If a specification of a limit state contains prestressing loads, the structure is considered as prestressed and then all the tendons of the groups of tendons of these loads are considered in the analysis. All these tendons are introduced in each sectional analysis that we carry out with FAGUS at their exact position and with their initial strain. The initial strain is the difference of the strain between a tendon and the adjacent concrete fibre. This is due to the force of the prestressing and to the strain of the adjacent concrete fibre at the end of the tautening process (decompressive strain).
The secondary effects can be influenced by the combination factors of the ‘Prestressing’ action in the limit state specification. However, this factor does not affect the initial strains of the tendons. Usually, for the enveloping forces at infinite time, the effects of the prestressing are multiplied by 0.8 in order to take into account the deferred forces, but, here we are speaking of a much more accurate way of evaluating losses using a especial analysis in FAGUS.
The program needs loads G1 and G2 to evaluate the decompressive strains and the losses at infinite time.
- G1 load to evaluate the decompressive strains on the tendons: the strains on the concrete when the tautening process is ended are evaluated with an estimation of the loads acting on the structure at that moment. This loads generally include:
- The prestressing loads (automatically included) and the parts below, which will automatically combine:
- The self-weight of the structure
- The support forces of the formwork
If the formwork is very stiff, the structure will be lifted when tautening it. G1 will contain a) and b). If the formwork is flexible and the structure is always supported, even after tautening it, then b) and c) are canceled and we will only have a).
Truly, we will have an intermediate situation in which the formwork will support a part of the weight of the structure, that is why the STATIK manual recommends to have G1 with only a percentage of its weight. This can be done in STATIK through a combination of load hypotheses, which we can call G1, group it in ‘indeterminate’ actions so that it does not affect other force envelopes and which, for example, can contain the self-weight hypothesis weighnen by a factor of 0.9.
Estimating what part of the self-weight will still be supported by the formwork once the tautening process is carried out is not a simple process, especially in the project phase. For that reason, and based in our own experience, we recommend considering the whole of the self-weight, which is equivalent to considering that the formwork is stiff and to put the self-weight load hypothesis on G1. Nevertheless, this option must always be defined based on the engineer’s criterion.
- G2 load for permanent additional loads: This load will be defined to complete the loads that we are going to compensate with our prestressing for the whole useful life of the structure. Generally the rest of the permanent forces will be included in G2 although occasionally a percentage of the overloads could be included depending how the prestressing is designed (depending on the engineer’s approach).
yp Distance from the c.o.g of the active reinforcements to the c.o.g of the net cross section of the concrete
n Equivalence coefficient = Ep/Ec
ᵩ(t,t0) Creep coeff. for a load age equal to the age of the concrete at tauntening (t0)(art. 39.8)
εcs(t,t0) Shrinkage strain developed after tauntening (art.39.7)
σcp Stress on the concrete at the height of the c.o.g. of the active reinforcement due to the prestressing and the permanent loads.
Δσpr Loss due to constant length relaxation.
Ac Net cross sectional area of the concrete.
Ic Moment of inertia of the net cross section of the concrete.
χ Ageing coefficient ≅0.80
Looking at the FAGUS manual (page B-28), considering the option ‘with Prestress’ and its combinations G1 and G2 affect the calculation in the following way:
If we apply that on a simple example of a prestressed beam like the following one:
In which we define three different analyses with FAGUS
a) Without the ‘with Prestressing’ option
b) With the ‘with Prestressing’ option - G1
c) With the ‘with Prestressing’ option - G1+G2
Let’s see what values are affected by the different considerations.
- a) Without the ‘with Prestressing’ option
- b) With the ‘with Prestressing’ option - G1
- c) With the ‘with Prestressing option - G1+G2
Looking at the results it is clear that G1 affects the calculation of the elastic shrinkage of concrete and the creep and that G2 affects the calculation of the creep, modifying, logically, the value of the total losses.
The fact that the losses are reduced occurs because each time we are adjusting even more the calculation of the losses, from the consideration of a more conservative global factor to a more accurate calculation optimising the values.
To end with an example, let’s see how the values on the table are indeed taken to FAGUS for their analysis. If we go to FAGUS and look at the value of the losses, for, let’s say, the last case we have shown, in the cross section positioned on structure line SL1_1, at a distance of 5.94, and we analyse the SG4 tendon, we will see that 16.6% of the total losses correspond to it. In other words, at infinite time the value of the prestressing will be close to 0.834 times the original value (if the tendons were not inclined it would be exactly that value):
If we access the properties of the SG4 tendon:
We see that the values on the STATIK table are reflected on the properties box of the tendon relative to the initial elongation, to the losses factor and to the concrete decompression. As we mentioned before, the losses factor of 0.8453 is 16.6% of the total losses, but affected by the inclination angle of the tendon at that point. That is why there is no coefficient equal to 1-0.166=0.834, that we would obtain if the tendon was orthogonal to the analysed cross section.