FINITE ELEMENT ANALYSIS AND EXPERIMENTAL VERIFICATION OF
A SRC FRAME-TUBE STRUCTURE WITH SETBACK IN ELEVATION
Kun Ding1, Ying Zhou1, Xilin Lu1, Xuefeng Chen1, Ningfen Su1
ABSTRACT
In this paper, shaking table test on a 1/35 scale model of an irregular steel reinforced concrete
(SRC) frame-tube tall structure with setback in elevation is briefly described. The structural
dynamic property and displacement response under frequent earthquakes of intensity 7 are
analyzed by Ansys finite element procedure. Seismic behavior and weak position of structure are
discussed by pushover analysis. The analytical results are compared with test ones. It is shown
that the first three vibration modes of structure are translation in X direction, translation in Y
direction and torsion, respectively. The inter-story drifts of the structure under frequent and rare
earthquakes of intensity 7 satisfied the provision of Chinese code. The setback story is the weak
position because the sudden change of stiffness. The ductility of the setback and adjacent stories
should be improved.
INTRODUCTION
Setback in elevation is very normal in tall buildings and it includes setback in upper structure and
setback in the top of podiums. It is researched that setback in elevation would cause incontinuity
in vertical stiffness, the inter-story drifts will change suddenly in setback and the internal forces
in vertical members will increased. It is very disadvantageous for seismic resistance. Many
setback buildings had been damaged severe in Kobe earthquake. Analysis results also indicate
maximum inter-story drift is tended to appear in setback story which became the weak region of
earthquake resistant buildings.
In this paper, finite element analysis of a steel reinforced concrete (SRC) frame-tube tall building
in Shanghai is performed. Dynamic property and displacement response on structure are
analyzed. The structural seismic performance is evaluated and weak region is discussed by
pushover analysis. Mechanical performance and response characteristics of the structure are
revealed and some suggestions for improving the structural seismic behavior are given.
DESCRIPTION OF THE STRUCTURE
The South tower is a 58-story building composed of upper 24 stories hotel area, lower 23 stories
office area, refuge stories, podiums and basement. The building has a total structural height of
244.8m and architectural height of 260m.
The building has a lateral load resistant system of SRC concrete frame and tube. The rectangular
plan dimension decrease from 60.0m×60.0m in lower office area to 28.5m×54.0m in upper hotel
area and the tube dimension change from 28.4m×29.1m to 10.5m×29.1m. Steel braces are set up
for load transmission between frame columns and tube. Inclined columns are arranged in two
1
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China
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positions (five inclined columns with 11.5° in story 16-21, three with 13.2° in story 21-22) and
the SRC beams are connected with inclined columns. In addition, belt trusses are installed to
form strengthened story in story 46. Figs. 1-2 show the typical plan layouts and structural
illustration model.
D
D
A
A
C
B
B
N
N
(a) Office area plan
(b) Hotel area plan
Fig. 1. Typical plan layouts
(a) 3D model
(b) Concrete tube
Fig. 2. Structural model view
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According to the Chinese design code-Technical Specification for Concrete Structures of Tall
Building (TSCSTB, JGJ3-2002), the building height clearly exceeds the stipulated maximum
height of 190m for a mixed frame-core wall structure. Moreover, the building has a 50% setback
nearly at 41.7% structural height. Setback will brings to a problem for rational arrangement of
vertical members. So, the south tower is an especially irregular building.
FINITE ELEMENT MODEL
Two element types were adopted to analyze the seismic response on prototype structure in Ansys
procedure. Element beam188 were selected for columns, beams and trusses, and element
shell143 were used for shear walls, coupling beams and floors respectively. The calculating
model including 14696 beams, 19375 shells, 35797 nodes and weight 2.69×105 T (dead loads +
0.5*live loads). Figs. 3-4 show the analytical model.
Fig. 3. Overall structural model
Fig. 4. Inclined columns model
SHAKING TABLE TEST VERIFICATION
Besides the finite element analysis of prototype structure, a 1/35 scale model shaking table test
was performed in the State Key Laboratory of Disaster Reduction in Civil Engineering at Tongji
University. Fine-aggregate concrete and fine iron wire were selected to substitute the concrete
and rebar. And steel members were simulated by copper. In consideration of the size of shaking
table, construction, lifting and material property, the final similitude relationship of model
structure are determined as indicated in Table 1. The fine iron wire area was designed based on
the principle of equivalent flexural and shear capacity and the steel were designed based on the
principle of equivalent stiffness. In general, the model would have some distortion, but the errors
can be acceptable after careful consideration. The completed model has a height of 7.729m and
weight of 25 tons. Seventy-two sensors were installed to measure displacement, acceleration and
strain of structure under earthquakes. The input signals to the shaking table modeled acceleration
are histories of the 1940 El Centro record, the 1952 Pasadena record and Shanghai artificial
accelerogram. More detailed information can be found in the work by Su et al. (Su, Lu, Zhou et
al., 2009)
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Table 1. Similitude relationship of model structure
Variable
Scaling factor
Variable
Scaling factor
Length (Sl)
1/35
Damping (Sc)
8.36E-04
Strain (Sε)
1.00
Period (ST)
0.10
Stress (Sσ)
0.30
Frequency (Sf)
10.25
Density (Sρ)
3.50
Acceleration (Sa)
3.00
Mass (Sm)
8.16E-05
Gravity acceleration (Sg)
1.00
SEISMIC RESPONSE ON PROTOTYPE STRUCTURE
Dynamic Property
Natural vibration periods and modes were acquired by modal analysis considering 50 modes.
The analytical and test results are compared in Table 2. The results indicated test model are rigid
than analytical one. The reason may be explained that the smaller members are difficult to
construct entirely match the scaling factor and the hinge joints are very hard to achieve. So the
natural vibration periods of test results smaller than analytical results. The period ratios of the
first two translation modes in both directions and the first torsion mode are less than 0.85
stipulated in the Chinese design code-Technical Specification for Concrete Structures of Tall
Building (TSCSTB, JGJ3-2002).
Table 2. Natural vibration periods and modes (Units: s)
Dynamic property
1
2
3
4
5
Test
3.000
3.000
1.615
1.105
0.954
Periods
Analysis
3.632
3.415
2.390
1.532
1.484
Vibration modes
Translation
in X
Translation
in Y
Torsion
Translation
in X
Translation
in Y
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0.777
1.051
Torsion
Displacement Response
Three earthquake waves of El Centro record, Pasadena record and Shanghai artificial
accelerogram were selected for elastic time history analysis input. The peak acceleration of three
earthquake waves was set to be 0.035g corresponding to frequently occurring earthquake based
on the Chinese Code for Seismic Design of Buildings (CCSDB, GB50011-2001) and the
damping ratio is 0.05. Figs. 5-6 show the displacement and inter-story drift curves under
different earthquake waves. It is shown that the inter-story drift increased suddenly above the
setback story in elevation and obvious decreased in strengthened story. The displacement
diagram has an increased trend above the setback and appears clearly flexure type.
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65
65
65
65
60
60
60
60
55
55
55
55
50
50
50
50
45
45
45
45
40
40
40
40
35
35
35
35
30
30
30
30
25
25
El - Cent r o
25
20
SHW2
20
15
Pasadena
15
10
10
5
5
0
El - Cent r o
SHW2
Pasadena
40
80
120
160
displacement in direction X(mm)
0
40
80
120
160
20
SHW2
15
0
0
25
El - Cent r o
20
10
5
5
0
0
0
displacement in direction Y(mm)
4
8
12
16
20
drift in direction X (1/10000)
Fig. 5 Analytical displacement curves
El - Cent r o
15
Pasadena
10
SHW2
Pasadena
0
3
6
9
12
15
drift in direction Y (1/10000)
Fig. 6 Analytical inter-story drift curves
Table 3-4 shows the maximum displacement and inter-story drift results of analysis and test
under frequent earthquake of seismic intensity 7. It is shown that the displacement responses in
direction X are closed, but those in direction Y have bigger errors. Generally, the test results
smaller than analytical ones which are in accord with the fore-mentioned rigid model. The
maximum inter-story drifts are both less than 1/500 required in Chinese design code- Technical
Specification for Concrete Structures of Tall Building. In additional, the maximum inter-story
drifts gained by shaking table test are 1/207 in direction X and 1/308 in direction Y under rare
earthquake of seismic intensity 7. Both drifts are less than 1/100 that needed to meet in TSCSTB.
Table 3. Maximum displacement in frequent earthquake of seismic intensity 7 (Units: mm)
Location
Roof
Story 47
Story 38
Story 31
Story 21
Story 16
Story 10
Story 5
Base
Direction X
Test
Analysis
152.17
97.13
68.93
52.24
33.48
23.43
12.26
5.54
0.00
158.6
103.3
65.9
43.4
22.8
15.6
7.7
2.7
0.0
5
Direction Y
Test Analysis
93.16
64.54
55.39
42.11
24.52
19.78
12.95
6.31
0.00
137.1
102.0
75.5
54.1
24.7
14.6
5.9
1.7
0.0
Table 4. Maximum inter-story drift in frequent earthquake of seismic intensity 7
Location
Roof – Story 47
Story 47-38
Story 38-31
Story 31-21
Story 21-16
Story 16-10
Story 10-5
Story 5-1
Roof drift
Direction X
Test
Analysis
1/838
1/1134
1/1702
1/2430
1/2189
1/2256
1/3201
1/3970
1/1609
1/835
1/907
1/1266
1/2214
1/3049
1/3201
1/4287
1/8084
1/1544
Direction Y
Test
Analysis
1/1611
1/2499
1/2069
1/2521
1/3716
1/3337
1/3236
1/3487
1/2628
1/1312
1/1284
1/1327
1/1550
1/2173
1/2904
1/5071
1/13171
1/1785
Seismic Performance Evaluation
A pushover analysis is performed by subjecting the structure to two load patterns of equivalent
lateral force (ELF) distribution and SRSS distribution in direction X and Y for seismic
performance evaluation. Figs. 7-8 show the relationship between base shear and peak
displacement in the two lateral load distributions. Because the two curves were so close that only
ELF distribution discussed in later.
Fig. 7 Pushover curves in X direction
Fig. 8 Pushover curves in Y direction
Based on the pushover analysis, an improved capacity spectrum method was used to evaluate the
seismic capability of prototype structure under rare earthquake. Firstly, POA curves have been
transformed to the capacity diagram. Then, the elastic and inelastic demand spectra that ductility
demand μ equal to 1, 1.5, 2 are established respectively. Both the demand spectra and the
capacity diagram have been plotted in the same graph (Figs. 9-10), so the seismic demand for
equivalent SDOF system can be determined by using the graphical procedure. The objective
displacements were 85.2cm, 52.3cm, 38.6cm when the ductility demand μ equal to 1, 1.5, 2
respectively under the earthquake action in direction X in equivalent lateral force distribution.
When the earthquake acts in direction Y, the objective displacements were 75.8cm, 43.6cm,
23.6cm when the ductility demand μ equal to 1, 1.5, 2 respectively. It is clear that the structure
has better seismic behavior and structural stiffness in direction Y is greater than that in direction
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X.
Spect r al Accel er at i on, Sa( m/ s^2)
6
5
μ = 1.0
4
3
μ = 1.5
2
μ = 2.0
μ = 3.0
1
0
0
20
40
60
80
Spect r al Di spl acement , Sd( cm)
100
Fig. 9 Elastic and inelastic demand spectra versus capacity diagram in direction X
Spect r al Accel er at i on, Sa( m/ s^2)
6
5
μ = 1.0
4
3
μ = 1.5
2
μ = 2.0
1
μ = 3.0
0
0
20
40
60
Spect r al Di spl acement , Sd( cm)
80
100
Fig. 10 Elastic and inelastic demand spectra versus capacity diagram in direction Y
In order to find out the elastoplastic mechanical properties on the tube under earthquake, two
states of roof drift equal to 1/500 and 1/100 were selected to research stress distribution in tube.
The analytical results indicated the compression stresses at the bottom of tube obviously higher
than other place and huge tension stresses occurred in the setback wall. Although the bottom tube
have large compression stresses, but no crack founded in there according to the test results. It
could be explained that abundant shaped steels embedded at the bottom of tube increased the
ductility of wall. Whereas diagonal crack to be seen in the setback tube and numerous cracks
occurred in frame columns. It is obvious that the setback in elevation is the location of structural
weakness. Moreover, horizontal and vertical cracks are observed in columns above the inclined
columns in story 21-22 based on shaking table test, it shows that the stresses in there are
influenced by inclined columns.
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CONCLUSION AND SUGGESTIONS
The following conclusions can be drawn from finite element analysis and shaking table test on
the structural system with setback in elevation.
(1) The first three vibration modes are translation in direction X, translation in direction Y and
torsion, respectively, the structural stiffness in direction Y is greater than that in direction X.
(2) Peak inter-story drift meets the requirement of China code CCSDB.
(3) Setback story is the weak region of structure, some methods improving the ductility in this
story and adjacent region should be adopted.
(4) The inclination of the columns in story 21-22 may be larger, steps reducing column
inclination or increasing cross-section capacity should be taken.
ACKNOWLEDGEMENTS
The authors are grateful for the financial support from National Natural Science Foundation of
China (NSFC) (Grant No.90815029) and National Key Technology R&D Program (Grant
No.2006BAJ13B01).
REFERENCES
Lu, X. L. 2007. Seismic theory and application on complex high-rise buildings. Science Press,
Beijing, China.
Lu, X. L, Zhou, Y., and Lu, W. S. 2007. Shaking table model test and numerical analysis of a
complex high-rise building. Struct. Design Tall Spec. Build. 16, 131–164
Bahram, M. S., and Jcak P. M. 1990. Seismic response and design of setback building. Journal of
Structural Engineering 116(5): 1423-1439
Sharon, L. W. 1992. Seismic response of R/C frames with irregular profiles. Journal of
Structural Engineering 118(2): 545-566
Su, N. F., Lu X. L., Zhou Y., et al. 2009. Shaking table model test of a super high-rise building
with setbacks in elevation. Proceedings of the 3rd International Conference on Advances in
Experimental Structural Engineering. San Francisco, USA.
Technical Specifications for Concrete Structures of Tall Building (JGJ3-2002). China Ministry of
Construction. China Architecture and Building Press, Beijing, China (in Chinese).
Code for Seismic Design of Buildings (DGJ08-9-2003). Shanghai Government Construction and
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Code for Seismic Design of Buildings (GB50011-2001). China Ministry of Construction. China
Architecture and Building Press, Beijing, China (English edition).
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