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Abstract

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

In performance-based seismic design of a structure, the inelastic deformation demand of structural members or system is the primary input, whereas in conventional design procedure the input is the equivalent static loads to represent seismic effects. The National Building Code of Canada (NBCC) 2005 requires that for irregular and buildings higher than 60 m, dynamic analysis must be conducted to calculate seismic design forces and deflection, while for other cases, equivalent static loads can be used for the design. In this paper, the performance of a 20-story steel moment resisting steel frame building, designed for western part of Canada, has been presented. Simulated and actual (scaled) ground motion records are used to evaluate the dynamic response. While NBCC does not provide any performance-based design method, various techniques for displacement-based design have been explored here in the context of the 20-story building. A wide range of variation amongst these methods in terms of their application and results was found. Amongst these methods the direct displacement-based design method seems to be more suitable for carrying out the performance-based design of a building. Copyright © 2009 John Wiley & Sons, Ltd.


1. INTRODUCTION

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

Only the severe action of earthquake is not responsible for the high volume of casualties but the study has shown that faulty design of man made structure like buildings, bridges, dams, transportation infrastructure, etc., is also responsible. Therefore, necessity of a safe structure to minimize the damage of earthquake is unavoidable. But the conventional force-based design is not enough to ensure the safe performance of the structure under seismic action. The damage caused by earthquake of Northridge, California (1994) and Kobe, Japan (1995) expose the limitations of the code guided force-based seismic design as has been practiced currently. During these earthquakes, more than 150 steel moment resisting buildings (Lee and Foutch, 2002) were extensively damaged although all those buildings were designed by fulfilling the requirements of the corresponding codes of the time. However, the performance of the buildings were not evaluated or incorporated in the design. The buildings were designed for equivalent static loads but their performances under dynamic loading such as ground shaking were unknown. After these earthquakes the necessity of the evaluation of the performance of buildings designed for equivalent static earthquake load become more necessary. The current versions of IBC (2006) and National Building Code of Canada (NBCC, 2005) addressed some of these issues.

The response parameters such as the inter-story drift, peak roof displacement, lateral load resisting capacity and residual inter-story drift, can be specified or targeted as the performance objectives. In SEAOC Vision 2000 Committee (1995), both the peak and residual inter-story drifts are utilized in defining performance levels as an indicator of damage. The lateral load resisting capacity of a structure, strain-energy based damage criteria, plastic rotation, curvature and energy-based damage indices can also be used as performance parameters. However, the inter-story drift is simple and more intuitive performance parameter from a designer's perspective. Hence, only the inter-story drift has been used here for performance estimation. In evaluation of performance reliability-based probabilistic approach, FEMA-350 (2000) has been utilized because of the uncertainties involved in the judgment and prediction of the characteristics of the earthquake parameters. In FEMA-350 (2000), main levels of performance are defined as immediate occupancy (IO), life safety (LS) and collapse prevention (CP) and corresponding transient drift levels for steel moment resisting frames are of 0·7, 2·5 and 5%, respectively. SEAOC Vision 2000 Committee (1995) also defined four different types of structural performances and these are: fully functional, operational, life safe and near collapse. The transient interstory drift limits corresponding to these levels of performance are suggested as 0·2, 0·5, 1·5 and 2·5%, respectively. In the development of NBCC (2005), some of the above recommendations have been considered (CJCE, 2003). However, only the CP performance corresponding to the drift demand of 2·5% (similar to the SEAOC Vision 2000 Committee (1995) recommendation) has been explicitly provided. Other levels of performance can be defined using the international codes and standards as indicated above.

In Canada, the western region is more vulnerable to earthquake than the eastern region because of the matrix of the rock of the specific region. The repetitive seismic ground shaking in the western part of Canada for the last several years make the rock formation of that region more fragile to earthquake than rest of the part of the country. According to Foo et al. (2001), the earthquake near Seattle in 28 February 2001, which rattled buildings and occupants in Vancouver, could be viewed as a reminder to people living in Canada's most active seismic zone, the pacific coast. It has also been reported by Foo et al. (2001) that the earthquake occurred at Saguenay in Quebec in 1988 was the strongest event in the eastern North America within the last 50 years. But Canada has record of suffering from a stronger earthquake that occurred in 1949 with magnitude 8·1. An average of 1500 earthquakes (NRCAN, 2008) occurs in Canada every year. Thus the design of structures with earthquake-resistant capability by ensuring the required level of performance, located in different region of Canada has become very important.

The objective of this paper is to present the evaluation technique of performance as well as the evaluated performance of 20-story moment resisting steel frame building and to study the prominent performance-based seismic design methods in the context of the 20-story building considered here and compare the design process provided in NBCC (2005).

2. BACKGROUND OF NBCC (2005)

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

Seismic loading provisions in most existing building codes focus on the minimum lateral seismic forces for which the building must be designed (Yousuf and Bagchi, 2009). But only specifying the lateral load is not enough to ensure that the building will perform at the desired level of performance. The structure designed to withstand cyclic seismic force must be properly configured with accurate continuity including adequate strength, stiffness and deformation capacity. One important concept in the seismic design is capacity design or strong column/weak beam concept, which means that the beam will yield first and then the column. This condition is required to prevent the brittle failure of the building. The percentage of strong column/weak beam joints in each story of each line of moment resisting frames shall be greater than 50% for LS and 75% for IO (FEMA-310, 1998). In designing of the steel moment resisting frame, design of connection is very important and sensitive.

In the current edition of NBCC (2005), the seismic design provisions are described by relying on the minimum lateral seismic forces for which the building must be designed and also the acceptable drift under this forces are considered. The minimum requirements for seismic design given in NBCC incorporate considerations of the characteristics and the probability of occurrence of the ‘design’ seismic ground motion, the characteristics of the structure and the foundation, the allowable stresses in the materials of construction, including the foundation soils and the amount of damage that is considered tolerable (CJCE, 2003). NBCC (2005) presents an objective-based format where the design is achieved through the attainment of acceptable solution, rather than just satisfying the minimum requirement (CJCE, 2003). In NBCC (2005), the site-specific spectral acceleration (Humar and Mahgoub, 2003) is used to express the seismic hazard that is presented as uniform hazards spectrum (UHS). This hazard spectrum has 2% probability of exceedance in 50 years (return period 2500 years), whereas the NBCC (1995) based on 10% probability of exceedance in 50 years (return period 475 years). The probability of exceedance of the UHS is a function of period (Adams and Atkinson, 2003) that may be constant or uniform. The major changes of seismic design provisions that included in new NBCC are: the revised formula to calculate the base shear, site specific response spectra, new force reduction factor, incorporation of site coefficient comes from the soil condition and revised method to take the higher mode effect in account. The revision of the code comes from the accumulated knowledge and experience gathered from the earthquake of last two decades. During this period the earthquakes were observed through extensive instrumentation of building located in the moderate to high seismic zones. An updated method of analysis for the seismic forces has been adopted in the NBCC (2005). Dynamic analysis for the calculation of seismic design forces and deflection for higher seismic zone, tall buildings and building with structural irregularity of the lower height is specified in the latest edition of NBCC. A description of structural irregularity is also provided in NBCC (2005) (Table 1).

Table 1. Structural performance level (adapted from SEAOC Vision 2000 Committee (1995))
Performance levelTransient drift limit (%)Permanent drift limit (%)Description of damage
Fully functional<0·2No significant damage has occurred to structural and non-structural components. Building is suitable for normal intended occupancy and use.
Operational<0·5No significant damage has occurred to structure, which retains nearly all of its pre-earthquake strength and stiffness. Non-structural components are secure and most would function, if utilities available. Building may be used for intended purpose, albeit in an impaired mode.
Life safe<1·5<0·5Significant damage to structural elements, with substantial reduction in stiffness, however, margin remains against collapse. Nonstructural elements are secured but may not function. Occupancy may be prevented until repairs can be instituted.
Near collapse<2·5<2·5Substantial structural and nonstructural damage. Structural strength and stiffness substantially degraded. Little margin against collapse. Some falling debris hazards may occur.

3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC (2005) PROVISIONS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

A simplified floor plan and elevation of a typical ductile frame of the building are shown in Figure 1. The building is assumed to be situated in Vancouver, the western part of Canada. The performance of the building along the north-south direction has been evaluated. The building consists of a series of frames in the east-west (E-W) direction and three bays in the north-south (N-S) direction. In the N-S direction, two exterior bays are 9 m and the interior one is 6 m in length and center-to-center spacing of the frames in the E-W direction is 6 m. The height of first story of the building is 4·85 m and others are of 3·65 m each. The frames are symmetrical along the vertical center line. All transverse frames are assumed to ductile lateral load resistant frames. The lateral load-resisting systems are modelled as two-dimensional frames, and the accidental torsion has not been accounted for in the analysis and design of the frame.

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Figure 1. Simplified geometric details of the buildings: (a) plan of the buildings; (b) elevation of the frames

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For the simplicity of the analysis and design, the exterior and interior frames are kept similar. One interior frame with mass of its tributary area for each type of building has been designed and analyzed. The beam members of the same floor level are grouped in the same section type and the column sections are changed at every sixth level. Column continuity represents benefit in seismic resistance by helping in redistributing the inelastic demand along the building height (Tremblay and Poncet, 2005). A simplified model of the frames has been developed in the DRAIN-2DX (Prakash et al., 1993) software using the beam-column elements, an elasto-plastic (i.e., bilinear) hysteretic behaviour with 5% strain hardening of steel. Using the capacity design method (strong column—weak beam concept), as provided in CSA S16-01 (CSA, 2001), the elements of the frames are detailed to develop ductile response under cyclic inelastic deformation due to seismic action and other elements including connections are detailed to remain elastic under gravity load and the maximum earthquake induced lateral load. Frames of the building are modelled by using the plastic hinge beam-column element available in DRAIN-2DX (Prakash et al., 1993). The connections of beam to column are assumed to be fully rigid and chosen from the FEMA-350 (2000) predefined or pre-approved connection type (WUF-W) that is welded, fully restrained with welded un-reinforced flanges and welded web. The ductility demands and energy dissipation in steel buildings can be affected by a number of factors including high strain rate effects, low cycle fatigue, steel over-strength, strain hardening, connection details, thermal effect. etc. Rigid beam-column connection and 5% critical damping has been assumed in the modelling of the frames. Other factors as indicated above have not been modelled. The moment-curvature relationships for individual beam and column sections have been determined using the procedure described in CISC (2004). While shear deformation in the beam-column elements have been ignored.

The building frame has been designed to satisfy the NBCC (2005) requirements and the steel structural elements have been designed according to CSA S16-01 (CSA, 2001). The equivalent static lateral load procedure for the seismic load as prescribed by NBCC (2005) has been used in the preliminary design of the building, which is followed by detailed dynamic analysis. The following loadings have been considered in the design: gravity loads (dead load (D), live load (L)) and seismic load (E). The gravity loads from the live loads are calculated according to NBCC (2005) guidelines. The computed dead load is 3·4 kPa for the roof and 4·05 kPa for a typical floor. The live load on a typical floor is assumed to be 4·8 kPa on the corridor and 2·4 kPa on other areas. The roof snow load has been calculated as 2·32 kPa.

Design base shears are calculated by using the empirical expressions given in NBCC (2005). Linear gravity analysis of frames has been performed using DRAIN-2DX to determine the member forces. The base shear is distributed along the height of the frame in the form of an inverted triangle from top level to bottom as suggested in NBCC (2005), and the force assigned to each story level is proportional to the weight and the story height of the respective story level. The above distribution is made after a portion of the base shear is added to the top story to account for higher mode effects when the design value of the fundamental period exceeds certain limit.

The initial design is performed based on the fundamental period (Ta) calculated using the empirical formula given in NBCC (2005). Subsequently, modal analysis of the frame is performed, and the fundamental period obtained from the modal analysis (T0) has been found to be longer than that calculated using the empirical formula in all these cases. The seismic force has been revised using the modal period T0 or 1·5Ta, whichever is smaller (NBCC, 2005). The parameters used in the calculation of equivalent seismic force are: importance factor IE = 1·0, factor for higher mode effect Mv = 1·0, ductility factor Rd = 5·0 (i.e., fully ductile frame) and the force reduction factor R0 = 1·5. A soil type-C which is very dense soil and soft rock, has been considered with a site specification factor Fv = Fa = 1·0. As indicated earlier, fully ductile beam-column elements with FEMA (Federal Emergency Management Agency) pre-approved rigid connections have been utilized in the design of the ductile frames. Also the capacity design philosophy (i.e., strong column and weak beam) has been used as required in CSA S16-01 (CSA, 2001) for the design of ductile moment resisting frames.

The steel sections used in the design are of CSA G40·21 with yield strength, Fy = 345 MPa for both beam and column. Beam-column concept is used in the designing of column to avoid yielding and buckling. The calibration of the plastic hinge properties is usually done through testing of the beam column joints. Here the pre-approved moment connection and the beam-column element with standard hinge properties and hysteretic behaviour have been used in modelling the frames using DRAIN2DX (Prakash et al., 1993). The modulus of elasticity of steel (E) is 200 GPa. As a part of the check for capacity-design, the column and beam capacities at shakedown condition have been calculated as required in CSA S16-01 (CSA, 2001). The shakedown condition of a structure refers to a state in which it has undergone repeated yielding under cyclic loads such that yielding takes place only in the first few loading cycles, after which load repetitions only cause responses in a stable and linear range.

After the preliminary design using the equivalent static loads calculated based on the NBCC (2005) procedure, the fundamental periods of the buildings have been determined using modal analysis. The fundamental period of the building obtained from the result of modal analysis and the empirical formula in NBCC (2005) are 4·78 and 2·149 s, respectively. As provided in NBCC (2005), the period of the building has been revised to 3·22 s, which is given by the period obtained from the modal analysis or 1·5 times the period calculated using the empirical formula provided in NBCC (2005), whichever is less. The modified value of the design base shear for the building frame is found to be 401 kN. The details of the beam and column sections for the frames are shown in Table 2.

Table 2. Designed sections of elements
Story levelExterior columnInterior columnBeam
Story 1–5W310X283W360X314W310X129
Story 6–10W310X253W360X287W310X129
Story 11–15W310X202W360X262W310X129
Story 16–19W310X179W360X262W310X129
Story 20W310X179W360X262W310X107

4. EVALUATION OF PERFORMANCE OF THE BUILDING

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

In defining the level of performance of the structure the selection of performance objective is very important and three performance objectivities as defined in SEAOC Vision 2000 Committee (1995) and used in this study are: resist minor earthquake without damage, moderate earthquake with some damage to non-structural but no structural damage and major earthquake without collapse. According to Gupta and Krawinkler (2000), the evaluation of performance of the structures necessitates the ability to predict global (e.g., roof), inter-mediate (e.g., story) and local (element) deformation demands.

Although the methodology of the evaluation of the performance of a structure is still under development, some linear and nonlinear static and dynamic methods have developed and are widely used in evaluation of the seismic performance of structures like buildings. Modal analysis is used to calculate the higher mode effect and determine the mode shapes of the structure. Pushover and dynamic analysis are used to evaluate the lateral load capacity and performance objectives. The evaluated performance of the frame and the technique of evaluation are presented here.

4.1 Pushover analysis

Pushover analysis is a nonlinear elastic analysis method used to evaluate the performance of buildings under seismic action. Pushover analysis is simple and widely used for seismic performance evaluation and performance-based design that is defined as identification of the hazards, selection of performance criteria and objectives with desired performance level.

The pushover analysis of the building frame is performed using a nonlinear computer programme, DRAIN-2DX for plane two dimensional model of the frame. The equivalent static seismic load has applied along the frame in the shape of inverted triangle. The analysis is carried out by considering P-Δ effect with 5% strain hardening. The capacity of the frame is calculated from the pushover graph by calculating the yield and ultimate displacement due to seismic load. The pushover graph of the building frame is shown in Figure 2. The yielding of the members is also observed in the pushover analysis and the base shear corresponding to the yield displacement is calculated. The distribution of base shear in the pushover analysis is shown in the Table 3. In this case, the inverted triangular distribution of the lateral forces is used, which considers the first mode effect to be dominant. To account the higher modes effect, modal pushover (Chopra and Goel, 2002) analysis can be used.

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Figure 2. Pushover graph

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Table 3. Distribution of base shear
Story levelHeight (hi), mWeight (Wi), kNhiWi, kNmF (design), kNMass (m), kgFirst mode vector, φF (modal p*m*φ), kNF (uniform), kN
2074·20590·8743 842·55113·5960·231·0025·4220·048
1970·55758·0053 476·8628·2077·270·9932·2820·048
1866·90758·0050 710·1726·7477·270·9731·6320·048
1763·25758·0047 943·4725·2877·270·9530·9820·048
1659·60758·0045 176·7723·8277·270·9230·0020·048
1555·95758·8242 456·1522·3977·350·8929·0520·048
1452·30759·6539 729·5220·9577·440·8527·7820·048
1348·65759·6536 956·8119·4977·440·8126·4720·048
1245·00759·6534 184·1018·0277·440·7624·8420·048
1141·35759·6531 411·3916·5677·440·7123·2020·048
1037·70762·3728 741·3015·1577·710·6621·6420·048
 934·05765·0926 051·3413·7477·990·6019·7520·048
 830·40765·0923 258·7612·2677·990·5317·4420·048
 726·75765·0920 466·1810·7977·990·4715·4720·048
 623·10765·0917 673·609·3277·990·4013·1620·048
 519·45767·1314 920·717·8778·200·3310·8920·048
 415·80769·1712 152·936·4178·410·268·6020·048
 312·15769·179 345·454·9378·410·196·2920·048
 28·50769·176 537·973·4578·410·123·9720·048
 14·85786·733 815·622·0180·200·062·0320·048
Total 15 104·39588 851·63400·961539·691·00400·89400·96

From the pushover graph it has been observed that the first yielding occurs at a base shear coefficient, Cv or (V/W, where V is the base shear and W is the weight of the structure) of 0·048 in beam and at 0·066 in column in the bare frame. Those events for the infilled frame occur at Cv of 0·059 and 0·072 in beams and columns, respectively. The design value of Cv for the building is 0·0264 that is almost half of that corresponding to the first yielding in the bare frame. The interstory drift at the point of instability is 3·40% for bare frame and 3·45% for infill frame, for which the roof drift is 1·83 and 1·90%, respectively. Since the point of instability for this type of frame occurs beyond 2·5% interstory drift, the maximum roof displacement at 2·5% interstory drift is regarded as the collapse point. The roof drift corresponding to interstory drift of 2·5% is 1·76% for the bare frame and 1·79% for the infilled frame. The estimated yield displacements are 0·76% for the bare frame and 0·79% for infilled frame of total height of the frame. Considering the stability of the structure, the system ductility capacity for both bare and infilled frames is close to 2·4. However, with the NBCC (2005) criterion for collapse, the ductility capacity of the structure is estimated to be close to 2·3 in both cases. While the pattern of hinge formation for the 20-story frames is not shown here to conserve space, it shows that the bare frame responds in accordance with the capacity design principle where plastic hinge is formed in a beam before a column at any joint. On the other hand, the pattern of hinge formation is affected by the presence of infill panels, in which case a column sometimes yields before a beam connected to it. The observation is consistent with earlier findings in similar contexts (Fajfar et al., 1997; Bagchi, 2001).

4.2 Dynamic analysis

Rigorous nonlinear time history analysis is necessary to evaluate the performance of the building under seismic ground motion. Estimation of roof displacement and interstory drift induced by ground excitation due to earthquake is the objective of dynamic analysis. The maximum ductility demands in member are also calculated from the output of nonlinear time history analysis. If the ductility demands are less than the ductility capacities and the deflections are within acceptable limits, the design is satisfactory (Saatcioglu and Humar, 2003).

To consider the effect of gravity load in the lateral displacement, the P-Δ effect has been also considered in the dynamic analysis. The response history analysis has been performed using a nonlinear computer programme, DRAIN-2DX, and a set of 30 ground-motion records has been used in the analysis. Amongst these, eight sets are artificial and compatible to the seismic hazard spectrum for Vancouver, Canada (Tremblay and Atkinson, 2001) and 22 are real ground motion collected from data base of Pacific Earthquake Research Center (PEER, 2008) by comparing the peak acceleration (A) to peak velocity ratio (V) of seismic motion to that of Vancouver. The ratio of acceleration to velocity (A/V) (A in g. V in m/s, where g is the acceleration due to gravity) of Vancouver is close to 1·0 (Naumoski et al., 2004), therefore, the range of A/V of 0·8–1·2 has chosen to select the seismic motion for the response history analysis (Table 4). The details of the recorded accelerograms are given in Table 5. Four of the eight synthesized records are long period and four are of short period. Details of the synthesized accelerograms are given in Table 5 and the corresponding time history plots are shown in Figure 3.

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Figure 3. Samples of the synthesized ground motion records. (a) Short period (SP) event; (b) long period (LP) event

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Table 4. Summary of real ground motion time histories
Record no.LocationPeak acceleration (g)Peak velocity (m/s)A/V
 1Imperial Valley0·3480·3341·04
 2Kern Country0·1790·1771·01
 3Kern Country0·1560·1570·99
 4Borrego Country0·0460·0421·09
 5San Fernando0·1500·1491·01
 6San Fernando0·2110·2111·00
 7San Fernando0·1650·1660·99
 8San Fernando0·1800·2050·88
 9San Fernando0·1990·1671·19
10Record No.S-8820·070·071·00
11Record No.S-6340·0780·0681·15
12Monte Negro-20·1710·1940·88
13Report Del Archivo: SUCH850919AL.T0·1050·1120·94
14Report del Archivo: VILE850919AT.T0·1230·1051·17
15Kobe, Japan0·0610·0491·24
16Kobe, Japan0·6940·7580·92
17Kobe, Japan0·7070·7580·93
18Kobe, Japan0·1440·1500·96
19Northridge, CA0·4690·5710·82
20Northridge, CA0·5100·4931·03
21Northridge, CA0·0880·0721·22
22Northridge, CA0·0800·0820·98
Table 5. Summary of stochastic ground motion
Record no.LP1LP2LP3LP4SP1SP2SP3SP4
  1. a

    LP: long period, SP: short period.

Peak acceleration (cm/s2)266·2279·4248·6271·7523527567380
Duration (s)18·2418·2418·2418·248·558·558·558·55

The selected real ground motions are scaled to be compatible to the hazard spectra of Vancouver. There are number of methods available for scaling the ground motion records, two methods of scaling, used in this research to scale the ground motion records, are: (a) based on the acceleration ordinates and (b) based on partial area under the acceleration spectrum (Naumoski et al., 2004).

At the beginning of analysis the spectral analysis of each set of ground motion record is performed. The response spectrum is then scaled to match the design spectrum of Vancouver. The ordinate method of record scaling is performed based on the fundamental period, T1 of vibration of the structure, as explained here with reference to Figure 4(a). The response spectral acceleration corresponding to the fundamental period (Sa2) is scaled up or down to the value of the design spectral acceleration (Sa1) corresponding to the same period. In other words, all record values are scaled based on the factor Sa1/Sa2. On the other hand, the partial area method of record scaling (Figure 4(b)) is based on the first and second period of vibration of the structure. The area (A2) under the response spectral acceleration curve between 1·2 times the fundamental period, T1 and the second period, T2 is scaled to equal the area (A1) under the design spectral acceleration curve between the same period values. All the values of this record are scaled based on the factor A1/A2. As the scaling factors by both of the above-mentioned methods are dependent on the periods of the structure, they have been calculated for each building considering the bare and infilled frames separately. The response spectra of the scaled accelerograms corresponding to 5% damped single degree of freedom system are shown in Figure 5.

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Figure 4. Scaling method of ground motions: (a) ordinate method; (b) partial area method

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Figure 5. Scaled spectra (a) scaled by partial area method; (b) scaled by ordinate method

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From the inelastic time history analysis, the maximum interstory drift of every record is calculated. The mean drift (M) and mean plus standard deviation (M + SD) of the real ground motion for each frame is calculated and checked with the code specified value. The maximum interstory drift of each synthesized record is recorded and used for evaluation. Number of synthesized records is not enough to calculate the mean and mean plus standard deviation. The dynamic drift demands of the building frames due to the stochastic and recorded ground motion are shown in the Figures 6 and 7, respectively.

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Figure 6. Dynamic analysis for stochastic ground motion, (a) dynamic analysis of Bare frame; (b) dynamic analysis of Infill frame

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Figure 7. Graph of dynamic analysis of 20 story building's frame by real ground motion; (a) bare frame scaled by partial area method; (b) bare frame scaled by ordinate method; (c) infill frame scaled by partial area method; (d) infill frame scaled by ordinate method

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The maximum interstory drift and the M + SD value for the real ground motion records for bare frames are 2·44 and 1·99, respectively, when the partial area method of scaling is used; and 3·98 and 2·48, respectively, when the ordinate method of scaling is used. These quantities are 1·66 and 1·46, respectively, with the partial area method; and 3·74 and 2·14, respectively, with the ordinate method. The mean (M) value of the maximum interstory drifts of bare and infilled frames are 1·59 and 1·26%, respectively, with the partial area method; and 1·67 and 1·43%, respectively, with the ordinate method. The maximum interstory drift values for the long period synthesized records are 1·06 and 1·19% for the infilled and the bare frames, respectively. Similarly, the maximum drift values for the short period records are 1·55 and 1·91%, respectively.

The M + SD value of the global damage index for the bare frame is 0·48 and 0·69 for partial area and ordinate methods of scaling, respectively; and the envelope value of that due to synthetic records is 0·42. For the infilled frame, the corresponding damage indices are 0·35, 0·60 and 0·34, respectively. The envelope values of the story level damage index due to the synthetic records are within 0·74 for the bare frame and 0·66 for the infilled frame, which occurs at the seventh story level. The maximum ductility demand due to the synthetic records on some of the beams at this level is found to be close to 4·5 for the bare frame and 3 for the infilled frame. The ductility demand on the bottom story columns is less than 3. Based on these observations, the building can be said to have achieved the CP level performance according to NBCC (2005) and ASCE 41-06 (2007) guidelines.

5. PERFORMANCE-BASED SEISMIC DESIGN

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

It has been observed from the results of conventional strength-based design that while the NBCC (2005) produces a robust design of the lateral load resisting system of buildings, the level of performance achieved by different buildings is not uniform. Performance-based seismic design approach is an alternative to the strength-based design to achieve uniform performance level. The performance-based design is currently evolving and it is informally in practice in the structural design for some time by designing the structures to fulfill the criteria of service limit state and ultimate limit state. That is an indirect implementation of performance-based design. In seismic design, the desired performance is ensured by supplying it with adequate deformation capacity. But if a structure can be designed based on targeted performance, it will be better than fixing the performance through evaluation.

The focus of the research on the performance-based seismic design is on the development of an efficient and reliable design methodology that can easily be used in designing of the structure for the target performance level. SEAOC Vision 2000 Committee (1995) report considered the following three types of performance-based earthquake resistant design: (a) strength-based design, (b) displacement-based design and (c) energy-based design. In the first and third categories of design, the performance is established through the evaluation of performance and in the second one, the design is done by specifying the required level of performance in the beginning and determining the corresponding capacity of the structure. Thus, it can be said that the displacement-based seismic design is the direct performance-based seismic design. The methodology of performance-based seismic design involves the following steps (Kunnath, 2006): (a) define a performance objective by incorporating the description of the hazard and the expected level of performance; (b) select a trial design; (c) determine the seismic demands on the system and its components through an analysis of the mathematical model of the structure and (d) evaluate the performance of the structure through static and dynamic nonlinear analysis to verify the performance objectives as defined initially. If the performance level does not satisfy the performance objective, the design must be revised to achieve the required performance objective.

As a part of seismic design, a comparative study of different type of performance-based seismic design methodology proposed by several researchers are presented here. The following four different methods of performance-based seismic design have been explored here:

  • a
    Capacity-demand-diagram (CDD) Method (Chopra and Goel, 1999)
  • b
    Nonlinear analysis (N2) method (Fajfar, 2000)
  • c
    Displacement-based seismic design (DBSD) method (Humar and Ghorbanie-Asl, 2005)
  • d
    Yield point spectra (YPS) method (Aschheim, 2000)

To evaluate the above-mentioned design methods, the 20-story building designed earlier using NBCC (2005) is considered here. The above-mentioned methods are briefly reviewed here while using them in the Canadian context to the evaluation of the building considered here.

6. CDD METHOD

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

CDD method as proposed by Chopra and Goel (1999) is based on the capacity spectrum method proposed by Freeman et al. (1975). It a simplified nonlinear analysis procedure for predicting earthquake demands of a structure. In the development of the capacity diagram a multiple degrees of freedom (MDOF) system is transformed to an equivalent single degree of freedom (SDOF) system using a transforming factor. The factor is determined based on an assumed deformed shape, Φ. The first modal deformation shape has been selected as the deformed shape of the structure to determine the capacity diagram. The masses and the modal displacements corresponding to the first mode, Φ at different story level are shown in the Table 3.

To transform MDOF to SDOF system, a factor called transformation factor, Γ is used. The following equations (Chopra and Goel, 1999) are used in the transformation process.

  • equation image(1)
  • equation image(2)

Where mi is the mass of ith story, m* is the mass of the equivalent single-degree-of-freedom system, and Φi is the assumed displacement (e.g., the first mode shape) of the ith story, φ is the modal vector and m is the vector of story masses.

Using the above equations, the transformation factor, Γ is found to be 1·3, and the SDOF equivalent mass, m* is found to be 950 tons. The pushover curve of the MDOF system is idealized in a bilinear form, which is converted to the capacity curve of the equivalent SDOF system by dividing the roof displacement at yield by the transformation factor, Γ, and the yield base shear by the equivalent mass, m*. The pushover curve to be used here can be generated using an assumed distribution of the lateral loads, such as the inverted triangular distribution suggested in NBCC (2005), a mass-weighted mode proportional distribution, or a uniform distribution as shown in Figure 8. Figure 9 indicates that the pushover curve is sensitive to these distributions. As the uniform distribution is somewhat unrealistic, and the triangular and mode proportional distributions yield similar results; the triangular distribution has been considered here in further work. The capacity curve is overlaid with the seismic demand spectrum that is expressed in the so called acceleration-displacement format (A-D spectrum). The hazard spectra presented in NBCC (2005) has been used determining the demand diagram. To determine the demand curve in A-D format, the following equation is be used.

  • equation image(3)

where, D is the inelastic displacement, A is acceleration, T is the period of vibration, μ is the ductility capacity and Ry, a ductility reduction factor which is a nonlinear function of μ, T and material properties that is known as R-μ-T relationship. There are a number of R-μ-T relations available in the literature such as, Newmark and Hall (1982); Krawinkler and Nassar (1992); Vidic et al. (1994); and Miranda and Bertero (1994). Figure 10 shows the demand spectra constructed using different R-μ-T relations, which shows that of them produce similar demand spectra. In this study, the R-μ-T relation by Krawinkler and Nassar (1992) has been used for further analysis. The capacity diagram and the demand diagram are shown in the Figure 11.

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Figure 8. Distribution of lateral loads for pushover analysis

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Figure 9. Effect of the vertical distribution of lateral loads on the pushover analysis

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Figure 10. Seismic demand curves using different R-μ-T relations (KN = Krawinkler and Naser (1992); VFF = Vidic et al. (1994); and NH = Newmark and Hall (1982))

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Figure 11. Application of the CDD, N2 and DBSD methods

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The pushover curve of the bare frame as presented in Figure 2 has been idealized in a bilinear form, and the base shear coefficient and roof displacement at yield are found to be 0·063 and 0·9%, respectively. For the equivalent SDOF system, the yield strength and displacement are obtained by dividing the F by equivalent mass m*, D by Γ in the idealized pushover graph, and they are Fy* = 932 kN and Dy* = 514 mm. Figure 11 shows the capacity diagram of the single-degree-of-freedom system (curve CC1) overlaid with the demand curve for different values of ductility.

From the intersection of capacity diagram and the elastic demand diagram as indicated by point 1 in Figure 11, the displacement demand to the SDOF system is found to be 450 mm. For the MDOF system, the displacement demand is (450*1·3) or 585 mm (0·79% of the building height). Assuming an average ratio of story drift to roof drift to be 1·6 as suggested by Gupta and Krawinkler (2000), the maximum interstory drift demand can be estimated to be 1·26%, which is somewhat lower than the mean interstory drift obtained from the dynamic time history analysis (about 1·6 to 1·7% depending on the method of scaling). Considering the SEAOC Vision 2000 Committee (1995) prescribed level of performance, both the CDD method indicates the achievement of the LS performance of the structure, which is consistent with the dynamic analysis presented earlier.

7. THE N2 METHOD

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

The N2 method proposed by Fajfar (2000) is a modified version of the capacity-spectrum method. The capacity diagram is constructed the same way as described in the previous section, except that the yield based shear is divided by m*Γ, instead on m*. The elastic period, T* of the idealized bilinear system is calculated by using the Equation (5) (Fajfar, 2000).

  • equation image(5)

The elastic period, T* of the system considered here calculated using Equation (5) is found to be 4·678 s. The capacity curve is indicated by CC2 in Figure 11. The acceleration at the yield point (Say) is determined to be 0·077 g. As the capacity curve CC2 does not intersect the elastic demand curve, the intersection of the line following the slope of the capacity curve with the demand curve as indicated by point 2 in Figure 11, is considered for estimating the elastic acceleration (Sae), which is found to be 0·088 g. The corresponding elastic displacement (Sde) is found to be 590 mm.

The ductility reduction factor (Rμ = Sae /Say) is then calculated to be 1·14. The elastic period of system (T* = 4·523 s) is greater than the critical period, Tc = 0·2 s, when the velocity dependent part of the response spectrum meets the acceleration dependent part. Therefore, μ = Rμ = 1·14. For the period of T* > Tc, the elastic displacement and the inelastic displacement become the same, i.e. Sd = Sde (Fajfar, 2000). Therefore, the inelastic displacement demand of SDOF system is 590 mm. So, the inelastic displacement demand of the MDOF system is (590*1·30) or 767 mm (1·04% of building height), and the ultimate capacity of the building is about 874 mm (1·18% of building height). The ductility demand as determined here is less than the ductility capacity of 1·94 as determined from the pushover curve in Figure 2. Therefore, the system has adequate ductility and it can be said that the design is satisfactory. In the N2 method, the local deformation such as the interstory drift demand for the MDOF system is obtained using the second stage pushover analysis where the structure is pushed until roof displacement corresponding to the demand is reached.

8. DBSD METHOD

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

The DBD method as proposed by Humar and Ghorbanie-Asl (2005) in the context of concrete shear wall systems uses a target roof displacement to estimate the design base shear. The initial target displacement is estimated based on the following limits: (a) code defined maximum roof displacement, (b) roof displacement at the P-Δ instability limit in pushover analysis and (c) roof displacement at which the element's ductility demand exceeds its ductility capacity. Equation (9) (Humar and Ghorbaine-Asl, 2005) has been used for the calculation of design base shear.

  • equation image(9)

where m* is the mass of equivalent single-degree-of-freedom system and calculated by dividing the mass of the MDOF system with a modification factor (Γ); R0 is the overstrength related force reduction factor taken as 1·5 for the steel moment resisting frame according to NBCC (2005); and Ay is the spectral acceleration.

Initially a preliminary design of a building frame is performed using the building code procedure, and the pushover curve obtained (Figure 2). The initial design base shear obtained by using the NBCC (2005) provisions is 401 kN. The yield and ultimate displacements as obtained from the pushover curve in Figure 2 are 668 and 1296 mm, respectively. The ductility capacity (μ = Δu /Δy) is 1·94 but the code permitted ductility for a fully ductile moment resisting frame is 5, which is higher than the value assumed initially. So, the revised ductility of 1·94 is used in the design. Using the transformation factor, Γ of 1·3 as calculated earlier, the yield (δy) and ultimate displacements (δu) of the SDOF system are: δy = (Δy / Γ) = 514 mm, and δu = (Δu / Γ) = 997 mm. The inelastic demand curve for a ductility of 1·94 has been constructed (Figure 11), and the intersection of the inelastic demand curve and the capacity curve as indicated by point 3 in Figure 11 is used for determining the inelastic demand acceleration (A), which is to be 0·06 g. The new design base shear is then calculated to be 380 kN (Equation (9)), while the base shear used in the equivalent static load-based design is 401 kN. As the base shear calculated using the displacement-based design method is smaller than the one used in the original static load based design of the structure, the original design is satisfactory from the strength point of view, but conservative.

9. YPS METHOD

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

The YPS method as proposed by Aschheim (2000) is a simplified form of capacity spectrum method. The yield point is constituted by the yield strength (Vy) and yield displacement (Δy). The following equation is used to determine the yield point spectra.

  • equation image(10)

where Sa is the inelastic elastic spectral acceleration as obtained by diving the elastic spectral acceleration (Sae) at a given period, T by the ductility factor (Ry).

Using the seismic hazard spectra for Vancouver as provided in NBCC (2005), the yield point spectra for different values of ductility are obtained (Figure 12). In order to determine the performance of the building using the yield point spectra, the following two performance levels are considered: (a) CP based on the SEAOC Vision 2000 Committee (1995) recommendation and NBCC (2005) requirement of 2·5% interstory drift and (b) LS based on SEAOC Vision 2000 Committee (1995) recommendation of 1·5% interstory drift. Considering the CP level of performance, a performance demand curve indicated by ABCD in Figure 12 has been constructed. According to Gupta and Krawinkler (2000), the story drift to roof drift ratio for low to medium rise building varies from 1·2 to 2·0. Considering the average value of 1·6, the roof displacement corresponding to an interstory drift of 2·5% is (2·5%/1·6) or 1·56%, which corresponds to a roof displacement of 1159 mm. For the first modal displacement the transformation factor for SDOF is 1·3. So, the maximum roof displacement of SDOF is calculated to be 1159/1·3 or 892 mm. Point A in Figure 12 corresponds to an elastic YPS with yield displacement of 892 mm, point B corresponds to a YPS with ductility 2 and yield displacement of 892/2 or 446 mm, point C corresponds to a YPS with ductility 4 and yield displacement of 892/4 or 223 mm and point D corresponds to a YPS with ductility 8 and yield displacement of 892/8 or 111·5 mm. Similarly, the LS performance demand curve is constructed (Figure 12) based on the interstory drift of 1·5% which corresponds to a roof displacement of 535 mm. The pushover curve as shown in Figure 2 indicates that the MDOF system, the base shear coefficient and roof drift at yield are 0·063 and 0·9% of building height, respectively. Using the procedure described in the CDD method and Equations (1) and (2), these quantities are transformed to those for an equivalent SODF system. The base shear coefficient and roof displacement at yield for and equivalent SDOF systems are found to be 0·1 and 514 mm, respectively, which is indicated by point P in Figure 12. As point P lies above both LS and CP levels of performance demand curve, the building satisfies both of these levels of performance. Thus, the YPS methodology indicates that the building is overdesigned from performance point of view.

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Figure 12. Yield-point-spectra (YPS) for NBCC (2005) response spectrum of Vancouver for different ductility demand

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10. DISCUSSION AND CONCLUSIONS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES

From the push over graph it has observed that the first yielding occurs at the base shear coefficient of 0·048 in beam no. 23, and at 0·066 in column no. 41. The design base shear coefficient for the building is 0·0264 that is almost half the base shear coefficient corresponding to the occurrence of the first yield. The interstory drift at the point of instability is estimated to be 1·10%, and the ultimate roof displacement is 1·4%. The yield displacement is 0·56% of the total height of the frame.

From the dynamic analysis, the maximum interstory drift observed for the stochastic ground motion is 1·8% of the story height. The envelope of the mean (M) and M + SD of the interstory drift of due to the real ground motions are 1·6 and 2·0%, respectively, when the partial area method of scaling is used. On the other hand, these values are 1·6 and 2·5%, respectively, when the ordinate method of scaling is used. It has been observed that method of scaling affects the evaluated performance of the structure.

From the analysis of the results of the performance-based seismic design it has been observed that except in the direct displacement-based seismic design method, the displacement demand is calculated and compared to the displacement of static analysis or the response history analysis. Most of the methods studied here primarily compare the seismic performance of buildings, and the performance-based design concept has not been fully reflected in them. In a performance-based seismic design, the design of a structure should be based on the performance attributes such as displacement, curvature, damage index, etc., and the output will be the structural details including the deformation and strength capacities provided in the structure. However, in all the above discussed methods the design of the structure is first carried out based on the anticipated seismic load, then the performance is evaluated to check the sufficiency of the design, and the load carrying capacity recalculated, if necessary. From that point of view they are not truly performance-based seismic design methods. As an exception, in the direct displacement-based seismic design, the base shear of the building is calculated for seismic force based on a target displacement and then compared to the equivalent static base shear calculated using the method provided in the building code. Thus, the direct displacement-based design of performance-based seismic design is more suitable for performance-based seismic design as compared to other methods.

The advantage of the performance-based seismic design methods considered here is that these methods are simple and the performance objective can be easily determined without rigorous analysis or calculation. The main disadvantage of these methods is that the accuracy is not high because all of them are based on many assumptions to simplify the representation of a structure, such as, the conversion of MDOF system to an SDOF one using an assumed displacement shape. In the SDOF system, the total mass of the MDOF system may not be accounted for properly. Also there is a huge variation of results obtained from different methodologies for performance-based seismic design and from dynamic or static analysis. Clearly the methods need further development in order for them to be used in the design practice.

REFERENCES

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. BACKGROUND OF NBCC ()
  5. 3. DESIGN OF THE STRUCTURE ACCORDING TO NBCC () PROVISIONS
  6. 4. EVALUATION OF PERFORMANCE OF THE BUILDING
  7. 5. PERFORMANCE-BASED SEISMIC DESIGN
  8. 6. CDD METHOD
  9. 7. THE N2 METHOD
  10. 8. DBSD METHOD
  11. 9. YPS METHOD
  12. 10. DISCUSSION AND CONCLUSIONS
  13. Acknowledgements
  14. REFERENCES
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  • ASCE 41-06. 2007. Seismic Rehabilitation of Existing Buildings, ASCE-SEI Standard 41-06. American Society of Civil Engineers: Reston, VA.
  • Aschheim M. 2000. Yield Point Spectra: A Simple Alternative to the Capacity Spectrum Method, Advanced Technology in Structural Engineering, American Society of Civil Engineering (ASCE) Structures Congress 2000, Philadelphia, Pennsylvania, USA.
  • Bagchi A. 2001. Evaluation of the seismic performance of reinforced concrete buildings. PhD Thesis, Department of Civil and Environmental Engineering, Carleton University, Ottawa, Canada, Archived by National Library of Canada, ISBN: 0612609499, http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/ftp04/NQ60949.pdf.
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  • Humar J, Ghorbanie-Asl M. 2005. A New Displacement-Based Design Method for Building, 33rd Annual General Conference of the Canadian Society for Civil Engineering, GC-136, Toronto, Ontario, Canada.
  • IBC. 2006. International Building Code, International Code Council, Washington, D.C., USA.
  • Krawinkler H, Nassar, AA. 1992. Seismic design based on ductility and cumulative damage demands and capacities. Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings, FajfarP, KrawinklerH (eds). Elsevier Applied Science: New York.
  • Kunnath SK. 2006. Performance-Based Seismic Design and Evaluation of Building Structures, Earthquake Engineering for Structural Design, ed. Chen, Lui and Taylor. Francis Group, FL, USA.
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  • Miranda E, Bertero VV. 1994. Evaluation of the Strength Reduction Factors for Earthquake Resistant Design. Earthquake Spectra 10: 357379.
  • Naumoski N, Saatcioglu M, Amiri-Hormozaki K. 2004. Effects of scaling of earthquake excitations on the dynamic response of reinforced concrete frame buildings. In 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 August; Paper No. 2917.
  • NBCC. 1995. National Building Code of Canada, 1995. Canadian Commission on Building and Fire Codes, National Research Council of Canada: Ottawa, Canada.
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  • Newmark NM, Hall WJ. 1982. Earthquake Spectra and Design. Earthquake Engineering Research Institute: Berkeley, CA.
  • NRC (Natural Resources Canada). 2006. Earthquakes Canada—East. http://seismo.nrcan.gc.ca/major_eq (Updated on September 2006).
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  • Prakash V, Powell, Graham H, Campbell SD, Scott D. 1993. Drain-2DX: Static and Dynamic analysis of Inelastic Plane Structure. Department of Civil Engineering, University of California: Berkeley, CA.
  • Saatcioglu M, Humar J. 2003. Dynamic Analysis of Buildings for Earthquake-Resistant Design. Published on the NRC Research Press Web site: http://cjce.nrc.ca.
  • SEAOC Vision 2000 Committee. 1995. Performance-based seismic engineering. Report prepared by Structural Engineers Association of California, Sacramento, CA.
  • Tremblay R, Atkinson GM. 2001. Comparative study of in elastic seismic demand of eastern and western Canadian sites. Earthquake Spectra 17(2): 333358.
  • Tremblay R, Poncet L. 2005. Seismic Performance of Concentrically Braced Steel Frames in Multistory Buildings with Mass Irregularity. Journal of Structural Engineering 131(9): 13631375.
  • Vidic T, Fajfar P, Fischinger M. 1994. Consistent inelastic design spectra: strength and displacement. Earthquake Engineering and Structural Dynamics 23(5): 507521.
  • Yousuf M, Bagchi A. Seismic Design and Performance Evaluation of Steel-Frame Buildings Designed using NBCC-2005. Canadian Journal of Civil Engineering 38(2): 280294.