COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
The Dynamic Analysis of Main Building of Hangzhou International
Conference Center
H. J. Song 1*, Y. F. Luo 1, Z.Y. Shen 1, J. H. Li 2
1
2
College of civil Engineering, Tongji University, Shanghai, 200092 China
Second Institute of Project Planning and Research, Ministry of Machinery Industry, Hangzhou,310006 China
Email: [email protected], [email protected]
Abstract: Hangzhou International Conference Center (HICC) is a high-rise steel building. Its structure is much
complex. The main building is a sun-shaped braced-frame structure. Lots of curved beams, slanting columns and
struts are adopted in the structure. Plane arrangement of the members is extremely complex. Horizontal stiffness and
vertical stiffness vary greatly. Since the irregularity of the structure, the dynamic spectrums are much dense. The
calculation of dynamic responses is much complicated. The coupled reaction of different modes is obvious. The
response spectrum method and time-history method are both used to analyze the dynamic characters and seismic
response of the complicated main building in this paper. The dynamic characters of the structure are obtained. The
capacity of seismic resistance is also calculated. It is a valuable reference for design of this structure and similar
structures.
Keywords: slanting column, sun-shaped braced frame, dynamic character, response spectrum method, time-history
method
INTRODUCTION
Hangzhou International Conference Center, composed of 19 storeys main building, 2 storeys skirt building and 2
storeys basement, is a typical three-dimensional structure. The height of the main building is 85 m. Above 79 meter
is a reticulated shell roof structure. The total area of building is 116730 m2 (71600 m2 over ground and 46030 m2
underground). The structure of the main building is a sun-shaped braced-frame structure. Plain layout of the
structure is much complex. Lots of curved beams, slanting columns and struts are adopted in the structure. The
structure is shown in Fig.1 and Fig. 2.
机房层
十八层
十七层
十六层
十五层
十四层
十三层
十二层
十一层
十层
九层
八层
七层
六层
五层
四层
三层
二层
一层
Figure 1: Plain view of HICC
Figure 2: Elevation view of HICC
Because of the complexity and irregularity of the structure, the dynamic spectrums are much dense and complex.
The calculation of dynamic response is much complicated. The coupled reaction of different modes is obvious under
frequently occurred earthquake and seldom occurred earthquake. According to the national specification of seismic
design of buildings, the response spectrum method and time-history method are applied to analyze the dynamic
character and seismic responses of the structure in this paper. Natural frequencies, mode shape characters,
displacements, base shears and other numerical results are obtained through analysis. It can be valuable for structure
design.
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RESULTS OF RESPONSE SPECTRUM ANALYSIS
1. Natural frequencies and mode shapes Mode shape analysis is the preparation of dynamic analysis. The
frequencies and corresponding mode shapes of the structure is obtained by solving eigenvalues of the following
undamped dynamic equation.
..
M υ + Kυ = 0
Subspace method is employed here to calculate the eigen values. According to the specification, the first 18 modes
are adopted. Participating mass ratio reaches 97%. Dynamic characters of the structure are listed in Table 1. Fig. 3
shows the first six mode shapes.
Table 1: Natural period and frequency of structure
Mode
Period
/s
Frequency
/Hz
Mode
Period
/s
Frequency
/Hz
Mode
Period
/s
Frequency
/Hz
1
3.22172
0.31039
7
0.67468
1.48219
13
0.29167
3.42857
2
2.93438
0.34079
8
0.62679
1.59543
14
0.25830
3.87151
3
2.55243
0.39178
9
0.49505
2.02002
15
0.22704
4.40451
4
0.85985
1.16300
10
0.45482
2.19866
16
0.16253
6.15257
5
0.73541
1.35979
11
0.38061
2.62734
17
0.13091
7.63899
6
0.71481
1.39897
12
0.36461
2.74262
18
0.11400
8.77172
(a) the 1st mode shape
(d) the 4th mode shape
(b) the 2nd mode shape
(e) the 5th mode shape
(c) the 3rd mode shape
(f) the 6th mode shape
Figure 3: The first six mode shapes
The following dynamic properties are obtained through analysis:
(1) The basic frequency is much low. The first frequency is 0.31039. It indicates that the stiffness of the structure is
weaker.
(2) Dynamic spectrums are much dense. Frequency jumping phenomenon appears. The reason is that the stiffness of
the top part is weaker than the bottom part. Both parts can not work together. It can be found from the fourth mode
shape.
(3) Most mode shapes are horizontal. The reason is that the horizontal stiffness of the structure is much weaker than
vertical stiffness, which causes this kind of mode shapes easily excited.
(4) The first mode shape of the structure is translation in X direction. The second mode shape is translation in Y
direction. The third mode shape is torsion around Z axis. The ratio of the first torsion period to the first translation
period is 0.729, which is less than the limited value 0.85 of code.
2. Results of response spectrum analysis The seismic fortification intensity of the building is 7 degree. The seismic
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influence coefficient is αmax=0.08. The characteristic period of ground is Tg=0.35s. The damping ratio is taken as
ξ=0.02. In the process of response spectrum analysis, structural seismic responses in X and Y direction are computed
respectively. Correlation of different mode shapes must be taken into account because Hangzhou International
Conference Center is a complex braced-frame structure and the dynamic spectrums are much dense. Therefore,
Complete Quadratic Combination Method is adopted in modal combination.
25
20
X Direction
Y Direction
18
20
16
14
Storey
Storey
15
10
12
10
8
6
4
5
2
Storey Shear/KN
0
0
1000
2000
3000
4000
Storey Shear
5000
6000
7000
Drift/m
0
0
0.0002
0.0004
0.0006
0.0008
Storey Drift
0.001
Figure 4: Maximum shear in storeys and storey Drift
Fig. 4 shows the maximum shears in storeys and the storey drifts. The maximum storey drift angles calculated from
the spectrum analysis in X direction and Y direction are 1/7362 and 1/4618 respectively. Both of them are less than
1/1000, which satisfy the code demand. Compared with the lower storeys of structure, there are big holes in the
middle storeys which weaken their lateral stiffness greatly. So the storey drift of middle storeys is much larger under
earthquake. The largest storey drifts in X direction and Y direction are 8.49E+10-4m and 6.36E+10-4m respectively.
Storey shears are corresponding to structural inner forces. It can be concluded from Figure 4 that storey shear varies
gradually along its height. The storey shears and storey stiffness do not change abruptly.
RESULTS OF TIME-HISTORY ANALYSIS
Because of the complexity of the structure, the dynamic response is an important issue that has attracted
considerable attention during the design procedure. This paper focuses attention on dynamic responses of the
structure excited by three kinds of seismic waves in two individual directions.
Hangzhou International Conference Center is located on the field of the second class soil. According to the code of
seismic design of buildings, three seismic waves (El-Centro seismic wave, Tar-Tarzana seismic wave and Tangshan
artificial seismic wave) are selected in this paper. In the time-history analysis, the peak acceleration is adjusted as
0.35 m/s2 and the damping ratio is taken as 0.02 under 7 degree frequently occurred earthquake (FOE). The peak
acceleration value is adjusted as 2.2 m/s2 and the damping ratio is taken as 0.05 under 7 degree seldom occurred
earthquake (SOE).
1. Displacement Responses Under Earthquake Top point displacements at different moments are given in Fig. 5.
Maximum displacements of top point under 7 degree frequently occurred earthquake in X direction and Y direction
are Ux,max = 0.054 m and Uy,max = 0.089 m (El-Centro Seismic Wave), Ux,max = 0.002 m and Uy,max = 0.017 m (TarTarzana seismic wave), and Ux,max = 0.047 m and Uy,max = 0.071 m (Tangshan Artificial Seismic Wave) respectively.
Maximum displacements of top point under 7 degree seldom occurred earthquake in X direction and Y direction are
Ux,max = 0.271 m and Uy,max = 0.408 m (El-Centro Seismic Wave), Ux,max = 0.012 m and Uy,max = 0.011 m (Tar-Tarzana
seismic wave), and Ux,max = 0.344 m and Uy,max = 0.593 m (Tangshan Artificial Seismic Wave). The maximum storey
drift obtained from time-history analysis is greater than that from response spectrum analysis.
Storey drifts obtained from time-history analysis are given in Figure 6. The following results are gained through the
data:
(1) The big holes in the middle storeys weaken the lateral storey stiffness greatly. Therefore the storey drifts of
middle storeys are much larger under earthquake. The storey drift of the top storey is very small.
(2) Under 7 degree frequently occurred earthquake, the maximum story drift angles are 1/742(X direction) and
1/686(Y direction) which satisfy the code demand of 1/500.
(3) Under 7 degree seldom occurred earthquake, the maximum storey drift angles are 1/121(X direction) and
1/117(Y direction) which satisfy the code demand of 1/100.
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0.06
0.08
0.05
0.06
0.04
0.04
0.02
0.02
TPD/m
TPD/m
0.03
0.01
0
-0.01 0
5
10
15
20
25
30
0
-0.02
35
-0.02
0
10
20
30
40
-0.04
-0.03
-0.06
-0.04
-0.05
-0.08
X Direction
Y Direction
Time/s
Time/s
(a) El-Centro seismic wave (7dFOE)
0.0005
0.02
0.015
0
0
10
20
30
40
0.01
50
0.005
T PD /m
TPD/m
-0.0005
-0.001
0
-0.005
0
10
20
30
40
50
60
70
-0.01
-0.0015
-0.015
-0.02
-0.002
X Direction
Y Direction
Time/s
Time/s
(b) Tar-Tarzana seismic wave (7dFOE)
0.06
0.1
0.08
0.04
0.06
TPD/m
0.02
0.04
0.02
0
10
20
30
40
50
TPD/m
0
60
0
-0.02 0
-0.02
10
20
30
40
50
60
70
-0.04
-0.04
-0.06
-0.06
-0.08
-0.08
X Direction
-0.1
Time/s
Time/s
Y Direction
0.6
0.3
0.4
0.2
0.2
TPD/m
TPD/m
(c) Tangshan artificial seismic wave (7dFOE)
0.4
0.1
0
-0.1 0
10
20
30
0
-0.2
40
0
10
20
30
40
-0.4
-0.2
Time/s
-0.3
Time/s
-0.6
Y Direction
X Direction
0.1
0.002
0
-0.002 0
-0.004
-0.006
-0.008
-0.01
-0.012
-0.014
0.05
20
30
40
50
0
TPD/m
10
-0.05
0
10
20
30
40
50
-0.1
Time/s
Time/s
-0.15
X Direction
Y Direction
(e) Tar-Tarzana seismic wave (7dSOE)
10
20
30
40
50
60
Time/s
0.8
0.6
0.4
0.2
0
-0.2 0
-0.4
-0.6
TPD/m
0.4
0.3
0.2
0.1
0
-0.1 0
-0.2
-0.3
-0.4
TPD/m
TPD/M
(d) El-Centro seismic wave (7dSOE)
X Direction
20
(f) Tangshan artificial seismic wave (7dSOE)
Top point displacement
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60
Time/s
Y Direction
Figure 5:
40
20
El-Centro
Tar-Tarzana
Tangshan
18
16
20
16
14
14
12
Storey
storey
El-Centro
Tar-Tarzana
Tangshan
18
10
8
12
10
6
8
6
4
4
2
2
Drift/m
0
Drift/m
0
0
0.0005
0.001
0.0015
X Direction Storey Drift
0.002
Figure 6:
0
0.0005
0.001
0.0015
Y Direction Storey Drift
0.002
Storey drift (7dFOE)
2. Base Shears According to response spectrum analysis, structural base shears are Vx = 5046 kN and Vy = 5809 kN.
Fig. 7 shows the time history curves of base shears. Under El-Centro Seismic Wave, maximum base shears of the
structure are Vx,max = 9439 kN and Vy,max = 11408 kN. Under Tar-Tarzana Seismic Wave, maximum base shears of
the structure are Vx,max = 5433 kN and Vy,max = 7738 kN. Under Tangshan Artificial Seismic Wave, maximum base
shears of the structure are Vx,max = 10677 kN and Vy,max = 11172.92 kN. Structural base shears of every time-history
curve are all greater than 65% of response spectrum analysis results. Average values of structural base shears from
multiple time-history curves analysis are greater than 80% of response spectrum analysis results. The structural
dynamic responses obtained from time-history analysis all meet the code demand.
15000
X Direction
Y Direction
10000
15000
X Direction
Y Direction
8000
10000
0
5
10
15
20
25
30
35
-5000
4000
2000
0
-2000 0
10
20
30
50
-4000
5000
0
0
10
20
30
40
50
60
-5000
-10000
-6000
-10000
-15000
-8000
-15000
40
Base Shear/KN
0
Base Shear/KN
Base Shear/KN
6000
5000
X Direction
Y Direction
10000
Time/s
El-Centro Seismic Wave
-10000
Time/s
Tar-Tarzana Seismic Wave
-20000
Time/s
Tangshan Seismic Wave
Figure 7: Time history curves of base shears
CONCLUSIONS
Three important conclusions can be drawn based on the above analysis:
(1) Hangzhou International Conference Center is a complicated structure with big holes in the middle storeys and
weaker lateral stiffness. In the process of calculation, the floor should be assumed to be elastic floor because floor
deformation affects structural displacement greatly.
(2) The structural dynamic responses are similar under El-Centro seismic wave, Tar-Tarzana seismic wave and
Tangshan artificial seismic wave. Displacements and base shears obtained from time-history analysis are greater
than those from response spectrum analysis.
(3) The results of time-history analysis indicate that structural strength and displacement under 7 degree frequently
occurred earthquake meet the code demand. Structural members are almost work in elastic stage. The structure
deformation also satisfy the code requirement under 7 degree seldom occurred earthquake. Weak storeys do not
appear in analysis.
REFERENCES
1. ATC. Seismic Evaluation and Retrofit of Concrete Buildings. Report No.ATC-40, Applied Technology
Council, Redwood City, California, USA, 1996.
2. Leger P, Ide IM, Paultre P. Multiple-support seismic analysis of large structures. Computer and Structures,
1990; 36(6): 1153-1158.
3. National Standard of the People’s Republic of China. Code for Seismic Design of Buildings GB50011-2001.
Beijing, China, 2001.
4. Clough RW, Penzien J. Dynamics of Structures. 2nd Edition, McGraw-Hill Inc., 1993.
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