5.5 Sensitivity from Nonlinear Time-History Analyses
5.5.3 Sensitivity Based on Tornado Diagram Analysis
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.
length represents the variation in average maximum seismic responses caused by variation in each individual parameter. The extreme ends of the tornado show the 16th and 84th percentile values for the output response due to the variation in different random variables.
Based on tornado diagram analysis, it is validated that the basic parameters that influence the structural performance of a bare frame are Bc and fck. In OGS frames also, Bc shows the highest influence on the sensitivity of displacement response. Other parameters influencing the OGS frame response are fck and ξ similar to that for the bare frame. Additionally, for OGS frames, the infill load (IL) acting on the members of the frame also seems to be equally important as viscous damping (ξ). Celik and Ellingwood (2010) also observed with the help of tornado diagrams that structural damping and concrete strength are the key parameters influencing the sensitivity of response of RC frames designed for gravity loads in low-seismic regions. The effect of uncertainty in damping and ultimate and yield rotation in columns is also shown to be significant on RC frame responses by Dolšek (2009).
(a) (b) (c)
Figure 5.9 Tornado diagrams for displacement response sensitivity for (a) bare frame, (b) OGS frame, and (c) FI frame. (Figure shows the 16th and 84th percentile values of response for each uncertain parameter. The displacements are normalized with respect to the maximum response obtained for each ground motion).
In the present study, additionally the infill load (IL) acting on the members of the OGS frame also seems to be equally important as viscous damping. Other factors, such as Ws and εm are not considered for the OGS frame since the upper floor infills do not affect the overall performance of the frame (Choudhury and Kaushik 2018a). On the contrary, the parameters, such as, fm′ and Ws show the highest sensitivity on the response
0.5 1 1.5
Bc Db fck fy γc IL ξ
Disp (normalized) BF 16%
fy 84%
fck Db Bc γc ξ IL
0.5 1 1.5
Bc Db fck fy γc IL ξ
Disp (normalized) OGS
16%
84%
γc fy fck Db Bc ξ IL
0.5 1 1.5
Bc Db fck fy γc IL ξ ɛm fm՛
Ws
Disp (normalized) FI 16%
84%
m
fm′
γc fy fck Db Bc Ws
ξ IL
5.5 Sensitivity from Nonlinear Time-History Analyses
of FI frame. This observation is further supported by the swings calculated for the three different frames for all the random input parameters (Table 5.2). The swing values, which can be used to quantitatively assess the sensitivity, are calculated as the difference between the extreme ends of the tornado diagram, i.e., the difference between the 16th and 84th percentile values in percentage. A high value of swing represents a higher sensitivity of the parameter on the output response. Highest swing is observed for parameters fm′ and Ws in case of FI frame; these swing values are about 7 times higher than that for Bc, and about 3 times higher than that for εm and ξ. This clearly implies that one has to be very careful with the values of fm′ and Ws when analyzing FI frames.
Based on the swing values reported in Table 5.2, the order of response sensitivity to different random input parameters of the different frames is as below-
BF: Bc > fck > ξ > fy > IL>γc, Db
OGS: Bc > fck > ξ > IL > γc >fy > Db
FI: fm՛ > Ws > ɛm >ξ > IL > γc > Bc >fck >fy > Db
Table 5.2 Swing values obtained for different frames for considered random input variables.
Parameters Swing values
BF OGS FI
Bc 16 20 11
Db 4 1 4
fck 14 15 8
fy 6 3 6
γc 4 7 18
IL 5 10 19
ξ 10 11 23
ɛm NA NA 27
fm՛ NA NA 78
Ws NA NA 73
Note: NA = not applicable
The uncertain parameter, which has the greatest effect on the seismic response quantities, can vary from structure to structure since the structural collapse mechanism depends on the design process (Celarec and Dolšek 2013). Nevertheless, it is clearly observed that the order of response sensitivity to random input variables is similar in bare and OGS frame, i.e., parameters Bc and fck shows the highest sensitivity in output response. However, in FI frame, uncertainty in the parameters related to infills have
dominating influence on the sensitivity of displacement response. This is in agreement with Celarec et al. (2012) where results of nonlinear static analysis indicated that in fully infilled RC frames, uncertainty in the characteristics of the masonry infills has the highest impact on the response parameters.