## 3 Assessment
### Assessment of Pilotis Columns
#### 3.2.3 Brittle Mechanisms: Shear and Lap-Splices  
The calculations in Section 3.2.2 for determining the flexural response of the ground storey columns ignored the columns' shear capacity. The preceding calculations are meaningful provided the columns are able to develop the lateral force \(\rm V_{fl}\) that corresponds to flexural capacity, i.e., \(\rm V_{fl}=M_{y}/L_{V}\). Thus, for corner columns \(\rm V_{fl}=89/1.35\approx 66\) kN and for peripheral \(\rm V_{fl}=115/1.35\approx 85\) kN. Note that \(\rm V_{fl}\) should be multiplied by a safety factor \(>\)1 aiming to account for the over-strength of columns. More specifically, in accordance with EN1998-1 [35], for medium ductility r.c. buildings (DCM), the over-strength for beams and columns may be found by the product of the flexural capacity with (i) the material safety factor 1.15 for steel, (ii) a factor equal to 1.2 due to design-action effects at the end sections of critical regions, and (iii) a factor equal to 1 and 1.1 due to steel strain hardening for beams and columns, respectively. Thus, for columns the overstrength factor is \(\rm 1.15\times 1.2\times 1.1\approx 1.5\). The shear capacity of the columns is given by Equation (6) (from [33]):  
\[\rm V_{Rd,o}=1/\gamma_{el}\ [(h-x)/(2L_{V})\cdot min(N,\ 0.55A_{c}f_{c})+[1-0.05 min(5,\rm\mu_{\theta}^{pl})](V_{Rd,c}+V_{Rd,s})] \tag{6a}\] \[\rm V_{Rd,c}=0.41\sqrt{(f_{c})}b\times x\] (6b) \[\rm V_{Rd,s}=\rho_{sw,y}b_{o}h_{o}f_{yst}=A_{sy}/(s_{h}b_{o})b_{o}h_{o}f_{yst} \tag{6c}\]  
where \(\rm\gamma_{el}=1.15\), x = \(\rm\xi d\) (\(\rm\xi\) from Table 1, multiplied also with the correction factor 0.9 as explained before). Applying Equation (6b,c), for corner columns result to \(\rm V_{Rd,c}\approx 29\) kN, for peripheral to \(\rm V_{Rd,c}\approx 32\) kN and \(\rm V_{Rd,s}=28\) kN. For the definition of \(\rm\mu_{\theta}^{pl}=(\rm\theta_{u}-\rm\theta_{y})/\rm\theta_{y}=\rm\mu_{0}-1\), among procedures (a-c) above, procedure (b) is chosen because it results to a more conservative estimation of \(\rm V_{Rd,o}\). Thus for the corner columns the term \([1-0.05\ {\rm min(5,\rm\mu_{\theta}^{pl})}]\) in Equation (6a) is \([1-0.05\ {\rm min(5,\rm 3.1-1)}]=0.89\) and for peripheral columns is 0.92 (\(\rm\mu_{\theta}^{pl}=2.6-1=1.6\)). Next, Equation (6a) is implemented: for corner columns is \(\rm V_{Rd,o}\approx 60\) kN \(<1.5\ \rm V_{fl}=1.5\times 66=99\) kN and for peripheral \(\rm V_{Rd,o}=80\) kN \(<1.5\ \rm V_{fl}=1.5\times 85\approx 128\) kN. It may conclude that both corner and peripheral columns will fail in shear near yielding at almost the same drift \((\rm\theta_{y}V_{Rd,o}/V_{fl}\): for corner columns is 0.64% \(\times\) 60/66 = 0.59% and for peripheral 0.64% \(\times\) 80/85 = 0.6%). Another concern is whether the available splice length \(\rm l_{o}\) suffices for the reinforcing bars to develop their yielding strength. The available bond strength is given by Equation (7):  
\[\rm\tau_{b}=2\mu_{fr}/(\pi D_{b})\times[2 cf_{ctk}+0.33\ (A_{st}\ f_{yst})/(N_{b} \rm s)] \tag{7}\]  
and yielding is secured when \(\rm\tau_{b}\geq\gamma_{el}D_{b}f_{sy}/(4b_{o})\). Values for the parameters are: \(\rm\mu_{f}=1\), \(\rm D_{b}=14\) mm, \(\rm f_{ctk}=0.33\ f_{cm}^{0.5}=0.33\ \times\ 16^{0.5}=1.3\) MPa, c = 20 mm, \(\rm A_{st}=2\times\pi\times 6^{2}/4=56.5\ mm^{2}\), \(\rm f_{yst}=240\) MPa, \(\rm N_{b}=3\) bar pairs, s = 150 mm, \(\rm\gamma_{el}=1.15\), \(\rm f_{sy}=500\) MPa, thus Equation (7) yields to \(\tau_{\rm b}\) = 2.82 MPa. For a splice with a hook (\(\rm l_{o}\) = 875 mm) is \(\tau_{\rm b}\) = 2.8 MPa \(>\)\(\rm y_{\rm cel}D_{\rm fgy}/(4l_{o})\) = 2.3 MPa, thus lap splice suffices longitudinal reinforcement yielding, but after that milestone (where \(\rm\mu_{\rm\Theta}>1\)) cover cracking is anticipated; this implication diminishes cover contribution (i.e., 2\(\rm cfcfc}\approx 0\)) in defining bond strength thus a splice failure is also anticipated.