SYSTEM IDENTIFICATION, MODELING AND PERFORMANCE PREDICTION OF A 20-STORY OFFICE BUILDING

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1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 26 Paper No. 279 SYSTEM IDENTIFICATION, MODELING AND PERFORMANCE PREDICTION OF A 2-STORY OFFICE BUILDING He Liu 1, Rakesh Goel 2, Feifei Bai 3, William Scott 4 and Toshifumi Kono 5 ABSTRACT The Atwood Building, a 2-story office building in Anchorage Alaska, is one of the heavily instrumented buildings by the USGS Advanced National Seismic System. The instrumentation includes 32-channel seismic sensors at 1 levels of the building and 21-channel seismic sensors at a downhole array near the building. This paper describes a three-dimensional Finite Element (FE) model, which has been calibrated in two horizontal directions by matching the natural periods from FE analysis with those from system identification applied to ambient vibration data. This model has been used to examine the nonlinear behavior of the building using Incremental Dynamic Analysis (IDA) and Modal Pushover Analysis (MPA) procedures. The extension of MPA to compute member forces is also applied. It is envisioned that this building would serve as a benchmark building for other researchers to use in developing improved analysis and design procedures as well as predicting performance of buildings to future damaging earthquakes. Keywords: Instrumentation, Modeling, Performance Prediction, IDA, MPA INTRODUCTION Alaska is one of the most active seismic areas in the world. The observed seismicity in Anchorage and its adjoining south-central Alaska results from the underthrusting of the Pacific Plate beneath the North American Plate (Ratchkovsky and Biswas 1965, Combellick and etc., 1999). The megathrust zone lies at a depth of about 35 km beneath Anchorage. The largest earthquake in US history, i.e. the Prince William Sound earthquake (M W = 9.2) of 1964, referred to as 1964 Alaska earthquake in rest of this paper, was located along this zone and caused extensive damage to Anchorage area in the form of large-scale landslides, and building damage due to the long duration of shaking (approximately 18 sec). The Atwood building, located in the downtown Anchorage, has been chosen for seismic instrumentation in order to study the building s seismic response and effects of soil-structure interaction, because this area suffered extensive damage during the 1964 Alaska earthquake. The instrumentation of the Atwood building, sponsored by the Advanced National Seismic System (ANSS) program of United States Geological Survey (USGS), was completed in 23 (Celebi, 23). The 1 Professor, Dept. of Civil Engineering, University of Alaska, Anchorage, AK, afhl@uaa.alaska.edu 2 Professor, Dept. of Civil & Environmental Engineering, California Polytechnic State University, CA, rgoel@calpoly.edu 3 Graduate Student, Dept. of Civil Engineering, University of Alaska, Anchorage, AK, asffb@uaa.alaska.edu 4 Principle Engineer, VECO Alaska Inc., Anchorage, AK 9958, william.scott@veco.com 5 Graduate Student, Dept. of Civil Engineering, University of Alaska, Anchorage, AK, antk@uaa.alaska.edu

2 instrumentation consists of 32 channels of strong-motion sensors distributed on 1 levels of the building, and 21 seismic sensors at a downhole array near the building. The seismic instrumentation of the Atwood building is briefly described in this paper first. Then the three-dimensional (3D) Finite Element (FE) baseline model of the building developed to predict its response in the future earthquakes is presented. This model is used to examine the nonlinear behavior of the building using Incremental Dynamic Analysis (IDA) and Modal Pushover Analysis (MPA) procedures. Meanwhile, the extension of MPA to compute member forces is also performed. It is envisioned that this building would serve as a benchmark building for other researchers to use in developing improved analysis and design procedures as well as predicting performance of buildings to future damaging earthquakes. Description of Building and the Deployment of Strong Motion Instrumentation The Atwood building was designed and constructed in the early 198's according to the 1979 Edition of the Uniform Building Code. The building has 2 stories with a basement that is used as a parking garage. This building is square in plan with dimensions of 38.5 m by 38.5 m and 8.5 m tall. The lateral load resisting system of the building consists of a moment-resisting steel frame and a central steel shear walled core of dimension m by m. The foundation is reinforced concrete spread footings. The typical elevation and plan views are shown in Fig. 1. Figure 1. Typical elevation and plan of the Atwood building in Anchorage, Alaska. The instrumentation of the Atwood building, sponsored by the ANSS program of USGS, was completed in 23. The 32-channel seismic sensors (CH 1 CH 32) are located in the basement garage, on the 1 st, 2 nd, 7 th, 8 th, 13 th, 14 th, 19 th, 2 th, 21 st floors and at the roof level of the building, as shown in Fig. 2. Among the sensors, there are 29 uni-axial and one tri-axial Force Balance Accelerometers with 1.25 V/g sensitivity. The tri-axial sensor is located at the northwest corner of the basement. There are two vertical accelerometers in the northeast and southwest corners of the building. These sensors are included to capture the rocking response of the building. At each instrumented floor of the building, two orthogonal accelerometers (north-south and east-west) are placed at the east side and one accelerometer (north-south) is at the west side of the building. This instrumental configuration is used to capture torsional motion of the building. There are three recorders in the data acquisition system,

3 which are housed on the 18th floor of the building. Each recorder is connected with an individual GPS receiver located at the roof of the building. The recorded signal is sampled at 2 samples/sec and the recorders are operating in trigger mode with triggering thresholds varying from 1 gal at the basement to 4 gal at the roof level. To investigate the effect of soil-structure-interaction, a downhole array (see Fig. 3) at about 1 m south of the building in the Delaney Park is also instrumented. The array includes six tri-axial strong motion sensors located at the bottom of six boreholes of 3 to 68 m depths. In addition to this, the array also includes one tri-axial surface sensor. The real time data acquisition system of the array consists of four high dynamic range digital recorders. The array has been operational since September 24. Figure 2. Seismic instrumentation of the Atwood building. Figure 3. Downhole array instrumentation. System Identification of Atwood Building The dynamic characteristics of the Atwood building were estimated by system identification approach using the recorded data from several local earthquakes and two ambient tests by a computer software ARTeMIS Extractor (Structural Vibration Solutions A/S) (Liu and etc. 25). The transverse natural periods, in the EW and NS directions, and the torsional periods of the Atwood building identified from system identification are listed in Table 1. The system identification from the ambient tests led to the first EW, NS, and torsional vibration periods of 2.19 sec, 1.84 sec, and 1.58 sec, respectively. Table 1. Vibrational natural periods of the Atwood building. Direction EW NS Torsion Data source Natural Periods (sec) 1 st Mode 2 nd Mode 3 rd Mode Ambient SAP2 Model Ambient SAP2 Model Ambient SAP2 Model

4 3D Finite Element Model of the Atwood Building A 3D Finite Element model, shown in Fig. 4, has been developed using SAP2 (Wilson 21; CSI, 2). The x, y, z coordinates in the FE model are corresponding to the EW, NS and vertical directions, respectively. An initial Design Model was developed based on the typical assumptions used by practicing engineers. However, the fundamental periods of this design model were much shorter than those obtained form the ambient vibration tests. Therefore, this model was calibrated by the identification results and refined to improve the matching between the computed natural periods and that from the ambient vibration tests. Particularly, the refinements included: (1) improved calculation of the quantity and eccentricity of building masses based on the evaluation from site visit; (2) refined calculation of the mass moment inertia for each floor; (3) modification of panel zone rigidities of beam/column connections; (4) inclusion of composite actions between the concrete slabs and steel beams; and (5) adjustment in damping to consider the effects of nonstructural components. The Rayleigh-Ritz method was adopted in the analysis where the total seventy modes in the E-W and N-S directions provide the total mass participation factor of 99.8% and 99.7%, respectively. With these refinements, the computed natural periods of the Atwood building match closely with those identified from the ambient vibration tests. For example, the first vibration period in the EW direction of the 3D FE model is exactly equal to that from ambient tests whereas those in the NS and torsional directions differ only by less than 1%. Figure 4. 3D Finite Element model of the Atwood Building in SAP 2. The 3D FE model is further verified by comparing the computed time history response of the model with that recorded during a recent low-intensity earthquake. For this purpose, the motions of the Atwood building recorded during a relative weak ground shaking, the February 16, 25 Southeast Anchorage earthquake of magnitude M L =4.6, have been chosen for the modal validation study. The results presented in Fig. 5 show a good match between the recorded and computed time histories as well as the Fourier amplitude spectra in both EW and NS directions. Prediction of Seismic Response The seismic response of the building is predicted by IDA (Vamvatsikos and Cornell 22) and MPA (Chopra and Goel, 24; Goel and Chopra, 24) procedures. For this purpose, five recorded ground

5 acceleration listed in Table 2 and the selected time histories of Denali and Nenana earthquakes, shown in Fig.6, which include short and long duration ground motions, from far and near sources of subduction zone and strike-slide seismic faults would be used. The seismic response prediction and the selected results are presented next. Displacemet(cm) Acceleration (cm/s/s) FAS(cm/sec) Acceleration Timehistory (EW) Displacement Timehistory (EW) Fourier Acceleration Spectrum (EW) Period (sec) Recorde d FEA Recorde d FEA Recorde d FEA Acceleration (cm/s/s) Displacemet(cm) FAS (cm/s/s) 2 Acceleration Time history (NS) Displacement Time history (NS).2 Recorded FEA Fourier Acceleration Spectrum (NS) Period (sec) Recorded FEA Recorded FEA Figure 5. Comparison of recorded and FE mode simulated results in E-W (top three figures) and N-S (bottom three figures) directions

6 Table 2. Recorded ground motions to be considered in seismic response prediction. Event Date Magnitude Epicenter 1964 Alaska Prince Earthquake 3/15/ M W William Distance (km) Depth (km) PGA (cm/s 2 ) Nenana Sound 2 Denali Fault Denali Earthquake 11/3/ M W Fault Nenana Mountain earthquake 1/23/ M W Mountain Southeast Anchorage 4 earthquake 1 st main 2/6/ M b Southeast shock Anchorage 5 Southeast Anchorage earthquake 2 nd main shock 2/6/ M b Southeast Anchorage Denali Fault earthquake 4 Nenana Mountain earthquake Acceleration (cm/s/s) Acceleration (cm/s/s) Figure 6. Recorded Ground Acceleration In this study, considering the sizes of columns are changed at the 1 st to 4th, 7th, 12 th, 13 th, and the top three floors, plastic hinges - axial, shear, and bending (or flexural) - were specified only in these stories. Because the moment connections of columns are about the major axis only, flexural plastic hinges about the minor axis were ignored. The properties of plastic hinges were calculated based on FEMA 356 for steel design. Considering the length of this paper, only the brief results for Denali, Nenana and two local earthquakes are presented here. Fig. 7-8 show the resulting maximum roof displacements of IDA and MPA procedures from these two earthquakes implemented on EW direction of the Atwood building. In the IDA procedure, for Denali earthquake, basic scaling levels were set according to the 5% damping pseudo-spectrum acceleration (PSA) at the first natural period of the building. According to the IBC 23, at the building site, the maximum considered earthquake ground motion for.2 sec and 1. sec spectral response accelerations with 5% of critical damping and site class C are 1.5 g and.715 g, respectively. The corresponding design pseudo-spectrum acceleration at the first period of the building structure is about.2 g. Therefore the ground acceleration records were scaled so that the resulting PSA at the first period of the structure were.5 g,.1 g,.15 g and.2 g, respectively. The ground inputs were only applied to the E-W direction of the building. To take into account the secondary effects between axial forces and bending moments, the P-delta effects were included. The first plastic hinge was formed in the Denali seismic event with input peak ground acceleration (PGA)

7 .1 g, corresponding to PSA.5 g. As for Nenana earthquake, the PGA was also used to control the scaling process. The original input ground motion (PGA.4g) was scaled to.1g,.2g,.5g,.1g and.2g for use respectively. In order to avoid convergence problems, no P-delta effects were considered in Nenana earthquake analysis. The first plastic hinge formed in this event with input peak ground acceleration (PGA).5g. In the MPA procedure, the first five modes of both E-W and N-S direction were chosen as the push modes. Obviously after the structure reaches the inelastic range, the natural periods, mode shapes and linear response spectra are all changed. To observe how significant the change is for this particular real structure, we applied the push forces, simulating the effective earthquake forces (Chopra, 21), proportional to the mode shapes taken from the linear analysis for the condition of nonlinear pushover. The maximum inelastic response value (i.e. the maximum roof displacement) of each mode was determined by MPA procedure (see detailed procedure in Chopra and Goel, 24). NONLIN program was used here to compute the peak deformation of the five modes inelastic single-degree-of freedom (SDF) system defined by the modal force-deformation relation converted from idealized base shear-roof displacement curve with modified natural periods. The peak roof displacement in both E- W and N-S directions of each selected pushover curve was then calculated associated with five modes inelastic SDF system. Finally the five peak roof displacements, each from one modal pushover case, were combined by the square-root-of-sum-of-squares (SRSS) rule and complete quadratic combination (CQC) rule to get the total response. The results of the maximum roof displacement versus PGA are also shown in Fig. 7 and 8. The MPA results of N-S direction from Denali and Nenana earthquakes are shown separately in Fig. 9. Figure 7. Maximum roof Displacement vs. PGA of Denali earthquake Figure 8. Maximum roof Displacement vs. PGA of Nenana earthquake 1 Denali earthquake 1 Nenana earthquake.8.8 PGA (g).6.4 PGA (g) MPA MPA Maximum Roof Displacement (cm) Maximum Roof Displacement (cm) Figure 9. MPA curves for two selected earthquake inputs with different PGA s (N-S direction)

8 The preliminary comparison shows that the close results from IDA and MPA occur in the lower PGA level (PGA.5g) in E-W direction. It implies that the results from the MPA procedure can represent the structural response in the elastic range quite appropriately for a complicate 3D structure. After the plastic hinge occurs, the structure behaves nonlinearly, although the nonlinearity is not very strong in this building because the steel shear wall is quite stiff in the core area. The very limited differences between the IDA and MPA curves in the nonlinear range can be seen from Fig.7 and 8. It implies that the MPA procedure can provide prediction quite well in the nonlinear range for this complicate three-dimensional structure. It also can be seen from Fig.7-8 that, in any cases, the SRSS and CQC procedures provide the almost identical results for this building. MPA Analysis to Compute Member Forces In the nonlinear static procedure (NSP) or pushover analysis, the seismic demands are computed at the target displacement and compared against acceptability criteria. Since the acceptability criteria specified in the FEMA-356 document (ASCE 2) are in terms of the deformation demands such as story drift, therefore, most of the past researches are mainly focused on deformation demands. However, with the increasing need to estimate force demands, it is useful to develop procedures for computing force demands in the NSP (Goel and Chopra 25). In the FEMA-356 NSP, force demands are given by member forces in the structure pushed to the target displacement, however, the seismic demands in MPA method, as we discussed earlier, are computed by combing contributions of all significant modes. Although, it was shown that the MPA procedure provide satisfactory estimates for deformations, story drifts, the MPA procedure is still not applicable to estimating member forces because forces computed by this procedure may exceed the specified member capacity. Therefore, Goel and Chopra extend the MPA procedure to compute member forces that provide estimates consistent with the specified capacity. (Goel and Chopra 25). In this paper, the extended MPA procedures were applied for the Atwood Building analysis. Since there is a sudden change in size of columns in the 18 th (W14x74) and 17 th floor (W14x19), one typical column of 18 th floor was chosen for the application. Plastic hingesaxial (P), shear (V) and bending (M) (or flexural) were also specified in the element. The section and material properties of the column are listed in Table 3. Elastic modulus E (GPa) Table 3. Section and Material Properties of the Selected Column Section Yield Stress F y (MPa) Section modulus Z major (cm 3 ) Moment of Inertia I major (cm 4 ) Length (cm) 2 W14x ,27 32, The procedures to compute the bending moment of the selected column includes: 1. Compute the axial force P in the nonlinear column element by combining the peak modal axial forces, P n, and the axial force due to the gravity load, P g, according to the combination rule specified in the MPA procedure (see Goel and Chopra 24). The combined axial force P for the selected column is 1,54 KN. 2. Compute the bending moment at column ends I and J, M I and M J of the column element by combining the peak modal moments, M n, and the moments due to the gravity load, M g, according to the combination rule. The bending moments M I and M J at both ends of the column after combination are 74 KN m and KN m, respectively.

9 3. Determine the yield moment M yp of the elastic-plastic component corresponding to the axial force, P, computed in step 1 from the specified P-M interaction relationship (AISC 2) and add the moment in the elastic component to obtain the total yield moment: M y =M yp /(1-α). The second moment-rotation (M-θ) slope α is set 3% here and the corresponding total yield moment M y is 518 KN m. Since the axial forces at two ends of the column element are same, so the yield moment for the two ends is also the same. 4. Compare the bending moments, M I and M J, which were computed in step 2 with the yield moment, M y, computed in step 3. Since both M I and M J are larger than M y, then additional steps are needed to compute the bending moments. 5. Compute the rotation θ I and θ J at ends I and J of the column by combining the peak modal rotations, θ n, and the rotations due to the gravity load, θ g, according to the procedure specified in the MPA procedure. The combined rotation θ I and θ J are.22 and.2 rad., respectively. 6. Compute the bending moment in the elastic component from EI EI M e, I = α ( 4θ I + 2θ J ) and M e, J = α ( 4θ J + 2θ I ) L L then compute the total bending moment by adding the elastic component ad plastic component (step 3) as M I M yp + M e, I = and M J = M yp + M e, J The final total bending moments M I and M J at both ends of the selected column are 58.6 KN m, and 58.5 KN m, respectively. In the more accurate procedure, the total hinge rotation should be obtained by adding the yield rotation to the plastic hinge rotation that is computed indirectly from the total story drift. However, although not very accurate for estimating the total hinge rotation, the procedure presented in steps above is appropriate for computing the hinge moment because it varies slowly with rotation for hinges deformed beyond the elastic limit. As a result, even a larger error in the hinge rotation leads to only small error in the computed moment (Goel and Chopra, 25). CONCLUSION This paper described the seismic instrumentation and a calibrated three-dimensional Finite Element model of the Atwood building located in downtown Anchorage, Alaska. The Finite Element model of Atwood Building developed in this study is expected to serves as the baseline model which can be used in further research by both engineering community and researchers to predict the structural behavior in the future earthquakes. Using the recorded earthquake acceleration data, the IDA and MPA procedures are applied to the building. The extended MPA procedures are also applied to a typical column of the building to compute the internal member forces. The preliminary results show that the IDA and MPA procedures can both provide essential estimates of seismic demands of the building in both linear and nonlinear ranges. However, the IDA procedure may request longer computational time and possibly encounter convergent difficulties. From this point of view, the MPA has superior preponderance. ACKNOWLEGMENT Construction of downhole array provided by Experimental Program to Stimulate Competitive Research (EPSCoR) and instrumentation of Atwood Building sponsored by Advanced National Seismic System (ANSS) are gratefully acknowledged.

10 REFERENCE American Society of Civil Eningeers (ASCE), (2). Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Report No. FEMA-356, Federal Emergency Management Agency, Washington, D.C. American Institute of Steel Construction (AISC), (21). Manual of steel construction, third edition. Section H Celebi, M., Seismic instrumentation of buildings. (April 23).Open-file report -157, United States Geological Survey. Chopra, A. K, (21). Dynamics of Structures, Prentice-Hall, Inc. A Simon & Schuster Company Upper Saddle River, NJ Chopra, A. K., and Goel, R.K., (24). A modal pushover analysis procedure to estimate seismic demands for unsymmetric buildings.. Earthq. Engrg. Struc. Dyn., 33(8) Combellick, R.A., Simplified Geologic Map and Cross Sections of Central and East Anchorage. Alaska, 1999 State of Alaska, Department of Geological and Geophysical Surveys. CIS (Computers and Structures, Inc.), Berkeley, CA, SAP2-integrated finite element analysis and design of structures: analysis reference, August 2. Version Goel, R.K. and Chopra, A.K., (24). Evaluation of Modal and FEMA pushover analysis: SAC buildings, Earthquake Spectra, 2(1) Goel, R.K. and Chopra, A.K., (25). Extension of Modal Pushover Analysis to Compute Member Forces, Earthquake Spectra, 21(1) Liu, H., Yang Z., Scott W., Kono T. and Dutta U., Seismic Response Of Atwood Building, Anchorage, Alaska: Comparison Study By Finite Element Modeling And Recorded Data, (25), Proceedings of McMat25: 25 Joint ASME/ASCE/SES Conference on Mechanics and Materials, June 1-3, Baton Rouge, Louisiana. Ratchkovsky, N., Jose, P., and Biswas, N. N., Relocation of earthquakes in the Cool Inlet area, southcentral Alaska, using joint hypocenter determination method. (1997). Bulletin of Seismological Society of America, 87: Vamvatsikos, D. and Cornell, C.A., Incremental Dynamic Analysis, (22). Earthquake Engineering and Structural Dynamics 31, Wilson, E.L., Three dimensional static and dynamic analysis of structures: a physical approach with emphasis on earthquake engineering. (21). 3rd ed. Berkeley (CA 9474, USA): Computers and Structures, Inc.