Download Design of a Low-rise RC Building with Damping System

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.