Trusses

An assembly of members used to span long distances. Idealized as

• Connected by frictionless pin joints at their ends
• Developing axial forces

Aka. Ties-Struts model. Predominant force is axial force.

Types

2 types:

• Plane truss (2D)
• Space truss (3D)

A truss requires 3 external reactions for equilibrium.

Advantages of truss

• High span
• Material efficiency

Triangulation

To create a truss:

• Start with a triangle ($3$ bars and $3$ joints)
• Add $2$ more bars and $1$ joint repeatedly

This type of truss is a simple truss.

Simple (Closed) Truss

When a truss is only made of bars and joints.

Open Truss

When a truss is pinned directly to a foundation. It has 1 member & 2 free joints less than a closed truss.

Stability of trusses

When a truss is:

• unstable: it’s called a mechanism
• stable: it’s called a structure

Stable truss

When the shape cannot be altered, the structure is internally stable.

Stable & determinate (simply stiff)

Determinate means internal forces can be determined by laws of statics alone.

Stable & indeterminate

Indeterminate means laws of statics alone are not sufficient to determine forces; relative stiffness of members will influence the solution. One or more compatibility equations (related to truss deformation) must be used. Indeterminate trusses are safer.

Unstable truss

When the shape can be altered, the truss is called a mechanism.

Necessary condition for being simply stiff

Note

These are necessary (but not sufficient) conditions.

Here:

• $m$ - Number of members (bars)
• $j$ - Number of joints

For a 2D simple (closed) truss

• $m<2j-3$ - truss is unstable
• $m=2j-3$ - truss is determinate if stable
• $m>2j-3$ - truss is indeterminate if stable

For a 2D open truss

• $m<2j$ - truss is unstable
• $m=2j$ - truss is determinate if stable
• $m>2j$ - truss is indeterminate if stable

For a 3D simple (closed) truss

$m=3j-6$

For a 3D open truss

$m=3j$