Celebrating the introduction of a European truss standard and an effort to answer more of the common questions on this subject, this post will initiate a short series of posts, all looking a bit deeper into different structural aspects of truss systems; beginning with the simple equations used when drafting load tables and some of the related questions.

Pls. do note, this post is not intended to provide a comprehensive guide for DIY static calculations, but merely published to increase end-user knowledge and awareness of the structural engineering applied in the Entertainment Industry.

## How is a truss load table created?

Generally, load tables are based on static calculations of a simply supported beam for each of the load cases: UDL, CPL, TPL, QPL, and FPL.

Using a spreadsheet, some simple logic and the commonly available equations used to calculate a simply supported beam for each specific load case, a load table can easily be composed for a range of spans (L), only requiring knowledge of the truss self-weight (g), the allowable bending moment (M) and the allowable shear force (V) of the truss. Further adding a derived formula of deflection for each of the load cases, typically using a rate of maximum deflection, (eg. L/400), and some general design values of the truss section, will result in a more accurate allowable line or point load for a given span, when the lowest of the 3 calculated loads is applied. (Below a screenshot, showing an example of how the calculations could be structured).

Small variations do occur when comparing results directly with the load table provided by the manufacturer, primarily originating from the rounding of numbers, the selected value of the standard gravity used during conversion from forces (usually Newton in Europe) to load (given in kg in Europe) and the selected deflection rate.

An overview of the most common derived formulas for each load case is added at the end of this post. Do note any use of the provided formulas are at your own risk.

## How is the deflection rate defined and should it be used as a limiter?

Deflection refers to the degree of displacement of an element under load, and should generally be divided into two main types: irreversible permanent deforming aka. yielding and reversible (covering the state, when the truss regains it non-deflected form after the load is removed).

Commonly the deflection rate should be set dependent on the intended use of the truss, eg. if the truss is intended to support a glass structure, the allowable deflection rate should be as low as possible, to prevent unintended stress’ in the supported structure.

When using deflection as a limiter, the calculation should use the partial safety factors of the serviceability state (SLS) including the deflection caused by self-weight. Due to the decrease of allowable spans, the load tables provided by the manufacturer, often do not include the deflection caused by self-weight. Adding to the reasons why load tables only should be used for initial planning purposes.

Do note, when referring to the Eurocode, the National Annexes (defining specific changes or interpretations of the code for each country) may specify limits of maximum allowable deflection.

## What information is needed to calculate the design values of a truss?

The design values of a truss section commonly refer to the allowable bending moments (M), shear forces (V) and normal forces (N) of the truss. All determined through a thorough analysis of the resistances of all truss components; including cross sections, main and lattice members, each individual part of the connection system used to assemble the truss, as well as all welded and bolted connections. And requiring specific information of material properties and geometrical data of all parts.

The upcoming posts in this series will look at each individual step of the calculation process. [A direct link will be added to the next post]

## Appendix: A short list of derived formulas.

Definition of symbols: Truss span (L), bending moment (M), shear force (V), deflection (Δ), moment of inertia (I), self-weight (g), Young’s modulus (E), Point load force (P), line load (q).