{"id":184,"date":"2021-03-01T09:00:31","date_gmt":"2021-03-01T14:00:31","guid":{"rendered":"http:\/\/pressbooks.library.upei.ca\/statics\/?post_type=chapter&p=184"},"modified":"2025-08-01T16:38:33","modified_gmt":"2025-08-01T20:38:33","slug":"trusses-introduction","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.upei.ca\/statics\/chapter\/trusses-introduction\/","title":{"raw":"5.1 Trusses Introduction","rendered":"5.1 Trusses Introduction"},"content":{"raw":"Trusses are rigid structures made up of two-force members, which are objects with exactly two forces\/connections. Trusses are commonly found in the frame of a roof and the sides of a bridge:\r\n\r\n[caption id=\"attachment_1372\" align=\"aligncenter\" width=\"400\"]\"Metal Source:Engineering Mechanics, Jacob Moore, et al. http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-1_structures\/structures.html[\/caption]\r\n\r\n \r\n\r\n \r\n\r\n[caption id=\"attachment_552\" align=\"aligncenter\" width=\"472\"]\"A<\/a> Image Source: Billbeee at English Wikipedia. - Transferred from en.wikipedia to Commons., CC BY-SA 3.0,[\/caption]\r\n\r\nYou'll analyze these structures more in your Structures course, but for Statics, you will need to know how to calculate the force in each member, using the method of joints and the method of sections. The method of joints is more like a particle analysis, wherein you use only x and y equilibrium equations. The method of sections is more like a rigid body analysis, where you can also include the moment equilibrium equation. Those are in the next sections.\r\n

5.1.1 Two Force Members<\/h1>\r\nBefore we discuss the structure of trusses, we must begin by defining two force members:\r\n
\r\n\r\nA\u00a0<\/span>two-force member<\/strong> is a body that has forces (and only forces, no moments) acting on it in only two locations. In order to have a two-force member in static equilibrium, the net force at each location must be equal, opposite, and collinear. This will result in both force members being in either tension or compression as shown in the diagram below.<\/span>\r\n\r\n[caption id=\"attachment_2747\" align=\"aligncenter\" width=\"391\"]\"Diagram The forces acting on two force members need to be equal, opposite, and collinear for the body to be in equilibrium.[\/caption]\r\n\r\nImagine a beam where forces are only exerted at each end of the beam (a two-force member). The body has some non-zero force acting at one end of the beam, which we can draw as a force vector. If this body is in equilibrium, then we know two things: 1) the sum of the forces must be equal to zero, and 2) the sum of the moments must be equal to zero.\r\n\r\nIn order to have the sum of the forces equal to zero, the force vector on the other side of the beam must be equal in magnitude and opposite in direction. This is the only way to ensure that the sum of the forces is equal to zero with only two forces.\r\n\r\nIn order to have the sum of the moments equal to zero, the forces must be collinear. If the forces were not collinear, then the two equal and opposite forces would form a couple. This couple would exert a moment on the beam when there are no other moments to counteract the couple. Because the moment exerted by the two forces must be equal to zero, the perpendicular distance between the forces (d) must be equal to zero. The only way to achieve this is to have the forces be collinear.\r\n\r\n[caption id=\"attachment_2748\" align=\"aligncenter\" width=\"449\"]\"Two-force In order to have the sum of the moments be equal to zero, the forces acting on two force members must always be collinear, acting along the line connecting the two points where forces are applied.[\/caption]\r\n\r\nSource: Engineering Mechanics, Jacob Moore, et al. http:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-1_structures\/structures.html<\/a>\r\n\r\n<\/div>\r\n

5.1.2 Trusses<\/h1>\r\n
\r\n\r\n[caption id=\"attachment_1373\" align=\"alignright\" width=\"250\"]\"Truss Adapted from image by ToddC4176 CC-BY-SA 3.0[\/caption]\r\n\r\nA\u00a0<\/span>truss<\/strong>\u00a0is an engineering structure that is made entirely of\u00a0<\/span>[pb_glossary id=\"195\"]two force members[\/pb_glossary]<\/strong>. In addition, statically determinate trusses (trusses that can be analyzed completely using the equilibrium equations), must be\u00a0<\/span>independently rigid<\/strong>. This means that if the truss was separated from its connection points, no one part would be able to move independently with respect to the rest of the truss.<\/span>\r\n\r\nWhen we talk about analyzing a truss, we are usually looking to identify not only the external forces acting on the truss structure, but also the forces acting on each member internally in the truss. Because each member of the truss is a two-force member, we simply need to identify the magnitude of the force on each member and determine if each member is in tension or compression.\r\n\r\nTo determine these unknowns, we have two methods available: the method of joints<\/strong>\u00a0and the method of sections<\/strong>. Both will give the same results, but each through a different process.\r\n\r\nThe method of joints focuses on the joints, or the connection points where the members come together. We assume we have a pin at each of these points that we model as a particle, we draw out the free body diagram for each pin, and then write out the equilibrium equations for each pin. This will result in a large number of equilibrium equations that we can use to solve for a large number of unknown forces.\r\n\r\nThe method of sections involves pretending to split the truss into two or more different sections and then analyzing each section as a separate rigid body in equilibrium. In this method, we determine the appropriate sections, draw free-body diagrams for each section, and then write out the equilibrium equations for each section.\r\n\r\nThe method of joints is usually the easiest and fastest method for solving for all the unknown forces in a truss. The method of sections, on the other hand, is better suited to targeting and solving for the forces in just a few members without having to solve for all the unknowns. In addition, these methods can be combined if needed to best suit the goals of the problem solver.\r\n\r\nSource: Engineering Mechanics, Jacob Moore, et al. https:\/\/mechanicsmap.psu.edu\/websites\/5_structures\/5-1_structures\/structures.html\r\n\r\n<\/div>\r\n \r\n\r\nHere are common types of bridge trusses:\r\n\r\n[caption id=\"attachment_1438\" align=\"aligncenter\" width=\"1024\"]\"Pictures<\/a> Source: https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses[\/caption]\r\n\r\n \r\n\r\nHere are common types of roof trusses:\r\n\r\n[caption id=\"attachment_1439\" align=\"aligncenter\" width=\"1024\"]\"Pictures<\/a> Source: https:\/\/eng.libretexts.org\/Bookshelves\/Civil_Engineering\/Book%3A_Structural_Analysis_(Udoeyo)\/01%3A_Chapters\/1.05%3A_Internal_Forces_in_Plane_Trusses[\/caption]\r\n

5.1.3 Parts of a Truss<\/h1>\r\nA truss is composed of:\r\n