A truss is a structural framework consisting of slender members connected at joints, designed to support external loads while minimizing material usage and weight. Simple trusses are a type of planar truss where all members lie within a single two-dimensional plane.
The most basic planar truss is a simple truss with three members arranged in a triangular formation. This triangular truss is inherently stable and rigid due to its geometry, making it an ideal starting point for creating more elaborate truss structures. A simple truss can be expanded by strategically adding two members and a joint to the existing framework. This process can be repeated to create a larger truss structure capable of supporting greater loads over longer spans. The configuration of the truss members is critical in determining its overall strength and stability, with common simple truss types including the Pratt, Howe, and Warren trusses.
The design and analysis of simple trusses rely on two key assumptions:
The rigidity and determinacy of a simple truss dictate the relationship between the number of members (m) and the number of joints (j). For a truss to be statically determinate and stable, m = 2j - 3 must hold. This condition ensures that there are enough members to resist deformation under load while maintaining the stability of the structure. If a truss does not satisfy this equation, it is either indeterminate or unstable, which can lead to structural failure.
From Chapter 6:
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