpeg\" alt=\"\" class=\"wp-image-223112\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A cantilever wood beam consists of eight 2 in. thick planks glued together to form a cross section that is 16 in. deep. Each plank has a width ofin. The cantilever beam has a length offt and it supports a concentrated load oflb. (a) Calculate the magnitude of the horizontal shear stress at points A, [&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-223111","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223111","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=223111"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223111\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}