## 4 Results
Table 4 shows example 1 from [PERSON] (2017) versus the new model (the column in the center of the footing):  
1. For Problem 1.1, the minimum area appears in Case I, and for Problems 1.2, 1.3, and 1.4, the minimum area appears in Case V.
2. For Problem 1.2, in terms of the contact area between the footing and the ground, there is no difference (theoretical areas) when using the new model. 3. For Problem 1.3, there is a reduction of 2.89% (theoretical areas) in the contact area between the footing and the ground when using the new model. 4. For Problem 1.4, there is a reduction of 42.37% (theoretical areas) in the contact area between the footing and the ground when using the new model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \(L_{x}\) & \(L_{y}\) & \(L_{x1}\) & \(L_{y1}\) & \(\sigma_{max-act}\) & \(A_{min}\) \\  & **(m)** & **(m)** & **(m)** & **(m)** & **(kN/m\({}^{2}\))** & **(m\({}^{2}\))** \\ \hline \multicolumn{8}{c}{Problem 1.1: \(P=1000\) kN, \(M_{x}=225\) kN-m, \(M_{y}=150\) kN-m, \(x_{c}=0\), and \(y_{c}=0\)} \\ \hline I & 2.52 & 3.78 & - & - & 180.00 & 9.52 \\ II & & & & No solution available & & \\ III & 9.77 & 1.24 & 110.85 & 1.24 & 180.00 & 12.15 \\ IV & 0.83 & 14.65 & 0.83 & 166.28 & 180.00 & 12.15 \\ V & 4.38 & 2.19 & 26.03 & 3.33 & 180.00 & 9.60 \\ FS-I & 2.55 & 3.80 & - & - & 176.29 & 9.69 \\ \hline \multicolumn{8}{c}{Problem 1.2: \(P=850\) kN, \(M_{x}=225\) kN-m, \(M_{y}=150\) kN-m, \(x_{c}=0\), and \(y_{c}=0\)} \\ \hline I & 2.43 & 3.64 & - & - & 180.00 & 8.84 \\ II & & & & No solution available & & \\ III & 7.63 & 1.41 & 58.74 & 1.41 & 180.00 & 10.79 \\ IV & 0.94 & 11.45 & 0.94 & 88.11 & 180.00 & 10.79 \\ V & 2.43 & 3.64 & 5.22 & 7.83 & 180.00 & 8.83 \\ FS-V & 2.45 & 3.65 & 6.58 & 9.70 & 156.63 & 8.94 \\ \hline \multicolumn{8}{c}{Problem 1.3: \(P=750\) kN, \(M_{x}=225\) kN-m, \(M_{y}=150\) kN-m, \(x_{c}=0\), and \(y_{c}=0\)} \\ \hline I & 2.40 & 3.60 & - & - & 173.61 & 8.64 \\ II & & & & No solution available & & \\ III & 6.41 & 1.55 & 37.37 & 1.55 & 180.00 & 9.94 \\ IV & 1.03 & 9.62 & 1.03 & 56.05 & 180.00 & 9.94 \\ V & 2.37 & 3.55 & 4.70 & 7.05 & 180.00 & 8.39 \\ FS-V & 2.40 & 3.55 & 4.82 & 7.03 & 176.68 & 8.52 \\ \hline \multicolumn{8}{c}{Problem 1.4: \(P=600\) kN, \(M_{x}=225\) kN-m, \(M_{y}=150\) kN-m, \(x_{c}=0\), and \(y_{c}=0\)} \\ \hline I & 3.00 & 4.50 & - & - & 88.89 & 13.50 \\ II & & & & No solution available & & \\ III & 4.87 & 1.81 & 18.11 & 18.01 & 180.00 & 8.83 \\ IV & 1.21 & 7.30 & 1.21 & 27.17 & 180.00 & 8.83 \\ V & 2.28 & 3.42 & 3.97 & 5.96 & 180.00 & 7.78 \\ FS-V & 2.30 & 3.45 & 4.03 & 6.05 & 175.30 & 7.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Example 1: [PERSON] model against the new model. The main difference between the current model and the new model is that the current model considers Case I (the load, \(P\), is located in the central nucleus of the footing), and the new model takes into account Cases I, II, II, IV, and V (the load, \(P\), is located anywhere on the footing, that is, inside and outside the central nucleus of the footing). The limitations of this study are as follows:  
1. When the columns are very close to each other, the isolated footings tend to overlap. In this case, a combined footing must be used. 2. When an isolated footing is limited by space situations (property boundary), a combined footing must be used. The main conclusions are as follows:  
1. Other authors propose very complex equations to find the maximum load capacity of the footing due to the soil, and other authors obtain the sides of the footing through iterations. 2. It is also observed that for the minimum area of the examples considered under biaxial bending, when Case II appears, Case V is not present. This means that when the resultant force decreases, Case II appears, and, conversely, Case V does not appear. This can be seen in Figure 2; when the resultant force is very small, the resultant force tends to fall in zone II. Therefore, it is not possible to obtain a solution for both cases of the same problem. 3.