# Result Combinations 1 | Basis

### Technical Article

RFEM and RSTAB provide two different methods for the superposition of load cases. Using load combinations, the loads of individual load cases are superimposed and calculated in a ‘big load case’. On the other hand, result combinations only combine the results of the individual load cases. This article describes the basis of defining result combinations and explains it in detail in two examples.

#### Basis of Definition

A combination of load cases using result combinations allows for a simple addition as well as a comparison of the results (either/or). Therefore, the definition of result combinations is more complex than the definition of load combinations and depends largely on a ‘Factor,’ ‘Criterion’ and ‘Group’.

Figure 01 - Result Combination

The ‘Factor’ multiplies the results of load cases. Usually, a partial factor or a combination factor is defined here. Positive values mean addition, negative values mean subtraction.

The ‘Criterion’ determines whether the results of a load case are always applied in the combination (‘Permanent’) or have only an occasional effect (‘Variable’). Thus, the results of a load case with the ‘Variable’ criterion are only considered in the superposition if they make an unfavourable contribution to the result. Since it is not clear whether the maximum positive or the maximum negative value contributes to the unfavourable result, both values are recorded.

The ‘Group’ allows you to set alternative actions of load cases. For example, if there are two load cases assigned to the same group, either the results of the first load case or the second load case will be taken into account in the combination.

In the following two examples, result combinations are used for the addition of results (Example 1) and for finding the maximum and minimum of several load situations with alternative actions (Example 2).

#### Example 1: Addition of Results

There are the results of three different load cases on the same x‑location in the model. Only the normal force N, shear force V_{z}, and the bending moment M_{y} are considered in a simplified way. Load Case 1 includes permanent loads, the other two load cases are imposed load cases.

Figure 02 - Internal Forces by Load Case

By using the result combination, all three load cases will now be added up. The load cases are defined as follows:

Figure 03 - Addition Using Result Combination

Since Load Case 1 includes permanent loads, the ‘Permanent’ criterion is assigned to it. The imposed load cases may act but not necessarily. Therefore, this criterion is set to ‘Variable’. Also, both imposed load cases may occur simultaneously. Thus, the group is not defined. To simplify the theoretical recalculation, no partial factors are applied (factor = 1.0).

As a result, you get the maximum value and the minimum value for each internal force. Similarly, the corresponding internal forces are displayed.

Figure 04 - Resulting Result Combination

Let's explain the results in more detail in the calculation of the values Max N in the first line. In this case, the basis of the calculation is Load Case 1 as this has been defined as a ‘Permanent’ action. The normal forces of the other two load cases are only used if they increase the normal force. Load Case 2 increases the maximum normal force, while Load Case 3 reduces this again. Therefore, only Load Case 1 and Load Case 2 apply to the maximum normal force:

$$\mathrm{Max}\;\mathrm N\;=\;-20\;+\;200\;=\;180\;\mathrm{kN}$$The related internal forces must be calculated using the same combination:

$$\begin{array}{l}\mathrm{rel}.\;{\mathrm V}_\mathrm z\;=\;25\;+\;5\;=\;30\;\mathrm{kN}\\\mathrm{rel}.\;{\mathrm M}_\mathrm y\;=\;-50\;+\;(-10)\;=\;-60\;\mathrm{kNm}\end{array}$$In the same way, the following lines are calculated and the maximum and minimum values for each internal force, including the associated values, are obtained. These can now be used for further design.

#### Example 2: Result Envelope of Load Situations with Alternative Actions

In the second example, the results of three load combinations are calculated. These cannot be combined, of course, but it is possible to compare the alternatively acting ones to each other. The aim is to get the maximum and minimum forces in a similar way as in the first example. The following values are available:

Figure 05 - Internal Forces by Load Case

The result combination is defined as follows:

Figure 06 - Result Combination as Envelope of Alternatively Acting Load Situations

The results of the load combinations already include almost all partial safety factors and combination coefficients. Thus, the factor remains 1.0. To perform the alternative analysis, each load combination must have the same group number. In this way, the result of CO1 or CO2 or CO3 is recorded.

It is also important to assign the ‘Permanent’ criterion to all combinations. That is, a result of three combinations must always be used. If the ‘Permanent’ criterion is assigned to all combinations, the minimum normal force would not be 150 kN, but 0 kN. In this case, the normal force is zero if none of the three load combinations is acting. The maximum and minimum internal forces are displayed in the following table:

Figure 07 - Resulting Result Combination

For clarification, the first line will be explained again. We are looking for the maximum normal force. These can be found in CO2 as 350 kN. To get V_{z} and M_{y}, it is only necessary to adopt the corresponding internal forces from CO2. Thus, the resulting V_{z} is −5 kN and M_{y} is 8 kNm. These results can be further used for design in add‑on modules.

#### Summary

This article describes the basis of defining result combinations and explains the most common applications in an example. Of course, it is also possible to combine these definition procedures. This will be explained together with comparison of load combinations in Part 2 of this article series.

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