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As many of you may already know, STATIK and FAGUS programs are able to interact to carry out sectional analysis of all sections of a structure modeled in STATIK. This interaction allows to analyze and dimension the reinforcement of all sections without the need to manually export neither the sections themselves, nor the stresses. Structures may even have prestressing tendons, in which case, they will also be exported to FAGUS with all their properties.
To analyze sectionally in FAGUS a prestressed section of a STATIK structure, the total stresses due to prestressing will be exported, but separated into two parts:
- One part will be the isostatic of the prestressing, which will be brought into FAGUS through the tendon in the position it has and with the corresponding tensioning force.
- The other part will be the hyperstatic prestressing stresses. These stresses will be the ones requested to our sections together with those resulting from the rest of the loads.
The aim of this article is to explain how to proceed in the case where we want to carry out the FAGUS analysis of the sections of a prestressed structure defined in STATIK using the tool that allows the direct interaction between both programs, but at infinite time, i.e. taking into account the losses at infinite time of the prestressing.
The purpose of this article is to explain how to proceed in case we want to carry out the FAGUS analysis of the sections of a prestressed structure defined in STATIK using the tool that allows the direct interaction between both programs, but at infinite time, i.e. taking into account the losses at infinite time of the prestressing.
To indicate to FAGUS at what time we want to perform the analysis, i.e. at time=0 or at time=oo, we have these two options in the analysis parameters tab corresponding to the prestressing:
This option will affect the prestressing force “P” of the tendon that STATIK exports to FAGUS for each of the sections and, therefore, will affect the prestressing isostatic P*e.
When STATIK exports the tendons for each of the sections to FAGUS, it exports not only the position and force, but also the infinite time loss factor P/Poo and the angle of inclination of the tendon with that section. Here lies the power of this functionality that connects both programs, since we will automatically have everything we need to accurately analyze all our prestressed sections.
If the option t=0 is selected from the analysis parameters tab, FAGUS will not apply the loss factor at infinite time, whereas, if we select the option t=oo, FAGUS will apply it, which will reduce the prestressing force “P” in each section and, therefore, the isostatic moment. Let's take a look at it.
Suppose we have the following structure, in which we have some tendons inserted:
If we select the option t=0 of the analysis parameters, take any section of this structure and do a “check with FAGUS”, we can see, for one of the stress lines, the axial force introduced by the prestressing is -27230.6kN.
As we have checked the option for t=0, the program is not applying the loss factor. As we can see in this table, the total losses in this section are (18.3%+20%+20.1%)/3=19.47%, i.e. the average of the values of the 3 tendons in the section:
If we now check the option t=oo in the analysis parameters, we will see that the axial force will change from -27230.6 to -27230.6*(1-0.1947)=21929.47kN. If we look for that value again, we see that it is -22207.2kN.
The value is not exactly the 21929.47 kN that we have obtained by hand because of the number of decimal places used in our calculation. If we export our section to FAGUS and check the loss factors with 4 decimal places, we see that they are 0.8110, 0.8254 and 0.8103, which provide an average factor of 0.81557.
If we redo the manual calculation -27230.3*0.81557=-22208.22kN, very similar to the one provided by the program of -22207.2kN, which shows us that the number of decimal places indeed has a lot of influence. Fortunately the program uses many more than we can see.
And... What about the hyperstatic stresses of the prestressing that STATIK takes to FAGUS? How do we make them also be affected at infinite time?
In order for STATIK to export to FAGUS hyperstatic forces affected by a loss factor at infinite time, the additional parameter “RFPT=factor” must be included in the dialog box where we define the special analysis with FAGUS. This factor is not calculated automatically by the program, so it must be chosen by the user.
If, for example, we want to take into account losses of 15%. We will have to enter a factor of 0.85:
To clearly see the effect of this factor, we have defined an envelope in which we have only included the prestress.
Without the parameter introduced, we see that the stresses that STATIK takes to FAGUS for a given section are:
That is, a moment of 2659.63kNm.
If we introduce the factor “RFPT”:
We see that the moment is 2260.68 kNm, i.e. 2659.63*0.85.
The inclusion of this parameter is the simplest way to take into account the infinite time losses of the prestressed hyperstatic part, which not only affects the prestressed structure lines, but as we can see in this simple example can also affect other non-prestressed members of the structure.
Here we have a column connected to a lintel by a spherical plain bearing. If we apply a compression on the lintel, (or if we have a prestressing tendon centered on it), we see that we have no moments in that element, because the compression acts on the axis of the member, i.e. there is no eccentricity, while the column has moments due to the prestressing, even though it has no prestressing tendons in it. These moments are the hyperstatic moments of the prestressing.
To obtain the prestressing losses, the program performs a very complex analysis in each of the sections where prestressing exists, i.e. it requires a prestressing element to calculate precisely the loss factor in which relaxation, creep and shrinkage are involved. In those sections where there is no prestress the program, logically, cannot perform this calculation, which means that, if the “RFPT” factor that we have explained is missing, we could not affect the hyperstatic moments of the column.
¡WARNING! this parameter is independent of the analysis parameters, so if we enter it, it will always be applied to the hyperstatic forces, regardless of what we select there.
That said, to proceed correctly we must remember that:
- If we want to do an analysis at t=0: we select option t=0 in the analysis parameters and do not put the additional parameter.
- If we want to make an analysis at t=oo: select option t=oo in the analysis parameters and set the additional parameter.
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