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Design of a Low-rise RC Building with Damping System Eunjin LEE1, Changkook HYOUN1, Youngchan YOU2, Younghun OH3 1 Dongyang Structural Engineering and Remodeling Co.,Ltd,Seoul, Korea, [email protected] Korea Institute of Construction Technology, Il-san, Kyungi-do, Korea 3 Dept. of Architectural Eng., Konyang University, Non-san, Chungchengnam-do,Korea 2 Summary This thesis intends to introduce design cases of low-rise RC buildings constructed according to the analysis/design standard of seismic structures defined by the U. S. ASCE 7-05. Especially for school buildings 5 story-high above the ground, this study analyzed the kinds of dampers, the locations of installing dampers and the number of dampers through the dynamic analysis by applying the viscous damper and hysteretic damper. The target performance for the seismic design of the subject buildings was fixed as the range of similar elastic design, and to meet this qualification, this study estimated the number of dampers used for per damping stem and reflected it on the design. It was found that the number of dampers decreased in proportion to the amplification ratio of each damping system, and as for two-story toggle system, it was found that the number of dampers decreased up to one sixth of that of the existing a bracing system. Keywords: seismic design; damping system; RC structures; Toggle System 1. Introduction Due to reports about frequent earthquake damages increased all over the world and an increase of earthquake risk in the Korean Peninsula, MLTM (Ministry of Land, Transport and Maritime Affairs) has constantly reinforced the seismic design of buildings, and as one of the measures to secure a higher-level seismic safety, seismic-isolation and damping designs are attracting lots of attention in Korea. That is, the existing seismic designs can minimize earthquake-caused casualties, but since they allow partial damages of a building, it is pointed out that an enormous restoration expense is required after earthquake. As a result, in such advanced countries as America, Japan and Canada where the seismic-isolation design is established for moderate earthquakes, the application of damping design is on the rise for main buildings. Even in Korea, especially government-level measures are being prepared to secure the seismic safety of non-seismic isolation designed buildings constructed before the related regulation was enforced, and as part of the Green School Project of Ministry of Education, Science and Technology, the vibration-control reinforced method of construction has been applied to school building through damping device/system according to the Seismic-isolation Reinforcement Project in Korea since 2009. However, there is no design standard provided for structures with damping system in Korea yet, further confusing engineering staffs in actual sites. Accordingly, this study was conducted to introduce a case of low-rise RC buildings constructed on the basis of the interpretation/design standard of structures with damping system regulated by the U. S. ASCE 7-05. The entire process of damping design can be described as Figure 1. 2. Summary of the Subject Building The subject building is a RC structure with 5 stories above the ground, and Fig. 2 shows its ground plan. This building can be examined by being divided into a seismic load resisting system and a damping system (damper + brace + frame). The strength of materials was 24MPa of concrete, 400MPa (SD400) of iron bars and 235MPa (SN400) of structural steel, and the wind load and seismic load applied are as shown in Table 1 and 2. Figure 1: Process of Damping Design Figure 2: Structural Ground Plan Table 1: Wind Load Applied Basic Wind Velocity Vo(m/sec) Ground Surface Roughness Importance Factor (Iw) Gust Effect Factor (Gf) 30 B 1.0 (special) X-direction : 2.12 Y-direction : 2.11 Table 2: Seismic Load Applied Zoning Factor (A) 0.22 Response Displacement Importance Factor Kinds of Ground Modification factor Amplification Factor (Ie) (S) (R) (Cd) 1.5(special) SD 5 4.5 3. Structural Analysis To determine a design earthquake wave for the time history analysis prior to a structural analysis, this study applied the mean value of 7 earthquake waves. After drawing up seismic waves into a design acceleration spectrum by calculating seismic loads according to KBC2009, this study prepared an acceleration spectrum in 5%-damped artificial seismic waves. The spectrum prepared this way was revised through Equation 1. (1) Table 3 shows the design seismic wave prepared and the mean value of the base shearing force by the response spectrum and the base shearing force by 7 different seismic waves had a ratio of about 3.0. Since this value is equal to the ratio (R/I) of the response modification factor and the importance factor, it was verified to be applicable to the subject building. Figure 3: Time History Data of Seismic Wave Figure 4: Acceleration Spectrum of Seismic Wave Table 3: Base Shearing Force for the Calculation of Design Seismic Wave (kN) Analysis X-direction Y-direction Response Spectrum 6,960 5,160 California(all) 20,610 16,463 El centro(all) 19,859 14,919 Mexico(all) 19,043 18,867 Northbridge(all) 19,855 17,634 San Fernando(all) 20,793 18,409 San Francisco(all) 24,071 18,598 Taft(all) 21,607 16,369 Average of Seismic Waves 20,834 17,323 3.0 3.4 Seismic Waves Ratio 3.1 Modeling of a Damping System The damping system of this building consists of dampers, braces and frameworks, and as dampers, a hysteretic damper and a viscoelastic damper were both applied for examination. The forms of a hysteretic damper and a viscoelastic damper are as shown in Fig. 5, and nonlinear physical properties for the structural analysis were input to make the maximum load and hysteretic characteristics similar to the research results. The nonlinear physical properties applied with the analysis are as shown in Table 4 and 5. The brace was modelled in a general-link type, and the stiffness of a brace was calculated through Equation 2. 200kN/mm2 ×6,260mm2 2,831mm = 440kN/mm (2) Since amplification effect varies depending on how to install dampers, this study classified braces by the form into diagonal brace type, inter-story toggle type and two-story toggle type. The diagonal brace type has about 0.7 times of amplification effect in the lateral drift, while the interstory toggle type and two-story toggle type have about 3.0 times of amplification effect depending on the angle of arranging toggles. Figure 5: hysteretic Damper (left) and Viscoelastic Damper (right) Table 4: Nonlinear Physical Properties of hysteretic Damper Table 5: Nonlinear Physical Properties of Viscoelastic Damper Hysteretic system Viscoelastic damper Stiffness 73.5 kN/mm Damping 75 kN Yield strength 150 kN Reference velocity 1 mm/sec Post yield stiffness ratio 0.03 Yielding exponent 1 Damping exponent 0.2 Hysteretic parameter(a) 0.5 Bracing stiffness 350 kN/mm Hysteretic parameter(b) 0.5 Figure 6: Diagonal Brace Type Figure 7: Inter-story Toggle Type and Two-story Toggle Type 4. Results To select a damping device for accomplishing the target performance of this building, this study investigated what effect the kinds of dampers, the number of dampers and the amplification ration have on the diagonal brace type, inter-story toggle type and two-story toggle type. Fig. 8 shows a model where a damping device was installed in the subject building. Figure 8: Model of the Subject Structure 4.1 Comparison of the Performance of Each Kind of a Damper Since the maximum displacement of a hysteretic damper is limited by fracture of small displacement, it is applied to neither the inter-story brace type nor the two-story toggle type, which are displacement-amplifying types. Instead, it was applied to the diagonal brace type, and this study compared the analytic results by changing only the kinds of dampers. In the damping system below 1.0 time of amplification ratio, the maximum displacement of a damper was found to be 28mm, showing differences within 5% in the damping ratio of each kind of a damper. In other words, in the diagonal brace type, it was found that there was not large difference in the performance between the hysteretic damper and the viscoelastic damper. Figure 9: Base Shearing Force Ratio by the Kind of a Damper 4.2 Comparison of the Performance by the Number of Dampers Since the amplification ratio of the diagonal brace type is about 0.7, it is a system whose amplification ratio cannot be regulated. Therefore, this study selected hysteretic dampers and viscoelastic dampers separately and applied them to the subject building. To calculate the number of dampers in order to compare the performance by the number of dampers and accomplish the target performance, this study installed 1, 2, 4, 8, 10 units (4EA/1Unit) in the damping system respectively. In the diagonal brace type, the hysteretic damper and the viscoelastic damper showed about 2.5% and 3.3% of base shearing force reduction effect per unit respectively. It seems that the displacement generated by the lateral drift of the building attributes to small displacement. Figure 10: Comparison of the Base Shearing Force by the Number of Dampersof the Inter-story Figure 11: Comparison (Amplification Ratio of the Inter-story Toggle Type: 2.0) Displacement Angle by the Number of Dampers (Amplification Ratio of the Inter-story Toggle Type: 2.0) In the inter-story toggle type, when the amplification ratio was 1.0, 2.0 and 3.0 times, it showed about 4.3%, 6.8% and 7.2% of the base shearing force reduction effect per unit (4) respectively. On the other hand, when 4 Unit was applied with 2.0 times of amplification ratio, it showed 30.9% of the base shearing force reduction effect to the maximum, through which this study confirmed an increased reduction effect. Especially in the two-story toggle type, when the amplification ratio was 1.0, 2,0 and 3.0 times, it showed about 5.3%, 10.0% and 12.5% of the base shearing force reduction effect per 1 Unit (2) respectively, through which this study confirmed an additionally increased reduction effect. However, as the number of dampers increased, the reduction effect increased as well, but this study found that it was not a proportional increase of each system or amplification ratio but reflected the number of dampers which had the optimal efficiency. When the amplification ratio was 2.0 times in the inter-story type, the application of 4 Unit showed the best efficiency, and when the amplification ratio was 3.0 times in the two-story toggle type, the application of 3 Unit showed the highest reduction ratio. 4.3 Comparison of the Performance by the Displacement Amplification Ratio This study compared the reduction performance by displacement amplification ratios with the interstory toggle type and the two-story toggle type, while comparing the values when 2 units were used. As the amplification ratio increased, the reduction effect increased as well, and it was found that the reduction effect was superior when the amplification ratio changed from 1.0 to 2.0. Thus, it is possible to reduce the number of dampers in order to satisfy the target performance by using the displacement amplification system. Yet, it is judged that due to the problem that the maximum displacement of a hysteretic damper is limited, this study found it difficult to apply it to the displacement amplification type. 4.4 Comparison of the Performance by Each Damping System With the performance of each system to show the equal performance, it was found that the reduction effect is superior in such order as Diagonal Brace Type < Inter-story Toggle Type < Twostory Toggle Type. The number of dampers used to satisfy the target performance of each damping system can be analyzed as follows. The target performance was defined by being classified into a perfectly-elastic design, which makes a seismic force-resisting system remain in the elastic region, and a pseudo-elastic design, which the bracing force exceeds around 1.5 times the nominal strength. In designing a damping device for the subject building, the perfectly-elastic design had below 10752 kN, which is the design base shearing force, while the pseudo-elastic design had below 16125 kN, 1.5 times more than the design base shearing force. When the pseudo-elastic design is aimed as shown in Fig. 13, it was found that the two-story toggle type needs the least number of dampers. 5. Conclusions For the damping design for the subject building, the target performance was set up within the range of pseudo-elasticity, and to satisfy this condition, this study selected the number of dampers used for each damping system and reflected it on the design. As shown in Table 6, it was found that the number of dampers used increased in proportion of the amplification ratio of each damping system, and the two-story toggle type reduced the number of used dampers to 1/6, compared to the existing diagonal brace type. Figure 12: Base Shearing Force Ratio by the Displacement Amplification Ratio Figure 13: Comparison of the Performance by Each Damping System Table 6: The Number of Dampers Used for Each damping System Damping System Diagonal Brace Type Inter-story Toggle Type Two-story Toggle Type 6. Kinds of Dampers Amplification Ratio X-direction pseudo-elasticity Design Y-direction Number of Dampers in total Hysteretic 0.7 8 unit(32) 4 unit(16) 48 Viscoelastic 0.7 8 unit(32) 4 unit(16) 48 Viscoelastic 0.7 8 unit(32) 4 unit(16) 48 Viscoelastic 1.0 6 unit(24) 4 unit(16) 40 Viscoelastic 2.0 3 unit(12) 3 unit(12) 24 Viscoelastic 3.0 3 unit(12) 3 unit(12) 24 Viscoelastic 1.0 4 unit(8) 4 unit(8) 16 Viscoelastic 2.0 2 unit(4) 2 unit(4) 8 Viscoelastic 3.0 2 unit(4) 2 unit(4) 8 Acknowledgement This research was supported by a grant (07-UR-B04) from High-tech Urban Development Program (HUDP) funded by Korea Ministry of Lang, Transport and Maritime Affairs. 7. References 1) Architectural Institute of Korea (2009), “Korean Building code-Structural", pp.337-394 2) FEMA 450, NEHRP recommended Provisions for Seismic Regulations for New Buildings and Other Structures., 2003 3) ASCE 7-05, Minimum Design Loads for Buildings and Other Structures, 2006 4) MAIDAS IT, MIDAS/Genw Analysis and Design, MIDAS IT.