PERFORMANCE EVALUATION OF VIBRATION CONTROLLED STEEL STRUCTURES UNDER SEISMIC LOADING

Transcription

1 Department of Civil and Environmental Engineering Stanford University PERFORMANCE EVALUATION OF VIBRATION CONTROLLED STEEL STRUCTURES UNDER SEISMIC LOADING by Luciana R. Barroso and H. Allison Smith Report No. 133 June 1999

2 The John A. Blume Earthquake Engineering Center was established to promote research and education in earthquake engineering. Through its activities our understanding of earthquakes and their effects on mankind s facilities and structures is improving. The Center conducts research, provides instruction, publishes reports and articles, conducts seminar and conferences, and provides financial support for students. The Center is named for Dr. John A. Blume, a well-known consulting engineer and Stanford alumnus. Address: The John A. Blume Earthquake Engineering Center Department of Civil and Environmental Engineering Stanford University Stanford CA (650) (650) (fax) stanford.edu The John A. Blume Earthquake Engineering Center

3 PERFORMANCE EVALUATION OF VIBRATION CONTROLLED STEEL STRUCTURES UNDER SEISMIC LOADING by Luciana R. Barroso and H. Allison Smith The John A. Blume Earthquake Engineering Center Department of Civil and Environmental Engineering Stanford University Stanford, CA Report No. 133 June 1999

4 cfl Copyright 1999 by Luciana R. Barroso All Rights Reserved ii

5 Abstract The structural engineering community has been making great strides in recent years to develop performance-based earthquake engineering methodologies for both new and existing construction. For structural control to gain viability in the earthquake engineering community, understanding the role of controllers within the context of performance-based engineering is of primary importance. Design of a structure/controller system should involve a thorough understanding of how various types of controllers enhance structural performance, such that the most effective type of controller is selected for the given structure and seismic hazard. The goal of this research is to evaluate the role of structural control technology in enhancing the overall structural performance under seismic excitations. This study focuses on steel moment resisting frames and three types of possible controllers: (1) friction pendulum base isolation system, FPS (passive); (2) linear viscous brace dampers, VS (passive); (3) and active tendon braces, ATB. Two structures are selected from the SAC Phase II project, the three story system and the nine story system. Simulations of these systems, both controlled and uncontrolled, are prepared using the three suites of earthquake records, also from the SAC Phase II project, representing three different return periods. Several controllers are developed for each structure, and their performance is judged based on both roof and interstory drift, normalized dissipated hysteretic energy, and peak floor acceleration demands. This investigation has the following specific objectives: (1) To evaluate the effect of the various controller architectures on seismic demands as described through performance-based design criteria; (2) To evaluate the sensitivity of the structurecontroller performance based on a variation of control parameters, load levels and structural modeling; (3) To evaluate different systems using a probabilistic format. iii

6 The control parameters investigated for the FPS system include the isolation period and the coefficient of friction. These parameters were varied to span a range of possible values. For the VS damper system, the effect of variation in effective damping and its distribution over the height of the structure were evaluated. A representative ATB control scheme was then designed with actuator saturation levels comparable to the VS damper system for comparison. Results indicate that structural control systems are effective solutions that can improve structural performance. All three control strategies investigated can significantly reduce the seismic demands on a structure, thereby reducing the expected damage to the structure. However, no one system is consistently the best at all hazard levels. The viscous system proves to be the most insensitive to modeling assumptions. The isolation system can maintain the demands close to the structure's elastic limit. However, the onset of nonlinear behavior decreases the system's effectiveness. The active system is also sensitive to design assumptions, such as output parameters and structural model parameters used in design. Peak responses alone do not describe the possible damage incurred by the structure as cumulative damage results from several incursions into the inelastic range. Accurate evaluations should involve consideration of the dissipated hysteretic energy. For isolation systems, selection of isolation period has the greatest impact in the resulting seismic demands on the superstructure. Lowering the friction coefficient can cause small reductions in drift demands, but the cost of this reduction in structural demands is an increase in bearing displacements. This system of control proves to be very effective system for both the 3-Story and 9-Story structures and all three sets of ground motions. The median response of the superstructure remains close to elastic even under severe ground motions. This system, however, is sensitive to the stiffness of the structure, and its effectiveness begins to deteriorate once noticeable nonlinearities occur. The viscous damper system is very sensitive to both the amountofeffective damping provided and the distribution of dampers over the height of the structure. Different damper distributions have little impact on the roof drift. However, by distributing dampers according to relative story stiffness and expected peak plastic deformations, the drift demands are more evenly distributed among the different stories. If the dampers are located in only a few stories for the same amount of effective damping, iv

7 however, the system can be highly ineffective and may increase story demands at stories without dampers. The capacity of the actuators for the ATB system contributes greatly to the effectiveness of the control system. Higher actuator capacities provide the controller a greater opportunity to reduce drift demands. The resulting systems may increase story drift demands from the uncontrolled system, particularly in stories without actuators. However, careful design of the control system for the 3-story structure results in a system that consistently reduces the median story drift demands. The impact on seismic demands of placing the actuators only at select story locations is investigated in the 9-story. The result of this placement is that at high level excitations the drift demands at stories without actuators are increased from the uncontrolled case. The use of a probabilistic format allows for a consideration of structural response over a range of seismic hazards. Stable relationships can be developed between the spectral acceleration and controlled structural demands. Similar relationships are also possible for the demands on the control system, such as the peak bearing displacement for the isolation system. As a result, fewer control analyses may be required to estimate the expected structural behavior. The resulting annual hazard curves can be used to evaluate the effect of different control parameters as well as provide a basis for comparison between different control strategies. v

8 Acknowledgements The research presented in this report is based on the doctoral dissertation of Luciana Barroso. The work presented here would not have been possible without the support from numerous individuals, a few of whom are presented here. Discussions with Dr. Steven Winterstein into the extension of the research into the probabilistic realm greatly influenced the direction of the project. Dr. Helmut Krawinkler provided valuable technical advice and direction into the seismic performance of steel structures. Special thanks are also due to Dr. Akshay Gupta the technical input and background information for the case studies. The authors would also like to thank Scott Breneman for his collaboration in the development of the analysis software and research into active control systems for the seismic resistance of steel moment-resisting frames. vi

9 Contents Abstract Acknowledgements List of Tables List of Figures Notation iii vi xii xx xxi 1 Introduction Motivation Objective and Scope Overview Performance Evaluation of Structures Introduction Damage to Nonstructural Elements Damage to Structural Elements Damage Indices Maximum Deformation Damage Indices Cumulative Damage Indices Combined Indices: Maximum Deformation and Cumulative Damage Maximum Softening Damage Indices Weighted Average of Damage Indices vii

10 2.5 Recent Developments in Performance-Based Engineering Performance Levels Excitation Levels Structural Performance Parameters Structural Control in Civil Engineering Structures Introduction Background and Recent Developments in Structural Control General Classification of Control Systems Isolation Systems Elastomeric Bearings Sliding Bearings Passive Control Systems Viscous and Viscoelastic Dampers Friction-Slip Dampers Active Control Basic Principles Control Algorithms Role of Structural Control in Performance-Based Engineering Description of Case Studies Objective of Simulations Description of Structures Earthquakes Control Systems Designed and Evaluated Friction Pendulum Isolation System Fluid Viscous Damper Active Tendon System Description of Modeling and Analysis Introduction Structural Modeling Approach Finite Element Model Modeling of P-delta Effects viii

11 5.3 Evaluation Platform and Implementation Beams Hysteresis Modeling P-M Interaction Geometric Nonlinearities: P-Delta Viscous Damper Friction Pendulum Isolation (FPS) Element Active Control Solution Procedure Evaluation of Seismic Demands Introduction Seismic Demands for Uncontrolled System Effect of Controller Architecture Design FPS Isolation System Fluid Viscous-Brace Damper Active Tendon System Comparison of Seismic Demands Across Control Systems Deformation Demands Hysteretic Energy Demands Acceleration Demands Conclusions Effects of Modeling on Seismic Demands Introduction Effect of Nonlinearities on Controlled Structural Performance Story Structure Story Structure Effect of Initial Stiffness on Dynamic Response Effect of Variations in Strain-Hardening Ratio Conclusions Probabilistic Seismic Control Analysis Introduction ix

12 8.2 Background Probabilistic Seismic Hazard Analysis (PSHA) Probabilistic Seismic Demand Analysis (PSDA) Probabilistic Seismic Control Analysis (PSCA) Spectral Acceleration Hazard Relationship between Ground Motion and Demand Parameters Estimate of Peak Story Drift Estimate of Control System Demand Number of Analyses Drift Demand Hazard Curves Effect of Control Parameter Variation Comparison Between Control Systems Conclusions Summary, Conclusions, and Future Work Summary Results Seismic Demands Modeling Effects Probabilistic Seismic Control Analysis Conclusions Future Work Appendix A: Response Statistics 187 Bibliography 189 x

13 List of Tables 2.1 General Structural Performance Level Definitions and Indicative Drifts for Steel Moment Frames (FEMA 273) Probabilistic Hazard Levels and Corresponding Return Periods (FEMA 273) Frictional Properties of PTFE in Contact with Polished Stainless Steel High Capacity Fluid Viscous Dampers from Taylor Devices, Inc Column Sections for 9-Story Structure - North-South Frame Modal Properties for Frames Statistics on Roof Drift Angle Demands Frictional Properties for Isolator System Peak Bearing Response for 3-Story Structure Isolation Bearing: 2 in 50 Set of Ground Motions Global Demand Parameters for 9-Story Structure with FPS Isolation, 2in50Setof Ground Motions Median Response Properties for Viscous Dampers, 2 in 50 Set of Ground Motions Increases in Story Drift Demands for 3-Story Structure due to Additional Control, 2in50Setof Ground Motions Effect of Modeling on Percent Roof Drift Reduction Parameters for Spectral Acceleration Hazard Curve Fit xi

14 8.2 Parameters for Fit of Relationship Between Spectral Acceleration and Story Drift, 3-Story Structure Parameters for Fit of Relationship Between Spectral Value and Story Drift, 3-Story Structure with FPS Isolation System Parameters for Fit of Relationship Between Spectral Value and Story Drift, 3-Story Structure with FPS Isolation System - Ignoring Simulated Ground Motions Parameters for Fit of Relationship Between Spectral Value and Story Drift for VS System Parameters for Fit of Relationship Between Spectral Value and Story Drift for ATB System Parameters for Fit of Relationship Between Spectral Value and Peak Damper Force Parameters for Fit of Relationship Between Spectral Value and Peak Bearing Displacement, 3-Story Structure with FPS Isolation System Parameters for Fit of Relationship Between Spectral Value and Peak Bearing Displacement, 3-Story Structure with FPS Isolation System - No Simulated Records Parameters for Fit of Relationship Between Spectral Velocity and Story Drift, Variation in Isolation Period of FPS Isolation System Parameters for Fit of Relationship Between Spectral Value and Story Drift, VS Damping Systems Parameters for Fit of Relationship Between Spectral Value and Bearing Displacements, Variation in Isolation Period of FPS Isolation System Parameters Drift Hazard Calculation of Individual Stories, 3-Story Structure Parameters Drift Hazard Calculation of Individual Stories, 9-Story Structure xii

15 List of Figures 3.1 Free-body Diagram for FPS Isolation System Basic Elements of a Closed-Loop Active Control Design Process for Controlled Structural Systems Story Structure: North-South Moment-Resisting Frame Story Structure: North-South Moment-Resisting Frame Mean Elastic Spectral Acceleration for Ground Motion Sets Dispersion of the Elastic Spectral Acceleration for Ground Motion Sets Story Structure with VS dampers Lumped Plasticity Modelfor Beam-Column Element Bilinear diagram for P-M Interaction P- Forces Associated with a Gravity Column Schematic Diagram for Viscoelastic Damper Flowchart of StructODE function Comparison of Third Story Drift Response under la15 Ground Motion with DRAIN-2DX Global Pushover Curves for LA 3- and 9-Story Structures Median Values for Peak Story Drift Angle for 3-Story Structure, All Sets of Ground Motions Median Values for Peak Story Drift Angle for 9-Story Structure, All Sets of Ground Motions Dispersion of Peak Story Drift Angle for 3-Story Structure, All Sets of Ground Motions xiii

16 6.5 Dispersion of Peak Story Drift Angle for 9-Story Structure, All Sets of Ground Motions Median Values for Peak Roof Drift Angle as Function of Isolation Period, 3-Story Structure, 10 in 50 and 2 in 50 Set of Ground Motions Peak Bearing Displacements for 3-Story Frame with FPS Isolation, 2 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 3-Story Frame with FPS Isolation, 10 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 3-Story Frame with FPS Isolation, 2 in 50 Set of Ground Motions th Percentile Values for Peak Story Drift Demands for 3-Story Frame with FPS Isolation, 2 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 9-Story Frame with FPS Isolation, 2 in 50 Set of Ground Motions Median Values for Peak Roof Drift Angle for 3-Story Frame as Function of Percent of Critical Damping, 10 in 50 and 2 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 3-Story Frame with Viscous-Brace Dampers D1, 10 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 3-Story Frame with Viscous-Brace Dampers D1, 2 in 50 Set of Ground Motions Dispersion of Peak Story Drift Angle for 3-Story Structure with Varying Added Effective Damping Periods Beam-Column Subassembly for an Interior Column Median Values for Peak Roof Drift Demands for 3-Story Frame with Viscous-Brace Dampers in Different Distributions Effect of Damping Distribution on Median Values for Peak Story Drift Demands for 3-Story Frame, 2 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for 9-Story Frame with Viscous-Brace Dampers D1, 2 in 50 Set of Ground Motions Effect of Damping Distribution on Median Values for Peak Story Drift Demands for 9-Story Frame, 2 in 50 Set of Ground Motions xiv

17 6.21 Median Values for Peak Story Drift Demands for 3-Story Frame with ATB Control, 10 in 50 Set Median Values for Peak Story Drift Demands for 3-Story Frame - ATB Control with Varying Saturation, 2 in 50 Set th Percentile Values for Peak Story Drift Demands for 3-Story Frame -ATB Control with Varying Saturation, 2 in 50 Set Median Values for Peak Story Drift Demands for 3-Story Frame with ATB Control, Variation in Design, 2 in 50 Set Dispersion of Peak Story Drift Angle for 3-Story Structure with ATB Systems of Different Controlled Outputs Median Values for Peak Story Drift Demands for 9-Story Frame with ATB Control, 10 in 50 and 2 in 50 Set of Ground Motions Maximum Values for Peak Story Drift Demands for 3-Story Frame, 50 in 50 Set of Ground Motions Maximum Peak Story Drift Demands for 3-Story Frame, 10 in 50 Set of Ground Motions Maximum Peak Story Drift Demands for 3-Story Frame, 2 in 50 Set of Ground Motions Maximum Residual Story Drift Demands for 3-Story Frame, 50 in 50 Set of Ground Motions Maximum Residual Story Drift Demands for 3-Story Frame, 10 in 50 Set of Ground Motions Maximum Residual Story Drift Demands for 3-Story Frame, 2 in 50 Set of Ground Motions Median Peak Story Drift Demands for 3-Story Frame, 50 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 3-Story Frame, 50 in 50 Set of Earthquakes Median Peak Story Drift Demands for 3-Story Frame, 10 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 3-Story Frame, 10 in 50 Set of Earthquakes xv

18 6.37 Median Peak Story Drift Demands for 3-Story Frame, 2 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 3-Story Frame, 2in50Setof Earthquakes Median Peak Story Drift Demands for 9-Story Frame, 10 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 9-Story Frame, 10 in 50 Set of Earthquakes Median Peak Story Drift Demands for 9-Story Frame, 10 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 9-Story Frame, 10 in 50 Set of Earthquakes th Percentile Values for Peak Story Drift Demands for 9-Story Frame, 2in50Setof Earthquakes th Percentile Values for Peak Story Drift Demands for 9-Story Frame, 2in50Setof Earthquakes Comparison of Maximum Peak Story Drift Demands for VS and ATB Control for 9-Story Structure Median Values of Normalized Hysteretic Energy for 3-Story Frame, 50 in 50 Set of Ground Motions Median Values of Normalized Hysteretic Energy for 3-Story Frame, 10 in 50 Set of Ground Motions Median Values of Normalized Hysteretic Energy for 3-Story Frame, 2 in 50 Set of Ground Motions Median Values of Normalized Hysteretic Energy for 9-Story Frame, 10 in 50 Set of Ground Motions Median Values of Normalized Hysteretic Energy for 9-Story Frame, 2 in 50 Set of Ground Motions Median Values of Floor Accelerations for 3-Story Frame, 50 in 50 Set of Ground Motions Median Values of Floor Accelerations for 3-Story Frame, 10 in 50 Set of Ground Motions xvi

19 6.53 Median Values of Floor Accelerations for 3-Story Frame, 2 in 50 Set of Ground Motions Median Values of Floor Accelerations for 9-Story Frame, 10 in 50 Set of Ground Motions Median Values of Floor Accelerations for 9-Story Frame, 2 in 50 Set of Ground Motions Effect of Modeling on Median Values for Peak Story Drift Demands, 2 in 50 Set of Ground Motions Maximum Roof Drift Demands for 3-Story Frame L Model, 2 in 50 Set of Ground Motions Maximum Roof Drift Demands for 3-Story Frame NL2 Model, 2 in 50 Set of Ground Motions Maximum Roof Drift Demands for 3-Story Frame NL3 Model, 2 in 50 Set of Ground Motions Median Values for Peak Story Drift Demands for L Evaluation Models - 3-Story, 2in50Set Median Values for Peak Story Drift Demands for NL3 Evaluation Models - 3-Story, 2in 50 Set Effect of Modeling on Median Values for Peak Story Drift Demands for FPS T3 - f1, 2 in 50 Set Effect of Modeling on Median Values for Peak Story Drift Demands for VS -30,D1,2in50Set Effect of Modeling on Median Values for Peak Story Drift Demands for ATB - S1k, 2in50 Set Effect of Modeling on Median Values for Peak Story Drift Demands for 9-Story Structure, 2in50Set Effect of Modeling on Median Values for Peak Story Drift Demands for 9-Story Structure with FPS T4 - f1, 2 in 50 Set Effect of Modeling on Median Values for Peak Story Drift Demands for 9-Story Structure with VS - 30, D1, 2in50 Set Effect of Modeling on Median Values for Peak Story Drift Demands for 9-Story Structure with ATB, 2in50Set xvii

20 7.14 Median Values for Peak Story Drift Demands for Linear Evaluation Models of LA 9-Story Structure, 2in50Set Median Values for Peak Story Drift Demands for Linear Evaluation Models of LA 9-Story Structure, 2in50Set Median Values for Peak Story Drift Demands for Uncontrolled System, Varying Fundamental Period, 2 in 50 Set Median Values for Peak Story Drift Demands for FPS Isolation System T3, Varying Fundamental Period, 2in50 Set Median Values for Peak Story Drift Demands for VS 30 System, Varying Fundamental Period,2in50Set Median Values for Peak Story Drift Demands for ATB - S1k, Varying Fundamental Period, 2 in 50 Set Median Values for Peak Story Drift Demands for Half the Original Fundamental Period, 2 in 50 Set Median Values for Peak Story Drift Demands for Twice the Original Fundamental Period, 2 in 50 Set Median Values for Peak Story Drift Demands for Uncontrolled System, Variation Strain-Hardening Ratio, 2 in 50 Set Median Values for Peak Story Drift Demands for FPS T3 System T3, Variation Strain-Hardening Ratio, 2 in 50 Set Median Values for Peak Story Drift Demands for VS 30 System, Variation Strain-Hardening Ratio, 2 in 50 Set Median Values for Peak Story Drift Demands for ATB System, Variation Strain-Hardening Ratio, 2 in 50 Set Annual Hazard Curve for Spectral Acceleration, LA 3-Story Structure Annual Hazard Curve for Spectral Acceleration, LA 9-Story Structure Relationship between Spectral Acceleration and Maximum Peak Story Drift for LA 3-Story Structure Relationship between Spectral Acceleration and Maximum Peak Story Drift for LA 3-Story Structure with FPS Isolation Relationship between Spectral Acceleration and Maximum Peak Story Drift for LA 3-Story Structure with Viscous Brace System xviii

21 8.6 Relationship between Spectral Acceleration and Maximum Peak Story Drift for LA 3-Story Structure with ATB System Relationship between Spectral Acceleration and Peak Damper Force for LA 3-Story Structure VS Dampers Relationship between Spectral Acceleration and Peak Bearing Displacement for LA 3-Story Structure FPS Isolation Relationship between Spectral Velocity and Peak Bearing Displacement for LA 3-Story Structure FPS Isolation Standard Error in Peak Drift Estimation due to Limited Sample Size Using Full Data Set, 3-Story Structure Comparison of Drift Demand Hazard Curves of FPS Isolation System for 3-Story Structure, Variation in Isolation Period Comparison of Drift Demand Hazard Curves of VS Damping system for 3-Story Structure, Variation in Effective Damping Comparison of Drift Demand Hazard Curves of VS Damping system for 3-Story Structure, Variation in Damping Distribution Comparison of Bearing Displacement Demand Hazard Curves for 3- Story Structure, Variation in Isolation Period Comparison of Bearing Displacement Demand Hazard Curves for 3- Story Structure, Variation in Isolation Period Comparison of Drift Demand Hazard Curves for LA 3-Story Structure Comparison of Drift Demand Hazard Curves for LA 9-Story Structure Comparison of Individual Story Drift Demand Hazard Curves for LA 3-Story Structure Comparison of Individual Story Drift Demand Hazard Curves for LA 3-Story Structure with FPS Isolation Comparison of Individual Story Drift Demand Hazard Curves for LA 3-Story Structure with VS Damping Comparison of Individual Story Drift Demand Hazard Curves for LA 3-Story Structure with ATB System Comparison of Individual Story Drift Demand Hazard Curves for LA 9-Story Structure xix

22 8.23 Comparison of Individual Story Drift Demand Hazard Curves for LA 9-Story Structure with FPS Isolation Comparison of Individual Story Drift Demand Hazard Curves for LA 9-Story Structure with VS Damping Comparison of Individual Story Drift Demand Hazard Curves for LA 9-Story Structure with ATB System xx

23 Notation The following notation is used in this dissertation unless otherwise noted: ff ff d a A B rx c C C strain hardening ratio; orifice coefficient for fluid damper; coeff. controlling dependency of friction on velocity; cross-sectional area; mapping matrix between nodal and relative displacements; equivalent viscous damping coefficient; numerical coefficient related to soil type and period; viscous damping matrix; t time step; d nodal displacement vector; E E d f max f min E s F y F d F s modulus of elasticity; work done by damping; coeff. of friction at high velocity; coeff. of friction at low velocity; elastic-plastic work; yield strength; damping force vector; static resisting force vector; ( ) gamma function; g G h I gravitational constant; shear modulus of elasticity; height; moment of inertia; xxi

24 J J k E k H K 00 d K ISO K L( ) flg L μ S M R S a S v S d ο Jacobian matrix; cost functional; element elastic stiffness; element hysteretic stiffness; loss stiffness for a viscous damper; stiffness of isolation bearing; stiffness matrix; Lagrangian; mapping vector to horizontal degrees of freedom; length; sliding coefficient of friction; mass matrix; radius of curvarure for spherical sliding surface; spectral acceleration; spectral velocity; spectral displacement; equivalent viscous damping ratio; rotational displacement; T u v ffi V W x _x ẍ ψ fundamental period; horizontal displacement; vertical displacement; interstory drift ratio; base shear; seismically effective weight; displacement; velocity; acceleration; shape function;! circular natural frequency; xxii

25 Chapter 1 Introduction 1.1 Motivation In recent years, research in the development of control systems has made significant progress in the reduction of the overall response of civil structures subjected to seismic excitations. However, much of this research has utilized highly simplified linear models of structural systems. To address the broader role of control technology in improving the overall performance of structures, the control analyses presented here consider more sophisticated structural models and include information about the nonlinear response of individual members. In general, control studies in civil engineering can be divided into two categories: those which address serviceability issues and those whose main concern is safety. When serviceability is the main concern, control is used to reduce structural acceleration in order to increase occupant comfort during relatively mild wind or seismic excitations. However, for those controllers developed for stronger excitations, where occupant safety is the main concern, the goal is to improve structural response by reducing peak interstory drift or by increasing energy dissipation. The majority of these studies have dealt mainly with linear systems and analyses. Improvement of structural performance under moderate to severe excitations requires a reduction of damage under dynamic loading, and damage is an inherently nonlinear process. Peak responses alone do not describe the possible damage incurred by the structure as cumulative damage results from several incursions into the inelastic range. As such, the reduction of peak interstory drifts alone is not sufficient unless 1

26 Introduction Chapter 1 we also have information about the capacity of the structure. One cannot assume a structure will remain linear even under moderate seismic loads. The structural engineering community has been making great strides in recent years to develop performance-based earthquake engineering methodologies for both new and existing construction. Both SEAOC's Vision 2000 project (SEAOC 1995) and BSSC's NEHRP Guidelines for Seismic Rehabilitation of Buildings (BSSC 1997) present the first guidelines for multi-level performance objectives. One of the intents of these provisions is to provide methods for designing and evaluating structures such that they are capable of providing predictable performance during an earthquake. For structural control to gain viability in the earthquake engineering community, understanding the role of controllers within the context of performance-based engineering is of primary importance. Design of a structure/controller system should involve a thorough understanding of how various types of controllers enhance structural performance, such that the most effective type of controller is selected for the given structure and seismic hazard. Controllers may be passive, requiring no external energy source, or active, requiring an external power source. Applications of certain passive systems, including base isolation and viscous dampers, have become more common, leading to a reasonable understanding of how such systems reduce the dynamic behavior of structures. However, few full-scale applications of active controllers exist and their enhancement of structural performance, particularly for larger events, is less understood. Furthermore, neither passive or active systems have been investigated with the objective ofquantifying and comparing their ability to improve structural performance under the parameters established by the recently developed performance-based design criteria. 1.2 Objective and Scope The objective of the research presented here is to evaluate the role of structural control technology in enhancing the overall structural performance under seismic excitations. This study focuses on steel moment-resisting frames, and three types of possible controllers: (1) base isolation system (passive); (2) viscous brace dampers (passive); (3) and active tendon braces. Two structures are selected from the SAC Phase II project, the three story system and the nine story system. The lateral force 2

27 Chapter 1 Introduction resisting system for both buildings is composed of perimeter steel moment-resisting frames. These buildings are represented as two-dimensional nonlinear finite element models using centerline dimensions. Simulations of these systems, both controlled and uncontrolled, are prepared using the three suites of earthquake records, also from the SAC Phase II project, representing three return different periods. Several controllers are developed for each structure, and the resulting system performance is judged based on drift, floor accelerations, and dissipated hysteretic energy demands. This investigation has the following specific objectives: (1) To evaluate the effect of the various controller architectures on seismic demands as described through performance-based design criteria; (2) To evaluate the sensitivity of the structurecontroller performance to variation of control parameters, load intensities, and structural modeling techniques; and (3) To compare the benefits of the controllers in both a deterministic and probabilistic format. 1.3 Overview In Chapter 2 an overview of building damage and the available indices used for damage assessment is presented. A discussion of the current performance-based guidelines and their application to steel moment-resisting frames is included. The basic ideas and concepts of structural control as applied to civil engineering structures are discussed in Chapter 3. Previous work in the area is presented and reviewed. Current provisions for the use of supplemental control systems are discussed. A description of how structural control methods fit within the goals of performance engineering is then presented. Chapter 4 provides a description of the two structures that are analyzed and the ground motions utilized for seismic demand calculations. Three different types of control systems were then selected for implementation with these structures. The reasoning behind the selection of these systems and the basic design philosophy of each one is discussed. The modeling of the structure and control systems is given in Chapter 5. Time history analysis of these systems is performed using software written expressly for this purpose. The representation of the element behavior in the analysis software is discussed, including the modeling assumptions of element behavior. The analysis 3

28 Introduction Chapter 1 software was verified by benchmarking the results against those from DRAIN-2DX. Example results from this verification process are given at the end of the chapter. Global roof drift and story parameters for the different systems investigated in this study are presented in Chapter 6. The emphasis of the discussions are on roof and story drift demands. The effect of variation in selected control design parameters are presented. A representative system is chosen for each type of control system for comparison on the basis of peak and residual drifts, dissipated hysteretic energy, and peak floor accelerations. Chapter 7 provides an analysis of the sensitivity of initial period and strainhardening ratio. The effect of performing different types of analysis, for example linear vs. nonlinear, are investigated for both structural systems. The performance of the systems are developed in a probabilistic format in Chapter 8. A procedure developed by Cornell (1996) is used in this process. The curves generated from this procedure are used to assess the impact of different control parameters and to perform a comparison between control systems for a given structure. A summary of the research and its conclusions are presented in Chapter 8. Possible directions of future research are then discussed. 4

29 Chapter 2 Performance Evaluation of Structures 2.1 Introduction The structural engineering profession suffered significant setbacks after the 1994 Northridge Earthquake in Los Angeles and the 1995 Great Hanshin Earthquake in Kobe, Japan. Until that time, the general seismic design philosophy was to safeguard against the collapse of structures and loss of lives. In these recent earthquakes, however, damage to structures and their contents lead to losses of billions of dollars. So in addition to ensuring against collapse, structural engineers are being required to design structures that are designed to minimize the damage based on the function of the building and within the constraints of available resources. The basic performance requirement of life-safety needs to be met for all structures. However, depending on its function, the structure should conform to a variety of performance requirements. For example, critical facilities such as hospitals, which need to remain operational after a severe earthquake, should be designed for very different criteria than a warehouse. New guidelines for building structures have been set forth by different organizations to fulfill these requirements. Two such set of guidelines are the Vision 2000 project by the Structural Engineers Association of California (SEAOC 1995) and NEHRP Guidelines for Seismic Rehabilitation of Buildings (BSSC 1997) issued by the Federal Emergency Management Agency (FEMA). These guidelines are the first to 5

30 Performance Evaluation of Structures Chapter 2 introduce a framework for performance-based design. In this framework, the seismic demand of a structure needs to be calculated as accurately as possible and compared with the allowable limits for the desired performance level. The definition of limits are based on expected damage states for a given demand level. This chapter presents an overview of building damage and the available indices used for damage assessment. A discussion of the current performance-based guidelines and their application to steel moment-resisting frames is presented in the last section. 2.2 Damage to Nonstructural Elements The nonstructural system in a building is comprised of architectural components (cladding, ceilings, partitions, windows, etc.), mechanical systems (ducts, HVAC, elevators, etc.), electrical systems (security, communications, etc.), and contents (furniture, computer equipment, etc.). Traditionally, building codes have emphasized life safety as their primary goal. So, while structural integrity has been of primary concern, little regard has been paid to nonstructural components. For example, a survey conducted after the Loma Prieta Earthquake of 129 medium and large office buildings showed that only 9% of the buildings had structural damage, while 86% of them had nonstructural damage, with a mean monetary value of $941,000/building (LOMA 1990). Three types of risk are associated with seismic damage to nonstructural components (FEMA 74): 1. Life Safety: Damaged or falling components can injure or kill building occupants. Potentially life threatening hazards from past earthquakes include: broken glass, overturned bookcases, and fallen ceiling panels and light fixtures. 2. Property Loss: For most commercial buildings, only 20-25% of the original construction cost can be attributed to the foundation and superstructure. The remaining cost is due to the mechanical, electrical, and architectural components. Building contents introduced by the occupants are also at risk and can often correspond to significant additional expense. 3. Loss of Function: Damage incurred during an earthquake may also make it difficult to carry out the normal activities performed at the location. This loss 6

31 Chapter 2 Performance Evaluation of Structures of function can have significant monetary consequences for businesses; however, in critical facilities such as hospitals, a loss of function can also represent a life safety risk. Each of the nonstructural systems described above are governed by different factors. One possible classification, based on the governing mode of damage, for nonstructural components is: ffl Acceleration-sensitive components: Components are sensitive to the inertial forces experienced during an earthquake. Examples include file cabinets, free standing bookshelves, and office equipment. ffl Deformation-sensitive components: Components are sensitive to building distortion or separation joints between structures. Examples include glass panes, partitions, and masonry infill or veneer. 2.3 Damage to Structural Elements Damage of materials occurs through a progressive process in which theybreak. This can be considered in three levels: the microscale level, the mesoscale level, and the macroscale level. At the microscale level, damage is incurred by the accumulation of microstresses at defects or interfaces and by bond breaking. At the mesoscale level, damage is observed as the initiation and growth of cracks. At the macroscale level, damageisrelatedto the deterioration of parts of the entire structure. In analyzing a structure, performing a damage evaluation in detail at every point of the structure is impossible or not of primary interest (Williams and Sexmith 1995). Several methods to determine an indicator of damage at the structure level have been presented in literature. Generally, these methods can be divided into four categories of structural demand parameters: 1. Strength demands, both elastic and inelastic 2. Ductility demands 3. Energy dissipation 4. Stiffness degradation 7

32 Performance Evaluation of Structures Chapter 2 Strength Demands If strength demands remain below the yield capacity of the structure, the structural damage will be small. However, if demands approach or exceed the ultimate strength of the structure, the damage to structure may also be high. Once yield is exceeded, strength capacity may become reduced in future cycles into the inelastic range. Ductility Demands Ductility is the ability of an element to deform inelastically without total fracture. It is usually expressed in terms of a ratio between the maximum deformation incurred during loading and the yield deformation. Any deformation quantity may be used to determine the ductility demand. Energy Dissipation Energy dissipation is the capacity of member to dissipate energy through hysteretic behavior. An element has a limited capacity to dissipate energy in this manner prior to failure. As a result, the amount of energy dissipated serves as an indicator of how much damage has occurred to structural members during loading. Stiffness Degradation Damage suffered during loading may result in a loss of stiffness and, consequently, longer natural periods for the structure. As the determination of the fundamental period is easily accomplished, this parameter can also be used as a damage indicator. 2.4 Damage Indices The major task in damage assessment is finding clear quantitative measures to represent the amount of damage a structure has suffered. During the past years, a considerable amount of research has been performed on the development of such methods. Desirable characteristics of these procedures include: 1. General applicability - valid for a variety of structural systems under different load histories. 8

33 Chapter 2 Performance Evaluation of Structures 2. Simple to evaluate - indices are easily formulated and evaluated. 3. Physically interpretable - resulting value has a physical meaning. In general, structural damage has been defined in terms of either economics or safety/strength considerations. Economic damage indices are usually expressed as some ratio of repair costs to replacement costs for a structure or structural element. Though specific knowledge of this information is desired, an accurate determination of repair costs can be difficult to determine and is usually taken to be related to a physical response parameter. Safety/strength damage indices are normally related to deterioration of structural resistance. The following sub-sections describe damage indices based on safety/strength approach Maximum Deformation Damage Indices Maximum deformation damage indices are based on the peak value of a specified deformation, such as element rotation or member displacement. Two of the earliest and simplest forms of a damage index are the ductility and interstory drift. These two indices as well as the flexural damage ratio are described below. Ductility Ratios Ductility is defined as ability to deform inelastically without total fracture and substantial loss of strength. In literature, it is commonly expressed as a ductility ratio, μ R, as defined below: μ R = u m u y (2.1) where u m is the maximum deformation experienced and u y is the yield deformation. The maximum deformation is determined from the load-deformation history of the structure under a given load. The deformation quantity can be any one desired: displacement, rotation, etc. At the structural level either displacements or drifts are usually used. A problem with the ductility ratio is that it cannot account for both duration and frequency content of the typical ground motion (Banon and Veneziano 1982). Also, determination of yielding can be difficult, especially at the structural level. 9

34 Performance Evaluation of Structures Chapter 2 Interstory Drift Interstory drift is defined as the relative interstory displacement of a story. Culver (1975) proposed a damage index defined as the observed maximum story displacement to the story displacement at failure. A problem with this index is that determination of drift at failure is difficult. Toussi and Yao (1983) proposed a damage index defined as the ratio between the maximum interstory displacement, i, and the story height, h, as given below, and provided guidelines for interpretation of results. This drift ratio, ffi i, has been widely used in a variety of structural systems as an indicator of the deformation demands on a structure. ffi i = i h (2.2) As with ductility ratios, peak interstory drift measures cannot take into account the effects of repeated cycling, which can be a significant source of damage to structural members. Flexural Damage Ratio To counteract the limitations of the above measures, a number of parameters related to stiffness degradation were proposed. Banon (1981) correlated damage to the ratio of the initial structural stiffness to the secant stiffness at the maximum displacement forming the Flexural Damage Ratio, (FDR). This index relies on stiffness degradation as an indicator of damage. Roufaiel and Mayer (1983) later suggested a modification of the flexural damage ratio so that it was defined as the ratio of the secant stiffness at the onset of failure in a one-cycle test to the minimum reduced secant stiffness. A ratio of zero corresponds to no damage, while a ratio of 1 corresponds to failure. However, the authors admitted that this index would be difficult to calculate for an actual structure Cumulative Damage Indices Capturing the accumulation of damage sustained during dynamic loading is of particular interest to structural engineers. This process is usually accomplished through 10