5.5 Sensitivity from Nonlinear Time-History Analyses
5.5.2 Sensitivity of Response Using Bar Charts
and Ws as seen from the formation of spiral in Fig. 5.5(a) and Fig. 5.5(b), respectively.
Individual COVs for different ground motions are also very high with a maximum of 58%
and 52% for fm′ and Ws, respectively. On the other hand, the variation in response due to a change in εm is negligible for most ground motions, except for the two cases where the COV is 11%. Thus, the effect of fm′ and Ws should be emphasized in the sensitivity of displacement response of FI frames.
(a) (b) (c)
Figure 5.5 Displacement sensitivity radar charts for uncertain input parameters in FI frames:
(a) fm′, (b) Ws, and (c) εm, with their coefficient of variation (COV) for seven ground motions.
5.5 Sensitivity from Nonlinear Time-History Analyses
at their best estimates, and thus, gives normalized response near or equal to 1.0. However, it is not always necessary that the median parameter model result in the median seismic response as also observed by Vamvatsikos and Fragiadakis (2010).
Figure 5.6 Response sensitivity bar diagrams for normalized top displacement in bare frames for different ground motions.
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Norm Disp fckDbBc fy γc IL ξ
Chile
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Norm Disp fckDbBc fy γc IL ξ
Duzce
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Norm Disp fckDbBc fy γc IL ξ
El Centro
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Norm Disp fckDbBc fy γc IL ξ
Indo Burma
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Norm Disp fckDbBc fy γc IL ξ
Kobe
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Norm Disp fckDbBc fy γc IL ξ
Kocaeli
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Norm Disp fckDbBc fy γc IL ξ
Tabas
For majority of the ground motions, it is observed that a change in the parameters Bc, fck, IL, and ξ incurs a large variation in the estimates of roof displacement, i.e., values of the displacement response larger or smaller than 1.0 are obtained for the range of each input parameter considered (16 samples of each parameter). Varying the remaining parameters (Db, fy, γc) do not have much influence on the displacement response (i.e., their normalized displacement values are more or less equal to 1.0). Thus, it appears that in case of BF, of all geometrical properties, a change in column dimension is more influential than any dimensional change in beams. Liel et al. (2009) also conducted sensitivity analysis on a 4-storey RC frame and reported that the effect of column strength is more on the median collapse capacity compared to that of the beam strength. Out of the different material characteristics considered, the nonlinear displacements obtained are more sensitive to a change in fck and ξ, rather than fy or γc.
Response sensitivity bar charts for normalized roof displacement are also obtained by varying different random input parameters for OGS frames (Fig. 5.7). Similar to the bare frame, for most ground motions, it is observed that the variation in parameters Bc, fck, IL, and ξ result in higher variation in response from the median estimate. A large oscillation in displacement response about the median value for these parameters indicates large deviations from the median estimate of displacement. Thus, it can be concluded that even though the structural behavior of bare frames and OGS frames differ significantly, the sensitivity of their global displacement response to random input parameters is quite similar. Column dimension, compressive strength of concrete, infill load, and system viscous damping are the major random input parameters affecting the sensitivity of global response of OGS frames.
In addition to the random input parameters considered for the bare and OGS frame, three additional parameters – ultimate strain in masonry (εm), compressive prism strength of masonry ( fm′), and width of equivalent diagonal strut (Ws) – are considered for sensitivity analysis of FI frames. Response sensitivity bar diagrams for fully infilled frames for different ground motions are shown in Fig. 5.8. Interestingly, for the FI frame, comparing all the random input parameters together, there is practically no variation in response output due to a change in the parameters Bc, Db, fck, fy, γc, IL, ξ, and εm. The most influential parameters for FI frames are fm′ and Ws indicating that uncertainty in these parameters has a major impact on the displacement response of FI frames. It can be
5.5 Sensitivity from Nonlinear Time-History Analyses
inferred from the results that the structural parameters (fm′ and Ws) related to infill primarily affects the response of FI frames.
Figure 5.7 Response sensitivity bar diagrams for normalized top displacement in OGS frames for different ground motions.
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Norm Disp fckDbBc fy γc IL ξ
Chile
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Norm Disp fckDbBc fy γc IL ξ
Duzce
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Norm Disp fckDbBc fy γc IL ξ
El Centro
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Norm Disp fckDbBc fy γc IL ξ
Indo Burma
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Norm Disp fckDbBc fy γc IL ξ
Kobe
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Norm Disp fckDbBc fy γc IL ξ
Kocaeli
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Norm Disp fckDbBc fy γc IL ξ
Tabas
Figure 5.8 Response sensitivity bar diagrams for normalized top displacement in FI frames for different ground motions.
It is also interesting to note that in both bare and OGS frames, the response sensitivity of different parameters changes drastically for different ground motions. As mentioned already, Bc, fck, IL, and ξ show highest sensitivity in bare and OGS frame, more
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Norm Disp fckDbBc fy γc IL ξ
Chile
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
Duzce
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
El Centro
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
Indo Burma
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
Kobe
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
Kocaeli
εm fm՛ Ws
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Norm Disp fckDbBc fy γc IL ξ
Tabas
εm fm՛ Ws
5.5 Sensitivity from Nonlinear Time-History Analyses
specifically for Duzce, Kocaeli, and Chile ground motion. This is possibly due to the reason that these ground motions have high energy density (Arias Intensity in the range of 0.17 m/s to 0.32 m/s) values as compared to the other ground motions considered. On the other hand, for FI frames the response sensitivity is dominantly highest for fm′ and Ws
only for all the ground motions without displaying much dependence on the energy content of the ground motions. Thus from these observations, it is clear that for relatively flexible systems (such as, bare and OGS frames), the sensitivity of displacement response is more for those ground motions, which have higher energy density. In contrast, for stiffer systems (such as, the FI frame), response sensitivity is independent of the energy content of the ground motion.
In OGS frame, the highest median frame response is obtained for Tabas (0.13 m) and Kobe (0.11 m) probably due to their high PGA values of 0.84g and 0.82g, respectively (Table 3.5). However, the sensitivity of response to different parameters for these ground motions is lesser than that for the other ground motions as shown in Fig. 5.7. Again, in BF the median frame response for Kobe (0.216 m) is higher than that for Chile (0.15 m), but the sensitivity of response to parameters is highest for Chile and lowest for Kobe (Fig.
5.6). Apparently, the sensitivity of the frame response is not dependent on the peak response of the frames or PGA of the ground motion. Similarly, in case of FI frame, the displacement response of the median frame is highest for Duzce (0.07 m) ground motion, whereas, sensitivity is least for the same (Fig. 5.8). Thus, although the number of ground motion considered is limited in the study, it can be concluded that the record-to-record variability can be obtained by concentrating more on energy characteristics of the ground motion. Increasing the number of records would have resulted in more elaborate description of record-to-record variability. However, the present study is concerned more on the sensitivity of the frame response to epistemic uncertainties.