Classification of Coplanar Trusses its Indeterminacy and Stability

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.

Simple Truss Simple Truss

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.

Compound Truss

2. Trusses may be joined by three bars.

Compound Truss

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.

Compound Truss Compound Truss

Complex Truss

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

Complex Truss

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

Determinacy of Coplanar Trusses

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

Stability of Coplanar Trusses

External stability

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

External stability External stability

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

Internal stability of structure truss Internal stability of structure truss Internal stability of structure truss

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