IMPACT OF THE 1994 NORTHRIDGE EARTHQUAKE ON THE ART AND PRACTICE OF STRUCTURAL ENGINEERING

IMPACT OF THE 1994 NORTHRIDGE EARTHQUAKE ON THE ART AND PRACTICE OF STRUCTURAL ENGINEERING Farzad Naeim, Ph.D., S.E., Esq. Vice President / General Co...
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IMPACT OF THE 1994 NORTHRIDGE EARTHQUAKE ON THE ART AND PRACTICE OF STRUCTURAL ENGINEERING Farzad Naeim, Ph.D., S.E., Esq. Vice President / General Counsel John A. Martin & Associates, Inc., Los Angeles, California

Abstract The 1994 Northridge earthquake has impacted structural engineering practice in several very important ways. Since then we have learned to avoid unjustified extrapolations, we have recognized to value and promote seismic instrumentation, we have improved our codes and guidelines and at the same time created a maze of various codes and standards which are confusing at best, and we have started our long journey along the road of performance based seismic engineering. This paper provides an overview of the impacts of the 1994 Northridge earthquake on the art and practice of structural engineering. Introduction The January 17, 1994 Northridge earthquake affected the art and practice of structural engineering probably more than any other earthquake in the recent history of our profession. It is true that the 1933 Long Beach earthquake resulted in the Field’s act and more stringent design of school buildings. It is also true that the 1971 San Fernando earthquake fundamentally changed our approach to design of reinforced concrete structures. No single earthquake, however, like the 1994 Northridge earthquake caused an overall and widespread reevaluation of engineering practices so deeply rooted in the structural engineering community for decades. This paper provides an overview of the most significant changes in philosophy and practice of structural engineering caused by this earthquake such as: • • • • • • • •

understanding the dire consequences of unjustified extrapolations; significant improvements in our knowledge of design characteristics of strong ground motions; the limits of our understanding of ultimate behavior of structures; the value of seismic instrumentation and its widespread use; insufficiency of design practice targeted only to life-safety and collapse prevention; the significant role of nonstructural components in post-earthquake functionality of a building; development and application of performance-based design methodologies; and significant changes and additions to building codes and standards

These changes and their consequences on structural engineering practice are described through the use of some examples. The topics which are described in more detail in other papers presented in this conference are lightly touched on while others are described in more detail.

The Dire Consequences of Unjustified Extrapolations Prior to the 1994 Northridge earthquake, welded steel moment resistant frames (WSMRF) were considered the most reliable and sought after structural systems for earthquake-resistant construction. The magic ingredient was full-penetration welding of beam flanges to columns. In fact, this was the only prequalification required by the code (ICBO 1991, 1994) at the time needed to make this system perform its magic. Along the way it was forgotten that this universal conclusion was based on a limited number of laboratory tests, a limited number of beam and column sizes of certain steel material, limited types of welding electrodes, and particular types of welding practice. The poor performance of many WSMRFs during the Northridge earthquake opened our eyes not only to the specific problem of WSMRFs --for which solutions were found after several years of intense research- but to the inherent dangers of forgetting the valid bounds of experimental research and getting comfortable with solutions that we are used to without rethinking the limitations that could be involved in such applications. After Northridge earthquake testing and validation is more widely required for a variety of systems and components, from anchorage systems to material strength and connection systems across the wide spectrum of materials and systems utilized in structural engineering practice. Design Characteristics of Earthquake Ground Motions The near-fault large velocity pulses and forward and backward directivity effects were recognized as early as 1966 and clearly demonstrated by earthquake records obtained from the 1978 Tabas, 1979 Imperial Valley and 1992 Landers earthquakes. It was, however, the 1994 Northridge earthquake that focused the attention of structural engineers and code writers on detailed aspects of earthquake ground motions. The near-fault effects were codified by adaptation of near-fault factors in 1997 UBC (ICBO 1997) and had a profound impact on structural design of buildings located near active and semi-active faults. In some cases, the design base shear was increased by a factor of almost two for such buildings. The consideration of earthquake ground motion characteristics, however, was not limited to near-fault effect as terms such as foot-wall, hanging wall, basin effect, basin-edge effect, and event-to-event versus location to location variability, entered the vocabulary of structural engineers and affected their designs. Furthermore, explicit requirement of considering vertical ground motion entered the building codes, although explicit consideration of vertical component of earthquake ground motion in everyday structural design has not been widespread. Importance of Building Configuration The impact of building configuration on seismic response was observed as early as 1906 where many soft/weak-story building collapses occurred during the great 1906 San Francisco earthquake. During the 1994 Northridge earthquake, most of the fatalities occurred in buildings suffering from this particular type of irregular configuration. California engineers had classified and codified building irregularities as early as 1980s. The 1994 Northridge earthquake, however, resulted in further fine-tuning of these definitions and introduction of a new factor, called redundancy factor, influencing structural design. While the importance of redundancy as means of redistribution of forces throughout the structure in case of failure of certain elements or components is beyond dispute, the redundancy factor as implemented in the contemporary building codes has been criticized as imprecise and sometimes leading to counterintuitive and unreasonable results. It is likely that the formulation of redundancy factor(s) will be revised and enhanced in the future edition of building codes and standards. Ultimate Capacity of Structures

The 1994 Northridge earthquake once again proved our inability to assess the ultimate capacity of the buildings we design. In other words, the buildings we design generally have an ultimate capacity above and beyond what we design them for (setting aside the special case of pre-Northridge WSMRF buildings). We do not, however, know the level of this excess capacity and exactly what kind of demand is necessary to bring down a code designed building. Probably this was best demonstrated by a California Geologic Survey (CGS) sponsored study of 20 extensively instrumented buildings which experienced large earthquake ground motions during the Northridge earthquake (Naeim 1998). Many of these buildings experienced base shears significantly in excess of their design capacity base shears and showed little, if any, signs of structural damage (see Table 1). Table 1. Examples of discrepancy between capacity anticipated by design and actual capacity of buildings (from Naeim 1997). Building

Structural System

Burbank 10 Story Residential Los Angeles 3 Story Commercial Los Angeles 19 Story Office

Shear Walls Steel Braced Frames SMRF and Steel Braced Frames

Max. Base Shear Experienced (% weight) 34

Code/Design Ultimate Base Shear 14

Overall Structural Damage Insignificant

49

18

None

34

8

Insignificant

The 1994 Northridge earthquake made it obvious that in order to advance the practice of seismic design it was necessary to (1) learn more about various aspects of earthquake ground motions and building response during earthquakes, and (2) develop procedures and technologies that enable structural engineers to predict with reasonable reliability the performance of buildings subjected to various levels and types of earthquake ground motions. These two conclusions in turn have probably resulted in the most significant advances in seismic design and disaster assessment ever since: the development of performance based design procedures and implementation and use of distributed seismic networks across United States. Value of Seismic Instrumentation If shake-maps such as the one presented in Figure 1 were available immediately after the Northridge earthquake, engineers and emergency response officials would not have been as baffled about the extensive damage in Santa Monica and West Los Angeles as they were in the days immediately following the Northridge earthquake. Over the past few years shake-maps have become and indispensable tool for early assessment of structural damage distribution during the first minutes and hours after an earthquake. The shake-map technology is based on automated evaluation of digital earthquake records obtained from the affected area immediately after an earthquake. The accuracy of a shake-map, therefore, is a very strong function of the density of the strong motion instruments (or seismic network) installed in the affected area prior to the earthquake. Shake-maps are also being used more frequently to depict the effect of anticipated or scenario events as shown in Figure 2. The utility of shake-maps has resulted in a national effort for implementation of seismic networks, similar to what exists in southern California, across the United States. So far shake-maps are operational for all areas of California (with varying accuracy), Seattle (Washington) and Salt Lake City (Utah).

Figure 1. Shake map of the 1994 Northridge earthquake produced after the event (www.trinet.org).

Figure 2. Shake map of a scenario magnitude 7.1 event on the Palos Verdes fault (www.trinet.org).

The Advanced National Seismic System Network (ANSS) currently under implementation by the United States Geological Survey (USGS) will be a nationwide network of at least 7000 shaking measurement systems (Figure 3), both on the ground and in buildings (USGS 2000) that will make it possible to: • • •

Provide emergency response personnel with real-time earthquake information. Provide engineers with information about building and site response. Provide scientists with high-quality data to understand earthquake processes and solid earth structure and dynamics.

The full implementation of ANSS is estimated to cost $170 million for equipment and $47 million each year for operation and maintenance. It is being funded, however, at a rate of about $2 to $3 million each year over the past several years. As a result, it would take a long time for the full benefits of ANSS to be realized at the current level of funding.

Figure 3. The ANSS plan for nationwide seismic network (USGS 2000). Another significant development fueled by advancements in geological information systems (GIS), distributed seismic networks, and progress in understanding of building behavior is the release and widespread use of a national loss estimation methodology as represented by the FEMA sponsored HAZUS-99 software system and the newly released multi-hazard version of the program (HAZUS-MH). Damage estimation using HAZUS is based on fragility curves for various structural systems and components. Therefore, reliability of its damage estimation is dependent on our knowledge of ultimate capacity of buildings which is at best limited at this time. Over time, however, with advancement of the performance based design methodologies and development of more reliable fragility functions, the accuracy of damage estimation tools such as HAZUS are bound to improve. Figure 4 shows two types of map that can be produced using HAZUS. These maps are for a hypothetical event in southern California and depict the ground motion characteristics and casualties postulated by HAZUS for this event.

∃∃

99 99

Ventura Ventura County County

99

∃∃

99

∃∃

∃∃ ∃∃ 99

99 99

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I-10 I-10 I-10 I-10 I-10 I-10

99

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60 - 80

KEY

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Total Casualties [by census tract]

School

10 - 20

9

Hospital



EOC

SSa ann AAn ndd rree aass

0 - 10

∃∃

ltt ltlt uulltlt FFaaauuu dFFFaa dd dd ood oo ooo oo wwwo gggleleleww Inggglele In In -In In tt-t-In orrrrtrrt-t-oo oo po pp pp wwwp Neeeeeewww NN NN N

99 99 9999

PGV [cm/sec] Over 100 80 - 100

99

555 III-II--5--55

99

Los Los Angeles Angeles County County I-405 I-405 I-405 I-405 I-405 I-405

∃∃

Over 20 [510 tracts]

Fire Station

10 - 20 [480 tracts]

Police Station 5 - 10 [378 tracts]

FF aauu lltt

Pacific Pacific Ocean Ocean

1 - 5 [625 tracts] None

99 0 00 00 0

5 55 55 5 kil kilo ki o lometers meters meters

10 10 10 10 10 10

0 00 00 0

99

(a) Peak ground velocity map superimposed on the map of essential facilities.

10 10 10 10 10 10

20 20 20 20 20 20

Miles Miles Miles Miles Miles Miles

(b) Casualty density map.

Figure 4. Typical damage assessment maps obtained from HAZUS for a hypothetical earthquake in southern California.

A new development that is anticipate to accelerate our knowledge of building performance utilizing the data that is gathered from seismic response of instrumented buildings is a system called CSMIP-3DV (Naeim et al. 2004) which is scheduled for release in May 2004. CSMIP-3DV is a software system developed for California Strong Motion Instrumentation Program (CSMIP) of California Geologic Survey (CGS). This system enables engineers to download, analyze and visualize performance of instrumented buildings during earthquakes. At the time of release, it will contain information regarding performance of 30 buildings during several earthquakes (Naeim, et al. 2004). CGS/CSMIP plans to make available in the near future the information obtained from more than 180 instrumented California buildings through this system. Facilitates provided by CSMIP-3DV include selection of various buildings and earthquakes (Figure 5), real-time visualization of response of a building during an earthquake (Figure 6), calculation and display of recorded story displacements and drifts and envelopes of these values during an earthquake (Figures 7 and 8) and identification of building periods and mode shapes and changes of these values during an earthquake (Figure 9).

Figure 5. The newly developed CSMIP-3DV will permit evaluation of seismic performance of more than 180 instrumented buildings.

Figure 6. CSMIP-3DV real-time visualization of response of Sylmar County Hospital to 1994 Northridge earthquake.

Figure 7. CSMIP-3DV depiction of envelope N-S lateral displacements experienced the Sylmar County Hospital during the 1994 Northridge earthquake.

Figure 8. CSMIP-3DV depictions of story drift ratio time history at the first floor of the Sylmar County Hospital during the 1994 Northridge earthquake.

Figure 9. Plots of variation of predominant frequencies of structure versus time provides means for identifying possible damage due to softening of the structure. Insufficiency of Design Practice Targeted Only to Life-Safety and Collapse Prevention For decades, the guiding philosophy of building codes has been to produce buildings that resist minor earthquakes with no damage, resist moderate earthquakes without structural damage but some nonstructural damage, and resist major earthquakes without collapse Loss of use. Statements of this philosophy may be found in virtually all editions of SEOAC Blue Book. -30,000

Inco me C h an ge [$ Mil l

-20,000 -10,000 0 10,000 20,000 30,000 Agriculture FIRE Manufacting Miscellaneous Trade

40,000 50,000 60,000

Construction Government Mining Service Transportation

70,000 Year 1

Year 2

Year 3

Year 4

Year 5

Elapsed Time afte r Earthquake

Figure 10. Typical long-term losses from an earthquake like 1994 Northridge (from HAZUS-99 Training Material).

The 1994 Northridge earthquake clearly demonstrated the inadequacy of this longstanding guiding philosophy. This earthquake which seriously damaged less than 2% of building stockpile of the city resulted in tens of billions of dollars in direct and indirect damage. The $2 billion dollars in structural damage was a very small fraction of total loss suffered by the community such as loss of jobs, productivity, and occupancy. In fact all sectors of economy, perhaps with the exception of construction industry, suffer long term and significant losses in the after-math of an earthquake like 1994 Northridge occurring in a heavily populated metropolitan area (see Figure 10). Significant Role of Nonstructural Components If a design philosophy that addresses only life safety and collapse prevention for the structure is inadequate, then such a philosophy cannot hold ground for building contents and nonstructural systems that typically encompass more than 80% of a building value. A case in point is the performance of the Sylmar County Hospital building during the 1994 Northridge earthquake (see Figure 6). This building which experienced a maximum base shear almost equal to its full weight (Figure 11a) did not suffer any apparent structural damage. Nevertheless, building contents and nonstructural systems were damaged to the extent that it was evacuated and lost its function for an extended period of time (Figure 11b and 11c).

(a) No structural damage despite extremely large maximum base shear

(c) damaged blood laboratory contents

(b) damage to patient files

Figure 11. Contrast between structural and nonstructural performance of the Sylmar County Hospital Building during the 1994 Northridge earthquake.

Development and Application of Performance-Based Design Methodologies Perhaps the most significant post-Northridge development in the field of structural engineering is the birth and development of performance-based seismic engineering (PBSE) concepts and methodologies. PBSE is an attempt to address the inherent shortcomings on prescriptive code provisions that impose a black and white filter on the real colorful world of structural performance. Performance-based design concepts and methods are not new. They have been successfully used in design and manufacturing of airplanes and automobiles for decades where thousands of identical units are manufactured based on design and extensive testing of a few prototypes. What makes application of performance-based design concepts difficult and challenging for building structures is the fact that virtually each building is unique and cannot be prototyped or mass produced. The FEMA-273 guidelines and commentary published in 1997 was a bold move towards making PBSE a reality for structural engineers. It defined performance of components and systems in terms of a spectrum varying from continuous operation to collapse prevention (see Figure 12). Consistent with these ranges methods were developed for evaluation of performance status of a building given a level of seismic hazard. These methods varied from simple to complex. Rationally, the more simple methods were designed to be more conservative than the more complex methods. These PBSE methods in the order of their complexity are: • • • •

Linear Static Procedure (LSP) Linear Dynamic Procedure (LDP) Nonlinear Static Procedure (NSP), and Nonlinear Dynamic Procedure (NDP)

FEMA-273/356 Component Curves Immediate Occupancy Normalized Force

P

Life Safety S

P

Collapse Prevention S

P C B D A

E

Deformation or Deformation Ratio Figure 12. Typical performance curves for structural and nonstructural components used in PBSE (after FEMA 1997, ASCE 2000)

While the PBSE methodology as introduced by FEMA-273 was complete, the metrics suggested by this document were not well-calibrated with the observed performance of buildings. For example, it was not a

rare incident to find a newly designed building which was in full compliance with the modern codes to fail FEMA-273 life-safety criterion. The FEMA-356 Prestandard resolved many of the inconsistencies of FEMA-273 and is a document that can be generally relied on to produce sensible evaluations. An example of application of various PBSE methods in evaluation of an existing building will be illustrative at this point. A 54 story residential building in a zone of high seismicity was constructed to the 38th floor when construction stopped because of a dispute over the building’s safety during the anticipated major earthquakes. Briefly stated, the structural system of the building consisted of shear walls and slabs only. The local code, similar to IBC and UBC provisions, did not permit such a system for buildings taller than 160 feet. This building, however, is about 500 ft (160 m) tall. In addition, ductile detailing procedures usually followed in zones of high seismicity were not followed to the extent normally desired. The building consisted of three wings with identical plan dimensions each approximately 48 meters by 22 meters. The three wings were not separated by expansions/seismic joints. Figure 13 shows a typical floor plan of the building.

Wing A

Spine Wall

Wing B

Wing C

Cross Wall

Figure 13. A typical floor plan of the example building. The structural system consists of solid floor and roof slabs spanning to transverse and longitudinal walls. These walls provide gravity as well as wind and seismic resistance for the building. Due to the unique geometry and design of the building, lateral translational resistance is provided by the longitudinal walls (spines) and torsion is resisted solely by the transverse walls (cross walls). The walls have no seismic boundary elements along either exterior edges or interior openings. Reinforcement detailing is typically non-ductile except possibly for coupling beams of the transverse walls. It was assumed that this additional reinforcement was indeed included in the construction of the building at all floors. Foundation consists of a reinforced concrete mat with variable and substantial thickness. Pictures of the partially constructed building which illustrate the various components of the building are presented in Figure 14.

(a) view of the building

(b) typical cross wall coupling beam or lintel

(c) view of a typical floor slab and cross walls

(d) typical slab reinforcement

Figure 14. Photos of example building under construction The original design engineers relied solely on the longitudinal walls (spines) for lateral load resistance and did not count on transverse walls to participate in resisting lateral forces. Since the three spine walls concur at the center of the building, they cannot provide the building with any torsional resistance. The torsional resistance must come from the transverse walls. Although this building is basically a symmetric building in plan and elevation, the rotational components of earthquake ground motions and accidental as well as actual plan eccentricities can subject the building to a significant amount of torsion during its response to major earthquakes.

Site-specific design spectra corresponding to exceedance probabilities of 10% in 50 years and 2% in 50 years were developed. Ensembles of seven pairs of recorded time histories were selected so that on average they represented the level of hazard depicted by the corresponding design spectrum. The selected ground motion time histories were then scaled according to the FEMA-356 scaling procedure is to match or exceed the design spectrum in the range of 20% to 150% of the first translational period of the building. LDP evaluations were performed by a local committee of engineers where initially the accidental eccentricity was not modeled and the first mode (purely torsional) was dismissed as a numerical anomaly and not a physical characteristic of the building. Response spectrum analysis was used. The FEMA-356 provisions for accidental eccentricity associated with the LDP procedure, however, significantly penalize a building with such a configuration. As a matter of fact, calculations show that the building should have been subjected to 15% rather than the usual 5% eccentricity commonly used. This would have substantially worsened the already dire prediction obtained by LDP for this building summarized as: •

The demand on the lintels of the transverse walls was significantly larger than their capacities.



The axial stress on the lower levels of the transverse walls significantly exceeded their capacities



The main central walls would satisfy the capacity requirements and would not need modification.

The situation with transverse walls based on LDP was so out of control that a practical solution based on LDP seemed unattainable to the local committee of engineers. As a result, assistance of an expert group was sought to evaluate the building using the nonlinear dynamic procedure (NDP). The NDP computer model was composed of nonlinear walls and nonlinear beams. Flexural nonlinearity of walls was captured via the use of nonlinear fiber elements, modeling fibers of vertical concrete and steel layers. Flexural nonlinearity of the lintels was found to be non-controlling as all these beams invariably failed in shear. Shear behavior of walls and beams was modeled as elastic-plastic shear hinges. The effect of stiffness degradation in reducing the energy dissipation capacity of members was also included in this model. Consistent with the nonlinear material models of FEMA-356, a trilinear backbone with an optional strength drop was used as the basic nonlinear material model for steel reinforcement in tension and for concrete in compression (see Figure 15). ACTION

Strain Hardening U

Initial stiffness

Ultimate strength L Strength loss

Y

R DEFORMATION Area of hysteresis loop

Figure 15. Primary nonlinear material behavior model. The NDP evaluation revealed that due to limited capacity of the lintels of transverse walls no excessive axial stress is produced on the lower levels of transverse walls. Contrary to LDP evaluation, however, NDP results indicated significant demand and not enough capacity on the wall segments in between successive door openings on alternative floors on the main walls. As a matter of fact, more than 40% of entire hysteretic energy was consumed by the main (spine) walls. The overall energy balance picture for the nonlinear time history analyses and the concentration of hysteretic energy at the main walls are shown in Figures 16 and 17, respectively.

70,000

60,000

Energy (ton-m)

50,000 Elastic

40,000

Plastic Internal

30,000

External

20,000

10,000 External 0

Internal RUN 11

RUN 12

Plastic RUN 13

RUN 14

Elastic RUN 15

RUN 16

RUN 17

RUN 11

RUN 12

RUN 13

RUN 14

RUN 15

RUN 16

Elastic

2,180

2,537

2,698

2,738

2,458

2,537

RUN 17 2,144

Plastic

11,307

28,161

24,454

12,101

17,791

22,516

20,821

Internal

29,634

64,136

64,421

35,261

40,112

48,840

48,586

External

30,049

65,296

65,871

36,140

40,660

49,678

49,321

Figure 16. Energy balance and energy consumed by elastic and inelastic actions at the end of each analysis.

Figure 17. Energy versus time (top) and percent of hysteretic energy consumed by spine of Wing C (bottom) for a typical nonlinear time history analysis. The results also indicated that on average, the demand on lintels were within the acceptable range. Further retrofit studies indicated that if the spine walls of the 16 unconstructed upper floors were thickened and a type of cross-bar detailing was utilized, the demand on the lower floor coupling panels of main walls were reduced and the building could be brought to substantial compliance with FEMA-356 life safety objectives. The construction of the building resumed shortly after the above findings reflecting the

suggested modification of design and detailing on the yet unconstructed upper floors. Application of advanced analysis techniques and use of the newly developed performance based design methodologies saved a significant investment and preserved what will be the tallest residential building in a zone of high seismicity. Significant Changes in Building Codes and Standards Everyone who has been practicing structural engineering in California is intimately familiar with the scope and frequency of changes in code provisions since 1994 Northridge earthquake. Initially, UBC-97 brought in more strict design provisions and higher ground motions. Then, a floury of documents that could or could not affect design appeared, including multiple guidelines governing steel structures issued by SAC Joint Venture and FEMA. This was accompanied by publication of new AISC provisions for seismic design, ASCE-7 provisions, SBC-1953 provisions for rehabilitation of hospitals in California, IBC and dichotomy, and so forth. Practice of structural engineering has become increasingly more complex since the time of 1994 Northridge earthquake. Some of this complexity is needed, but much of it in terms of numerous and often conflicting code requirements is unnecessary and analogous to a cruel and unusual punishment imposed on structural engineers who in general were not guilty of a crime deserving such a harsh punishment. Conclusion The 1994 Northridge earthquake has forever changed the practice of structural engineering at least in California. Much of these changes reflect advancements which are good for the community as well as for engineering practice. A sizeable portion of these changes, however, represent over-reactions and uncoordinated code provisions which make engineering practice unnecessarily more difficult. References Federal Emergency Management Agency (FEMA), 2000, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA-356, Washington, D.C., US.A. International Conference of Building Officials (ICBO) 1997, Uniform Building Code –1997 Edition, Whittier, California, USA. International Code Council (ICC), 2003, International Building Code, Falls Church, Virginia, USA. Naeim, Farzad, 1998, “Lessons Learned from Seismic Performance of Extensively Instrumented Buildings,” Proceedings of the 8th U.S.-Japan Workshop on Improvement of Structural Design and Construction Practices, Applied Technology Council. Naeim, F., H. Lee, H. Bhatia, K. Skliros and S. Hagie (2004), CSMIP-3DV: An Interactive Software System for Three-Dimensional Visualization and Analysis of Earthquake Response of Instrumented Buildings, A report to CGS-CSMIP, in preparation United States Geological Survey (USGS), 2000. ANSS-Advanced National Seismic System, Fact Sheet 075-00. http://geopubs.wr.usgs.gov/fact-sheet/fs075-00/fs075-00.pdf.

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