Differences between dimensioning building cores grouping or ungrouping the ‘wall pillar’ elements that constitute them.

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The last version of CEDRUS 7, with its building module, includes a new way of introducing the elements that constitute ‘walls’. A new ‘wall pillar’ element is introduced. It is a ‘wall’ but with more properties to consider in the structural model. The ‘wall pillars’ can also group to make stiffer cores supportevely interacting with each other.

In this article we are going to analyse the differences between dimensioning the elements that constitute the core of a building when they are introduced in the model in a group or ungrouped.

• If the core is entered without grouping the wall pillars it is made of, each one of them will work as an independent cross section that will have to be dimensioned from the external forces resulting from the load distribution from the analysis of the global model of the building.
• If the ‘wall pillars’ that constitute the core are grouped, it will behave as a complete cross section against the external forces from the global model of the building.

Let’s see, from the example of a complete building, how the behaviour of a core varies depending on the way it is introduced in the model.

The following building is modelled in CEDRUS 7:

 

In it there are two communications cores that, in top view, have the following shape:

 

The building module of CEDRUS 7 allows the conversion of the model to a STATIK 7 framework model, from which it will be possible to analyse any cross section. In this case, if we independently introduce the ‘wall pillars’ of the cores, in the model there will be 4 bars corresponding to each of them. If, on the other hand, the grouping is done, the cores will correspond to one only bar that will be analysed as a full cross section.

UNGROUPED MODEL

 

In red, the 4 bars that correspond to the cross sections of the 4 wall pillars that constitute the core.

GROUPED MODEL

 

In red, the only bar that corresponds to the full cross section that constitutes the core.

By dimensioning the longitudinal reinforcements of each of the elements by a calculation with FAGUS 7, the following results are obtained:

UNGROUPED MODEL

To facilitate the identification of each of the elements we will name them:

 

NOTE: The results that are shown below come from the most unfavourable combination of forces.

• RESULTS FOR ELEMENT W1

 

The total longitudinal reinforcement obtained is: As = 17952 mm2

• RESULTS FOR ELEMENT W2

 

The total longitudinal reinforcement obtained is: As = 4153 mm2

• RESULTS FOR ELEMENT W3

 

The total longitudinal reinforcement obtained is: As = 6670 mm2

• RESULTS FOR ELEMENT W4

 

The total longitudinal reinforcement obtained is: As = 6343 mm2

If the results are added together it is found that the core group needs 35118 mm2 of longitudinal reinforcement.

GROUPED MODEL

If the same analysis is carried out but considering all the grouped elements:

 

The total longitudinal reinforcement is : As = 25783 mm2

This is, approximately, 27% less reinforcement than when doing the analysis with ungrouped elements.

The difference is due to the fact that:

• In the case of the ungrouped elements, the external forces for each of them come from a load distribution in the global model that is a function of the stiffnesses of each of them separately. In the grouped case the stiffness is obtained from its full cross section.
• The analysis with the group of elements is done over a full cross section that will have a completely different behaviour to that of each separate element. That is, the distribution of forces in each of the individual wall pillars (that make up the only grouped wall pillar) will be different because there is an interaction between parts (attachments).

It is very important to clearly know that, in order for the cores to behave as if they were one only full cross section (grouped wall pillars) and, therefore, for the model to reflect reality, the connections between wall pillars must be materialised so that they make attachments. Otherwise there will be cores working in an ungrouped way that will not be reinforced to work like that.

To see the influence that these concepts have on the slabs of a building, read the related article clicking here.