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Three-dimensional nonlinear dynamic seismic behaviour of a seven story reinforced concrete building Doulatabadi, Peyman Rahmatian 1997

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T H R E E - D I M E N S I O N A L N O N L I N E A R D Y N A M I C SEISMIC B E H A V I O U R O F A SEVEN STORY REINFORCED C O N C R E T E BUILDING by  PEYMAN RAHMATIAN  DOULATABADI  B . S c , Bogazici University, 1991 M . S c , Bogazici University, 1993  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F THE REQUIREMENTS FORTHE DEGREE OF M A S T E R OF APPLIED  SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Civil Engineering  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A  March 1997  © Peyman Rahmatian Doulatabadi, 1997  In  presenting this  degree  at the  thesis  in  University, of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  ABSTRACT  The three-dimensional seismic dynamic behaviour of reinforced concrete buildings has not been studied as extensively as their planar behaviour. Experimental studies, although limited, demonstrate that there is significant interaction of torsional response with the response of a building along its two principal axes. In order to gain better understanding of this interaction, a recently developed computer program called C A N N Y - E was used in this study to evaluate the three-dimensional response of a reinforced concrete structure subjected to prescribe seismic excitations.  The purpose of this research was to study the seismic behaviour of a well-instrumented seven story reinforced concrete building in V a n Nuys, California. This building has been subjected to ground motions from several earthquakes since 1971 and sustained severe structural damage during the 1994 Northridge earthquake. The lateral force resistance of the building is provided by both interior column-slab and exterior column-spandrel beam frames.  Typical floor plan  dimensions are 19 by 49 meters.  The behaviour of the building during three earthquakes having different levels of demand was investigated.  The first strong ground excitation that the building experienced was in 1971,  during the San Fernando earthquake. The 1987 Whittier and the 1994 Northridge earthquakes were the other two recorded ground excitations used in this study.  Detailed time and frequency domain analyses of the recorded motions from these three earthquakes were conducted to determine the dynamic characteristics o f the system at the beginning and during each event. Then, three-dimensional, linear and nonlinear dynamic time  ii  history analyses of the building were conducted for each earthquake.  The results of this study showed that by performing a nonlinear analysis, even based on material properties obtained from the design specifications rather than on material properties determined from core samples, one can effectively predict the real response of a building during an earthquake. The state and sequence of damage could also be predicted.  iii  TABLE OF CONTENTS  ABSTRACT  ii  TABLE OF CONTENTS  iv  LIST OF TABLES  vii  LIST OF FIGURES  viii  ACKNOWLEDGEMENTS  xi  Chapter 1 Introduction  1  1.1 General Remarks  1  1.2 Objectives and Scope  2  1.3 Organization  2  Chapter 2 Nonlinear Analysis  4  2.1 W h y Nonlinear Analysis  4  2.2 Literature Review  6  Chapter 3 Description of the Holiday Inn hotel building  10  3.1 Introduction  10  3.2 Structural System  11  3.3 Building Materials  14  3.4 Recorded Earthquakes and Observed Damage  15  3.5 Building Instrumentation and Recorded Earthquake Responses  16  Chapter 4 Data Analysis  •••23  4.1 Introduction  23  4.2 Time Domain Analysis  23  4.3 Frequency Domain Analysis  28  4.4 Summary  37  iv  Chapter 5 Three dimensional linear analysis of the reinforced concrete building  38  5.1 Introduction  38  5.2 Developement of a Linear Model for the Holiday Inn Building  39  5.3 Calibration of the Model and Period Sensitivity during the Whittier Earthquake. 40 5.4 Elastic Time History Analysis of the Building during the Wittier Earthquake .... 42 5.4.1 Comparison of predicted and recorded time histories 5.5 Response of the Building during the Northridge Earthquake  43 46  5.5.1 Response of the model during the early part of excitation  47  5.5.2 Response of the model during the late part of excitation  48  5.6 Summary  52  Chapter 6 Description of the Nonlinear Program  54  6.1 Introduction  54  6.2 Elements  56  6.3 Canny Hysteresis Models  61  6.4 More information about the Program  62  Chapter 7 Three-dimensional Nonlinear analysis of the Holiday Inn Building  64  7.1 Introduction  64  7.2 Description of the Model  64  7.3 Pushover Analysis  66  7.3.1 Analytical prediction of longitudinal response  67  7.3.2 Analytical prediction of transverse response  69  7.4 Cyclic Analysis .  71  7.4.1 Analytical prediction of longitudinal response  72  7.4.2 Analytical prediction of transverse response  72  7.5 Time History Analysis  75  7.5.1 Response of the building during the Whittier earthquake  76  7.5.1.1 Comparison of recorded and predicted time histories  76  7.5.1.2 Comparison of peak responses  79  7.5.2 Response of the building during the San Fernando earthquake  v  82  7.5.2.1 Comparison of recorded and predicted time histories  83  7.5.2.2 Comparison of peak responses  85  7.5.3 Response of the building during the Northridge earthquake  88  7.5.3.1 Comparison of recorded and predicted time histories  88  7.5.3.2 Comparison of peak responses  94  7.5.3.3 Comparison between the predicted and reported damages  99  7.6 Shear Demand  102  7.7 Performance of the Computer Program  102  7.7 Summary  104  Chapter 8 Summary, Conclusions and recommendations  105  8.1 Summary  105  8.2 Predicted and Recorded Behaviour of the Building  107  8.3 Recommendations for Further Research  109  REFERENCES  HI  Appendix A  Floor Plans and Details of the Building  Appendix B  Recorded Data of the Building during the San Fernando, Whittier and  Northridge earthquakes  115  120  Appendix C  Estimated Weight and Mode Shapes of the Building  129  Appendix D  Comparison of the Nonlinear Analysis Time Histories with the records  133  vi  LIST O F  T A B L E S  Table 4.1. Properties of construction materials  14  Table 3.2. Summary of recorded accelerations, drifts and fundamental periods from several earthquakes for the Holiday Inn building (longitudinal direction) Table 4.1. Probable natural frequencies of the building at the end of earthquake.  15 36  Table 4.2. Comparison of fundamental frequencies in the longitudinal direction predicted here with other studies (CSME? 96)  36  Table 4.3. Descriptions of the four models  42  Table 7.1. Execution times and memory requirements for each analysis  vii  105  LIST O F F I G U R E S  Figure 3.1. Holiday Inn Hotel in VanNuys  10  Figure 3.2. Holiday Inn, typical floor framing plan  12  Figure 3.3. Holiday Inn, Sections and details  13  Figure 3.4. View of the damage in the columns of the south perimeter frame  17  Figure 3.5. A close view of damage in the columns of the south perimeter frame  17  Figure 3.6. Instrumentation plan of the building during the San Fernando earthquake  19  Figure 3.7. Instrumentation plan of the building during the Whittier and the Northridge earthquakes.  19  Figure 3.8. Recorded (processed) accelerations during the 1971 San Fernando earthquake. . 20 Figure 3.9. Recorded (processed) accelerations during the 1987 Whittier earthquake Figure 3.10. Figure 4.1.  Recorded (processed) accelerations during the 1994 Northridge earthquake. ... 22 A selected Instantaneous three-dimensional displaced position of the building  during the Whittier earthquake Figure 4.2.  21  24  Selected Instantaneous deformed shape of building  25  Figure 4.3. Linear-elastic response spectra of horizontal ground motions recorded at the ground floor of the building (5% Damping) Figure 4.4. In plane particle motions during each earthquake  26 27  Figure 4.5. Frequency response function (magnitude) corresponding to 13-16 seconds segment, Northridge earthquake 29 Figure 4.6. Original natural frequencies and mode shapes of the building at the beinning of the record obtained during the San Fernando earthquake Figure 4.7. Natural frequencies and mode shapes of the building at the beginning at the beinning of the record obtained during the San Fernando earthquake  31 31  Figure 4.8. Natural frequencies and mode shapes of the building from the record obtained during the Whittier earthquake  32  viii  Figure 4.9. Natural frequencies and mode shapes of the building at the end of the record obtained during the Northridge earthquake Figure 4.10.  34  Changes in the fundamental natural frequencies of the building over the time  during three earthquakes  35  Figure 5.1. Linear model of the building  39  Figure 5.2. Comparison of recorded and calculated roof absolute acceleration responses, Whittier earthquake  44  Figure 5.3. Comparison of recorded and calculated roof relative displacement responses, Whittier earthquake  45  Figure 5.4. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake, early part  48  Figure 5.5. Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake, early part  49  Figure 5.6. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake, late part  50  Figure 5.7. Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake, late part.  .-  51  Figure 6.1. Column idealized by multi-spring model  57  Figure 6.2. Concrete part of spring element for rectangular section  57  Figure 6.3. Spring force-displacement relationship  59  Figure 6.4. Concrete stress-strain curves  59  Figure 7.1. Base shear versus roof displacement, east-west direction  68  Figure 7.2. Step of yielding in south perimeter frame, east-west direction  68  Figure 7.3. Base shear versus roof displacement, north-south direction  70  Figure 7.4. Step of yielding in south perimeter frame, north-south direction  70  Figure 7.5. R o o f displacement versus base shear, east-west direction  73  Figure 7.6. Moment-rotation, fourth story columns, east-west direction  73  ix  Figure 7.7. Base shear versus roof displacement, cyclic analysis, north-south direction  74  Figure 7.8. Moment-rotation, fourth story columns, north-south direction  74  Figure 7.9. Comparison of recorded and calculated roof absolute acceleration responses, Whittier earthquake Figure 7.10.  77  Comparison of recorded and calculated roof relative displacement responses, Whittier earthquake  78  Figure 7.11. Peak story shear and acceleration responses, whittier earthquake  80  Figure 7.12. Peak story drift and displacement responses, whittier earthquake  81  Figure 7.13. Comparison of recorded and calculated roof absolute acceleration responses, San Fernando earthquake  84  Figure 7.14. Comparison of recorded and calculated roof relative displacement responses, San Fernando earthquake  :  84  Figure 7.15. Peak story shear and acceleration responses, San Fernando earthquake  86  Figure 7.16. Peak story drift and displacement responses, San Fernando earthquake  87  Figure 7.17. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake Figure 7.18.  89  Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake  90  Figure 7.19. Predicted shear time histories, Northridge earthquake  93  Figure 7.20. Top moment-rotation, fourth story columns, each-west direction  93  Figure 7.21. Biaxial bending demand time histories at the base of the ground and top of fourth story selected columns  95  Figure 7.22. Axial load-moment demand time histories of selected columns  96  Figure 7.23. Peak story shear and acceleration responses, Northridge earthquake  97  Figure 7.24. Peak story drift and displacement responses, Northridge earthquake  98  Figure 7.25. Comparison of story shear capacity versus demand  104  Figure 7.26. Comparison of story shear demand, Northridge earthquake  104  ACKNOWLEDGMENTS  I am deeply indebted to my supervisor, Dr. Carlos E . Ventura, for suggesting this project, all the time and effort he put in advising me, his encouraging enthusiasm, and editing the early drafts of this thesis.  I would like to thank Dr. Donald Anderson who, along with Dr. Carlos E . Ventura, reviewed the final draft o f this thesis.  I would also like to thank Dr. Kang-Ning L i for providing his  program, C A N N Y - E and explaining its various features.  The invaluable help of some of my  colleagues, Mahmud Rezai and Vincent Latendresse, and my brother, Farnoosh Rahmatian, is deeply appreciated.  The financial support provided by a research grant from the Natural Science and Enginearing Research Council of Canada is gratefully acknowledged.  Finally, I would personally like to offer my deepest appreciation to my parents, Hossein and Ferideh, for their endless encouragement and financial support throughout the course of this work.  xi  Chapter 1  INTRODUCTION  1.1 G e n e r a l R e m a r k s  Reinforced Concrete Buildings are generally analyzed and designed by various methods that include certain assumptions regarding the behaviour of structural components and materials. There are some differences between the predicted dynamic response of a building's analytical model and its real response.  O f special interest is the response of reinforced concrete  buildings during earthquakes which has often been significantly different from what was anticipated in design offices.  Some of these differences may be related to the uncertainties  about seismic excitations, the difficulties in predicting the inelastic cyclic response, or complexity of the dynamic response of the reinforced concrete structures.  Another important factor which is often neglected may be the three-dimensional nature of both the excitation and response of the structure. In fact, the three-dimensional behaviour of reinforced concrete structures has not been studied as extensively as that of planar or twodimensional behaviour.  Computational costs and lack of an adequate model for member  behaviour are some reasons for this.  Experimental  studies,  although limited, have demonstrated that there is a  significant  interaction between the responses of a non-symmetric structure along its two principal axes. Even though there are a limited number of experimental studies related to the three. dimensional behaviour of concrete structures, the results of only a few of them, and under restricted conditions have been fully predicted by current available analytical models.  1  It is  postulated here, however, that i f the accuracy of current analytical modeling techniques is reasonably verified and demonstrated for a variety of earthquake simulations, it will then be possible to increase the confidence of structural engineers on such techniques and on the subsequent development of more effective seismic resistant design methods.  1.2 Objectives and Scope  The  primary objective of this study was to use a recently developed analytical model,  incorporated in a computer program, to obtain the three-dimensional response of an existing reinforced concrete structure to recorded seismic base excitation, and to compare this calculated response with the actual recorded response.  This comparison would be done for  three earthquakes with various levels of excitation.  The building under this study was modeled based on specifications and informations included in the design drawings. The emphasis of the study conducted here was on the linear and nonlinear global response and behaviour of the structure, rather than on any of its elements.  1.3 Organization  A short discussion about linear versus nonlinear analysis, together with a literature review on nonlinear modeling of reinforced concrete members are covered in Chapter 2.  In Chapter 3 a complete description of the building studied is given.  Some of the topics  discussed here are: the structural system, construction materials, seismic instrumentation plan, description of the earthquakes studied and description of the observed damage in the building after each earthquake.  2  Strong Motion Data analysis results, which reflect the state of the building at the beginning and during each earthquake, are discussed in Chapter 4.  Chapter 5 is concerned with a three-dimensional  linear-elastic modeling of the structure.  Three-dimensional analyses of the structure were performed for two input ground motions with different levels of demand. The purpose of these analyses was to identify the extent of contribution of various elements in the overall response of the building.  A general review of the nonlinear analytical program used in this study and some of its unique features are presented in Chapter 6.  The  Nonlinear-inelastic three-dimensional analysis of the building is discussed in Chapter 7.  The development of the model, the underlying assumptions, and finally the response of the structure during three different earthquakes are presented here. In addition to the time history analysis, pushover and cyclic analysis of the building were also conducted.  Finally, a summary of the results of this study followed by recommendations for further analytical studies are given in Chapter 8.  3  Chapter 2  NONLINEAR ANALYSIS  2.1 W h y Nonlinear Analysis  The poor performance of certain types of reinforced concrete buildings has been demonstrated through the catastrophic consequences of earthquakes during last three decades. these buildings were designed member-by-member for strength.  Most of  The results from linear  elastic analysis performed using computers were dominantly used to determine member strength demands.  In contrast, member strength capacities were calculated using formulas  included in design codes and that account for various types of nonlinearity rising from material behaviour. In this approach, for member demand calculations the nonlinear effects were ignored, whereas for the capacity calculations they were taken into account. Demandcapacity comparisons based on this approach were considered good enough for making design decisions, eventhough the inconsistency of it was acknowledged by engineers. However, the extensive damage and collapse of structures designed following this approach could not be prevented during past earthquakes.  There are some significant weaknesses and limitations associated with linear analysis. For instance, there should be a rational way to account for the strength reserve between first hinge formation and actual collapse of a structure. Different structures and different designs for the same structure can have different reserve strengths which cannot be calculated using linear analysis.  Furthermore, linear analysis cannot predict the response and demand of certain  types of reinforced concrete structures during strong motion earthquakes. The reason for this  4  is the instantaneous change in the state of such structures during the intensive part of the shaking from an earthquake.  Even if one has a good estimation of the initial state of a  structure, the structural characteristics of the system, such as strength, stiffness, and damping, may change  significantly  during highly inelastic cycles of response  which cannot be  considered by performing a linear analysis.  So, we could consider using nonlinear analysis with the goal of creating a more efficient design.  The purpose of such analysis would be to simulate on a realistic manner the actual  behaviour of the structure and generate information that could be used in design.  Nonlinear analysis, attempting to represent more realistically the behaviour of a concrete structure, has its own problems. Traditionally, it is regarded as not cost effective and needs a qualitative interpretation of the overall inelastic response of the structure. For linear analysis, by assigning reasonable values for the member stiffnesses one ends up with reasonable member strength demands, but for nonlinear analysis one must specify much more parameters than the member stiffnesses.  The nonlinear behaviour aspects that are essential to capture may be difficult to model.  A  complete realistic relation between the complex mechanics of material nonlinearity and the three-dimensional structural response of a system have not been well established through analytical work and experimental testings.  Therefore, decisions must be made on which  aspects of nonlinearity are significant, and how to capture them in the analytical model.  Recent enhancements in computational techniques and the development of more sophisticated models allow structural analysts to have integrated tools, based on components' behaviour,  5  which are capable of determining the behaviour of three-dimensional structures in a realistic manner.  2.2 Literature Review  Literature on nonlinear modeling of reinforced concrete structures is vast. A summary of the development of the common techniques used for modeling members in reinforced concrete buildings is given in this section.  The literature review conducted revealed that at the member level, an element can be treated by two different approaches: first, a lumped nonlinearity approach which leads to macromodeling procedure and second, a discretized section or distributed nonlinearity approach which forms the basis of filament models and micromodeling schemes.  Early studies of the response of multistory buildings were based on shear-beam idealizations (Penzien, 1960).  The entire structure was modeled as a series of single lateral degree of  freedom systems, one at each floor, having the global hysteretic characteristics representative of the cyclic inelastic response of the corresponding floor. Analysis of regular frames based on solution of dynamic equations of motion by Runge-Kutta and Milne's Predictor-corrector methods was first achieved by Berg and DaDeppo (1960).  A parallel component element modeling approach consisting of one elastic and one perfect elasto-plastic component was introduced by Clough et al. (1965).  The element stiffness  matrix was simply formed by summation of the stiffness matrix of both components. this model was modified and extended by several researchers.  Later  Aoyama and Sugano (1968)  applied the same approach to multi-component member by considering different yield levels  6  through two different elasto-plastic springs, one at each end.  A general single component  model in which all the inelastic behaviours are modeled by two rotational springs was first developed by Giberson (1969). This was the first model which had the ability to account for variation of stiffness.  Several  lumped  spring constitutive  models  have  been  characteristics of inelastic behaviour of reinforced concrete.  proposed  based  on  observed  Such models include the cyclic  stiffness degradation in flexure and shear (Clough and Johnson, 1966; and Takeda et al., 1970), pinching under load reversal (Banon et al., 1981; and Kabeyasawa et al., 1983), fixed end rotations due to bond slip at joint-column interface, (Otani and Sozen, 1972; Lai et al., 1984; and Fillipou et al., 1983), and strength deterioration (Ozdemir, 1976; and Park et al., 1987).  The dependence of flexural strength on axial load and biaxial bending has also been explicitly included in modeling of the beam columns by several researchers.  Available lumped  nonlinearity models are either based on yield surface criteria characterized by a flow rule, in accordance with classical plasticity theory as suggested by Takizawa and Aoyama (1976) or triaxial-spring model originally proposed by Lai et al. (1984). A refinement to Lai's model was provided by L i et al. (1988), by increasing the number of springs and considering the neutral axis translation in response to stiffness change of springs. A viscoplastic forcedeformation model for biaxial bending has also been developed by Kunnat and Reinhorn (1989) based on coupled differential equations for isotropic hysteretic suggested by Park et al. (1986).  7  restoring  forces  The inelastic behaviour of a reinforced concrete section is not concentrated at the joints, instead it is spread into the member toward contraflexure point. deformation throughout the member has been  The spread of inelastic  considered by various discrete  single-  component models. Wen and Janssen (1965) discretized a member to smaller elasto-plastic segments.  Powell (1975) proposed more inelastic springs at connections. Takayagani and  Schnobrich (1977) used distributed stiffness for the discrete segments.  A model which could efficiently estimate the variation of the stiffness through distributing flexibility across member length was the results of studies of Otani and Sozen (1972) and Takizawa (1976).  Takizawa assumed a parabolic distribution of stiffness with an elastic  flexibility at contraflexure point.  The effect of shear deterioration has been considered by Bazant and Bhat (1977). developed multiaxial constitutive model of the fiber concrete sections.  They  Their model was  based on endochronic theory.  A model considering variable displacement transformations, which are continuously updated and are consistent with internal yielding at any time, was developed by Kaba and Mahin (1984). Work by Roufaiel and Meyer (1987) included the finite size of plastic regions at the ends of the member.  Aktan and Pecknold (1974), Suharwardi and Pecknold (1978) and Zeris and Mahin (1988) suggested various approaches to modeling the biaxial bending using filament model.  These  models are direct extension of the filament models used for uniaxial bending. Mender et al. (1988) had even incorporated the strain-rate effects in filament type models.  8  Even though  several behaviour such as strength deterioration, stiffness degradation and slip behaviour of members can be considered in the above models, enormous computational time is required even for a single element.  The model used in this study to represent columns is the multi-spring model proposed by L i et al. (1993) and applied in a general purpose computer program, C A N N Y - E (1995).  It was  developed through modification of the triaxial-spring model originally proposed by L a i et al. (1984).  This model has the capability to simulate the flexural behaviour of reinforced  concrete columns under varying axial load and bi-directional lateral load reversal (Li and Otani, 1993).  The C A N N Y sophisticated trilinear model ( C A N N Y - E , 1995) was chosen to model beam elements.  This model is based on a lump plasticity approach which considers the stiffness  degradation, strength deterioration and pinching behaviour of reinforced concrete members.  9  Chapter 3  D E S C R I P T I O N O F T H E H O L I D A Y INN H O T E L B U I L D I N G  3.1 Introduction  The Holiday Inn hotel in Van Nuys, Southern California, is a seven-storey reinforced concrete frame building located east o f the intersection of Roscoe Boulevard and the San Diego Freeway.  The building, which has about 5860 square meters of floor area, was designed in  1965 and constructed in 1966. The plan configuration of each floor, except for two small areas at the ground floor which are covered by one-story canopies, are the same. A n overview o f the building is shown in Fig. 3.1.  Figure 3.1. Holiday Inn Hotel in Van Nuys.  10  3.2 Structural System  The foundation system consists of groups of two to four cast-in-place reinforced concrete friction piles with 965 mm deep pile caps. A grid of tie or foundation beams connects all pile caps. Each pile is about 12 m long, has a 610 mm diameter and has a design capacity of over 445 k N vertical and 89 k N lateral loads (J.A. Blume & Associates, 1973).  Geological data  indicates that the site is located on a deep alluvium area.  The vertical load carrying system is composed of reinforced concrete flat slab floors, 203-254 mm thick, supported by concrete columns in the inner frames and concrete columns with spandrel beams along the perimeter frames. 45.72m.  Typical floor plan dimensions are 19.10 m by  Story heights are 4.11 m at the ground floor and 2.65 m at the upper floors.  A typical story plan and details of the building are shown in Figs. 3.2 and 3.3.  The columns  are located every 5.71 m in the longitudinal direction and 6.12 m and 6.35 m in the transversal direction. In each direction, the lateral loads are resisted by both interior column-slab frames and exterior column spandrel beam frames. The spandrel beams in the exterior frames make them approximately twice as stiff as the interior frames. More structural plans and details of the building are presented in appendix A .  Interior partitions are generally gypsum walls on metal studs. Exterior walls in the east and the west end of the building, together with stairs and elevator openings, are covered by 2.5 centimeter cement plaster with double 16-gauge metal studs. Four bays o f nonstructural brick masonry walls between the ground and the second floor are located at the east end of the north side of the building.  The walls are separated from the exterior columns and underside of  second story beams by 2.5 and 4 centimeter expansion joints, respectively.  11  Although, they  ® ,  ® 6.12 m  6.35 m  ,  6.12m  '  356 x 508 mm  r exterior concrete  column (typ.)  450 mm square interior concrete column (typ.)  a  216: mm concrete slab (typ.)  -Q--  'Stairwell  Figure 3.2. Holiday Inn, typical floor framing plan.  12  Exterior spandrel beam at periphery concrete slab (typ.)  § I  m  3 101 nkm 406 mm  356 mm  Section B  Section A  406 mm  3  TJ  C  'E  'Slope J:6 . . . max.-  L 75x75 cont. 4- #4 cont.  #4 @ 610 mm 1- #4 cont.  50 mm clearence  Section C Typical Column Detail  Figure 3.3. Holiday Inn, sections and details.  13  o  IT  were not designed as part of lateral load-resisting mechanism, the response of the building during past earthquakes shows their contribution to the stiffness of the structure.  The main structure may be considered symmetrical. However, the existence of some light framing  members  supporting the  stairways  and elevator  openings  together  with  the  nonstructural infill walls along the north side of the building, and the exterior cement plaster may cause some asymmetry of the stiffness in the longitudinal direction.  3.3 B u i l d i n g Materials  Regular weight reinforced concrete was used in construction. The specified properties of structural materials are given in Table 3.1.  Table 3.1. Properties of construction materials. Concrete (regular weight, 24,000 N/m ) 3  Minimum Specified Compressive Strength f ' (MPa)  Modulus of Elasticity E (MPa)  Column, first to second floors  34.5  28,960  Column, second to third floors  27.5  25,510  Beams and slabs, second floors  27.5  25,510  All other concrete, third to roof  20.7  22,753  Location in structure  c  Reinforcing Steel Minimum Specified f (MPa)  Modulus of Elasticity E (MPa)  276  200,000  414  200,000  Yield Strength  Member  y  Beams and slabs Intermediate-grade ( A S T M A 15 and A-305) Column bars Deformed billet bars ( A S T M A 15 and A-305)  14  3.4 Recorded Earthquakes and Observed Damage  Several earthquakes, since the 1971 San Fernando through the 1994 Northridge, have been recorded by the instrumentation installed in this building.  A complete list of recorded  earthquakes together with some ambient measurements and relevant information ( C S M I P 1996) are given in Table 3.2. Table 3.2. Summary of recorded accelerations, drifts and fundamental periods from several earthquakes for the Holiday Inn building (longitudinal direction).  (g)  Max. Drift Roof-Base (cm)  Fund. Period (Second)  Fund. Freq. (Hz)  -  -  -  0.52  1.92  0.14  0.32  7.8  1.3  0.77  Post-1971 ambient measurement  -  -  -  0.7  1.43  1987 Whittier (M=6.1, d=41 km)  0.14  0.17  2.8  1.1  0.91  1992 Landers (M=7.5, d= 187 km)  0.04  0.13  3.2  1.2  0.83  1992 Big Bear (M=6.6, d= 152 km)  0.02  0.06  1.6  1.2  0.83  1994 Northridge (M=6.7, d=7 km)  0.45  0.58  23.0 '  1.5 - 2.0  0.67-0.5  Pre-1971 ambient measurement 1971 San Fernando (M=6.5,d=20 km)  Max. Base Accel.  Max. Roof Accel.  (g)  M= magnitude, d= epicentral distance.  The three earthquakes considered in this study are the 1994 Northridge, 1987 Whittier and 1971 San Fernando earthquakes.  The building experienced its first strong ground motion  during San Fernando earthquake, which had its epicenter about 20 km north of the building. During this event the building suffered minor structural damage which was  subsequently  repaired ( N O A A , 1973). The total cost of damage was about 11% of the initial construction cost, which was mainly due to nonstructural repair. The structural repairs included patching the beam-column joint at the north-east corner of the second floor and epoxy repair of exterior beam soffits.  Nonstructural damage was very extensive and affected  partitions, bathroom tiles and plumbing fixtures ( N O A A 1973).  15  mostly dry walls  The epicenter of the 1987 Whittier earthquake was located about 41 km south-east of the building. Because of the epicentral distance and size of the earthquake, no serious damage was reported during this earthquake.  The epicenter of the 1994 Northridge earthquake was about 7 km west of the building. The building was seriously damaged during this event. Significant structural damage was localized at the longitudinal perimeter frames. In the transverse direction, only minor flexural cracks in the end bays were observed. The top of several exterior columns at the south side of the fourth story had shear failure and compression spalling (see Figs. 3.4 and 3.5).  Significant interior  damage had also been reported in this story (Ventura, Finn and Schuster, 1995).  Below the fifth floor, minor to moderate flexural cracks were observed in many beam-column joints, at the bottom of several spandrel beams. The nonstructural brick infill walls along the north side of the building together with beam soffits at the corner of some panels were also cracked. The nonstructural damage was mainly observed at the fourth story.  The building has recently being repaired and seismically upgraded. Shear walls were added at selected locations on the perimeter of the building. More photographs of the damage and state of the building as of February of 1996 are included in Appendix A .  3.5 Building Instrumentation and Recorded Earthquake Responses  During the San Fernando earthquake, the building was instrumented with three strong motion accelerometers (ground floor, fourth floor and roof). It was the closest instrumented building to the epicenter of the 1971 San Fernando earthquake. recorded at these locations.  Three components of motions were  After this event, the building was instrumented more extensively  16  with 16 sensors by the California Strong Motion Instrumentation Program, CSMIP.  The  instrumentation plans of the building during the San Fernando as well as Whittier and Northridge earthquakes are shown in Figs. 3.6 and 3.7.  The acceleration records from San Fernando earthquake are shown in F i g . 3.8. Recorded peak acceleration values are included at the right side of figure above each record. accelerations  at the ground and roof levels were 0.13g  longitudinal direction (East-West).  and 0.32g, respectively,  Peak in the  Peak accelerations in the transverse direction (North-  South) were 0.25g at the ground level and 0.3 8g at the roof.  Note that the peak ground  acceleration in the longitudinal direction was half of the corresponding value in the transverse direction and was amplified about 2.5 times through the roof.  In contrast, the acceleration  amplification in the transverse direction was only about 1.5 times.  The records from the Whittier and Northridge earthquakes are shown in Figs. 3.9 and 3.10 respectively.  These records were obtained by C S M I P (Shakal, et al.,1987 and 1994).  Peak  accelerations during Northridge earthquake in the longitudinal direction at the ground and the roof were 0.45g and 0.58g, respectively. The corresponding values during Whittier earthquake were 0.14g and 0.18g. In the transverse direction, the peak accelerations were 0.42g and 0.57g at the ground and roof level respectively.  These values were 0.17g and 0.18g during Whittier  earthquake. The integrated velocity and displacement records are included in Appendix B .  18  Roof 7  6 5 4  3 2 Fourth Floor  Gound E-W Elevation N  A Ground Floor  Roof  Figure 3.6. Instrumentation plan of the building during the San Fernando earthquake.  Roof 7  6 5 4  3  3  2  Third Floor  Gound  E-W Elevation  1  © t Second Floor  Roof N  A Sixth Floor  © t Ground Floor  Legend: Small arrows show positive direction of measured motion in the plane of the paper. Dots show positive direction of measured motions out of the plane of the paper.  Figure 3.7. Instrumentation plan of the building during the Whittier and the Northridge earthquakes.  19  Ground Floor (NS)  0.4  -~JWfYWrf^^  0.0 -0.4 0.4  — _J  I  —  —  0.25 g  •  L  i—  Fourth Floor (NS)  0.20 g  0.0 _l  -0.4 0.4  r-  I  .  L_  Roor (NS)  0.41 g  0.0  I  -0.4  ra  o.o  Q) H  -0.4 0.4  i  i  i  i  Ground Floor (EW)  0.13 g  Fourth Floor (EW)  0.25 g  I  "  _j i—  .  i i_  .  Roor(EW)  0.33 g  Ground Floor (Vertical)  0.18 g  Fourth Floor (Vertical)  0.24 g  o.o -0.4 0.4  I  I  I  I  I  '  I  I  I  I  1  1  L_  i—  0.0 -0.4 0.4  0.0  _j  i  i  1_  i—  Afi^fjIYf^h'tyt^  —  -0.4 0.4  j—  Roof (Vertical)  o.o ik«vvYY\/\^^ -0.4  I  I  I  0.24 g  *->~K^S*~~^~^~— I  I  I  I  I  I  I  I  I  I  I  10  1  15  1  L  1  1  1  1  1  1  20  Time (sec) Figure 3.8. Recorded (processed) accelerations during the 1971 San Fernando earthquake.  20  1  25  0.2  Ground Floor (SW Corner) - chan.1  0.16 g  0.0 I  -0.2 0.2  I  I  I  I  _ lI  I  I 1_  I I I 1 — - J 1 1 1 Second Floor (SW Corner) - chan. 7  1  ' 1 0.17 g  ww^/yill^  0.0 -0.2 0.2  I  -  Third Floor (SW Corner) - chan. 5  r-  0.19 g  0.0 -0.2 0.2  i  i  i  l  I  I  l_  !_U  I  I  I  I  1  L  Roof (SW Corner) - chan. 2  0.18 g  Ground v j i u u n u Floor n u u i (SE V - Corner) U U M ICI / - chan. <_-• i a i i . 13 io  0.12 g  0.0 -0.2 0.2  _l  I  I  I  I  1  1  J  L_  I  O L  0.0 -0.2 0.2 i -  _1  I  I  I  c o  -0.2 0.2  ro — i a>  0.0  8 o  _l  L  I  I  _1  U  I  I  I  1  1—  i  _i  i  i_  _l  I  _l  L  I  1_  I  I  i  L_  _L Third I IIIIU Floor I l u u i (East y i _ a o i Wall) w a n ; -- chan. VIIQII. 6 w  I  _l  0.14 g  vw>~^^  ~JdiMhh^^  -0.2 0.2  1  Second Floor (East Wall)-chan. 8  0.0 3  I  i  i  i  I  i  i  i  i  I  i  i  I  i I  i I  I  i  I  I  0.16 w . i wg y  i I  I 1  L. 1  1  Sixth Floor (East Wall) - chan. 4  0.08 g  Roof (East Wall) - chan. 3  0.15 g  J i i i , L Second Floor (East Wall) - chan. 12  0.13 g  < 0.2 0.0 -0.2 0.2  i  _i  i  i_  i  i  r -  0.0 -0.2  i  i  i  i  i  I  I  I  i  i_  J  I  Third Floor (East Wall) - chan. 11  10  15 Time (sec)  Figure 3.9. Recorded (processed) accelerations during the 1987 Whittier earthquake.  21  L.  0.6  Ground Floor (SW Comer)-chan.1  0.39 g  ~ ^ | | Y V l A l / ^ — - ~ - — -  0.0 -0.6 0.6 (-  i  i  '  i  I  i  i  i  i  l i_  _J  I  I  ~  L_  Second Floor (SW Corner) - chan. 7  - ~ - ^ i y y v A / v ^ —  0.0 -0.6 0.6  _l  I  _J  L_  I  0.33 g  •  _l  L-  ~  I  Third Floor (SW Comer) - chan. 5  L_  0.41 g  0.0 i  -0.6 0.6  i  i  I  i  i  i  i  I  i  '  i  i  I  i  i  i  i  1 _j1  1 i  i  Roof (SW Corner) - chan. 2  L_  0.56 g  0.0 -0.6 0.6  Ground Floor (SE Corner) - chan. 13  —  0.0 i  -0.6 0.6  i  i  I  i  i  i  i  I  i  _1  i  I  i  I  i  !_  I  i  i  i  i  0.42 g  — 1  _1 1  I1  — ~ I1  Ground Floor (SE Comer) - chan. 14  L_ 1  1  0.40 g  0.0  __i  -0.6 0.6 r -  i  I  i  i  i  i  I  i  1  1  1  1  1  1  1  1  1  1  Second Floor (East Wall) - chan. 8  0.34 g  Third Floor (East Wall) - chan. 6  0.45 g  0.0  g  m \2  -0.6 0.6 0.0  _j  i  i  i  l  i i_  •~ ^\j\^\f\f\^^  •  J  ~  <D O  3  -0.6 0.6  Ground Floor (SE Corner) - chan. 16  0.45 g  0.0 _J  -0.6 0.6 0.0  I  _l  L_  Second Floor (East Wall) - chan. 12  ***~jS*tiJ\fi/d\^i^  L_  0.29 g  —  Ground floor (SE Comer) - chan. 15  | - - < ^ y « \ W * A V ^ H ^ | ^ I i i i i I _i i i_  — ———  ,  -0.6  I  10  Time (sec.)  _i 15  i  0.27 g  — — — •—  L.  20  Figure 3.10. Recorded (processed) accelerations during the 1994 Northridge earthquake.  22  25  Chapter 4  DATA ANALYSIS  4.1 Introduction  Different data analysis techniques can be used to identify the dynamic characteristics of a structural system from its recorded response during an earthquake. The techniques are based either on time domain analyses or frequency domain analyses. Some o f these techniques can also be used for damage detection or detection of unusual building responses. Recently, some new techniques such as the wavelet transformation, which utilizes a combination of time and frequency domain analyses (Rezai and Ventura, 1995), have been implemented in signal analysis of recorded responses of buildings to determine dynamic characteristics and possible structural damage.  A parallel study using the wavelet transformation technique is currently  being conducted on recorded responses of the building. investigation are outside the scope of this thesis.  However, the results of this  Time and frequency domain analysis  techniques were used in this study to evaluate the earthquake behaviour of the building  4.2 T i m e D o m a i n Analysis  The displacement response of a building can be better understood by computer animation of a model of the building using the recorded motions of different elements of the computer model. A commercial signal analysis and animation program (ME'scope Version 3.0) was used for this purpose.  A selected three-dimensional displaced position of the building during the  Whittier earthquake is shown in Fig. 4.1.  One top view, two side views, and one three-  dimensional view of the building are shown in this figure.  23  The dashed lines represent the  undeformed (original) state of the building and the solid lines represent the displaced position of the structure. The double solid lines in the front side view show the displaced position at the two ends of the building. The displaced position at each end of a story was obtained by either assignment  of existing  records to corresponding nodes or by  linear interpolation  of  neighboring nodes. Selected instantaneous states of displacement for the three earthquakes are shown in F i g . 4.2.  A dominant torsional response can be observed over long intervals during  the Northridge earthquake, especially during the strong ground shaking part (see Fig. 4.2.(e)).  Figure 4.1. A selected instantaneous three-dimensional displaced position (t=16 sec.) of the building during the Whittier earthquake.  24  Front  IFrort  .Front (+>q-5.2 Seconds  - 3.2 Seconds  - 6.2"S«cdrid«""  Front i+iq - 73 Seconds  (Front f,*X) -11 Seconds  (a)  L jRight (+Y)-15 Seconds  Right (+V) - 6.4 Seconds  (b)  I Fro ni (>!q-aB Seconds  .Front i>X)-7.8 Seconds  Front {+X}-67 Seconds  Front (+X)-11 Seconds  IFront (+X) -15 Seconds  (c) Ji  i\  L,  L, Rijht(+V)-7.0 Second*  (d)  J. Front {+X) - 7.9 Seconds  Front (+XJ-6.3 Seconds  (e)  ..u Right (+VJ-4.1 Seconds  L, |fiiaht(+¥)-7.3S«cond>  (0  J,  Figure 4.2. Selected instantaneous displaced position of the building, (a) San Fernando Transverse, (b) San Fernando Longitudinal, (c) Whittier Transverse, (d) Whittier Longitudinal, (e) Northridge Transverse, (f) Northridge Longitudinal.  25  The ground motion records at the ground floor of the building were used to calculate the absolute motions.  acceleration and pseudo-velocity  response  spectra for different components  The results for 5% viscous damping are shown in F i g . 4.3.  of  For reference, the  response spectra for the site as given by the 1994 version of the Uniform Building Code ( U B C ) is also included in this figure.  The spectral acceleration of the Northridge earthquake in the  east-west (longitudinal) direction is more than twice that of the San Fernando earthquake over the period of interest (0-1.5 seconds). There were no recorded data available in the east-west direction at the ground floor during the Whittier earthquake.  •  2.0 ,  0  .  1  .  2  ,  3  ,  4  ,  ,  5  0  Period (sec)  :  0  =  ,  1  —  1  10  Period (sec)  2.0  0  1  2  3  4  5  0  Period (sec)  0  1  10  Period (sec)  Figure 4.3. Linear-elastic response spectra of horizontal ground motions recorded at the ground floor of the building (5% Damping).  26  For the Northridge earthquake the acceleration response spectra is greater than l g in both the east-west and north-south directions between the periods of 0.1 to 0.5 seconds.  This value is  much higher than the design response spectra for this site given by the U B C - 6 7 (equivalent to design code o f the building (J. A . Blume & Associates, 1973)) and even the U B C - 9 4 .  The  difference in level of demand between the earthquakes is well demonstrated in this figure.  The pseudo-velocity response spectra of the Northridge earthquake in the east-west direction is about twice that of the San Fernando earthquake over the period range of 0 to 2 seconds. In the north-south direction these values for both events are not too different for the periods over 0.4 seconds.  -25  0 E-W(Transv.)  25 -25  0 E-W(Transv.)  San Fernando  Whittier  25 -25  0 E-W (Transv.)  Northridge  Figure 4.4. In plane particle motions during each earthquake. 27  25  In-plane particle motions of absolute ground floor displacement, absolute roof displacement and relative roof displacements during the three earthquakes are shown in Fig. 4.4. In the eastwest direction, the record from the second floor sensor is used for the Whittier earthquake, since the ground motions in this direction were not measured due to instrument malfunction.  The displacement amplification from ground floor to roof and the different displacement demands of each earthquake can be determined from these plots.  Even though the ground  floor displacement is larger during the San Fernando earthquake, the relative roof displacement is much larger during the Northridge earthquake. The above observation provides a possible indication of either the difference in the excitation of higher modes or the change in stiffness of the structure and possible damage. It can also be observed that the dominant response of the building is in the transverse (N-S) direction during the San Fernando earthquake and in the longitudinal ( E - W ) direction during the Northridge earthquake. This helps to explain why the failure of the fourth story columns happened in the east-west direction during the Northridge earthquake.  4.3 Frequency D o m a i n Analysis  Detailed frequency domain analyses of recorded responses were performed to determine the dynamics characteristics o f the building. The probable natural frequencies and mode shapes of the structure were estimated based on a Fourier Transform analysis of selected segments of the recorded  motions.  Frequency Response  Functions (FRF) were  evaluated  using  the  acceleration at the ground level as input and relative displacement at different floors of the building as output. A sample F R F for the 13 to 19 second portion of the Northridge earthquake is shown in F i g . 4.5.  The peak points in this figure are an indication of possible natural  28  frequencies of the building at the corresponding time interval.  Changes  in the  dynamic characteristics of the  system  during  each  earthquake  were  investigated. Natural periods and mode shapes were estimated from F R F analyses of segments of the records, each with a duration ranging from three to six seconds. analysis  and animation program was used to determine natural  M E ' S c o p e modal  periods and animate  corresponding mode shapes.  15  E o  ~  i  •  Roof -—  10  'c ro ^  :  h  6th Floor 3rd Floor 2nd Floor  5  H 2  3 Frequency (Hz)  2  3 Frequency (Hz)  Figure 4.5. Frequency response function (magnitude) corresponding to 13-19 seconds segment, Northridge earthquake, a) east-west direction, (b) north-south direction.  29  (a) i  1  1  Before the strong shaking of the San Fernando earthquake, the fundamental frequency of the building in the transverse direction was estimated as 1.29 H z (T= 0.78 sec), with a second mode frequency of about 4.3 H z (T= 0.23 sec) (Fig. 4.6). These values are fairly constant over the first 7 seconds. After the first few seconds the natural frequency of the system started to change, such that the fundamental natural frequency in this direction became 1.1 H z (T= 0.91 sec) at around 12 seconds, 0.85 H z (T= 1.18 sec) at around 14 seconds and 0.71 H z (T= 1.41 sec) at around 17 seconds. Finally, the fundamental frequency of the system dropped to 0.65 H z (T= 0.42 sec) and the second mode frequency changed to 2.6 H z (T= 0.38 sec). A decrease of about 49% in the fundamental frequency and about 40% in second mode frequency of the building was observed throughout the duration of the shaking.  The initial fundamental natural frequency of the structure in the longitudinal direction was determined as 1.3 H z (T= 0.77 sec). sec).  The second mode frequency was about 4.1 H z (T= 0.24  The change of frequency begins after the first 4 seconds such that the building had a  fundamental frequency of about 1 H z between 5 to 10 seconds and 0.83 H z (T= 1.20  sec)  between 10 to 15 seconds. Finally, during the free vibration part of response, the fundamental frequency of the structure was estimated to be 0.77 H z (T= 1.30 sec) and the second mode frequency to be about 2.82 H z (T= 0.35 sec).  These values correspond to 41% and 31%  decrease in the fundamental and second longitudinal mode frequencies, respectively.  The  mode shapes of the building at the end of earthquake are shown in F i g . 4.7. Even though only minor structural damage had been reported during this earthquake, the change in the natural frequencies of the system was significant.  Torsional behaviour of the building could not be  studied here, because the building was instrumented with only one triaxial strong motion accelerometer at each floor during this earthquake.  30  CD T3 O  f = 4.1 Hz CD X3 O  / (  O O (D  i  \-i  00  Transverse M o d e  Longitudinal M o d e  Figure 4.6. Original natural frequencies and mode shapes of the building at the beginning of the record obtained during San Fernando earthquake.  cu o  CD T3  o  T3  c o  CJ  CO  Transverse M o d e  Longitudinal Mode  Figure 4.7. Natural frequencies and mode shapes of the building at the end of the record obtained during San Fernando earthquake. 3 1  During the Whittier earthquake, the amplitude and duration of excitation were very small compared to the San Fernando and Northridge earthquakes.  The response o f the building  during this earthquake can be considered as, or almost, linear elastic.  The fundamental and  second mode frequencies of building were 0.78 H z (T= 1.28 sec) and 2.85 H z (T= 0.35 sec) in the transverse direction.  In the longitudinal direction, the fundamental and second mode  frequencies were estimated as 0.94 H z (T= 1.06 sec) and 3.33 H z (T= 0.3 sec), respectively. These values were fairly consistent throughout the whole excitation. The corresponding mode shapes are shown in Fig. 4.8.  f =0.9 Hz  X  Longitudinal Mode  Transverse Mode  Torsional Mode  Figure 4.8. natural frequencies and mode shapes of the building from the record obtained during the Whittier earthquake. Epoxy repair o f the beams and columns, specially at the first floor, was reported after the San Fernando earthquake. These repair works might have changed to some extent the dynamic  32  characteristics of building. Therefore, the increase in the frequencies of building, compared to free vibration response during the San Fernando earthquake, could be due to the repair work, effect o f nonstructural elements and also the level of excitation.  The torsional response of the building during the Whittier earthquake was obtained by subtracting the records of sensors at opposite side of each floor assuming that the floors were infinitely rigid in their own plane.  The fundamental torsional frequency of the building was  estimated to be 0.90 H z (T= 1.11 sec).  The second mode frequency was about 2.8 H z (T=  0.357sec).  During the Northridge earthquake, in the transverse direction after the first few seconds of shaking, the fundamental frequency of the building dropped to 0.6 H z (T= 1.67 sec).  This  frequency value did not change till around 10 seconds. This is interesting, because the high peaks of acceleration records were mostly concentrated at this interval. Immediately after 10 seconds, the fundamental frequency shifted to 0.47 H z (T= 2.13 sec).  Finally, during the free  vibration response of the building this frequency became 0.44 H z (T= 2.27 sec).  The second  mode frequency was about 1.54 H z (T= 0.65 sec) at this instant.  Unlike the transverse direction, in the longitudinal direction the damage in the building most likely happened during the first few seconds. The fundamental frequency of the system in this direction shifted to 0.47 H z (T= 2.12 sec) at around 4 to 5 seconds. This frequency was more or less dominant during the rest of the record. estimated to be 1.19 H z (T= 0.84 sec).  The frequency of the second mode was  The above values are within the interval of spectral  peaks shown in (Fig. 4.3), which caused high demands on the building during this event.  33  The torsional response of the building was significant during Northridge earthquake.  The  fundamental torsional frequency of the building was determined as 0.48 H z (T= 2.08 sec). The torsional response of the structure was similar to that of the longitudinal direction. The above value was reached only after 3 to 4 seconds of vibration from the beginning of recorded motion. The drastic drop in the fundamental natural frequencies, together with the existence of high frequency components are indication of probable damage in the building.  Modal coupling between lateral and torsional modes was observed.  The first and second  transverse mode shapes had significant torsional response at the higher floors. The effect of transverse modes were also observed in the rotational mode shapes of the structures.  These  interactions are well demonstrated at the plotted mode shapes shown in F i g . 4.9.  CD  •a o  f = 2.0 Hz  1  [if  •2'  r  X  Longitudinal M o d e  Transverse Mode  Torsional M o d e  Figure 4.9. Natural frequencies and mode shapes of the building at the end of the record obtained during Northridge earthquake.  34  T  The changes in the fundamental natural frequencies of the building over the duration of shaking for the three earthquakes are illustrated in Fig. 4.10.  The change in the fundamental  frequencies o f the building during each earthquake clearly reflects the nature of the response of the structure during that event.  During the San Fernando earthquake, the change in the  fundamental frequencies is significant, but gradual. It is consistent with the observed damage in the building; minor cracking of members and minor damage in a few connections.  The  identified fundamental frequency at the start of the earthquake is lower than that detected by the pre-1971 ambient vibration test measurements (1.29 H z vs. 1.92 Hz).  The post-1971  ambient vibration test results are not consistent with the values obtained from the records (see Table 3.2).  There are not apparent changes of these frequencies during the Whittier  earthquake.  Assuming that the fundamental frequencies o f the building at the start of the  Northridge earthquake would have been about the same as those for the Whittier event, it can be noticed in that the frequencies change drastically in the first few seconds of strong shaking. The drastic and sudden drop of frequencies can be used as an indication of severe damage.  1.3 1.29  0.83 1.1 0.85  1  0.71  20  10  0  0.77 0.65  longitudinal transverse b San Fernando 30 0.9 torsional 0.94 longitudinal 0.78 transverse  0.9 0.94 0.78 •  20  10  0 0.48 0.47 0.6  0.48 0.47 0.44  0.6 0.47  Whittier  30  torsional longitudinal transverse  •  0  20  10  Northridge  30  time (sec.) Figure 4.10. Changes in the fundamental natural frequencies of the building during the duration of shaking from the three earthquakes.  35  The identified probable natural frequencies of the structure at the end of each event are also summarized in Table 4.1. The estimated equivalent viscous damping ratio for the fundamental natural frequencies of the building is also included. The latter values were computed using the Half-Power (Band-Width) Method (Clough and Penzien, 1993).  Table 4.1. Probable natural frequencies of the building at the end of each earthquake. Northridge  Whittier  San Fernando  Freq. Hz  Tors.  Trans.  Long.  Tors.  . 0.94  0.9  0.44  0.47  0.47  2.85  3.33  2.8  1.54  1.19  -  _  4.7  6.2  4.4  2.28  1.9  2.0  —  ' —  7  -  6.4  3.3  -  8  _  —  —  -  -  4.34  -  -  7-8  9  -  4-5  5  5  8  10  8-9  Trans.  Long.  Tors.  Trans.  1st  0.65  0.77  _  0.78  2nd  2.6  2.82  —  3rd  4  4.2  4th  5.9  5th Damping 1st mode % Critical  Long.  .  -  A comparison of fundamental frequencies in the longitudinal direction predicted in this study with other studies reported by C S M I P (1996) is presented in Table 4.2.  The differences  between the estimated and reported values are small and may be due to differences on the methods used to estimate the values.  Table 4.2. Comparison of fundamental frequencies in the longitudinal direction predicted here with other studies (CSMIP 96). Estimated (Hz)  CSMIP 96 (Hz)  1971 San Fernando  0.77  0.76  1987 Whittier  0.94  0.9  1994 Northridge  0.47  0.5  Event  36  4.4 S u m m a r y  A detailed analysis of the recorded data of the building has been conducted during three earthquakes and presented in this chapter. The state of the building at the start and during each event has been investigated.  The results of analysis showed the large contribution of second  and higher modes to overall response of the building and that the peak spectras of the base excitation was closer to the natural frequencies of system at the time of the Northridge earthquake.  This relative closeness of the frequencies together with high amplitudes put  higher demand on the building during this event. The original fundamental frequencies of the building (pre-1971  San Fernando earthquake) were estimated to be about 1.3 H z .  They  dropped to about 0.47 H z at the end of the Northridge earthquake which shows that the building fundamental frequencies were shortening about three times the original ones at the end of the Northridge earthquake.  Although the building is regarded as a symmetric one, the torsional response of the building was significant during all events.  High frequency components of response were observed.  This is generally accepted an indication of possible existence of structural damage.  The  building three-dimensional animation showed combination, or coupling, of translational and torsional responses over a wide range of frequencies.  The basic dynamic characteristics of the building was studied and presented in this chapter. These information would be used to develop and calibrate an analytical model which can reflect the actual behaviour of the building.  37  Chapter 5  THREE-DIMENSIONAL LINEAR ANALYSIS OF THE HOLIDAY INN BUILDING  5.1 Introduction  The primary objective of performing a three-dimensional linear analysis was to understand the behaviour of the building during the Whittier earthquake, where the building is believed to have responded as a linear elastic system.  The results from this analysis also helped to  determine the extent of contribution of the different structural components as well as the nonstructural components to the overall response of the building. The linear model and the related analytical studies were used to form a basis for the development of the nonlinear model.  The secondary objective of performing a three-dimensional linear analysis was to study the nonlinear response of the building during the Northridge earthquake by a series of linear analyses. During inelastic response, the dynamic characteristics of a building vary due to the change of stiffness, strength degradation, and damping of the system.  It is obvious that by  performing a linear analysis it is not possible to predict the entire response of the building during the Northridge excitation when the building responded in a highly nonlinear-inelastic manner.  However, by performing linear analyses of the building using different dynamic  properties, it is possible to produce the response of the building during different stages of shaking.  This approach was attempted here by developing two models of the building. The  first model (Model 1), used to study the behaviour of the building during the early part of the Northridge earthquake, was essentially the same as that used to analyze the response during the Whittier event but with different damping values. The second model (Model 2) was developed by subsequent modification of the first model using information from the analysis of the  38  recorded  responses and that about the damage in the building during the Northridge  earthquake.  5.2 Development of a L i n e a r M o d e l of the Holiday Inn Building  Program ETABS Version 6.1 (1996) was used for the three-dimensional linear analysis of the Holiday Inn building.  The program was chosen because of its substantial capabilities  (Habibullah, 1992) and its reliability which makes it one of the most popular tools for routine analysis of structural systems.  The building was modeled as a Single frame consisting of 36 main column lines and 59 bays. To account for bending stiffness of the slabs, the interior frames were connected with onemeter wide beams with the same thickness as their corresponding slabs. The model of the building is shown in Fig. 5.1.  Figure 5.1. Model of the building used for linear analysis. 39  The in-plane stiffness of the floor system was considered to be high (the thickness of the floor slabs at each level is more than 200 mm), and therefore, the floor diaphragms were assumed to be rigid.  Under this constraint, each diaphragm can be shown to consist of three in-plane  degrees of freedom, one rotational and two translations.  The building was assumed to be fixed at the ground level.  A l l the beam and column center  lines were considered to coincide with column line coordinates. Thus, the effects of the offset of longitudinal spandrel beams were neglected.  Additional frames were used to model the  elevator opening and the stairs at both ends of the building. Some floors with no diaphragm were also added between the stories to model the stairs.  The masses of the beam and column members associated with each floor were calculated from the specified geometric dimensions of elements and combined with the mass of slab to determine the total story mass at corresponding floor.  The estimated final mass and mass  moment of inertia were lumped at the center of mass at each floor. The estimated weight of the structure at each story level is shown in Table C . l of Appendix C . The total mass of the building was estimated to be about 4500 tons.  The model representing the behaviour of the building during the Whittier earthquake was developed through four stages, considered as four models. They are; a) Model 1: "the Gross Section Property Model" (GSP), often used in the analysis of reinforced concrete structures (Zeris, 1986). For this model, the nominal specified values of various material strengths and gross section geometries were used; b) Model 2: "the Gross Section Property plus Wall" ( G S P W ) , which is the same as the G S P model with the addition of the brick infill wall between the ground and second floor at the north perimeter frame; c) Model 3: "the Cracked  40  Section Model" (CS), which is based on suggested ranges of cracked section properties recommended for design and/or analysis (Paulay et al., 1995); d) Model 4: "the Calibrated Cracked Section Model" (CCS), which involves calibrating the cracked section properties to best match the fundamental periods of the building in each direction.  The non-structural brick walls at the first floor of the north east side of the building were modelled using panel elements.  It was postulated that the modelling of these walls was  essential in order to capture the torsional behaviour of the structure. The stairs at both sides of the building and elevator opening were also modelled to consider their torsional effects. The 25 mm cement plaster exterior walls in the east and west end of the building were not included in the stiffness computation, but were included in the mass computation.  5.3 Calibration of the Model and Period Sensitivity during the Whittier Earthquake Table 5.1 summarizes the descriptions of the four models used to study the response of the building during the Whittier earthquake. The computed fundamental periods are also included for reference.  It was observed that the periods of the C C S model, which represented the state of the building at the time of the earthquake, were between the periods of the G S P W and C S models.  To  capture these periods, the cracked section properties (cracked section moment of inertia) were increased by about 30 percent of the moment of inertia values used for the C S model. The mass moment of inertia was also increased by the same percentage to capture the fundamental torsional frequency.  These increases may be explained by the overstrength of the materials  used in the structure and the mass contributions of some non-structural elements, such as  41  cement plaster exterior walls in the east and west end of the building. The above observation was also indicated in an independent study of the building by Islam (1996). However this study was limited to planar nonlinear analysis of a longitudinal frame during the Northridge earthquake. The mode shapes CCS of the building are shown in Appendix C. Table 5.1. Descriptions of the four models used for linear analysis. Effective Moment of Inertia  Model  GSP  GSPW  Column Beams  h  Columns Beams  h h  Walls  CS  CCS  Columns Beams Walls Columns Beams Walls  0.82 0.99 1.12 (1.23) (1.01) (0.89)  0.05I 0.6I  g  0.6I  g  0.05I 0.8I  Fundamental Natural Frequencies of the Building H z (Periods sec) Trans. Tors. Long.  0.82 1.03 1.14 (1.23) (0.97) (0.88) g  0.69 0.85 0.92 (1.45) (1.18) (1.08) g  g  0.8-0.9I 0.05I  g  0.76 0.91 0.95 (1.31) (1-10) (1.05)  g  0.78 Whittier Data Analysis  0.90  0.94  (1.28) (1.11) (1.06)  I„: Gross section moment of inertia  It should be noted that even though the addition of the infill brick walls to the model had little influence on the fundamental periods of the structure, it changed the torsional mode shapes and consequently affected the response of the building.  5.4 Elastic Time History Analysis of the Building during the Whittier Earthquake  The three-dimensional response of the building during the Whittier earthquake was predicted analytically. The purpose of such an analysis was to correlate the recorded responses with the analytical results, and to assess the effects of various members on the overall three-  42  dimensional behaviour of the structure for low levels of excitation.  The response of the building was computed for the first 40 seconds of the recorded excitation. A total number of nine modes were used (3 for each direction) such that the sum of the effective modal mass contributions in each direction was equal to approximately 98 percent of the total mass of the building. A viscous damping ratio of 5 percent critical was used. The mass distribution reflected only the dead loads as shown in Appendix C .  Two independent input ground excitation, horizontal translations, were used.  The record of  channel 13 at the east wall of the building was selected as the north-south input (see Fig. 3.7). Unfortunately, there were no records available in the east-west direction at the ground floor during this event.  Therefore, the east-west input was set to 85 percent of the record of  instrument 12 at the second floor of the building (corresponding to the same amplitudes at the second floor).  5.4.1 Comparison of predicted and recorded time histories  Figure 5.2 and 5.3 show the recorded and predicted (Model C C S ) roof absolute acceleration and relative displacement time history responses of the building. A good match between the two responses implies that the model is able to predict the frequency content of the actual response of the structure. In the north-south direction the agreement of the peak amplitudes is poor, especially between 17-25 seconds. This difference in behaviour may be due to the effect of nonstructural partitions made of cement plaster panels at both ends of the building in this direction that has not been accounted for in the computer model.  During such a small  excitation, these non-structural elements may make significant contributions to both rigidity and damping of the structure. 43  200 o CD  w E c o CD CD O O  <  -200  15 Time (sec)  200 o  CD  in  E  c o 0) CD O O <  -200  15 Time (sec)  200 o cu  c o  2 cu o o <  -200  15 Time (sec)  Figure 5.2. Comparison of recorded and calculated roof absolute acceleration responses, Whittier earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  44  15  Time (sec)  15  Time (sec)  From Channel  A A A'  ki* *  •  I / >' •  9  y  V *  V/ \ V  4  (c)  i 10  15  20  25  Time (sec)  Figure 5.3. Comparison of recorded and calculated roof absolute acceleration responses, Whittier earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  45  30  Even though the input ground excitation in the east-west direction was only an approximation to the actual ground motion, there exists a good correlation between the predicted and the actual response of the building in this direction.  The correlation between predicted and  recorded accelerations were better than that for displacements. the way in which displacements processing techniques  This difference may be due to  are inferred from recorded accelerations.  and integration routine of recorded accelerations  The type of  used by C S M I P  depends on the level of excitation and its frequency content.  5.5 Response of the Building during the Northridge Earthquake  A  correlative three-dimensional  linear elastic time history analysis of the building was  conducted using the Northridge earthquake records. The response of the building during this event was investigated in two parts using two models. Model 1, representing the undamaged state of the structure was essentially the Calibrated Cracked Section Model developed in the previous section.  Model 2 represented a damaged state of the building, which was modelled  by a significant reduction in the stiffness and minor adjustments of the first model.  Some of  these modifications were: columns and beams effective moments of inertia were reduced by approximately 50 percent of Model 1 for all floors; to model the damaged columns and loss of stiffness between fourth and fifth floors, only 5 percent of gross section moment of inertia for perimeter columns were assigned in this floor; a 50 percent panel zone rigidity reduction was assumed to reflect the probable loss of stiffness of joints due to formation of minor diagonal cracks. A modal viscous damping ratio of 8-10 percent of critical was used.  46  5.5.1 Response of the model during the early part of the excitation  Figure 5.4 shows the recorded and predicted (Model 1) roof absolute acceleration time history responses of the building.  The figure shows that the model can estimate the recorded  accelerations only during the first 3 to 4 seconds in the east-west direction. After 5 seconds it overestimates the response of the building.  In the north-south direction, the predicted and  recorded responses are comparable for a longer time interval, first 8-9 seconds; thereafter, the predicted and recorded responses are quite different.  Figure 5.5 shows the recorded and predicted (Model 1) roof relative displacement time history responses of the building. The same behaviour is observed in these records.  The above observations suggest that the structure responded in a nearly linear elastic manner only during the first few seconds. After approximately 4 to 5 seconds, some elements started to behave in an inelastic nonlinear manner. This was probably when the cracks in the beamcolumn joints and perimeter columns between the fourth and the fifth floors were formed. The predicted north-south response at the east wall shows that the shear failure of the columns may have occurred at about 8-9 seconds.  5.5.2 Response of the model during the late part of the excitation  Figure 5.6 and 5.7 show the recorded and predicted (Model 2) roof absolute acceleration and relative velocity time history responses of the building. In the east-west direction, the model can quite well predict the exact behaviour of the building over the entire recorded excitation. There are only slight discrepancies between 4 to 7 seconds.  In the north-south direction, the  predicted acceleration responses match the recorded ones only after 7-8 seconds. However, the  47  0  5  10  15  Time (sec)  Time (sec)  Figure 5.4. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake, early part, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  48  20  30  5  10 Time (sec)  15  20  5  10 Time (sec)  15  20  30  Figure 5.5. Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake, early part, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  49  5  10  15  20  25  30  20  25  30  Time (sec)  600  0  5  10  15 Time (sec)  Figure 5.6. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake, late part, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  50  30  «  -r+- •  i '  i» E o  A  /'  CD O  \  ro Q.  w  b  A:  A"* v  c a> E  -30  /•  I» 1  f  V  From Channel 2  M  <\  »'  r  i »  I 1  — _ _ . A/8LsvYW  k  A IV M  \f\  »  ry i \ !  A  /  V / i  yi  (a)  ».'  «  10  15 Time (sec)  20  15 Time (sec)  20  25  E c <D  E  CD O JO Q. W  E o c CD  E  CD O  ra Q.  in  15 Time (sec)  Figure 5.7. Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake, late part, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  5 1  30  displacement responses in F i g . 5.7 significantly differ till 14 seconds.  After the 14 seconds,  the predicted displacement responses, specially the time history at the west end, are very close to recorded ones both in frequency and amplitude sense.  A comparison of the records from the accelerometers in the north-south direction indicates the existence of significant rotational components  in the response  of the building.  There  correlation between the recorded and predicted rotational responses of the building was poor and no attempt was made to improve this correlation.  It is interesting to note that in the north-south direction, Model 1 predicts better than Model 2 the east end response of the building during the early part of the shaking. In contrast, Model 2 predicts better the west end response of the building during this event.  5.6 Summary  The best match between analytical and experimental values was obtained when the cracked section properties for the linear model of the building were taken as 0.8I for columns and g  0.8I to 0.9I for beams during the Whittier earthquake. g  g  These were found to be about 30  percent larger than the cracked section properties normally recommended for design and/or analysis (Paulay et al., 1995).  These increases can be explained by the overstrength of the  materials used in the structure and the mass contributions of some non-structural elements, such as cement plaster exterior walls in the east and west end of the building. The addition of the infill brick walls to the model had little influence on the fundamental periods of the structure, but, it had a significant effect on the torsional response of the building.  Linear analysis only predicted the response of the building when the dynamic characteristics of  52  the structure were well defined and did not change significantly.  The linear analysis failed to  predict the actual response of the building during high levels of excitation due to yielding and nonlinear behaviour of member. However, a good prediction for different time portions of the actual response of the building during the Northridge earthquake was obtained by updating the member stiffnesses based on the observed damage.  The result of analysis showed that a nonlinear analysis is essential in order to predict the actual response and sequence of damage in the building during high levels of excitation.  53  Chapter 6  DESCRIPTION OF THE NONLINEAR ANALYSIS PROGRAM  6.1 Introduction  C A N N Y - E (1995) is a general purpose computer program for 3-dimensional nonlinear static and dynamic analyses of reinforced concrete and steel building structures.  The program is  based on a lumped plasticity model and has the capacity for analyzing large structures.  Some  general features of the program are as follows.  The  structure is idealized as a number of nodes, or joints, connected by a number of  deformable elements.  The program has both rigid and flexible floor modeling capabilities.  Geometric nonlinearities (large deformation) are not included. The analysis is limited to small deformations, but the P - A effect can be considered.  In the analysis every member in the  structure is treated as a massless straight linear element. The mass of structure can be lumped at structural joints or can be concentrated at the center of gravity of every floor level if a rigid floor slab is assumed. The state of elements (stiffnesses) under initial load can be considered as initial conditions before the start of static and dynamic analyses.  The nonlinear dynamic analysis is conducted step by step in a specified small time interval. The time interval is selected considering the characteristics of the input motion and taking into consideration the following relations: (1) nonlinear relations between forces and resultant displacements; (2) compatibility relation of displacements at a structural joint; (3) equilibrium relation of forces at a structural joint; and (4) differential relation among time  response  functions. The current version of the program used for this study does not iterate during time steps to account for the stiffness changes, but, the unbalanced force at the end of each time step  54  is calculated and added to the next time step.  The equation of motion includes total degrees of freedom with or without mass of the structure.  The program does not implement any static condensation technique.  The skyline  matrix technique is used in the program to assemble and memorize the structural matrices. The matrix decomposition due to the change of stiffnesses is carried out by the Square-rootfree Choleski method.  A n internal optimum renumbering system was developed and utilized  in the program to minimize the total size of the skyline matrix.  Such approach reduces the  required size of computer core memory and speeds up the computing time.  The incremental  equation of motion is expressed as:  [M]{AX}  + [C]{AX}  + [K]{AX> = {AF } e  - {F } u  where, [M] is the diagonal mass matrix of the system, [C] = a  k  instantaneous viscous damping matrix, {AX} structure relative to the base, {AX}  +  {AF } t  m  0  0  is the vector of displacement increments of the  is the increment of the velocity vector, {AX]  increment of acceleration vector, [K] is the instantaneous stiffness matrix, [K ] 0  stiffness matrix,  is the  [K]+a [M]+a [K ]  is the  is the initial  is the increment of earthquake inertia force vector, {F }  is the  unbalanced force vector at the beginning of the present time interval and {AF }  is the  {AF } e  u  t  incremental time-varying external load vector.  Two numerical procedures, the Newmark's Beta-Method and the Wilson's Theta-Method (Zienkiewicz and Morgan, 1983), are available and employed in the program to solve the equations of motion. Linear variation of acceleration is assumed in the numeric integration of the equations of motion during a specified time interval. used in this study.  55  The Newmark's Beta-Method was  6.2 Elements  The elements used in the program to present the structural members are beams, columns, shear panels, trusses, cables and constraint spring elements.  A beam element is limited to have uniaxial bending with optional shear and axial deformation. The inelastic flexural deformation of the beam element is assumed to be concentrated at its ends, and represented by the rotation of two nonlinear bending springs.  The shear and axial  deformations of beam are approximated by independent shear and axial springs placed at midspan. The model does not include the interactions among the bending, shear and axial forces. The beam axial deformation option can not be included i f it is in a rigid floor slab.  Columns are idealized by any one of three models: a one-component model for uniaxial bending, a biaxial bending model, or a multi-spring model. Interaction between the axial load and bending moment can be taken into account only by the multi-spring model.  Shear and  torsional deformation of the column element can be included in the analysis.  The main feature of this program, which separates it from many other programs, is its multispring column model.  It was developed based on a modification of the original model  proposed by L a i et al.(1984) to simulate the flexural behaviour of reinforced concrete columns under varying axial load and bi-directional lateral load reversal. The column was idealized to be a linear element with its length equal to the column clear height and two multi-spring elements with zero length at the base and the top (Fig. 6.1). The original multi-spring element consisted of 5 concrete and 4 steel longitudinal springs to represent the inelastic flexural rotation and the axial load/moment interaction of column.  However, it was difficult to  determine the spring's parameters to model the member behaviour. 56  Multi-spring Element Elastic Linear Element Inelastic Axial Spring  Multi-spring Element (5-Spring Model)  Figure 6.1. Column idealized by multi-spring model.  (D-tJ/2 d/3\d/$ X  X  b/4  (B-tjM 6  ® Shell concrete spring  _ 1/2(B-tJ(D-tJ/2+(3/8)B  2  y  s^cs ~  • Core concrete spring  B+D _ 1/2(B-tMD-t )/2+(3/8)D  2  Y  d=D-2t,  s  CS ~  b=B-t  s  t = thickness of shell concrete s  16 Concrete Springs  Figure 6.2. Concrete part of spring element for rectangular section.  57  A modification (Li et al., 1988) increased the number of springs in the multi-spring element. The  spring properties were determined based  on the material properties  and section  geometries. With the increased number of springs, the simulation capacity of the interaction behaviour was improved, and the determination of the stiffness properties of each spring was simplified (Li etal., 1993).  The number of steel and concrete springs are selected according to the section shape and location of reinforcing bars. For a rectangular reinforced concrete section, with reinforcing bars evenly distributed on all faces, a typical example using 16 concrete spring (8 core concrete and 8 shell concrete) is shown in Fig. 6.2. right side of the figure.  The location of each spring is shown in  A concrete spring is located at the centroid of a subdivided area.  A  steel spring may be located at a reinforcing bar, or placed at the center of multiple reinforcing bars.  A trilinear force-deformation relationship is shown in Fig. 6.3 for the steel and concrete springs. The spring force is calculated based on the tributary area of the spring and the stress of the material at the centroid of the area. The Bernoulli's hypothesis (Park and Paulay, 1975) is used to determine the deformation distribution in a multi-spring element.  In order to  calculate the deformation for a given strain, an imaginary spring of length r | L representing the 0  plastic zone is assumed. member depth.  The plastic zone length is arbitrarily assumed to be one half of the  Additional deformation is considered to approximate the amount of pull-out  deformation by an empirical parameter K.  The force-deformation relationship for a concrete  spring is assumed identical for both core and shell concrete until maximum resistance, f , is cy  attained at a concrete comprehensive strength  a. B  58  Steel spring  Concrete spring  Figure 6.3. Spring force-displacement relationship  The deformation at the maximum resistance is calculated to be K d , where d c y  the strain at the strength a ).  concrete.  cy  = e r)L (e B  0  B  is  The elastic stiffness of the concrete spring is changed at  B  deformation 0.3f  c y  and resistance 0.5f  cy  to approximate the stress-strain curve of the reinforced  The descending branch o f the stress-strain relationship is different for the core and  shell concrete in order to consider the effect of confinement. zero resistance is defined as d  u  = U K d , where u=s / e . u  c y  B  The ultimate displacement d at u  The e  u  strain is calculated by the  equations (Park et al., 1982) included in Fig. 6.4.  1/^=2((3+0.29oJ/(14/£a -1000)+07ftp,Vh7S -0.002K b  h  K=1+PSV B CT  Figure 6.4. Concrete stress-strain curves. 59  Displacement d length r\L , 0  s y  of the steel spring is determined by the yielding strain s  as d ^ = e r | L . s y  displacement of K d . s y  0  s y  and the plastic zone  The yielding resistance o f the steel spring reaches at the  The elastic stiffness is changed at 0.5f  sy  to consider the pullout effect.  The force-deformation of a steel spring is symmetric in tension and compression.  The shear panel element is based on the original formulation of Kabeyesawa et al.(1985) and is considered to have bending, shear and axial deformations in the panel plane. The element has no effect in the out of plane direction. The bending, shear and axial springs are simple onecomponent springs without interaction between them.  It is possible to have an edge-column attached to the side of a panel. Such an edge-column is treated as a central tension and compression element in the panel plane. For the edge column, the multi-spring model is to be used to represent the interaction between inplane axial deformation and out of plane bending.  A link element connects two nodes and subjects them to tension and compression with no bending. The link element can be defined in a three-dimensional space or a two-dimensional plane. The cable element has a start node and a terminal node. Between the start node and the terminal node, there may be some middle nodes that cause the cable to change its direction in space. The cable has stiffness in tension only.  The constraint spring element is a simple one-component element. It is used to change any one o f the displacement components at a node. It can be used to analyze a substructure or partial frames without changing the properties of structural members.  60  6.3 C A N N Y Hysteresis Models  The program includes a number of hysteresis models expressing nonlinear force-displacement relationships. Some are used for one-component models to simulate the inelastic behaviour of uniaxial bending, shear and axial deformation, and some used for multi-spring present the behaviour of biaxial-bending and axial force interaction.  The uniaxial hysteresis models included in the program are:  For bending and shear deformation: - N o . 1 Linear Model. - N o . 2 Degrading Bilinear Model. - No. 3 Modified Clough Model. - N o . 4 Degrading Clough Model - N o . 5 Takeda-Rule Bilinear Model. - N o . 6 Takeda-Rule Trilinear/Bilinear Model. - N o . 7 Takeda-Rule Trilinear/Bilinear Pinching model. - No. 8 Trilinear/Bilinear Origin-Oriented Model. - N o . 9 Trilinear/Bilinear Peak-Oriented Model. - N o . 10 Bilinear Slip Model. - N o . 11 Trilinear/Bilinear Slip Model. - No. 12 Bilinear Elastic Model. - No. 13 Trilinear/Bilinear Elastic Model. - N o . 14 Trilinear C A N N Y Simple Model. - No. 15 Trilinear/Bilinear C A N N Y Sophisticated Model.  61  model to  For axial Deformation: - N o . 18 Axial Stiffness Model.  - N o . 19 Axial Stiffness Model 2.  A detailed description of hysteresis models is presented in the C A N N Y - E users' manual.  6.4 M o r e Information about the P r o g r a m  Program  CANNY-E  is  executed  in  three  phases:  "PRECANNY",  "CANNY",  and  "PSCANNY".  P R E C A N N Y is a pre-processing program for reading the input data file and preparing it for the main program.  It reads the text free format data file and performs memory allocation,  automatic renumbering, and initialization of element and structural matrices.  It generates a  binary-format data file, called " C A N N Y data file". C A N N Y is the main program where all the numerical computations are carried out.  It stores the calculated results into a binary-format  file, called "Binary result file". P S C A N N Y is a post-processing program which reads the calculated results from the binary result file and transforms them into text-format file.  The  program has two different modules called V C A N N Y and D C A N N Y ,  which are the  graphical interface and animation programs. V C A N N Y is used to check the contents of the C A N N Y data file and show peak values of forces for each element. D C A N N Y is used to show dynamic responses at floor levels and stories.  The program uses the computer core memory and part of the hard disk as virtual memory i f required to memorize the stiffness matrices and conduct the analysis.  62  Therefore, it does not  have any limitation regarding to the size of the structure.  The program is very efficient regarding to the computational time for an analysis.  A time  history analysis of the building studied subjected to 40 seconds (8000 steps) of shaking takes about 146 minutes.  This program was selected to study the behaviour of the Holiday Inn building because it is a three-dimensional program which has elements that consider the biaxial bending/axial force interaction, It does not have any memory limitations, it has the capability of analyzing buildings with large number of components, and it is cost effective.  63  Chapter 7  THREE-DIMENSIONAL NONLINEAR ANALYSIS O F T H E H O L I D A Y INN B U I L D I N G  7.1 Introduction  T h i s chapter describes the nonlinear analyses of the H o l i d a y Inn building. T h e planar pushover and cyclic analysis of the three-dimensional model of the building were performed first. Then, three-dimensional nonlinear time history analyses of the building were conducted to simulate the building response during three earthquakes.  A s mentioned before, the objective in performing nonlinear analyses was to determine i f and how such analyses can predict the response and behaviour of a reinforced concrete building during earthquakes. There was no intention of simulating the behaviour of the building by artificially changing the properties and variables of the system in order to achieve a perfect match between computed and recorded motions. These nonlinear analyses were performed to clarify qualitatively the load resisting mechanism. Specified member characteristics based on a reasonable model which could predict the hysteretic behaviour of reinforced concrete members were used in these analyses.  7.2 Description of the M o d e l  A detailed finite element model was developed based on both architectural and structural drawings o f the building. It had common basic features with the linear model.  The building was modeled as a single frame of seven stories with 40 column lines and 61 bays. Floors were modeled as a rigid diaphragms with three degrees of freedom each. To account for  64  out-of-plane stiffness of slabs, columns of interior frames were modeled to be connected with two-meter wide beams having the same thicknesses as their corresponding slabs.  The building was assumed to be fixed at the base. The estimated mass of each floor (Appendix C ) was lumped at the center o f mass o f the corresponding diaphragm (mass o f columns was included in floor masses), and all members were assumed to be massless elements.  Hysteresis behaviour of each member was simulated by a hysteresis model expressing the nonlinear force-displacement relationship. The strength of each member was calculated based on its specified nominal material strength.  Flexural characteristics of reinforced concrete beam members were predicted based on sectional analysis by M u l l e r ' s method (Press et al. (1994)).  T h e moment-curvature  relationship of a reinforced concrete member was determined at a specified axial load. The iteration was performed based on material stress-strain relationships and assumption that a plane section remained planar after deformation. The equilibrium condition was maintained by iteration.  A l l perimeter beam elements were modeled assuming a one-meter contribution of floor slabs. The bending behaviour of each beam was modeled by hysteresis model #15 (see Chapter 6) considering the stiffness degradation and strength deterioration. Because of the thick slabs, the shear behaviour o f all beams was assumed to be linear elastic and was modeled by hysteresis model #1.  The flexural behaviour of column members was modeled by a multi-spring element.  16  concrete springs and as many steel springs as steel bars at any cross-section were considered at  65  each end of a column. Tri-linear force-deformation skeleton curves were assumed for both steel and concrete springs. From column details in the building drawings, a 70-mm concrete shell thickness (see fig. 6.2) was estimated for all columns. The plastic hinge zone length was assumed to be 350 mm for the second story and 250 mm for the rest of the floors.  The axial stiffness of column members was assumed to be linear elastic and was modeled by hysteresis model #1.  Two orthogonal independent shear springs (hysteresis model #15) were  used to model the shear behaviour of each column member.  Shear strength o f column  members was estimated by empirical formulas ( C A N 3 - A 2 3 . 3 - M 8 4 , March 1988).  The four bay perimeter brick walls at ground level were modeled using only shear springs. T h e initial state o f the building (under gravitational loads) was taken into account by considering the initial load data on the beams before any analysis was conducted.  7.3 Pushover Analysis  In order to estimate the lateral resistance of the building at ultimate load, static nonlinear (pushover) analyses were conducted. The model of the building used in this study was the three-dimensional model described in previous section. A predetermined lateral force pattern was applied incrementally in a step-wise manner in each direction independently. The results of pushover analysis were sensitive to the choice of load pattern. It is of common practice to assume that the load pattern has a triangular distribution, which is regarded as an equivalent lateral force pattern in most design codes. The analysis was performed in both longitudinal and transverse directions.  66  7.3.1 Analytical prediction of longitudinal response  The b u i l d i n g was analyzed based on a target displacement and applying the pushover procedure until a specified target displacement was reached. A target displacement of 50 cm (2.5 percent of the height of building) and an increment of 0.1 cm was selected for this study.  Figure 7.1 shows the base shear versus roof displacement for pushover analysis of the building in the east-west direction. Significant yielding in the structure occurs at roof deflection o f approximately 15 cm. Assuming that the building has a minimum overall ductility capacity of order 2, then it should be capable o f resisting a base shear o f about 17% (7600 k N ) o f the weight of the structure, subjected to 30 cm of roof displacement.  Figure 7.2 shows the yielding propagation steps in the south perimeter frame in the east-west direction. Each step corresponds to 0.1 cm displacement at the roof. The sequence of yielding and, subsequently, plastic hinge formation in the north frame were almost the same. The first yielding in beams occurred at the left side of the second story's corner beam at step 62 (first beam from left). The flexural yielding of columns could not be accurately determined because the reported yielding step was related to individual springs rather than the whole section. However, the sequence of yielding showed that the flexural yielding was first initiated at the columns between the fourth and the fifth floors at step 152 (second column line from left in F i g . 7.2).  Shear failure, rather than flexural failure, was the critical behaviour and was  dominant in almost all columns from the second to the fifth floors. The first shear failure occurred at the columns between the second and the third floors at step 103 (third column line from right in Fig. 7.2).  67  10000  7500  CD CD  5000 h  CO CD OT CO CQ  2500  0.10  0.00  0.20  0.30  0.50  0.40  T o p story d i s p l a c e m e n t (m)  Figure 7.1. Base shear versus roof displacement, east-west direction.  435  207 319 103 375  364 345 262Y 2931  8  6  251Y  255 1  190Y~ 1981 2  4  5  152Y 8 3  1651  1 1 7  -38*4  364XT 443 225 404 196  353 381  4  0  6  197Y 2071  1  156Y"  173 1  9 5  2401 ^ui 2341 go 220' 2311 79 258 1 224 T  -4-924  4  205Y 2121  3  1  1  209 216  0  207Y 111 214l m  269J  205 212  321 179 347  1  1  R  2981 <"»°1177 7 0  314+Vs  4»17R  9  1  1  Y|  277Y 289+ V5  110  265Y1H  1 7 7  2311  "310*1  291  2921  251J  255  255 J  233 238  IS]  V{J  220 226  248 114 224 i126 • » 292  228 204  253  348 361 357  189f 2201 113 198JL 183 237j  182*1 170 182Y, o 180 199+ || 204 1^4 202 \ £ ? 210 1 | |  1 1 0  -3044  355 186 420  373 181 417  181  2161 175 121 219" 016«fr 1931 154 86 203. "5  3521 259,  Figure 7.2. Step of yielding in south perimeter frame, east-west direction.  68  liof  251.  1 3 7  T h e failure mechanisms o f interior frames were quite different.  Flexural y i e l d i n g first  occurred at the base of the building. This behaviour can be explained as a consequence of fixed base assumption in the analysis. In reality, there would be some rotational relief due to the rotational stiffness of piles at the base of the structure. In the interior frames, opposite to the exterior ones, flexural yielding determined the behaviour of the columns. Shear capacities of almost all columns were more than their shear demands.  Similar analytical studies have been conducted by other researchers ( C S M I P ,  1996). The  results of the pushover analysis on the south perimeter frame performed by Islam  (1996)  appears to contradict the observed damage in the building during the Northridge earthquake. Some of the reported differences are both positive and negative extensive flexural cracks at both ends o f the beams, flexural cracks at the bases of the columns and flexural hinge formation rather than shear failure of columns below the fifth floor.  7.3.2 Analytical prediction of transverse response  The same target displacement (50 cm) and increment (0.1 cm) were selected for the analysis in the north-south direction.  Figure 7.3 shows the base shear versus roof displacement for pushover analysis of the building in the north-south direction. Significant yielding in structure occurred at a roof deflection of approximately 20 cm. The shear force at the base of the building subjected to 50 cm roof displacement was about  15.4% (6940 kN) of the weight of the structure. This value was about  16%o less than the amount of the base shear predicted for the east-west direction.  69  7500  0.00  0.10  0.20  0.30  0.40  0.50  T o p story displacement (m) Figure 7.3. Base shear versus roof displacement, north-south direction.  Figure 7.4. Step of yielding in east perimeterframe,north-south direction.  70  Figure 7.4 shows the steps of yielding in the east perimeter frame in the north-south direction. The sequence of yielding and, subsequently, plastic hinge formation in the west frame was also the same. The first beam yielding occurred at the left side of the third story's corner beam at step 60. Flexural yielding in almost all beams occurred before any column started to yield. The initiation of yielding in columns was first observed at the base of column A l (Appendix A , F i g . a.2) between the second and the third floors. However, all columns, except line A , failed due to the shear force before starting to yield. Except for some minor yielding of columns at the base of the building, and opposed to the behaviour of the building in the eastwest direction, the columns of the interior frames did not yield in the north-south direction under the specified target displacement. Therefore, we could not have any mechanism because of the three-dimensional state of the building.  7.4 C y c l i c Analysis  C y c l i c analysis, a static nonlinear (pushover) analysis under load reversal was conducted in order to estimate the ultimate lateral resistance of the building. A predetermined lateral force pattern was applied incrementally in a step-wise manner. The model was subjected to several load reversals, so that it would capture the dynamic characteristics of the reinforced concrete members as well as the whole structure.  The results o f the cyclic analysis are generally  sensitive to the number of load reversal cycles, the load increment, and the choice of load pattern.  In this analysis, a lateral load pattern of triangular shape was assumed in each  direction. The following analysis was performed based on displacement control. The analysis was performed in both longitudinal and transverse directions.  71  7.4.1 Analytical prediction of longitudinal response  Figure 7.5 shows the base shear versus roof displacement for the c y c l i c response o f the building in the east-west direction. It was observed that the building had a maximum base shear capacity of about 6150 k N , which was reached at about 14-15 cm.  The plot in F i g . 7.6 shows the moment-rotation relationship of selected columns between the fourth and the fifth floors.  T h e curvature demand o f selected fourth story columns is  illustrated in this figure. It can be noticed that the curvature ductility demand on the perimeter frame columns (i.e. A 4 ) is larger than that of the middle frame columns (i.e. B4). A typical perimeter column between the fourth and the fifth floors was subjected to a curvature ductility demand of around 5 before the middle frame columns started to yield. However, the shear failure of the correponding columns happened before flexural yielding.  A l l beams o f the exterior frames from the second to the fifth floors showed positive yielding (tension at bottom) during early cycles of the motion, but the ductility demand (displacement ductility) on them was relatively small, on the order of 2. Only the flexural demand on the beams connected to the outer columns was very large, on the order of 15.  7.4.2 Analytical prediction of transverse response  Figure 7.7 shows the base shear versus roof displacement for the cyclic analysis of the building in the north-south direction. It is observed that the building had a maximum base shear capacity of about 4679 k N , which is 23% less than that for the east-west direction.  Figure 7.8 shows a plot of the moment-rotation relationship of selected columns between the fourth and the fifth floors.  T h e curvature demand o f selected fourth story columns is  72  7500  -0.30  -0.20  -0.10  0.00  0.10  0.20  0.30  T o p story d i s p l a c e m e n t (m)  Figure 7.5. Roof displacement versus base shear, east-west direction.  250  -0.04  -0.02  0.00  0.02  0.04  R o t a t i o n (rad.)  Figure 7.6. Moment-rotation, top fourth story columns, east-west direction  73  5000  -0.30  -0.20  -0.10  0.00  0.10  0.20  0.30  T o p story d i s p l a c e m e n t (m)  Figure 7.7. Base shear versus roof displacement, cyclic analysis, north-south direction.  250  .250 I -0.004  1  1  -0.002  0.000  1 0.002  ' 0.004  R o t a t i o n (rad.)  Figure 7.8. Moment - rotation, top fourth story columns, north-south direction.  74  illustrated in this figure. It can be observed that the curvature ductility demand on all the columns in this direction was smaller than that of the east-west direction. A typical exterior middle frame column between the forth and the fifth floors was subjected to a curvature ductility demand of around 2, while the interior columns did not even yield. The shear type of failure was only dominant in the perimeter frame columns.  A l l beams of the perimeter frames connected to the outside columns from the second to the sixth floors showed positive yielding (tension at bottom) during the early cycles of motion, and the ductility demand (displacement ductility) on them was very large, on the order of 15.  7.5 T i m e H i s t o r y Analysis  The three-dimensional nonlinear time history responses o f the building were investigated during three strong ground motions. First, the behaviour of the building during the Whittier earthquake was considered because of the low level of demand. The response of the nonlinear model was compared with the recorded responses and also to some extent with the linear model developed in previous chapters. Next, the response of the building during the San Fernando earthquake was studied. Finally, the behaviour of the building during the Northridge earthquake was analyzed. The recorded responses were compared with the predicted ones, and the damage correlations were investigated.  Rayleigh Damping type was used such that damping coefficient was proportional to both mass and instantaneous stiffness matrices. The modal damping ratios for the first and the second modes of the vibrations were assumed to be 5% of critical damping.  75  Two independent input ground motions (two orthogonal) were applied for time history analysis for the San Fernando and three independent input ground motions (two orthogonal and one rotational) were applied for the Whittier and the Northridge time history analysis.  7.5.1 Response of the building during the Whittier earthquake  The three-dimensional response of the building during the Whittier earthquake is considered in this section.  The building was analyzed in the time domain for the first 30 seconds of the  recorded motions.  Three input ground motions, two horizontal translations and one rotation  were used. In the north-south direction, the recordings of instrument 13 at the base of building were selected as input ground motion. The recordings of instrument 12 at the second floor of the building were selected as the east-west input ground motion due to lack of existence of any record at the base of b u i l d i n g in this direction.  The difference between recordings of  instruments 1 and 13 was considered as the rotational ground input.  T h e b u i l d i n g was assumed to respond in a linear elastic manner d u r i n g the W h i t t i e r earthquake. A comparison of the results from C A N N Y ' s program with recorded motions from this event would be use to demonstrate the effectiveness of the nonlinear model in predicting the actual response of the building for low levels of excitation, or at least in the linear range. The following section presents the results from this analysis.  7.5.1.1 Comparison of recorded and predicted time histories  Figures 7.9 and 7.10 show the recorded and predicted absolute acceleration and relative displacement time history responses, respectively, at the roof of the building during the Whittier earthquake. A good comparison of the two responses implies that the model could  76  200 o  CD CO  E c g  E 0) CD O  o  <  -200 15 Time (sec)  200  0  5  10  15 Time (sec)  20  25  30  0  5  10  15 Time (sec)  20  25  30  200  Figure 7.9. Comparison of recorded and calculated roof absolute acceleration responses, Whittier earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  77  15 Time (sec)  10  15 Time (sec)  15 Time (sec)  Figure 7.10. Comparison of recorded and calculated roof relative displacement responses, Whittier earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  78  effectively predict the actual response of the building, both in magnitude and frequency sense. There were slight differences in time of occurrence of peak acceleration responses in the northsouth direction due to rotational behaviour of the building. Nevertheless, the correlation between the relative displacements were good in this direction; at the west-end, the peak recorded displacement is about 2.75 cm and the predicted one is 2.85 cm at 17.5 seconds.  Even though the input ground excitation in the east-west direction was only a good estimation of the actual ground motion, there was a good correlation between the predicted and the actual response of the building in this direction as well. Neglecting the small shift o f time, the correlation between the acceleration responses were excellent. There were some differences in displacement responses because the relative displacement of the recorded motions was calculated relative to the displacement of the second floor rather than the base of the building.  7.5.1.2 C o m p a r i s o n of peak responses  Figures 7.11 and 7.12 show the recorded and predicted absolute acceleration and relative displacement peak responses of the building during the Whittier earthquake.  The interstory  drift index and shear demand at each floor are also included in these figures.  The predicted response of the building was calculated at the center of mass of each floor. A s a result, in the north-south direction, the predicted peak responses were somewhere between the recorded responses of the east wall and the west end.  The predicted shear demand of the building was well below its shear capacity. The model appeared to predict the observed acceleration of the building at different floors accurately.  79  Roof  Roof  ._  o o  o o  5  Li-  Ground -4000  Fj-W -2000  0  2000  Ground -4000  4000  Recorded  7  2000  t. A  7  4000  Predicted  6  5  Rec. E-wall Rec. W-end  Predicted  6  o o  E-W  Ground -1000  0  Roof  Roof  o o  -2000  S h e a r (kN)  S h e a r (kN)  ^  N-S  -500  0  500  Ground -1000  1000  -500  1 0  N-S  500  Acceleration (cm/sec )  Acceleration (cm/sec )  Figure 7.11. Peak story shear and acceleration responses, Whittier earthquake.  80  1000  Roof - -  7 h  Record  Rec. W-end  7  Predicted  Rec. E-wall'  6  Predicted  6  o o  E-W -0.50  -0.25  0.00  0.25  N-S  Ground  0.50  -0.50  I n t e r s t o r y Drift I n d e x (%)  -0.25  0.00  0.25  I n t e r s t o r y Drift I n d e x (%)  Figure 7.12. Peak story drift and displacement responses, Whittier earthquake.  81  0.50  The interstory drift index of the recorded motions could only be calculated between the second and the third floors in the east-west direction and the ground to the second floors in the northsouth direction. The maximum calculated interstory drift index was about 0.28% between the fourth and the fifth floors in the east-west direction.  A s mentioned before, the recorded relative peak displacements were calculated and plotted relative to the second floor in the east-west direction.  C o n s i d e r i n g that the relative  displacement o f this floor would have probably been about 0.8 cm, the correlation o f the predicted and the recorded displacements was good.  B y comparing the two responses, it can be appreciated that the model could predict the actual response o f the building sufficiently well in both direction.  7.5.2 Response of the building during the San Fernando earthquake  T h e three-dimensional response of the building during the San Fernando earthquake is considered in this section. The building was analyzed in time domain for 30 seconds of the recorded motions. Two independent input ground motions, two horizontal translations were used.  In the north-south direction, the record of instrument E Q 1 4 2 and in the east-west  direction the record of instrument EQ143 were selected as the input ground motions.  This was the first strong ground excitation that the building experienced after construction. The result of such an analysis would demonstrate the effectiveness of the nonlinear model in predicting the actual response of the building for moderate to high levels of excitation in the early years of the building.  82  7.5.2.1 Comparison of recorded and predicted time histories  Figures 7.13 and 7.14 show the recorded and predicted absolute acceleration and relative displacement time history responses at the roof of the building. The predicted time histories were calculated at the center of mass of the roof. A comparison o f the two responses shows that the model was able to predict reasonably well both the frequency components and peak amplitude o f the actual acceleration response of the building. Considering the location o f sensors at the ground floor and roof of the building (sensors were located at opposite sides of the building), and the level of excitation, the difference in some peak amplitudes was expected due to the significant inherent rotational component of motion.  A good comparison of the displacement responses implies that the model could predict the actual response of the building sufficiently in the east-west direction. In the north-south direction the comparison is not as good. This difference in the early part o f displacement responses was more pronounced i n the north-south direction and may be due to the contribution of cement plaster walls at both ends of the building to the overall stiffness of the structure in this direction. The model could not predict the free vibration part of the response. The duration o f the vibration, and the number of cycles involved made the model too soft.  Another reason for this discrepancy may be due to the processing techniques of the recorded data. A filter with 0.07 Hertz cutoff low frequency limit was utilized in processing o f the recorded accelerations during the San Fernando earthquake. The low cutoff frequency limit results in long period components in the record, that when doubly integrated result in large displacement time histories. The validity o f these long period components in filtered records have been questioned by several studies (Zeris et al.,1987).  83  600 Recorded  o </>  E  ^o, c o  ro 0)  cu o o  <  -600 15 Time (sec) 600  o E  c o co _Q) CD O O <  -600 15 Time (sec) Figure 7.13. Comparison of recorded and calculated roof absolute acceleration time histories, San Fernando earthquake, (a) north-south direction , (b) east-west direction.  15 Time (sec) 20 From Record E  cu  E  CD O  ro  a A» A r\ */V it  c  V  fV  W' V N  t  A  S8N-X  r V /' \  \ i r"i  CL  to  (b)  b 25  Figure 7.14. Comparison of recorded and predicted roof relative displacement time histories, San Fernando earthquake, (a) north-south direction, (b) east-west direction. 84  The result of the analysis showed that some minor yielding occurred at the beams connected to the edge columns between the third and the sixth floor, but the ductility demand on them were small (below 2).  7.5.2.2 Comparison of peak responses  Figures 7.15 and 7.16 show the recorded and predicted peak absolute acceleration and associated peak relative displacement responses of the building during the San Fernando earthquake. The interstory drift index and shear demand at each floor are also demonstrated in these figures.  The predicted shear demand at each story of the building was below the estimated shear capacity of the building at the corresponding level. The building was subjected to larger shear demands in the east-west than the north-south direction. The maximum shear demand at the base of the building was about 6450 k N (15% of the weight) in the east-west direction.  The computer analysis was able to predict the recorded peak accelerations o f the building during the earthquake (see Fig. 7.15). This prediction was better in the north-south direction, rather than the east-west direction.  The interstory drift index from the recorded motions could not be calculated for this event, because there were not enough available records at any consecutive floors. The maximum predicted interstory drift index was about 1.1% between the fourth and the fifth floors in the north-south direction and 0.8% between the third and the fourth floors in the east-west direction.  85  Roof  Roof  o o  o o  Ground -10000  E-W -5000  0  5000  Ground -10000  10000  N-S  -5000  10000  Roof  Roof Recorded  7  7  Predicted  •  Recorded  —  Predicted  6  6 5  o o  o  Ground -1000  5000  S h e a r (kN)  S h e a r (kN)  ,_ O  0  -500  i  Acceleration  E-W 500  N-S  Ground -1000  1000  -500  0  Acceleration  (cm/sec ) 2  500 (cm/sec )  Figure 7.15. Peak story shear and acceleration responses, San Fernando earthquake.  86  1000 2  Roof  Roof  ^  o o  5  o o  5 4 3  2  i  Ground -2.00  -1.00  0.00  E-W  1.00  Ground -2.00  2.00  N-S  -1.00  0.00  1.00  I n t e r s t o r y Drift I n d e x (%)  I n t e r s t o r y Drift I n d e x (%)  Figure 7.16. Peak story drift and displacement responses, San Fernando earthquake.  87  2.00  The correlation between the peak relative displacement records is not as good as that for the acceleration ones. However, by comparing the relative displacement responses, it can be observed that the computer analysis was able to predict satisfactorily the recorded motions of the building in both directions.  7.5.3 Response of the building during the Northridge earthquake  The three-dimensional response of the building during the Northridge earthquake is considered in this section.  The building was analyzed in time domain for 30 seconds of the recorded  motions. Three input ground motions, two horizontal translations and one rotation, were used. In the north-south direction, the recordings of sensor 13 at the base of the building were selected as the input ground motion. The recordings of sensor 16 at the base of the building were selected as the east-west input ground motion. The difference between the recording of sensors 1 and 13 was considered to be the rotational input ground motion.  A s discussed in chapter 3, the building responded in a nonlinear inelastic manner and substantial damage happened during this event. The result of the analysis would demonstrate the capability of the nonlinear model in predicting the actual response of the building for such a high level of seismic excitation.  7.5.3.1 Comparison of recorded and predicted time histories  Figures 7.17 and 7.18 show the recorded and predicted absolute accelerations and associated relative displacement time history responses at the roof of the building during the Northridge earthquake. A comparison of the acceleration responses shows that the model could predict the well frequency components of recorded north-south response of the building at the east  88  600  o CD  in E  c o ro l-  0)  <D O O <  -600 10  15 Time (sec)  20  25  30  10  15 Time (sec)  20  25  30  10  15 Time (sec)  20  25  30  600  o CD  in E  c o _CD CD O O <  -600  600  o CD  in E c o  CD O O <  -600  Figure 7.17. Comparison of recorded and calculated roof absolute acceleration responses, Northridge earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  89  15  Time (sec)  15  Time (sec)  10  15  20  25  Time (sec)  Figure 7.18. Comparison of recorded and calculated roof relative displacement responses, Northridge earthquake, (a) north-south direction (east wall), (b) north-south direction (west end), (c) east-west direction.  90  30  wall. There were only small discrepancies from 18 to 21 seconds.  The peak amplitudes of  acceleration did not take place at the same time. The model also showed some softening after 6.2 seconds.  A t the west end, the predicted response was quite different after 18 seconds, but  the peak absolute acceleration responses occurred at the same time (at about 4.6 seconds) although there was a 20% difference in the amplitudes. In the east-west direction, the model could not predict satisfactorily the recorded response after 16 seconds.  The discrepancy in  amplitude started after 8 seconds.  The recorded displacement time histories were calculated through integration of the base-line corrected and filtered recorded acceleration time history data (Shakal, 1994). Considering the damage and the highly nonlinear inelastic response of the building, some of the low and high frequency components of the motion would probably have been removed by the selection of high and low band pass filter. On the other hand, in the dynamic analysis, there was only a direct integration relation, and no filtering, between the acceleration and displacement time histories. Therefore, some differences were expected and the comparisons o f displacement time histories was probably not as reliable as that for the accelerations.  The result of the analysis showed that the building was not able to return to its initial static position after the earthquake. There were a few centimeters o f permanent drift in both directions. Comparing the relative displacement time histories in the north-south direction, especially at the east wall, one could see a good correlation between the observed and the predicted motions. The model could predict the observed responses both in amplitude and frequency senses. The predicted peak relative displacement was about 15.4 cm at 7.4 seconds and the observed one was 17.6 cm at this instant. However, in the west end, where the  91  accelerometer was located adjacent to the south perimeter frame, the correlation was not as good. In the east-west direction, the model could predict the recorded motion quite well for the first 4.5 seconds of ground excitation, and moderately well till 9.6 seconds. This is believed to be the time o f failure of the south perimeter frame columns.  The predicted peak relative  displacement was about 19.5 cm at 8.8 seconds and the observed one was 23.3 cm at this instant. After that, there was poor correlation between the observed and predicted responses.  The predicted shear time history responses of the building at the base and the fourth story are plotted in fig. 7.19.  The results of analysis suggested that the maximum shear demand on the  fourth floor in the east-west direction was about 5640 k N at 3.94 seconds. However, the failure of columns would probably have occurred at about 9.2 seconds when the shear demand was of the same order (about 5435 kN), but the shear capacity of the columns was much smaller due to the cracking of the concrete in previous cycles.  The predicted maximum shear demand in the north-south direction was smaller than that in the east-west direction. The maximum shear demand on the fourth floor in the north-south direction was about 4200 k N at around 9.5 seconds.  Figure 7.20 shows a plot of the moment rotation relationship of two selected columns between the fourth and the fifth floors during the Northridge earthquake. The curvature demand of the columns is illustrated in this figure. Here, it is assumed that the columns behave in a complete ductile manner. It is observed that the curvature ductility demand on the perimeter frame columns ( A 4 ) was much larger than that of the middle frame columns (B4).  A typical  perimeter column between the fourth and the fifth story was subjected to a curvature ductility demand of around 4 even before the middle frame columns started to yield. However, the  92  10  15 Time (sec)  10  15 Time (sec)  20  25  10000  to CD  .c  CO  -10000  Figure 7.19. Predicted shear force time histories, (a) east-west direction, (b) north-south direction. 250  125  c cu E o  -125  -250 -0.02  -0.01  0.00  0.01  0.02  R o t a t i o n (rad.) Figure 7.20. Top moment - rotation, 4th story columns, east-west direction.  93  30  shear failure of the correponding columns happened before flexural yielding.  Figure 7.21 shows the biaxial bending demand of selected columns in the ground floor and fourth story. The bending demand of the columns at the base of the building was much higher than that at the fourth story (note that scales are different). For the fourth story columns, the moment demands on the perimeter columns (e.g. column A 4 ) are larger in the east-west direction than in the north-south direction. In contrast, the corner (e.g. column D I ) and middle columns (e.g. column B4) were subjected to a higher biaxial bending demand.  The predicted moment-axial load at each time step for selected columns are shown in fig. 7.22 (note that scales are different).  The fluctuation of axial load, which has a significant effect on  the shear capacity of the columns was larger for the perimeter columns of the upper stories. The variation of axial load in perimeter frames was larger for a corner column (column D I ) than a middle one (column A 4 ) . There was not a significant variation of axial load for a middle frame column (column B4).  7.5.3.2 C o m p a r i s o n of peak responses  Figures 7.23 and 7.24 show the recorded and predicted peak absolute acceleration and associated peak relative displacement responses of the b u i l d i n g during the Northridge earthquake. The interstory drift index and shear demand at each floor are also shown in these figures.  The predicted response of the building was calculated at the center of mass of each floor. A s a result, in the north-south direction, the predicted peak responses were expected to be somewhere between the recorded responses of the east wall and the west end.  94  800  400  400  200  z c  CD  c  0  0  CD  e  E o  o  >- -200  >- -400  -800 -800  0  -400  400  -400 -400  800  -200  0  200  400  X Moment (kN-m)  X Moment (kN-m) 400  800 Ground Floor Col. D1  400  c  0  CD  E o  >_ -400  -800 -800  -400  0  400  -400 -400  800  -200  0  200  400  X Moment (kN-m)  X Moment (kN-m) 400  800 Ground Floor Col. B4  E 200  400  I  c  CD  z  0  E o  c  >_ -400  >o -200  CD  -800 -800  E  -400  0  400  X Moment (kN-m)  -400 -400  800  -200  0  200  X Moment (kN-m)  Figure 7.21. Biaxial bending demand time histories at the base of ground and the top of 4th story selected columns. 95  400  1200  2400  J n  Ground Floor  2000  1000  Col. A4  • 1600  -a 1200 CO o ^ co  800  <  400  ^  800  TT  600  i  Col. A4  CO  o 400 co <  -400 0 400 X M o m e n t (kN-m)  800  0 400 X M o m e n t (kN-m)  800  200 0 -200 -400  -400 -800  4th Story  -200 0 200 X M o m e n t (kN-m)  400  0  400  200  X M o m e n t (kN-m) 1600 1400 1200 •g 1000  co o  co X <  800 600 400  0  400  200 -400  800  X .M. . oWm e n t (vk, N MW... , -m)  -200  0  200  X M o m e n t (kN-m)  V  Figure 7.22. Axial load-moment demand time histories of selected columns.  96  400  Roof  Roof  /Wax shear Shear N-S  5  ._  5  ^  4  4  3  3  2  2  o o  o o  Ground -10000  E-W -5000  0  5000  Ground -10000  10000  N-S -5000  0  5000  10000  S h e a r (kN)  S h e a r (kN)  Shear in the north-south direction at maximum shear in the east-west direction.  1  7  Roof  Recorded  -^k  7  Predicted  o o ^  5  1  A\  Rec. W-end  A  Rec. E-wall  —  Predicted  4  -Jk'i 3 ;  2  k-i j  V  E-W -1000  -500  500  Ground-1000  1000  -500  500  Acceleration (cm/sec )  Acceleration (cm/sec )  Figure 7.23. Peak story shear and acceleration responses, Northridge earthquake.  97  1000  Roof  Roof Record *  7 -  Rec. E-wall'  7  Predicted  Rec. W-end  6 -  u_  5  ^  4  o o  o o  r i i i  2  3  i i  E-W  _L -  1  0  7  *il  1  11  2  -  -  1  0  1  |Rec. E-wall *  i  •  ,1  — j Predicted  Record *  1  2  A A  1  II  6  2  I n t e r s t o r y Drift I n d e x (%)  1—A  1  ! i N-S  Ground  I n t e r s t o r y Drift I n d e x (%)  I  IT"  ,±-J__ i!  2  J  rJ  Ground  o o  5 4  3  Roof  ^-Predicted  6  Rec. W-end Predicted  i  j-Jk  5  I  I  4 3 2  1 1  Ground -40  -20  Ar  \  -A  i  1  \  0  20  N-S  E-W 40  -20  Displacement (cm)  0  20  Displacement (cm) ' Obtained from recorded accelerations.  Figure 7.24. Peak story drift and displacement responses, Northridge earthquake.  98  40  The predicted shear demand at each story of the building was below the estimated floor shear capacity of the building. The building was subjected to larger shear demand in the east-west rather than the north-south direction. The model predicted quite well the peak accelerations of the building. The correlation was better for the lower floors and in the east-west direction. The interstory drift index computed from the recorded motions (observed drift) could be calculated for only the first and the second stories, because there were not sensors located at consecutive floors after that. As shown in Fig. 7.24, the model could predict the observed drift accurately only at the ground story in the east-west direction. At the second story and in the other direction, the predicted drifts were considerably smaller than the observed ones. The maximum calculated interstory drift index was about 1.45% between the third and the forth floors in the east-west direction and 1.21% between the fourth and the fifth floors in the northsouth direction. Considering that the observed drift index of the second story in the east-west direction was about 2% and considering that the torsional response of the building was significant, it would have been expected that the actual interstory drift along the south perimeter of the building was much larger than that was estimated in original design.  The model satisfactorily predicted the observed peak relative displacements of the building. The correlation was much better for lower stories in the east-west direction and upper stories in the north-south direction.  7.5.3.3 C o m p a r i s o n between the predicted and reported damages  In this section, it has been attempted to establish a correlation between the reported maximum ductility demand (as a measure of damage) for members by the analysis program and the actual  99  observed damage (see F i g s , b.7 to b . l l in A p p e n d i x B ) at the end o f the N o r t h r i d g e earthquake. The result of the numerical analysis showed signs of positive yielding (tension at the bottom) in the beams from the third to the sixth floors. Ductility demand on the south perimeter beams was a little higher than that of the north side in the east-west direction. The second floor perimeter beams did not yield at all. The third floor beams yield at 3.25 seconds and were subjected to a ductility demand of 2. The yielding in the fourth, fifth and sixth floor beams were started at about 3.48, 7.68 and 9.16 seconds with maximum ductility demands of 1.6, 1.4 and 1.2, respectively. It was observed that the beams at the lower stories yielded first and were subjected to higher ductility demand than the beams at the upper stories.  A l l the  beams connected to the four corner columns, from second to sixth floors were subjected to higher ductility demand ranging from 4.5 to 2. The only exceptions were the second and third floor beams connected to column A l in the east-west direction, which showed significant yielding and, subsequently a definite failure with a ductility demand o f more than 20. Note that even at the end of the San Fernando earthquake, where the reported structural damage was minor and insignificant, cracking of concrete and minor damage were reported at this specific location.  L o o k i n g at the possible predicted damage in the columns, there was minor yielding in all columns at the base of the building. There was no flexural yielding in most columns till the fourth floor. Shear type of failure determined the critical state of the perimeter columns from the second to the sixth floors. The shear demand on the second story columns was the highest one where initiation of shear cracking was at 3.46 seconds at this story. The columns between the fourth and the fifth floors were subjected to the second highest shear demand. Flexural yielding of some exterior perimeter columns was also observed in the fourth story.  100  The predicted damage of the beams was similar to the reported damage after the earthquake. In contrast to the observed damage after the earthquake, the result of the analysis predicted the failure of the second story perimeter columns prior to that for the fourth story. This discrepancy in performance of the building may be due to the relative overstrength of the concrete used at the second story's columns with respect to the other stories. A series of tests of material samples from these members is essential to support the above notion. Another probable reason for the discrepancy is that the computer model did not have the capability to account for the interaction between the flexure and the shear behaviours of each member, resulting in lower demands for the fourth story's columns. So, why did the shear type of failure happen only at the south perimeter frame? Figure 7.23 includes the floor shear in the north-south direction at the time when the maximum shear was reached in the east-west direction. It was noted earlier that the largest shear demand on the north-south direction existed at the fourth story columns at the time of maximum shear in the east-west direction. Only about 1/4 of the shear capacity of the fourth story columns in the east-west direction came from the perimeter columns. This value was about 20-30% less than the contribution of the other stories' perimeter columns to the overall shear capacity of the corresponding stories. The poor design of the fourth story perimeter columns, the torsional asymmetry due to the presence of brick infill walls along the north perimeter frame and the perimeter frames twice stiffer than interior frames might have resulted in a significantly high demand on the south perimeter frame columns than other columns in the building and their subsequent damage.  101  7.6 Shear Demand  For comparison purpose, the shear demands of the building based on different force modification factors " R " were calculated in accordance with N B C C 90 and plotted in Fig. 7.25. The shear capacity at each story was calculated in accordance with CAN3-A23.3-M84 standards and also included in this figure. The design and detailing of the structural members suggest that the building probably should be classified as a moment-resisting space frame with nominal ductility (R=2). In this case and according to N B C C 9 0 , the building would be subjected to a base shear demand of about 12500 k N which is much larger than the design shear capacity (11000 kN) of the structure. It is obvious that the building was not designed to resist such a force. Considering the seismic zone where the building is located, the building should probably be designed and detailed as a ductile moment resisting frame. Assuming that the building was originally designed as a ductile moment resisting frame with a force modification factor of 4, the least reserve shear capacity (the difference between capacity and demand) exists between the fourth and the fifth floors.  The shear capacity and demand during the Northridge earthquake are shown in the Fig. 7.26. The results of the Northridge earthquake nonlinear time history analysis also suggest that the fourth story columns have the minimum reserve shear capacity. The ductility demand on the building during the Northridge earthquake was estimated to be about 3.  7.7 Performance of the Computer Program  The performance of the program for the various types of analysis conducted in this study is reported in this section. Execution times and memory requirements for each analysis are  102  -  ii  -  T l  NBCC90(R=2) NBCC90  (R=4)  Shear Cap.  (CAN3-A23.3)  I I I I  -1_  1 I  5000  10000  15000  Story S h e a r (kN) Figure 7.25. Comparison of story shear capacity vesus demand.  T L  Max. Demand (Northridge)  L.  Shear Demand at 3.94 sec Shear Cap.  II  (CAN3-A23.3)  Shear Demand at 9.2 sec  i i i i  i —  ii' i 5000  10000  15000  Story S h e a r (kN) Figure 7.26. Comparison of story shear demand, Northridge earthquake.  103  presented in Table 7.1.. Table 7.1. Comparison of execution times and memory requirements. Memory Demands (Byte)  Step of Analysis (Number)  Total CPU* Time (Seconds)  1157808  5486  502  272  Cyclic  1157986  5486  1514  764  Time History  1191508  11808  8000  9974  Linear "ETABS"  ETABS File.eko  Time History  73745  -  2000  586  Type of the Analysis  Size of the Model (Byte)  Nonlinear "CANNY"  C A N N Y Data Size  Pushover  * Pentium 100 with 16 Megabyte of ram.  The size of data file required by the nonlinear program is about 15 times larger than the linear one. This is a good measure and indication of relative time and effort needed for modeling of the building for the two types of analyses. The memory required for nonlinear time history analysis of the seven story building (with 738 members and total of 843 degrees of freedom) is about 11800 bytes. The C P U time for a nonlinear time history analysis with the same number of step is about 4 times the linear one (Note that there was 8000 step involved in nonlinear and 2000 step in linear analyses)  7.8 Conclusions Based on the design specifications, a three-dimensional nonlinear model of the building was developed and analyzed using different analytical techniques. The pushover and cyclic analyses showed the probable sequence of damage under lateral load. Three-dimensional nonlinear dynamic analyses satisfactorily predicted the basic response of the building during all three earthquakes.  104  The result of the analysis during the Whittier earthquake showed no yielding of any member and had almost a perfect correlation with the recorded responses of the building. The calculated peak absolute acceleration for the San Fernando earthquake showed how well the model could predict the state and the response of the building during the event. The nonlinear analysis did satisfactorily predict the overall response of the building during the Northridge excitation. There were good correlations between the predicted and recorded peak responses. The predicted demand and damage appeared to be consistent with the observed damage in the building: The model predicted slightly higher demand on the south, rather than the north, perimeter frame. All perimeter columns were predicted to be shear critical. The building seemed to have experienced a significantly higher seismic shear force than that of the original design. The other interesting observation was the similarities between the pushover and dynamic time history analysis during the Northridge earthquake. The sequence of yielding and subsequently plastic hinge formation were almost the same for both type of analysis.  105  Chapter 8 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 8.1. Summary This study was concerned with the conceptual and analytical modeling of reinforced concrete frame buildings and with investigating and understanding the influence of seismic excitation on three-dimensional structural response. The subject of this work is an instrumented seven story reinforced concrete building which sustained severe structural damage during the California 1994 Northridge earthquake. The type of the damage observed suggested that the building had not been designed and detailed according to the weak-beam strong-column philosophy. The behaviour of the building during three earthquakes that induced different levels of demand was investigated. These were the 1971 San Fernando earthquake, which was the first strong ground excitation that the building experienced, the 1987 Whittier earthquake, and finally the 1994 Northridge earthquake. The motions of these earthquakes were recorded by the strong motion instrumentation installed at different locations of the structure. The dynamic characteristics of the building were determined by analyses of its recorded responses during each event. Three-dimensional linear elastic time history analyses of the building were conducted using information obtained from data analyses of the recorded responses and the observed behaviour of the structure during each earthquake.  106  N o n l i n e a r i n e l a s t i c analyses o f the b u i l d i n g were performed. analyses w e r e considered.  T h e shear capacity o f the b u i l d i n g and the sequence o f y i e l d i n g  w e r e estimated i n each d i r e c t i o n . analyses w e r e performed.  F i r s t , p u s h - o v e r and c y c l i c  N e x t , three-dimensional n o n l i n e a r i n e l a s t i c t i m e history  T h e correlation between the observed and p r e d i c t e d damage w a s  also studied.  8.2. Predicted and Recorded Behaviour of the Building  T h e f o l l o w i n g c o n c l u s i o n s are d r a w n regarding the b e h a v i o u r o f the b u i l d i n g d u r i n g the earthquakes.  These are based on the d i s c u s s i o n o f the b u i l d i n g responses and damage, and on  the a n a l y t i c a l studies o f the structure.  L i n e a r a n a l y s i s o n l y predicted the response o f the b u i l d i n g w h e n the d y n a m i c characteristics o f the structure w e r e w e l l defined and d i d not change significantly. T h e c o r r e l a t i o n b e t w e e n the p r e d i c t e d and recorded responses o f the b u i l d i n g d u r i n g the W h i t t i e r earthquake w a s a clear i n d i c a t i o n for the above observation. T h e g o o d match between the t w o responses i m p l i e s that the l i n e a r elastic m o d e l w a s able to predict the actual response o f the structure d u r i n g this event.  L i n e a r a n a l y s i s f a i l e d to predict the actual response o f the b u i l d i n g d u r i n g h i g h l e v e l s o f e x c i t a t i o n due to y i e l d i n g and nonlinear b e h a v i o u r o f its members. T h e results o f a l i n e a r t i m e history a n a l y s i s u s i n g the N o r t h r i d g e earthquake records s h o w e d the i n a b i l i t y o f the m o d e l to p r e d i c t the actual response o f the b u i l d i n g for this event.  H o w e v e r , a g o o d p r e d i c t i o n for  segments o f the actual response d u r i n g the N o r t h r i d g e earthquake w a s obtained b y u p d a t i n g i n each segment the m e m b e r stiffnesses based on the observed damage.  107  In a global sense, nonlinear analysis did satisfactorily predict the overall response of the structure during the three earthquakes. The results of nonlinear time history analysis using the Whittier earthquake records showed no yielding of any element and had a good correlation with the recorded response of the building. This was consistent with the results obtained from the linear analysis. In contrast, there were some discrepancies between the recorded and computed motions during the early parts of the San Fernando earthquake.  The model  underestimated some peak acceleration values and overestimated some peak displacement values. Material overstrength and uncracked state of columns at the start of shaking are believed to be the two major reasons behind such a difference in responses. Minor yielding of members was observed in this case. For the Northridge earthquake, there was a good correlation between responses during the first few cycles of the intensive shaking. After that, the correlation of responses was poor, especially in the east-west direction. The model did not have the capability to consider the interaction between shear and flexure. Even though, the shear failure of the perimeter columns were well predicted by the model at this stage, the. flexural stiffness of the corresponding members was still retained. This phenomenon limited the drastic change in the stiffness of members; and therefore, the predicted displacements were less than the actual ones, especially in the east-west direction. The correlation between the acceleration responses was better than the displacement ones. A source for this discrepancy might be due to the type of processing techniques and integration routine of recorded accelerations used by CSMIP. The predicted damage in the building appeared to be consistent with the observed damage during the. Northridge earthquake.  The model predicted a higher demand on the south  108  perimeter frame, rather than the north perimeter frame, due to the interaction of the frame with the masonry walls. Most of the middle floors' perimeter beams showed tension yielding at the bottom. All perimeter columns were predicted to be shear critical. The only discrepancy was that the second story's perimeter frame columns were predicted to be subjected to higher shear demands and earlier failure, as compared to the fourth story's perimeter columns. However, flexural yielding was observed only in the fourth story columns. The interaction between the shear and flexure probably resulted in higher demands on the fourth story's columns. Another factor contributing to this behaviour might have been the relative overstrength of the second story's columns with respect to the other stories. The concrete strengthused in second story columns was different than that of the other columns. The building seemed to have experienced a significantly higher seismic shear force than that of the original design. The building was subjected to base shear force of about 8000 kN during the Northridge earthquake. The results of the analysis showed a permanent drift of about 2-3 centimeters in both principal directions. The inherent material overstrength was probably the reason behind the partial structural damage, of some fourth story perimeter columns at the south side of the structure and large number of beams, rather than a total collapse of the building. 8.3. Recommendations for Further Research The three-dimensional nonlinear analysis only accounted for the interaction between the axial load and flexure. In the analysis of buildings with shear critical columns, an element that can model the interaction between the shear and flexure behaviour of components will probably lead to more accurate results.  109  The result of analysis suggested that a significant inherent material overstrength exists in this building (see section 5.3). The capacity and behaviour of each component, especially in the inelastic range, are determined by its material strength.  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(1987), "CSMIP Strong Motion Records from the Whittier, California Earthquake of 1 October 1987", California Department of Conservation, Division of Mines and Geology, office of Strong Motion Studies, Report OSMS 87-05, October 1987, 198 pages. Shakal, A., Huang, M., Darragh, R, Cao, T.Q., Sherburne, R.W., Malhotra, P, Cramer, C , Sydnor, R., Graizer, V , Maldonado, G., Peterson, C , and Wampole, J. (1994) "CSMIP Strong Motion Records from the Northridge, California Earthquake of January 17, 1994", California Department of Conservation, Division of Mines and Geology, office of Strong Motion Studies, Report OSMS 94-07, February 1994, 308 pages. Suharwardy, M.I.H. and Pecknold, D.A. (1978), "Inelastic Response of Reinforced Concrete Columns Subjected to Two-Dimensional Earthquake Motions", Civil Engineering Studies, Structural Report Series No. 455, University of Illinois, Urbana. Takeda, T, Sozen, M.A. and Neilsen, N.N. (1970), "Reinforced Concrete Response to  113  Simulated Earthquakes," Journal of the Structural Engineering, A S C E , Vol. 96, S T 2, pp. 2557-2573. Takizawa, H . and Aoyama, H . (1976), "Biaxial Effects in Modelling Earthquake Response of R C Structures", Earthquake Engineering and Structural Dynamics, Vol. 4, 523-553. Takizawa, H . (1973), "Strong Motion Response Analysis of Reinforced Concrete Buildings", Concrete Journal, Japan National Council on Concrete, Vol. 11, N o . 2. Takayanagi, T and Schnobrich, W.C. (1977), "Computed Behaviour of Coupled Shear Walls", Proceedings of 6th W C E E , New Dehli. Ventura, C . E . , Finn, W . D . L . and Schuster, N D . (1995), "Seismic Response o f Instrumented Structures During the 1994 Northridge, California Earthquake", Canadian Journal of Civil Engineering, Vol. 22, pp. 316-337. Vibrant Technology (1995), " M E ' S c o p e ™ Operating Manual", Version 3.0. Wen, R . K . and Jensen, J . G . (1965), "Dynamic Analysis of Elasto-Plastic Frames", Proceedings of 3rd World Conference on Earthquake Engineering", Vol. II, N e w Zealand. Zeris, C . and Mahin, S . A . (1988), "Analysis of Reinforced Concrete Beam-Columns under Uniaxial Excitation", Journal of Structural Engineering, A S C E , Vol. 114, pp. 804-820. Zeris, C . A . , Mahin, S.A. and Bertero,V.V. (1987), "Analysis of the Seismic Performance of the Imperial County Service Building", Journal of the Structural Engineering, A S C E , Vol. 96, S T 2, pp. 2557-2573. Zienkiewicz, O . C . , and Morgan (1983), "Finite Elements and Approximations", Wiley. Zienkiewicz, O . C . , and Taylor, R . L . (1989), "The Finite Element Method", Fourth Edition, Vol.1 and Vol.II, McGraw-Hill.  114  Appendix A  Floor Plans and Details of the Building  115  ©  ®  ®  24.715I 6.12 m  6.12 m  6.35 m  leaeb-H^Jeciiel —rtr—  L  1  fecaeteHss^eEae'E  —rlr—  1  6.12 m  —rlr—' i  1  1  IG ! G '  3--6~k  IQTOT \  IO O i 3—ta-fez-: [O i O i  iOjpi_< P-o-E i O i Oi  7  495x610 mm grade beam  fotoi :a - a - E  1  Mr  X457x 30^jrnm f typical ti&peam  0-  —T*I—  iii 356x508 mii(i grade beanjij  •US-IG%43  1  .—I+I—i  HH^--B---fe----^;|--Eaep.  IO ! O f  io; or  508 mm square interior concr ste column (typ j  to,-' ~*\ 3pi5x305 mm r  'beam  ,-'Oj IO i/Oi OiO -£^43333^3--1?--fzz-: :--1..,e> 787x610 mnrT>fcjl lQ^j_Oj grade beam • 3048 mm Square typical pile!c^ap _!iL_ •—'T'—I 0]_ IO i :_-3-4-t3 "1. <3 IO i G | —Hi i  roN  r  To  w  o] . t3333=315-set  LP Qf  lOiOj  N£i  0  I  |OjO  3333i-EIGJ::  IO i O i  \Q&- 4 - — - - - a . . - & - t OiO  IQr"  3i^31-fPtJtlOiOj  'Mr "'' 1  Elevator JiH  0-  3-OGte Stairwell  -lis  Figure a.l. Holiday Inn, foundation plan.  116  Figure a.2. Holiday Inn, first floor framing plan.  117  ®  ©  ®  ®  19.10 m 6.12 m  -pj^r- —  J . 6.35 m  6.12 m  - - - Z U I - Z Z L - - - - - - - I A . Z . - Z - - zz----zz-^3  356 x 508 mm  r exterior concrete  column (typ.)  a  —  —a-  -H  450 mm square  interior concrete column (typ.) &  4*j  6•  Q  263 mm concrete slab  Figure a.3. Holiday Inn, roof framing plan.  118  Exterior spandrel beam at periphery concrete slab (typ.)  C-11 to C-17 Col. I Details C-21 to C-26  C-4 TO C-7 C-30 TO C-34  C-11, C-12 C-20  C-10, C-18 C19, C-27  C-2, C-3, C-18| C-1, C-9 C-28, C-36 C-29, C-35  C1A C10A  C17A C26A  .Size 457x457 mm 457x 457mm 355x508 mm 355x508mm 355x508 mm 355x508 mm 305x254 305x254| mm mm I Level 4 #5 6 #7 6 #7 6 #7 6 #7 6 #7 6 #7 #2 @ 300 mm #2 @ 300 mm #2 @ 300 mm #2 @ 300 mm #2 @ 300 mrrj #2 @ 300 mrrj #2@ 250 mm I Seventh Storey  4 #5 #2@ 250 mm I Sixth storey  • 6 #8 #2 @ 300 mm  Fifth Storey  8 #9 6 #8 #3 @ 300 mm #3 @ 300 mm  6 #7 #3 @ 300 mm'  Fourth Storey 4LJ  8 #9 8 #9 6 #9 12 #9 8 #9 #3 @ 300 mm #3 @ 300 mm #2 @ 300 mm #3 @ 300 mm #3 @ 300 mm  —i  ^  Third Storey 4DI  4 #6 #2@ 250 mm  t_  10 #9 #3 @ 300 mm Second Storey  ^  •—i—k  i _  1 vl  508x508 mm 508x508 mm 8 #9 10 #9 12 #9 10 #9 12 #9 10 #9 #3 @ 300 mm #3 @ 300 mm #3 @ 300 mm #3 @ 300 mm #3 @ 300 mm #3 @ 300 mm Ground Storey  ^ i—i —a ^  r -4  Figure a.4. Columns reinforcement detail.  119  4 #8 4 #6 #2@ #2@ 250 mm 250 mm  Appendix B  Recorded Data at the Building during the San Fernando, Whittier and Northridge Earthquakes  120  Ground Floor (NS)  O (D W  E o o  3  10  15  Time (sec) Figure b. 1. San Fernando earthquake, velocity time histories from recorded accelerations.  121  0  10  20  30  40  50  Time (sec)  Figure b.2. San Fernando earthquake, displacement time histories from recorded accelerations.  122  20  Ground Floor (SW Corner) - chan.1  0 _)  -20 20  I  I  L  i  i  i  i  L  J  I  I  L  L  Second Floor (SW Corner) - chan. 7  0 _J  -20 20  I  I  L_  J  I  l  I  L_  I  I  I  I  L  Third Floor (SW Corner) - chan. 5  0 -20 20  Roof (SW Corner) - chan. 2  0 -20 20  _l  I  l_  Ground Floor (SE Corner) - chan. 13  0 _J  -20 20  o CD in E  I  1  l_  Second Floor (East Wall) - chan. 8  0  .  -20 20  L  0  o o  -20 20  >  0  CD  -20 20 0 -20 20  Second Floor (East Wall) - chan. 12  0 -20 20  Third Floor (East Wall) - chan. 11  0  I  -20 20  Sixth Floor (East Wall) - chan. 10 •N  0 -20 20  J  I  L  1  r-  Roof (East Wall) - chan. 9  0 -20  _1  I  I  L  10  20  30  Time (sec.)  Figure b.3. Whittier earthquake, velocity time histories from recorded accelerations.  123  40  Ground Floor (SW Corner) - chan.1  E -*—*  c  CO E CO  o  TO Q . W  Figure b.4. Whittier earthquake, displacement time histories from recorded accelerations.  124  Ground Floor (SW Corner) - chan.1  20  Time (sec.) Figure b.5. Northridge earthquake, velocity time histories from recorded accelerations.  125  t  25  Ground Floor (SW Corner) - chan.1  0  _L  -25 25  Second Floor (SW Comer) - chan. 7  0 -25 25 0 -25 25 0 -25 25 0 -25 25 0 -25 25 0  c CD E  3 OS  Q.  b  -25 25 0 -25 25 0 -25 25 0 -25 25 0 -25 25 0 -25 25 0 25  Sixth Floor (Easth Wall) - chan. 10  0  L  -25 25 0 -25 25  Ground floor (SE Corner) - chan. 15  0 -25 10  20  30  40  50  Time (sec.)  Figure b.6. Northridge earthquake, displacement time histories from recorded accelerations.  126  60  Figure b.7 North view of the building (March 1996).  Figure b.8 South view of the building (March 1996).  127  Figure b.9 Three bays concrete wall replacement for brick walls.  Figure b. 10 A close view of added shear walls.  Figure b. 11 Repair work on beam-column joints. 128  Appendix C  Estimated Weight and Mode Shapes of the Building  129  Table c. 1. Estimated weight of the building.  STORY  COMPONENTS  WEIGTH (kN)  ROOF  Floor Slab Columns Spandrel beams Interior frame partitions Floor finishes and other Nonstructural Exterior stud walls and windows Penthouse and Mechanical equip. Total  4058 224 733 200 92 88 586 5981  TYPICAL FLOOR  Floor Slab Columns Spandrel beams Interior frame partitions Floor finishes and other Nonstructural Exterior stud walls and windows Total  4278 450 770 399 184 175 6256  Floor Slab Columns Spandrel beams Interior frame partitions Floor finishes and other Nonstructural Exterior stud walls and windows Total  5025 608 983 479 284 426 7805  SECOND FLOOR  Total Estimated Weight of the Building  45066  130  3  ^  Figure c.2. 1st transvers mode shape (f = 0.76 Hz).  Figure c.3. 1st torsional mode shape (f = 0.91Hz).  Figure c.4. 1st longitudinal mode shape (f= 0.95 Hz).  131  Figure c.5. 2nd transvers mode (f= 2.76).  Appendix D  Comparison of the Nonlinear Analysis Time Histories with the Records  133  200  o co in  c  o  ro JD 0)  O O <  -200  15 Time (sec)  200  o  CD  m  E c o  _a> Cl)  o o  <  -200  15 Time (sec)  200  o  CD  in  E o c o To u_  jD  0 O CJ  <  -200  15  10  Time (sec)  200 Recorded  o CD  W3N-YW  w E c o  jir f'»i i  2 _CD CD CJ O <  H  i i  (d)  -200  15  10  20  25  30  Time (sec) Figure d. 1. Comparison of recorded and predicted acceleration time histories during the Whittier earthquake (a) second floor, north-south direction (west end), (b) second floor, north-south direction (east wall), (c) second floor, east-west direction, (d) third floor north-south direction (west end).  134  200  o  Recorded  CD  Ui  E CJ  o ca i_  JD  CD O CJ  <  -200 15  Time (sec) 200  o CD  c/> E  c o  _CD CD O O <  -200 15  Time (sec) 200  o  Recorded  CD  W6N-YE  <> / E  c o  mm nmmlt a t  —*- *  1  jD CD O O  <  (c) -200 15  10  20  25  30  Time (sec) 200 Recorded  o CD  W6N-X  t/> E  c o 2 _CD CD CJ O  <  -200 15  10  20  25  Time (sec) Figure d.2. Comparison of recorded and predicted acceleration time histories during the Whittier earthquake (a) third floor, north-south direction (east wall), (b) third floor, east-west direction, (c) sixth floor, north-south direction (east wall), (d) sixth floor east-west direction.  135  30  4 From Record  E  W2N-YW  c CD  E  0  CD O  ra Q.  (a)  co Q  15  10  20  30  25  Time (sec) From  E  Record  W2N-YE  c CD  E  8  0  m o. <n Q  (b) 15  10  20  30  25  Time (sec) From  E  Record  W2N-X  c CD  E  CD O TO Q. CO  4-  0  v \i V -V  b  (c) 10  15  20  30  25  Time (sec) From  E o  Record  W3N-YW  c  CD  E  CD O  0  m CL CO  b  (d)  _L  -4  15  10  20  25  30  Time (sec) Figure d.3. Comparison of recorded and predicted relative displacement time histories during the Whittier earthquake (a) second floor, north-south direction (west end), (b) second floor, north-south direction (east wall), (c) second floor, east-west direction, (d) third floor north-south direction (west end).  136  From Record W3N-YE  10  i 15 Time (sec)  \ ;  i 20  j *  It rvt  \  *""»*MI •  v\ V  j  \ I  i  (a) 30  25  From Record W3N-X  , ;  /.  r.  t'  (b) _L  10  15 Time (sec)  20  25  30  20  25  30  15 Time (sec)  10  15 Time (sec)  Figure d.4. Comparison of recorded and predicted relative displacement time histories during the Whittier earthquake (a) third floor, north-south direction (east wall), (b) third floor, east-west direction, (c) sixth floor, north-south direction (east wall), (d) sixth floor east-west direction.  137  300  0  I 0  5  ;  i 5  10  ;  i 10  15 Time (sec)  i  i  15 Time (sec)  20  i  i  20  25  i  i  25  30  i  l 30  Figure d.5. Comparison of recorded and predicted fourth floor acceleration and relative displacement time histories during the San Fernando earthquake (a) north-south direction, (b) east-west direction, (c) north-south direction, (d) east-west direction. 138  600  0  _600  '  0  5  '  ' 5  10  '  I 10  15 Time (sec)  '  i 15 Time (sec)  20  '  I 20  25  '  I 25  30  '  -J 30  Figure d.6. Comparison of recorded and predicted acceleration time histories during the Northridge earthquake (a) second floor, north-south direction (west end), (b) second floor, north-south direction (east wall), (c) second floor, east-west direction, (d) third floor north-south direction (west end).  139  600 o cu  Recorded  in  c o cc _cu  cu o o  <  -600 15 Time (sec) 600  o CD m c o •4—»  CO  cu o o <  -600 15 Time (sec) 600  o cu in  o To JjD  cu o o  <  -600 10  15 Time (sec)  20  25  30  10  15 Time (sec)  20  25  30  600 o cu m c o  2 cu o o  <  -600  Figure d.7. Comparison of recorded and predicted acceleration time histories during the Northridge earthquake (a) third floor, north-south direction (east wall), (b) third floor, east-west direction, (c) sixth floor, north-south direction (east wall), (d) sixth floor east-west direction.  140  15 Time (sec)  15 Time (sec)  15 Time (sec)  10  15 Time (sec)  20  25  30  Figure d.8. Comparison of recorded and predicted relative displacement time histories during the Northridge earthquake (a) second floor, north-south direction (west end), (b) second floor, north-south direction (east wall), (c) second floor, east-west direction, (d) third floor north-south direction (west end). 141  15 Time (sec) 30 From Record  E o  N3N-X  c  CD  E  0 —  8  H ^ a ft  m CL  52  Q  -30  i  i  \  10  15 Time (sec)  i 20  ! (b)  i 25  30  30 From Record  E  N6N-YE  c CD  E  CD O  m Q.  <n Q  -30 10  15 Time (sec)  20  10  15 Time (sec)  20  30 E c CD  E  CD O  ra  o. w  -30 25  30  Figure d.9. Comparison of recorded and predicted relative displacement time histories during the Northridge earthquake (a) third floor, north-south direction (east wall), (b) third floor, east-west direction, (c) sixth floor, north-south direction (east wall), (d) sixth floor east-west direction.  142  

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