## 3 Assessment
### Assessment of Pilotis Columns
#### 3.2.2 Deformation and Strength Indices from Flexure  
The strength and deformation capacity were assessed as per the response of the building in y-y direction (strong axis: bending about x-x in Figure 1a). The corner columns are expected to yield first due to the lower axial load. The central column C5 is susceptible to crushing before yielding due to the high axial load. For lightly reinforced concrete elements, the curvature at the onset of tension reinforcement yielding \(\phi_{\text{y}}\) is approximated \(\phi_{\text{y}}=(2\varepsilon_{\text{sy}})/\text{h}=2\times 0.0025/350=0.0143/ \text{m}\), common for all columns. The moment at yielding as per the point of action of the concrete force can be approximated by Equation (1):  
\[\text{M}_{\text{y}}=\text{A}_{\text{s,l}}\cdot\text{f}_{\text{ym}}\cdot\text {jd}+\text{N}_{\text{Ed}}(0.5\text{ h}-0.4\times 0.25\cdot\text{d}) \tag{1}\]  
where jd = 0.85 d is the internal lever arm between tensile force of bottom steel reinforcement and concrete compressive force and \(\text{A}_{\text{s,l}}=3\times\pi\times 14^{2}/4=462\) mm\({}^{2}\) is the area of tensile reinforcement. The implementation of Equation (1) for corner columns (\(\text{N}_{\text{Ed}}=181.3\) kN) results to \(\text{M}_{\text{y}}\approx 89\) kNm and for peripheral columns (\(\text{N}_{\text{Ed}}=362.5\) kN) to \(\text{M}_{\text{y}}\approx 115\) kNm. A more precise calculation of curvature and moment at yielding can be deduced from cross section analysis by using Response2000 [31], where for corner columns \(\phi_{\text{y}}=0.0128/\text{m}\), \(\text{M}_{\text{y}}=90\) kNm and for peripheral columns \(\phi_{\text{y}}=0.0148/\text{m}\), \(\text{M}_{\text{y}}=109\) kNm. The two procedures for definition of \(\phi_{\text{y}}\), \(\text{M}_{\text{y}}\) result to similar values. The curvature at ultimate \(\phi_{\text{u}}=\epsilon_{\text{cu}}/(\xi\text{d})\), at concrete crushing strain \(\epsilon_{\text{cu}}=0.0035\), may be found by using the graph of Figure 3 (similar graphs were derived in [32]): for symmetrically reinforced cross section (present case), the normalized compression zone \(\xi=\times/\text{d}\) (d = 323 mm) is plotted against the total longitudinal reinforcing ratio \(\rho_{\text{l}}\) for several axial load ratios. This graph was deduced at yielding of tensile reinforcement; aiming to address the fact that at ultimate the compressive zone x becomes shorter, a reduction factor 0.9 is also applied to \(\xi\) value. Thus, for \(\rho_{\text{l}}=1.06\%\) for corner columns (\(\text{v}_{\text{Ed}}=0.13\)) is \(\xi=0.24\) and \(\phi_{\text{u}}=0.0035/(0.9\times 0.24\times 323)=0.05/\text{m}\) and for peripheral (\(\text{v}_{\text{Ed}}=0.26\)) is \(\xi=0.27\) and \(\phi_{\text{u}}=0.044/\text{m}\). All useful values of the assessment are summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Cross Section Analysis: Approximations**} & \multicolumn{6}{c}{**Chord Rotation from**} \\ \multicolumn{6}{c}{**Procedures (a–c)**} \\ \hline \multirow{3}{*}{**Column**} & \(\phi_{\text{y}}=\) & \multirow{3}{*}{**(\(\text{M}_{\text{y}}\)**)**} & \multirow{3}{*}{**(\(\text  
The secant to yield effective stiffness of the columns is given as \(\text{EI}=\text{M}_{\text{y}}/\phi_{\text{y}}\). Hence, for the two groups of columns: (i) \(\text{EI}=89/0.0143\approx 6250\)\(\text{kNm}^{2}\) for corner columns, (ii) \(\text{EI}=115/0.0143\approx 8050\)\(\text{kNm}^{2}\) for peripheral one. For concrete grade C16/20 the Young Modulus is \(\text{E}=29\) GPa, the moment of inertia of uncracked section is \(\text{I}=\text{bh}^{3}/12=8.93\,\times\,10^{8}\)\(\text{mm}^{2}\) (no consideration of internal reinforcement) thus the elastic stiffness is \(\text{EI}_{\text{el}}\approx 25,\text{900}\)\(\text{kNm}^{2}\). This is near threefold the effective values above (in pushover analysis cross sections are assumed cracked, hence 50% of the elastic value is used, \(\text{EI}_{\text{cr}}=50\%\text{EI}_{\text{el}}=12,\text{950}\)\(\text{kNm}^{2}\)).