## 2 Materials and Methods
### Influence of Main Design Variables to Column Ductility and Failure Mode  
One important goal in seismic structural assessment procedures is the reliable estimation of the available capacity of structural members for inelastic deformation, as well as their available ductility. Ductility drives assessment since its magnitude underlies the general design philosophy (i.e., through the q-u-T relationships it controls the magnitude of strength reduction from the elastic demands that may be tolerated before failure) and, in current code practice (EN 1998-1 2004 [18] and AASHTO LRFD 2013 [19], FEMA 440 2005 [20]), its magnitude is reflected on the specific reinforcing requirements of members and structures. In the experimental database report of [PERSON] and [PERSON] (2004) [12], the nominal column failure mode was classified as (a) flexure critical, (b) flexure-shear critical, or (c) shear critical, according to the following criteria:  
* If no shear damage was reported by the experimentalist, the column was classified as flexure critical. * If shear damage (diagonal cracks) was reported, the absolute maximum effective force (\(F_{eff}\): absolute maximum measured force in the experimental column response) was compared with the calculated \"ideal\" force corresponding to a maximum axial compressive strain in the concrete cover set equal to 0.004, which corresponds to the spalling of unconfined concrete (\(F_{0.004}\)). The failure displacement ductility at an effective force equal to 80% maximum \(\mu_{fail}\) was determined from the experimental envelope. If the maximum effective force \(F_{eff}<0.95\)-\(F_{0.004}F_{eff}<0.95\)-\(F_{0.004}F_{eff}<0.95\)-\(F_{0.004}\) or if the failure displacement ductility was less than or equal to 2 (\(\mu_{fail}\leq 2\mu_{fail}\leq 2\)), the column was classified as shear critical. Otherwise, the column was classified as flexure-shear critical. All columns in the database are divided into two sub-groups according to cross-sectional shape (rectangular and circular section columns). In this section, the displacement ductility value clouds--as defined by the reported experimental responses--are correlated against important design parameters and plotted in graphs to illustrate the parametric dependencies of this variable on the column failure mode. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Rectangular Reinforced (306 Tests)**} & \multicolumn{3}{c}{**Spiral Reinforced (177 Tests)**} \\ \hline
**Column** & **Mean** & **Std** & **CoV** & **Mean** & **Std** & **CoV** \\
**Property** & & & & & & \\ \hline Depth (mm) & 323.43 & 116.5 & 0.36 & 420.97 & 202.11 & 0.48 \\ \hline Aspect Ratio & 3.44 & 1.44 & 0.42 & 3.31 & 1.96 & 0.59 \\ \hline Axial-Load Ratio & 0.27 & 0.19 & 0.73 & 0.14 & 0.14 & 1.04 \\ \hline \(\rho_{l}\) (\%) & 2.45 & 1.00 & 0.41 & 2.62 & 1.02 & 0.39 \\ \hline \(\rho_{s}\) (\%) & 1.34 & 1.07 & 0.80 & 0.93 & 0.74 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Column property statistics. For example, considering the concrete strength, the following points are made: (a) higher strength materials are marked by lower ultimate strain, (b) strain can be enhanced through confinement, (c) a higher concrete strength results in a lower compression zone both at yielding and at failure. In general, it can be said that higher concrete strength causes a reduction in ductility. This finding is confirmed by both groups of rectangular tied columns and by the spiral reinforced columns, as can be seen in Figures 1 and 2. For the spiral reinforced columns, it is more clearly evident that the ductility is increased for specimens with lower concrete strengths. During the flexural analysis of a section both at yielding and at failure, the presence of a compressive axial load increases the depth of the compressive zone, as compared to an identical section without axial force. Based on the above remark, the presence of the compressive axial load reduces the curvature ductility of a section.