{"id":153638,"date":"2023-07-31T12:09:15","date_gmt":"2023-07-31T06:39:15","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=153638"},"modified":"2023-07-31T12:09:17","modified_gmt":"2023-07-31T06:39:17","slug":"a-square-footing-of-4-m-side-is-placed-at-1-m-depth-in-a-sand-deposit-the-dry-unit-weight-g-of-sand-is-15-kn-m3-this-footing-has-an-ultimate-bearing-capacity-of-600-kpa","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-square-footing-of-4-m-side-is-placed-at-1-m-depth-in-a-sand-deposit-the-dry-unit-weight-g-of-sand-is-15-kn-m3-this-footing-has-an-ultimate-bearing-capacity-of-600-kpa\/","title":{"rendered":"A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight (g) of sand is 15 kN\/m3. This footing has an ultimate bearing capacity of 600 kPa"},"content":{"rendered":"\n<p>Q. A square footing of 4 <em>m <\/em>side is placed at 1 <em>m <\/em>depth in a sand deposit. The dry unit weight (g) of sand is 15 <em>kN\/m<sup>3<\/sup><\/em>. This footing has an ultimate bearing capacity of 600 <em>kPa<\/em>. Consider the depth factors: <em>dq <\/em>= <em>d<\/em>g\u00a0= 1.0 and the bearing capacity factor: <em>N<\/em>g\u00a0= 18.75. This footing is placed at a depth of 2 <em>m <\/em>in the same soil deposit. For a factor of safety of 3.0 as per Terzaghi\u2019s theory, the safe bearing capacity (in <em>kPa<\/em>) of this footing would be\u00a0<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Skide of square footing = 4 m<br>depth of footing = 1m<br>Unit weight of soil = 15 KN\/m3<br>Ultimate bearing capacity = 600 KPa<br>Depth factors,\u00a0dq\u00a0=\u00a0d\u03b3\u00a0= 1<br>N\u03b3\u00a0= 18.75<br>According to terzaghi, the ultimate bearing capacity of square footing is given as at depth of footing = 1 m<br>qu\u00a0= 1.3 CNc\u00a0+ qNqdq\u00a0+ 0.4B\u03b3N\u03b3d\u03b3<br>For sand, C = 0, q =\u00a0\u03b3Df\u00a0= 15\u00a0\u00d7\u00a01 = 15 KN\/m2<br>600 = 0 + 15\u00a0\u00d7\u00a0Nq\u00a0\u00d7\u00a01 + 0.4\u00a0\u00d7\u00a04\u00a0\u00d7\u00a015\u00a0\u00d7\u00a018.75\u00a0\u00d7\u00a01<br>\u21d2\u00a0Nq\u00a0= 10<br>Now at depth of footing at 2 m<br>qu=1.3CNc\u00a0+qNq\u00a0+ 0.4B\u03b3N\u03b3\u00a0d\u03b3<br>qu\u00a0= 0 + (2\u00a0\u00d7\u00a015)10\u00a0\u00d7\u00a01 + 0.4\u00a0\u00d7\u00a04\u00a0\u00d715\u00a0\u00d7\u00a018.75\u00a0\u00d7\u00a01<br>qu\u00a0= 750 KPa<br>\u2235\u00a0We know that<br>qnu\u00a0=\u00a0qu\u00a0&#8211;\u00a0\u03b3Df<br>qnu\u00a0= 750 -15\u00a0\u00d7\u00a02<br>qnu\u00a0= 720 KPa<br>and safe bearing capacity\u00a0qsafe<\/p>\n\n\n\n<p>q<sub>safe<\/sub>\u00a0=\u00a0q<sub>nu<\/sub>\/FOS\u00a0+\u00a0\u03b3D<sub>f<\/sub><\/p>\n\n\n\n<p>=\u00a0720\/3\u00a0+ 15\u00a0\u00d7\u00a02<\/p>\n\n\n\n<p>= 270 KPa<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight (g) of sand is 15 kN\/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors: dq = dg\u00a0= 1.0 and the bearing capacity factor: Ng\u00a0= 18.75. This footing [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":153645,"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-153638","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\/153638","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=153638"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153638\/revisions"}],"predecessor-version":[{"id":153647,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153638\/revisions\/153647"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/153645"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=153638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=153638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=153638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}