{"id":188,"date":"2021-03-01T09:01:05","date_gmt":"2021-03-01T14:01:05","guid":{"rendered":"http:\/\/pressbooks.library.upei.ca\/statics\/?post_type=chapter&#038;p=188"},"modified":"2025-08-01T16:44:44","modified_gmt":"2025-08-01T20:44:44","slug":"method-of-sections","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.upei.ca\/statics\/chapter\/method-of-sections\/","title":{"raw":"5.3 Method of Sections","rendered":"5.3 Method of Sections"},"content":{"raw":"The <span style=\"text-decoration: underline\"><em><strong>method of sections<\/strong> <\/em><\/span>uses rigid body analysis to solve for a specific member or two. Instead of looking at each joint, you make a cut through the truss, turning the members along that line into internal forces (assume in tension). Then you solve the rigid body using the equilibrium equations for a rigid body: $latex \\sum F_x=0\\;\\sum F_y=0\\;\\sum M_z=0$\r\n\r\nThe truss:\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_1365\" align=\"aligncenter\" width=\"424\"]<a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels.png\" alt=\"Truss bridge with 60\u202fkN and 80\u202fkN vertical loads.\" class=\"wp-image-1365\" width=\"424\" height=\"215\" \/><\/a> Source: Engineering Mechanics, Jacob Moore, et al. <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html<\/a>[\/caption]\r\n\r\nis split into two to solve for F<sub>E<\/sub>.\r\n\r\n[caption id=\"attachment_1356\" align=\"aligncenter\" width=\"400\"]<a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection.png\" alt=\"Free-body diagram of left truss section with labeled forces and angles.\" class=\"wp-image-1356 size-full\" width=\"400\" height=\"270\" \/><\/a> Source: Engineering Mechanics, Jacob Moore, et al. <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html<\/a>[\/caption]\r\n\r\nFor this example, you could choose the right half or the left half. For some problems, being strategic is necessary; otherwise, you need to make multiple cuts. In this problem, you had to solve for the reaction forces first, but that isn't always the case, as you can sometimes just make the cut (see example 2 below).\r\n\r\n&nbsp;\r\n\r\nHere are more examples of how to make a cut and show the naming convention:\r\n<div class=\"textbox\">\r\n\r\n&nbsp;\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-1024x342.jpg\" alt=\"Section cut of a truss to analyze internal forces using method of sections.\" class=\"aligncenter wp-image-1446 size-large\" width=\"1024\" height=\"342\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-1024x277.jpg\" alt=\"Truss cut and isolated joint diagram showing internal forces and reactions.\" class=\"aligncenter wp-image-1447 size-large\" width=\"1024\" height=\"277\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-1024x664.jpg\" alt=\"Multiple views of a truss with loads, reactions, and internal force analysis using sections.\" class=\"aligncenter wp-image-1448 size-large\" width=\"1024\" height=\"664\" \/>\r\n\r\nSource: Internal Forces in Beams and Frames, Libretexts. https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses\r\n\r\n<\/div>\r\nHere is a detailed explanation:\r\n<div class=\"textbox\">\r\n\r\n<span>The\u00a0<\/span><strong>method of sections<\/strong><span>\u00a0is a process used to solve for the unknown forces acting on members of a\u00a0<\/span><strong>truss<\/strong><span>. The method involves breaking the truss down into individual sections and analyzing each section as a separate rigid body. The method of sections is usually the fastest and easiest way to determine the unknown forces acting in a specific member of the truss.<\/span>\r\n<h2>Using This Method:<\/h2>\r\nThe process used in the method of sections is outlined below:\r\n<ol>\r\n \t<li>In the beginning, it is usually useful to label the members in your truss. This will help you keep everything organized and consistent in later analysis. In this book, the members will be labelled with letters.\r\n\r\n[caption id=\"attachment_2756\" align=\"aligncenter\" width=\"441\"]<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-300x145.png\" alt=\"Truss with labeled members and loads.\" class=\"wp-image-2756 \" width=\"441\" height=\"213\" \/> The first step in the method of sections is to label each member.[\/caption]<\/li>\r\n \t<li>Treating the entire truss structure as a rigid body, draw a free body diagram, write out the equilibrium equations, and solve for the external reacting forces acting on the truss structure. This analysis should not differ from the analysis of a single rigid body.\r\n\r\n[caption id=\"attachment_2757\" align=\"aligncenter\" width=\"442\"]<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-300x150.png\" alt=\"Truss with vertical loads.\" class=\"wp-image-2757 \" width=\"442\" height=\"221\" \/> Treat the entire truss as a rigid body and solve for the reaction forces supporting the truss structure.[\/caption]<\/li>\r\n \t<li>Next, you will imagine cutting your truss into two separate sections. The cut should travel through the member that you are trying to solve for the forces in, and should cut through as few members as possible (The cut does not need to be a straight line).\r\n\r\n[caption id=\"attachment_2758\" align=\"aligncenter\" width=\"482\"]<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-300x160.png\" alt=\"Truss with vertical forces and a dashed line showing an imaginary cut through members D, E, and F.\" class=\"wp-image-2758 \" width=\"482\" height=\"257\" \/> Next, you will imagine cutting the truss into two parts. If you want to find the forces in a specific member, be sure to cut through that member. It also makes things easier if you cut through as few members as possible.[\/caption]<\/li>\r\n \t<li><span>Next, you will draw a free-body diagram for either one or both sections that you created. Be sure to include all the forces acting on each section.<\/span>\r\n<ul>\r\n \t<li>Any external reaction or load forces that may be acting on the section.<\/li>\r\n \t<li>An internal force in each member that was cut when splitting the truss into sections. Remember that for a two-force member, the force will be acting along the line between the two connection points on the member. We will also need to guess if it will be a tensile or a compressive force. An incorrect guess now, though, will simply lead to a negative solution later on. A common strategy then is to assume all forces are tensile, then later in the solution, any positive forces will be tensile forces, and any negative forces will be compressive forces.<\/li>\r\n \t<li>Label each force in the diagram. Include any known magnitudes and directions, and provide variable names for each unknown.\r\n\r\n[caption id=\"attachment_2759\" align=\"aligncenter\" width=\"400\"]<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-300x188.png\" alt=\"Truss cut with forces FD, FE, FF shown on right side.\" class=\"wp-image-2759 \" width=\"400\" height=\"251\" \/> Next, draw a free-body diagram of one or both halves of the truss. Add the known forces, as well as the unknown tensile forces for each member that you cut.[\/caption]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Write out the equilibrium equations for each section for which you drew a free body diagram. These will be extended bodies, so you will need to write out the force and the moment equations.\r\n<ul>\r\n \t<li>You will have three possible equations for each section: two force equations and one moment equation. [latex]\\sum\\vec F=0\\; \\; \\sum\\vec M=0\\\\\\sum F_x=0\\; \\; \\sum F_y=0\\; \\; \\sum M_z=0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Finally, solve the equilibrium equations for the unknowns. You can do this algebraically, solving for one variable at a time, or you can use matrix equations to solve for everything at once. If you assumed that all forces were tensile earlier, remember that negative answers indicate compressive forces in the members.<\/li>\r\n<\/ol>\r\nSource: Engineering Mechanics, Jacob Moore, et al. https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\u00a0<a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><\/a>\r\n\r\n<\/div>\r\nAdditional examples from the <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">Engineering Mechanics webpage<\/a>\r\n<h3><a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample1.pdf\">Example 1:<\/a><\/h3>\r\n<div class=\"textbox\">\r\n\r\nFind the forces acting on members BD and CE. Be sure to indicate if the forces are tensile or compressive.\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2.png\" alt=\"Bridge truss with 60\u202fkN and 80\u202fkN downward loads spaced 10\u202fm apart.\" class=\"aligncenter wp-image-1366 size-full\" width=\"500\" height=\"270\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-1002x1024.png\" alt=\"Solution to the problem. \" class=\"aligncenter wp-image-1357\" width=\"382\" height=\"391\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-667x1024.png\" alt=\"Solution to the problem. \" class=\"aligncenter wp-image-1358\" width=\"506\" height=\"777\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-1024x422.png\" alt=\"Solutions to the problem. \" class=\"aligncenter wp-image-1359\" width=\"495\" height=\"204\" \/>\r\n<p style=\"text-align: center\">Source: Engineering Mechanics, Jacob Moore, et al. https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample1.pdf<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h4><a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample2.pdf\">Example 2:<\/a><\/h4>\r\n<div class=\"textbox\">\r\n\r\nFind the forces acting on members AC, BC, and BD of the truss. Be sure to indicate if the forces are tensile or compressive.\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1.png\" alt=\"Vertical truss with two angled loads: 40\u202fkN and 50\u202fkN at the top ends.\" class=\"aligncenter wp-image-1367 size-full\" width=\"500\" height=\"345\" \/>\r\n\r\nIf we make a cut in the top section, we don't need to solve for the reaction forces.\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-757x1024.png\" alt=\"Solution to the problem. \" class=\"aligncenter wp-image-1360\" width=\"491\" height=\"664\" \/>\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-1024x737.png\" alt=\"Solution to the problem. \" class=\"aligncenter wp-image-1361\" width=\"413\" height=\"297\" \/>\r\n\r\nSource: Engineering Mechanics, Jacob Moore, et al.\u00a0 https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample2.pdf\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nEven more examples are available at: <a href=\"https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses\">https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses<\/a>\r\n\r\n&nbsp;\r\n\r\nIn summary:\r\n\r\n<img src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-1024x839.png\" alt=\"Summary of the method of sections approach.\" class=\"aligncenter wp-image-1363 size-large\" width=\"1024\" height=\"839\" \/>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div class=\"textbox__content\">\r\n\r\n<i>Basically, the Method of Sections is an analysis technique to find the forces in some members of a truss.<\/i> It separates the truss into two sections and then uses the rigid body equilibrium equations.\r\n\r\n<em>Application<\/em>: To calculate the loads on bridges and roofs, especially if you need to know only one or two of the members.\r\n\r\n<em>Looking Ahead<\/em>: The next section explores a trick that makes solving faster, especially for the method of joints.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<p>The <span style=\"text-decoration: underline\"><em><strong>method of sections<\/strong> <\/em><\/span>uses rigid body analysis to solve for a specific member or two. Instead of looking at each joint, you make a cut through the truss, turning the members along that line into internal forces (assume in tension). Then you solve the rigid body using the equilibrium equations for a rigid body: [latex]\\sum F_x=0\\;\\sum F_y=0\\;\\sum M_z=0[\/latex]<\/p>\n<p>The truss:<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_1365\" aria-describedby=\"caption-attachment-1365\" style=\"width: 424px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels.png\" alt=\"Truss bridge with 60\u202fkN and 80\u202fkN vertical loads.\" class=\"wp-image-1365\" width=\"424\" height=\"215\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels.png 400w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels-300x152.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels-65x33.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels-225x114.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSlabels-350x178.png 350w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/a><figcaption id=\"caption-attachment-1365\" class=\"wp-caption-text\">Source: Engineering Mechanics, Jacob Moore, et al. <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html<\/a><\/figcaption><\/figure>\n<p>is split into two to solve for F<sub>E<\/sub>.<\/p>\n<figure id=\"attachment_1356\" aria-describedby=\"caption-attachment-1356\" style=\"width: 400px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection.png\" alt=\"Free-body diagram of left truss section with labeled forces and angles.\" class=\"wp-image-1356 size-full\" width=\"400\" height=\"270\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection.png 400w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection-300x203.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection-65x44.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection-225x152.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/MOSsection-350x236.png 350w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><figcaption id=\"caption-attachment-1356\" class=\"wp-caption-text\">Source: Engineering Mechanics, Jacob Moore, et al. <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html<\/a><\/figcaption><\/figure>\n<p>For this example, you could choose the right half or the left half. For some problems, being strategic is necessary; otherwise, you need to make multiple cuts. In this problem, you had to solve for the reaction forces first, but that isn&#8217;t always the case, as you can sometimes just make the cut (see example 2 below).<\/p>\n<p>&nbsp;<\/p>\n<p>Here are more examples of how to make a cut and show the naming convention:<\/p>\n<div class=\"textbox\">\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-1024x342.jpg\" alt=\"Section cut of a truss to analyze internal forces using method of sections.\" class=\"aligncenter wp-image-1446 size-large\" width=\"1024\" height=\"342\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-1024x342.jpg 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-300x100.jpg 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-768x257.jpg 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-1536x514.jpg 1536w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-65x22.jpg 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-225x75.jpg 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1-350x117.jpg 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/sections1.jpg 1758w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-1024x277.jpg\" alt=\"Truss cut and isolated joint diagram showing internal forces and reactions.\" class=\"aligncenter wp-image-1447 size-large\" width=\"1024\" height=\"277\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-1024x277.jpg 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-300x81.jpg 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-768x208.jpg 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-1536x416.jpg 1536w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-65x18.jpg 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-225x61.jpg 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2-350x95.jpg 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/section-2.jpg 1707w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-1024x664.jpg\" alt=\"Multiple views of a truss with loads, reactions, and internal force analysis using sections.\" class=\"aligncenter wp-image-1448 size-large\" width=\"1024\" height=\"664\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-1024x664.jpg 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-300x195.jpg 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-768x498.jpg 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-1536x996.jpg 1536w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-65x42.jpg 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-225x146.jpg 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints-350x227.jpg 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/joints.jpg 1966w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Source: Internal Forces in Beams and Frames, Libretexts. https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses<\/p>\n<\/div>\n<p>Here is a detailed explanation:<\/p>\n<div class=\"textbox\">\n<p><span>The\u00a0<\/span><strong>method of sections<\/strong><span>\u00a0is a process used to solve for the unknown forces acting on members of a\u00a0<\/span><strong>truss<\/strong><span>. The method involves breaking the truss down into individual sections and analyzing each section as a separate rigid body. The method of sections is usually the fastest and easiest way to determine the unknown forces acting in a specific member of the truss.<\/span><\/p>\n<h2>Using This Method:<\/h2>\n<p>The process used in the method of sections is outlined below:<\/p>\n<ol>\n<li>In the beginning, it is usually useful to label the members in your truss. This will help you keep everything organized and consistent in later analysis. In this book, the members will be labelled with letters.<br \/>\n<figure id=\"attachment_2756\" aria-describedby=\"caption-attachment-2756\" style=\"width: 441px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-300x145.png\" alt=\"Truss with labeled members and loads.\" class=\"wp-image-2756\" width=\"441\" height=\"213\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-300x145.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-65x31.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-225x109.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450-350x169.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122450.png 705w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><figcaption id=\"caption-attachment-2756\" class=\"wp-caption-text\">The first step in the method of sections is to label each member.<\/figcaption><\/figure>\n<\/li>\n<li>Treating the entire truss structure as a rigid body, draw a free body diagram, write out the equilibrium equations, and solve for the external reacting forces acting on the truss structure. This analysis should not differ from the analysis of a single rigid body.<br \/>\n<figure id=\"attachment_2757\" aria-describedby=\"caption-attachment-2757\" style=\"width: 442px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-300x150.png\" alt=\"Truss with vertical loads.\" class=\"wp-image-2757\" width=\"442\" height=\"221\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-300x150.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-65x32.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-225x112.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612-350x174.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122612.png 694w\" sizes=\"auto, (max-width: 442px) 100vw, 442px\" \/><figcaption id=\"caption-attachment-2757\" class=\"wp-caption-text\">Treat the entire truss as a rigid body and solve for the reaction forces supporting the truss structure.<\/figcaption><\/figure>\n<\/li>\n<li>Next, you will imagine cutting your truss into two separate sections. The cut should travel through the member that you are trying to solve for the forces in, and should cut through as few members as possible (The cut does not need to be a straight line).<br \/>\n<figure id=\"attachment_2758\" aria-describedby=\"caption-attachment-2758\" style=\"width: 482px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-300x160.png\" alt=\"Truss with vertical forces and a dashed line showing an imaginary cut through members D, E, and F.\" class=\"wp-image-2758\" width=\"482\" height=\"257\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-300x160.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-65x35.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-225x120.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950-350x187.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-122950.png 687w\" sizes=\"auto, (max-width: 482px) 100vw, 482px\" \/><figcaption id=\"caption-attachment-2758\" class=\"wp-caption-text\">Next, you will imagine cutting the truss into two parts. If you want to find the forces in a specific member, be sure to cut through that member. It also makes things easier if you cut through as few members as possible.<\/figcaption><\/figure>\n<\/li>\n<li><span>Next, you will draw a free-body diagram for either one or both sections that you created. Be sure to include all the forces acting on each section.<\/span>\n<ul>\n<li>Any external reaction or load forces that may be acting on the section.<\/li>\n<li>An internal force in each member that was cut when splitting the truss into sections. Remember that for a two-force member, the force will be acting along the line between the two connection points on the member. We will also need to guess if it will be a tensile or a compressive force. An incorrect guess now, though, will simply lead to a negative solution later on. A common strategy then is to assume all forces are tensile, then later in the solution, any positive forces will be tensile forces, and any negative forces will be compressive forces.<\/li>\n<li>Label each force in the diagram. Include any known magnitudes and directions, and provide variable names for each unknown.<br \/>\n<figure id=\"attachment_2759\" aria-describedby=\"caption-attachment-2759\" style=\"width: 400px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-300x188.png\" alt=\"Truss cut with forces FD, FE, FF shown on right side.\" class=\"wp-image-2759\" width=\"400\" height=\"251\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-300x188.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-65x41.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-225x141.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407-350x219.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screenshot-2025-07-17-123407.png 703w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><figcaption id=\"caption-attachment-2759\" class=\"wp-caption-text\">Next, draw a free-body diagram of one or both halves of the truss. Add the known forces, as well as the unknown tensile forces for each member that you cut.<\/figcaption><\/figure>\n<\/li>\n<\/ul>\n<\/li>\n<li>Write out the equilibrium equations for each section for which you drew a free body diagram. These will be extended bodies, so you will need to write out the force and the moment equations.\n<ul>\n<li>You will have three possible equations for each section: two force equations and one moment equation. [latex]\\sum\\vec F=0\\; \\; \\sum\\vec M=0\\\\\\sum F_x=0\\; \\; \\sum F_y=0\\; \\; \\sum M_z=0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>Finally, solve the equilibrium equations for the unknowns. You can do this algebraically, solving for one variable at a time, or you can use matrix equations to solve for everything at once. If you assumed that all forces were tensile earlier, remember that negative answers indicate compressive forces in the members.<\/li>\n<\/ol>\n<p>Source: Engineering Mechanics, Jacob Moore, et al. https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\u00a0<a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-5_method_of_sections\/methodofsections.html\"><\/a><\/p>\n<\/div>\n<p>Additional examples from the <a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/methodofsections.html\">Engineering Mechanics webpage<\/a><\/p>\n<h3><a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample1.pdf\">Example 1:<\/a><\/h3>\n<div class=\"textbox\">\n<p>Find the forces acting on members BD and CE. Be sure to indicate if the forces are tensile or compressive.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2.png\" alt=\"Bridge truss with 60\u202fkN and 80\u202fkN downward loads spaced 10\u202fm apart.\" class=\"aligncenter wp-image-1366 size-full\" width=\"500\" height=\"270\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2.png 500w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2-300x162.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2-65x35.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2-225x122.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P1-2-350x189.png 350w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-1002x1024.png\" alt=\"Solution to the problem.\" class=\"aligncenter wp-image-1357\" width=\"382\" height=\"391\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-1002x1024.png 1002w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-294x300.png 294w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-768x785.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-65x66.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-225x230.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM-350x358.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.57.59-PM.png 1182w\" sizes=\"auto, (max-width: 382px) 100vw, 382px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-667x1024.png\" alt=\"Solution to the problem.\" class=\"aligncenter wp-image-1358\" width=\"506\" height=\"777\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-667x1024.png 667w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-195x300.png 195w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-768x1179.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-1000x1536.png 1000w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-65x100.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-225x346.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM-350x537.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.58.48-PM.png 1094w\" sizes=\"auto, (max-width: 506px) 100vw, 506px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-1024x422.png\" alt=\"Solutions to the problem.\" class=\"aligncenter wp-image-1359\" width=\"495\" height=\"204\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-1024x422.png 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-300x124.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-768x316.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-65x27.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-225x93.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM-350x144.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-9.59.14-PM.png 1122w\" sizes=\"auto, (max-width: 495px) 100vw, 495px\" \/><\/p>\n<p style=\"text-align: center\">Source: Engineering Mechanics, Jacob Moore, et al. https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample1.pdf<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h4><a href=\"https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample2.pdf\">Example 2:<\/a><\/h4>\n<div class=\"textbox\">\n<p>Find the forces acting on members AC, BC, and BD of the truss. Be sure to indicate if the forces are tensile or compressive.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1.png\" alt=\"Vertical truss with two angled loads: 40\u202fkN and 50\u202fkN at the top ends.\" class=\"aligncenter wp-image-1367 size-full\" width=\"500\" height=\"345\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1.png 500w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1-300x207.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1-65x45.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1-225x155.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/P2-1-350x242.png 350w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>If we make a cut in the top section, we don&#8217;t need to solve for the reaction forces.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-757x1024.png\" alt=\"Solution to the problem.\" class=\"aligncenter wp-image-1360\" width=\"491\" height=\"664\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-757x1024.png 757w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-222x300.png 222w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-768x1039.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-1136x1536.png 1136w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-65x88.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-225x304.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM-350x473.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.02.51-PM.png 1310w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-1024x737.png\" alt=\"Solution to the problem.\" class=\"aligncenter wp-image-1361\" width=\"413\" height=\"297\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-1024x737.png 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-300x216.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-768x553.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-65x47.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-225x162.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM-350x252.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Screen-Shot-2021-08-23-at-10.03.05-PM.png 1170w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/p>\n<p>Source: Engineering Mechanics, Jacob Moore, et al.\u00a0 https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-4_method_of_sections\/pdf\/MethodOfSections_WorkedExample2.pdf<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Even more examples are available at: <a href=\"https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses\">https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>In summary:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-1024x839.png\" alt=\"Summary of the method of sections approach.\" class=\"aligncenter wp-image-1363 size-large\" width=\"1024\" height=\"839\" srcset=\"https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-1024x839.png 1024w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-300x246.png 300w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-768x629.png 768w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-1536x1259.png 1536w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-65x53.png 65w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-225x184.png 225w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections-350x287.png 350w, https:\/\/pressbooks.library.upei.ca\/statics\/wp-content\/uploads\/sites\/56\/2021\/03\/Meth-of-sections.png 1568w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<p><i>Basically, the Method of Sections is an analysis technique to find the forces in some members of a truss.<\/i> It separates the truss into two sections and then uses the rigid body equilibrium equations.<\/p>\n<p><em>Application<\/em>: To calculate the loads on bridges and roofs, especially if you need to know only one or two of the members.<\/p>\n<p><em>Looking Ahead<\/em>: The next section explores a trick that makes solving faster, especially for the method of joints.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":74,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-188","chapter","type-chapter","status-publish","hentry"],"part":58,"_links":{"self":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/188","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/users\/74"}],"version-history":[{"count":23,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/188\/revisions"}],"predecessor-version":[{"id":2861,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/188\/revisions\/2861"}],"part":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/parts\/58"}],"metadata":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/188\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/media?parent=188"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapter-type?post=188"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/contributor?post=188"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/license?post=188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}