# Influence of Pile Foundation Stiffness on Column Design in One-Story Reinforced Concrete Frames
## 4 Examples  
Examples of calculations of bending moments in reinforced concrete frame columns are shown below. The calculations were carried out using the rigorous method of second-order analysis with nominal stiffnesses, as described in [15]. The calculations were conducted for both fully restrained columns and columns fixed in a piled foundation. The columns were assumed to have equal cross-sections of \(b\) = 0.40 m and \(h\) = 0.45 m and were made of concrete C30/37 and steel RB500.  
For comparison purposes, we assumed the same geotechnical conditions (Figure 7; Table 1), which were the same for all the structural variants analyzed. The pile supports under the columns were adopted in the form of reinforced concrete rectangular pile caps  
Figure 6: Comparison of selected shear modulus degradation functions [21; 33; 34].  
topping the heads of two piles with an axial spacing of \(sp=1.2\) m. The pile types were reinforced concrete piles, prefabricated, driven and with a square cross-section of \(0.35\times 0.35\) m.  
The lengths of the piles varied (\(L_{\text{p}}=10\), \(14\) and \(15\) m), as they were selected according to the assumptions of the limit state method in order to obtain a similar degree of bearing capacity reserve in each case (ensuring fulfillment of the limit state condition for piles loaded with compressive forces). Figure 8 shows the settlement curves of the assumed piles obtained from the calculations.  
The calculation of the stiffness of the column/foundation connection was based on the calculation of pile settlements in the column support, taking into account the interaction between the two according to the method outlined above.  
The resulting rotation angle \(\varphi\) allows for the static calculation of the column to be carried out, taking into account the second-order theory. Considering the stiffness of the pile support leads to new values for the internal forces and nodal forces (reactions). The described procedure requires iterative calculations according to the following scheme:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No. of Layer**} & \multirow{2}{*}{**Soil**} & \multicolumn{2}{c}{**Unit Weight**} & \multirow{2}{*}{\(\tau_{f}\) [kPa]} & \multirow{2}{*}{\(q_{\text{f}}\) [kPa]} & \multirow{2}{*}{\(G_{\text{max}}\) [MPa]} \\  & & & [kN/m\({}^{3}\)] & & \\ \hline
1 & fill & 16.0 & 5 & - & 24 \\ \hline
2 & organic soil & 5.0 & 5 & - & 7 \\ \hline
3 & clayy silt & 11.5 & 40 & - & 40 \\ \hline
4 & sandy clay & 11.0 & 53 & 1800 & 54 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters adopted for the pile settlement calculations.  
Figure 7: Assumed geotechnical profile.  
1. Static calculation of the hall's structural system, assuming that the columns are restrained at their supports and obtaining nodal forces;
2. Determination of the pile loads \(Q_{i}\), verification of the ultimate limit state of the pile, calculation of the pile settlement and foundation rotation (Figure 9);
3. Making a static calculation of the hall's structural system according to the second-order theory, taking into account the rotational stiffness of the pile supports and obtaining new values for the nodal forces;
4. Determination of new loads on the pile \(Q_{i}\), verification of the ultimate limit state of the pile, calculation of pile settlement and foundation rotation as in step (II).  
Steps (II)-(IV) are performed until the results converge. The calculations performed for the example presented here required two or three iterations.