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 (
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. 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
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