Classification of Coplanar Trusses its Indeterminacy and Stability

Co-planar trusses are classified into three types which are

  • Simple Truss
  • Compound Truss
  • Complex Truss

Simple Truss

  • The simplest framework that is rigid or stable is a triangle.
  • Therefore, a simple truss is constructed starting with a basic triangular element and connecting two members to form additional elements.
  • As each additional element of two members is placed on a truss, the number of joints is increased by one.

Compound Truss

  • This truss is formed by connecting two or more simple trusses together.
  • This type of truss is often used for large spans.

There are three ways in which simple trusses may be connected to form a compound truss:

1. Trusses may be connected by a common joint and bar.

2. Trusses may be joined by three bars.

3. Trusses may be joined where bars of a large simple truss, called the main truss, have been substituted by simple trusses, called secondary trusses.

Complex Truss

This is a truss that cannot be classified as being either simple or compound.

Determinacy of Coplanar Trusses

Since all the elements of a truss are two-force members, the moment equilibrium is automatically satisfied.
Therefore there are two equations of equilibrium for each joint, j, in a truss. If r is the number of reactions and b is the number of bar members in the truss, determinacy is

obtained by

b + r = 2j Determinate
b + r > 2j Indeterminate

Stability of Coplanar Trusses

If b + r < 2j, a truss will be unstable, which means the structure will collapse since there are not enough reactions to constrain all the joints.
A truss may also be unstable if b + r  2j. In this case, stability will be determined by inspection

External stability

A structure (truss) is externally unstable if its reactions are concurrent or parallel.

Internal stability

May be determined by inspection of the arrangement of the truss members.

  • A simple truss will always be internally stable
  • The stability of a compound truss is determined by examining how the simple trusses are connected
  • The stability of a complex truss can often be difficult to determine by inspection.
  • In general, the stability of any truss may be checked by performing a complete analysis of the structure.
  • If a unique solution can be found for the set of equilibrium equations, then the truss is stable

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