Foreplay
=============

Some civil engineering structures consist not only of concrete and passive steel reinforcements, but also of prestressed cables. The analysis of these structures by the finite element method then requires integrating not only the geometric and material characteristics of these cables but also their initial tension.

The operator DEFI_CABLE_BP was designed according to the requirements of regulation BPEL 91, which allows the voltage to be defined on a fixed basis. The mechanisms taken into account by this operator are then as follows:


* the tensioning of a cable by one or both ends,


* the loss of tension due to friction developed along rectilinear and curvilinear paths,


* the loss of tension due to anchor recoil,


* the loss of tension due to the relaxation of the cable,


* the loss of tension due to the shrinkage and creep of concrete.

It is also possible to use the ETC -C requirements to define the voltage. In this case, the mechanisms taken into account are as follows:


* the tensioning of a cable by one or both ends,


* the loss of tension due to friction and line losses,


* the loss of tension due to anchor recoil,


* the loss of tension due to the relaxation of the cable.

Finally, the tension in the cable can be obtained by a mechanical calculation using modeling CABLE_GAINE and law CABLE_GAINE_FROT which is inspired by BPEL 91. In this case, the mechanisms taken into account are as follows:


*
    *


* the tensioning of a cable by one or both ends,


* the loss of tension due to friction developed along rectilinear and curvilinear paths,


* the loss of tension due to anchor recoil.

The cables are modelled by elements BARRE with two nodes or by elements CABLE_GAINE with 3 nodes, which implies adopting an approximate path in the case of curved paths. This can be done as close as possible to reality without major restrictions (the cable nodes must be within the volume of the concrete elements) with respect to the mesh of the concrete elements. The concrete part of the structure can be modelled using any type of solid element :math:`\mathrm{2D}` and :math:`\mathrm{3D}` or with the plate elements DKT. The DEFI_CABLE_BP operator has the ability to create kinematic conditions between element nodes BARRE and elements :math:`\mathrm{2D}` or :math:`\mathrm{3D}` that do not coincide in space. This has the advantage of simplifying the creation of the mesh and of leaving free choice to the user in terms of the arrangement of the elements and their number. For elements BARRE and elements CABLE_GAINE in the adherent case, the prestressed cable/concrete connection is of the perfect type, with no possibility of relative sliding. In other cases, the cable may slide in its sheath. The operator also makes it possible to define a stress diffusion cone around the anchors (only in the case where the cable is adherent) in order to limit the stress concentrations that are much higher than reality and which are due to modeling.

The second main function of the operator DEFI_CABLE_BP is to assess the tension profile along the prestressing cables by considering the technological aspects of their implementation. During the installation of the cables, prestress is obtained thanks to the hydraulic cylinders placed at one or both ends of the cables. The tension profile along a cable is affected by friction (rectilinear and/or curvilinear), by the deformation of the surrounding concrete, by the retreat of the anchors at the ends of the cables and by the relaxation of the steels.

This tension can then be taken into account as an initial stress state when solving the complete finite element problem. The problem is that in this case, under the effect of cable tension, the concrete and cable assembly is compressed, causing a decrease in cable tension. To avoid this problem and to have exactly the voltage prescribed by BPEL or ETC -C in the structure in balance, the voltage must be applied through the macro command CALC_PRECONT. In addition, thanks to this method, it is possible to phase the tension of the cables or to impose the loading in several steps of time, which can be interesting in the case where the behavior of the concrete becomes non-linear as early as the phase of tension of the cables.

In the slippery and rubbing cases of element CABLE_GAINE, the tension profile calculated by DEFI_CABLE_BP is not used. The voltage is obtained by a finite element calculation using always the macro command CALC_PRECONT.