Simulation of the Seismic Performance of

Nonstructural Systems

Alicia Echevarria University of Nevada

PI: E. “Manos” Maragakis Mentors: Arash E. Zaghi and Joe Wieser

9/9/2010

2

Table of Contents

1.0 Abstract 3 2.0 Introduction 3 2.1 The Grand Challenge Project 3 2.2 NEES REU Project 3 3.0 Buildings, Data, and Analysis Procedure 4 4.1 OpenSees Buildings 4 4.2 Northridge Buildings 5 4.3 Analysis Procedure 6 4.0 Analysis Plots 6 5.1 Spectral Acceleration 7 5.2 Spectral Amplification 7 5.3 Amplification Factor Vs. z/H Ratio 9 5.0 Equation Representation and Code Recommendations 10 6.1 ASCE7-05 Structural Design Spectrum 10 6.2 Amplification Factor 12 6.3 Spectral Amplification Design Spectrum 14 6.0 Conclusion and Further Studies 17 7.0 Acknowledgements 18 8.0 References 18 Appendix A: ATC 63 Tables 19 Appendix B: Design Example Using Code Recommendations 21

3

1.0 Abstract In this work a more refined procedure for the design of nonstructural components in steel moment frame buildings was proposed. The current design process for nonstructural components consists of an equation for the force demands on the nonstructural components. An integral piece to this equation is the acceleration amplification factor which is a function of the ratio of the height at which the nonstructural component is located in the building (z) divided by the total building height (H). While the current acceleration amplification factor equation: amp = (1+2(z/H)) offers a linear relationship for the acceleration amplification, this study shows that a linear representation is not the best possible demonstration of the data obtained from incremental dynamic analysis of four buildings in OpenSees. This research presents a refined amplification factor and the addition of a spectral amplification design spectrum for nonstructural components. The equations presented in this study were developed using acceleration records from ATC-63 and checked against actual acceleration data obtained from the 1994 Northridge Earthquake.

2.0 Introduction

2.1 The Grand Challenge Project While a structure may remain standing and appear to have no visible failure modes after an earthquake occurs, it is quite possible that there will be considerable damage to the internal nonstructural systems. When an earthquake occurs, the structure responds to the acceleration of the ground motion, and the nonstructural systems respond to the acceleration of the motion of the structure. The ground motion is amplified by the structure and the nonstructural systems can be damaged by a much smaller earthquake than would damage the building itself. The failure of the nonstructural systems has a pronounced effect on the overall performance of the building since it accounts for 79% of the total earthquake damage. One of the major nonstructural systems of buildings is the ceiling-piping-partition system which is the system of interest for the Grand Challenge project. The goal for this project is to study the resilience of buildings and their nonstructural components when subjected to seismic activity in order to provide engineers and architects with guidelines for the improvement of the seismic response of the ceiling-piping-partition nonstructural system (Maragakis, 2010). 2.2 NEES REU Project Current codes for seismic design provide a highly refined design procedure for structures themselves, but the design procedure for the nonstructural components of a building is quite immature. Research conducted by Chen and Soong from the University of Buffalo (1988) provided an in-depth look at the current engineering practice for secondary systems. The study reported on recent advances in the area of seismic engineering design and discussed future research. Two methods for engineering analysis and response calculations were discussed: 1. Floor response spectrum approach, and 2. Primary-secondary system approach. The Research Experience for Undergraduates (REU) project followed the floor response spectrum approach by analyzing floor acceleration response histories. The main objective of the REU project was to analyze and plot the data obtained from four analytical models subjected to Incremental Dynamic Analysis (IDA) in OpenSees and then compare the results to the current code outlining nonstructural component design in ASCE 7-05. The current design process for nonstructural components consists solely of an equation for the force demands on the nonstructural components. An integral piece to this equation is the acceleration amplification factor which is defined as the peak floor acceleration divided by the peak ground

4

acceleration. The current equation for the amplification factor is a linear function of the ratio of floor height to the total building height (z/H) (ASCE 7-05). However, this study showed that the actual relationship between the z/H ratio and acceleration amplification is not linear for the higher floors of taller buildings. The REU project presents a new bilinear equation for the acceleration amplification factor. In Seismic Response of Acceleration Sensitive Nonstrucutral Components Mounted on Moment-Resisting Frame Structures (2007), Sankaranarayanan evaluated and quantified the dependence of peak component accelerations at the location of the nonstructural component within the structure, the damping ratio of the component, and the properties of the supporting structure. This study presents a proposed design spectrum for spectral amplification which incorporates the amplification factor into the design process of nonstructural components. When applied in conjunction with the ASCE7-05 chapter 11 design spectrum, the spectral amplification design spectrum from this study will provide engineers with the design acceleration for nonstructural components at any floor height. The proposed equations for the amplification factor and the spectral amplification design spectrum were derived from the analysis of four steel moment frame buildings modeled with 21 far-field ground motions from the ATC-63 report and checked against field data from the 1994 Northridge Earthquake. All of the 1994 Northridge Earthquake information used was obtained from Naeim’s report (1995). 3.0 Buildings, Data, and Analysis Procedure

3.1 OpenSees Buildings Four steel moment frame buildings of different heights were modeled and subjected to incremental dynamic analysis in OpenSees for this study. Building A was a three story commercial building with an overall height of 39 feet and fundamental periods of 1.03 seconds in both the major and minor horizontal directions. Building B was redesigned to represent a three story hospital with an overall height of 52 feet and fundamental periods of 0.95 seconds in the major horizontal direction and 0.98 seconds in the minor horizontal direction. Building C was a nine story commercial building with an overall height of 122 feet. Its fundamental periods were 2.33 seconds in the major direction and 2.41 seconds in the minor direction. Lastly, Building D was a twenty story commercial building with an overall height of 265 feet. Its fundamental periods were 3.40 seconds and 3.86 seconds in the major and minor horizontal directions respectively. A visual representation of the buildings can be seen in Figure 1.

Figure 1. Four steel moment frame buildings used for incremental dynamic analysis in OpenSees

5

The peak ground acceleration and spectral acceleration values at ground level may vary significantly depending on site conditions. For the evaluation of peak ground acceleration values, the site characterization requires the study of a large amount of geological, seismological and geotechnical data (K.S. Vipin, 2009). The ground acceleration sets used in this study consisted of 21 far-field ground motions obtained from the ATC-63 record set found in the PEER-NGA database. These ground motions represent a large variety of locations and earthquake magnitudes. Figure 2 displays a table containing general information for each of the 21 events. Tables with more in depth information for the 21 events used in this study can be found in Appendix A.

ID Name Year Magnitude Name Owner1 Northridge 1994 6.7 Beverly Hills-Mulholland USC2 Northridge 1994 6.7 Canyon Country-WLC USC3 Duzce, Turkey 1999 7.1 Bolu ERD4 Hector Mine 1999 7.1 Hector SCSN5 Imperial Valley 1979 6.5 Delta UNAMUCSD6 Imperial Valley 1979 6.5 El Centro Array #11 USGS7 Kobe, Japan 1995 6.9 Nishi-Akashi CUE8 Kobe, Japan 1995 6.9 Shin-Osaka CUE9 Kocaeli, Turkey 1999 7.5 Duzce ERD10 Kocaeli, Turkey 1999 7.5 Arcelik KOERI11 Landers 1992 7.3 Yermo Fire Station CDMG12 Landers 1992 7.3 Coolwater SCE13 Loma Prieta 1989 6.9 Capitola CDMG14 Loma Prieta 1989 6.9 Gilroy Array #3 CDMG15 Manjil 1990 7.4 Abbar BHRC16 Superstition Hills 1987 6.5 El Centro Imp. Co. CDMG17 Cape Mendocino 1992 7 Rio Dell Overpass CDMG18 Chi-Chi, Taiwan 1999 7.6 CHY101 CWB19 Chi-Chi, Taiwan 1999 7.6 TCU045 CWB20 San Fernando 1971 6.6 LA-Hollywood CDMG21 Friuli 1976 6.5 Tolmezzo --

Earthquake Recording Station

Figure 2. General information for the 21 ground acceleration sets used for the OpenSees incremental

dynamic analysis.

3.2 Northridge Buildings

Upon completion of the incremental dynamic analysis of the four steel moment frame buildings in OpenSees, the results were then compared to similar results from the analysis of field data from the 1994 Northridge Earthquake. The information for the buildings and acceleration data from the Northridge earthquake were obtained from Naeim’s report (1995). The report contained information on nineteen different buildings with a wide variety of framing systems. Some buildings had steel moment frames, concrete moment frames, and others with shear walls. For the purposes of this study, six of the Northridge buildings were selected for direct comparison based on their framing systems. An additional 54-story sky scraper with a steel moment frame was compared to see if this study’s results could accommodate high rise buildings. Since only two of the buildings from Naeim’s report consisted entirely of steel moment frames, other framing systems were used in the comparison with the four buildings from OpenSees. The first building used for comparison was a six story commercial office building located in Burbank, CA. This building had a steel moment frame and fundamental periods of 1.28 seconds in both horizontal directions. A three

6

story commercial office building from Los Angeles was also chosen for comparison. This building had a steel braced frame. This building has a fundamental period of 0.51 seconds in the major horizontal direction, and a fundamental period of 0.55 seconds in the minor direction. A seven story math and science building from the UCLA campus was also chosen for comparison. This building was treated as a four story building due to the uniqueness of its framing; its bottom floors consist of concrete shear walls while its higher floors are steel moment frames. The analysis of this building showed that the shear walls are very rigid and provide no acceleration amplification from the ground and, the stories enclosed by shear walls were neglected. The fundamental periods of this UCLA building were 0.66 seconds and 1.02 seconds in the major and minor directions respectively. A thirteen story commercial building in Sherman Oaks and a twenty story hotel in North Hollywood with concrete moment frames also proved to be good buildings for comparison. The thirteen story Sherman Oaks building has fundamental periods of 2.6 seconds and 2.9 seconds, while the twenty story hotel in North Hollywood has fundamental periods of 2.20 seconds and 2.50 seconds. The incremental dynamic analysis from OpenSees included intensities that would result in the yielding of a structure. A seven story hotel from Van Nuys experienced large amounts of damage in the Northridge earthquake and was used to check the results obtained from yielding in the OpenSees models. The initial fundamental period of this building in the major direction was 1.4 seconds. After yielding, this was extended to 2.2 seconds. Additionally in the minor direction, the fundamental period was extended from 1.3 seconds to 1.8 seconds. 3.3 Analysis Procedure Each of the 21 ground acceleration sets taken from ATC-63 was run at various intensities for each of the four buildings modeled in OpenSees. This produced between from 200 and 300 acceleration data sets which were then categorized into four performance levels. Runs causing a maximum interstory drift of less than 0.7% in the building were placed in Performance Level 1 (Immediate Occupancy). Runs producing a maximum interstory drift between 0.7% and 2.5% in the building were placed in Performance Level 2 (Life Safety). Runs causing a maximum interstory drift of 2.5%-5% in the building were placed in Performance Level 3 (Collapse Prevention), and runs producing a maximum interstory drift greater than 5% were placed in Performance Level 4 (Collapse). After all of the acceleration data sets were placed into their corresponding performance levels, they were run through various Matlab scripts to produce data structures containing information such as: peak ground accelerations, peak floor accelerations, peak velocities, spectral accelerations, spectral amplifications, and amplifications by floor height. Everything from these data structures was then imported into Microsoft Excel where analysis plots were constructed. These plots led to the development of equation representations for amplification factor and a spectral amplification design spectrum. The equation representations led to code recommendations which were then checked against the analysis of buildings from the 1994 Northridge Earthquake. 4.0 Analysis Plots

The design equations developed from this study were based on the 85th percentile of all of the data and correspond to Performance Level 2. Therefore, the plots shown in the body of this report will correspond to the same data set. Although studies were conducted in both the major and minor horizontal directions, all of the plots shown in the main body of this report correspond to the major direction. Additional plots with significant information can be found in Appendix B.

7

4.1 Spectral Acceleration

Spectral acceleration is defined as the acceleration a building would experience if it were oscillating with a particular period. Thus, acceleration in terms of gravity is plotted on the y-axis, and period is plotted on the x-axis. Spectral acceleration data is obtained by assuming the building acts as a single degree-of-freedom system modeled as a particle on the end of a massless vertical rod. In this study, spectral accelerations for every run from the OpenSees incremental dynamic analysis were plotted for each floor of each building and also plotted by performance level. Figures 3-4 show examples of the spectral acceleration plots created from the Matlab data in Excel.

Figure 3. Spectral acceleration data obtained for events occurring in Performance Level 4 on Floor 3 of Building A

Figure 4. 85th Percentile Spectral Acceleration Performance Level Comparison for Floor 3 of Building A

4.2 Spectral Amplification

The spectral amplification plots for this study were obtained by taking the spectral acceleration of each floor and dividing it by the spectral acceleration of the ground. Examples of these plots can be seen in Figures 5-6. The spectral amplification plots expose the period at which the ground’s acceleration is

0.00

5.00

10.00

15.00

20.00

25.00

30.00

0.0 1.0 2.0 3.0 4.0

Spec

tral

Acc

eler

atio

n [S

a] (g

)

Period [T] (sec)

Events Mean Mean +/- STD

0.002.004.006.008.00

10.0012.0014.00

0.0 1.0 2.0 3.0 4.0

Spec

tral

Acc

eler

atio

n [S

a] (g

)

Period [T] (sec)PL1 PL2 PL3 PL4

8

amplified the most. As expected, the period experiencing the greatest amplification is the fundamental period of the building to which the plot corresponds. To better display this peak in amplification at each building’s fundamental period, additional spectral amplification plots were made by normalizing the period on the x-axis. To accomplish this, the values on the x-axis now were divided by the fundamental period of the building (T/T1). If the peak amplification does indeed occur at the fundamental period of the building, this peak should now occur when T/T1 = 1.0. Examples of spectral amplification plotted against normalized period can be seen in Figures 7-8.

Figure 5. 85th percentile Spectral Amplification for events in Performance Level 2 for Building A

Figure 6. 85th percentile Spectral Amplification for events in Performance Level 2 for Building D

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 1.0 2.0 3.0 4.0 5.0

Spec

tral

Am

plifi

catio

n [S

A,F

loor

/SA

,Gro

und]

Period [T] (sec)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 2.0 4.0 6.0 8.0

Spec

tral

Am

plifi

catio

n [S

A,F

loor

/SA

,Gro

und]

Period [T] (sec)

9

Figure 7. 85th percentile Spectral Amplification vs. Normalized Period for events in Performance Level 2 for Building A

Figure 8. 85th percentile Spectral Amplification vs. Normalized Period for events in Performance Level 2 for

Building D

4.3 Amplification Factor Vs. z/H Ratio Amplification factor is defined as the peak floor acceleration divided by the peak ground acceleration (PFA/PGA). This amplification factor was an area of emphasis for this study because it is used in current code design specifications. The amplification factor was plotted against the z/H ratio to show how the peak ground acceleration is amplified as floor height increases. Amplification plots were made for all four performance levels to show that amplification of the peak ground acceleration decreases as the building yields. These plots depicting the amplification obtained from the OpenSees incremental dynamic analysis are shown in Figures 9-10. Also shown in Figures 9-10 is a bold line representing the current code equation for amplification factor, AMP = 1 + 2 �z

H�. Even though the same equation is used

in the code for buildings of all heights, the two plots expose the significant difference in peak ground acceleration amplification between shorter buildings and taller buildings.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0

Spec

tral

Am

plifi

catio

n [S

A,F

loor

/SA

,Gro

und]

Normalized Period [T/T1]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0

Spec

tral

Am

plifi

catio

n [S

A,F

loor

/SA

,Gro

und]

Normalized Period [T/T1]

10

Figure 9. 85th Percentile for Amplification Factor for all performance levels of Building B

Figure 10. 85th Percentile for Amplification Factor for all performance levels of Building C

5.0 Equation Representation and Code Recommendations

5.1 ASCE7-05 Structural Design Spectrum The building design response spectrum used in this study was constructed following the procedure from chapter 11 of ASCE7-05. Figure 11 shows the most general form of the design response spectrum.

0.00.10.20.30.40.50.60.70.80.91.0

1.0 1.5 2.0 2.5 3.0

Floo

r H

eigh

t/Tot

al B

uild

ing

Hei

ght

[Z/h

]

85% Amplification Factor

PL1 PL2 PL3 PL4 CODE

0.00.10.20.30.40.50.60.70.80.91.0

1.0 1.5 2.0 2.5 3.0

Floo

r H

eigh

t/Tot

al B

uild

ing

Hei

ght

[Z/h

]

85% Amplification Factor

PL1 PL2 PL3 PL4 CODE

11

Figure 11. Design Response Spectrum from ASCE 7-05 Chapter 11

where: SDS = (2/3)SMS Eqn. 1 SD1 = (2/3)SM1 Eqn. 2 T0 = 0.2(SD1/SDS) Eqn. 3 TS = (SD1/SDS) Eqn. 4 For this study mean seismicity parameters for California and were used in the development of the design response spectrum shown in Figure 12. The mean seismicity parameters for California to be used in Eqn. 1 and Eqn.2 were 1.508 and 0.75 for SMS and SM1, respectively:

Figure 12. Design Response Spectrum and MCE Response Spectrum for mean seismicity parameters of California

The design response spectrum from Figure 12 was then plotted in comparison with the mean spectral acceleration for Performance Levels 1, 2, and 3 of Building A. This plot showed that the design response spectrum for structures corresponds to Performance Level 2 (Life Safety) which is the performance level used for the development of the equations and code recommendations in this study. The design response

0.000.200.400.600.801.001.201.401.60

0.0 0.5 1.0 1.5 2.0 2.5Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

Period (s)

MCE Response Spectrum Design Response Spectrum

12

spectrum from ASCE 7-05 superimposed on the spectral accelerations of Building A can be seen in Figure 13.

Figure 13. Design Response Spectrum and MCE Response Spectrum from ASCE 7-05 plotted with mean spectral

accelerations for Performance Levels 1, 2, and 3 for Building A 5.2 Amplification Factor The current code equation for the designing nonstructural components incorporates a factor accounting for the amplification of the peak ground acceleration throughout the height of the structure. The current equation for this amplification factor is represented by the Eqn 5. 𝐴𝐴𝐴𝐴𝐴𝐴 = 1 + 2 ∗ (𝑧𝑧

𝐻𝐻) Eqn. 5

where: H = total height of the building measured in ft z/H = the ratio of the story height to the total building height Analytical results have shown that the current equation is a conservative estimate in the general shape of the analytical data for short buildings. However for taller buildings, the data showed that this linear relationship is no longer a good estimate for the amplification factor. To better represent the analytical results found this study, a new equation to determine the amplification factor was proposed. This new equation was a bilinear representation of the amplification of the peak ground acceleration as story height increases. The slope of the line at the lower floor levels is a function of total building height and becomes constant at a maximum amplification as story height becomes large. The linear relationship for the lower levels of the buildings is a function of overall building height as wells as the z/H ratio for the design. Every building has a maximum amplification factor based on overall building height which was implemented for the second line of the bilinear equation. Equations 6-8 were used to develop the new amplification factor.

0

0.5

1

1.5

2

2.5

3

0.0 0.5 1.0 1.5 2.0

Acc

eler

atio

n (g

)

Period (s)

PL 1 PL2PL3 MCE Response SpectrumDesign Response Spectrum

13

AMP = PFAPGA

= 1 + 𝛼𝛼 𝑧𝑧𝐻𝐻

≤ 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 Eqn. 6 where: 𝛼𝛼 = 0.01𝐻𝐻 + 1.6 Eqn. 7 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 = 1 + 𝛼𝛼 60

𝐻𝐻 Eqn. 8

Figures 14-17 show the results obtained for the acceleration amplification factor from the incremental dynamic analysis in OpenSees. Each of these plots also display a line depicting the current code equation in addition to the new bilinear proposal.

Figure 14. Proposed Acceleration Amplification Factor Fit to Building A

Figure 15. Proposed Acceleration Amplification Factor Fit to Building B

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Hei

ght R

atio

[z/H

]

Amplification Factor [PFA/PGA]

X-Dir Y-Dir Fit Code

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Hei

ght R

atio

[z/H

]

Amplification Factor [PFA/PGA]

X-Dir Y-Dir Fit Code

14

Figure 16. Proposed Acceleration Amplification Factor Fit to Building C

Figure 17. Proposed Acceleration Amplification Factor Fit to Building D

5.3 Spectral Amplification Design Spectrum This study proposed a spectral amplification design spectrum that will provide the spectral amplification experienced at the floor height for which a nonstructural component is to be installed. This new spectral amplification design spectrum will use the amplification factor obtained from Equations 6-8 (presented in section 6.2) and will provide a better design estimate for the acceleration the nonstructural component is expected to experience. After determining the amplification factor following the procedure in section 6.2, the following procedure outlined by Equations 9-14 were used to determine the spectral amplification (SAmp) for all of the model buildings. Figures 18-21 display the spectral amplification design spectrums for all of the floors for the four buildings. The lines in the plots represent all the floors in ascending order starting with the 2nd floor at the bottom and ending with the roof being represented by the top line. Figures 22-23 show the spectral amplification and spectral amplification design spectrums for two buildings from the Northridge earthquake.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Hei

ght R

atio

[z/H

]

Amplification Factor [PFA/PGA]

X-Dir Y-Dir Fit Code

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Hei

ght R

atio

[z/H

]

Amplification Factor [PFA/PGA]

X-Dir Y-Dir Fit Code

15

𝐹𝐹𝐹𝐹𝐹𝐹 𝑇𝑇

𝑇𝑇1≤ 0.2:

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 Eqn. 9 𝐹𝐹𝐹𝐹𝐹𝐹 0.9 ≤ 𝑇𝑇

𝑇𝑇1≤ 1.1:

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝛽𝛽 × 𝐴𝐴𝐴𝐴𝐴𝐴 Eqn. 10 𝐹𝐹𝐹𝐹𝐹𝐹 𝑇𝑇

𝑇𝑇1≥ 2.25:

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 Eqn. 11 where: 𝛽𝛽 = 𝑧𝑧

𝐻𝐻+ 𝑇𝑇1

2𝑧𝑧𝐻𝐻

+ 1 Eqn. 12 Slope of the line connecting the points (0.2, AMP) and (0.9, βAMP): (𝛽𝛽−1)×𝐴𝐴𝐴𝐴𝐴𝐴

0.7 Eqn. 13

Slope of the line connecting the points (1.1, βAMP) and (2.25, AMP): (1−𝛽𝛽)×𝐴𝐴𝐴𝐴𝐴𝐴

1.15 Eqn. 14

Figure 18. Spectral Amplification Design Spectrum for Building A

0.01.02.03.04.05.06.07.08.0

0.0 0.5 1.0 1.5 2.0

S Am

p[S a

,Flo

or/S

a,G

roun

d]

Normalized Period [T/T1]

16

Figure 19. Spectral Amplification Design Spectrum for Building B

Figure 20. Spectral Amplification Design Spectrum for Building C

Figure 21. Spectral Amplification Design Spectrum for Building D

0.01.02.03.04.05.06.07.08.09.0

0.0 0.5 1.0 1.5 2.0

S Am

p[S a

,Flo

or/S

a,G

roun

d]

Normalized Period [T/T1]

0.01.02.03.04.05.06.07.08.09.0

0.0 0.5 1.0 1.5 2.0

S Am

p [S

a,Fl

oor

/ Sa,

Gro

und]

Normalized Period [T/T1]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.5 1.0 1.5 2.0

S Am

p [S

a,Fl

oor

/ Sa,

Gro

und]

Normalized Period [T/T1]

17

Figure 22. Design Amplification Spectrum for a 3-Story Los Angeles Commercial Building from the 1994

Northridge Earthquake with H = 50 ft and T1 = 0.55 sec

Figure 23. Design Amplification Spectrum for a 13-Story Commercial Building in Sherman Oaks from the 1994

Northridge Earthquake with H = 164 ft and T1 = 2.6 sec 6.0 Conclusion and Further Studies

Sufficient evidence was presented to justify a need for revision of the current code. The amplification factor equation used in the design for nonstructural components should be adjusted. An equation that can be used as a representation for all buildings would be more practical than the current linear relationship which is sufficient only for short buildings. The bilinear representation presented in this paper provides great improvement, yet it further improvements could still be made. The proposal for a spectral amplification design spectrum should also be considered as a revision to current code for nonstructural design.

Although some different framing systems from the 1994 Northridge Earthquake were used for comparisons, the scope of this study was restricted to steel moment frames. It is recommended that future

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0

S Am

p[S

a, F

loor

/Sa,

Gro

und]

Normalized Period [T/T1]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.5 1.0 1.5 2.0

S Am

p[S

a,Fl

oor/S

a,G

roun

d]

Normalized Period [T/T1]

18

studies include many types of frames including but not limited to: steel braced frames, concrete moment frames, and shear walls. This study was also limited to the two principal horizontal motions, so further research may include vertical motion along with possible rotational motions.

For further information on NEESR-GC Simulation of the Seismic Performance of Nonstructural Systems, contact Joe Wieser at the University of Nevada, email: wieser85@gmail.com 7.0 Acknowledgements

Special thanks to Dr. Maragakis, Dr. Itani, and Dr. Pekcan for their guidance on the Grand Challenge project. The mentorship provided by Joe Wieser and Arash Zaghi was also greatly appreciated. In addition, I would like to thank Kelly Lyttle for coordinating the REU program at UNR.

The NEES@UNR equipment site is funded in part by the Geoge E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Program of the National Earthquake Hazards Reduction Program (NEHRP) of the National Science Foundation (NSF) under Award Number CMS-0086624. 8.0 References American Society of Civil Engineers (2005). ASCE 7-05 - Minimum Design Loads for Buildings and Other Structures. ASCE.

K.S. Vipin, P. A. (2009). Estimation of peak ground accleration and spectral acceleration for South India with local site effects: probabilistic approach. Natural Hazards and Earth System Sciences , 865-878.

Manos Maragakis, P. (2010). Simulation of the Seismic Performance of Nonstrucutral Systems., (pp. 1-35). Buffalo, NY.

Ragunath Sankaranarayanan, P. D. (2007). Seismic Response of Acceleration-Sensitive Nonstrucutral Components Mounted on Moment-Resisting Frame Structures. College Park, Maryland: University of Maryland, College Park.

Yongqi Chen, T. S. (1988). Seismic Response of Secondary Systems. Engineering Structures 10 (4) , 218-228.

19

Appendix A: ATC 63 Tables

1 D 356 Thrust 13.3 17.2 17.2 9.42 D 309 Thrust 26.5 12.4 12.4 11.43 D 326 Strike-Slip 41.3 12 12.4 124 C 685 Strike-Slip 26.5 11.7 12 10.45 D 275 Strike-Slip 33.7 22 22.5 226 D 196 Strike-Slip 29.4 12.5 13.5 12.57 C 609 Strike-Slip 8.7 7.1 25.2 7.18 D 256 Strike-Slip 46 19.2 28.54 19.19 D 276 Strike-Slip 98.2 15.4 15.4 13.610 C 523 Strike-Slip 53.7 13.5 13.5 10.611 D 354 Strike-Slip 86 23.6 23.8 23.612 D 271 Strike-Slip 82.1 19.7 20 19.713 C 289 Strike-Slip 9.8 15.2 35.5 8.714 D 350 Strike-Slip 31.4 12.8 12.8 12.215 C 724 Strike-Slip 40.4 12.6 13 12.616 D 192 Strike-Slip 35.8 18.2 18.5 18.217 D 312 Thrust 22.7 14.3 14.3 7.918 D 259 Thrust 32 10 15.5 1019 C 705 Thrust 77.5 26 26.8 2620 D 316 Thrust 39.5 22.8 25.9 22.821 C 425 Thrust 20.2 15.8 15.8 15

Min 192 8.7 7.1 12 7.1Max 724 98.2 26 35.5 26Avg. 381 40.7 15.90476 18.78762 14.51429

X X

Site DataSource TypeID NEHRP

ClassVs 30 (m/s) Joyner

Boone

Site-Source Distance (km)

Epicentral Closest Plane

Campbell

Figure 24. Site information for ATC-63 Ground Motions.

Component 1 Component 21 953 0.25 NORTHR/MUL009 NORTHR/MUL279 NORTHR\MUL-UP

2 960 0.13 NORTHR/LOS000 NORTHR/LOS270 NORTHR\LOS-UP

3 1602 0.06 DUZCE/BOL000 DUZCE/BOL090 DUZCE\BOL-UP

4 1787 0.04 HECTOR/HEC000 HECTOR/HEC090 HECTOR\HECVER

5 169 0.06 IMPVALL/H-DLT262 IMPVALL/H-DLT352IMPVALL\H-DLTDWN

6 174 0.25 IMPVALL/H-E11140 IMPVALL/H-E11230 IMPVALL\H-E11-UP

7 1111 0.13 KOBE/NIS000 KOBE/NIS090 KOBE\NIS-UP

8 1116 0.13 KOBE/SHI000 KOBE/SHI090 KOBE\SHI-UP

9 1158 0.24 KOCAELI/DZC180 KOCAELI/DZC270 KOCAELI\DZC-UP

10 1148 0.09 KOCAELI/ARC000 KOCAELI/ARC090 KOCAELI\ARCDWN

11 900 0.07 LANDERS/YER270 LANDERS/YER360 LANDERS\YER-UP

12 848 0.13 LANDERS/CLW-LN LANDERS/CLW-TR LANDERS\CLW-UP

13 752 0.13 LOMAP/CAP000 LOMAP/CAP090 LOMAP\CAP-UP

14 767 0.13 LOMAP/G03000 LOMAP/G03090 LOMAP\G03-UP

15 1633 0.13 MANJIL/ABBAR--L MANJIL/ABBAR--T MANJIL\ABBAR--V

16 721 0.13 SUPERST/B-ICC000 SUPERST/B-ICC090 SUPERST\B-ICC-UP

17 829 0.07 CAPEMEND/RIO270 CAPEMEND/RIO360 CAPEMEND\RIO-UP

18 1244 0.05 CHICHI/CHY101-E CHICHI/CHY101-N CHICHI\CHY101-V

19 1485 0.05 CHICHI/TCU045-E CHICHI/TCU045-N CHICHI\TCU045-V

20 68 0.25 SFERN/PEL090 SFERN/PEL180 SFERN\PEL-UP

21 125 0.13 FRIULI/A-TMZ000 FRIULI/A-TMZ270 FRIULI\A-TMZ-UP

File Names-Horizontal File Names-Vertical

PEER-NGA Record InformationLowest

Freq (Hz)ID Record Seq. No.

Figure 25. Acceleration Record Information for ATC-63 Ground Motions

20

1 0.5165 62.7695 4.673 30.00 9.742 0.4820 44.9105 2.052 20.00 9.353 0.8224 62.1012 3.868 55.90 13.814 0.3368 41.7434 1.939 45.31 14.125 0.3511 33.0033 3.418 99.92 63.906 0.3796 42.1446 4.069 39.04 16.827 0.5093 37.2881 3.483 40.96 12.218 0.2432 37.7950 0.859 40.96 16.559 0.3579 58.8529 2.763 27.19 14.4810 0.2188 39.5687 0.601 30.00 13.2911 0.2448 51.4082 0.480 44.00 25.4812 0.4169 42.3347 9.027 27.97 17.3413 0.5285 35.0142 9.161 39.96 13.9514 0.5550 44.6650 4.337 35.95 13.2715 0.5146 52.0893 3.960 53.52 33.4616 0.3579 46.3598 2.208 40.00 22.5217 0.5489 43.8051 1.294 36.00 18.8818 0.4401 115.0360 6.229 90.00 30.4119 0.5120 39.0747 2.900 90.00 11.7720 0.2099 18.8738 0.676 28.00 12.2921 0.3513 30.7968 2.489 36.35 6.62

Min 0.2099 18.8738 0.480 20.00 6.62Max 0.8224 115.0360 9.161 99.92 63.90Avg. 0.4237 46.6493 3.356 45.29 18.58

Shortened Duration (s)

PGV (cm/s)

Arias Intensity (m/s)

Recorded Duration (s)ID PGA (g)

Figure 26. Analysis results for peak ground acceleration, peak ground velocity, and arias intensity for the far-field ground motions used for incremental dynamic analysis

21

Appendix B: Design Example Using Code Recommendations This example design is for nonstructural components that will be installed in a building with a total height of 180 feet and a fundamental period of 2.75 seconds. This example shows the steps for two different floor heights, one corresponding to a z/H ratio of 0.25 and one corresponding to a z/H ratio of 0.75. The design response spectrum is obtained following the procedure from ASCE 7-05. In this case, the response spectrum corresponds for the San Jose area and Site Class C. SMS = 2.0 SM1 = 0.87 SDS = (2/3)SMS SD1 = (2/3)SM1 T0 = 0.2(SD1/SDS) TS = (SD1/SDS)

B.1 Amplification Factor

AMP =PFAPGA

= 1 + 𝛼𝛼𝑧𝑧𝐻𝐻

≤ 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 Where:

𝛼𝛼 = 0.01𝐻𝐻 + 1.6

𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 = 1 + 𝛼𝛼60𝐻𝐻

B.2 Calculations

𝛼𝛼 = 0.01(180) + 1.6 = 3.4

𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 = 1 + (3.4)60

180= 2.133

AMP0.25 = 1 + 3.4(0.25) ≤ 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚

AMP0.25 = 1.85

0.00

0.50

1.00

1.50

2.00

2.50

0.0 1.0 2.0 3.0 4.0Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

Period (s)

MCE Spectral Accel. Design Spectral Accel.

22

AMP0.75 = 1 + 3.4(0.75) ≤ 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚

AMP0.75 = 2.133 B.3 Spectral Amplification Design Spectrum

Calculations for z/H = 0.25

β = 0.25 +2.75

2∗ 0.25 + 1 = 1.594

𝑇𝑇𝑇𝑇1

< 0.2

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 = 1.85

0.9 <𝑇𝑇𝑇𝑇1

< 1.1

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝛽𝛽𝐴𝐴𝐴𝐴𝐴𝐴 = 2.95

𝑇𝑇𝑇𝑇1

> 2.25

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 = 1.85

Calculations for z/H = 0.75

β = 0.75 +2.75

2∗ 0.75 + 1 = 2.781

𝑇𝑇𝑇𝑇1

< 0.2

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 = 2.133

0.9 <𝑇𝑇𝑇𝑇1

< 1.1

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝛽𝛽𝐴𝐴𝐴𝐴𝐴𝐴 = 5.93

𝑇𝑇𝑇𝑇1

> 2.25

𝑆𝑆𝐴𝐴𝑚𝑚𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴 = 2.133

The new acceleration design spectrum is obtained by multiplying the spectral amplification design spectrum by the fundamental period of the design building and then by the design spectrum from ASCE 7-05 Chapter 11.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0

S Am

p[S a

,Flo

or/S

a,G

roun

d]

Normalized Period [T/T1]

23

For full spectral amplification design spectrum procedure refer to text section 6.3.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.0 1.0 2.0 3.0 4.0

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

Period (s)

New Design Spectrum For z/H=0.75New Design Spectrum For z/H=0.25