This study investigates seismic behavior of base isolated structures considering torsional effects. LRB and FPS type base isolation systems were designed with 0%, 10% and 20% of plan dimension eccentricity between mass center of structure and stiffness center of base isolation system. The same target displacement value was used at design stage to compare the effect of torsional irregularity and base isolator types on seismic response, properly. Since the torsional effects of the system were reflected by placement of isolators, there was no need to create torsional irregularity in the superstructure. Therefore, the superstructure models do not contain any torsional irregularities and are fully symmetrical. The torsional irregularity occurring in the isolator system is much more critical since a significant part of the seismic demands will be damped by the isolator system before transmitting to the structure. In the scope of this study, 528 different nonlinear time history analyses of 24 different models were performed considering 11 pairs of spectrum compatible record set.
The building model parameters are summarized in Table 5 as total seismic weight (W), dominant vibration periods (Tx, Ty and Tz) and base shear force values (Vtx and Vty). The period shifting is obvious for base-isolated system compared to fixed-base models. It is obvious that FPS type base isolated models tend to have lower vibration periods compared to the LRB type base isolated models. The reason for this outcome is that FPS type isolators modeled according to the same design displacement have generally higher effective stiffness values.
Table 5. Comparisons of model parameters.
Model
|
3-story
|
5-story
|
7-story
|
9-story
|
Fixed
|
Tx (s)
|
0.51
|
0.87
|
1.15
|
1.51
|
Ty (s)
|
0.48
|
0.82
|
1.12
|
1.34
|
Tz (s)
|
0.47
|
0.78
|
1.05
|
1.32
|
W (kN)
|
4623.6
|
12753.8
|
19885.5
|
32623.2
|
Vtx (kN)
|
1549.8
|
3200
|
3472.6
|
4836.1
|
Vty (kN)
|
1399.7
|
2996.7
|
3009.6
|
4565.2
|
e0
LRB
|
Tx (s)
|
2.98
|
3.34
|
5.01
|
5.51
|
Ty (s)
|
2.36
|
3.32
|
4.84
|
5.18
|
Tz (s)
|
1.95
|
3.15
|
4.24
|
4.87
|
e0
FPS
|
Tx (s)
|
2.58
|
3.03
|
4.05
|
4.82
|
Ty (s)
|
2.01
|
2.94
|
3.62
|
4.02
|
Tz (s)
|
1.69
|
2.37
|
2.97
|
3.61
|
Seismic response of building models with seismic isolators are compared using displacement and interstory displacement demands. The obtained displacement demands are normalized by building height while the interstory displacement demands are normalized by story height to obtain “roof drift ratio (RDR)” and “interstory drift ratio (IDR)” values.
4.1 Evaluation of displacement demands
The displacement values at the base isolation and roof level of the base isolated symmetrical building models subjected to the scaled ground motion records are listed in Table 6 for LRB and FPS type isolator models. The roof displacement demand ratios are plotted in Figure 6. The figure illustrates that FPS type base isolated buildings tend to have higher roof drift demands compared to the LRB type base isolated buildings.
Table 6. The displacement values at the base isolation and roof level of the base isolated symmetrical buildings models
RSN
|
Roof Displacement (mm)
|
Isolator Displacement (mm)
|
LRB
|
FPS
|
LRB
|
FPS
|
3-
story
|
5-
story
|
7-
story
|
9-
story
|
3-
story
|
5-
story
|
7-
story
|
9-
story
|
3-
story
|
5-
story
|
7-
story
|
9-
story
|
3-
story
|
5-
story
|
7-
story
|
9-
story
|
88-0
|
74.7
|
88.7
|
87.0
|
97.7
|
124.1
|
171.0
|
132.4
|
232.6
|
69.3
|
81.9
|
77.0
|
88.5
|
117.9
|
159.7
|
123.5
|
221.6
|
88-90
|
173.4
|
192.6
|
227.2
|
225.5
|
177.3
|
199.8
|
302.7
|
363.1
|
161.4
|
179.0
|
204.7
|
207.5
|
165.0
|
186.2
|
275.6
|
335.2
|
164-0
|
113.6
|
128.5
|
151.2
|
161.8
|
122.6
|
133.3
|
208.6
|
275.0
|
105.5
|
118.7
|
133.3
|
149.4
|
115.7
|
122.1
|
190.1
|
257.6
|
164-90
|
71.0
|
79.7
|
86.7
|
92.2
|
122.5
|
139.0
|
164.9
|
184.6
|
65.8
|
72.8
|
77.1
|
83.6
|
115.9
|
132.4
|
151.5
|
170.4
|
302-0
|
79.5
|
86.4
|
89.6
|
73.4
|
114.6
|
155.3
|
189.1
|
231.2
|
74.0
|
79.6
|
79.7
|
68.2
|
109.0
|
148.7
|
174.2
|
214.2
|
302-90
|
197.1
|
230.7
|
239.7
|
270.2
|
222.9
|
325.0
|
371.0
|
320.3
|
183.7
|
214.3
|
215.1
|
248.1
|
207.1
|
300.7
|
334.5
|
293.5
|
313-0
|
138.1
|
176.8
|
163.4
|
130.4
|
194.2
|
259.2
|
168.8
|
236.3
|
128.5
|
162.6
|
147.5
|
121.3
|
182.1
|
236.5
|
155.7
|
217.4
|
313-90
|
185.4
|
241.4
|
208.7
|
170.2
|
279.1
|
327.8
|
220.2
|
252.2
|
172.6
|
225.5
|
185.3
|
155.0
|
259.7
|
305.8
|
201.0
|
232.4
|
548-0
|
112.2
|
132.3
|
115.8
|
111.7
|
135.0
|
171.6
|
154.8
|
151.8
|
104.2
|
121.0
|
102.7
|
96.5
|
127.2
|
160.7
|
139.2
|
140.6
|
548-90
|
147.2
|
188.3
|
164.5
|
164.7
|
207.2
|
266.6
|
255.4
|
189.3
|
136.8
|
174.5
|
148.7
|
152.8
|
192.4
|
248.1
|
234.2
|
180.8
|
1614-0
|
137.5
|
131.8
|
172.0
|
227.9
|
162.5
|
145.2
|
202.9
|
325.1
|
127.6
|
121.4
|
153.8
|
209.1
|
152.5
|
136.9
|
186.1
|
301.0
|
1614-90
|
178.9
|
179.1
|
212.7
|
291.4
|
144.7
|
188.4
|
299.7
|
294.8
|
166.5
|
166.0
|
192.3
|
271.9
|
134.3
|
176.8
|
270.8
|
272.5
|
1633-0
|
254.6
|
286.3
|
290.1
|
275.2
|
374.9
|
431.6
|
436.0
|
464.8
|
237.6
|
267.4
|
264.7
|
255.0
|
334.6
|
400.0
|
391.1
|
422.8
|
1633-90
|
183.1
|
205.4
|
218.2
|
256.5
|
147.8
|
192.5
|
343.4
|
275.9
|
170.5
|
193.2
|
194.8
|
240.0
|
132.1
|
171.0
|
311.0
|
251.4
|
3750-0
|
221.0
|
221.5
|
263.3
|
325.1
|
211.5
|
237.3
|
282.4
|
287.4
|
207.0
|
208.6
|
242.2
|
305.2
|
197.0
|
224.4
|
257.6
|
269.3
|
3750-90
|
358.5
|
406.3
|
436.5
|
479.4
|
376.0
|
432.5
|
446.7
|
500.5
|
335.1
|
382.1
|
400.0
|
450.0
|
335.2
|
400.0
|
400.0
|
450.0
|
3759-0
|
128.6
|
111.5
|
175.9
|
251.9
|
131.9
|
218.9
|
286.2
|
291.4
|
119.6
|
102.6
|
157.1
|
232.8
|
124.7
|
205.9
|
261.2
|
272.7
|
3759-90
|
78.4
|
106.0
|
95.8
|
76.2
|
145.5
|
183.9
|
129.9
|
220.9
|
72.7
|
98.2
|
86.3
|
68.6
|
136.4
|
173.2
|
120.5
|
208.7
|
5815-0
|
319.3
|
398.0
|
317.2
|
275.6
|
400.7
|
438.0
|
412.0
|
326.6
|
298.4
|
374.6
|
285.8
|
254.2
|
335.4
|
400.0
|
370.3
|
290.4
|
5815-90
|
275.7
|
315.1
|
324.1
|
318.4
|
363.7
|
431.3
|
445.5
|
482.1
|
257.8
|
295.3
|
297.5
|
297.5
|
337.6
|
400.0
|
400.0
|
441.0
|
6915-0
|
99.8
|
111.3
|
129.2
|
164.5
|
115.7
|
177.9
|
217.8
|
207.7
|
92.6
|
103.7
|
115.3
|
151.8
|
108.9
|
167.6
|
200.9
|
186.0
|
6915-90
|
205.5
|
249.5
|
269.9
|
269.4
|
166.0
|
240.3
|
336.5
|
290.3
|
191.5
|
233.7
|
246.5
|
249.8
|
155.4
|
224.7
|
308.2
|
264.4
|
Average
|
169.7
|
194.0
|
201.8
|
214.1
|
201.8
|
248.5
|
273.0
|
291.1
|
158.1
|
180.8
|
182.2
|
198.0
|
185.3
|
231.0
|
248.1
|
267.9
|
The roof level displacement demand ratios for asymmetric/symmetric models are also illustrated in Figure 7. It is observed that LRB type isolators are more sensitive to torsional effects. The average displacement demands of 10% and 20% asymmetric LRB type isolator models are 11% and 14% higher than symmetrical models in average. This difference is less than 5% for FPS type isolators. It should be noted that the obtained displacement demand values were obtained from total displacement of building and isolators with respect to ground. Therefore, it does not reflect the superstructure demands.
The obtained results indicate that significant scatter exists in displacement demands of individual ground motion records for all models. The effect of eccentricity in terms of mean values is limited. Similar to the previous studies, it is observed that frequency content of several ground motion records affects the dynamic response of the base isolated system (Güner 2012; Matsagar and Jangid 2010; Tena-Colunga and Zambrana-Rojas 2006). The scatter observed in Figure 7 illustrates that the frequency content effect is more critical especially for FPS type isolators.
The ratio of the maximum displacement of the isolator to the total displacement of the building is given in Figure 8. Since the demand ratios showed a similar trend for all models, 3, 5, 7 and 9-story models were evaluated together. More than 90% of displacement demands were experienced by the isolator system regardless of the eccentricity ratio and isolator type. The eccentricity due to the distribution of isolator stiffness values have very limited effect on the isolator displacement demands. The superstructure displacement demands are significantly small. Therefore, the torsional effects on seismic behavior of structure are negligible. Since the eccentricity in the isolator members is much more critical, it can be predicted that the torsional irregularity on building plan will have a very limited effect. Besides, it is apparent that the base isolation system considerably decreases the superstructure displacement demands subjected to ground motion records.
The average utilization rate of the isolator displacement capacity is given in Figure 9. The used isolator capacities are calculated as 43.1%, 49.4% and 49.5% for e0, e10 and e20 eccentricity of LRB type isolators while these values are 63.5%, 66.3% and 66.5% for FPS type isolators. The outcomes obviously show that the capacity utilization rate of FPS type isolators modeled according to the same design displacement value is significantly higher than the LRB type isolators. When the results are analyzed separately, it is seen that the capacity utilization rate for some ground motion records were approached to 100% for FPS type isolators. Therefore, the evaluation based on average values may be misleading. Moreover, the difference between minimum and maximum capacity utilization is more striking between e0 and e10 models compared to e10 and e20 models.
4.2 Evaluation of IDR demands-
Interstory drift is recognized as an important damage indicator. Roof drift given in the previous section includes the displacement demand of base isolator. Therefore, the evaluation of interstory drift ratio (IDR) values is important parameter to determine the superstructure demand. Figure 10 compares maximum IDR values of all models. Damage limit levels according to TEC-2018 (TEC 2018) is also illustrated on the figure as “UU” and “LD” abbreviations corresponding to uninterrupted use and limited damage limits, respectively. The controlled damage level is not shown on the figure because no model has reached to this damage level.
When the IDR values are examined, they have similar trend with roof displacement demand ratios. The maximum IDR values are calculated for FPS type isolators. While none of LRB type isolator models exceeded to limited damage state, six cases of FPS type isolators are at the LD state for 3-story and 5-story asymmetric models.
In previous studies related with base isolated systems, it is concluded that torsional irregularity may have significant effects on seismic response. However, in these studies limited number of ground motion records were considered (Nagarajaiah et al. 1993; Nagarajaiah et al. 1993; Tena-Colunga et al. 1997). By the nature of dynamic analysis, high ratio of scatter in seismic demands is also observed in the scope of this study. In Figure 11, the IDR profiles of 7-story model is given for RSN-5815 record as an example. While the differences in average results are negligible for e0 and e10 eccentricity of LRB type isolators, e10 eccentricity model estimated almost 100% higher IDR value compared to e0 eccentricity model for RSN-5815 record. A similar trend is seen for the FPS type isolator with e20 eccentricity for the same ground motion record. Since the displacement demands highly depend on the nature of ground motion records, the use of several records can result in remarkably different demands compared to the demands of 11 pairs of ground motion records. The evaluation based on the average displacement demands using 11 pairs of ground motion records indicate that effect of asymmetry is limited on the base isolated systems. Therefore, the number of records is substantially important. The outcomes of this study underline the careful selection of number of ground motion records in dynamic analysis as mentioned in the previous study (Huang et al. 2008).
The average IDR values of all building models are compared for symmetric and asymmetric models in Figure 12. When all models regardless of story number are evaluated together, the base isolated e20 models demand 20% higher IDR values compared to the symmetrical models. Although there may be cases with significant differences due to asymmetry, almost all IDR values (except few cases) are within UU damage level. Therefore, all models considered in this study may be assumed at an acceptable level considering the average IDR values.
4.3 Torsional coefficient values
Torsional coefficients defined in TEC-2018 (TEC 2018) were calculated at the time of maximum IDR and plotted in Figure 13. The torsional irregularity coefficient limit of 1.2 is also shown on the figure. All coefficient values are smaller than the torsional irregularity limit for symmetric models of all buildings. As expected, the torsional irregularity coefficient values increase as the eccentricity ratio increases. Although the average coefficient values of the asymmetric models with 10% eccentricity is around the limit value, there are considerable number of cases that exceed the limit coefficient value. Moreover, the average coefficient values of the asymmetric models with 20% eccentricity are higher than the limit value except the 3-story models. The outcomes clearly indicate that the eccentricity at the isolator causes torsional irregularity at the superstructure. Besides, the LRB type isolators are more vulnerable to torsional irregularity compared to the FPS type isolators.
The ratio of the average coefficient values of the asymmetric system to the symmetric system is given in Figure 14. Both scatter and the average values of torsional irregularity coefficient are quite high for the LRB type isolator models. Torsional irregularity coefficient values of LRB models with 20% eccentricity are 47% higher than symmetrical models in terms of averages. The FPS type isolator models are less affected from the asymmetry.
Since significant part of the demands is absorbed by the isolator system, the remaining seismic demands for the superstructure is relatively low. The variation of the torsional irregularity coefficient for RDR and IDR history is given as an example for RSN-1633 record in Figure 15 to better understand the effects of torsional irregularity on the superstructure behavior. Since similar trends were observed in all ground motion records, these graphs were not given separately for all sets. The figure illustrates the time dependent variation of the scattering of the torsional irregularity factor for the RDR and IDR values. As the eccentricity increases in base-isolation models, the frequency of torsional coefficients approaching maximum values increases significantly. Although the structural behavior is distorted by the torsional irregularity, its effect is limited due to significant damping of demands by the base isolator system. For this reason, it is more important to investigate the effects of torsional behavior on isolator behavior rather than superstructure behavior.