Masao TERASHIMA 1, Norihisa KAWAMURA 1, Yoshinao KONISHI 1 Tomoyuki SOMEYA 2, Shoichi KISHIKI 3, Satoshi YAMADA 4 ABSTRACT

Transcription

1 CONTRIBUTION TO EMERGENCY ACTION AND POST-EARTHQUAKE EVALUATION OF A SEISMICALLY ISOLATED HOSPITAL BUILDING EXPERIENCED THE GREAT EAST JAPAN EARTHQUAKE Masao TERASHIMA 1, Norihisa KAWAMURA 1, Yoshinao KONISHI 1 Tomoyuki SOMEYA 2, Shoichi KISHIKI 3, Satoshi YAMADA 4 ABSTRACT The Great East Japan Earthquake, occurred on March 11 th 211, caused significant damage in Tohoku area, Japan. Ishinomaki City was one of the most significant damage areas that approximately 4, people were killed or missing. There stands Ishinomaki Red Cross hospital, which is about 13km away from the epicentre of the M9. main shock. The hospital was able to eliminate damage, thanks to its countermeasures incorporated into the design. These features are the followings, 1) Seismically isolated system was applied. It reduced floor response acceleration and prevented the main frame from damaging and important medical equipment from toppling and damaging. 2) An embankment protected the hospital from Tsunami. 3) The ground had been improved with sand piles against liquefaction, so important facilities such as the hospital building and the heliport eliminated the damage from liquefaction. As a result, these countermeasures contributed to resume its functions immediately and saved many lives. In addition, the shaking was the strongest ever seen by isolated buildings. The base isolation layer of the hospital building experienced as much as 26cm of maximum displacement. Such an intense earthquake shaking presented an unusual opportunity to investigate the effects of the isolation systems. So, analytical study had been implemented in order to verify the effects of the isolation system applied to the hospital building. Furthermore, it is also important to investigate post-earthquake characteristics of seismic isolation system for continuous use. So, comprehensive post-earthquake evaluations of U-shaped steel dampers were conducted to verify their residual fatigue capacity. The following methods were implemented in the evaluation. 1) Scratch plate based method: verify relative displacement orbit of the base isolation layer from a scratch plate record and evaluate their damage based on its fatigue capacity represented by the Manson-Coffin relation. 2) Time history analysis method: conduct time history analysis using nearby actual recorded ground motions and evaluate damage of U-shaped steel dampers based on its fatigue capacity. 3) Experimental method: remove some of U-elements from the hospital and conduct loading tests. 1 Nippon Steel & Sumikin Engineering Co., Ltd. Tokyo, Japan terashima.masao@eng.nssmc.com, kawamura.norihisa@eng.nssmc.com, konishi.yoshinao@eng.nssmc.com 2 Nikken Sekkei Ltd. Tokyo, Japan, someya@nikken.jp 3 Osaka Institute of Technology, Osaka, Japan, kishiki@archi.oit.ac.jp 4 Tokyo Institute of Technology, Yokohama, Japan, yamada.s.ad@m.titech.ac.jp 1

2 These evaluation results indicated that the damage of U-shaped steel dampers experienced the M9. Great East Japan Earthquake was very minor and that U-shaped steel dampers had ample fatigue capacity for continuous function after the extreme seismic event. This paper presents the effects of the countermeasures which enabled the hospital to withstand the intensive ground motions and subsequent Tsunami, as well as post-earthquake verifications in terms of contribution of the isolation system to reduce floor response and U-shaped steel dampers residual fatigue capacity. INTRODUCTION The Great East Japan Earthquake caused significant damage especially in Tohoku region, which is northeast area in Japan. A great number of buildings suffered from damage due to severe ground shakings and Tsunami. Ishinomaki Red Cross hospital located at Ishinomaki City, which is one of the most intensive damage areas, was designed as local base hospital in time of disaster. This hospital was able to eliminate major damage from both the strong ground shakings and Tsunami because of its architectural and structural plans considered in the design. Consequently, this hospital resumed its function immediately and contributed to save many lives. This paper describes how this hospital eliminated damage from the disaster and resumed its functions immediately after the Great East Japan Earthquake. Also, the shaking experienced by the Great East Japan Earthquake was the strongest ever seen by isolated buildings and result in maximum horizontal displacements of 2-25cm in a number of cases, and in one instance a maximum movement of 41cm. This intensive ground shaking presents an unusual opportunity to investigate the effects of isolation systems. So, analytical study had been implemented in order to verify the effects of the isolation system applied to the hospital building. Furthermore, it is important to investigate post-earthquake characteristics of seismic isolation system for continuous use. U-shaped steel dampers, which were applied to the hospital as dampers, were observed residual deformation. It means they absorb seismic energy through their plastic deformation. Therefore, comprehensive post-earthquake evaluations were conducted to verify the residual fatigue characteristics. This paper also presents overviews of these verifications. OUTLINE OF THE HOSPITAL BUILDING Building outline Ishinomaki Red Cross Hospital was established in 26 as a local base hospital at the time of disaster. Facade and bird s eye view of the building are shown in photo 1and photo 2. The hospital building has seven floors, and one basement floor. Total floor area is 32,486m 2, and maximum height is 26.2m. Structural design concept Since the hospital is assumed to be a local base hospital, a lot of countermeasures against disasters were applied as seen in figure1. To take some examples, soil stabilization is implemented to the areas which are required to maintain functions at the time of disaster, such as the main building and heliport by sand pile method, because liquefaction may occur at lower layer of foundation when an extreme earthquake occurs. A structural steel is chosen for the superstructure to reduce the weight of the building as much as possible, which achieves.9 ton/m 2 of building weight, because of the ground conditions. Because the site is along the Old Kitakami River, embankment which is 3m high in maximum is applied to eliminate flood damage. Moreover, seismic isolation system is adopted in order to prevent the superstructure from damage due to intensive ground shakings (photo 3). 2

3 PHFL 7FL 6FL 5FL 4FL 3FL 2FL 1FL B1FL TD± TD-1m TD-2m TD-3m TD-4m TD-5m TD-6m TD-7m TD-8m TD-9m M. Terashima, N. Kawamura, Y. Konishi, T. Someya, S. Kishiki, S. Yamada 3 The Old Kitakami River Photo1.Facade of the hospital Photo 2. Bird s eye view of the hospital steel structure ISS trusses N2 N4 N1 seismic isolation layer (1ST Floor,basement) alluvial sand alluvial cray friction piles (PHC pile) alluvial sand 5m 沖積砂質土層 (As1) 沖積砂質土層 (Ac1) 沖積砂質土層 (As2) 沖積砂質土層 (As2-c) 沖積砂質土層 (As2) 1m 2m 7m alluvial cray 沖積砂質土層 (Ac2) 沖積砂質土層 (Ac2-s) 沖積砂質土層 (Ac2) 2m 沖積砂質土層 (Ac2-s) diluviam layer firm solid qroand Figure 1. Elevation plan 洪積砂礫層 (Dg1) 洪積粘性土層 (Dc) 洪積砂泥互層 (Dalt) TP-95m Photo 3. Seismic isolation layer at basement Seismic isolation system The hospital building applies natural rubber bearings, elastic sliding bearings, and U-shaped steel dampers as seismic isolation devices as shown in figure 2 and the properties of seismic isolation layer and superstructure are listed in figure3 and table 1. Because the predominant natural period of the ground is 1.4 seconds, which is relatively long, base isolation layer is designed with comparatively long natural period to prevent natural period of base isolation layer from corresponding to the one of the ground. As a result, base isolation layer obtains 1.45sec of natural period in its initial condition, 3.73sec when it reaches maximum deformation of 49cm based on the design criterion as mentioned below. Total applied shear force owing to U-shaped steel dampers is about 5% of the total weight of the superstructure. And natural period of superstructure was 1.1 sec. In the original design, non-linear time history analysis was implemented by using six seismic waves as described in table 2; three of them were observed waves which were amplified to correspond to 5cm/sec in maximum velocity, and rest of them were notification waves which correspond to 8cm/sec 2 (.16 T.64) and 8cm/sec (.64 T) at bedrock and amplified in consideration of amplification property of ground surface. Subsequently, three different phases from observed waves were applied to create time history ground motion. The response spectrums were shown in figure 4.

4 Elastic sliding bearings at basement U-shaped steel dampers Shear force (kn) Max. disp.(49cm) U-shaped steel dampers NRBs at basement Elastic sliding bearings at 1 st floor Figure 2. Allocation of seismic isolation devices 1 Sliding bearings Displacement (cm) Figure 3. Shear force - displacement relation of isolation layer Table 1. Properties of superstructure Layer Weight [kn] Stiffness [kn/cm] RF F F F F F MF F F Table 2. Input ground motions Notificarion wave Observed wave Input wave Amplification Max. acce. factor (cm/sec 2 ) HachinoheEW Tohoku Univ. NS Ishinomaki EW El Centro NS Taft EW Hachinohe NS Sa[cm/sec 2 ] EL CENTRO NS TAFT EW 14 HACHINOHE NS 12 Notification wave at surface 1 Notification wave at bedrock T[sec] Figure 4. Acceleration response spectrum of input ground motions Table 3 shows maximum displacement of isolation layer and maximum story drift. Based on the analytical result, isolation layer of the hospital assumed to deform 16.cm~ 2.3cm in case of observe waves, 23.3cm~44.8cm in case of notification waves, which conformed to the design criterion (49cm). Also, the maximum story drift was relatively small in all cases, and floor response acceleration was within the area of 35%~5% at lower floors, 4%~9% at higher floors compared with maximum ground acceleration in case of observed waves and 8%~1% at lower floors, 1%~19% at higher floors in case of notification wave. This means that seismic isolation system assumed to work effectively to reduce floor displacement and acceleration against an extreme shaking. 4

5 M. Terashima, N. Kawamura, Y. Konishi, T. Someya, S. Kishiki, S. Yamada 5 Table 3. Displacement of isolation layer and maximum story drift Notificarion wave Observed wave Input wave Direction Disp. of isolation layer(cm) Max. story drift HachinoheEW Tohoku Univ. NS Ishinomaki EW El Centro NS Taft EW Hachinohe NS X X X X X X /378 (4F) 1/418 (4F) 1/377 (4F) 1/3 (4F) 1/379 (4F) 1/336 (4F) Y Y Y Y Y Y /324 (4F) 1/36 (4F) 1/312 (4F) 1/27 (4F) 1/337 (4F) 1/322 (4F) RF 7F 6F 5F 4F 3F 2MF 2F El Centro NS Taft EW Hachinohe NS Notif. ISHINOMAKI Notif. Tohoku. U NS Notif. Hachinohe EW 1F [cm/sec 2 ] B Figure 5. Maximum response acceleration CONDITIONS AFTER THE EARTHQUAKE Foundation After the main shock, Tsunami attacked around the hospital building. Most of the buildings near the hospital suffered inundation damage due to Tsunami. However, the hospital building eliminated this disaster because of the embankment as previously mentioned (figure 6). In addition, liquefaction was eliminated owing to ground stabilization implemented to the important area. As a result, main functions of the hospital were maintained, and these facts contributed to emergency action, resulting in saving many lives (photo 4). Tsunami inundation area Ishinomaki Red Cross Hospital Figure 6. Tsunami inundation area around Ishinomaki City Photo 4. Emergency action at the airport Seismic Isolation Layer The conditions of the seismic isolation layer were observed after the M9. main shock and subsequent aftershocks. The maximum relative displacement of seismic isolation layer turned out to be approximately 26cm by observing a displacement orbit scratch plate located at the isolation layer (photo 5). This value was about half of the maximum value (49cm) of design criterion. Photo 6 shows appearance of the U-shaped steel dampers. Most of the dampers slightly remained residual plastic deformation. It means that U-shaped steel dampers absorbed seismic energy through their plastic deformation.

6 Approx. 26cm Photo 5. Scratch plate record Photo 6. Appearance of U-shaped steel damper after the earthquakes Building Conditions Photo 7 shows the conditions of the 1 st floor after the main shock and subsequent Tsunami. Although the hospital building experienced significant ground motions, toppling of important equipments such as medical equipment were able to be eliminated, and it enabled the hospital building to resume its function immediately and worked effectively as a local base hospital. These facts indicate that the hospital building withstood the M9. main shock and aftershocks without major functional losses. In addition, this hospital was the only hospital in Ishinomaki City that maintained its function even after the intensive shakings and Tsunami. Therefore, it proved that seismic isolation system applied to the hospital building contributed to prevent damage from the disaster as well as other countermeasures. Analytical verification in terms of effects of seismic isolation system is described in detail below. Entrance hall Outpatient s waiting room Photo 7. Emergency action at 1 st floor after the disaster IMMIDIATE OBSERVATION OF FLOOR RESPONSE As discussed above, the hospital eliminated damage and major functional losses thanks to the countermeasures. Seismic isolation system also played an important role in eliminating major damage. So, the effect of the isolation system on the floor response was investigated by using non-linear time history analysis. In this analytical investigation, seismic isolation layer is modelled by Multiple Shear Spring (MSS) model and superstructure is modelled by multi-body shear system. For comparison, another analytical model whose isolation layer was omitted was employed. For input ground motion, the observed ground motion recorded at K-net MYG1 at 14:46 on 11 th March 211, about 3.4km away from the hospital, was adopted. The acceleration response spectrum and velocity response spectrum are shown in figure 7 and figure 8. Compared to observed waves applied to the original design, response between 1 sec and 2 sec was predominant. 6

7 M. Terashima, N. Kawamura, Y. Konishi, T. Someya, S. Kishiki, S. Yamada 7 18 Sa[cm/sec 2 ] MYG1 NS MYG1 EW Notification wave at surface Notification wave at bedrock T[sec] Figure 7. Acceleration response spectrum Sv[cm/s] MYG1 NS MYG1 EW T[sec] Figure 8. Velocity response spectrum Figure 9 describes maximum story drift and figure 1 describes maximum acceleration. According to the analytical result, the isolation layer deformed about 21cm in maximum which roughly corresponded to the scratch plate record (26cm). The maximum story drift was 1/259 which was also relatively small. Furthermore, the maximum floor acceleration was within the area of 35%~5% at lower floors, 4%~9% at higher floors compared with maximum ground acceleration. In comparison, the model which omitted isolation layer caused significant story drift and floor acceleration. These results show that the isolation system worked effectively to reduce both relative story displacement and floor acceleration significantly, which verified that seismic isolation system contributed to reduce the floor response and eliminate major functional losses. Isolated structure Fix foundation structure RF 7F 6F 5F 4F 3F 2MF 2F 1F B Figure 9. Story drift RF 7F 6F 5F 4F 3F 2MF 2F 1F Isolated structure Fix foundation structure B [cm/sec 2 ] Figure 1. Floor response acceleration POST-EARTHQUAKE EVALUATIONS OF U-SHAPED STEEL DAMPERS As mentioned above, the shaking experienced was the strongest ever seen by isolated buildings. The severity and duration of shaking presented an unusual opportunity to evaluate post-earthquake characteristics of seismic isolation devices after actual earthquake loading. It is important to verify the post-earthquake properties of seismic isolation system. Since U-shaped steel dampers absorbed seismic energy through their plastic deformation, slight residual deformation was observed. So, postearthquake evaluation of U-shaped steel dampers, especially residual fatigue life, was implemented to determine that the damage had little impact on the characteristics and replacement was not necessary. Because it was the first opportunity, elaborative investigations were implemented by using three different methods. Detail of each evaluation method was mentioned as follow,

8 Scratch plate based method First of all, it is essential to determine U-shaped steel dampers residual fatigue life immediately as an initial investigation. Hence, simplified damage estimation was conducted by using the scratch plate record for quick evaluation. In previous researches, the fatigue evaluation curves of U-shaped steel dampers in degree and 9 degree direction have been established based on Manson-Coffin relation (Kishiki et al., 212) described as following equations. direction t =237 N f -.66 (2% t 5%) (1) 9 direction 9 t = N f -.55 (2% t < 254%) (2) 9 t =664 9 N f -.23 (254% t 5%) (3) 9 o direction o direction Isolation bearing = / h U-element h Figure 11. Definition of loading direction and horizontal shear angle This evaluation method requires displacement history. This information, however, can t be readily obtained from the scratch plates. Moreover, the large numbers of smaller deformation excursions less than 8mm were not distinguishable. Considering these issues, evaluation of residual fatigue life was conducted on the basis of the following assumptions: (1) The amplitude was decoupled to its x and y components, then the peak points were paired in successive order from the furthest away from the origin in each direction, and the resulted distance between the peak points of each pair was taken as the amplitude, such as 1 δ x for X direction, 1 δ y for Y direction as described in figure 9. (2) Damage of each component can be evaluated by eq. (1), (2) and (3), and total cumulative damage(d total ) can be estimated by summation of each component s damage. The evaluation result is shown in table 4. Based on this method, the total damage of U-shaped steel damper was estimated to be.41(4.1%), which is quite minor comparing to overall fatigue capacity. -3 N -2 y x PLAN Y[mm] X[mm] -1 1δ x R8 Figure 12. Copy of displacement orbit and assumed amplitude 1δ Y Table 4. Fatigue evaluation result Amplitude [mm] X ( ) direction γ t [%] Assumed cycles to fracture D Amplitude [mm] Y (9 ) direction γ t [%] Assumed cycles to fracture D 9 1δ x δ y δ x δ y δ x δ y δ x δ y δ x δ y δ x δ y δ x δ y δ x δ y δ x δ y ΣD ΣD D(=ΣD +ΣD 9 )=.41 8

9 M. Terashima, N. Kawamura, Y. Konishi, T. Someya, S. Kishiki, S. Yamada 9 Non-linear time history analysis method Subsequently, non-linear time history analysis was used for damage prediction of U-shaped steel dampers. In this analytical investigation, the analytical result obtained from previous study regarding floor response mentioned above was used. Figure 13 shows the displacement orbit of isolation layer obtained from the analysis. Although main direction of the amplitude was slightly different, the maximum amplitude and other characteristics almost corresponded with the scratch plate record, so this analytical result was able to capture the behaviour of the isolation layer. Then, fatigue evaluation was conducted based on the displacement orbit and eq. (1), (2) and (3). Table 5 shows the evaluation result. According to this method, damage of the dampers was assumed to be.69(6.9%). This evaluation method resulted in evaluating the damage slightly bigger than the result of the scratch plate method because this method also evaluated the amplitudes less than 8mm although the scratch plate method didn t. However, the effect of the amplitudes less than 8mm was relatively minor and it is important to point out that the evaluation results obtained from both methods illustrate U-shaped dampers abundant residual fatigue life even after a significant seismic event. Y[mm] N y PLAN x X[mm] Figure 13. Displacement orbit obtained by the analysis Table 5. Fatigue evaluation result Amplitude [mm] γ t [%] Frequency Damage 9 D D 9 D +D 9 6 ~ 8 18 ~ ~ 1 24 ~ ~ 12 3 ~ ~ ~ ~ ~ ~ ~ ~ 2 54 ~ ~ 22 6 ~ ~ ~ ~ ~ ~ ~ ~ 3 84 ~ ~ 32 9 ~ ~ ~ ~ ~ Total Experimental Examination Finally, experimental examination was performed on U-elements detached from the hospital building to make sure the abundant residual fatigue capacity visually for non-engineers such as residents and patients. The eight U-elements of the damper unit were removed from the hospital for loading test. The test set-up is shown in photo 8. The U-shaped steel damper unit was divided into four test specimens, each with two U-elements as shown in figure 14. According to the scratch plate record, deformation in the East-West direction was predominant, so each U-element was set along the direction which deform similarly toward the deformation experienced under the earthquake because strain accumulation depends on the orientation of the U-element to the direction of loading. With this configuration, additional imposed strain will be further concentrated in the locations previously loaded by the earthquake movement and thus the fatigue test would be the most severe. Uni-axial constant amplitude static loading tests were performed by using two loading amplitudes. The first amplitude, used for Specimen1, 2 and 3, was chosen to be maximum peak-to-peak displacement observed in the scratch plate (426mm). The second testing amplitude, used for Specimen 4, was chosen to be allowable maximum design displacement (98mm(+/-49mm)) to confirm whether the dampers experienced the earthquakes still satisfy the initial design criterion in terms of fatigue life which is 1 cycles of +/-49mm (98mm) to fracture.

10 (8) (8) (7) (6) (5) (1) (2) (7) (1) (2) Specimen 2 Specimen 1 (4) (3) (3) (4) Detached U-shaped steel damper unit Loading direction (6) (5) Predominant displacement direction Photo 8. Test set-up Specimen 4 Specimen 3 Loading direction Figure 14. Test specimen Force(kN) Force(kN) Figure 15 shows hysteretic behaviour of specimen 1 and 4, figure 16 shows fluctuation of the energy dissipation per a cycle regarding specimen 1 and 4 as examples. These specimens displayed stable hysteretic behaviours and the degradation of energy dissipation capacity was minor until just before fracture Displacement(m) Displacement(m) Specimen 4 Specimen 1 Figure.15. Force-displacement relationship 25 Energy dissipation 2 per a cycle (kn m) Specimen 1 o damper fracture (25 cycles) Specimen 4 o 9 damper fracture (41 cycles) 15 o 9 damper NOT fracture (Loading was stopped at 3 cycles) 1 5 damper fracture (76 cycles) Loading cycles Figure.16. Fluctuation of energy dissipation capacity Table 6 shows loading cycles until fracture and Figure 17 shows comparison of fatigue evaluation curve to test results. These test results obviously displayed U-shaped steel dampers continuous postearthquake fatigue capacity, as well as satisfaction of the initial design criterion even after the earthquakes. 1

11 M. Terashima, N. Kawamura, Y. Konishi, T. Someya, S. Kishiki, S. Yamada 11 Table 6. Loading cycles to fracture and assumption of residual fatigue capacity Specimen Testing amplitude Cycles to fracture (Test result) Estimated cycles to fracture (Undamaged product) * 2 +/-213mm(γt=127%) 7 3* * 4 +/-49mm(γt=292%) * Test stopped without specimen fracture 1 3 γ t [%] [%] Test stopped without fracture This experimental result Previous test data(undamaged product) Fatigue Evaluation Curve: eq. (1) Number of Cycles to Fracture, N f direction This experimental result Previous test data(undamaged product) Fatigue evaluation curve: eq. (2). (3) Number of Cycles to Fracture, N f 9 direction Figure.17. Comparison of fatigue evaluation curve and test results for number of cycles to fracture CONCLUSION Ishinomaki Red Cross hospital, located at 13km away from the epicentre of M9. the Great Tohoku Earthquake, was able to eliminate significant damage and contribute to emergency action owing to structural and architectural contemplation considered in the design as follows. 1) Seismically isolated system was applied. It reduced floor response acceleration and prevented important medical equipment from toppling and damaging. 2) The hospital was able to eliminate the damage from inundation due to Tsunami thanks to the embankment provided on the site. 3) The ground had been improved with sand piles against liquefaction, resulting in elimination of major functional losses. As these facts illustrate, it is possible to eliminate the major damage due to extreme earthquakes and subsequent Tsunami by applying seismic isolation system as well as other countermeasures. Moreover, effects of isolation layer were investigated by analytical method. It was proven that seismic isolation system worked effectively to reduce floor response and had great impact on eliminating damage and major functional losses. Thus, seismic isolation system is one of the most practical options to mitigate earthquake damage. Finally, comprehensive post-earthquake evaluations of U-shaped steel dampers fatigue life had been conducted to verify their abundant residual fatigue capacity to use continuously from diverse point of view. Through these evaluations, it was verified that U-shaped steel dampers suffered minor damage comparing to their overall fatigue capacity. Consequently the seismic isolation system including U- shaped steel dampers had enough durability for continuous function after the intensive shakings.

12 ACKNOWLEDGEMENT The authors utilized the ground motion record that belong to National Research Institute for Earthquake Science and Disaster Prevention (NIED) REFERENCES T Someya, (213) Seismically Isolated Hospital Offers Ray of Hope in Disaster Ishinomaki Red Cross Hospital- 13 th World Conference on Seismic Isolation, Sendai, Japan, September, Paper #98 N Kawamura, et al, (213) Evaluation of the Fatigue Life of U-shaped Steel Dampers after Extreme Earthquake Loading 13 th World Conference on Seismic Isolation, Sendai, Japan September, Paper #45 Y Konishi, et al., (212) Evaluation of the fatigue life and behavior characteristics of U-shaped steel dampers after extreme earthquake loading 15 th World Conference in Earthquake Engineering, Lisbon, Portugal, September, Paper #5597 H Yoshikawa, et al., (212) Experimental study on characteristics of U-shaped damper under two directional horizontal loading Part 1-4. AIJ Annual Meeting, September, Y Konishi, et al., (212) Evaluation of remaining fatigue life of U-shaped steel damper after earthquake Part 1, 2 AIJ Annual Meeting, September, S Kishiki, et al., (212) Experimental evaluation of cyclic deformation capacity of U-shaped dampers subjected to bi-directional loadings - Bi-directional characteristics of U-shaped steel dampers for base-isolated structures Part 1 - Journal of Structural and Construction Engineering, AIJ, vol. 77 No. 68 October, , 12