Co-planar trusses are classified into three types which are

- Simple Truss
- Compound Truss
- Complex Truss

Contents

## 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