Trusses
Also known as Ties-Struts model.
Definition
An assembly of members used to span long distances. Idealized as
- Connected by frictionless pin joints at their ends
- Developing axial forces
Types
2 types:
- Plane truss (2D)
- Space truss (3D)
A truss requires 3 external reactions for equilibrium.
Predominant force is axial force.
Advantages of truss
- High span
- Material efficiency
Triangulation
To create a truss:
- Start with a triangle (
bars and joints) - Add
more bars and 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 (Indeterminate trusses are safer).
Unstable truss
When the shape can be altered, the truss is called a mechanism.
Necessary condition for being simply stiff
Here:
- Number of members (bars) - Number of joints
For a 2D simple (closed) truss
- truss is unstable - truss is determinate if stable - truss is indeterminate if stable
For a 2D open truss
- truss is unstable - truss is determinate if stable - truss is indeterminate if stable