Analysis on Out-of-Plane Stability of Large-span Single Space Tube Truss during Hoisting

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Analysis on Out-of-Plane Stability of Large-span Single Space Tube
Truss during Hoisting
To cite this article: S H Chen et al 2021 IOP Conf. Ser.: Earth Environ. Sci. 668 012064

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

Analysis on Out-of-Plane Stability of Large-span Single Space
Tube Truss during Hoisting

 S H Chen1, T Y Yin2, X X Sang3, B R Ye4 and M Ding4*
 1
 Beijing No.3 Construction Engineering Co., Ltd, Beijing, China
 2
 Beijing Michanized construction group Co., Ltd, Bejing, China
 3
 Beijing Construction Engineering group Co., Ltd, Beijing, China
 4
 College of Water Resources and Civil Engineering, China Agricultural University,
 China
 Email: dingmin@cau.edu.cn

 Abstract. In order to study the out-of-plane stability of the large-span single space tube truss
 during lifting, the eigenvalue buckling mode of the truss was calculated by mode analysis in
 ANSYS, the eigenvalue buckling mode with different combination coefficients was applied to
 the truss, and the stability bearing capacity was taken as the measurement to conduct the whole
 process tracking analysis. Finally, the most appropriate eigenvalue buckling mode combination
 was found as the initial imperfection, and it was applied to a large-span single regular triangle
 space tube truss and inverted triangle space tube truss to verify its stability during hoisting,
 respectively. The results show that the combination form of the eigenvalue buckling mode
 is the most appropriate initial imperfection. When the
 large-span single regular triangle space tube truss and inverted triangle space tube truss are
 hoisted, local buckling occurs when the body force is up to 0.30 times and 0.15 times of
 gravity, respectively, and overall instability occurs when the body force is up to 0.56 times and
 0.51 times of gravity, respectively. It can be obviously obtained that the large-span single space
 tube truss may be destabilized under its own weight during hoisting, local buckling has
 occurred in some member bars before overall instability, and it is necessary to check the truss
 stability before hoisting in actual engineering.

1. Introduction
As a new type of space structure system, space tube truss has characteristics including large stiffness,
small amount of steel consumption, convenient construction and excellent economic and
environmental performance. It is widely used in large-span space structures such as large power
transformer stations, gymnasiums, railway stations and coal sheds, etc [1].
 In the construction of long-span space tube truss structure, the single trusses or sectional trusses are
generally moved to the design position of the structure by hoisting and then assembled [2]. During the
hoisting of a single truss, the lifting force applied to the structure is slightly larger than its dead weight
due to the upward acceleration of the structure [3]. In addition, the structure itself has a large span and
a large dead weight and lacks out-of-plane support. As a result, some bars, especially the upper chords
under the compression-bending action between various hoisting points, are prone to out-of-plane
instability, which will lead to the length change of the bars due to buckling, thus affecting the
installation accuracy [4]. It will also reduce the bearing capacity of the structure and reduce the safety
of the structure in the stage of construction and service.

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

 In recent years, some problems existing in the process of hoisting gradually have attracted the
attention of scholars, but there are few the research data about the stability of the truss during hoisting
considering the initial imperfections. For the stability problem of the hoisted structure, Guo Yanlin et
al. [5] obtained the selection method of the lifting point according to the principle that the relative
axial deformation of the two ends of the hoisted beam is equal or close to zero under the effect of dead
weight, and suggested to simulate the truss into solid-web components for its stability analysis, or
apply the finite element software to calculate the out-of-plane buckling load, and then judge the
feasibility of the hoisting plan. Cui Xiaoqiang et al. [6] took the hoisting of a 58m long plane truss of
Guangzhou Stadium as an example, and verified that enough hoisting points must be set to ensure the
strength, stiffness and stability requirements of the truss in the hoisting process. Peng Yufeng et al. [7]
combined with engineering examples of the large-span truss structure, held that it was not enough to
rely on experience when determining the hoisting point and its distribution. It could only be
determined through necessary analysis and calculation, and it was necessary to ensure that there would
be no out-of-plane instability during the hoisting process under the condition of in-plane stability. For
the deformation problem of the hoisted structure: Chang Jianxin et al. [8] simulated and analyzed the
hoisting scheme of the steel structure roof of the natatorium in the resource-sharing area of Songjiang
University Town, Shanghai. The results showed that dividing the primary truss into five sections while
hoisting can effectively reduce the deflection of each section of the primary truss and effectively
control the deformation as well. Zhu Yiju et al. [9] deemed that the single truss can easily deform
during the hoisting process, thus the section hoisting should be carried out after completion of the
whole assembly of the truss, and the deformation calculation should be performed for section units.
Only in this way, the deformation of the selected section unit can be controlled in the range of
elasticity, and the initial condition can be ensured after the rack is in position. In the engineering
practice, the influence of initial imperfections on the stability bearing capacity of the structure cannot
be ignored, which is harmful to the safety of the structure hoisting. It is of great significance to
consider the initial imperfections when studying the hoisting stability of the truss.
 For the large-span single space tube truss in the hoisting process, ANSYS finite element software
will be used to study the influence of different eigenvalue buckling modes and their combinations on
the stability bearing capacity in this paper, then the most appropriate form of initial imperfections will
be found, and the hoisting stability of the single regular triangle and inverted triangle space tube
trusses will be analyzed, respectively.

2. Initial Imperfection Analysis of a Single Space Tube Truss
The lower chord bracing space truss model with two lower chords and one upper chord was
established with the ANSYS finite element software. The pedestal footing was hinged support. First,
the first five eigenvalue buckling modes of the structure were obtained by modal analysis, then the
static analysis was carried out by applying the concentrated force vertically downward in the midspan
of the structure. The ultimate stability bearing capacity of the truss considering different combinations
of eigenvalue buckling modes was calculated successively on this base. In the analysis, the benchmark
coefficients were used to represent the influence of different buckling modes, which was taken as the
maximum strain of 1 / 500 of the structure total span divided by the current order i, denoted as . The
finite element model was built with the span direction as x axis and the height direction as y axis, as
shown in figure 1. The span is 120m and the height is 34m. The members are all made of Q345 steel
circular tube. The specifications of the upper chords are Φ325mm × 16mm and Φ273 mm × 12 mm,
among which the closer ones to the basis are Φ325mm × 16mm and the farther ones are Φ273 mm ×
12 mm. The specifications of the lower chords are Φ450mm × 20mm and Φ351mm × 16mm, among
which the closer ones to the basis are Φ450mm × 20mm and the farther ones are Φ351mm × 16mm.
The specification of the web members is Φ140mm × 7mm. The element type is beam188. The
calculation results of structural instability of different imperfection combinations are shown in table 1,
where the difference value refers to the percentage of structural stability bearing capacity when each
imperfection combination is applied compared with that when no imperfection is applied.

 2

HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

 Figure 1. Finite element model of single space tube truss.

 Table 1. Comparison of structural instability of different imperfection combinations.
 Differen
Imperfection Instability Ultimate Bearing
 Combination Coefficient ce
Combination Form Capacitiy (kN)
 Value
Zero
 0 Out-of-plane 285.75 0
Imperfection
1 Out-of-plane 278.00 -2.71%
2 Out-of-plane 285.44 -0.11%
3 Out-of-plane 284.21 -0.54%
4 （In-plane buckling mode） Out-of-plane 285.68 -0.03%
5 Out-of-plane 285.56 -0.07%
6 Out-of-plane 277.76 -2.80%
7 Out-of-plane 276.51 -3.23%
8 Out-of-plane 277.83 -2.77%
9 Out-of-plane 276.25 -3.33%
10 Out-of-plane 275.91 -3.45%
11 Out-of-plane 276.12 -2.80%
12 Out-of-plane 281.63 -1.44%
13 Out-of-plane 277.83 -2.77%

 As shown in table 1,
 (1) When each eigenvalue buckling mode is applied to the truss separately, the ultimate bearing
capacity applied with the first mode is considered the minimum, indicating that this method is
relatively safe to consider the initial imperfection. The ultimate bearing capacity applied with the
fourth order is relatively larger, because the mode of this order is in-plane instability. The most prone
instability of the structure is out-of-plane instability, so the imperfection has little influence on the
overall stability at this time.
 (2) When the four kinds of out-of-plane buckling modes are considered for combination, it can be
found that the difference value between the ultimate bearing capacity of each combination model and
the bearing capacity of the model without considering imperfections is approximately equal to the sum
of the difference value when considering separately.
 (3) When the five eigenvalue buckling modes are considered comprehensively, the 12th and 13th
combination methods are still equal to the sum of the individual cases. The 11th combination method
is less than the sum of the individual cases, which may be due to the fact that the coefficients of all
modes are 1 and the imperfections cancel each other out.
 (4) The bearing capacity of the 13th combination method is not much different from that of the first
one. This method can not only comprehensively consider the buckling modes of the first five orders,
but also is relatively safe and conservative, which indicates it can be adopted.

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

3. Stability Analysis in Hoisting Process

3.1. Selection of Hoisting Points
From the two aspects of structural stress and engineering practice, the selection of hoisting points
needs the consideration of many factors, and at the same time requires that the deformation of the
structure under the force slightly greater than its dead load in the hoisting process should not exceed
the allowable value, in order to ensure the installation accuracy of the structure [10-11].
 According to the criteria above, the following requirements are proposed for the selection of
hoisting points: 1) During the hoisting process, the axial deformation of the structure should be strictly
controlled to meet the requirements of installation accuracy; 2) In the process of lifting and hoisting,
the structural stress should be uniform without excessive stress areas, so as to prevent the bearing
capacity of some members from being affected.
 In this paper, the method recommended in literature [2] for selecting the hoisting point position of
simply supported beams was adopted. The hoisting point positions are shown in figure 2, and the
calculation formulas is shown as Equation (1),

 Figure 2. Schematic diagram of lifting point selection.

 √ −
 = = ; = ( − √ ) (1)
 Equation (1) provides a basis for the selection of hoisting points, but it does not take the influence
of section change into account. When considering the hoisting of complex structures, the section
change should be considered, which can be solved by the finite element software. At the same time,
for structures with complex forms, the sling and the structure transfer load at a certain angle during the
hoisting process, and some members will be subjected to axial pressure, which may lead to out-of-
plane instability. Next, the finite element software ANSYS will be used to analyze the hoisting
construction of triangular space tube truss model.

3.2. The Regular Triangle Space Tube Truss
Based on the results of the modal combination analysis in the above section, a single regular triangle
space tube truss model during the hoisting process was established. The upper hoisting points were
selected above the center of gravity, and the lower hoisting points were selected according to the
 √ −
formula = = after roughly checking.
 The forms of the first five eigenvalue buckling modes are shown in figure 3:

 (a-1) The front view of the first-order (a-2) The vertical view of the first-order

 4

HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

 (b-1) The front view of the second-order (b-2) The vertical view of the second-order

 (c-1) The front view of the third-order (c-2) The vertical view of the third-order

 (d-1) The front view of the fourth-order (d-2) The vertical view of the fourth-order

 (e-1) The front view of the fifth-order (e-2) The vertical view of the fifth-order
 Figure 3. The Eigenvalue buckling modes of the regular triangle space tube truss.

 The first five eigenvalue buckling modes were selected and the coefficients were set as
 which were applied to the models as the initial geometric imperfection
for the nonlinear stability checking calculation. The data indicating the displacement of the node at
the most dangerous position of the upper chord changing with the load was extracted as shown in
table 2. The parameter represents the acceleration of the structure vertically downward, which starts
from 0.5 , gradually increases to 5.56 . It can be multiplied with the structure mass to obtain
the vertical downward body force. At the same time, the analysis was conducted with the upper chords
between the hoisting points as the research objects. The force condition of the members was tracked in
chronological order of the load changing. Then the stress ratios was calculated and listed in table 2.
The formula for calculating the stress ratio is given in the steel structure code [12], which is that
when conducting the checking calculation of the stability of the circular tube under biaxial bending
and compression, should represent the value of the bar stress divided by the design stress. The
formula is as follow:
 mx x
 = (2)
 m ( −0 8 ′ ) 
 Ex

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

Table 2. Comparison of stress ratio and displacement of regular triangle space tube truss in hoisting
process.
 −
 ( ) (mm)
 0.5 -0.45 0.325
 1 -0.90 0.468
 1.50 -1.34 0.611
 2.00 -1.79 0.753
 2.50 -2.24 0.896
 3.00 -2.69 1.039
 3.50 -3.13 1.182
 4.00 -3.58 1.325
 4.50 -4.03 1.466
 4.99 -4.49 1.614
 5.56 -4.87 1.735

 For the convenience of observation, the load was divided by the cardinal number 0 =9.8m/s2
(here is the acceleration of gravity) to obtain the multiple n of dead weight. The relationship curves
between n and the displacement and n and the stress ratio were plotted respectively, as shown in
figure 4 and figure 5.

 Figure 4. The relationship curve between n and of the regular triangle space tube
 truss during hoisting process.

 It can be seen from figure 4 that when the body force of the structure reaches 0.56 times its dead
weight, an inflection point appears in the n- curve, indicating that the whole structure is unstable at
this time.

 Figure 5. The relationship curve between n and of the regular triangle space tube
 truss during hoisting process.

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

 As shown in figure 5, when the body force of the truss reaches 0.30 times its dead weight, the stress
ratio of the member reaches 1, indicating the instability of the member occurs. By observing the n-
 curve, it can be found that the whole structure can still withstand the load at this time.
 Through this example, it can be found that during the hoisting process, the instability of a large-
span single regular triangle space tube truss under the action of dead weight will occur. The body force
of structure when local instability occurs is less than that when overall instability occurs. Therefore,
the overall stability and the member stability of the truss should be checked at the same time in
practical engineering.

3.3. The Inverted Triangle Space Tube Truss
The same method was used to establish a large-span single inverted triangle space tube truss model in
the hoisting process. The first five order buckling modes are shown in figure 6.

 (a-1) The front view of the first-order (a-2) The vertical view of the first-order

 (b-1) The front view of the second-order (b-2) The vertical view of the second-order

 (c-1) The front view of the third-order (c-2) The vertical view of the third-order

 (d-1) The front view of the fourth-order (d-2) The vertical view of the fourth-order

 (e-1) The front view of the fifth-order (e-2) The vertical view of the fifth-order
 Figure 6. The eigenvalue buckling modes of the inverted triangle space tube truss.

 The first five eigenvalue buckling modes were selected and the coefficients were set as
 which were applied to the models as the initial geometric imperfection
for the nonlinear stability checking calculation. The data indicating the displacement of the node at

 7

HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

the most dangerous position of the upper chord changing with the load was extracted as shown in
table 3, which is the same with the regular triangle space tube truss model. At the same time, the
analysis was conducted with the upper chords between the hoisting points as the research objects. The
force condition of the members was tracked in chronological order of the load changing. Then the
stress ratios was calculated and listed in table 3.

Table 3. Comparison of stress ratio and displacement of inverted triangle space tube truss in hoisting
process.
 −
 ( ) (mm) X1
 0.5 -0.15 0.605
 1 -0.30 0.793
 1.50 -0.45 0.982
 2.00 -0.60 1.170
 2.50 -0.75 1.359
 3.00 -0.90 1.548
 3.50 -1.05 1.737
 4.00 -1.20 1.924
 4.48 -1.35 2.119
 5.06 -1.48 2.277
 5.02 -1.71 2.566

 Identically, for the convenience of observation, the load was divided by the cardinal number
 2
 0 = 9.8m/s (here is the acceleration of gravity) to obtain the multiple n of dead weight. The
relationship curve between n and the displacement and n and the stress ratio was plotted
respectively, as shown in figure7 and figure 8.

 0.60
 0.51
 0.50

 0.40
 n

 0.30

 0.20

 0.10

 0.00
 0.00 1.00 2.00
 y /mm

 Figure 7. The relationship curve between n and of the inverted triangle space tube truss
 during hoisting process.

 It can be seen from figure 7 that when the body force of the structure reaches 0.51 times its dead
weight, an inflection point appears in the n- curve, indicating that the whole structure is unstable at
this time.

 8

HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

 0.60

 0.50

 0.40

 0.30

 n
 0.20
 0.15
 0.10

 0.00
 0.00 1.00 1 2.00 3.00

 Figure 8. The relationship curve between n and of the inverted triangle space tube truss
 during hoisting process.

 As shown in figure 8, when the body force of the truss reaches 0.15 times its dead weight, the stress
ratio of the member reaches 1, indicating the instability of the members occurs. By observing the n-
 curve, it can be found that the whole structure can still withstand the load at this time.
 Through this example, it can be found that during the hoisting process, the instability of a large-
span single inverted triangle space tube truss under the action of dead weight will occur. The body
force of structure when local instability occurs is less than that when overall instability occurs.
Therefore, the overall stability and the member stability of the truss should be checked at the same
time in practical engineering.

4. Conclusion
In this paper, considering the initial defects, the possible instability state of the large-span single space
tube truss in the hoisting process was studied, and the following conclusions can be drawn:
 (1) To consider the initial imperfection of the large-span single space tube truss, the combination
form of the eigenvalue buckling modes was supposed to be
applied to the structure, which can not only ensure the safety but also consider the first five buckling
modes comprehensively.
 (2) During the hoisting process of the large-span single space tube truss, the instability problem
will occur, and before the overall instability occurs, local instability of some members will occur. It is
suggested that the influence of member instability on the overall instability should be considered in
practical engineering.
 (3) If the hoisting stability checking calculation results show that the instability of the structure will
occur in the hoisting process, the construction should be carried out by segmental hoisting to ensure
the safety of the structure.

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HECE 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 668 (2021) 012064 doi:10.1088/1755-1315/668/1/012064

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