## 3 Assessment
### Assessment of Pilotis Columns
#### 3.2.1 Slenderness  
A first step is to check the slenderness of the columns. The total gravity load of each floor, W\({}_{\rm floor}\), is calculated by the seismic combination, G + 0.3 Q, where G stands for the total dead load (25 kN/m\({}^{3}\) of reinforced concrete for the slab of thickness h\({}_{\rm f}\) = 0.2 m and additional 2 kN/m\({}^{2}\)) and Q is the total live load (3.5 kN/m\({}^{2}\)), hence, W\({}_{\rm floor}\) = plan area-(Gh\({}_{\rm f}\) + 0.3 Q) = 120 m\({}^{2}\)-(25 \(\times\) 0.2 + 2 + 0.3 \(\times\) 3.5) = 966 kN whereas the total weight carried by the building's ground floor columns is W\({}_{\rm tot}\) = 3 \(\times\) 966 = 2900 kN (three floors). For simplicity the weight of the external brick masonry walls of the 2 nd and 3 rd floor was not considered in the building mass because it represents about 5-10% of the weight of the r.c. elements. For example, the masonry weight per floor is W\({}_{\rm masonry}\)\(\approx\) 165 kN (see the detailed calculation in Table A1 of Appendix A--the same is valid for the next calculations where it is deemed necessary). Thus, the total masonry weight is 330 kN--this is an upper limit since the calculation does not consider any openings. Each ground column undertakes part of the total axial load after multiplying W\({}_{\rm tot}\) by the ratio of the tributary area (i.e., the light hatched area as per column C1 in Figure 1a) to the total floor area. The values of axial loads N\({}_{\rm Ed}\) along with the corresponding axial load ratios, v\({}_{\rm Ed}\) = N\({}_{\rm Ed}\)/(bhf\({}_{\rm cm}\)) are N\({}_{\rm Ed}\) = 181.3 kN--v\({}_{\rm Ed}\) = 0.13 for the corner columns C1/3/7/9, and N\({}_{\rm Ed}\) = 362.5 kN--v\({}_{\rm Ed}\) = 0.26 for all the peripheral columns C2/4/6/8. The central column C5, by having N\({}_{\rm Ed}\) = 725 kN--v\({}_{\rm Ed}\) = 0.52, is prone to crushing before yielding due to the high  
Figure 2: (**a**) Column cross section detailing and splice arrangement at column base and (**b**) beam geometry and longitudinal reinforcement detailing.  
axial load. In order to reduce \(v_{\text{Ed}}\) below 0.4, thus securing a dominant flexural response, the increase in the cross-section dimensions is required. The slenderness effect is taken into consideration by following the procedure of ACI 318-19 [30]. The radius of gyration for the cross section of the column with respect to the weak axis y-y (Figure 1a) is \(\text{i}=\sqrt{(\text{I}_{\text{g}}/\text{A}_{\text{g}})}\approx 0.3\) b = 75 mm and the associated slenderness is \(\lambda=(\beta_{\text{o}}\cdot\text{H})/\text{i}=36>\lambda_{\text{lim}}=\text {max}\{25;\ 15/\sqrt{v_{\text{Ed}}}=20.8\}=25\). The reduction in slenderness is achieved by increasing the cross section to \(h^{\text{new}}=450\) mm and \(b^{\text{new}}=350\) mm. The new calculations are: \(v_{\text{Ed}}^{\text{new}}=0.29\), \(i^{\text{new}}\approx 0.3\)\(b^{\text{new}}=105\) mm and \(\lambda^{\text{new}}=25.7<\lambda_{\text{lim}}=\text{max}\{25;\ 27.9\}=27.9\). Note that \(v_{\text{Ed}}^{\text{new}}=0.29\) is an upper value given that the increase in the cross section dimensions is usually implemented by using concrete of higher quality.