Concrete Models for Time-Dependant Material Effects

The program includes the following concrete models (Reference 1)

ACI 209R-92 Model
CEB MC90-99 Model
Bazant-Baweja B3 Model

Further details about these models can be found in the reference. In the sub-sections below, additional information is provided to clarify some implementation details.

ACI 209R-92 Model

The value for f_cm28 (concrete mean compressive strength at 28 days) is calculated from ACI 318 - Table 5.3.2.2 as follows:

f_{c m 28} = {\begin{matrix} f_{c m} + 1000 & f_{c m} < 3000 p s i \\ f_{c m} + 5000 & f_{c m} \leq 5000 p s i \\ 1.10 f_{c m} + 700 & f_{c m} > 5000 p s i \end{matrix}

In calculation of creep coefficient and shrinkage strains, shape and size effects are considered (i.e., (A-3) is implemented).

Ultimate creep coefficient (ϕ_u, A-19) is modified according to equation (A-20).

The ambient relative humidity coefficient γ_sh,RH (A-7) is implemented as follows:

γ_{s h, R H} = {\begin{matrix} 1.40 - 1.02 h & 0.40 \leq h \leq 0.80 \\ 3.00 - 3 h & 0.80 < h \leq 1.0 \\ 1.0 & h < 0.40 \end{matrix}

where

relative humidity

Equations (A-26) and (A-27) are for the average thickness method to account for effect of member size. This method is not implemented (instead, the equation (A-25) is enforced).

Creep coefficient is assumed to be zero if t ≤ t_o (t_o = age of loading in days)

Shrinkage strain is assumed to be zero if t ≤ t_c (t_c = start of drying in days)

CEB MC90-99 Model

The value for f_cm28 (concrete mean compressive strength at 28 days) is calculated as follows (A-73):

f_{c m 28} = f_{c m} + 8 (MPa)

(in SI units)

Effect of curing temperature is not considered. In other words, age of concrete at loading adjusted to concrete temperature is ignored (i.e., (A-81) is not implemented)

Table A.13 is not implemented. Hence, E_cm28 (A-72) is not modified with the value of α_E from the Table A.13.

Creep coefficient is assumed to be zero if t ≤ t_o (t_o = age of loading in days)

Shrinkage strain is assumed to be zero if t ≤ t_c (t_c = start of drying in days)

Bazant-Baweja B3 Model

The value for fcm28 (concrete mean compressive strength at 28 days) is calculated as follows:

f_{c m 28} = f_{c m} + 1, 200 (psi)

The concrete modulus Ecm28 is calculated according to the Equation (A-39).

Creep deformation is composed of basic creep and drying creep. Both creep calculations are included in the program.

Creep coefficient is assumed to be zero if t ≤ t_o (t_o = age of loading in days)

Shrinkage strain is assumed to be zero if t ≤ t_c (t_c = start of drying in days)