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.
Table 3. Distribution of base shear
|Story level||Height (hi), m||Weight (Wi), kN||hiWi, kNm||F (design), kN||Mass (m), kg||First mode vector, φ||F (modal p*m*φ), kN||F (uniform), kN|
| 9||34·05||765·09||26 051·34||13·74||77·99||0·60||19·75||20·048|
| 8||30·40||765·09||23 258·76||12·26||77·99||0·53||17·44||20·048|
| 7||26·75||765·09||20 466·18||10·79||77·99||0·47||15·47||20·048|
| 6||23·10||765·09||17 673·60||9·32||77·99||0·40||13·16||20·048|
| 5||19·45||767·13||14 920·71||7·87||78·20||0·33||10·89||20·048|
| 4||15·80||769·17||12 152·93||6·41||78·41||0·26||8·60||20·048|
| 3||12·15||769·17||9 345·45||4·93||78·41||0·19||6·29||20·048|
| 2||8·50||769·17||6 537·97||3·45||78·41||0·12||3·97||20·048|
| 1||4·85||786·73||3 815·62||2·01||80·20||0·06||2·03||20·048|
|Total|| ||15 104·39||588 851·63||400·96||1539·69||1·00||400·89||400·96|
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.
Table 4. Summary of real ground motion time histories
|Record no.||Location||Peak acceleration (g)||Peak velocity (m/s)||A/V|
| 1||Imperial Valley||0·348||0·334||1·04|
| 2||Kern Country||0·179||0·177||1·01|
| 3||Kern Country||0·156||0·157||0·99|
| 4||Borrego Country||0·046||0·042||1·09|
| 5||San Fernando||0·150||0·149||1·01|
| 6||San Fernando||0·211||0·211||1·00|
| 7||San Fernando||0·165||0·166||0·99|
| 8||San Fernando||0·180||0·205||0·88|
| 9||San Fernando||0·199||0·167||1·19|
|13||Report Del Archivo: SUCH850919AL.T||0·105||0·112||0·94|
|14||Report del Archivo: VILE850919AT.T||0·123||0·105||1·17|
Table 5. Summary of stochastic ground motion
|Peak acceleration (cm/s2)||266·2||279·4||248·6||271·7||523||527||567||380|
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.
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.
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.