Motivation

Analysis Framework

Results & Discussion

Future work References

Acknowledgement

• Examine the seismic response with superelastic shape memory alloy (SMA) dampers.

• Validate the equivalent SDOF system by MDOF structures.• Identify the optimal design parameters of dampers. • Investigate effective means to reduce non-structural

damage induced by floor acceleration.

1. Yazhou, X., Jian, Z., & Wang, X. (2018). Effectiveness evaluation and optimal design of nonlinear viscous dampers for inelastic structures under pulse-type ground motions. Earthquake Engineering and Structural Dynamics.

2. Chopra, A. K., & Chopra, A. K. (2007). Dynamics of structures: theory and applications to earthquake engineering (Vol. 3). Upper Saddle River, NJ: Pearson/Prentice Hall.

3. Simo, J. C., & Hughes, T. J. R. (1998). Computational Inelasticity (Interdisciplinary Applied Mathematics)(Volume 7).

This research project was conducted as a part of the Nakatani Foundation's 2018 Nakatani RIES Fellowship for Japanese Students. For more information, visit http://nakatani-ries.rice.edu/. Special thanks to the Natural Hazards Mitigation Research Group at Rice University for their research mentorship and to Prof. Junichiro Kono, Sarah Phillips, Aki Shimada, and Kennji Ogawa for their support.

Bouc-Wen model!" #, #

= ε()# * + (1 − /)()123(*)

Elastic stage

Plastic stage

#

!"

Yiel

d fo

rce

Yield strain

Bilinear model

!4!4 # = 54 #(*)

6789 (#(*)

Fragility function

• Significant earthquake damage on buildings (e.g. cause 9,000 casualties in 2015 Nepal earthquake).

• Innovative protective devices like viscous dampers can improve the seismic performance of civil structures.

• Probabilistic methods such as fragilityfunctions can be used to account for the earthquake uncertainties to quantify both structural and non-structural damages.

Simplify

Deterministic time history analysis

Conclusions• Damper can significantly reduce the structural and permanent damage of the building. • Damper is effective in reducing non-structural damage under small ground motions, but it has

adverse effect when subject to large ground motions. • Optimal design of viscous dampers is required to reduce structural and non-structural damages

simultaneously, which would improve the seismic resilience of the built environment.

320 earthquake motions are used

pulse-typereal earthquake

damper

:# + 5# + <= = >(*)

:# + 5# + <= + <? = >(*)

:# + 5# + <= + <? = −@AB (C)

Add nonlinear damper

Earthquake ground motion

Bilinear model & Newmark- D method,Newton-Raphson Iteration

Bouc-Wen model & ODE Method

PSDM(Probabilistic

seismic demand model)

• Consistent results by Newmark-D method with bilinear model and ODE method with Bouc-Wen model.

• Considerable permanent deformation under pulse motions.

• Viscous dampers alters the PSDMs substantially.• Residual drift ratio yields large standard deviation when conditioned on PGA.

Input

EF = 0.18

IF = J

IK = 2J

9 = 15

E = 0.8554

P = 0.1920

E = 1.2409

P = −0.0242

E = 1.4628

P = −8.0785

E = 1.5218

P = −9.5263

E = 1.0338

P = −5.5506

E = 1.3225

P = −6.0202

Fragility function(Moderate)

Peak Drift Ratio Residual Drift Ratio Peak Acceleration

Peak Drift Ratio Residual Drift Ratio Peak Acceleration

!"

column

Structural(Displacement)

Permanent(Residual)

Non-structural(Acceleration)

PSDM

IM

P

3 *

= −1

12{

}

W # * 3 * 3 * XYZ

+ D# * 3(*) X − #(*)

Seismic fragility analysis of building structures using equivalent SDOF systems Gen Hayakawa1,2, Yazhou (Tim) Xie3, Reginald DesRoches3

1Department of Civil Engineering, the University of Tokyo, Japan2Nakatani RIES: Research and International Experiences for Student, Nakatani Foundation, Japan

3Department of Civil and Environmental Engineering, Rice University, U.S.A.

ln(IM)

ln(E

DP)

ln(EDP) = a ln(IM) + b