     # 02 Pre Tensioning

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• Code_Aster, Salome-Meca course materialGNU FDL licence (http://www.gnu.org/copyleft/fdl.html)

Modeling of steel elements in civil engineering structures

• 2 - Code_Aster and Salome-Meca course material GNU FDL Licence

Outline

Modeling of pre-tensioning

Modeling of reinforcing steel

• 3 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : principles

Cable = bar elements embedded in a 3D or DKT mesh Mesh of bars independent of the concrete mesh

• 4 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : principles

The DEFI_CABLE_BPcommand creates loads corresponding to : The link (assumed perfect) between the cable and concrete : automatic definition of Lagrange multipliersThe calculation of tension in the cables as recommended by BPEL (ETCC implementation in progress).

CAB1 = DEFI_CABLE_BP (...)

CMCABbi=AFFE_CHAR_MECA(

MODELE=MO,

RELA_CINE_BP=_F(CABLE_BP=CAB_BPi,

SIGM_BPEL=OUI' or 'NON',RELA_CINE='OUI' or 'NON'))

• 5 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommandcabl_pr = DEFI_CABLE_BP (

MODELE = modele,

CHAM_MATER = chmat,

CARA_ELEM = caelem,

GROUP_MA_BETON = grmabe,

DEFI_CABLE = _F (

GROUP_MA = grmaca,

GROUP_NO_ANCRAGE = l_gnoa,)

TYPE_ANCRAGE = (ACTIF, PASSIF),

TENSION_INIT = f0,

RECUL_ANCRAGE = delta,

RELAXATION = _F ( R_J = rj, )

CONE = _F ( RAYON = rayon,

LONGUEUR = long,

PRESENT = ('OUI','NON'))

TITRE = l_titr, [l_tx]

Required for calculating the tension

Defining acable

• 6 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommandcabl_pr = DEFI_CABLE_BP ( MODELE = modele,

CHAM_MATER = chmat,

CARA_ELEM = caelem,

GROUP_MA_BETON = grmabe,

DEFI_CABLE = _F (

GROUP_MA =' cable1 ',

GROUP_NO_ANCRAGE = (' GRI',' GRF' ,)

TYPE_ANCRAGE = ( ACTIF , PASSIF ),

TENSION_INIT = f0,

RECUL_ANCRAGE = delta,

RELAXATION = _F ( R_J = rj, )

CONE = _F ( RAYON = rayon,

LONGUEUR = long,

PRESENT = ('OUI','NON'))

TITRE = l_titr, [l_tx]

GRI GRFN1 N6N5N4N3N2

cable1

• 7 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : potential difficulties[U4.42.04]

• 8 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : diffusion cone

Possibility of introducing a diffusion cone

Real situation Without modelling the shaft With modeling of the effect of shaft vanishing

mesh size required

management of redundant boundary conditions

[U4.42.04]

• 9 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommandcabl_pr = DEFI_CABLE_BP ( MODELE = modele,

CHAM_MATER = chmat,

CARA_ELEM = caelem,

GROUP_MA_BETON = grmabe,

DEFI_CABLE = _F (

GROUP_MA = 'cable1',

GROUP_NO_ANCRAGE = ('GRI','GRF',)

TYPE_ANCRAGE = (ACTIF, PASSIF),

TENSION_INIT = f0,

RECUL_ANCRAGE = delta,

RELAXATION = _F ( R_J = rj, )

CONE = _F ( RAYON = rayon,

LONGUEUR = long,

PRESENT = ('OUI','NON'))

TITRE = l_titr, [l_tx]

Calculation of the tension

• 10 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : calculating thetension in the cables

Calculating the tension at any point of the cable as recommendedby BPEL91

F (s)= F (s){x fluF 0+x retF 0+r ( j)5100

1000[ F (s)S a f prg 0]F (s)}

F c (s)=F 0 exp ( f s )

F c (s) F (s)=[F c(d )]2

Taking into account the instant losses by friction and anchor recoil

• 11 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : calculating thetension in the cables

Calculating the tension at any point of the cable as recommendedby BPEL91

F (s)= F (s){x fluF 0+x retF 0+r ( j)5100

1000[ F (s)S a y 0] F (s)}

Taking account of losses depending on time

Creep ofconcrete

Relaxation of steelShrinkage of concrete

• 12 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : calculating thetension in the cables

Data settingMBETON=DEFI_MATERIAU(ELAS=_F(E= 30.E9,...),

BPEL_BETON= _F( PERT_FLUA = 0,

PERT_RETR= 0),);

MCABLE=DEFI_MATERIAU( ELAS=_F(E=200.E9 ),

BPEL_ACIER=_F( FROT_COURB =3.0E-3,

FROT_LINE =1.5E-3,

F_PRG =1.94E11,

RELAX_1000 = 0,

MU0_RELAX = 0),)

in DEFI_CABLE_BP

in AFFE_CARA_ELEM

F 0, , r ( j )

S a

• 13 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : two strategies

Solving with STAT_NON_LINE, instant tensioning

Loss of tension due to the instant deformation of the concreteNo possible phasing

Tensions le long du cble

0,E+00

1,E+06

2,E+06

3,E+06

4,E+06

5,E+06

6,E+06

1 11 21 31 41 51 61 71 81 91 101 111 121 131

Elment

Tensio

n (

N)

BPEL DCBP sans correction DCBP aprs correction

Command CALC_PRECONTFinal tension in the cables = BPELAllows successive tensioning in cables

• 14 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : two strategies

Strategy #1

chcab =AFFE_CHAR_MECA(...

RELA_CINE_BP=_F(

CABLE_BP=cable,

SIGM_BPEL=OUI',

RELA_CINE='OUI') )

RES1 = STAT_NON_LINE(...

EXCIT=(_F(CHARGE = CLIM,),

_F(CHARGE = chcab )),

...,)

Strategy #2

chcab =AFFE_CHAR_MECA(...RELA_CINE_BP=_F(

CABLE_BP=cable,SIGM_BPEL=NON' ,RELA_CINE='OUI' ,) ,);

RES1 = CALC_PRECONT(...EXCIT=(_F(CHARGE =CLIM,),

_F( CHARGE = chcab )),CABLE_BP=cable ,

...,)

• 15 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : two strategies

STAT_NON_LINEInstant tensioningLoss of tension due to the instant deformation of the concreteNo possible phasing

Easier implementation

Tensions le long du cble

0,E+00

1,E+06

2,E+06

3,E+06

4,E+06

5,E+06

6,E+06

1 11 21 31 41 51 61 71 81 91 101 111 121 131

Elment

Tensio

n (

N)

BPEL DCBP sans correction DCBP aprs correction

CALC_PRECONTProgressive tensioningFinal tension in cables = BPEL

Allows successive tensioning in cables

A little more complex

Strategy #2 : CALC_PRECONT

Strategy #1 : STAT_NON_LINE

• 16 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : tips for strategy #1

Combine a maximum cables in DEFI_CABLE_BPOption CONE: Pay attention to redundant connections (not factorable matrix) + size of elementsIf TYPE_ANCRAGE = ('PASSIF', 'PASSIF') , there is no tension in the cable !In case of a continuation calculation (POURSUITE), define a new load without tension, otherwise the two tensions will be added

chcab2=AFFE_CHAR_MECA(MODELE=MO,

RELA_CINE_BP=_F(CABLE_BP=CAB_BPi,

SIGM_BPEL=NON' ,

RELA_CINE='OUI' ,),);

RES1 = STAT_NON_LINE(reuse =RES1,

ETAT_INIT=_F(EVOL_NOLI=RES1,

EXCIT =(_F(CHARGE = CLIM,),

_F(CHARGE = Chcab2 ),

),)

• 17 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommand

statnl [evol_noli] = CALC_PRECONT( reuse = statnl, ETAT_INIT = _F()

MODELE = mo ,

CHAM_MATER = chmat ,

CARA_ELEM = carac ,

COMP_INCR = _F()

INCREMENT =_F( LIST_INST = litps ,

INST_FIN = instfin,),

EXCIT =(_F( CHARGE = chi ), ),

CABLE_BP = cabl_pr ,

CABLE_BP_INACTIF = cabl_pr ,

+ mot-cl facteur STAT_NON_LINE )

The cables that will be strained between instini and instfin

Inactive cables (no stiffness)

• 18 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommand, example

CAB_BP=DEFI_CABLE_BP(...)

CH_L=AFFE_CHAR_MECA(MODELE=MO,RELA_CINE_BP=_F(CABLE_BP=CAB_BP,

SIGM_BPEL=NON', RELA_CINE='OUI' ,),);

EVOL = CALC_PRECONT(CABLE_BP = CAB_BP,

EXCIT = _F(CHARGE = CL),

INCREMENT =_F(LIST_INST=L,

INST_FIN = 1.,

)

EVOL = STAT_NON_LINE(reuse =EVOL,

ETAT_INIT =_F(EVOL_NOLI= EVOL)

EXCIT=(_F(CHARGE= CL),

F(CHARGE=CH_L),

1. definition of cables2. CH_Lcontains the

• 19 - Code_Aster and Salome-Meca course material GNU FDL Licence

Modeling of pre-tensioning : DEFI_CABLE_BPcommand, example

CAB_BP=DEFI_CABLE_BP(...)

CH_L=AFFE_CHAR_MECA(MODELE=MO, RELA_CINE_BP=_F(CABLE_BP=CAB_BPi,

SIGM_BPEL=NON', RELA_CINE='OUI' ,),);

EVOL = CALC_PRECONT(CABLE_BP = CAB_BP,

EXCIT = _F(CHARGE = CL),

INCREMENT =_F(LIST_INST=L,

INST_FIN = 1.,

)

EVOL = STAT_NON_LINE(reuse =EVOL,

ETAT_INIT =_F(EVOL_NOLI= EVOL)

EXCIT=(_F(CHARGE= CL),

F(CHARGE=CH_L),

.

Tensioning of cables defined in CAB_BP, from t= 0 to 1

• 20 - Code_Aster and Salome-Meca course material GNU FDL Licence

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