COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China
©2006 Tsinghua University Press & Springer
Overall Stability of the Large Span Roof Structure of Hangzhou
International Conference Center
Y. F. Luo1*, X. Liu1, Zh. B. Wang1, Z. Y. Shen1, J. H. Li2
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]
Abstact Large span structures are widely used in modern buildings because of their novel forms or shapes, light
self-weight and lower construction cost. The buckling behavior of the large span structures under loads are much
complex and hard to understand. The non-linear stability analysis and the incremental-interation tracing methods are
necessary for design complementory during design. The geometry imperfection influences on structure stability are
also needed to be considered .There are no special analysis technics and judging methods for overall stability of the
large span structures in current national design codes of our country. It is necessary to carry on non-linear overall
stability analysis for every specific structure to obtain the overall stability behavior of structures during design.
According to the design demand, the large displacement and elasto-plastic overall stability analyses of the perfect and
imperfect steel roof structure are conducted. The reliable numerical data are provided to the design. The valuable ideas
about the overall stability behavior of the large span structure are concluded. It is a useful reference for design of
similar structures.
Keywords: Large span structure, Overall stability analysis, Curved truss system
INTRODUCTION
Hangzhou International Conference Center is located in the middle of Qianjiang new town in Hangzhou. Composed of
main building tower, skirt building and basement, the whole area of the building is 117630 m2. The tower is nineteen
storeys above the ground and two storeys underground. The skirt building is two storeys. The height of the tower is
85m. The structure arrangement is shown in Fig.1. The plane of skirt building is approximately oblong. The axes are
179m and 142m respectively. The area of the skirt building is about 68080m2. Composed of space trusses, plane
trusses, lattice girders and purlins, the large span roof structure is a curved truss system. The trusses over the entrance
are positioned on the lattice girders and have 17m in cantilever. The lattice girders are supported on the columns located
at two sides of the entrance. The largest span of the main truss is 60.8m.
Because of the complex system and the large span, the buckling modes of the skirt roof structure under loads are more
complex compared with the traditional structural system. According to the design demand, the finite element models
of the structure are created in the paper. The large displacement and elasto-plastic overall stability analyses of the
perfect and imperfect steel roof structure are conducted. The critical loads and maximum displacements under different
load combinations are obtained. The reliable numerical data are provided to the design. The valuable ideas about the
overall stability behavior of the large span structure are concluded.
MODELS FOR NUMERICAL ANALYSIS
Composed of trusses and purlins, the roof structure is a reticulated steel shell system. I-Shaped and pipe section
members are used. The member steels are Q345 and Q235 respectively. The model contains 8055 members and 2692
joints. The space beam element is adopted in analysis. All nodes are rigid connection. All supports are hinged supports.
The position of the supports can be found in Fig. 1. The mechanical models are shown in Fig. 2.
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Figure 1: Plane arrangement of the structure
Figure 2: Mechanical model of the skirt roof structure
According to the structure characters and the design conditions, three loads adopted in the stability calculation are
0.5kN/m2 of dead load (DL) in upper surface, 1kN/m2 of dead load in lower surface and 0.5kN/m2 of live load (LL).
The fundamental wind pressure is 0.45kN/m2. The shape coefficients are determined according to wind tunnel
experiments. The most unfavorable load combinations are applied to the structure for the analyses of linear and
nonlinear (large displacement, elasto-plastic) overall stability. Two load combinations are load combination 1
(LC1=dead load + live load) and load combination 2 (LC2=dead load + live load + wind load (along the zero degree)).
The finite element analysis software ANSYS is adopted for numerical analysis.
THE LINEAR STABILITY ANALYSIS
In order to obtain the upper limit of the buckling load and the corresponding buckling modes of the structure under
different load combinations, the sub-space iteration method is adopted to conduct the linear elastic stability analysis.
For shortening the paper, the first ten buckling coefficients are listed in Table 1. The first four buckling modes under
LC1 are shown in Fig. 3.
The stiffness of the plane trusses is so weak that the local buckling occurs in the plane trusses of the structure firstly.
The buckling models develop from nodes buckling to strip buckling with the increment of the load factor λ.
Table 1 Linear Buckling Coefficients λ
Model
LC
LC1
LC2
LC
LC1
LC2
1
2
3
4
5
41.731
32.342
6
54.124
42.012
48.253
35.204
7
55.600
43.234
50.981
37.168
8
55.841
43.664
51.804
38.866
9
58.418
45.317
53.665
41.361
10
60.788
46.492
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1
1
NODAL SOLUTION
NODAL SOLUTION
APR 17 2006
16:49:36
STEP=1
SUB =1
FREQ=41.731
USUM
(AVG)
RSYS=0
DMX =.759009
SMX =.759009
APR 17 2006
16:50:03
STEP=1
SUB =2
FREQ=48.253
USUM
(AVG)
RSYS=0
DMX =.854473
SMX =.854473
YZ
YZ
X
X
MN
MN
MX
MX
0
.168669
.084334
.337337
.253003
.506006
.421672
.674675
.59034
0
.189883
.759009
.094941
(a) The 1st buckling mode
.379766
.569648
.284824
.474707
.759531
.66459
.854473
(b) The 2nd buckling mode
1
1
NODAL SOLUTION
NODAL SOLUTION
APR 17 2006
16:50:23
STEP=1
SUB =3
FREQ=50.981
USUM
(AVG)
RSYS=0
DMX =1.011
SMX =1.011
APR 17 2006
16:50:47
STEP=1
SUB =4
FREQ=51.804
USUM
(AVG)
RSYS=0
DMX =1.003
SMX =1.003
YZ
YZ
X
X
MN
MX
MN
MX
0
.224761
.11238
.449521
.337141
.674282
.561902
.899043
.786662
0
1.011
.222801
.1114
(c) The 3rd buckling mode
.445601
.334201
.668402
.557001
.891202
.779802
1.003
(d) The 4th buckling mode
Figure 3: The buckling modes of the structures under LC1
THE LARGE DISPLACEMENT STABILITY ANALYSIS
The lowest buckling model is taken as the initial imperfection model. According to the technical specification for
latticed shells, the initial imperfection is taken as 1/300 of shorter span of the structure. The sensitivity of the structure
to the imperfections can be obtained by geometric nonlinearity analyses of perfect and imperfect structures. The
buckling deformations and load-deflection curves of perfect and imperfect structures under different load combinations
are shown in Fig. 4 to Fig. 11.
Figure 4: Geometric nonlinear buckling of the perfect structure under LC1
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Figure 5: Geometric nonlinear buckling of the perfect structure under LC1
Figure 6: Geometric nonlinear buckling of the perfect structure under LC2
Figure 7: Geometric nonlinear buckling of the imperfect structure under LC2
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Figure 8: Load-deflection curves of node 667 of the perfect structure under LC1
Figure 9: Load-deflection curves of node 802 of the imperfect structure under LC1
Figure 10: Load-deflection curves of node 1889 of the perfect structure under LC2
Figure 11: Load-deflection curves of node 1964 of the imperfect structure under LC2
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From the load-deflection curves, it can be found that the load factor goes higher with the increment of load steps if the
plastic deformation is not considered. The critical load can not be obtained by estimating the singularity of tangent
stiffness. The tangent stiffness degrades formerly and increases subsequently. The critical load is obtained at the point
where the first derivative of tangent stiffness equal to zero. The displacement is too large for normal use of the structure
at the load level. The geometric nonlinear stability factors of the perfect and imperfect structures are listed in Table 2.
Table 2 The geometric nonlinear stability factors of the perfect and imperfect structures
LC
perfect structure
imperfect structure
LC1
LC2
25
36.5
24
34.7
From Table 2, it can be concluded that the stability factors are greater than 5.0. The structure system meets the demand
of the overall stability. The stability factors of perfect structure are approximately equal to that of imperfect structure.
Therefore, the structure is not sensitive to the imperfections.
THE ELASTO-PLASTIC OVERALL STABILITY ANALYSIS
The elasto-plastic overall stability is analyzed in this paragraph. The large deformations and imperfections are
considered as above at the same time. The buckling deformations and load-deflection curves under different load
combinations are shown in Fig. 12 to Fig. 15.
Figure 12: Elasto-plastic buckling of the imperfect structure under LC1
Figure 13: Elasto-plastic buckling of the imperfect structure under LC2
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Figure 14: Load-deflection curves of node 742
under LC1(λ=4.77)
Figure 15: Load-deflection curves of node 802 under LC2 (λ=4.17)
From the load-deflection curves, it can be found that the load factor goes higher with the increment of load steps until
tangent stiffness equal to zero. The critical load can be obtained by estimating the singularity of tangent stiffness if the
plastic deformation is considered. The critical load is much lower than that of the large displacement stability analysis
under the same load combination. The buckling occurs in the middle of the largest span trusses. The displacements are
smaller than that of the large displacement stability analysis.
CONCLUSION
The numerical results show that the stability factors of the structure are greater than 5.0 for geometric nonlinear
analysis and greater than 2.0 for elasto-plastic analysis. The structural system meets the demands of the overall
stability. The buckling occurs in the middle of the largest span trusses of the structures due to the weak stiffness. Proper
braces should be better set against the instability of the weaker trusses.
REFERECES
1. Shen ZY. Stability, Aseismic and Nonlinear Analysis Theories of Steel Structures. Building Industry Press,
BeiJing, China, 2004 (in Chinese).
2. Wang XC. Finite Element Methoed. Tsinghua University Press, BeiJing, China, 2003 (in Chinese).
3. Structural Analysis Eqequide (ANSYS Release 5.7). ANSYS Inc.
4. Technical Specification for Latticed Shells (JGJ61-2003, J258-2003). 2003.
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