A Brief Introduction to Trusses - Julian Rimolirimoli.gatech.edu/documents/A Brief Introduction to...
Transcript of A Brief Introduction to Trusses - Julian Rimolirimoli.gatech.edu/documents/A Brief Introduction to...
A Brief Introduction to Trusses Julian J. Rimoli
School of Aerospace Engineering Georgia Institute of Technology
Trusses are one of the most widely adopted structural designs, many times being utilized as the structural solution of choice for bridges, roofs, cranes, aircrafts, and even robots and spaceships! Figure 1 shows some well-‐known examples of truss structures.
(a) (b) (c)
Figure 1: Examples of structures composed of trusses. (a) Little Belt truss bridge in Denmark, (b)
Eiffel Tower in Paris, and (c) NASA’s Morpheus moon lander. Trusses are defined as structures composed of slender bars connected to each other through pins at their end points. In practice, joints do not have to be pinned: we can assume a joint behaves as if it was pinned as long as all the bars passing through a joint intersect at a single point. For example, figure 2(a) shows a real truss bridge. Its members are joined together through metallic plates and bolts. Since all members intersect at a single point for every joint, we can idealize the structure of the bridge for purposes of analysis. Figure 2(b) shows the idealized bridge, where the light blue joints represent frictionless pins.
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Figure 2: (a) Real truss bridge, and (b) idealized structure. Another characteristic of trusses is that they can be connected to the supports only through its joints. Consequently, 2-‐dimensional trusses can only use two types of supports: pins and rollers. Figure 3 shows the common schematic representations
for these supports. Since bars are attached to its supports through frictionless pins, a single bar attached only to one support is always free to rotate about it, regardless of the type of support. Thus, the only difference between pins and rollers is that pins prevent all possible translations, while a single bar attached to a roller is allowed to translate in the roller direction.
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Figure 3: Schematics for typical supports. (a) Pin: attached bars could possibly rotate about the pin, but translation is prevented. (b) Roller: attached bars could possibly rotate about the pin and
translate in a specified rolling direction. The final consideration when dealing with trusses is related to the point of application of external loads: all external loads must be applied at the joints, see Figure 4. If an external load is applied, for example, at some point within the central region of a bar, then the structure will stop behaving like a truss and common analysis methods for trusses cannot be applied. In addition, application of loads to places other than joints would most likely result in premature failure of the structure due to bending of the bar under consideration.
Figure 4: Loads can only be applied on joints of trusses, either by directly placing them on the joints
(left) or by using an extra bar to attach them to the desired joint (right). In summary, a structure should satisfy the following requirements to be considered as a truss:
1) It must be composed of slender bars joined to other bars only through frictionless pins at their ends.
2) It is connected to external supports (if any) only through its joints. 3) External loads are applied only on its joints.
If all these conditions apply, methods of analysis become really simple, as we will see in the document entitled “The Method of Joints”.