Result Combinations 2 | Application Example and Comparison with Load Combinations

Technical Article

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My previous article Result Combinations 1 explained the basic principles of result combinations on simple examples. This article describes a further application case, which combines the definition options of Example 1 and Example 2. Likewise, the effort should be compared to a combination by means of load combinations.

Application example

The following load cases are given:
LC1 - Self-weight
LC2 - Snow
LC3 - Payload Alternative 1
LC4 - Payload Alternative 2

We are looking for the internal force envelope for the ULS according to EN 1990 - DIN. The payload cases have to be considered alternatively in the combination.

Combination by means of result combinations

According to EN 1990 - Eq. 6.10, the actions have to be provided with partial safety factors as well as combination coefficients. However, when defining a result combination, only one factor can be defined. If it is not clear which variable action is the governing factor, several action combinations have to be created.

Figure 01 - Result Combinations

Combination by means of load combinations

The same four load cases will now be superimposed by means of load combinations. To ensure that the most unfavorable internal forces are found, all possible combinations are created. These, too, must be created taking into account the predominantly variable loads as well as the alternative effect of the payloads. The basic prerequisite for the subsequent comparison to the result combinations is a linear system as well as the calculation of the load combinations according to the first-order theory.

Figure 02 - Envelope

Comparison of Results

If you compare the internal forces of RC3 and RC4, there are no differences in this example. However, it should be emphasized that the solution using load combinations requires a total of nine combinations (8 COs + 1 RC), whereas the solution using result combinations only requires a total of three combinations. This saving effect not only affects the calculation time, but also the overview in the program and especially in the report.


In geometrically linear models that can be calculated according to the first-order theory, result combinations are an effective means of combining load cases. It may be useful for structures with a multitude of load cases (for example, loads from motion), which otherwise lead to a high number of load combinations and make the documentation confusing.


[1]  Eurocode 0: Basics of structural engineering; DIN EN 1990: 2002
[2] Manual RSTAB. Tiefenbach: Dlubal Software, February 2016. Download



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