5.3: Trusses

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A truss is an engineering structure that is made entirely of two-force members. In addition, statically determinate trusses (trusses that can be analyzed completely using the equilibrium equations) must be independently rigid. 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.

Two identical horizontal rods. The one above has tension forces of equal magnitude acting on each end, each force vector pointing away from the midpoint of the rod. The one below has compression forces of equal magnitude acting on each end, each force vector pointing towards the midpoint of the rod. — Figure \(\PageIndex{1}\): Trusses are made entirely of two-force members. This means that each member will either be in tension or compression, as shown here.

Trusses can be broken down further into plane trusses and space trusses. A plane truss is a truss where all members lie in a single plane. This means that plane trusses can essentially be treated as two-dimensional systems. Space trusses, on the other hand, have members that are not limited to a single plane. This means that space trusses need to be analyzed as a three-dimensional system.

A roof truss made of connected wooden beams which all lie in the same plane, next to a house under construction in a snowy field. — Figure \(\PageIndex{2}\): The members of these trusses all lie in a single plane. These roof trusses are an example of a plane truss. Image by Riisipuuro CC-BY-SA 3.0.

A metal truss bridge containing a paved roadway. A label points out that the sides of the bridge are plane trusses, and another label indicates stringers at the top of the bridge's sides and below the road surface as connecting the plane trusses. — Figure \(\PageIndex{3}\): This bridge consists of two plane trusses connected by members called stringers. Adapted from image by ToddC4176 CC-BY-SA 3.0.

An auditorium with a ceiling consisting of square tiles, each row supported by a network of metal trusses that form triangular prisms whose base is formed by the tiles. — Figure \(\PageIndex{4}\): This roof supporting truss does not lie in a single plane. This is an example of a space truss. Image by IM3847 CC-BY-SA 4.0.

A metal power line tower in a snowy field. — Figure \(\PageIndex{5}\): The power line tower also does not lie in a single plane and is therefore a space truss. Image by Anders Lagerås CC-BY-SA 2.5.

Analyzing Trusses:

When 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.

To determine these unknowns, we have two methods available: the method of joints, and the method of sections. Both will give the same results, but each through a different process.

The 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 we 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.

The 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.

The 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.

Video lecture covering this section, delivered by Dr. Jacob Moore. YouTube source: https://youtu.be/jn8sR-lS4tw.