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Figure 15: Variation of CMR with variations in F, and r2for IM 9

Figure 15 Variation of CMR with variations in F, and r2for IM 9

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Figure 1: Wood Shear Wall Cyclic Load Displacement Response (adapted from Folz and Filiatrault 2001) The hysteresis model parameters for the FEMA P-695 wood-frame example represent the baseline case in this paper and were derived by fitting the experimental data available at the time. Later additional experimental test data suggested a reduced unit shear capacity and improved displacement capacity for high aspect ratio walls. Analytically this behaviour can be modelled by adjustment of the D, parameter in combination with F, and r; parameter and these modified parameters provide a better fit of the hysteresis response to more recent shear wall test data. In addition to investigation of reduced values of F, parameter, increased values of F,, parameter is investigated to account for the greater strength due to factors such as conservatism in design or presence of sheathed wall in excess of that required by design.
Figure 1: Wood Shear Wall Cyclic Load Displacement Response (adapted from Folz and Filiatrault 2001) The hysteresis model parameters for the FEMA P-695 wood-frame example represent the baseline case in this paper and were derived by fitting the experimental data available at the time. Later additional experimental test data suggested a reduced unit shear capacity and improved displacement capacity for high aspect ratio walls. Analytically this behaviour can be modelled by adjustment of the D, parameter in combination with F, and r; parameter and these modified parameters provide a better fit of the hysteresis response to more recent shear wall test data. In addition to investigation of reduced values of F, parameter, increased values of F,, parameter is investigated to account for the greater strength due to factors such as conservatism in design or presence of sheathed wall in excess of that required by design.
Table 1: Design features of selected FEMA P-695 building models
Table 1: Design features of selected FEMA P-695 building models
Table 2: Overstrength and period based ductility results for IM 9 from pushover analysis with variations in F ,
Table 2: Overstrength and period based ductility results for IM 9 from pushover analysis with variations in F ,
Figure 2: Example backbone curves for varying F’,, D,, and rp parameters Hysteresis model parameter variations investigated as part of this study influence the modelled backbone curve i.e. load displacement shape) as depicted in Figure 2. The reference backbone curve is based on FEMA P-695 modelling parameters for the 1“ story shear wall line of M 9 when subjected to the CUREE Cyclic loading protocol (ASTM E2126 Method C, [9]) and is representative of other reference backbone curves for IM 9 and IM 10. The range of backbone load-displacement response investigated as part of this study is bounded by curves associated with 0.6F, and 1.4F,.
Figure 2: Example backbone curves for varying F’,, D,, and rp parameters Hysteresis model parameter variations investigated as part of this study influence the modelled backbone curve i.e. load displacement shape) as depicted in Figure 2. The reference backbone curve is based on FEMA P-695 modelling parameters for the 1“ story shear wall line of M 9 when subjected to the CUREE Cyclic loading protocol (ASTM E2126 Method C, [9]) and is representative of other reference backbone curves for IM 9 and IM 10. The range of backbone load-displacement response investigated as part of this study is bounded by curves associated with 0.6F, and 1.4F,.
Figure 3: Pushover curves for IM 9 with variations in F,, The complete pushover response of IM 9 with different peak strength factors and gravity load effects are shown in Figure 3. It is observed from the pushover curves that as the peak strength parameter increases, the corresponding displacement at the peak strength reduces and this is reflected in the reduction of the period based ductility summarized in Table 2.
Figure 3: Pushover curves for IM 9 with variations in F,, The complete pushover response of IM 9 with different peak strength factors and gravity load effects are shown in Figure 3. It is observed from the pushover curves that as the peak strength parameter increases, the corresponding displacement at the peak strength reduces and this is reflected in the reduction of the period based ductility summarized in Table 2.
Table 4: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in F,,
Table 4: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in F,,
Figure 6 shows the lognormal distribution of collapse spectral intensities for IM 10. The dispersion of the collapse spectral intensities around the median collapse spectral intensity is close of 0.44 in all cases and is fairly independent to the variation in peak strength parameter. Table 5: Median collapse spectral acceleration and CMR for IM 10 from IDA with variations in F,,
Figure 6 shows the lognormal distribution of collapse spectral intensities for IM 10. The dispersion of the collapse spectral intensities around the median collapse spectral intensity is close of 0.44 in all cases and is fairly independent to the variation in peak strength parameter. Table 5: Median collapse spectral acceleration and CMR for IM 10 from IDA with variations in F,,
Figure 4: Pushover curves for IM 10 with variations in F, Table 3: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in F.,
Figure 4: Pushover curves for IM 10 with variations in F, Table 3: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in F.,
Figure 5: Fragility plots for IM 9 with variations in F,, Figure 5 shows the fragility curves for IM 9 developed based on the results from IDA on collapse spectral intensities of 44 individual ground motions.
Figure 5: Fragility plots for IM 9 with variations in F,, Figure 5 shows the fragility curves for IM 9 developed based on the results from IDA on collapse spectral intensities of 44 individual ground motions.
Table 7: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in Du
Table 7: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in Du
Figure 6: Fragility plots for IM 10 with variations in F,
Figure 6: Fragility plots for IM 10 with variations in F,
Table 6: Overstrength and period based ductility results for index model IM 9 from pushover analysis with variations in D, Figure 7 shows the complete pushover curves for IM 9 with variations in displacement capacity at peak strength parameter. As compared to the case with the variation with peak strength, variation in displacement at peak strength parameter produced less effect on the overstrength. The period based ductility showed an improvement of 20 — 30% with the increase in displacement capacity from 0.7D, to 1.5D,,.
Table 6: Overstrength and period based ductility results for index model IM 9 from pushover analysis with variations in D, Figure 7 shows the complete pushover curves for IM 9 with variations in displacement capacity at peak strength parameter. As compared to the case with the variation with peak strength, variation in displacement at peak strength parameter produced less effect on the overstrength. The period based ductility showed an improvement of 20 — 30% with the increase in displacement capacity from 0.7D, to 1.5D,,.
Figure 7: Pushover curves for IM 9 with variations in D,
Figure 7: Pushover curves for IM 9 with variations in D,
Table 8: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in D, Figure 9 shows the fragility plots for IM 9 with the variations in displacement at peak strength parameter. The reduction in the probability of collapse at any specific spectral intensity with the increase in displacement capacity is clearer by observing the fragility curves.
Table 8: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in D, Figure 9 shows the fragility plots for IM 9 with the variations in displacement at peak strength parameter. The reduction in the probability of collapse at any specific spectral intensity with the increase in displacement capacity is clearer by observing the fragility curves.
Table 9: Median collapse spectral acceleration and CMR for index model IM 10 from IDA with variations in D,
Table 9: Median collapse spectral acceleration and CMR for index model IM 10 from IDA with variations in D,
Figure 8: Pushover curves for IM 10 with variations in D, Figure 8 shows the pushover curves for IM 10 with variations in displacement at peak strength parameter for the case with and without P-Delta effects. 4.2.2 Incremental Dynamic Analysis Table 8 summarizes the results from IDA for IM 9 with variations in displacement at peak strength parameter. When no P-Delta effects are included, collapse capacity is reduced by 8% with reduction in parameter from 1.0D, to 0.7D, and increased by 16% with increase in parameter from 1.0D, to 1.5D,. With the addition of P- Delta effects, the collapse capacities reduced between 5 — 7% compared to the cases without P-Delta effects. While there is an increase of up to 40% in CMR with the variation of peak strength parameter from 0.6F’, to 1.4F,, the increase in displacement at peak strength parameter from 0.7D, to 1.5D, produced an increase in CMR of up to 26%.
Figure 8: Pushover curves for IM 10 with variations in D, Figure 8 shows the pushover curves for IM 10 with variations in displacement at peak strength parameter for the case with and without P-Delta effects. 4.2.2 Incremental Dynamic Analysis Table 8 summarizes the results from IDA for IM 9 with variations in displacement at peak strength parameter. When no P-Delta effects are included, collapse capacity is reduced by 8% with reduction in parameter from 1.0D, to 0.7D, and increased by 16% with increase in parameter from 1.0D, to 1.5D,. With the addition of P- Delta effects, the collapse capacities reduced between 5 — 7% compared to the cases without P-Delta effects. While there is an increase of up to 40% in CMR with the variation of peak strength parameter from 0.6F’, to 1.4F,, the increase in displacement at peak strength parameter from 0.7D, to 1.5D, produced an increase in CMR of up to 26%.
Figure 10: Fragility plots for IM 10 with variations in D,, Fragility curves based on the lognormal distribution of ground motion collapse spectral intensities is given in Figure 10. Dispersion of the collapse spectral intensities from median response is close to 0.40 which is the recommended value from FEMA P-695.
Figure 10: Fragility plots for IM 10 with variations in D,, Fragility curves based on the lognormal distribution of ground motion collapse spectral intensities is given in Figure 10. Dispersion of the collapse spectral intensities from median response is close to 0.40 which is the recommended value from FEMA P-695.
Figure 9: Fragility plots for IM 9 with variations in D, Table 9 gives the summary of IDA results for IM 10 with variation in displacement at peak strength parameter. There is a relative reduction of 12% and increase of 16% in the collapse capacity with 0.7D, and 1.5D, from the baseline case of 1.0D,. Similar to the trend observed with the results from varying the peak strength parameter, inclusion of P-Delta does not produce much difference in the CMR results.
Figure 9: Fragility plots for IM 9 with variations in D, Table 9 gives the summary of IDA results for IM 10 with variation in displacement at peak strength parameter. There is a relative reduction of 12% and increase of 16% in the collapse capacity with 0.7D, and 1.5D, from the baseline case of 1.0D,. Similar to the trend observed with the results from varying the peak strength parameter, inclusion of P-Delta does not produce much difference in the CMR results.
Table 11: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in r, The complete pushover curves of IM 9 and IM 10 with variation in post yield stiffness parameter is shown in Figure 11 and Figure 12.
Table 11: Overstrength and period based ductility results for IM 10 from pushover analysis with variations in r, The complete pushover curves of IM 9 and IM 10 with variation in post yield stiffness parameter is shown in Figure 11 and Figure 12.
Table 10: Overstrength and period based ductility results for IM 9 from pushover analysis with variations in r,
Table 10: Overstrength and period based ductility results for IM 9 from pushover analysis with variations in r,
Figure 11: Pushover plots for IM 9 with variations in r>
Figure 11: Pushover plots for IM 9 with variations in r>
Table 12: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in r,
Table 12: Median collapse spectral acceleration and CMR for IM 9 from IDA with variations in r,
Figure 12: Pushover plots for IM 10 with variations in r>
Figure 12: Pushover plots for IM 10 with variations in r>
Table 13: Median collapse spectral acceleration and CMR for IM 10 from IDA with variations in r,
Table 13: Median collapse spectral acceleration and CMR for IM 10 from IDA with variations in r,
Table 14: CMR for IM 9 with variations in F, and r,
Table 14: CMR for IM 9 with variations in F, and r,
Figure 13: Fragility plots for IM 9 with variations in r, A better representation of seismic response are fragility curves for IM 9 and IM 10 as shown in Figure 13 and Figure 14. While the dispersion of collapse spectral intensities of individual ground motions from the median collapse spectral acceleration is greater than 0.50 for IM 9, the dispersion is close to 0.40 for IM 10.
Figure 13: Fragility plots for IM 9 with variations in r, A better representation of seismic response are fragility curves for IM 9 and IM 10 as shown in Figure 13 and Figure 14. While the dispersion of collapse spectral intensities of individual ground motions from the median collapse spectral acceleration is greater than 0.50 for IM 9, the dispersion is close to 0.40 for IM 10.
Figure 14: Fragility plots for IM 10 with variations in r,
Figure 14: Fragility plots for IM 10 with variations in r,
Figure 16: Variation of CMR with variations in F, and r2for IM 10
Figure 16: Variation of CMR with variations in F, and r2for IM 10
Related topics:
Structural Engineeringlinear dynamic analysisWood shear wall buildingsFEMA P-695
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