9. Appendix#

Here is an example of a commented application that is taken from Training TP FORMA42 available in the list of test cases [V6.04.165]. It is a pole crossed by 5 cables, and the load is composed of:

gravity
prestress in cables
pressure on the upper side (load not present in the test case)

The data set is common, then we show 3 scenarios to solve the problem. The implementation of the test will make it possible to compare the responses obtained in terms of tension in the cables. Depending on the scenario chosen, the tension in the cables and the deformations in the concrete are not the same.

The first scenario (FORMA42C) is the most physical and the phasing is as follows:

taking into account gravity
tension of cables 1 and 2
tension of cables 3 and 4
tension of the cable 5
pressurization

The second scenario (FORMA42B) is identical to the first but it uses the CALC_PRECONT operator and thus makes it possible to directly have the regulatory tension in the pretension cables.

The third scenario (FORMA42A) is the one we applied before the development of the CALC_PRECONT operator (up to version 6 of Code_Aster) and which is the method that remains recommended when using a DKT model for concrete

consideration of gravity and tension of the 5 cables
pressurization

The data setting of the problem

MY= LIRE_MAILLAGE (…) MY= DEFI_GROUP (…) MO= AFFE_MODELE (MAILLAGE =MA, AFFE =( _F (GROUP_MA =” VOLTOT “, PHENOMENE =” MECANIQUE “, MODELISATION =”3D”,), _F (GROUP_MA =( “CAB1”, “CAB2”, “”, “”, “CAB3”, “CAB4”, “CAB5”), PHENOMENE =” MECANIQUE “, MODELISATION =” BARRE “,),),) CE= AFFE_CARA_ELEM (MODELE =MO, BARRE =_F (…),) MBETON = DEFI_MATERIAU (ELAS =_F ( … ), BPEL_BETON =_F (),); MCABLE = DEFI_MATERIAU (ELAS =_F ( … ), BPEL_ACIER =_F (F_ PRG =1.94E11, FROT_COURB =0.0, FROT_LINE =1.5E-3,)) CMAT = AFFE_MATERIAU (…) CAB_BP12 = DEFI_CABLE_BP (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, GROUP_MA_BETON =” VOLTOT “, TYPE_ANCRAGE =( “ACTIF”, “PASSIF”,), TENSION_INIT =3.75E6, RECUL_ANCRAGE =0.001, DEFI_CABLE =( _F (GROUP_MA =” CAB1 “, GROUP_NO_ANCRAGE =( “PC1D”, “PC1F”,)), _F (GROUP_MA =” CAB2 “, GROUP_NO_ANCRAGE =( “PC2D”, “PC2F”, “”)) CAB_BP34 = DEFI_CABLE_BP (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, GROUP_MA_BETON =” VOLTOT “, TYPE_ANCRAGE =( “ACTIF”, “PASSIF”,), TENSION_INIT =3.75E6, RECUL_ANCRAGE =0.001, DEFI_CABLE =( _F (GROUP_MA =” CAB3 “, GROUP_NO_ANCRAGE =( “PC3D”, “PC3F”,)), _F (GROUP_MA =” CAB4 “, GROUP_NO_ANCRAGE =( “PC4D”, “PC4F”,))) CAB_BP5 = DEFI_CABLE_BP (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, GROUP_MA_BETON =” VOLTOT “, TYPE_ANCRAGE =( “ACTIF”, “PASSIF”,), TENSION_INIT =3.75E6, RECUL_ANCRAGE =0.001, DEFI_CABLE =_F (GROUP_MA =” CAB5 “, GROUP_NO_ANCRAGE =( “PC5D”, “PC5F”,))) CLIM = AFFE_CHAR_MECA (MODELE =MO, DDL_IMPO = … , PESANTEUR =…) CMCAB12 = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP12, SIGM_BPEL =” NON “, RELA_CINE =” OUI “,),) CMCAB23 = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP23, SIGM_BPEL =” NON “, RELA_CINE =” OUI “,),) CMCAB5 = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP5, SIGM_BPEL =” NON “, RELA_CINE =” OUI “,),); PRES = AFFE_CHAR_MECA (MODELE =MO, PRES_REP =_F (GROUP_MA = “HAUT”, PRES = 500,),) FCT = DEFI_FONCTION (NOM_PARA = “INST”, VALE = (0. ,0., 600., 600., 0., 0., 0., 1000., 1.),)

Reading and enriching the mesh. The creation of GROUP_NOliés to the cables is only essential for possible post-treatment along them. Definition of the models (3D for concrete, BARREpour the cables) Geometric characteristics (section) of bar elements Creation and assignment of material characteristics for cable and concrete: Concrete: elastic + regulatory data BPEL by default Steel: elastic +regulatory data BPEL + Definition of the 5 pretension cables It is possible to combine in the same: DEFI_CABLE_BP cables 1 and 2 on the one hand, and cables 3 and 4 on the other hand, since they have the same characteristics and are energized simultaneously. And in the case where all the cables are stretched simultaneously (scenario 2 and 3), we could group all the cables together. Load creation: boundary conditions and gravity Kinematic links connecting cable to concrete (here SIGM_BPEL =” NON “, because we don’t want to include the voltage in the cables in this load) Loads after the cables have been tensioned (here a pressure)

Scenario 1

LINST = DEFI_LIST_REEL (VALE =( 0.0,150.,300.,300.,450.,600.,1000.),); ETAPE 1: effect of gravity RES1 = STAT_NON_LINE (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =( _F (RELATION = “ELAS”, GROUP_MA =” VOLTOT “,), _F (RELATION = “SANS”, GROUP_MA = (“CABLE”),),), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12), _F (CHARGE = CMCAB34), _F (CHARGE = CMCAB5),), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 150.),) # ETAPE 2: tensioning cables 1 and 2 #——————————————————– RES1 = CALC_PRECONT (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =( _F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE”)), EXCIT =( _F (CHARGE = CLIM,),), CABLE_BP =( CAB_BP12), CABLE_BP_INACTIF = (CAB_BP34, CAB_BP5,), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 300.,),) # ETAPE 3: tension cables 3 and 4 #——————————————————– RES1 = CALC_PRECONT (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =( _F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE”)), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12,)), CABLE_BP =( CAB_BP34), CABLE_BP_INACTIF = (CAB_BP5,), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 450.),) ETAPE 4: tension cable 5 #———————————————————– RES1 = CALC_PRECONT (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =( _F (RELATION = “ELAS”, GROUP_MA =” VOLTOT “,), _F (RELATION = “VMIS_ISOT_LINE”, GROUP_MA = “CABLE”),), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12,), _F (CHARGE = CMCAB34,)), CABLE_BP =( CAB_BP5,), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 600.,),) ETAPE 5: pressure #———————————————————– RES1 = STAT_NON_LINE (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =_F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE)), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12,), _F (CHARGE = CMCAB34,), _F (CHARGE = CMCAB5,), _F (CHARGE = PRES, FONC_MULT = FCT,)), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 1000.),)

The cables do not intervene: where RELATION =” SANS “, but as they are present in the model, the kinematic links concerning them are included (otherwise the cables” fall “) are included (otherwise the cables” fall “). While the boundary conditions and gravity are maintained, CALC_PRECONT, will tension cables 1 and 2, while keeping cables 3, 4 and 5 inactive. Assign the law of real behavior to cables. Do not include kinematic links connecting cables to concrete, CALC_PRECONT takes care of them This time cables 1 and 2 are already stretched and are therefore no longer managed by CALC_PRECONT, which is why kinematic links for these 2 cables must be included in the load in addition to the boundary conditions. On the other hand, nothing to put on for cable 5, which is still inactive, and for cables 3 and 4 that CALC_PRECONT will put on tension at this stage Only cable 5 is managed by CALC_PRECONT, so kinematic links must be included for other cables that are already stretched (1, 2, 3 and 4). All cables are now active. The load should include boundary conditions, instant loads, kinematic links for all cables, and new loads to be applied (here PRES).

Scenario 2

LINST = DEFI_LIST_REEL (VALE =( 0.0, 600., 1000.),); # ETAPE 1: effect of gravity + cable tension RES1 = CABLE_PRECONT (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =_F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE)), CABLE_BP = (CAB_BP12, CAB_BP34, CAB_BP5), EXCIT =_F (CHARGE = CLIM,), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 600.),) ETAPE 2: pressure #———————————————————– RES1 = STAT_NON_LINE (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =_F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE)), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12,), _F (CHARGE = CMCAB34,), _F (CHARGE = CMCAB5,), _F (CHARGE = PRES, FONC_MULT = FCT,)), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 1000.),)

The load is composed of CLIMet the 5 cables are put on tension simultaneously Boundary conditions and gravity are always maintained, including pressure. For cables, we always need kinematic links for them.

Scenario 3

LINST = DEFI_LIST_REEL (VALE =( 0.0, 600., 1000.),); CMCAB12B = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP12, SIGM_BPEL =” OUI “, RELA_CINE =” OUI “,),) CMCAB34B = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP3, SIGM_BPEL =” OUI “, RELA_CINE =” OUI “,),) CMCAB5B = AFFE_CHAR_MECA (MODELE =MO, RELA_CINE_BP =_F (CABLE_BP = CAB_BP5, SIGM_BPEL =” OUI “, RELA_CINE =” OUI “,),); # ETAPE 1: effect of gravity + cable tension RES1 = STAT_NON_LINE (MODELE =MO, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =_F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE)), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12B), _F (CHARGE = CMCAB34B), _F (CHARGE = CMCAB5B),), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 600.),) ETAPE 2: pressure #———————————————————– RES1 = STAT_NON_LINE (reuse= RES1, ETAT_INIT =_F (EVOL_NOLI = RES1), MODELE =ME, CHAM_MATER = CMAT, CARA_ELEM =CE, COMPORTEMENT =_F (RELATION = “ELAS”, GROUP_MA =( “VOLTOT”, “CABLE)), EXCIT =( _F (CHARGE = CLIM,), _F (CHARGE = CMCAB12,), _F (CHARGE = CMCAB34,), _F (CHARGE = CMCAB5,), _F (CHARGE = PRES, FONC_MULT = FCT,)), INCREMENT =_F (LIST_INST = LINST, INST_FIN = 1000.),)

To directly apply the tension in the cables, we need to define new loads containing both the kinematic links connecting cable and concrete, and the value of the voltage to be included in the cables (where SIGM_BPEL =” OUI “, in contrast to the loads CMCABidéfinis initially). The load is composed of CLIMet of the CMCAB i j B containing the kinematic links and the tension in the cables Boundary conditions and gravity are always maintained, including pressure. For cables, it’s the CMCAB i because we just want to maintain the kinematic links (otherwise, we add the tension in the cables again)