# A Comparative Analysis of International Standards on Curved Surface Isolators for Buildings
## 3 Design Procedures
### Bounding Considerations  
According to ASCE/SEI 7-22 Appendix 17-A (Section 17.2.1), the modification of isolator design properties, such as the friction coefficient, is required for bounding analyses using Upper Bound Design Properties (UBDP) and Lower Bound Design Properties (LBDP). Similarly, EN 15129 (Clause 6.6.3.3.3) stipulates that variation of mechanical properties must be accounted for in the analysis to ensure safety under expected uncertainties due to aging, temperature, and loading rate. These provisions provide the basis for applying friction modification factors (e.g., \(\lambda_{\mathrm{max}}\) and \(\lambda_{\mathrm{min}}\)) as used in the case study to represent realistic bounds on isolator behavior under seismic loading. It is important to emphasize that the friction coefficient values used in seismic isolation design represent nominal (average) values. In real-world conditions, the dynamic coefficient of friction can vary due to several factors. These include temperature changes, material aging, pressure applied to the sliding surface, and the number of dynamic loading cycles [8]. To account for these variations, the friction coefficient is adjusted using property modification factors (\(\lambda_{\mathrm{max}}\) and \(\lambda_{\mathrm{min}}\)), which define the upper and lower bounds of the friction coefficient. This ensures a more robust \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Eurocode 8** & **ASCE/SEI 7-22** & **[\%]** \\ \hline Displacement \(D_{i}\) [mm] & 136.62 & 157.23 & 15.35 \\ Equivalent stiffness \(K_{\mathrm{eff}}\) [kN/mm] & 323.60 & 305.39 & 5.63 \\ Equivalent period \(T_{\mathrm{eff}}\) [sec] & 3.05 & 3.14 & 2.95 \\ Equivalent viscous damping \(\xi_{\mathrm{eff}}\) [\%] & 26.94 & 24.75 & 8.13 \\ Damping factor \(B_{M}\) & 0.56 & 1.59 & 12.30 \\ Acceleration \(A\) & 0.059 & 0.064 & 8.62 \\ Maximum displacement \(D_{\mathrm{max}}\) [mm] & 136.32 & 157.23 & 15.35 \\ Maximum horizontal force \(F_{\mathrm{max}}\) [kN] & 44,113.84 & 48,017.53 & 8.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between the European standard (EC8) and the American standard (ASCE/SEI 7-22) in terms of the key parameters governing isolator design and the percentage differences observed. and realistic evaluation of the seismic isolation system's behavior. For this case study, the UBDP and LBDP were determined based on experimental test results [9; 10; 11], ensuring high material quality and performance consistency. These values were selected following the European approach (EC8 [57] in case of ELA). In this analysis, only the coefficient of friction (\(\mu\)) is modified by the property factors:  
* Upper Bound Design Properties--UBDP: \(\mu\) = 2.5% with \(\lambda_{\text{max}}\) = 4%;
* Lower Bound Design Properties--LBDP: \(\mu\) = 2.5%, with \(\lambda_{\text{min}}\) = 2%. The final results are presented in Table 3 after performing an iterative analysis, ensuring convergence between the initial displacement \(D_{i}\) and the maximum displacement \(D_{\text{max}}\), following the same procedure used for the nominal friction coefficient case. It is also important to assess whether the observed percentage differences across standards hold practical engineering relevance. For example, the 15.35% difference in displacement estimates between EC8 and ASCE/SEI 7-22 (as shown in Table 2) is consistent with the 15% displacement amplification required by ASCE/SEI 7-22 to account for accidental torsional effects. Moreover, Eurocode 8 allows variability in mechanical properties of isolators, including equivalent stiffness and damping, up to \(\pm\)20% through property modification factors [EN 15129, Clause 6.3.3]. Given this regulatory context, the percentage differences reported in Tables 2 and 3 fall within the range of engineering tolerances accepted by international standards. Historically, similar levels of variability in isolation system performance have been documented in both full-scale experiments and post-earthquake assessments of isolated buildings [12; 54].