## Appendix B ACI Model  
In 2008, the American Concrete Institute (ACI) recommended the procedure for the prediction of creep and shrinkage in its code provisions. The most recent version, labeled as 209R-92, was published in 1992 and reapproved in 2008 [44,45]. This procedure is applicable to normal weight and all the light weight concretes (using both moist and steam curing and Types I and III cement) under the standard conditions. Correction factors are applied for conditions which are other than standard. For this model  
\[E_{c}(t)=0.043\sqrt{\rho^{3}f_{cm28}\left(\frac{t}{a+bt}\right)}\] (A19)  
with \(\rho=2500\), \(a=4\), and \(b=0.85\). The ACI-209R-92 code recommends the following expressions for shrinkage:  
\[\epsilon_{sh}(t,t_{c})=\frac{(t-t_{c})^{\alpha}}{f+(t-t_{c})^{\alpha}}\epsilon _{shu}\] (A20)  
where \(t_{c}\) in days is starting time of drying, \(f=26.0\text{exp}[1.42\times 10^{-2}(V/S)]\), \(\alpha=1\), and \(\epsilon_{shu}=780\gamma_{sh}\times 10^{-6}\) with  
\[\gamma_{sh}=\gamma_{sh,tc}\gamma_{sh,RH}\gamma_{sh,ps}\gamma_{sh,s}\gamma_{sh, \phi}\gamma_{sh,c}\gamma_{sh,\alpha}\] (A21)  
where \(\gamma_{sh}\) represents the cumulative product of correction factors. In the present work only the following factors are considered. The ambient relative humidity coefficient \(\gamma_{sh,RH}\) is \[\gamma_{sh,RH}=\begin{cases}1.4-1.02h&\text{for}\ \ 0.4\leq h\leq 0.8,\\ 3.0-3.0h&\text{for}\ \ 0.8\leq h\leq 1.\end{cases} \tag{100}\]  
where the relative humidity h is in decimals. Coefficient \(\gamma_{sh,\text{rs}}\) allows for the size of the member in terms of the volume-surface ratio as  
\[\gamma_{sh,\text{rs}}=1.2e^{[-0.00472(V/S)]} \tag{101}\]  
where \(V\) is the specimen volume in mm\({}^{3}\) and \(S\) the specimen surface area in mm\({}^{2}\). Whereas the other coefficients are not considered (\(\gamma_{sh,tc}=\gamma_{sh,s}=\gamma_{sh,\psi}=\gamma_{sh,c}=\gamma_{sh,\alpha}=1\)).  
The ACI-209R-92 code recommends the following expressions for creep compliance function:  
\[J(t,t_{0})=\frac{1+\phi(t,t_{0})}{E_{c}(t_{0})} \tag{102}\]  
\[\phi(t,t_{0})=\frac{(t-t_{0})^{\psi}}{d+(t-t_{0})^{\psi}}\phi_{u}\gamma_{c,t_{ 0}}\gamma_{c,s}\gamma_{c,s}\gamma_{c,\psi}\gamma_{sh,\alpha} \tag{103}\]  
where \(\phi_{u}=2.35\), \(\psi=0.6\), \(d=10\), \(\gamma_{t_{0}}\), \(\gamma_{\lambda}\), and \(\gamma_{h}\) are correction factors for different loading ages \(t_{0}\), ambient relative humidity \(h\) in decimals, slump of fresh concrete \(s\) (in mm), the ratio of fine aggregate to total aggregate by weight \(\psi\) expressed as percentage, air content \(\alpha\) in percent, and the member size effects through the volume-surface ratio \(V/S\), respectively.  
\[\gamma_{c,t_{0}}=1.25t_{0}^{-0.118},\quad\gamma_{c,h}=1.27-0.67h,\quad\gamma_{ c,\text{rs}}=\frac{2}{3}\left(1+1.13e^{[-0.0213(V/S)]}\right), \tag{104}\]  
\[\gamma_{c,s}=0.82+0.00264s,\quad\gamma_{c,\psi}=0.88+0.0024\psi_{1},\quad\gamma _{sh,\alpha}=0.46+0.09\alpha\]  
where \(s\) is the slump of fresh concrete (mm), \(\psi_{1}\) is the ratio of fine aggregate to total aggregate by weight expressed as percentage, \(\alpha\) is the air content in percent. In the numerical analysis reported in this work, the correction factors to allow for the composition of the concrete are not considered, i.e., \(\gamma_{c,s}=0.82\), \(\gamma_{c,\psi}=1\), and \(\gamma_{sh,\alpha}=1\).