1. General
When looking for a way to overcome a possibly huge amount of linear load combinations, users can look for load groups calculation instead. The „Maximum of load groups“ calculation is an effective way to combine many load cases into results without making the load combination for each situation separately.
In principle, the Maximum of load groups function calculates every load case and creates load combinations on the fly based on the maximum of the load case values. So, in theory, only the maximum load combinations are made by the software behind the scenes.
Alternatively, the load groups can be used to automatically generate all possible load combinations in the Load combination dialogue box
Note: Maximum of load groups calculation is linear! For non-linear calculation, load combinations need to be created
2. Defining the groups
After the definition of load cases either manually or using the macros (wind, deviation, moving load, etc.) users can create load groups with this function in the Load tab
Figure 1. Load groups tool
Selecting the function will open the load group dialogue window where we can see, create, modify and delete load groups.
Figure 2. Load groups dialogue window and options
Load cases that have not been assigned to any group yet will be located under the “Independent load cases” group. These cases will not be considered when calculating the Maximum of load groups results.
Note. Load cases in the “independent” group will not be selectable, when user wants to use the “Generate” function in the load combination dialogue window to automatically create load combination based on the load groups.
User can make new load group with the “Add group” tool in the bottom left. Each group can be one of the different types: Permanent, Stress, Temporary, Accidental or Seismic.
Each load case can be assigned to only one group. User can do it by clicking and dragging the load case from one group to the other. User can also select a group and then right click to have additional options. User can select the “insert load cases” option which will open a dialogue box to select multiple load cases from the “Independent load cases” group.
Figure 3. How to quickly move independet loads to groups
3. Load group parameters
Each load group has its own parameters. For example, the Permanent type has the combination factors γ and ξ, but the Temporary type has safety factor γ and combination factor ψ0 and factors for frequent and quasi-permanent variable actions (ψ1 and ψ2 respectively). All the factors and definitions come from Eurocode 1990.
Figure 4. Load groups parameters
For Temporary groups, the group can be set as “Potentially leading”. Then the load cases can take this position in the load combination:
Figure 5. Potentially leading temporary case meaning in Eurocode
Load groups also have an option for “Load case relationship”. This setting tells FEM-Design if the load cases that are in this group should act alternatively (one of them can act at a time), simultaneously (one, or more can act at the same time), entirely (all of the cases in this group act always together at the same time) or by custom settings (user can set which cases can act together and set the factors of how much they act at a time). We will describe the custom setting later.
User can also set a combination method for ULS combinations (6.10 or 6.10a+b). This is a common setting and affects all the groups and cases in the same way.
4. What happens behind the scenes while calculating
A simplified version of what happens in FEM-Design is this:
it will calculate all the cases that are assigned to any group and find the deformations, reactions, internal forces and stresses as usual for separate cases. Then it will find the biggest and smallest component for each one of them in each direction (for example biggest deformation for case1 in x+ direction, smallest deformation for case1 in x- direction, etc.).
After this it uses Combination method, Load case relationship and Load group parameters to combine the load cases into “combinations” which will produce the highest or lowest of the previously described components (biggest deformation for case1 in x+ direction, smallest deformation for case1 in x- direction, etc.).
For example, to get the biggest deformation in x+ direction, user does not have to define which combination produces it, but we can take the biggest deformation in x+ direction from all the load cases and combine the correct cases with the factors and relationship and thus producing the combination on the fly.
5. Examples of use and deep dive
Let us look at this example for deeper understanding how each function works. General about the following two examples:
We have a 6m long simply supported beam in X direction with 14 different load cases. One is permanent load (+Struc. dead load) and the others are all temporary load cases. Each case contains only one load.
Load case “add load” contains one continues load 3kN/m like in the picture:
Figure 6. Vertical load in "add load" case
We have divided the beam into 6 pieces with 1m length and placed a point load in the center of each piece. There will be a Y direction load and a X direction load in each center point. Y and X direction loads are in separate cases.
For example, the load case LLc1 contains a 10kN Y direction point load in the first piece of the beam, case LLc2 contains the Y load in the second piece of the beam and so on. Like this:
Figure 7. Y direction loads and load cases on the model
Similarly, the LLc1_h case contains a 2kN X direction point load in the center of first piece, LLc2 contains similar load in the center of the second piece and so on. Like this:
Figure 8. X direction loads and load cases on the model
Example 1:
We have divided the load cases into groups like this:
Figure 9. Load groups for example 1
Each temporary load group has the same parameters. Permanent load group has the same “Alternative” relationship as the temporary groups, but it does not matter, since there is only one load case in that permanent group, and it is always selected in the combinations.
Let us look at the results for example Maximum of load groups -> Translational displacement -> ex+ in ULS.
What has happened behind the scenes is that FEM-Design:
a) calculated all the displacements for all load case separately
b) finds the ‘x’ component for each load case’s displacement in each finite element node
c) selects the case that produces the maximum ‘x’ component in each group for each finite element node. Since the relationship was set to “Alternative” for each load group, then it can only take one of the cases from each group (or nothing from a group).
d) superimposes the cases from each group into a combination using the selected combination method (in this example it is 6.10a+b for the ULS) for each finite element node
e) displays the resulting total deformation from created load combinations in each finite element node (each node may have different load combination) and creates a “smooth” graph based on that.
Please note that the total deformation is shown, not only the component of the results direction (so it is not a graph of X+ direction deformation, but a total deformation in any direction, while the X+ was biggest).
In this example, the maximum X+ component in the middle of the beam was coming from a load combination that consists of 1,0*str dead load + 1,5*LLc3_h.
Figure 10. Example 1, Alternative relation in groups - Maximum of load groups, Translational displacement, ex+ in ULS
This combination is made because:
* a case from permanent load group needed to be taken, so the only case “str dead load” was taken from that group.
* From the group “Added Live” nothing was selected, since the only case there “add load” only produces 0 in the X+ direction and “Alternative” relationship allows us to not take any load case if needed.
* From load group “LL_Y direction” also nothing was taken since the load cases in this group also produce 0 in X+ direction (they have deformation in Y- direction).
* And finally, a case “LLc3_h” was taken from the load group “LL_X direction” since this case produces the maximum X+ deformation in the middle of the beam and only one load case can be taken from a group with “Alternative” relationship.
Now the combination factors come from the group and combination method selection. Here for example, the 6.10a would create a combination 1,0*str dead load + 1,5*0,7*LLc3_h for the favorable action and 1,35*str dead load + 1,5*0,7*LLc3_h for the unfavorable action (note that the dead load is not acting in X+ direction, so either one of them is “valid maximum” in X+ direction).
The 6.10b would create a combination 1,0*str dead load + 1,5*LLc3_h for the unfavorable and 1,35*0,85*str dead load + 1,5*LLc3_h for the favorable action (again the dead load is not acting in X+ direction, so either one of them is “valid maximum” in X+ direction).
If we would have set the relationship of group “LL_X direction” to “Simultaneous”, then the resulting combination would be this instead:
Figure 11. Example 1, Simultaneous relation in groups - Maximum of load groups, Translational displacement, ex+ in ULS
In this case the method of getting the result is similar, but since the relationship was set to “Simultaneous” then many load cases can be taken from the group (even all the cases from this group could be taken at the same time, but right now it was not necessary, because the cases 4, 5 and 6 in this group produce the “counteractive” deformation in X+ and thus make the X+ smaller).
If we would set the relationship of the group “LL_X direction” to “Entire”, then all the cases from that group must always be used together (or none at all).
Please note that all the cases from one group are considered the “same action” and thus receive the same safety and combination factors. So, in the 3 examples above, all the cases from group “LL_X direction” always receive safety factor 1,5 and all of them either do not receive the combination factor ψ0 (if the group is considered dominant or leading in 6.10b) or they all receive the same combination factor 0.7 (for 6.10a and also if the group is considered not dominant in 6.10b).
So if user wants to have different safety or combination factors, then they need to make multiple load groups with different values and place suitable load cases inside.
Also, note how the deformation value still is 1.825 in both pictures above. This is because the numeric values were placed using the “Automatic numeric values” function, which always shows the maximum vectorial deformation (so total max deformation in any direction).
User can see the X+ values using the “Numeric value” tool and selecting a predefined direction:
Figure 12. Looking at the value in only one direction
Example 2:
We use the same model and same loads like in example 1, but the groups have made differently. We have made two subgroups under the LL_Y direction group:
Figure 13. Load groups for example 2
The easiest way to get multiple load cases from one group to the other is to first insert them back into the “Independent load cases” group using function that was described above (Insert load cases) and then insert them to the new subgroup.
Now we delete the “X” group, as it is empty and no longer useful. We also add position tags to all load cases in these two new subgroups like this:
Figure 14. Example 2 - how the position is set
Inserting the position tag is a manual work, but it is needed for the next step. The tags must correlate between the two subgroups, so make sure the typing is correct.
If the tags are correct, then we can make the subgroup SG-2 to be a “slave” to the SG-1.
Figure 15. Marking one subgroup as slave
Finally, we can set relationship of the load group LL_Y direction to Custom and make some modifications there. For example, let’s add two situations like this:
Figure 16. Custom relationship
With these modifications we are forcing FEM-Design to:
* Use one combination from both subgroups so that only pos1 and pos1 can act together or pos2 and pos2 or pos3 and pos3, etc. This way it is not possible to get a combination with cases LLc1 and LLc4_h together. It is very useful especially in bridge engineering where there are vehicle vertical load and horizontal braking force acting at the same time.
* in the final combination will have the custom relation factors applied (in addition to the safety, combination and variable action factors). So we could see for example a “1.00*LLc1 + 0.66*LLc1_h” or 0.55*LLc4 + 1,00*LLc4_h”.
We can add as many situations as we like.
Now if we look at the results ez- for example, then we see how the master-slave subgrouping worked. We only get pairs with same position (for example the “LLc3 + LLc3_h“ or “LLc5 + LLc5_h“) or we get nothing from that group at all (for example the result in the beginning of the beam where it is “0,85*1,35*str dead load + 1,50*add load”).
We can also see how the custom situations that we made previously are acting here (we see the 0,66 multiplier on the LLc3_h case but of course the 1,00 multiplier is not shown for LLc3). “The situation 2” did not produce any “more negative” values for the ez- so that is why we do not see it here.
Figure 17. Example 2. Custom relations in groups - Maximum of load groups, Translational displacement, ez- in ULS