3. The macro command CALC_PRECONT

The purpose of the macro command CALC_PRECONT is to tension the cables in concrete using the data contained in the cable_precont concept from DEFI_CABLE_BP.

Two different cable tension procedures are present in this macro-command. One or the other of these procedures is chosen automatically depending on whether the cable_precont concept was created with the keyword ADHERENT = “OUI” or “NON”.

If ADHERENT = “OUI”, the voltage profile calculated in DEFI_CABLE_BP is transformed into the initial load by AFFE_CHAR_MECA.

Otherwise, the tension is simulated completely by a mechanical calculation by imposing forces on the sliding degrees of freedom of the elements CABLE_GAINEà based on the information contained in the cable_precont concept.

3.1. Adherent case: why a macro-command for powering up?

It is possible to transform the voltage in the cables, calculated by DEFI_CABLE_BP, into a loading directly taken into account by STAT_NON_LINE using the command AFFE_CHAR_MECA operand RELA_CINE_BP (SIGM_BPEL =” OUI “). In this case, tension is taken into account as an initial stress state when solving the complete finite element problem.

Solving the problem makes it possible to reach a state of balance between the prestress cable and the rest of the structure after instantaneous deformation. In fact, under the action of cable tension, the cable (s) and concrete assembly will compress with respect to the initial position (cable under tension, mesh not deformed). The length of the cable will therefore decrease, and the initial tension will also, as a result, decrease. A final state is therefore obtained with a voltage in the cable that is different from the voltage calculated initially. It is then essential to proportionally increase the voltage applied in situ at the level of the anchorages to take account of this loss.

The use of macro-control CALC_PRECONT makes it possible to avoid this correction phase, by obtaining the equilibrium state of the structure with a tension in the cables equal to the regulatory voltage. Moreover, because of the method adopted, it also makes it possible to apply tension in several steps of time, which may be interesting in the event of plasticization or damage to the concrete. It also makes it possible to stretch the cables non-simultaneously and therefore in a manner closer to the reality of construction sites.

To benefit from these advantages, the load is applied in the form of an external load and not as an initial state, which allows the gradual loading of the structure. Moreover, to avoid the loss of tension in the cable, the idea is to step away from the stiffness of the cables during the tension phase (cf. [bib3]).

The various steps carried out by the macro-command are detailed here.

3.1.1. Step 1: Calculate equivalent nodal forces

This step consists in transforming the internal cable tensions calculated by DEFI_CABLE_BP into an external loading. To do this, we perform a first STAT_NON_LINE only on the cables that we want to prestress, with the following load:

• embedded cable

• the voltage given by DEFI_CABLE_BP

Figure 3.1.1-a: Loading in step 1

The nodal forces on the cable are calculated. We are recovering these efforts thanks to CREA_CHAMP. And we build the associated load vector \(F\).

3.1.2. Step 2: applying prestress to concrete

The next step is to apply prestress to the concrete structure, without involving the stiffness of the cable. To do this, it is assumed for this calculation that the Young’s modulus of steel is zero. You can choose to apply the prestress load in a single time step or in several time steps if the concrete is damaged.

So the load is as follows:

• blocking rigid body movements for concrete,

• the nodal forces resulting from the first calculation on the cable,

• the kinematic connections between cable and concrete.

Figure 3.1.2-a: Loading in step 2

3.1.3. Step 3: switching external forces into internal forces

Before continuing with the calculation in the traditional way, it is necessary to retransform the external forces that made it possible to deform the concrete structure into internal forces. This operation is done without modifying the movements and the constraints of the entire structure, since balance was reached in step 2: it is a simple trick to be able to continue the calculation. So the load is as follows:

• blocking rigid body movements for concrete,

• the kinematic connections between cable and concrete,

• voltage in the cables.

Figure 3.1.3-a: Loading in step 3

3.2. Non-adherent case

The value given to the DEFI_CABLE_BP TENSION_INIT keyword is forcibly imposed on the degree of freedom GLIS of the active anchor nodes of the cable while on the passive nodes this degree of freedom is locked at zero.

In the case of a ACTIF/ACTIF anchor, it is necessary to proceed in two stages:

1. A force is imposed on the first active anchor while the degree of freedom GLIS is blocked on the second.

2. The calculation is repeated by imposing the force on the second anchor, the degree of freedom GLIS of the first anchor is then locked at zero with a DIDI load.

If an anchor recoil is specified in DEFI_CABLE_BP, another calculation is started by imposing on the degree of freedom GLIS a displacement equal to the given anchor recoil. This load is also of type DIDI.

To continue the calculation after CALC_PRECONT, simply block the GLIS degree of freedom of the anchor nodes with a DIDI load.