ACCELERATION RESPONSE OF RIGID AND FLEXIBLE NONSTRUCTURAL COMPONENTS IN BUILDINGS SUBJECTED TO STRONG GROUND MOTIONS

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering ACCELERATION RESPONSE OF RIGID AND FLEXIBLE NONSTRUCTURAL COMPONENTS IN BUILDINGS SUBJECTED TO STRONG GROUND MOTIONS A Thesis in Architectural Engineering by Jared M. Shoemaker 21 Jared M. Shoemaker Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 21

2 The thesis of Jared M. Shoemaker was reviewed and approved* by the following: Andres Lepage Assistant Professor of Architectural Engineering Thesis Advisor Ali Memari Professor of Architectural Engineering Gordon Warn Assistant Professor of Civil Engineering Chimay Anumba Professor of Architectural Engineering Head of the Department of Architectural Engineering *Signatures are on file in the Graduate School.

3 iii ABSTRACT A formulation is presented for estimating the maximum horizontal acceleration of nonstructural components attached to the floor system of multistory structures subjected to strong earthquake motions. First, a method is developed for rigid nonstructural components after shake-table acceleration data measured on the horizontal floor diaphragms of small-scale multistory reinforced concrete test structures. The observed dynamic nonlinear response of 3 structures involved in 74 earthquake simulations led to a general expression that directly incorporates a measure of the nonlinear response of the structures. Second, the formulation is tested against floor acceleration data recorded in existing multistory buildings during strong seismic events. Seven instrumented buildings located in California provided data associated with 3 ground motions histories recorded during four major earthquakes. Lastly, acceleration data calculated after nonlinear dynamic analyses of 6-story and 12- story buildings subjected to a suite of 1 ground motions are used to test the proposed formulation and expand its application to flexible nonstructural components. Floor acceleration spectra are developed at elevations near the third points of the building height. Results indicate that the proposed formulation for estimating maximum accelerations of rigid and flexible nonstructural components is satisfactory. The method is reliable and it is easy to incorporate into the framework of modern seismic design provisions.

4 iv 2. TABLE OF CONTENTS TABLE OF CONTENTS... iv LIST OF TABLES... vi LIST OF FIGURES... viii ACKNOWLEDGMENTS... xiv 1. INTRODUCTION Statement of the Problem Objectives and Scope Organization REVIEW OF SEISMIC PROVISIONS IN BUILDING CODES ON NONSTRUCTURAL COMPONENTS Introduction UBC NEHRP ASCE/SEI FLOOR ACCELERATIONS IN MULTISTORY TEST STRUCTURES SUBJECTED TO EARTHQUAKE SIMULATIONS Introduction Description of Test Structures Considered Earthquake Simulation Tests and Observed Acceleration Response Estimates of Floor Accelerations in Structures Subjected to Strong Ground Motions Summary FLOOR ACCELERATIONS IN MULTISTORY BUILDINGS SUBJECTED TO EARTHQUAKE MOTIONS Introduction Description of Existing Buildings Considered Warehouse Building at Los Angeles Parking Building at Los Angeles Hotel Building at Van Nuys Residential Building at Burbank Commercial Building at Sherman Oaks... 29

5 v Storage Building at Hollywood Hotel Building at North Hollywood Earthquake Events and Observed Acceleration Response Estimates of Floor Accelerations Summary ANALYTICAL STUDY OF THE ACCELERATION RESPONSE OF MULTISTORY BUILDINGS SUBJECTED TO EARTHQUAKE MOTIONS Introduction Description of Buildings Analyzed Numerical Model for Nonlinear Response Description of Ground Motions and Scaling Floor Acceleration Maxima Floor Acceleration Spectra Summary SUMMARY AND CONCLUSIONS A. SELECTED GROUND MOTIONS A.1 Introduction A.2 Characteristic Period of Ground Motion A.3 Idealized Response Spectrum TABLES... 5 FIGURES REFERENCES BIOGRAPHICAL SKETCH... 21

6 vi LIST OF TABLES Table 3.1 Small-Scale Test Structures Considered in this Study Table 3.2 Summary of Earthquake Simulations Table 3.3 Maximum Recorded Floor Accelerations for Test Structures Table 3.4 Effective Response Modification Coefficient of Test Structures Table 4.1 Building Structures Considered Table 4.2 Maximum Recorded Floor Accelerations for Existing Buildings Table 4.3 Effective Response Modification Coefficient of Existing Buildings Table 5.1 Building Load Data Table 5.2 Assumed Story Properties in Analytical Models Table 5.3 Assumed Frame Sections and Material Properties in Analytical Models Table 5.4 Dynamic Parameters for 6-Story Frames Based on Uncracked Sections Table 5.5 Dynamic Parameters for 12-Story Frames Based on Uncracked Sections Table 5.6 Frame Reinforcing Schedule Table 5.7 Yield Point Data for Nonlinear Links Table 5.8 Scaling of Ground Motions Table A.1 Ground Motions Considered... 78

7 viii LIST OF FIGURES Figure 3.1 The University of Illinois Earthquake Simulator and Typical Test Setup, After Lepage (1997) Figure 3.2 Test Structures D1, D2, D3, M1 Tested by Aristizabal (1976) Figure 3.3 Test Structures D1, D2, D3, D4, D5 Tested by Lybas (1977) Figure 3.4 Test Structure MF1 Tested by Healey (1978) Figure 3.5 Test Structure MF2 Tested by Moehle (1978) Figure 3.6 Test Structures FW1, FW2, FW3, FW4 Tested by Abrams (1979) Figure 3.7 Test Structures H1, H2 Tested by Cecen (1979) Figure 3.8 Test Structures FNW, FSW, FHW, FFW Tested by Moehle (198) Figure 3.9 Test Structures NS1, NS2, NS3 Tested by Wolfgram (1984) Figure 3.1 Test Structures SS1, SS2 Tested by Schultz (1985)... 9 Figure 3.11 Test Structure Tower Tested by Wood (1986) Figure 3.12 Test Structure Stepped Tested by Wood (1986) Figure 3.13 Test Structures ES1, ES2 Tested by Eberhard (1989) Figure 3.14 Maximum Measured Accelerations for Coupled-Walls Figure 3.15 Maximum Measured Accelerations for Frame-Wall Structures Figure 3.16 Maximum Measured Accelerations for Frames Structures with Yielding-Beams.. 95 Figure 3.17 Maximum Measured Accelerations for Frame Structures with Yielding-Columns 95 Figure 3.18 Maximum Measured Accelerations for All Test Structures Figure 3.19 Maximum Accelerations, Test Structure D1 (Aristizabal, 1976) Figure 3.2 Maximum Accelerations, Test Structure D2 (Aristizabal, 1976) Figure 3.21 Maximum Accelerations, Test Structure D3 (Aristizabal, 1976) Figure 3.22 Maximum Accelerations, Test Structure M1 (Aristizabal, 1976)... 1 Figure 3.23 Maximum Accelerations, Test Structure D1 (Lybas, 1977) Figure 3.24 Maximum Accelerations, Test Structure D2 (Lybas, 1977) Figure 3.25 Maximum Accelerations, Test Structure D3 (Lybas, 1977) Figure 3.26 Maximum Accelerations, Test Structure D4 (Lybas, 1977) Figure 3.27 Maximum Accelerations, Test Structure D5 (Lybas, 1977)... 15

8 ix Figure 3.28 Maximum Accelerations, Test Structure MF1 (Healey, 1978) Figure 3.29 Maximum Accelerations, Test Structure MF2 (Moehle, 1978) Figure 3.3 Maximum Accelerations, Test Structure FW1 (Abrams, 1979) Figure 3.31 Maximum Accelerations, Test Structure FW2 (Abrams, 1979) Figure 3.32 Maximum Accelerations, Test Structure FW3 (Abrams, 1979) Figure 3.33 Maximum Accelerations, Test Structure FW4 (Abrams, 1979) Figure 3.34 Maximum Accelerations, Test Structure H1 (Cecen, 1979) Figure 3.35 Maximum Accelerations, Test Structure H2 (Cecen, 1979) Figure 3.36 Maximum Accelerations, Test Structure FNW (Moehle, 198) Figure 3.37 Maximum Accelerations, Test Structure FSW (Moehle, 198) Figure 3.38 Maximum Accelerations, Test Structure FHW (Moehle, 198) Figure 3.39 Maximum Accelerations, Test Structure FFW (Moehle, 198) Figure 3.4 Maximum Accelerations, Test Structure NS1 (Wolfgram, 1984) Figure 3.41 Maximum Accelerations, Test Structure NS2 (Wolfgram, 1984) Figure 3.42 Maximum Accelerations, Test Structure NS3 (Wolfgram, 1984) Figure 3.43 Maximum Accelerations, Test Structure SS1 (Schultz, 1985) Figure 3.44 Maximum Accelerations, Test Structure SS2 (Schultz, 1985) Figure 3.45 Maximum Accelerations, Test Structure Tower (Wood, 1986) Figure 3.46 Maximum Accelerations, Test Structure Stepped (Wood, 1986) Figure 3.47 Maximum Accelerations, Test Structure ES1 (Eberhard, 1989) Figure 3.48 Maximum Accelerations, Test Structure ES2 (Eberhard, 1989) Figure 3.49 Measured-to-Calculated Acceleration Ratios for Coupled Walls, Based on A i = A g [ 1 + ( 3 / R ) (h i / h r ) ] Figure 3.5 Measured-to-Calculated Acceleration Ratios for Frame-Wall Structures, Based on A i = A g [ 1 + ( 3 / R ) (h i / h r ) ] Figure 3.51 Measured-to-Calculated Acceleration Ratios for Frame Structures with Yielding Beams, Based on A i = A g [ 1 + (3 / R ) (h i / h r ) ] Figure 3.52 Measured-to-Calculated Acceleration Ratios for Frame Structures with Yielding Columns, Based on A i = A g [ 1 + ( 3 / R ) (h i / h r ) ]

9 x Figure 3.53 Measured-to-Calculated Acceleration Ratios for Coupled Walls, Based on A i = A g [ 1 + ( 2 / R ) (h i / h r ) ] Figure 3.54 Measured-to-Calculated Acceleration Ratios for Frame-Wall Structures, Based on A i = A g [ 1 + ( 2 / R ) (h i / h r ) ] Figure 3.55 Measured-to-Calculated Acceleration Ratios for Frame Structures with Yielding Beams, Based on A i = A g [ 1 + (2 / R ) (h i / h r ) ] Figure 3.56 Measured-to-Calculated Acceleration Ratios for Frame Structures with Yielding Columns, Based on A i = A g [ 1 + ( 2 / R ) (h i / h r ) ] Figure 3.57 Measured-to-Calculated Acceleration Ratios, All Test Structures, Based on A i = A g [ 1 + ( 3 / R ) (h i / h r ) ] Figure 3.58 Measured-to-Calculated Acceleration Ratios, All Test Structures, Based on A i = A g [ 1 + ( 2 / R ) (h i / h r ) ] Figure 3.59 Measured-to-Calculated Acceleration Ratios, All Test Structures, Based on A i = A g [ 1 + ( C p / R ) (h i / h r ) ] Figure 4.1 Elevation and Plan Views of the Los Angeles Warehouse, after CESMD (21) Figure 4.2 Elevation and Plan Views of the Los Angeles Parking, after CESMD (21) Figure 4.3 Elevation and Plan Views of the Van Nuys Hotel, after CESMD (21) Figure 4.4 Elevation and Plan Views of the Burbank Residential, after CESMD (21) Figure 4.5 Elevation and Plan Views of the Sherman Oaks Commercial, after CESMD (21) Figure 4.6 Elevation and Plan Views of the Hollywood Storage, after CESMD (21) Figure 4.7 Elevation and Plan Views of the North Hollywood Hotel, after CESMD (21) Figure 4.8 Maximum Floor Accelerations, Los Angeles Warehouse Figure 4.9 Maximum Floor Accelerations, Los Angeles Parking Figure 4.1 Maximum Floor Accelerations, Van Nuys Hotel Figure 4.11 Maximum Floor Accelerations, Burbank Residential Figure 4.12 Maximum Floor Accelerations, Sherman Oaks Commercial Figure 4.13 Maximum Floor Accelerations, Hollywood Storage Figure 4.14 Maximum Floor Accelerations, North Hollywood Hotel

10 xi Figure 4.15 Maximum Floor Accelerations, All Buildings Figure 4.16 Measured-to-Calculated Acceleration Ratios, All Buildings, Based on A i = A g [ 1 + ( C p / R ) ( h i / h r ) Figure 5.1 Typical Floor Plan for 6- and 12-Story Buildings Considered Figure 5.2 Elevation of the Typical 6-Story Frame Figure 5.3 Elevation of the Typical 12-Story Frame Figure 5.4 Description of Notional Frame Figure 5.5 Typical Moment-Rotation Relationship Assigned to Nonlinear Links Figure 5.6 Nonlinear Link Property Assignments Figure 5.7 Scaled Acceleration Response Spectra, Case of 6-Story Building Figure 5.8 Scaled Acceleration Response Spectra, Case of 12-Story Building Figure 5.9 Calculated Peak Floor Accelerations, 6-Story Building, Linear Response (R = 1). 155 Figure 5.1 Calculated Peak Floor Accelerations, 6-Story Building, Nonlinear Response (R = 2.5) Figure 5.11 Calculated Peak Floor Accelerations, 6-Story Building, Nonlinear Response (R = 4.2) Figure 5.12 Calculated Peak Floor Accelerations, 6-Story Building, All Runs Figure 5.13 Calculated Peak Floor Accelerations, 6-Story Building, Average for 1 Ground Motions Figure 5.14 Measured (after Nonlinear Analysis)-to-Calculated Acceleration Ratios for 6-Story Building Based on A i / A g = 1 + ( C p / R ) ( h i / h r ) Figure 5.15 Calculated Peak Floor Accelerations, 12-Story Building, Linear Response (R = 1) Figure 5.16 Calculated Peak Floor Accelerations, 12-Story Building, Nonlinear Response (R = 2.5) Figure 5.17 Calculated Peak Floor Accelerations, 12-Story Building, Nonlinear Response (R = 4.5) Figure 5.18 Calculated Peak Floor Accelerations, 12-Story Building, All Runs

11 xii Figure 5.19 Calculated Peak Floor Accelerations, 12-Story Building, Average for 1 Ground Motions Figure 5.2 Measured (after Nonlinear Analysis)-to-Calculated Acceleration Ratios for 12-Story Building Based on A i / A g = 1 + ( C p / R ) ( h i / h r ) Figure 5.21 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Los Angeles 1994 NS Figure 5.22 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to El Centro 194 NS Figure 5.23 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Wrightwood 1994 NS Figure 5.24 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to El Centro 1987 NS Figure 5.25 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Lancaster 1994 NS Figure 5.26 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Richmond 1989 S1E Figure 5.27 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Berkeley 1989 NS Figure 5.28 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Beverly Hills 1994 NS Figure 5.29 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Santa Barbara 1952 S48E Figure 5.3 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Subjected to Lake Hughes 1971 N21E Figure 5.31 Floor Acceleration Spectra (5% damping), 6-Story Building (T a =.77 s) Average for 1 Ground Motions Figure 5.32 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Los Angeles 1994 NS

12 xiii Figure 5.33 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to El Centro 194 NS Figure 5.34 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Wrightwood 1994 NS Figure 5.35 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to El Centro 1987 NS Figure 5.36 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Lancaster 1994 NS Figure 5.37 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Richmond 1989 S1E Figure 5.38 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Berkeley 1989 NS Figure 5.39 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Beverly Hills 1994 NS Figure 5.4 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Santa Barbara 1952 S48E Figure 5.41 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Subjected to Lakes Hughes 1971 N21E Figure 5.42 Floor Acceleration Spectra (5% damping), 12-Story Building (T a = 1.4 s) Average for 1 Ground Motions Figure 5.43 Floor Acceleration Spectra (5% damping) for Selected Test Structures Figure 5.44 Floor Acceleration Spectra (5% damping) for Selected Existing Buildings

13 xiv ACKNOWLEDGMENTS The writer is grateful to his advisors, Dr. Andres Lepage and Dr. Ali Memari, for their assistance and guidance provided through this project and college career. He would also like to thank Michael Hopper for lessons on nonlinear modeling using SAP 2 and everyone whom I am sadly forgetting but am no less grateful to. I would not have finished without the help of others. The writer would also like to extend a special acknowledgment to both of his parents. Their encouragement and support were unerring and without bound.

14 1 CHAPTER 1 3. INTRODUCTION Nonstructural components are essential parts of most buildings and are commonly found attached to a primary structure. It is not unusual for the nonstructural components of a building system to make up the majority of the building s design and construction costs. Nonstructural component systems may include piping and ventilation systems, storage racks and shelves, cladding, hanging ceiling systems, lighting fixtures, partitions, non-load bearing interior and exterior wall systems, etc. Damage done to nonstructural components during a seismic event typically surpasses the economic losses due to structural damage and has been known to cause mandatory evacuation in buildings without major structural damage. In essential facilities, such as hospitals and fire stations, loss of life many may depend on the performance of nonstructural components during major earthquakes. Immediately following the 1994 Northridge earthquake, the Olive View Medical Center in Sylmar, California, a building with no documented structural damage to the primary structure, had to be evacuated and shut down because of damages to its nonstructural components (Miranda and Taghavi, 25). Despite such a high importance placed on nonstructural components, current building codes put forth minimal design provisions and parameters to address them. Further, the response of nonstructural components to floor accelerations in multistory buildings during seismic events remains a topic of limited understanding. This study aims to advance knowledge on this topic. The problem statement, the objectives and scope, and a brief description of the organization of this study are presented next.

15 Statement of the Problem The seismic response of nonstructural components attached to the structure of multistory buildings remains a subject of limited understanding for most structural engineers. Although current code provisions attempt to account for the response of nonstructural components to floor accelerations, many post-earthquake assessments indicate that such provisions are inadequate. Modern seismic design provisions contain gaps in the understanding of the response of nonstructural components to floor accelerations. The general method used to calculate floor accelerations in multistory buildings stems from emphasis on global response parameters of the building (base shear, base overturning, etc.) and on the limitations of the analytical tools commonly used in the design office. Most practicing engineers continue to rely on the equivalent lateral force method to generalize the building response to earthquake induced forces. Current state of practice to determine maximum accelerations of nonstructural components does not explicitly account for the type of seismic force-resisting system in the building nor directly incorporates a factor to account for the inelastic response of the seismic force-resisting system when subjected to strong ground motions Objectives and Scope The nonstructural components under consideration refer to secondary structural systems and elements attached to a single floor of a multistory building. Nonstructural components herein include building contents and architectural, mechanical, and electrical components, all of which can be represented by single-degree-of-freedom systems having a small mass as compared to the total mass of the building. It is assumed that the nonstructural components are attached to a rigid floor diaphragm and that there is no interaction (coupling) with the primary seismic-force resisting system (conventional floor response spectrum approach). Only horizontal seismic excitations are considered, vertical excitations are ignored.

16 3 There are two main objectives in this study. The first objective is to develop a method to estimate floor acceleration maxima in multistory buildings subjected to strong ground motions. The second objective is to expand the formulation for floor accelerations into a more general method to include nonstructural components, rigid and flexible, along the building height. The present study accounts for the nonlinear response of the building and the associated floor acceleration response. However, only linear response of the nonstructural components is considered. The recorded ground accelerations used in this study are predominantly from sites with soil classifications of either very dense soil or stiff soil (Site Class C or D in ASCE/SEI 7-1). The study is limited to mid- and high-rise buildings located at moderate to far focal distances. Ground records from buildings with less than 5 stories in height and/or with an epicentral distance of less than 5 km (3 mi) are not considered. The experimental data taken from previous studies and the recorded responses from existing buildings include seismic forceresisting systems predominantly comprised of reinforced concrete moment frames and reinforced concrete shear walls Organization Chapter 2 provides a review of the seismic provisions in modern building codes for the design of nonstructural components and how they have evolved in recent years. Chapter 3 studies the measured acceleration response of small-scale multistory test structures during earthquake simulations that induce inelastic response of the structure. A general formulation is developed to estimate floor acceleration maxima in building structures subjected to strong earthquake motions. Chapter 4 reviews the floor acceleration response recorded in existing buildings during actual seismic events and evaluates the adequacy of the formulation developed in Chapter 3. Chapter 5 involves an analytical study of the acceleration response of rigid and flexible nonstructural components in buildings subjected to a suite of ground motions. Analytical models for multistory buildings are developed for determining linear and nonlinear horizontal

17 4 floor acceleration response along the building height. The summary and conclusions are presented in Chapter 6.

18 5 CHAPTER 2 2. REVIEW OF SEISMIC PROVISIONS IN BUILDING CODES ON NONSTRUCTURAL COMPONENTS 2.1. Introduction A review of the seismic provisions for nonstructural components contained in modern building codes is presented. It is limited to building codes that have governed the design and construction in the U.S. around the turn of the century (199s to present). It is not intended to provide a detailed historical background concerning the development and evolution of the most recent seismic design provisions for nonstructural components. Although the building code represents the minimum standards for satisfying the functional requirements of the building, the seismic provisions (code and commentary) aid designers in comprehending the expected response of the building under the design earthquake. The primary objective of this review is to identify the main parameters in the building code that affect the determination of the seismic forces for the design of nonstructural components at various floor elevations and for a variety of conditions. In the U.S., after the Earthquake Hazard Reduction Act of 1977, the executive branch of the federal government created the National Earthquake Hazards Reduction Program (NEHRP). One of the early goals of NEHRP was to promote the development of consistent provisions for seismic regulations to use throughout the U.S. This goal was accomplished with the publication in the year 2 of the first coordinated set of the International Building Code by the International Code Council (ICC, 2). The International Building Code was the product of unifying the three building codes that were widely adopted throughout the U.S. before the year 2: the Uniform Building Code (UBC 1997), the National Building Code published by the Building Officials and Code

19 6 Administration International (BOCA 1996), and the Standard Building Code (SBC 1996) published by the Southern Building Code Congress International. The advent of the International Building Code marked the termination of the UBC, BOCA, and SBC codes. The International Building Code adopts by reference the ASCE/SEI 7 standard. The primary sources for the seismic provisions in ASCE/SEI 7-1 evolved from the Earthquake Design Chapter in the UBC 1997 and from the 1997 version of the NEHRP Recommended Provisions for Seismic Regulations of New Buildings and Other Structures. This chapter presents a summary of the building code requirements for nonstructural components that are part of the Uniform Building Code (UBC, 1997), the Recommended Provisions for Seismic Regulations of New Buildings and Other Structures (NEHRP, 1997), and the Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-1, 21) UBC 1997 The Seismology Committee of the Structural Engineers Association of California (SEAOC, 1999) was the main contributor in the development of the seismic provisions for the UBC The UBC 1997 introduced new equations for the design of elements of structures, nonstructural components, and equipment supported by a structure, including their attachments, anchorages, and required bracing. The equations were calibrated to a strength design approach with a target force level of about 1.4 times the force levels used in previous UBC editions which were based on allowable stress design. For strength design applications, a load factor of applies to the design seismic force defined by = R (1 3 ) 2.1 = =.7 2.3

20 7 where, F p = design seismic force on a nonstructural component a p = component amplification factor, 2.5 for flexible components and for rigid components. If the component has a fundamental period greater than 6 s then the component is considered flexible, else rigid. C a = design peak ground acceleration I p = importance factor, 1.5 for essential and hazardous facilities, for all other structures R p = component response modification factor, 3. for components with ductile material or attachments, 1.5 for components with nonductile material or attachments h x = component attachment elevation with respect to base of structure h r = average roof height of structure W p = component weight 2.3. NEHRP 1997 The design seismic force for nonstructural components in NEHRP 1997 was also developed for strength design applications: = ( R ) ( 1 2 ) 2.4 = = 2.3

21 8 where, F p = design seismic force on a nonstructural component a p = component amplification factor, 2.5 for flexible components and for rigid components. If the component has a fundamental period greater than 6 s then the component is considered flexible, else rigid. S DS = design spectral acceleration at short periods, for 5% damping it is defined as 2.5 times the design peak ground acceleration I P = importance factor. For components in essential and hazardous facilities, for components required to function after an earthquake, and for storage racks open to general public, use 1.5. For all others, use. R p = component response modification factor, it predominantly varies between 1.25 and 3.5. For components with high deformability elements and attachments use 3.5; for components with limited deformability elements and attachments, use 2.5; for components with low deformability elements and attachments, use z = component attachment elevation with respect to base of structure h = average roof height of structure W p = component weight Except for minor changes in notation where C a in UBC 1997 is replaced with S DS in NEHRP 1997, and the term h x /h r is now z/h, Equation 2.1 deviates from Equation 2.4 in the coefficient that multiplies the relative elevation of the component attachment. In the UBC 1997 a coefficient of 3 is used instead of 2 in NEHRP Thus, in UBC 1997 the force induced at the roof is 4 times the force induced at the base whereas in NEHRP 1997 the force induced at the roof is 3 times the force induced at the base.

22 9 The coefficient defining the design force in NEHRP 1997 changed slightly due to rounding of.3 from.7 x = 8. The maximum design force in both UBC 1997 (Equation 2.2) and NEHRP 1997 (Equation 2.5) is limited to 4 times the peak ground acceleration ASCE/SEI 7-1 The latest version of ASCE/SEI 7, published in 21, uses the same equations as in NEHRP 1997, except that minor adjustments have been made in the range of values permitted for a p, I p, and R p. ASCE/SEI 7-1 introduced an exception to Equation 2.4: = ( R ) 2.7 where, a i = acceleration at level i obtained from modal response spectrum analysis a p = component amplification factor, 2.5 for flexible components and for rigid components. If the component has a fundamental period greater than 6 s then the component is considered flexible, else rigid. For certain types of components, a value of 1.25 applies. W p = component weight A x = torsional amplification factor applied to the accidental torsional moments. between and 3.. It varies I P = importance factor. Values of, 1.25, or 1.5 are assigned depending on the risk category of the building. R p = component response modification factor, it predominantly varies between 1.5 and 3.5. For components with high deformability elements and attachments use 3.5; for components with

23 1 limited deformability elements and attachments, use 2.5; for components with low deformability elements and attachments, use 1.5. These definitions of a p, I p, and R p also apply to Equation 2.4 included in ASCE/SEI 7-1. The upper and lower limits defined by Equation 2.5 and Equation 2.6 still apply whether Equation 2.4 or Equation 2.7 is used.

24 11 CHAPTER 3 3. FLOOR ACCELERATIONS IN MULTISTORY TEST STRUCTURES SUBJECTED TO EARTHQUAKE SIMULATIONS 3.1. Introduction To understand and expand upon the knowledge of the response of nonstructural components in multistory buildings, it is essential to first understand the individual floor responses in multistory buildings. Seismic motions on a multistory building generally produce a unique response on each floor above the ground level. This chapter develops an understanding of the individual above grade floor responses in test structures subjected to earthquake simulations. Further, this chapter attempts to expand upon the current code-based methods for determining floor accelerations in building structures. Records from several experimental studies conducted in the 197 s and 198 s at the University of Illinois, Urbana-Champaign campus, are used in this portion of the study. Each of the experimental models was a small-scale reinforced concrete structure. The small-scale test structures were designed to represent the performance of a full-sized structure. A total of 3 specimens, having 6 to 1 stories, are reviewed. Experimental data on the acceleration response of these test structures for a total of 74 earthquake simulations are studied in this chapter Description of Test Structures Considered The population of 3 small-scale multistory reinforced concrete test structures is 6- to 1-story high and is herein grouped into four categories depending on the structural system: coupled walls, frame-wall structures, frames with yielding beams, and frames with yielding columns. Table 3.1 identifies the test structures and the information sources for the experimental investigations considered.

25 12 The specimens were tested on the University of Illinois earthquake simulator. The facility was designed in 1967 and began testing structures in 1968 (Sozen et al., 1969; Sozen and Otani, 197). The simulator was designed to test small-scale structures in laboratory conditions. The facility subjects test structures to base motions in one horizontal direction. Figure 3.1 is a sketch of the facility with a 1-story specimen prepared on it for testing. The test structures were not designed after any particular full-sized multistory buildings. Instead, the small-scale structures were designed to represent analytical concepts. Each of the test structures were designed with a specific set of parameters in mind. They were designed to produce responses similar to a full-sized multistory structure but within the parameters and limitations of the testing facility. All of the test structures were designed as two or three frames working in parallel. Each frame was a multi-bay and multistory two dimensional structure. The frames were then connected together to equally share the story weights so that all the elements of the structure experience the same horizontal displacement at a given floor level. To simulate a fixed-based connection, the structures had heavy base supports that were bolted to the test platform. Reference to a floor level of a particular test structure corresponds to the sequential position of the beam centerlines above the base support. Level zero corresponds to the top of the base support. Most of the researchers involved in the original series of earthquake simulations completed their work in one of the four primary groups, see Table 3.1. The first group, whose test structures were representative of coupled-wall systems, includes Aristizabal (1976) with structures D1, D2, D3, and M1 and Lybas (1977) with structures D1, D2, D3, D4, and D5. The sketches of the structures of Aristizabal and Lybas may be found in Figure 3.2 and Figure 3.3. These figures include dimensional properties of each structure. The specimens tested by Aristizabal are all 1 stories tall while the structures from Lybas work are 6 stories tall. Each structure comprised two planar walls with a 25 by 178 mm (1 by 7 in.) cross section, connected at each floor level by beams spanning 11 mm (4 in.). The tests performed by Aristizabal and

26 13 Lybas considered two main variables, stiffness and strength of beams. Both researchers reported measured compressive concrete strength in each of their test structures between 29 MPa (4.2 ksi) and 4 Mpa (5.8 ksi). Aristizabal reported a tensile strength of reinforcement of 5 Mpa (73 ksi) while Lybas reported 29 Mpa (42 ksi). The second group of test structures, frame-wall systems, was tested by Abrams (1979) with structures FW1, FW2, FW3, and FW4, Moehle (198) with structures FSW, FHW, and FFW, and Wolfgram (1984) with structures NS1, NS2, and NS3. Abrams test structures, shown in Figure 3.6, comprised three planar elements: two frames and a wall working in parallel. The main experimental variable was the wall strength; structures FW1 and FW4 had heavier wall reinforcement than FW2 and FW3. The test structures by Abrams had measured concrete compressive strengths varying between 32 Mpa (4.6 ksi) and 42 Mpa (6.1 ksi) while the yield strength of the reinforcement varied between 34 Mpa (49 ksi) and 36 Mpa (52 ksi). Moehle (198) included a wall of varying height in each of the test structures, FSW, FHW, and FFW. These test structures are shown in Figure 3.8 combining two 9-story planar frames and a wall acting in parallel. The height of the wall in the test structures was the primary experimental parameter, extending up to one, four, or nine stories and included a case without walls (assigned to the third group of test structures). The geometry and reinforcement schedule of each frame were identical in FSW, FHW, and FFW. The concrete compressive strength of these test structures varied between 35 Mpa (5.1 ksi) and 37 Mpa (5.4 ksi). The yield strength of the reinforcement was 4 Mpa (58 ksi) in frame members and 34 Mpa (49 ksi) in walls. Wolfgram (1984) tested 7-story structures NS1, NS2, and NS3 (Figure 3.9). Each structure comprised two exterior frames and one interior frame with a wall in the center bay. The test structures were 1/1 th scale models of a full-scale test structure that was tested at the large-scale testing facility of the Building Research Institute (BRI) in Tsukuba, Japan. The main variable in these tests was the reinforcement in the wall of each test structure. Test structure NS1 had reinforcement equivalent to that of the full-scale BRI test structure. Test structures NS2 and NS3 each included additional reinforcement at the top of the beams to account for the

27 14 contribution of the slab built integrally with the beams in the full-scale BRI test structure. The compressive strength of the concrete used in these test structures is reported between 28 Mpa (4.1 ksi) and 32 Mpa (4.6 ksi). The yield strength of the reinforcement varied from 37 Mpa (54 ksi) to 42 Mpa (61 ksi). The third group of multistory test structures includes models tested by Otani (1972), Healey (1978), Moehle (1978), Cecen (1979), and Moehle (198). Each model combined two parallel planar frames. This group of test structures was characterized by having columns flexurally stronger than the beams. Only structures in excess of five stories are considered herein, Otani s 3-story structures are therefore omitted. The test structures of Healey (1978), MF1, shown in Figure 3.4, and Moehle (1978), MF2, shown in Figure 3.5, were aimed at testing an irregular story height at the first story of the 1-story structures. The first story of both test structures was taller than the typical story. Furthermore, Moehle (1978) included a discontinuous beam at the first story. Both structures were otherwise identical in geometry. Healey reported a concrete compressive strength of 4 Mpa (5.8 ksi) while Moehle (1978) reported a concrete compressive strength of 38 Mpa (5.5 ksi). Both test structures had reinforcement yield strengths of 36 Mpa (52 ksi). Cecen (1979) tested 1-story structures, H1 and H2, consisting of two parallel planar frames of uniform distribution of story heights (Figure 3.7). Cecen reported a concrete compressive strength between 28 Mpa (4.1 ksi) and 32 Mpa (4.6 ksi) and a reinforcement yield strength between 48 Mpa (7 ksi) and 5 Mpa (72 ksi). Test structure FNW, from Moehle (198), adopted a geometry similar to the frames tested by Cecen, except that FNW omitted the first-story beams resulting in a 9-story structure with a tall first story. Structures H1 and H2 (by Cecen), MF1 (by Healey), and FNW (by Moehle) used the same cross-sectional member dimensions and story weights. Moehle (198) reported a concrete compressive strength of 4 Mpa (5.8 ksi) and a reinforcement yield strength of 4 Mpa (58 ksi).

28 15 The fourth and last group, frames with yielding columns, includes structures SS1 and SS2, tested by Schultz (1985), structures Tower and Stepped, tested by Wood (1986), and structures ES1 and ES2, tested by Eberhard (1989). All models in this group consisted of two 9- story frames acting in parallel. In each of these test structures, the column strength was the main experimental variable. The frames were characterized by having beams flexurally stronger than the columns. In structures SS1 and SS2 (Figure 3.1), the reinforcement in the columns was varied, with SS2 having heavier reinforcement. Further, these two test structures had a first-story height approximately 1.4 times the typical story height of the structure. The measured concrete compressive strength for SS1 and SS2 was between 36 Mpa (5.2 ksi) and 39 Mpa (5.7 ksi). The measured reinforcement yield strength was 38 Mpa (55 ksi). Wood tested two structures of irregular geometry. Test structures Tower (Figure 3.11) and Stepped (Figure 3.12) were not geometrically consistent with the other studies in the series. Structure Tower was designed as a 7-story single-bay tower on a 2-story three-bay pedestal. Structure Stepped had an asymmetrical arrangement of a 3-story single-bay tower, a 3-story two-bay middle section, and a 3-story three-bay base. In both structures Tower and Stepped, the story weights were proportional to the number of bays. The concrete compressive strength of these two test structures was about 41 Mpa (6. ksi) and the reinforcement yield strength was 38 Mpa (55 ksi) in beams and 39 Mpa (57 ksi) in columns. Eberhard tested structures ES1 and ES2 (Figure 3.13). Both structures had identical geometry but different strengths. The main experimental variable in these studies was the column reinforcement. ES1 had columns with 5 to 1 percent more reinforcement than ES2. Eberhard reports the concrete compressive strength as varying between 3 Mpa (4.4 ksi) and 33 Mpa (4.8 ksi). The yield strength of the reinforcement was 38 Mpa (55 ksi) in columns and 4 Mpa (58 ksi) in beams. All of the test structures considered were designed in accordance to the substitutestructure method by Shibata (1976). A key design parameter in the substitute-structure method is the damage ratio, defined as the ratio of the cracked member stiffness (secant to yield in moment-rotation relationships) to the secant stiffness associated with the design

29 16 displacement. For each of the four structural groups identified in Table 3.1, different damage ratios were used for the design earthquake. In coupled walls, typical damage ratios were 1 for the wall piers and 2 for the coupling beams. In the frame-wall systems and frames with yielding beams, the damage ratios were typically 1 for the columns, 3 for the walls, and 6 for the beams. In frames with yielding columns, typical damage ratios were between 1 and 4 for the columns, and 1 for the beams. Generally, run 1 corresponds to the design earthquake for which the target mean drift ratio (roof displacement divided by roof height) was about 1% Earthquake Simulation Tests and Observed Acceleration Response The test structures were mounted on the platform of the University of Illinois earthquake simulator (Figure 3.1) and subjected to unidirectional base accelerations. The majority of the specimens were subjected to several earthquake simulations. The intensity of each simulation was generally increased in successive runs. The base motions were selected from accelerations recorded during actual seismic events and scaled to obtain a satisfactory relationship between the initial frequency of the test specimens and the frequency content of the base motion. In total, 74 earthquake simulations were considered (Table 3.2). The table identifies the base motions with the time-scale compression factors used. Also identified are the recorded peak ground accelerations and the measured mean drift ratios. The experimental data in Table 3.2 exclude cases where the mean drift ratio was outside the.5% to 2.5% range. These boundaries were set to ensure that the experimental data are representative of nonlinear responses and in line with the expected maximum response of structures designed using modern building codes. In some cases, the researchers included base motions derived from sinusoidal motions; these are not considered in this study. Throughout each test, the displacements and accelerations were recorded at all levels of the test structure. The measured floor accelerations for each of the 74 earthquake simulations are indicated in Table 3.3. These accelerations are shown in Figure 3.14 to Figure 3.17 normalized by the peak base acceleration and corresponding to the floor elevation normalized

30 17 by the structure height. The acceleration data are grouped according to four categories: coupled walls (Figure 3.14), frame-wall structures (Figure 3.15), frames with yielding beams (Figure 3.16), and frames with yielding columns (Figure 3.17). The horizontal axis in Figure 3.14 to Figure 3.17 represents the amplification of the floor acceleration with respect to the ground acceleration. From the plotted data the following general observations are made: Maximum amplification generally occurs in the upper floors; Amplifications are generally larger during Run 1; Of the four structural types, the frames with yielding beams generally experience the least amplification with values not exceeding 2; Of the four structural types, the frames with yielding columns generally experience the largest amplification with values as high as 5; A low-bound amplification of.5 may be assigned to all of the structural types considered. Figure 3.18 includes the measured acceleration data from all 3 structures during the 74 earthquake simulations. The figure includes two lines that seem to be a good representation of the extreme values. Both of these lines are invoked in the UBC 1997: the low bound of.5 corresponds to the minimum floor acceleration for diaphragm design and the upper bound, based on h i / h r, corresponds to the floor acceleration for the design of rigid nonstructural components. The ratio h i / h r represents the floor height at level I divided by the roof height. These bounds put forth a safe envelope to which response accelerations may be estimated. For comparison, Figure 3.18 also includes the line based on h i / h r from ASCE/SEI 7-1. The data shown in Figure 3.18 represent the recorded floor accelerations of the test structures during strong base motions inducing nonlinear response. In Table 3.2, note that the runs with the lowest mean drift ratio are.52% (Structure D1, Run 3, by Lybas). Mean drift ratios of.5% translate to story drift ratios (story displacement divided by story height) that

31 18 generally exceed.7%, a value in the vicinity of yielding for frame members (and coupling beams). The observation that the first runs generally show the largest floor acceleration amplifications (Figure 3.14 to Figure 3.17) and knowing that subsequent earthquake simulations had larger base accelerations, suggest that amplifications are reduced with the increased nonlinear response of the structure. As the base acceleration increases, the structure reaches yielding and limits the induced story forces and therefore the floor accelerations. To determine seismic demands in nonstructural components, modern seismic provisions do not explicitly account for a reduction in floor accelerations due to the nonlinear response of the main seismic force-resisting system. A simple way to consider the nonlinear response of the building is to incorporate the response modification coefficient, R, into the expressions that represent the floor accelerations. A value of R=1 represents linear response, and values greater than 1 characterize nonlinear response. Figure 3.18 shows that the UBC 1997 expression for determining floor accelerations in the design of nonstructural components represents an envelope for the experimental data considered herein: = ( 1 3 ) 3.1 where A i is the maximum acceleration of the floor i expressed as a function of the maximum acceleration of the ground, A g, also known as the peak ground acceleration (PGA). In this study, Equation 3.1 is modified to include the effects of nonlinear response of the seismic force-resisting system. The R factor is incorporated in Equation 3.1 to divide the term h i / h r : = ( 1 3 R ) 3.2

32 19 where R is derived from the response modification coefficient, R, adjusted to account for structural overstrength Estimates of Floor Accelerations in Structures Subjected to Strong Ground Motions The proposed equation (Equation 3.2) for determining maximum floor accelerations is tested using the measured response of the 3 small-scale multistory structures subjected to simulated ground motions described in Section 3.2. A typical test setup is shown in Figure 3.1. Figure 3.2 to Figure 3.13 show the structural dimensions and layout of each test specimen. A summary of earthquake simulations (runs), indicating the measured peak ground accelerations and maximum mean drift ratios, is shown in Table 3.2. The main variables involved in obtaining R for use in Equation 3.2 to determine floor accelerations are listed in Table 3.3. The calculated and measured accelerations correspond to the data obtained from 74 earthquake simulations. The data shown include runs that were strong enough to cause yielding. Cases where the mean drift ratio was outside the range between.5% and 2.5% were excluded. For the test structures, the calculations of the effective response modification coefficient, R, is based on how the R value is used in modern seismic provisions when determining the seismic coefficient, C s. The design base shear, V b, is defined in ASCE/SEI 7-1 as: = 3.3 where, W = the total weight of the structure, and = R R 3.4

33 2 where, S DS, S D1 = spectral acceleration coefficients (units of gravity), assigned to the assumed constantacceleration region (S DS ) and to the assumed constant-velocity region (S D1 ), for 5% damping; R = response modification coefficient; T eff = effective fundamental period of vibration using cracked section properties; represented by the term C u T a in ASCE/SEI 7-1. For the test structures, the value of C s is taken from the maximum measured base shear divided by the weight of the structure: = 3.5 Following Equation 3.4, the value of the effective response modification coefficient, R, is derived using: R = 3.6 where, = 3.7 and = 3.8 The spectral acceleration, A Tg, for a linear SDOF system with period T g and damping factor of 5% is obtained from: = ( 2 2 ) 3.9

34 21 where, D Tg = the spectral displacement for a linear SDOF system with period T g and 5% damping; T g = the characteristic period for ground motion. It may be taken as the largest period where a significant peak (within 8% of the maximum spectral acceleration) is reached (see Appendix A). The value of D Tg was obtained from the linear response spectrum calculated for the recorded base acceleration as reported by each of the sources listed in Table 3.1. Substituting Equations 3.7, 3.8, and 3.9 into Equation 3.6 gives: R = 3.1 Note that R essentially represents a demand-to-capacity ratio, where the demand is simply defined by the acceleration response of a SDOF system having a period of vibration of T eff and a damping factor of 5%. The capacity is given by the base shear strength, also expressed in terms of C s. R is not to be taken less than unity. Table 3.3 shows all of the values leading to R and calculated using Equation 3.1. The resulting R for all 74 runs range from 1.2 to 6.3, an indication that nonlinear response did occur in the earthquake simulations considered. The calculated values of R for the test structures are used to test the proposed Equation 3.2 for estimating the peak floor accelerations during nonlinear response when subjected to earthquake motions. Figure 3.19 to Figure 3.48 show the proposed Equation 3.2 compared with the measured data for each of the 74 equation simulations considered. Summary plots are shown in Figure 3.49 to Figure 3.52 according to the four structural types described in Table 3.1. These figures show that for the frame-wall structures and frames with yielding beams, the proposed equation represents a satisfactory upper bound, whereas for the coupled-walled systems and frames with yielding columns, Equation 3.2 is more representative of an average response.