Trusses support load much like beams, but for longer spans.  As the depth and thus dead weight of beams increases with span they become increasingly inefficient, requiring  most capacity to support their own weight rather than imposed live load.  Trusses replace  bulk by triangulation to reduce dead weight.

1  Unstable square panel deforms under load. Only triangles are intrinsically stable polygons
2  Truss of triangular panels with inward sloping diagonal bars that elongate in tension under load (preferred configuration)
3  Outward sloping diagonal bars compress (disadvantage)
4  Top chords shorten in compression Bottom chords elongate in tension under gravity load
Gable truss with top compression and bottom tension

Warren trusses
Pompidou Center, Paris by Piano and Rogers

Prismatic trusses
IBM Sport Center by Michael Hopkins
(Prismatic trusses of  triangular cross section provide rotational resistance)

Space trusses 
square and triangular plan

Note: Two way space trusses are most effective if  the spans in the principle directions are  about equal, as described for two-way slabs above.  The base modules of trusses should  be compatible with plan configuration (square, triangular, etc.)

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