Real-time Hybrid Simulation: Validation of PBD Procedure for Steel Frames with Nonlinear Viscous Dampers

Transcription

1 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska Real-time Hybrid Simulation: Validation of PBD Procedure for Steel Frames with Nonlinear Viscous Dampers Baiping Dong 1, Richard Sause 2, James M. Ricles 3 ABSTRACT This paper presents the experimental validation of a performance-based design (PBD) procedure for seismic design of steel frames with nonlinear viscous dampers using real-time hybrid simulation (RTHS). The prototype structure in the study is designed for the code-based (ASCE7-1) design base shear, with supplemental nonlinear viscous dampers to control drift and thereby control damage to the building under various earthquake intensity levels. The PBD procedure with specified performance objectives is used to perform an integrated design of a steel moment resisting frame (MRF) and a braced frame with dampers (). Large-scale realtime hybrid simulations (RTHS) were conducted at the NEES Real-time Multi-directional (RTMD) Earthquake Simulation Facility at Lehigh University. In the RTHS, the experimental substructure is a large-scale 3-story, and the analytical substructure is comprised of the remaining parts of building, including a steel MRF, gravity load frames, seismic mass, and the inherent damping of the building. RTHS of the design basis earthquake (DBE) and the maximum considered earthquake (MCE) were successfully conducted. Results from the RTHS are evaluated and compared with expectations from the PBD procedure. The experimental results show that the structure with nonlinear viscous dampers achieves the specified performance objectives. The results show that RTHS is a practical technique to experimentally evaluate performance under simulated earthquake loading and to validate performance-based design procedures for structures with rate-dependent damping devices. 1 Graduate Student Researcher, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA Joseph T. Stuart Professor, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA Bruce G. Johnston Professor, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA 1815 Baiping Dong, Richard Sause, James M. Ricles. Real-time Hybrid Simulation: Validation of PBD Procedure for Steel Frames with Nonlinear Viscous Dampers. Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

2 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska Real-time Hybrid Simulation: Validation of PBD Procedure for Steel Frames with Nonlinear Viscous Dampers Baiping Dong 1, Richard Sause 2, James M. Ricles 3 ABSTRACT This paper presents the experimental validation of a performance-based design (PBD) procedure for seismic design of steel frames with nonlinear viscous dampers using real-time hybrid simulation (RTHS). The prototype structure in the study is designed for the code-based (ASCE7-1) design base shear, with supplemental nonlinear viscous dampers to control drift and thereby control damage to the building under various earthquake intensity levels. The PBD procedure with specified performance objectives is used to perform an integrated design of a steel moment resisting frame (MRF) and a brace framed with dampers (). Large-scale real-time hybrid simulations (RTHS) were conducted at the NEES Real-time Multi-directional (RTMD) Earthquake Simulation Facility at Lehigh University. In the RTHS, the experimental substructure is a large-scale 3-story, and the analytical substructure is comprised of the remaining parts of building, including a steel MRF, gravity load frames, seismic mass, and the inherent damping of the building. RTHS of the design basis earthquake (DBE) and the maximum considered earthquake (MCE) were successfully conducted. Results from the RTHS are evaluated and compared with expectations from the PBD procedure. The experimental results show that the structure with nonlinear viscous dampers achieves the specified performance objectives. The results show that RTHS is a practical technique to experimentally evaluate performance under simulated earthquake loading and to validate performance-based design procedures for structures with rate-dependent damping devices. Introduction Nonlinear viscous dampers are rate-dependent passive energy dissipating devices that are used to enhance the seismic performance of building structures. Performance-based design (PBD) procedures for structures with such damping devices need to be experimentally evaluated. Realtime hybrid simulation is an experimental testing method developed in recent decades to investigate the seismic behavior of a complex complete structural system subjected to earthquake ground motions. The complete structural system is divided into experimental (physical) substructures and analytical (numerical) substructures. The experimental substructures are subjected to simulated earthquake effects in the laboratory. The analytical substructures are subjected to numerical simulation of earthquake effects. During a hybrid simulation, the coupling 1 Graduate Student Researcher, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA Joseph T. Stuart Professor, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA Bruce G. Johnston Professor, ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA 1815 Baiping Dong, Richard Sause, James M. Ricles. Real-time Hybrid Simulation: Validation of PBD Procedure for Steel Frames with Nonlinear Viscous Dampers. Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

3 between the experimental and analytical substructures is achieved by maintaining the compatibility and equilibrium at the interfaces between the substructures. The displacement response of the structural system is calculated using an integration algorithm that solves the equations of motion based on restoring forces from the substructures developed under the imposed displacement response. In a real-time hybrid simulation, the displacements are imposed in real time. Real-time hybrid simulation is attractive as it allows the physical substructure, which has more uncertain seismic behavior, to be tested at a larger scale because the remaining of the structure is simulated numerically. Real-time hybrid simulation is also attractive in particular to evaluate the seismic performance of a structure system with rate dependent devices. This paper focuses on real-time hybrid simulation (RTHS) on a large-scale three-story steel structure with nonlinear viscous dampers to validate a performance-based design (PBD) procedure. The prototype structure includes a.6-scale three-story, one-bay moment resisting frame (MRF) and a three-story, one-bay braced frame with one nonlinear viscous damper in each story (). The MRF and the associated gravity load frames were modeled as the analytical substructure while the was tested in the lab as the experimental substructure. RTHS results from ground motions at the design basis earthquake (DBE) level and the maximum considered earthquake (MCE) level are presented and compared to predictions from the PBD. The results show that RTHS is a practical technique to experimentally evaluate the performance of structures with rate-dependent damping devices. Overview of Real-time hybrid simulation Large-scale Real-time Hybrid Simulation Fig. 1 shows the schematic overview of real-time hybrid simulation. During a real-time hybrid simulation, with the ground motion excitation force, F(t), the restoring forces computed from the analytical substructure, r a, and the restoring force feedback from the experimental substructure, r e, the equations of motion are solved at each integration time step to generate the target displacement responses, x t. This target displacement is imposed on the analytical substructure and experimental substructure to obtain r a and r e for the next time step, respectively. x t is input to an adaptive compensator before it is imposed on the experimental substructure. The compensator accounts for dynamic response of the servo-hydraulic controller, actuators, and test fixtures so that the displacement response of the experimental substructure x s closely approximates x t. The compensated target displacement response is called the command displacement, x c. The actuator displacement, x a, and the displacement response of the experimental substructure, x s, are directly measured during the real-time hybrid simulation. Figure 1. Overview of real-time hybrid simulation

4 Integration Algorithm for real-time response integration The unconditionally stable explicit CR integration algorithm developed by Chen and Ricles [1] was utilized to calculate x t. In this algorithm, α 1 and α 2 are integration parameters. Eq.1 shows α 1 and α 2 depend on the mass, M, initial damping, C, and initial stiffness, K, of the structure. = =4 (4 +2 +( ) ) (1) Since the structure is divided into an experimental substructure and an analytical substructure, the stiffness matrix K is the sum of K a and K e representing the initial stiffness matrix of the analytical and experimental substructures, respectively. The damping matrix C is the sum of C a and C e representing of the initial damping matrix of the analytical and experimental substructures, respectively. In this study, K a is the stiffness matrix of the MRF and the associated gravity load frames, and K e is the initial static stiffness matrix of the identified from initial static tests; C a is calculated assuming 2% Rayleigh damping in the analytical substructure, and C e is constructed by combining equivalent damping coefficients for the nonlinear viscous dampers in the. The equivalent damping coefficients used for the nonlinear viscous dampers were identified from characterization tests of an individual damper. Hydraulic-actuator dynamics compensation The adaptive time series (ATS) compensator developed by Chae et. al. [2] is utilized for the adaptive compensator. The ATS calculates x c from the state of the structure at each time step based on a 2 nd -order relationship between the input and output displacement, shown in Eq. 2. = + + (2) where,, and are the target displacement, velocity, and acceleration at time =, respectively, where is the time step index and is the time step. Typically =1/124 second.,, and are the ATS compensator coefficients at time, which are updated during the real-time hybrid simulation. Prototype Structure, Hybrid Simulation Model, and Experimental Setup Prototype structure Fig. 2 shows the prototype structure which is a three-story office building assumed to be located on a stiff soil site in Southern California. The plan view of the building, shown in Fig. 2, is symmetric. The structural system of the building consists of a lateral force resisting system, passive damping system, and gravity load system. The lateral force resisting system includes eight identical perimeter moment-resisting frames (MRF); the damping system includes eight braced frames with nonlinear viscous dampers (); and the gravity frames are uniformly distributed in the plan to support the gravity load. Fig. 2 illustrates the elevation view of the building in the North-South direction. It shows that the dampers are placed between chevron braces and floor beams. The horizontal movement of the building is restrained at the ground level and the columns of MRF and are fixed at the bottom in the basement.

5 Seismic tributary area South North MRF Gravity frame North East MRF MRF 12.5ft 12.5ft Figure 2. Prototype structure: plan view; elevation view Performance-based design of prototype structure The prototype structure was designed according to IBC 29 [3] and building seismic provisions from ASCE 7-1 [4]. The design of the prototype structure focuses on the design of the one-bay perimeter MRF and the one-bay. The MRF is designed to satisfy the strength criterion of IBC 29 and ASCE 7-1. The MRF does not satisfy the drift criterion and the story drift is controlled by adding the with supplemental dampers. The is designed to carry the expected maximum damper force and remain elastic under the DBE. Elastic analysis was performed using SAP2 [5] to determine the frame member sizes. The beams and columns were designed based on criteria from the AISC Load and Resistance Factor Design (LRFD) Provisions [6] and the AISC Seismic Provisions [7]. Wide flange sections with A992 material were selected for the beams and columns. A simplified performance-based design (PBD) [8] procedure was employed for the performance-based design of the MRF and with nonlinear viscous dampers. The PBD is based on a linearization of the brace and damper in series as an equivalent elastic-viscous model by equating the energy dissipation per cycle of the damper to the energy dissipation per cycle of the equivalent elastic-viscous model. The PBD enables the design demand to be determined without nonlinear time history analysis by linearizing the structure and utilizing the response spectrum analysis method. In this study, a design objective of.85% and 1.5% maximum story drift was established in the PBD for the prototype structure subjected to the DBE and MCE, respectively. Nonlinear viscous dampers from Taylor Device, Inc. were used in the structure, with one damper in each story. The dampers have a nominal capacity of 6 kn, with a damping coefficient C α =648 kn-s/m and damping exponent α=.4. Fig. 3 shows the damper forcedeformation loops at different frequencies from characterization tests with sinusoidal displacement input. The loops in Fig. 3 and Fig. 3 have a deformation amplitude of 25mm and 5mm, respectively. The final design of the prototype structure is presented in Table 1. Table 1. Prototype structure design Story level MRF Column Beam Column Beam Brace Viscous Damper 1st story W8x67 W18x4 W8x67 W12x4 HSS8x6x3/8 6kN/±125mm 2nd story W8x67 W14x38 W8x67 W12x4 HSS8x6x3/8 6kN/±125mm 3rd story W8x67 W1x17 W8x67 W12x4 HSS8x6x3/8 6kN/±125mm

6 Damper force (kn) f=4. Hz f=3. Hz f=1. Hz f=2. Hz f=.5 Hz Damper deformation (mm) Damper force (kn) f=.5 Hz f=1.5 Hz f=1. Hz f=2. Hz Damper deformation (mm) Figure 3. Damper force-deformation hysteresis loops from characterization tests: deformation=25mm; deformation=5mm Hybrid simulation model Owing to the symmetry of the prototype building, the hybrid simulation model includes only a single one-bay MRF and a single one-bay, as well as the gravity load frames and seismic mass that are tributary to one MRF and one, to investigate the seismic behavior in one direction. The MRF and the gravity frames were selected as the analytical substructure (Fig. 4) and the was selected as the experimental substructure (Fig. 4). The gravity forces and seismic mass are represented by a lean-on column with gravity loads and lumped seismic mass at each floor level (Fig. 4). The analytical substructure was modeled using a nonlinear finite element program developed by Karavasilis et al. [9]. The analytical model has a total of 296 degrees of freedom and 91 elements. Nonlinear beam-column fiber element and a panel zone element were utilized to model the members and panel zones of the MRF, respectively. The lean-on column was modeled with an elastic beam-column element with seismic mass lumped and gravity loads applied at each floor. Thus the P-delta effects on the gravity load resisting system and associated gravity loads were included in the analytical substructure. Raleigh damping with 2% damping in the first and second modes was used to model the inherent damping of the building. The experimental substructure is the with one nonlinear viscous damper placed between the braces and floor beam in each story, as shown in Fig. 4. Experimental setup Fig. 5 shows a photograph of the test setup for the experimental substructure. The was pinned to the test fixture at the base. The horizontal movement of in the north-south direction at the ground floor level was restrained by ground links. The reaction forces at the ground level were measured by load cells in the link. An external bracing frame provides out of plane (east-west direction) bracing for the while allowing in plane movement. The setup has three dynamic servo-hydraulic actuators to impose displacements on the at each floor. 23 kn, 17kN, and 17 kn capacity actuators are used for the first floor, second floor, and third floor, respectively. The actuators were fixed to the reaction wall at the north end and were attached to the through a set of loading beams at the south end. The

7 loading beams were attached to top flange of floor beams at the mid-span. The loading beams of each floor level consist of a pair of HSS 12x12x3/8 tubes. The loading beams were supported on shelves that were welded to columns, which were also used to laterally brace the columns as shown in Fig. 5. A MTS temposonic transducer with a range of ±38mm was mounted to the top flange of floor beam at each floor to measure the floor displacement. A load cell was installed in the damper-brace connection to measure the damper force. A Model-6 DAQ by Pacific Instruments was used for data acquisition. The DAQ Mainframe hosts a SCRAMNet card that broadcasts real time data over a fiber optic network for integrated simulation [1]. m 3 P 3 P 2 Rigid diaphragm Panel-zone element Typical Nonlinear viscous damper m 2 m 1 P 1 Lean-on column MRF Fiber element Ground level Diagonal Brace Ground link Figure 4. Model for RTHS analytical substructure; experimental substructure External bracing frame Actuator Ground link Loading tube South North Actuator Figure 5. Test setup for experimental substructure: photograph, schematic of loading tube detail. Real-time hybrid simulation results An ensemble of 7 ground motions was selected from the PEER NGA ground motion database [11] for the real-time hybrid simulations (RTHS). The ground motions were scaled to the DBE and MCE levels using a procedure described by Dong [8]. Table 2 summarizes the ground motions. Fig. 6 and Fig. 6 compare the median spectrum of the scaled ground motions with the hazard spectrum at the DBE and the MCE level, respectively.

8 The floor displacement time histories from the DBE-5 and MCE-6 real-time hybrid simulations are shown in Fig. 7 and Fig. 8, respectively, which have the same ground motion excitation. The maximum displacement in DBE-5 is 14.8mm, 3.4mm, and 41.8mm for first, second, and third floor, respectively. The structure remained elastic without residual displacement. The synchronization plot of the displacements, where the target displacements x t is plotted against the measured displacements x s, is shown in Fig. 7. The straight line relationship shown without hysteresis for each floor indicates the target displacement history was imposed accurately on the experimental substructure during the DBE real-time hybrid simulation. For MCE-6, the maximum displacement is 25.2mm, 53.2mm, and 73.mm with a maximum residual drift of 2.6mm, 6.mm, and 8.4mm for first, second, and third floor, respectively. The MRF yielded in this simulation. The straight line relationship between x t and x s of each floor shown in Fig. 8 indicates the imposed displacements were accurate (consistent with x t ) during the MCE real-time hybrid simulation. Table 5 and Table 6 summarizes the maximum story drift and maximum residual story drift for each ground motion, and the median and coefficient of variation (COV) of the maximum story drifts and residual story drifts from the real-time hybrid simulations at the DBE level and MCE level, respectively. For the DBE level simulations, the structure generally remains elastic with a median maximum story drift of.71%,.78%, and.54% for the first, second, and third story, respectively. The small COV value in the range of.6 to.11 shows little dispersion in structural response among the ground motions. The residual story drift is negligible in the DBE simulations. For the MCE level simulations, the median maximum story drift is 1.18%, 1.37%, and.99%, with the maximum residual story drift of.8%,.12%, and.9% for the first, second, and third story, respectively. The analytical substructure (MRF) yielded in the MCE level simulations. Fortunately, since the yielding occurs only in the analytical substructure, numerous real-time hybrid simulations with various ground motions could be performed on the same prototype structure without accumulating damage. The numerous simulations enabled a statistical assessment of the response to be made. Fig. 9 compares the calculated design demand for drift from the PBD with the median values for maximum story drift from the RTHS under the DBE and MCE ground motions. Fig. 9 shows the story drift design demand calculated by the PBD is close to but larger than the median maximum story drifts from the RTHS under DBE. The maximum story drift is in the second story with a design demand value of.81% from the PBD and a median value of.78% from RTHS. The discrepancy between the two is 4%. Fig. 9 shows the calculated story drift design demand from the PBD is close to the median values from the RTHS under the MCE. The maximum story drift demand in the second story is 1.41% from the PBD and the median value is 1.37% from RTHS. The discrepancy between the two is 3%. The good agreement between the PBD design demand and RTHS results both at DBE and MCE level response indicates that the PBD is experimentally validated through the RTHS. The prototype structure response under the DBE and MCE level real-time hybrid simulations meet the performance objectives of the PBD which are considered to be enhanced performance (FEMA 356 [12]) with respect to story drift. The DBE response essentially meets the Immediate Occupancy performance level, where the maximum story drift is.7% with negligible residual story drift. The MCE response meets the Life-Safety performance level, where the maximum story drift is 2.5% and the maximum residual story drift is 1.%.

9 Table 2. DBE and MCE ground motion information. Ground Earthquake Event Ground Record Earthquake Event Record Motion Motion component No. Year Name M Component No. Year Name M Chi-Chi, DBE Imperial Valley 6.5 H-DLT262 MCE Taiwan 7.6 TCU116-N Chi-Chi, DBE Imperial Valley 6.5 H-E314 MCE Taiwan 7.6 TCU55-N HECTOR- Kocaeli, DBE Hector Mine MCE Turkey 7.5 DZC27 HECTOR- Imperial DBE Hector Mine MCE Valley 6.5 H-E314 Imperial DBE Loma Prieta 6.9 HSP9 MCE Valley 6.5 H-ECC2 Loma DBE Loma Prieta 6.9 WVC27 MCE Prieta 6.9 HSP9 DBE Northridge 6.7 RRS318 MCE Northridge 6.7 RRS318 Table 3. Maximum and residual story drift from DBE level RTHS Ground Story drift (%) Residual story drift (%) Motion No. 1st story 2nd story 3rd story 1st story 2nd story 3rd story DBE DBE DBE DBE DBE DBE DBE Median COV Table 4. Maximum and residual story drift from MCE level RTHS Ground Maximum Story Drift (%) Residual Story Drift (%) Motion No. 1st story 2nd story 3rd story 1st story 2nd story 3rd story MCE MCE MCE MCE MCE MCE MCE Median COV

10 Spectral acceleration, Sa (g) DBE-1 DBE-2 DBE-3 DBE-4 DBE-5 DBE-6 DBE-7 Median spectrum Design spectrum Unif orm hazard spectrum Period, Tn (s) Period, Tn (s) Figure 6. Response spectrum of ground motions DBE level; MCE level Spectral acceleration, Sa (g) MCE-1 MCE-2 MCE-3 MCE-4 MCE-5 MCE-6 MCE-7 Median spectrum Design spectrum Unif orm hazard spectrum 3rd floor Floor displaccement (mm) 2nd floor 1st floor Time (s) Measured disp. Measured disp. Measured disp Measured displacement: x s (mm) 15 1st floor 35 2nd floor 45 3rd floor Target displacement: x t (mm) Figure 7. DBE-5 RTHS response Floor displacement; Synchronization plot 3rd floor Floor displacement (mm) 2nd floor 1st floor Time (s) Measured disp. Measured disp. Measured disp. Measured displacement: x s (mm) 3 1st floor 6 2nd floor 75 3rd floor Target displacement: x t (mm) Figure 8. MCE-6 RTHS response Floor displacement; Synchronization plot Story level DBE-PBD design demand DBE-RTHS median Maximum story drift (%) Story level MCE-PBD design demand MCE-RTHS median Maximum story drift (%) Figure 9. Comparison of maximum story drifts between PBD and RTHS DBE; MCE

11 Summary and Conclusions This paper presents real-time hybrid simulations (RTHS) on a large-scale three-story structure with a one-bay MRF and a one-bay braced frame with nonlinear viscous dampers under DBE and MCE level ground motions. The RTHS allowed numerous tests to be performed without damage accumulation in the MRF which was modeled as an analytical substructure. This approach enabled statistical evaluation of structural performance under simulated earthquake loading. The simulation results show that the structure with nonlinear viscous dampers achieves the specified performance objectives. The real-time hybrid simulation results were compared with design predictions from a performance-based design procedure (PBD). The results validate the PBD and show that real-time hybrid simulation (RTHS) is a practical technique to experimentally evaluate performance under simulated earthquake loading. Acknowledgments This paper is based upon work supported by grants from National Science Foundation, Award No. CMS in the George E. Brown, Jr. Network for Earthquake Engineering Simulation Research (NEESR) program, and Grant No. CMS-4249 for the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) consortium operations. Any opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsor. References 1. Chen C, Ricles JM, Marullo TM, and Mercan O. Real time hybrid testing using the unconditionally stable explicit CR integration algorithm. Earthquake Eng Struct Dyn 29; 38(1): Chae.Y, Kazemibidokhti. K, Ricles JM. Adaptive time series compensator for delay compensation of servohydraulic actuator systems for real-time hybrid simulation. Earthquake Eng Struct Dyn 213; 42(11): IBC 29, International Building Code. International Code Council (ICC), ASCE 7-1, Minimum design loads for buildings and other structures. American Society of Civil Engineers, SAP 2, Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures, Version 14. Computers and Structures Inc., Berkeley, CA, AISC, Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL, AISC, Seismic Provisions for Structural Steel Buildings. American Institute of Steel Construction, Chicago, IL, Dong, B. Performance-based Design for Cost-effective Seismic Hazard Mitigation in Buildings Using Nonlinear viscous Dampers. PhD Dissertation, Lehigh University, Bethlehem, PA (in preparation). 9. Karavasilis TL Seo C.Y., Ricles JM. HybridFEM. A program for dynamic time history analysis and real-time hybrid simulation of 2D inelastic framed structures. Updated ATLSS Report No. 8 9, Lehigh University, Bethlehem, PA, Lehigh RTMD Users Guide Chiou, B., Darragh, R., Gregor, N., and Silva W. NGA Project Strong-Motion Database. Earthquake Spectra: February 28, Vol. 24, No. 1, pp FEMA 356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, Washington, DC, 21.