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FAGUS allows carrying out a calculation in series for a cross section that will allow us to evaluate its behaviour when, for example, we apply , for example, a history of loads to it, and even when such cross section is compound and evolves in a series of building stages. As we know, this calculation in series can be defined in the ‘Analysis’ tab:
Logically, for any cross-sectional analysis, it is of total importance to have control over the point on which the forces are being applied, either it is the centre of gravity of the section or on the ‘axis point’ from STATIK, which can be used interacting with FAGUS.
The subject of this article is to explain on what point of the section we will be introducing the forces when we run a calculation in series in FAGUS. For that purpose, we will consider two cases:
NOTE: What is explained next will appear when there is a axial force in the section. If there is only a moment, the differences will not show up as it is a force without a point of application.
1.- Cross section used in STATIK in which there is an axis point:
Whenever there is an axis point in our cross section, the forces will be considered by the program as applied at that point automatically. Later, a translation of those forces will be carried out to ‘take them’ to the centre of gravity (COG) of the cross section and then run the analysis. It will be this way regardless of whether we choose the following option for the analysis or not:
We will have an ‘axis point’ when, for example, we introduce a beam of variable cross section in STATIK and we want the top face to be the one following the guideline of the bar we draw because, if we do not introduce that point, the bar will go through the centres of gravity and the beam will not reflect reality.
- Without an ‘axis point’:
- With an ‘axis point’:
In STATIK we can obtain the forces on the centre of gravity or on the axis point of the cross section as we want them to. However, it is important to know that if, later on, we make a calculation in series in FAGUS, we must enter the forces obtained on the axis point. In the opposite case, we would enter the forces on the COG and FAGUS will consider them at the axis point automatically, which is wrong.
Let’s look at an example:
We have a cross section made of a metallic HEB profile on top of which rests a concrete compression slab.
If we introduce an axis point in the middle of the top face of the concrete slab:
The centre of gravity (COG) being on the following position:
Implementing the following calculation in series, in which we will consider only one stage deactivating the concrete slab and carrying out an efficiency analysis, specifying that the forces are being introduced on the COG.
Now we will see how FAGUS automatically considers that forces are introduced in reality on the axis point and then are translated to the COG:
Indeed, on column ‘P’, ‘A’ indicates axis point and ‘S’ indicates the centre of gravity. In the row of ‘A’ we are looking at the forces introduced on the dialog box and, in the row of ‘S’, the translated ones.
One must, therefore, take special care of the forces introduced when we do a calculation in series of a cross section with an ‘axis point’.
2.- Compound cross section that evolves with certain building stages
The calculation in series gives us the option of starting off with a compound cross section in which we can activate and deactivate some of its parts to consider the different building stages. FAGUS will always consider that the COG is the corresponding to the complete cross section, whether we have deactivated some part of it or not.
That said, it is very important to know that, if we want to analyse an specific building stage derived from a compound cross section using a calculation in series in FAGUS, we must always enter the translated forces, taking them from the COG of the full cross section to the COG of cross section at the right stage. If we do not do this, we will be considering some forces on a different COG from the one corresponding to the cross section o the stage being analysed and, thus, the analysis would be wrong.
Let’s look at an example:
Consider the same cross section as in section 1, we are going to carry out a comparison of efficiencies when a calculation is series is done over the full cross section deactivating the concrete slab against when the analysis is done directly on the isolated metallic profile.
2.1.- Calculation is series over the full cross section deactivating the concrete slab:
2.2.- Calculation of the efficiency considering the isolated metallic profile:
We can see that, indeed, there is a difference in the results due to the different position of the centre of gravity in each of the cases. If we carry out the translation of forces taking them from the COG in case 1 to the COG in case 2 and knowing that the distance between them is 0.15 m:
N = -200 N
My* = My + N*e = 50 + (-200)*0.15 = 20 kNm
The results are equivalent.
In conclusion, we want to insist on the importance of controlling which forces we are introducing in our analysis in FAGUS because, depending on where we have obtained them, we might be introducing them in the wrong way.
It is important to clearly know that in a calculation in series it is not the same to deactivate parts of a cross section than to introduce some forces (that, as we have seen, will be on the axis point, if there is one, or on the centre of gravity of the full cross section) that start on a variant of the cross section. Loading a variant of the cross section, for FAGUS, is the same thing as loading a cross section with those characteristics, that is, the forces, unless there is an axis point, are going to be placed on the centre of gravity of the variant. Fortunately, it is usual that a cross section that evolves in STATIK has a defined axis point (so that the bar passes through it and to monitor the relative position of the elements that appear in the cross section through the variants), therefore, if we use a variant of a cross section to run a calculation in series, the most probable case is that it already has an axis point and so the forces are already on it. Hence, be careful if a calculation in series begins without the variant having an axis point.