# Trusses and buckling

Trusses are efficient and economical structural systems, since the members experience essentially axial forces and hence the material is fully utilised. For short and medium spans it is economical to use parallel chord trusses such as Warren truss, Pratt truss, Howe truss, etc. to minimise fabrication and erection costs. Especially for shorter spans the warren truss is more economical as it requires less material than either the Pratt or Howe trusses. However, for longer spans, a greater depth is required at the centre and variable depth trusses are adopted for economy.

### Detail of connection

Axes of all members should intersect at a single point.

If the members do not intersect at a single point, the eccentricity causes additional moment $\Delta M$ and therefore additional stresses

## Internal forces

Internal forces of members within a truss are usually obtained by one of the methods: 1) approximate solution, 2) model with continuous flanges (chords).

### Approximate solution

An advantage of the method is simplicity. The model assumes that members are connected into hinges so only normal forces are being solved (no moments).

### The flanges (chords) are continuous

This is more accurate method which results into slightly higher stresses. Diagonals and verticals are connected in hinges.

• On flanges: N, M,
• on diagonals, verticals: N.
1—The approximate solution assumes hinges within each node;
2—The more accurate model assumes diagonals/verticals are connected into a hinge but the chord si continuous

Some members of truss are exposed to compression and have to be considered for buckling.

The upper chord is typically restricted by purlins while the lower chord is unrestrained

Critical lengths for buckling of respective members are taken as

 Upper chord (restricted by purlins) Two independent planes have to be considered. Firstly, in the plane of truss $L_{cr}$ is determined by distance of nodes. Then in the plane orthogonal to the truss plane $L_{cr}$ is determined by distance of purlins. Lower chord $L_{cr}$ is determined by distance of supports (or, if present, by distance of girders constraining the lower chords) Diagonals $L_{cr}$ is determined by distance between joints

The cross-section parameters and/or support types can differ according to respective planes.

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