Option H, apart from allowing the introduction of horizontal loads, which will be included in our overlapping slabs model, generates a framework model for further analysis. This framework model, generated automatically , is a typical 3D model which will be handled with STATIK.It is especially made to design vertical elements and to analyse earthquakes on a building, since it automatically prepares the necessary calculations to easily carry out an equivalent forces analysis and compare it with one with a more accurate response spectrum (which it also prepares). If you wish to do earthquake analysis in STATIK, the dynamic option (D) will also be needed for that program.
With the framework model, normally, the basic behaviour of the building can be successfully simulated. It gives interpretable results, from which the dimensioning of the structural elements can be done. It should be taken into account that, logically, for buildings with a more especial typology, more complex models will be necessary. CEDRUS’ building module is very broad and can adapt to almost any kind of structure, however, the progres from the first geometric model of the building until an effective and representative framework model of what is going to be built is not always simple and it can become a challenge for the engineer.
The elements that constitute the floor slabs can be considered in different ways when generating the framework model. Depending on how we decide to take them into account our building will have one behaviour or the other.
- REGARDING THE DISPLACEMENTS
The slabs are modelled in their plane as stiff membranes. This is achieved using nodal constraints. One node in each storey is considered the master and the other nodes slaves with respect to DX, DY, and RZ, connected rigidly to the master nodes.
- REGARDING THE BENDING BEHAVIOUR
There are three available models depending on the activation or deactivation of the options ‘Include beams’ and ‘storeys with slab stiffness’, in the dialog box that we can find on the ‘framework model tab’ in CEDRUS:
a) Completely flexible: the flexural stiffness of the slabs is neglected. The slabs’ only role is to keep the distances between the nodes on the same plane constant. This is equivalent to modelling the building as a bracket.
This is done leaving both options on the dialog box in blank:
b) Gantries model: apart from the vertical elements, the horizontal ones (beams) are also considered. This requires a building model with gantries. All the defined horizontal members and slabs will be considered in the model.
We will get to this model selecting the indicated option on the dialog box:
c) Model with slab stiffness: The flexural stiffnesses determined in CEDRUS are introduced in the STATIK model affecting the behaviour of all the nodes contained in a storey. This is equivalent to modelling a lab using a finite element program.
For CEDRUS to generate this STATIK model, we will have to indicate, in the highlighted zone, the storeys we want to consider.
Let’s see, with another simple example, the differences between considering one model or the other.
If we look at the following building:
In which we introduce a horizontal wind load that is equivalent to a series of 100 kN point loads on each of the storeys:
We will now generate three framework models considering one of the three types of models explained before. In the figures below we will see the deflections on the top of the building for the wind load defined.
- TYPE A FRAMEWORK MODEL: COMPLETELY FLEXIBLE
- TYPE B FRAMEWORK MODEL: GANTRY MODEL
- TYPE C FRAMEWORK MODEL: MODEL WITH SLAB STIFFNESS
We can see that, as we change the models (A->B->C), we reduce the strains on the building.
At this point, it is important to have in mind that the choice of model can significantly condition the results. The engineer must be capable of modelling the structure with global coherency and, in order to do that, it is crucial that they correctly interpret the interaction between CEDRUS and STATIK for these kind of projects:
- If it is not wanted for the slabs to share these forces, they will be designed in CEDRUS only for the vertical loads and in STATIK we will design the vertical elements with the building working on cantilever (we would choose type A model).
- If on our storeys there were beams we could dimension them to help supporting the horizontal loads and in STATIK we would make a gantry structure model (we would choose type B model).
- If it is assumed that the slabs are going to collaborate on the behaviour of the building against horizontal loads they must be designed accordingly in CEDRUS (dimensioning of reinforcements including horizontal loads. See the article on this topic). It would also be necessary to have reinforcements on the pillars in accordance with that assumption (we would choose the type C model). This is, also, the option that should be chosen when the complexity of the building implies that option B, with both beams and slabs, it is too difficult to carry out. It is also the option chosen in the not very probable case that some pillars emerge in some storey without a beam below to carry the loads to other pillars that descend to the foundations.
Finally, we would like to make a statement on the flexural stiffness reduction factors of the elements (EI) that appear in the dialog box:
The selection of these factor will also affect the results we obtain. The program gives us a default factor of o.50, which will result in a reduction in half of the stiffnesses of the elements in the framework model.
The reason why this value is given to us as default is because of what is explained in page 30 of PrEN 1998-1: 200X:
As it is also indicated, these values can be calculated in a simpler way but they will never be lower than those obtained applying article 184.108.40.206 of EN1992-1:2002.
Lastly, if a type C model is not considered (storeys with slab stiffness), the EI factor indicated for the slabs will not have any effect.