Table 1.

Equivalent viscous damping $({\xi }_{\mathit{eq}})$ (%) and ductility $(\mu )$ relationships for different structural systems

Description	EVD Expression $({\xi }_{\mathit{eq}})$	Parameter definitions
Precast concrete walls and frames [43]	$5+\frac{25}{\pi }\left(1,-,\frac{1}{\sqrt{\mu }}\right)$
RC frame [44]	$max(4.7,-0.4{\mu }^2+7.1\mu -2)$
RC frame [34]	${\xi }_0+\frac{8}{\pi }\left(5,-,\frac{6}{{\mu }^{1.8}},+,0.2,{\mu }^{1.8}\right)$	${\xi }_0$: Initial elastic damping
BRB-RC frame [45]	$5+\left(\frac{150(\mu -1)(1-0.14)}{(\mu -0.14\mu +0.14{\mu }^2)\pi }\right)$
Steel-braced RC frame [34]	${\xi }_0+\frac{70}{\pi }\left(1,-,\frac{43}{{\mu }^4},-,\frac{4.7}{{10}^5},{\mu }^4\right);\mu \ge 3$	${\xi }_0$: Initial elastic damping
Infilled-RC frame [46]	${\xi }_0+80.4\left(\frac{\mu +0.83}{\mu \pi }\right)$; ${\xi }_0+80.4\left(\frac{\mu +0.05}{\mu \pi }\right)$	${\xi }_0$: Initial elastic damping
Steel members [47]	${\xi }_0+a\left(1,-,\frac{1}{{\mu }^b}\right)T^c$	${\xi }_0$: Initial elastic damping, a, b, and c: constants, T: Period
Hybrid-timber [40]	$5+\frac{62\times {\lambda }^{0.4}}{\pi }\left(1,-,\frac{1}{\sqrt{\mu }}\right)$	$\lambda =H/B$: slenderness ratio, H: height of frame, B: width of the frame
Steel frame with CLT infill [33]	${\xi }_0+C\left(\frac{\mu -1}{\mu \pi }\right)$	C: constant