## 3 Results and Discussions
### Tensile Strength  
Tensile strength is one of the important mechanical properties and is utilized in various design aspects of concrete structures such as those associated with the initiation and propagation of cracks, shear, and anchorage of steel reinforcement in concrete [45]. The indirect tensile strength tests were performed on 150 mm \(\times\) 300 mm cylinders after 28 days of casting according to ASTM C496/C496M-11. The effect of different mix design variables on indirect tensile strength is shown in Figure 8. It can be observed from the results of groups A and C that tensile strength of FS-GPC mixes increased by increasing the amount of slag and decreasing the AAS. As shown in Figure 8, mixes of group A designed with 10 M molarity NaOH solution exhibited lower tensile strengths as compared to the corresponding mixes of group B with higher molarity NaOH solution (12 M and 14 M). The tensile strength of FS-GPC was also increased by increasing the concentration of NaOH solution. Furthermore, it can be noted from the results of groups A and D that tensile strength of GPC mix increased significantly by varying SS/SH ratio from 2.0 to 2.5, while a decrease in strength was observed when the ratio was further increased from 2.5 to 3.0. The trends observed for the tensile strength results are the same as were observed for the compressive strength. The tensile strength of group E mixes prepared with reduced AAS content (35%) and additional water content (12 kg/m\({}^{3}\)) was decreased as compared to group C mixes with similar AAS and no additional water. This result is also identical to the compressive strength results discussed earlier. In conventional concrete design, the compressive strength is often used to estimate the tensile strength since a correlation exists between the two. The correlation is generally represented by a simple equation which is used to estimate uniaxial or split tensile strength. For example, the Equations (1)-(3) are recommended by the ACI 318-14, Eurocode BS EN 1992-1-1:2004 and Australian standard AS 3600, 2009 respectively to predict the tensile strength of OPC mixes. \[f_{ct}=0.56\ \sqrt{f_{c}^{t}} \tag{1}\]  
\[f_{ct}=0.30\ (f_{c})^{2/3}\ \text{for}\ f_{c}\ \leq\ 50\ \text{MPa} \tag{2}\]  
\[f_{ct}=0.36\ \sqrt{f_{c}^{t}} \tag{3}\]  
where \(f_{ct}\) = mean split tensile strength (MPa), \(f_{c}^{t}\) = characteristic compressive strength (MPa), and \(f_{c}\) = average compressive strength (MPa). Figure 11 shows the influence of mix design variables on tensile strength of FS-GPC at the age of 28 days. Figure 10: The influence of extra water on compressive strength of geopolymer concrete mixes (Group C vs. Group E). [PERSON] and [PERSON] (2013) and [PERSON] et al. (2007) have used the equations recommended by ACI 318-08 (Equation (1)) and Eurocode (Equation (2)) respectively to estimate the tensile strength of GPC mixes [30; 46]. They have found that the estimated strength values were higher than the measured values. By using the experimental results, the Equations (4) and (5) were proposed by [PERSON] and [PERSON] (2013) and [PERSON] et al. (2007) respectively to predict the split tensile strength of FA and SG based GPC. \[f_{ct}=0.45\ \sqrt{f_{c}^{\prime}} \tag{4}\]  
\[f_{ct}=0.48\ \sqrt{f_{c}^{\prime}} \tag{5}\]  
In the present study, Equation (4) ([PERSON] and [PERSON] (2013)) and Equation (5) ([PERSON] et al. (2007)) were used to estimate the tensile strength of GPC mixes based on their compressive strength [30; 46]. The calculated values from these equations along with the test values from the present study are presented in Table 6 and Figure 9. The comparison between predicted and measured values showed that the test values of the present study are lower as compared to the values predicted by the models of [PERSON] et al. (2007) (Equation (5)) and [PERSON] and [PERSON] (2014) (Equation (4)).