According to article 42.1.2 of the EHE 08, where the general hypotheses of the ultimate strength of the sections are introduced, the following is specified in relation with the total strain of the adherent active reinforcements:
- The fatigue is characterised by the value of the strain in some fibres of the section, defined by the fatigue strain domain shown in 42.2.3.
- Concrete strains follow a plane law.This hypothesis is valid for pieces in which the ratio of the distance between points of zero moment and the total height is greater than 2.
- The strain of the passive reinforcements remains equal to the one of the concrete surrounding them.
The total strains of the active adherent reinforcements must consider, apart from the strain resulting in the fibre on the fatigue strain plane (ε0), the strain resulting from the prestressing and the decompression strain (figure 42.1.2), defined as:
Δε p = ε cp + ε p0
ε cp : Decompression strain of the concrete to the level of the reinforcement fibre considered.
ε p0 : Initial strain of the active reinforcement due to the prestressing in the considered phase, taking the produced losses into account.
In the FAGUS user manual, section B 2.3.4, the way the program considers the parameters related to this topic is thoroughly explained.
If a section is analysed using a complete model of STATIK 7, all the parameters will be automatically imported, however, if the section is directly entered in FAGUS 7, they will have to be calculated manually and then entered on the dialogue box corresponding to the definition of the properties of the active reinforcements existing in the section.
Let’s look at a simple example:
A prestressed, doubly-supported beam with a 300x400 cross section and 10 m span is introduced. The tendon has a basic parabolic shape with the lowest point at mid-span.
If we launch FAGUS 7 to analyse one of the sections, the program will exactly consider the geometry and the properties of the defined tendon and will implement it on the corresponding section. In this case we will take the cross-section at X=4.17m:
On the section the tendon can be seen (in red) on its exact position according to the defined shape. If we open the dialog box the definition of the tendon is shown as:
The highlighted values are thus obtained directly and it will not be necessary to calculate them previously.
As it is explained on the FAGUS 7 manual, the value corresponding to the concrete decompression is normally very low in relation with ε0 and can be neglected. For the value of ε0, without a STATIK 7 license, and only with a FAGUS 7 one, there are two methods to solve the problem:
OPTION 1) Obtaining the value manually using the formula, for which the calculation of the initial losses due to the prestressing is necessary.
OPTION 2) Having a CEDRUS 7 license, a tendon can be introduced inside a slab with an equivalent shape. Once the geometry and the definition parameters are entered, the instantaneous losses of the prestressing can be evaluated, these are the necessary ones to obtain ε0. With this method the force of prestressing existent after initial losses would be available and the formula’s application to obtain ε0 would be straight forward.