6.2:
Simple Trusses
A truss is a framework of slender members connected at joints.
When all truss members lie in a single two-dimensional plane, it is called a planar truss.
The basic planar truss is a simple truss comprising three members in a triangular arrangement.
It can be expanded by the strategic addition of two members and a joint.
The design and analysis of the truss rely on two simplified assumptions.
Firstly, external loads are applied at joints, and the weight of each member is negligible.
When the weight of a member is significant, half of its magnitude is applied as equally distributed vertical forces at both ends.
Secondly, although members connect with welded, bolted or riveted joints, the joints can be assumed as smooth pins, provided the centerlines of the joining members are concurrent.
These assumptions ensure that truss members act as two-force members experiencing axial compression or tension.
The rigidity and determinacy of a simple truss dictate that the number of members m and the number of joints j are related through an equation.
6.2:
Simple Trusses
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:
- External loads are applied at joints: It is assumed that all external forces act only at the joints of the truss, and the weight of each member is considered negligible. If the weight of a member is significant, half of its magnitude is applied as equally distributed vertical forces at both ends of the member.
- Joints are treated as smooth pins: Although members may be connected using welded, bolted, or riveted joints, the joints can be assumed as smooth pins for analysis purposes. This assumption is valid as long as the centerlines of the joining members are concurrent, ensuring that truss members act as two-force members experiencing axial compression or tension.
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.
Leitura Sugerida
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall, Pp. 273-275
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P. (2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill, Pp. 300-302
- Meriam, J.L.; Kraige, L.G. and Bolton, J.N. (2020). Engineering Mechanics ‒ Statics. Hoboken, New Jersey: John Wiley, Pp. 171-172