Quake Summit 2012 July 9-12, 2012, Boston Real-Time Hybrid Simulation Studies of Complex Large-Scale Systems Using Multi-Grid Processing dampers Dampers Yunbyeong Chae James M. Ricles Thomas M. Marullo Stephanie Tong ATLSS Center Lehigh University

Objectives of Study Improving the speed of computational time in real-time hybrid simulation (RTHS) for investigation of dynamic response of large-scale structural systems Implementing RTHS for a large complex structure using multi-grid processing

Why Multi-Grid Real-Time Hybrid Simulation? photo from Maurer Sohne Difficult (size and $) to conduct shaking table tests for large-scale structural systems RTHS can be an effective tool to enable the investigation of dynamic response of large-scale structures with rate-dependent devices Fast computational demand can be resolved using multi-grid processing From www.worldofstock.com

Case Study: 9-Story ASCE Benchmark Structure Ohtori et al. 2004, ASCE Journal of Engineering Mechanics, 130(4), 366-385

Structural Design Performance Objective Limit story drift to 1.5% under the design basis earthquake (DBE) ground motion (satisfying the life safety performance level)  Use large-scale MR dampers to control the story drift MCE ground motion: a 2% probability of exceedance in 50 years DBE ground motion: a 2/3rd intensity of the MCE

Large-Scale Magneto-Rheological (MR) Damper by Lord Corporation Length = 1.47m (58in) Stroke = ±297mm (±12in) Weight = 280kg (615lb) Force capacity = 200kN at V=0.1m/sec, I=2.5A

Deployment of MR Dampers Performance Objective: to limit story drift to 1.5% under DBE How many MR dampers? Where to install dampers?  Simplified Analysis Procedure

Simplified Analysis Procedure Response prediction method for MDOF structure with MR dampers (Chae, Y., Ph.D. Dissertation, Lehigh University, 2011) Calculate representative loss factor of MR damper Assume x0 and set Determine maximum damper displacements Calculate equivalent damping ratio using lateral force energy method Calculate equivalent stiffness of MR dampers Perform response spectrum analysis with effective stiffness and equivalent damping ratio Update effective stiffness of structural system Update x0 using modal combination rules (SRSS, CQC, etc.) No Update modal frequency and modal vector Check x0 convergence Yes Calculate damper force from the Hershel-Bulkley quasi-static MR damper model

(based on Simplified Analysis Procedure, Chae 2011) Deployment of MR dampers (based on Simplified Analysis Procedure, Chae 2011) Number of MR dampers 1 damper 2 dampers 5 dampers 10 dampers MR damper

+ Schematic of Real-Time Hybrid Simulation Structure with MR dampers Analytical substructure + Experimental substructure(s) Actuators 1st story MR damper 2nd story MR damper

Real-Time Hybrid Simulation Structural analysis program: HybridFEM, a MATLAB-based nonlinear finite element analysis program (nonlinear fiber elements, panel zone elements, strength deterioration elements, geometric nonlinearities, etc.; Karavasilis et al. 2009) Integration algorithm: CR integration method, a unconditionally stable and explicit time integration algorithm (Chen and Ricles 2008, JEM) Integration time step: Δt=5/512 sec (≅0.01 sec) Actuator delay compensation method: Inverse Compensation (Chen and Ricles 2010, JSE) Hybrid simulation platform: Mathwork’s xPC Target Semi-active control of MR dampers: Linear Quadratic Regulator (LQR) 11

Multi-Grid Real-Time Hybrid Simulation 2 xPCs used xPC1 xPC1: Intel Core 2 Duo (2.66GHz CPU), 2GB RAM; runs at 512Hz (1/512sec) Ground motion Update accelerations from equations of motion Update displacements/ velocities Integration algorithm Structural response Experimental substructure restoring forces + xPC2 xPC2: Intel Pentium 4 (2.4GHz CPU), 1GB RAM; runs at 102.4Hz (5/512sec) Analytical restoring forces 12

Analytical Substructure: 9-Story Building (using HybridFEM) Beams and columns are modeled using a distributed plasticity displacement-based beam-column element (nonlinear fiber element) Bi-linear material model Gravity frames modeled as a lean-on column with a geometric stiffness to account for P-Δ effect Lean-on column Number of degrees-of-freedom: 508 Number of nonlinear fiber elements: 357

Maxwell Nonlinear Slider (MNS) Model – Modeling of MR Dampers in Analytical Substructure Maxwell Nonlinear Slider (MNS) Model – (Chae et al. 2012, EESD) Pre- and post-yield behaviors are described independently by the Maxwell element and the nonlinear slider, respectively, making it easy to identify model parameters Non-Newtonian fluid property is effectively accounted for by the nonlinear slider utilizing the Hershel-Bulkley visco-plasticity Suitable for a discretized frame work with moderate time steps

- MR dampers in the 1st and 2nd stories - Experimental Substructure - MR dampers in the 1st and 2nd stories - 2nd story MR damper 1st story 1700kN actuator Current driver Load cell

Input Ground Motion 1994 Northridge earthquake recorded at Beverley Hills station (009 component) Scaled to DBE level with scale factor of 1.17 Unscaled ground motion

Results of Multi-Grid RTHS Multi-grid RTHS Video

Story drifts for 9-story building with MR dampers Results of Multi-Grid RTHS Story drifts for 9-story building with MR dampers Performance objective (1.5% story drift) Performance objective (1.5% story drift) Performance objective (1.5% story drift)

Story drifts for 9-story building without MR dampers 1st story 2nd story 3rd story 1.5% story drift 1.5% story drift

- Comparison of displacements between RTHS and numerical simulation - Validation of Multi-Grid RTHS - Comparison of displacements between RTHS and numerical simulation - 9th floor 5th floor 3rd floor 1st floor

Comparison of Normalized TET Task Execution Time (TET): the amount of time needed to complete a single step during real-time hybrid simulation With Two xPCs xPC1 only xPC1 xPC2 Maximum TET (TETmax, sec) 0.0009 0.0048 0.0016 Running time step (δt, sec) 1/512 (=0.0019) 5/512 (=0.0098)

Summary and Conclusions Real-time hybrid simulation for a large-scale structure with large complexity has been conducted successfully using multi-grid processing procedure The use of multiple xPCs enables the computations to be completed over a shorter duration, which may not be achieved with the conventional implementation of the RTHS method (i.e., using a single xPC) Multi-grid real-time hybrid simulation enables the investigation of dynamic response of a large complex structural system under earthquake ground motions

Acknowledgements This study is based upon work supported by grants from the Pennsylvania Department of Community and Economic Development through the Pennsylvania Infrastructure Technology Alliance, and by the National Science Foundation under Award No. CMS-0402490 NEES Consortium Operation, and NEES REU Program. We would like to thank Lord Corporation and Professor Richard Christenson for their generous support of this research by providing the MR dampers. 23

Thank you 24