{"id":180,"date":"2025-01-28T04:05:52","date_gmt":"2025-01-28T04:05:52","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/3-4-stresses-in-the-soil-due-to-a-strip-pressure\/"},"modified":"2026-03-16T13:57:14","modified_gmt":"2026-03-16T13:57:14","slug":"3-4-stresses-in-the-soil-due-to-a-strip-pressure","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/3-4-stresses-in-the-soil-due-to-a-strip-pressure\/","title":{"raw":"3.4 Stresses in the soil due to a strip pressure","rendered":"3.4 Stresses in the soil due to a strip pressure"},"content":{"raw":"Stresses applied on the soil surface e.g., from a footing of \u201cinfinite\u201d length can be modelled as an infinitely long (strip) pressure acting on the surface of a homogeneous elastic half-space (Figure 3.7a<\/a>). As plane-strain symmetry conditions apply, additional stresses due to the application of the pressure qext<\/sub><\/em> can be calculated as:\n\n[caption id=\"attachment_2350\" align=\"aligncenter\" width=\"400\"]\"Diagram<\/a> Figure 3.7a. Stresses due to strip pressure acting on the surface of a homogeneous elastic half-space.[\/caption]\n\n \n\n[caption id=\"attachment_2351\" align=\"aligncenter\" width=\"400\"]\"Diagram<\/a> Figure 3.7b. Values of angles \u03b1 and \u03b2 in the special case where stresses are estimated below the axis of the strip pressure.[\/caption]\n\n(3.10)<\/strong> [latex]\\Delta {\\sigma _z} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\alpha + {\\rm{sin}}\\alpha \\cos \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]\n\n(3.11)<\/strong> [latex]\\Delta {\\sigma _x} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\alpha - \\sin \\alpha \\cos \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]\n\n(3.12)<\/strong> [latex]\\Delta {\\tau _{zx}} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\sin \\alpha \\sin \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]\n\n\u03a4he stress increment components and angles \u03b1<\/em> and \u03b2<\/em> are defined in Figure 3.6a<\/a>. Angles \u03b1<\/em> and \u03b2<\/em> must be input in Eqs. 3.10 to 3.12 in radians, not in degrees, and may attain negative values too, as shown in Figure 3.7b<\/a>.","rendered":"

Stresses applied on the soil surface e.g., from a footing of \u201cinfinite\u201d length can be modelled as an infinitely long (strip) pressure acting on the surface of a homogeneous elastic half-space (Figure 3.7a<\/a>). As plane-strain symmetry conditions apply, additional stresses due to the application of the pressure qext<\/sub><\/em> can be calculated as:<\/p>\n

\"Diagram<\/a>
Figure 3.7a. Stresses due to strip pressure acting on the surface of a homogeneous elastic half-space.<\/figcaption><\/figure>\n

 <\/p>\n

\"Diagram<\/a>
Figure 3.7b. Values of angles \u03b1 and \u03b2 in the special case where stresses are estimated below the axis of the strip pressure.<\/figcaption><\/figure>\n

(3.10)<\/strong> [latex]\\Delta {\\sigma _z} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\alpha + {\\rm{sin}}\\alpha \\cos \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]<\/p>\n

(3.11)<\/strong> [latex]\\Delta {\\sigma _x} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\alpha - \\sin \\alpha \\cos \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]<\/p>\n

(3.12)<\/strong> [latex]\\Delta {\\tau _{zx}} = \\dfrac{{{q_{ext}}}}{\\pi }\\left[ {\\sin \\alpha \\sin \\left( {\\alpha + 2\\beta } \\right)} \\right][\/latex]<\/p>\n

\u03a4he stress increment components and angles \u03b1<\/em> and \u03b2<\/em> are defined in Figure 3.6a<\/a>. Angles \u03b1<\/em> and \u03b2<\/em> must be input in Eqs. 3.10 to 3.12 in radians, not in degrees, and may attain negative values too, as shown in Figure 3.7b<\/a>.<\/p>\n","protected":false},"author":1,"menu_order":4,"template":"","meta":{"pb_show_title":"","pb_short_title":"3.4 Stresses in the soil due to a strip pressure","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-180","chapter","type-chapter","status-publish","hentry"],"part":165,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/180","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":1,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/180\/revisions"}],"predecessor-version":[{"id":181,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/180\/revisions\/181"}],"part":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/parts\/165"}],"metadata":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/180\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=180"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=180"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=180"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}