Calculations on a stage truss

This post is another addition to our ‘beyond the box’-category of application scope examples for Ple4Win. See the starting page for more information.

Stage or lighting truss

These kind of trusses allow lighting designers the freedom to hang LED or automated fixtures, often called “movers”, wherever they choose. Audio designers also often use these structures to affix loudspeakers to it. Stage trusses can be found in theaters, concert halls, performance arts halls, trade-shows, arenas or stadiums.  Anywhere staging equipment is deployed you are likely to find these aluminum trusses.

Trusses come in several different shapes and lengths. “Sticks” or sections of trusses can be connected together in multiple, complex ways to create almost any structure necessary, allowing lighting fixtures, video, audio or other staging equipment to be hung with ease.

Trusses at an events hall

As a truss is basically a collection of pipes welded together, the idea arose to model a simple truss in Ple4Win. From the available documentation of producers and (re)sellers of trusses it was possible to create a fairly accurate model of a  2 meter section of a triangular truss. Its behaviour under load was calculated using the program. Furthermore, with a 4 meter section (two connected 2 meter sections) calculations of a known loading situation were compared with its real-life measurements.

Model of a triangular 2 m truss

Model and behaviour of a 2 m F33 Standard Series truss

The “larger” triangular trusses are usually called F33 trusses. These have 50 mm diameter main pipes spaced 290 mm horizontally and 257 mm vertically. Common lengths are between 0.25 m and 4 m. The Ple4Win model of a 2 meter section consists of 1527 elements and 36 connections.

This truss has been rigidly fixed at both ends and loaded slightly asymmetric with a very heavy “loudspeaker” at about 85 cm from the right end. As can be seen from the calculation results, in this case the truss not only bends downwards but also twists a bit.

Truss (2 m) loaded slightly off-center (bending moment shown in colour, displacements × 5)

Model and behaviour of a 4 m F33 Standard Series truss

The model above is interesting as it shows the dynamics of a truss consisting of triangular units constructed with straight members under load, but it is not a realistic situation. To compare the model with reality, a 4 meter section has been constructed consisting of two connected 2 meter sections. For the 4 meter set-up a whole series of measurement results on physical trusses are available: Deflection of the truss is reported when uniformly distributed loads, center point loads, point loads in third-, quarter- or fifth-point are applied.

The center point load scenario has been chosen as test case. According to the specifications, a center load of 438 kg should result in a deflection of 9.5 mm.

Truss (4 m) loaded at the center (displacement shown in colour, displacements × 5)
Vertical displacement of the top beam of the truss (4m) under load

The result of the Ple4Win model calculations show a deflection of 9.3 mm, which is in very good agreement with the test results.