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.

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.

for g_ct = 33.0,

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.

Time Modification Factor

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

g_cp = 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

g_cp is linearly interpolated for other curing durations.

Relative Humidity Modification Factor

RH = Average Ambient Relative Humidity

Volume to Surface Ratio Modification Factor

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.

Time Modification Factor

t = time after loading (days)

Loading Age Modification Factor

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

Relative Humidity Modification Factor

RH = Average Ambient Relative Humidity

Volume to Surface Ratio Modification Factor

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 Type	Relaxation
Stress Relieved
Low Relaxation

CEB-FIP 1990

Compressive Strength

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

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.

Shrinkage Strain

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

Cement Type	bsc
Rapid Hardening High Strength (RS)	8
Normal Hardening (N)	5
Rapid Hardening (R)	5
Slowly Hardening (SL)	4

Creep Coefficient

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

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