PGSuper  3.0
Precast-prestressed Girder Bridges
Time-Dependent Material Models

Time-dependent material properties are computed using the AASHTO LRFD, ACI 209R-92, and CEB-FIP 1990 models.

AASHTO LRFD

Compressive Strength

AASHTO does not define a time-dependent model for concrete compressive strength. The ACI 209R-92 model is used.

Modulus of Elasticity

Modulus of elasticity is defined by a modified version of LRFD Equation 5.4.2.4-1. See Concrete Properties for details.

Shrinkage Strain

Shrinkage strain is defined by a modified version of LRFD Equation 5.4.2.3.3-1. See Concrete Properties for details.

Creep Coefficient

Creep coefficient is defined by a modified version of LRFD Equation 5.4.2.3.2-1. See Concrete Properties for details.

Relaxation of Prestressing Steel

AASHTO does not define an intrinsic model for strand relaxation. The ACI 209R-92 model is used.

ACI 209R-92

Compressive Strength

Compressive strength is computed by ACI 209R-92 Equation 2-1.

ACI_fc.png
ACI 209R-92 Eqn. 2-1

From ACI 209R-92 Table 2.2.1

Type of Curing Cement Type a b
Moist I 4.0 0.85
Moist III 2.3 0.92
Steam I 1.0 0.95
Steam III 0.7 0.98

Modulus of Elasticity

Modulus of elasticity is computed by ACI 209R-92 Equation 2-5.

ACI_Ec.png
ACI 209R-92 Eqn. 2-5

for gct = 33.0,

ACI_Ec_simplified.png

Shrinkage Strain

Shrinkage strain is computed by ACI 209R-92 Equations 2-7, 2-9, 2-10, 2-15, 2-16, and 2-22. Here we present the shrinkage strain as an ultimate shrinkage value multiplied by modification factors.

ACI_Shrinkage.png

Time Modification Factor

ACI_Shrinkage_Time_Factor.png

f = 35 for moist cured concrete (ACI Eqn. 2-9) and 55 for steam cured concrete (ACI Eqn. 2-10).
t = shrinkage duration

Curing Modification Factor

gcp = 1.0 for steam curing.

From ACI 209R-92 Table 2.5.3

Moist Curing Duration (days) gcp
1 1.2
3 1.1
7 1.0
14 0.93
28 0.86
90 0.75

gcp is linearly interpolated for other curing durations.

Relative Humidity Modification Factor

ACI_Shrinkage_Humidity_Factor.png
ACI 209R-92 Eqn 2-15 and 2-16

RH = Average Ambient Relative Humidity

Volume to Surface Ratio Modification Factor

ACI_Shrinkage_VS_Factor.png
ACI 209R-92 Eqn. 2-22

v/s = volume to surface ratio

Creep Coefficient

Creep coefficient is computed by ACI 209R-92 Equations 2-8, 2-11, 2-12, 2-14, and 2-21. Here we present the creep coeficient as an ultimate coefficient value multiplied by modification factors.

ACI_Creep.png

Time Modification Factor

ACI_Creep_Time_Factor.png
ACI 209R-92 Eqn. 2-8

t = time after loading (days)

Loading Age Modification Factor

ACI_Creep_Loading_Age_Factor.png
ACI 209R-92 Eqn. 2-11 and 2-12

tla is the age of the concrete at the time of loading (days)

Relative Humidity Modification Factor

ACI_Creep_Humidity_Factor.png
ACI 209R-92 Eqn. 2-14

RH = Average Ambient Relative Humidity

Volume to Surface Ratio Modification Factor

ACI_Creep_VS_Factor.png
ACI 209R-92 Eqn. 2-21

v/s = volume to surface ratio

Relaxation of Prestressing Steel

Relaxation is computed from the equations given in ACI 209R-92 Table 3.7.1.

Strand TypeRelaxation
Stress Relieved
ACI_Relaxation_SR.png
Low Relaxation
ACI_Relaxation_LR.png

CEB-FIP 1990

Compressive Strength

The concrete compressive strength is computed by CEB-FIP 1990 Eqn. 2.1-53.

CEBFIP_fc.png
CEB-FIP 1990 Eqn. 2.1-53 and 2.1-54
Cement Type s
Rapid Hardening High Strength (RS) 0.20
Normal Hardening (N) 0.25
Rapid Hardening (R) 0.25
Slowly Hardening (SL) 0.38

Modulus of Elasticity

The modulus of elasticity is computed by CEB-FIP 1990 Eqn. 2.1-57.

CEBFIP_Ec.png
CEB-FIP 1990 Eqn. 2.1-57 and 2.1-58

Shrinkage Strain

Shrinkage strain is computed by CEB-FIP 1990 Equation 2.1-74.

CEBFIP_Shrinkage.png
CEB-FIP 1990 Eqn. 2.1-74
CEBFIP_2_1_75.png
CEB-FIP 1990 Eqn. 2.1-75
CEBFIP_2_1_76.png
CEB-FIP 1990 Eqn. 2.1-76
Cement Type bsc
Rapid Hardening High Strength (RS) 8
Normal Hardening (N) 5
Rapid Hardening (R) 5
Slowly Hardening (SL) 4
CEBFIP_2_1_77.png
CEB-FIP 1990 Eqn. 2.1-77
CEBFIP_2_1_78.png
CEB-FIP 1990 Eqn. 2.1-78
CEBFIP_2_1_79.png
CEB-FIP 1990 Eqn. 2.1-79
CEBFIP_2_1_69.png
CEB-FIP 1990 Eqn. 2.1-69

Creep Coefficient

Creep coefficient is computed by CEB-FIP 1990 Equation 2.1-64.

CEBFIP_Creep.png
CEB-FIP 1990 Eqn. 2.1-64
CEBFIP_2_1_65.png
CEB-FIP 1990 Eqn. 2.1-65
CEBFIP_2_1_66.png
CEB-FIP 1990 Eqn. 2.1-66
CEBFIP_2_1_67.png
CEB-FIP 1990 Eqn. 2.1-67
CEBFIP_2_1_68.png
CEB-FIP 1990 Eqn. 2.1-68
CEBFIP_2_1_69.png
CEB-FIP 1990 Eqn. 2.1-69
CEBFIP_2_1_70.png
CEB-FIP 1990 Eqn. 2.1-70
CEBFIP_2_1_71.png
CEB-FIP 1990 Eqn. 2.1-71

Relaxation of Prestresing Steel

Relaxation is defined in CEB-FIP 2.3.4.5. For design purposes, the relxation lossses in CEB-FIP Figure 2.3.3 can be used. The curves in this figure have been fit into the following format

CEBFIP_Relaxation.png
CEBFIP_Relaxation_P.png
CEBFIP_Relaxation_k.png