Study on Inverse Analysis Technique Considering Influence of Construction Procedure on Performance of Large-Span Steel Latticed Arch

Abstract

In this paper, the influence of the construction process of large-span steel latticed arch on the geometric configuration and bearing capacity performance of the large-span steel latticed arch is calculated and analyzed by using the inverse analysis technique. By comparing the calculation results of single pre-deformation adjustment of the node co-ordinates in zero state of the whole structure and the dynamic adjustment of the node co-ordinates of the unconstructed part of the structure, it is found that the inverse analysis method of dynamic node co-ordinate adjustment is used to achieve the unification of the geometric configuration of the final structure and the bearing capacity performance of the structure. The results show that the inverse analysis method of dynamic node co-ordinate adjustment proposed in this paper can simulate and track the dynamic changes of structural geometry and stable bearing capacity performance in the actual construction process, which can not only consider the influence of the installed part of the structure on the co-ordinate adjustment value of the uninstalled part of the structure but also consider the deformation influence of the subsequent uninstalled structure on the installed structure and can realize the optimal approximation of the final state structure to the geometric configuration of the zero state structure and the accurate calculation of the bearing capacity performance with the progress of the construction process.

1. Introduction

With the promotion of the concept of sustainable building, environmental protection and energy-saving structures such as steel structures have received more and more attention. Because of its light weight and high strength, long-span space steel structure has been widely used in airports, stadiums, bridges and other large public buildings [1,2,3,4,5]. Similar to the bridge structure, the long-span steel structure will bear various loads during the long construction process and undergo significant structural system transformation, showing dynamic changes in complex stress conditions [6,7].

In building, steel structure for the analysis of the mechanics principle is not accurate and causes a series of quality problems, including construction deformation of the steel structure, unstable lifting of steel lattice members, etc. After the occurrence of these problems, it also easily impacts the steel structure building’s security, with stability severely affected. Therefore, it is necessary to strengthen the analysis of related mechanical problems in the construction of buildings in the new period [8,9]. It is challenging to accurately and efficiently install large-span space steel structures at target locations, especially in dynamic and crowded construction sites, where integral lifting is often used [10,11,12,13,14]. Currently, there is a lack of effective analysis considering the specific characteristics of the construction process during the installation of large-span space steel structures in integral lifting. In the construction process, it will be found that the installed structure does not meet the required accuracy and the installed content needs to be removed and rebuilt. This will cause idling and rework, resulting in a waste of resources, which is not conducive to sustainable development. Therefore, it is necessary to study the lifting construction technology of large-span space steel structure and form a fine construction method, and the dynamic adjustment of structural node co-ordinates is very essential.

For steel structure buildings, if the components are processed according to the design configuration and the design configuration is used as the initial configuration of the structure installation, there is a certain deviation between the structure configuration and the design configuration at the time of completion, which may lead to the architectural modeling not meeting the requirements of architectural aesthetics, and the building may not meet the requirements of architectural applicability in normal use; it may even affect the geometric configuration due to excessive deformation of the structure during construction [15]. For large complex steel structure buildings, this problem is especially prominent; in the construction process of these projects, the design often requires that the configuration of the structure in the completion state is consistent with the design configuration, which requires the configuration of the structure to be controlled during the construction process. For the rigid structure, the control measures are mainly to compensate the deformation of the structure in the construction process by setting the pre-deformation, so as to achieve the purpose of controlling the configuration. In the design of steel structure buildings, the whole structure is usually calculated but, in the actual construction, the steel structure building is gradually assembled from the component to the whole, and the stress and deformation of the structure will gradually accumulate with the advancement of construction progress and then produce construction errors deviating from the design value [16]. Two basic conditions must be met after the construction of the structure: first, the deviation between the geometry of the structure and the design of the building is within a certain range; second, the internal force and deformation of the structure are not beyond the limit, so that the combination of it and other load effects can meet the requirements of the structural bearing capacity and normal use [17].

Ma et al. [18] carried out construction simulation analysis by the finite element analysis software ETABS 18.1.0 to study the vertical deformation and deformation difference of vertical members under gravity load, taking the influence of construction processes and shrinkage and creep of concrete into consideration.

Xin et al. [19] compared Shanghai Tower’s vertical deformation calculation and elevation control scheme, considering foundation differential settlement, by using the time-dependent coupling effect analysis method. The results showed that the foundation differential settlement cannot be ignored in vertical deformation calculations and elevation control for supertall structures. They recommended adopting the multi-level elevation control method with relative elevation control and design elevation control, without considering the overall settlement in the construction process.

Tang et al. [20] analyzed the method to obtain the preset deformation value (PDV) of the truss installed with a cantilever structure of steel roof structure and made use of software ANSYS13.0 to calculate the truss PDV through a backward iteration method to ensure construction was completed.

Dai et al. [21] used computer simulation and analysis techniques in engineering to simulate construction processes. They used iterative theory to set the pre-deformation values for steel structure construction deformations, adjust the position of the building during the construction process, and allocate forces on the building through the use of jacks to achieve the desired structural state. This method ensured that the geometric configuration and stress state of the building met the theoretical design values upon completion.

Li et al. [16] introduced the concept of the PDV, which included manufacture preset deformation value and erection preset deformation value. In addition, they proposed a new computational method, namely the two-stage comprehensive iteration method (TSCIM), to determine PDVs of the new CCTV headquarters. They analyzed and provided the pre-deformation values for the structure as an important positioning basis for actual construction and installation.

Zhong et al. [22] proposed a new type of single-layer lattice web shell steel cooling tower. They established an optimization design method based on stress control principles and introduced a step-by-step relaxation iterative algorithm to address the convergence issue in the optimization process. By comparing with traditional double-layer cooling towers in terms of natural frequency, total steel consumption, maximum lateral displacement of the tower top and elastic buckling load, it was demonstrated that this new cooling tower had significant advantages in steel usage while meeting design criteria for lateral displacement.

Li et al. [23] introduced a new improved nonlinear analysis method called “the birth-death element method” and a forward iteration method for node rectification based on the principles of installation node deviation correction in rigid large-span steel latticed arches. This method could solve the “floating” problem of elements and could be easily integrated into commercial finite element software. The results of computer simulation analysis during the construction process of the main stadium of the Sports Center for the World Games closely matched the measured values, demonstrating that the new nonlinear time-dependent analysis method was effective for simulating complex rigid large-span steel structures. It provided valuable references for future design and construction.

Luo et al. [24] proposed a stochastic deviation method for structural configuration calculation based on the uncertainty and random distribution characteristics of the spatial positions of unmeasured nodes. The stochastic deviation method was used to calculate the actual configuration of the reticulated shell structure, and the overall stability analysis was carried out. The results showed that the identification and analysis results based on the stochastic deviation method were similar to the measured node data.

Yuan et al. [25] used the age-adjusted effective modulus method to analyze the equivalent elasticity problem, deduced the vertical deformation formula, discussed the optimal construction plan of the conjoined super-high-rise building, studied the calculation method of the pre-deformation of the conjoined super-high-rise building and verified its correctness through numerical simulation. The results showed that the maximum vertical deformation of the connected structure occurred in the corridor position and obvious mutation occurs. Proper delay of rigid connection timing between corridor and tower was beneficial to control the deformation difference and internal force of the whole structure and verified that the pre-deformation method was correct and effective.

Chen et al. [26] proposed a theory basis for the SSMT that was used in the constructional analysis of the Yujiapu Railway Station Building, and results obtained by the proposed method were compared with those by element birth and death technology. In addition, the preset construction deformation value was calculated to validate the correctness and efficiency of the proposed method.

Guangjing et al. [27] derived the anisotropic thermal conductivity ranges of Boom Clay: (λ_h, λ_v) = (1.55–1.95, 1.10–1.25) W/(m·K) based on an inverse analysis of two in situ heater tests: the small-scale ATLAS IV Heater test and the large-scale PRACLAY Heater test. This range was of interest for upscaling the THM behavior of the Boom Clay to the scale of a geological disposal facility in the same horizon as the HADES URF.

Zhengxiang et al. [28] presented an inverse analysis algorithm for deriving the softening relationship of concrete. The proposed inverse analysis method precisely reproduced the nonlinearity prior to peak load as well as the softening behavior of concrete during the post-peak phase, and the simulated loads yielded good agreement with the test ones in all regions of the load–CMOD curve. The fracture energy evaluated by the σ–w curve was consistent with that calculated by the load–CMOD curve, with an error of less than 4%; therefore, the rationality and validity of the algorithm were verified using test data.

Zhao et al. [29] developed a framework to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model (ROM) and probabilistic programming and utilized the ROM to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems. Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering and the results proved that the proposed framework provided a scientific, feasible and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

The method of adjusting node co-ordinates proposed in previous studies only considers the displacement calculated in the overall construction process of the structure and reversely added it to the zero state but did not consider the impact of the construction process on the structure performance and the dynamic adjustment of the corresponding structure during the construction process. Only when these two aspects are taken into account can the only definite target structure pursued by the initial design be obtained. The inverse analysis method mentioned above was for the geotechnical and concrete structures, and the inverse analysis method mentioned in this paper was for the large-span steel lattice arch, which was different from the inverse analysis method mentioned by predecessors.

2. Inverse Analysis Method

Normally, the pre-deformation of the node co-ordinates of the structure is calculated by finite elements to obtain the vertical displacement of each node, and then the calculation result is applied back to the design state of the structure, that is, the node co-ordinates in the design state are raised as a whole. This structure is used as a construction structure, so that, after the construction is completed, the structure will reach the design state under the action of its own gravity and other factors.

However, the construction process of the structure is a time-varying process and, at the same time, the co-ordinates of the structure affect each other after improvement and the final vertical deflection will also change, which makes the single co-ordinate adjustment unable to make the structure fully fit the design state. Therefore, the vertical displacement generated after the first co-ordinate promotion is continuously applied to the design state of the structure in reverse, which is recorded as the first co-ordinate iteration, and so on, which can gradually reduce the error between the structural state and the design state after the construction is completed [23,30].

The specific iteration steps are as follows:

(1)

On the basis of the design node co-ordinate $v_0$, the construction process simulation analysis of the structure is carried out by using the node correction life and death element method, and the node co-ordinate of the forming state of the structure is $v_0+u_1$;

(2)

Applying $-u_1$ to the design node co-ordinate in reverse, the initial pre-deformation node co-ordinate $v_0-u_1$ is obtained;

(3)

Based on the initial pre-deformation node co-ordinate $v_0-u_1$, the same method is used to simulate and analyze the construction process, and the new pre-deformation node co-ordinate $v_0-u_1+u_2$ after the second iteration deformation is obtained;

(4)

In order to minimize the error as much as possible, the difference (absolute value) between the design node co-ordinate $v_0$ and the new node co-ordinate $v_0-u_1+u_2$ satisfies the relationship $\left|u_1-u_2\right|\le \left[u\right]$ ($\left[u\right]$ is the allowable error), indicating that the error meets the convergence standard, and the iteration ends.

The above is the iterative method for single pre-deformation adjustment of the node co-ordinates. When the dynamic adjustment of the node co-ordinates is carried out, the structure needs to consider the installation error. The structure is divided into several parts for iteration according to the construction plan. Now, the installation error of the first part is added to the nodes involved in the first step structure and the remaining structure will be iterated. In this process, only the node co-ordinates involved in the remaining structure will be adjusted, and the node co-ordinates involved in the first part of the structure will not be adjusted. After the iteration is completed, the installation error of the second part will be added to the second part of the structure. Then, this is looped through until the iteration is completed, as shown in the following Figure 1.

In order to prevent excessive horizontal thrust caused by arching, the maximum pre-deformation value of the structure shall not exceed the standard value of the steel latticed arch specification. Using the iterative algorithm of joint correction, the pre-deformation value analysis of the large-span steel latticed arch shown in Figure 1 is carried out, assuming that the geometrical configuration of the steel beam is strictly controlled if the allowable error is $\left|u\right|=1 \mathrm{mm}$. The process and results of the pre-deformation iteration are shown below.

3. Inverse Analysis of the Example

3.1. Structural Information

In this paper, the exhibition hall of a large-span steel latticed arch project is taken as an example to verify this method. The exhibition hall is the east main entrance of the whole project, the roof shape plane size is 270 m × 170 m, and the main steel latticed arch includes frame structure, 16.75 m composite steel beams, roof trusses, atrium, arc trusses, floor arch of the door head area, connecting steel trusses, and overhangs. Only Q355 steel is involved in the model, and various parameter values of Q355 steel are as follows: elastic modulus is 2.06 × 10¹¹ (N/m²), Poisson’s ratio is 0.3, and mass density is 7.85 × 10³ (N/m³/g). The specific structure is shown in Figure 2 below.

3.2. Analysis of Single Pre-Deformation Adjustment

In the pre-deformation analysis of the structure construction of a large-span steel latticed arch exhibition hall, for all nodes involved in the component, it can be known that the node co-ordinate pre-deformation value is relatively small by the finite element software calculation, most of the node co-ordinate pre-deformation value is below 16mm, the minimum node co-ordinate pre-deformation value is almost 0 mm, and the maximum node total pre-deformation value is 71.60 mm. It can be calculated that the maximum node pre-deformation value in the X direction is 19.59 mm, the maximum node pre-deformation value in the Y direction is 19.42 mm, the maximum node pre-deformation value in the Z direction is 71.60 mm, the total pre-deformation value of the node in the X direction is 7814.52 mm, the total pre-deformation value of the node in the Y direction is 14,898.12 mm, and the total pre-deformation value of the node in the Z direction is 73,710 mm. And the maximum value of the total pre-deformation value of the node is not much different from the maximum value of the Z-direction pre-deformation; the specific situation is shown in Figure 3, so the node pre-deformation value is mainly controlled by the Z-direction pre-deformation value for all nodes and the node co-ordinate pre-deformation is mainly Z adjustment. When there is no strict requirement for the plate element, considering that the plate element adjustment is cumbersome, the plate element structure can be removed, so the plate element is not considered in the construction pre-deformation process.

For the structure of removing the plate element, the co-ordinate pre-deformation of the node of the rest of the structure is mainly in the vertical direction and the node pre-deformation is larger. If the pre-deformation is not carried out, it will cause large errors and affect the building requirements, so it is necessary to carry out the construction pre-deformation of the node of the rest of the structure and, when the construction pre-deformation analysis of the large-span complex steel structure is carried out in more literature, the node co-ordinate adjustment is mainly carried out on the structure of the removal plate element and the engineering needs can be satisfied [31].

After the completion of construction, the error between the structural state and the design state is:

$$X={\displaystyle \sum }_{i=1}^n{(x_i^0-x_i^a)}^2$$

In the formula, i is the node number; $x_i^0$ is the design value of the x-co-ordinate of node i; and $x_i^a$ is the x-co-ordinate of node i after one iterative transformation. The same is true for y-co-ordinates and z-co-ordinates.

According to

Table 1. Maximum error in each direction before and after single pre-deformation adjustment.

	Maximum Error in All Directions	$\mathit{m}\mathit{a}\mathit{x}\mathbf{\Delta }\mathit{x}\left(\mathbf{m}\mathbf{m}\right)$	$\mathit{m}\mathit{a}\mathit{x}\mathbf{\Delta }\mathit{y}\left(\mathbf{m}\mathbf{m}\right)$	$\mathit{m}\mathit{a}\mathit{x}\mathbf{\Delta }\mathit{z}\left(\mathbf{m}\mathbf{m}\right)$
Number of Iterations
When there is no iteration		19.59	19.42	71.60
First iteration		0.4814	0.3558	1.736
Second iteration		0.009339	0.007806	0.04348
Third iteration		0.000253	0.000196	0.001104

and

Table 2. Total error in each direction before and after single pre-deformation adjustment.

	The Sum of Errors in All Direction	X (mm2)	Y (mm2)	Z (mm2)
Number of Iterations
When there is no iteration		25,275.03	71,451.71	1,721,828
First iteration		6.482	5.271	182.966
Second iteration		0.00211	0.002023	0.0781
Third iteration		1.891 × 10−6	1.915 × 10−6	4.6 × 10−5

, it can be seen from the calculation, whether from the angle of the maximum error in all directions or from the angle of the sum of errors in all directions, it can be seen after comparative analysis that, after iterative adjustment of co-ordinates, the node co-ordinates after construction and the overall error of the node in the design state are rapidly reduced, which proves the effectiveness of the iterative method and provides a theoretical reference for practical engineering.

3.3. Single Overall Node Co-Ordinate Adjustment and Multiple Dynamic Node Co-Ordinate Adjustment Results and Analysis

It can be seen from the Figure 4 that, without iterative process analysis, under the influence of the overall structural self-weight, the maximum Z-displacement occurs on node 11,796, with a value of 71.60 mm. After iterative process analysis, the maximum Z-direction displacement of the whole structure under the influence of self-weight is 69.90 mm, but the most unfavorable position does not change. It can be found that, in the iterative process of the structure, the internal force and deformation generated by each construction step have no great influence on the whole structure after forming and the maximum displacement is reduced by 2.4%. However, unreasonable control will lead to the deviation of the node position of the structure before and after the formation, which will lead to a certain decline in the bearing capacity of the structure and some mechanical properties after the formation and cannot reach the expected effect. The displacement comparison results are as follows:

It can be seen from the Figure 5 that, without iterative process analysis, the overall maximum stress value of the structure is 108.31 MPa, while, after iterative process analysis, the maximum stress value of the structure is 106.51 MPa, which is reduced by 1.5%, but the corresponding maximum stress position does not change. Once again, the iterative calculation does not affect the most unfavorable position of the structure.

The contours of the stress ratio before and after the iterative calculation is drawn, it can be found in Figure 6 that, before the iteration process is adopted, the maximum value of the stress ratio is 0.6503, which occurs at the position of unit 11,1297, while, after the iteration process, the maximum value of the stress ratio is 0.6496, which decreases by 0.11% and occurs at the same position. After the iterative calculation, not only the displacement and stress of the structure will change correspondingly but also the structural stress ratio will change accordingly, but the most unfavorable position will not change. Therefore, in the construction process, we need to pay attention to the changes in the structural internal force and deformation and take corresponding measures to control the changes in these variables in order to make the final formed structure safer.

In order to further determine the uniqueness of the final formed structure, the structure is iteratively calculated according to three parts on the basis of the overall iteration, as shown in the Figure 7, Figure 8, Figure 9 and Figure 10. Specific steps: now the installation error of the first part is added to the nodes involved in the first-step structure, 3 mm shall be taken as the standard and the remaining two–three-part structure will be iterated. In this process, only the node co-ordinates involved in the two–three-part structure will be adjusted, and the node co-ordinates involved in the first-part structure will not be adjusted. After the iteration is completed, the installation error of the second part will be added to the second-part structure. Then, this is looped through until the iteration is completed.

The purpose of dynamic adjustment is to determine the uniqueness of structural performance. The second step in the dynamic adjustment process is taken as an example to analyze the impact of adjusting the structure of the second part on the structure of the first part and the structure of the third part. The displacement diagram, stress diagram and stress ratio diagram of the first-part structure and the third-part structure in the first and second steps of dynamic adjustment are compared. The results are shown in the Figure 11, Figure 12 and Figure 13 below:

In the

Table 3. The results of dynamic adjustment of the second step on the structural performance of the first and third parts.

	Structural Parts	The Second Step	The First Step	Change Ratio
displacement (mm)	the first part	69.94	69.93	1.4/10,000
	the third part	44.52	44.74	−5/1000
stress (MPa)	the first part	106.56	106.55	1/10,000
	the third part	98.56	98.71	−1.5/1000
stress ratio	the first part	0.3917	0.3916	2.5/10,000
	the third part	0.6482	0.6493	−1.5/1000

, by analyzing the second step of dynamic adjustment, it can be seen that the structure of the first part and the third part are not greatly affected when the installation error is applied in the second step. This proves the validity of the iterative algorithm and the uniqueness of the structure can be determined by dynamic adjustment.

In the

Table 4. Comparison of structural performance results of single pre-deformation adjustment and the dynamic adjustment of the node co-ordinates.

	No Iteration	Once Pre-Deformation Adjustment	The Dynamic Adjustment of the Node Co-Ordinates	Rate of Change of the Former	Rate of Change of the Latter	The Number of the Node/Element
error of coordinate	71.6	0.0011	0.0051	——	——	11,796
displacement (mm)	71.6	69.9	68.32	2.40%	2.30%	11,796
stress (MPa)	108.3	106.51	104.81	1.65%	1.60%	100,394
stress ratio	0.6503	0.6496	0.6475	0.11%	0.32%	111,297

, the above values are the maximum values of each parameter; error of co-ordinate refers to the error between the node co-ordinates of the component in each process and the node co-ordinates of the component in the zero state.

Whether single pre-deformation adjustment analysis or the dynamic adjustment of the node co-ordinates, the displacement and stress of the structure will change correspondingly and the structural stress ratio will also change accordingly but the displacement, stress and stress ratio will not change in the most unfavorable position. Because the co-ordinate error of single pre-deformation adjustment and the dynamic adjustment of the node co-ordinates are very small, the effect of two kinds of adjustment is very good. However, when dynamic node co-ordinate adjustment analysis is carried out, the displacement, stress and stress ratio of the structure will be reduced on the basis of single pre-deformation adjustment. Therefore, in the construction process, we need to consider the dynamic adjustment analysis, pay attention to the internal force and deformation changes of the structure, and take corresponding measures to control the changes in these variables, so as to make the final formed structure safer, and verify the feasibility of the iterative algorithm once again.

4. Conclusions

(1)

Based on the finite element analysis software, this paper uses an iterative algorithm to conduct construction simulation analysis of the structure and obtains the pre-deformation values of each node co-ordinate of the structure. By comparison, it can be seen that, after iterative adjustment of co-ordinates, the overall error of the node co-ordinates after construction is rapidly reduced from that of the nodes in the zero state, which proves the effectiveness of the iterative method. It provides theoretical reference for practical engineering.

(2)

In this paper, only considering gravity, the iterative calculation of construction simulation of the exhibition hall part of a large-span steel latticed arch simulation is carried out, including single pre-deformation adjustment and dynamic node co-ordinates adjustment. By comparing the data of structural stress, deformation and stress ratio before and after the iteration, we can find that dynamic node co-ordinates adjustment is better than only considering single pre-deformation adjustment, the deformation, stress and stress ratio are reduced on the basis of single pre-deformation adjustment, and the final-state geometry configuration required by the structure is obtained through single pre-deformation adjustment and dynamic adjustment, so as to determine the bearing capacity of the structure.

(3)

The inverse analysis method mentioned in this paper is different from the presetting method of steel structure deformation during construction mentioned by predecessors. The previous methods only consider the initial configuration of the structure obtained by the initial iteration adjustment but do not consider the dynamic node adjustment process. This method is based on the initial configuration of the structure obtained through preliminary iterative adjustment and then the dynamic node co-ordinate adjustment is carried out (the influence of the installed part of the structure on the co-ordinate adjustment value of the uninstalled part can be considered; the influence of the uninstalled structure on the deformation of the installed structure can also be considered). Thus, with the progress of the construction process, the optimal approximation of the final state structure to the structure geometry in zero state and the accurate calculation of the bearing capacity performance can be realized.