Fuzzy comprehensive evaluation method for integral stability of box girder with corrugated steel webs

Abstract

The traditional stability evaluation method of corrugated steel web box girder ignores the calculation of evaluation index weight, which leads to large deviation of evaluation results. Therefore, a new fuzzy comprehensive evaluation method for the overall stability of box girder with corrugated steel webs is proposed. According to the structural characteristics of corrugated steel web box girder, the stability coefficient of corrugated steel web box girder is calculated, and the stability calculation index of corrugated steel web box girder is obtained. In this paper, the constraint equation of bridge instability process is introduced, and Midas civil software is used to simulate the instability of box girder with corrugated steel webs during bridge construction. Based on this, the instability of the bridge is analyzed, the index weight of the anti-instability ability of the box girder with corrugated steel webs under different loads is calculated, and the overall stability of the box girder with corrugated steel webs is evaluated by fuzzy comprehensive evaluation. The test results show that this method can accurately evaluate the overall stability of box girder with corrugated steel webs, and the calculation accuracy is increased by 32.7% and the calculation speed is increased by about 1.62 seconds. It has high credibility and authenticity.

Keywords

Corrugated steel webs box girder stability fuzzy comprehensive evaluation constraint equation Midas civil software

1. Introduction

With the increase of modern bridge span and the complexity of structure, the limitations of traditional prestressed reinforced concrete box girder gradually appear. It is mainly manifested in two aspects: First, the dead weight of concrete box girder is large. Second, in the process of bridge construction and use, the stress concentration caused by temperature difference, shrinkage and creep of web concrete section is more prominent. Various cracks will appear at the junction of web, roof and floor, which will seriously affect the bearing capacity and durability of the structure [1]. It reduces the self-weight of reinforced concrete box girder without affecting the force performance, and reduces stress cracks (bending, cutting, torsion) and unstressed cracks (shrinkage and creep cracks, temperature cracks). However, in the later stage of prestressing of the bridge, the loss of the prestress of the steel web is serious, and the longitudinal stiffness of the flat steel web is much greater than that of the concrete top and bottom plate. The later shrinkage and creep cause heavy stress at the junction of the top, bottom plate and the steel web. Distribution, resulting in the overall instability of the corrugated steel web box girder [2].

In order to solve this problem, there have been some good research results in related fields. In order to evaluate the overall stability of box girder with corrugated steel webs in reference [3], based on the analysis of torsional vibration of box girder, according to the characteristics of concrete box girder with corrugated steel webs, the theoretical calculation method of torsional vibration of concrete box girder with corrugated steel webs is derived, and the influence of diaphragm on torsional vibration is considered. The model of concrete box girder with corrugated steel webs is made, and its dynamic test and detailed spatial finite element analysis are carried out. The theoretical calculation method is used to calculate. In reference [4], the finite element analysis method was used to analyze the flexural performance, shear performance, torsional performance and shear lag effect of corrugated steel web composite box girder and flat steel web composite box girder with the same span, material, prestressed steel, top and bottom plate sizes; Compare the deformation and internal force distribution on the mid-span section and quarter-point section of the two models under different loads; The dynamic characteristics of two kinds of prestressed concrete composite box girder are compared. Some foreign scholars have put forward some research methods. For example, in the literature [5], the seismic response of concrete curved bridge considering the difference of column height and the number of spans is proposed. Five kinds of bridge models are studied, and several dynamic nonlinear time histories are analyzed based on seven different records. It can be found that increasing the column height and decreasing the number of spans will increase the peak displacement of columns, thus increasing the seismic vulnerability of bridges. The above traditional methods have some problems, such as large error, low reliability and not in line with the actual situation.

Therefore, a new fuzzy comprehensive evaluation method for the overall stability of box girder with corrugated steel webs is proposed. Fuzzy comprehensive evaluation method is based on the membership theory of fuzzy mathematics, which makes an overall evaluation of things or objects restricted by many factors, that is, transforms qualitative evaluation into quantitative evaluation through fuzzy mathematics [6]. In order to simulate the instability phenomenon of corrugated steel web box girder during bridge construction, the constraint equation of bridge instability process and Midas civil software are introduced to analyze bridge instability, which improves the problem that the calculation of instability coefficient is not accurate enough. The index weight of buckling resistance of box girder with corrugated steel webs under different loads is calculated, which improves the reliability of calculation results. The experimental results show that the proposed method has ideal application effect.

2. Fuzzy synthesis method for integral stability of box girder with corrugated steel webs

2.1 Structural characteristics of box girder with corrugated steel webs

According to the existing literature, corrugated steel webs mainly have box section and I-section. In this paper, box section composite box girder is selected for analysis and research. The structural drawing of composite box girder with corrugated steel webs is shown in Fig. 1. Compared with the traditional concrete box girder, this structure can effectively improve the prestress efficiency, reduce the weight of the structure, speed up the construction progress, and avoid the cracking of concrete webs. The corrugated steel webs are folded along the longitudinal direction of the bridge, which is very small compared with the longitudinal stiffness and bending stiffness of the top and bottom slab concrete, so the setting of diaphragm and prestressed reinforcement is also changed accordingly.

Figure 1.

Physical drawing and model drawing of composite box girder with corrugated steel webs.

The corrugated steel web is usually processed and formed by the factory, and the main components are: Straight plate length, inclined plate length, bending angle, height and thickness. The quality assessment of corrugated steel webs is based on its impact toughness and nitrogen content. The thickness of corrugated steel webs should be based on the overall bridge structure’s load-bearing capacity and also consider the minimum specification of the thickness of the steel plate. Generally, the minimum plate thickness of corrugated steel webs considered in design is 8 mm, and the maximum thickness is determined according to the use and construction conditions. The mechanical requirements are the primary factors to be considered in the design of corrugated steel webs, and then the shear resistance of webs should be checked, which should meet the basic concepts and requirements of bridge design [6].

2.2 Stability calculation index and judgment standard

According to the structural characteristics of box girder with corrugated steel webs. The structural instability of bridge under force mainly refers to the instability phenomenon of bridge under the action of external force, such as the external disturbance, which will aggravate the deformation and gradually increase the degree of deformation, and finally lead to the destruction of bridge structure [7, 8]. In many bridge instability projects, if only strength and stiffness are calculated, the safety of bridge and bridge construction can not be guaranteed. In order to ensure the safety of bridge instability and the safety of construction personnel, the finite element calculation method for the overall stability of bridge instability is proposed. Based on the traditional calculation method, the optimization design is carried out for the purpose of improving the calculation accuracy and speeding up the calculation speed. In the research process of the calculation method, the overall safety factor of each state of the bridge is defined as the ratio of the load and the design load when the bridge construction loses the bearing capacity. The expression of the stability factor is:

$\displaystyle p^{\prime}=\partial\cdot p^{\prime\prime}$ (1)

In the formula, $P^{\prime}$ and $P^{\prime\prime}$ respectively represent the design load and actual total load of bridge construction structure under the corresponding working condition of actual bridge stress instability, and $\partial$ is the safety factor of stable bearing capacity. Due to the force instability of the bridge needs to use a number of temporary equipment, so in the calculation process, we need to fully consider a number of factors [9]. In the design process of the calculation method, the whole process of bridge replacement construction is simulated, and the stress of each component of the bridge is analyzed. All the factors that may affect the construction stability are integrated and quantified, so as to realize the calculation of the stability coefficient. In order to intuitively reflect the overall stability of the bridge under force instability, based on the calculated coefficient index, the instability mode is divided into four stages. The specific stage division and the interval range of corresponding coefficient are shown in Table 1.

Table 1

Standard data of instability mode

Instability mode stage	Description of construction instability	Value range of stability coefficient
First order	No deformation and tipping tendency	$\leqslant$ 43.35
Second order	Slight deformation and slight inclination of construction structure	[43.35, 49.89]
The third stage	Obvious deformation and obvious inclination of construction structure	[49.89, 78.2]
Fourth order	The construction structure is seriously deformed or inclined	$>$ 78.2

2.3 Instability simulation based on MIDAS civil bridge construction finite element model

In order to ensure the accuracy of the overall stability calculation results of bridge construction, Midas civil software is used to build the corresponding finite element construction model [10]. Midas civil is a general finite element analysis software, which can be divided into pre-processing mode and post-processing mode. The pre-processing mode is mainly used to define the material and load parameters of modeling, and the post-processing mode is mainly the output value of calculation results. Moreover, the software can simulate the actual construction environment for static and dynamic analysis and linear and nonlinear stability analysis. In Midas civil software, the finite element model of bridge construction is built according to the following steps [11]. Firstly, the construction node and construction unit are established, and the material and interface are defined according to the relevant materials of bridge stress instability construction. Then, according to the construction purpose of bridge launching engineering, the boundary conditions of construction are defined, and the load condition factors are added to input the load. According to the analysis and calculation of the bridge pushing construction process, the calculation results are finally output, which is convenient for the staff to call and view.

The stress instability of the bridge is implemented by the process route of factory section manufacturing, highway transportation site, assembly area leasing and section pushing. The site installation adopts the combination of stress instability and in-situ lifting. The construction materials and layout that need to be prepared include the layout of construction road, water, electricity, lighting and other aspects. In addition, we also need to prepare sufficient mechanical equipment resources, set up temporary support system, crane assembly site, etc., to ensure the bridge stress instability work can be carried out smoothly [12].

Under the overall finite element model of the bridge stress instability, the construction project is simulated according to the jacking process, and the specific construction process is shown in Fig. 2.

Figure 2.

Process of bridge stress instability.

Taking the initial instable state as the initial working condition, the whole bridge instable work is divided into seven working conditions, including the initial jacking, the maximum rear suspension, the maximum front suspension of the guide beam, the maximum front suspension of the system, the one-third of the guide beam passing the temporary pier, the two-thirds of the guide beam passing the temporary pier, the front end of the steel beam reaching the temporary pier and the jacking in place. Through the multiple pushing process of multiple bridge segments, the force instability of the bridge is realized [13].

Taking the launching process of a span continuous bridge as an example, the structure is divided into two units. Since there is a support at the intermediate stage to maintain the stability of the left and right sides, it can be assumed that the longitudinal displacement of the intermediate node is 0. On this basis, the constraint equation of bridge instability process is introduced:

$\displaystyle v_{i}+\frac{1}{2}L\cdot\theta_{i}+v_{j}-\frac{1}{2}L\cdot\theta_% {j}=0$ (2)

In Eq. (2), $v_{i}$ and $v_{j}$ respectively represent the longitudinal degrees of freedom of $i$ and $j$ at both ends of the launching support, $\theta_{i}$ and $\theta_{j}$ are the angular degrees of freedom of the two nodes, and $L$ is the span between $i$ and $j$ nodes in the construction process. Under the constraint of the constraint equation, the problem that the support boundary changes at any time in the process of bridge instability can be solved. By substituting the constraint equation into the construction finite element model, the bridge stress instability model can be obtained in Fig. 3 [14, 15].

Figure 3.

Model diagram of overall stress instability of box girder with corrugated steel webs.

2.4 Bridge stress instability

Under the finite element model, according to the construction process of the bridge pushing technology, for each stage of the construction work, fully consider the internal and external factors of the construction to carry out the overall stress analysis of the bridge [16].

In the construction stage of bridge launching, the load distribution is calculated considering the dead weight of temporary support structure, environmental factors and other factors. Among them, wind load refers to the transverse static gust load of girder unit degree under the action of transverse wind. It can be expressed as:

$\displaystyle F_{H}=H^{\prime}\cdot H^{\prime\prime}\cdot V_{F}$ (3)

In the above formula, $H^{\prime}$ and $H^{\prime\prime}$ are the resistance coefficient and projection height of main girder in bridge engineering, and $V_{F}$ is the static array wind speed. Using the same calculation method, we can get the distribution of dead load and permanent load and the specific value [17].

In the finite element model, the plate element is used in the beam section of the bridge, and the structure and action principle of the permanent pier, temporary pier, construction beam and guide beam are fully considered, so as to realize the stress analysis of the whole bridge [18]. The specific situation of stress analysis in the construction process is shown in Fig. 4.

Figure 4.

Schematic diagram of stress analysis of bridge in the process of stress instability.

A beam segment is added to the permanent pier and temporary pier, and the beam segment node forms a contact pair with the permanent pier slideway node. Then, the uniformly distributed load is applied directly above the beam segment to simulate the self-weight of the beam segment. At the same time, the longitudinal bridge displacement is applied to the beam segment, and the contact analysis is used to transfer the friction between the beam and the pier during the jacking process [19, 20]. As the launching beam moves forward gradually, the mechanical performance of each part of the bridge beam body changes constantly, and the launching force can be calculated by Eq. (4).

$\displaystyle\left\{{\begin{array}[]{l}T=N\cdot\cos\phi\\ Y=N\cdot\sin\phi\\ \end{array}}\right.$ (4)

where $T$ and $Y$ are the forces along the curve and deviating from the curve, $N$ is the applied jacking force, and $\phi$ is the angle between the jacking direction $T$ and the tangent direction $Y$ .

2.5 Weight calculation of anti – buckling capacity index of box girder with corrugated steel webs under different loads

For a box girder structure with few stories, if each story is a failure mechanism, the anti – instability ability of the whole bridge story mainly depends on the vertical seismic structure between the multiple stories of the bridge. If the basic anti – instability ability $E_{0}$ of the bridge structure needs to be calculated based on the first ultimate deformation capacity index, use Eq. (5) to give the calculation formula of the basic anti – instability ability $E_{w}$ of the bridge layer [21]:

$\displaystyle E_{0}=\phi\left({C+\sum_{j}{a_{j}C_{j}}}\right)$ (5)

In the above formula, $C_{1}$ represents the anti – instability index with the smallest ultimate deformation capacity among the bridge layers; $C_{j}$ represents the index of anti – instability capacity of the $j$ – class vertical member in the bridge structure, and the value of $C_{j}$ is the ratio of the ultimate lateral bearing capacity of the vertical member to the gravity borne by the member; $a_{j}$ represents the reduction factor of class $j$ members [22, 23].

The factors that affect the anti – instability ability of bridges are the lateral bearing capacity between stories, which is the ductility structure with the maximum bearing capacity of each bridge story, that is, after the bridge girder structure is damaged, the story shear will not decrease obviously, and the story shear lateral displacement deformation relationship has the characteristics of ductile failure [24]. Through the natural disaster response analysis results, the basic anti instability ability of the bridge layer can be determined. It is shown in Eq. (6):

$\displaystyle E^{\prime}_{0}=\left\{{\begin{array}[]{l}\phi\sqrt{E_{0}}\\ \phi\sqrt{({CF_{H}})^{2}}\\ \end{array}}\right.$ (6)

Obtain the weight of the anti – instability index under different loads by Eq. (6).

Combined with the calculation results of the above two factors affecting the anti – instability ability of bridges, the anti – instability regularity of the whole bridge structure and its influence on its service life are comprehensively analyzed, and obtain the comprehensive anti – instability index $P_{s}$ of different bridge layers, namely:

$\displaystyle P_{s}=E^{\prime}_{0}\cdot T$ (7)

In the above formula, $T$ represents the service life of the bridge structure, which mainly considers the service life of the entire bridge structure and the usage conditions that cause the performance of the entire bridge structure to decline [25]. According to the specific situation, we can get the accurate value of $P_{s}$ .

Considering the directionality of natural disasters, the index $E_{0}$ of different bridge layers is determined respectively, and the value of $P_{s}$ also needs to be determined according to the horizontal direction.

2.6 Fuzzy comprehensive evaluation of stability

According to the overall stress analysis results of the bridge, the factors affecting the construction stability include the volume weight of the bridge materials, the stiffness of the launching structure and the temporary construction load. Considering all the influencing factors of bridge instability, the stability can be divided into the first type and the second type. According to the principle of two types of stability, the stability coefficient index is calculated. The main body of the guide beam is a flexural member, and the compression flange may lose its stability in the maximum stress state just like the compression member. The fuzzy comprehensive evaluation method for the stability of box girder with corrugated steel webs is mainly based on the anti-instability ability of the bridge. The following are the main contents of this method:

(1)
The full probability anti instability coefficient can more comprehensively reflect the anti-instability ability of the bridge corresponding to its basic acceleration;
(2)
Based on the comprehensive analysis of the related natural disasters, the probability density functions of different risk characteristics are calculated;
(3)
Appropriate bridge data and vulnerability parameters are selected to evaluate the characteristic stability of box girder with corrugated steel webs.

According to the natural disaster prediction and natural disaster investigation, the probability distribution of bridges in different failure levels can be obtained, but it can not accurately reflect the anti – instability ability of these bridges. The following gives the probability distribution of bridge structures in different failure states and the corresponding anti instability ability index. The anti – instability ability of the bridge is calculated:

$\displaystyle S=P_{s}\sum_{i=1}^{n}S^{\prime}\times P_{d}$ (8)

In the above formula, $S^{\prime}$ represents the anti – instability index of the bridge at the present stage, $P_{d}$ represents the damage degree of the bridge under the specified action, and $i$ represents the number of instability indexes of box girder with corrugated steel webs.

The damage degree of bridge under different loads is different. According to the above formula, the relationship between the expected value of anti – instability ability index and anti – instability effect can be established.

Use the following formula to give the full probability anti – instability index of the bridge:

$\displaystyle S^{\prime}=\int_{0}^{1}S^{\prime\prime}\times f_{GA}(\rho)d\rho$ (9)

In the above formula, $S^{\prime\prime}$ represents the expected value of buckling resistance index under load, and $f_{GA}(\rho)$ represents the characteristic probability density function of box girder with corrugated steel webs.

The cumulative function of bridge instability probability is given by using the following formula:

$\displaystyle K=1-P\{{S^{\prime}\geqslant S^{\prime\prime}}\}$ (10)

If Eq. (10) is transformed, there are:

$\displaystyle 1gK=1g[{1-P\{{S^{\prime}\geqslant S^{\prime\prime}}\}}]$ (11)

If the transcendental probability $P=$ 10% is substituted into Eq. (11), then:

$\displaystyle 1gK=1g[{1-0.1\{{S^{\prime}\geqslant S^{\prime\prime}}\}}]$ (12)

Bridges are mainly composed of most group bridges, and the vulnerability analysis method of bridges is mainly given below. In this paper, the static elastic-plastic analysis method is selected to analyze, and the cumulative probability of bridge failure state is given by using the following formula:

$\displaystyle P[{\textit{dsi}|S_{d}}]=\varphi\left[{\frac{1}{\beta_{\textit{% dsi}}}In\left({\frac{S_{d}}{S_{d,\textit{dsi}}}}\right)}\right]$ (13)

In the above formula, $\varphi$ represents the cumulative probability function of the standard normal distribution; $S_{d,\textit{dsi}}$ represents the mean value of the spectral displacement of the bridge at the damage level; $\beta_{\textit{dsi}}$ represents the standard deviation of the normal distribution of the damage state system.

Combining full probability anti-instability ability index $f_{\textit{PGA}}$ and bridge anti-instability ability index $p_{ga_{1}}$ , the fuzzy comprehensive evaluation standard $f$ corrugated steel web box girder is determined, namely:

$\displaystyle G=\frac{P[{\textit{dsi}|S_{d}}]}{f_{\textit{PGA}}({p_{ga_{i}}})}$ (14)

Combined with the stress analysis results of the bridge guide beam, it can be concluded that the overall stability of the flexural members in the main plane of the maximum stiffness can be expressed as:

$\displaystyle\frac{M_{x}}{\phi_{b}W_{x}f}\leqslant 1.0$ (15)

In the above formula, $M_{x}$ is the maximum bending moment of the bridge, $W_{x}$ is the section modulus, and $\phi_{b}$ is the overall stability coefficient of the bridge. The calculation results of the overall stability coefficient of the cantilever beam are compared with the set stability criteria, so as to judge whether the corresponding bridge launching project is in the stable stage.
3. Experimental results and analysis

In order to verify the calculation function of MIDAS civil finite element calculation method for the overall stability of the bridge under force instability, the relevant data of the actual bridge construction are used for experimental analysis, and whether the design of the finite element calculation method solves the problems existing in the traditional method is verified. Through the on-site inspection of the actual bridge construction project, different methods are used to analyze and calculate the bridge construction data, and the experimental results are compared and analyzed.

3.1 General situation of bridge engineering

The bridge construction project selected in this experiment is a bridge reconstruction and expansion project. The total length of the project is about 3.93 km, with Shigang road and Minle road at the East and West ends respectively. The current location is basically along the existing Caohu Avenue. It passes through S228 and Wuxing road in the form of tunnel, and then it is grounded. It extends eastward in the form of viaduct, passes through the planned central park, and connects with the existing Taidong road. The whole bridge construction project includes a new main line Viaduct with the starting and ending stake number of K5 $+$ 165.400 to K6 $+$ 369.000. The total length of the main line viaduct is 1203.6 m. From the structure of the bridge, the ramp bridge is 200 m long and the pedestrian non ramp bridge is 60 m long. Among them, the main line viaduct adopts prestressed concrete continuous beam with standard span of 31 m, yuanhetang adopts 40 $+$ 60 $+$ 40 m continuous steel box beam, and Xiangcheng Avenue adopts 44 $+$ 66 $+$ 44 m continuous concrete box beam. In the launching part of the bridge instability project, the steel box girder is divided into 80 pieces, a total of 8 sections, a total of 1948 T; The total weight of the guide beam is 81 T, and the actual launching weight is 2029 T, which is also the permanent load of the bridge construction project.

3.2 Experimental results and analysis

Under the background of the selected experimental project, the real-time stability coefficient calculation results of the project in the construction process are obtained by using the proposed method, and whether the bridge is in a stable state is judged. In this experiment, we also need to test the calculation function and application performance of the design method. In order to form the experimental comparison, we use the method of literature [3] and the method of literature [4] to compare the results obtained by different methods with the actual working condition data, compare the accuracy of the results obtained by the two methods, and count the time consumption of different methods.

The calculation method is applied to an example. According to the calculation process of the design method, the corresponding stability calculation results are obtained, as shown in Table 2.

Table 2
Stability calculation results of experimental bridge in the stage of stress instability

Construction stage	Calculation results of stability coefficient	Morphological characteristics of construction instability
1-2	15.88	The sequence of instability is 26-27-24-25-23-22, and the direction of instability is longitudinal
3-5	12.74-70.34	The order of instability is 24-23-25-26-27-22, and the direction of instability is longitudinal
6-12	41.8-66.5	The construction instability sequence is 26-23-25-24-27, the instability direction is longitudinal,
		and the instability direction of No. 26 beam end is transverse
13-15	39.9-39.3	According to the order of 26-23-25-24, the longitudinal instability of No. 26 beam end is
		followed by the longitudinal instability of No. 27 beam end
16	44.6	The longitudinal instability is in the order of 25-24-26-23, followed by 26-25 lateral instability
17-18	41.1-40.9	The order of instability is 26-25-24-23-27-22, and the direction of instability is longitudinal
19	45.9	The sequence of instability is 26-27-23-25-24-22, and the direction of instability is longitudinal
20	44.9	The sequence of instability is 27-26-25-24-23-22, and the direction of instability is longitudinal
21-22	44.5	The order of instability is 27-26-25-24-22-23, and the direction of instability is longitudinal
23-25	34.9-46.3	The order of instability is 26-27-25-23-24-22, and the direction of instability is longitudinal

According to the calculation results in Table 2, the relationship curve between the stability coefficient and the construction stage in the construction of bid Section 2 of bridge reconstruction and expansion project is drawn, as shown in Fig. 5.

According to the actual data of the second bid section of the reconstruction and expansion project, the corresponding stability calculation results are obtained by this method and the traditional method respectively. By comparing with the standard data, the evaluation errors of different methods are obtained. The evaluation error and evaluation time of this method, literature [3] method, literature [4] method and literature [5] method are calculated, and the comparison results about the calculation function are obtained, as shown in Table 3.

By analyzing and calculating the data in Table 3, it is found that the average error of the methods in Literature [3], Literature [4] and Literature [5] is greater than 0.5, and the average time consumption is higher than 3 s. The average evaluation error and time consuming of this method are 0.41 seconds and 2.71 seconds, respectively. Therefore, compared with the traditional method, the accuracy of this method is improved by 32.7%, and the calculation speed is improved by about 1.62 s.

Based on the above experimental results, the authenticity of the fuzzy comprehensive evaluation results of the overall stability of box girder with corrugated steel webs is tested by using the methods of literature [3], literature [4] and the proposed method. In this experiment, the model of composite box girder with corrugated steel webs including three, four and five middle diaphragms are established, as shown in Fig. 6.

Table 3

Comparison of error and time consumption of different methods

Construction stage	Methods of literature [3]		Methods of literature [4]		Methods of literature [5]		The proposed method
	Evaluation error	Evaluation time/s	Evaluation error	Evaluation time/s	Evaluation error	Evaluation time/s	Evaluation error	Evaluation time
The first stage	0.58	2.72	0.61	3.73	0.59	3.56	0.52	1.55
The second stage	0.12	5.84	0.58	4.83	0.54	4.21	0.76	1.65
The third stage	0.19	1.05	0.67	5.07	0.61	3.26	0.29	1.07
The fourth stage	0.59	2.83	0.37	5.85	0.41	3.68	0.37	1.73
The fifth stage	0.96	7.07	0.75	3.09	0.54	2.98	0.31	1.21
The sixth stage	0.47	5.28	0.77	2.73	0.52	3.64	0.41	1.03
The seventh stage	0.39	6.93	0.79	7.86	0.53	5.14	0.26	1.39

Table 4

Evaluation results of stress increase factor under the change of diaphragm number (unit: MPa)

Number of diaphragms/ piece	Symmetrical load	Eccentric load	Stress augmentation factor
			True value	Methods of literature [3]	Methods of literature [4]	The proposed method
3	0.80	1.22	1.46	1.86	1.86	1.46
4	0.89	1.58	1.35	1.92	1.55	1.35
5	0.95	1.76	1.32	1.77	1.10	1.32

Figure 5.

Relation curve of bridge stress instability stage and stability coefficient.

Figure 6.

Model of composite box girder with corrugated steel webs.

Figure 7.

Relationship between stress increasing factor and number of diaphragms of composite box girder with corrugated steel webs.

The symmetrical load and eccentric load are simulated on the composite box girder model with corrugated steel webs in Fig. 6, and the accuracy of stress increase factor is used to reflect the authenticity of evaluation results of different methods. The stress augmentation factor is the ratio of the maximum bending stress of fatigue damage to the maximum bending stress of straight pipe with the same bending moment, diameter and thickness. In this experiment, the relationship between the real stress increasing factor and the number of diaphragms of composite box girder with corrugated steel webs is shown in Fig. 7.

The evaluation results of stress increase factor under the three methods are shown in Table 4.

It can be seen from the data in Table 4 that the composite box girder with corrugated steel webs produces stress increase factor under symmetrical load and eccentric load. Under normal conditions, the greater the load is, the greater the stress increase coefficient is. However, when there are diaphragms in the composite box girder with corrugated steel webs, the more the number of diaphragms is, the smaller the stress increase coefficient of the composite box girder with corrugated steel webs is, which indicates that the more the number of diaphragms is, the better the stability of the composite box girder with corrugated steel webs is. Moreover, the stress increase coefficient obtained by the proposed method is completely consistent with the real value, which also verifies that the results obtained by the proposed method are more authentic.

4. Conclusion

This paper presents a fuzzy comprehensive evaluation method for the overall stability of box girder with corrugated steel webs. By analyzing the characteristics of box girder structure, the stability coefficient is calculated, and the instability coefficient is restrained by constraint equation, and the control coefficient is stable in a certain range. The instability process is simulated numerically, and the fuzzy comprehensive evaluation of the overall stability of box girder with corrugated steel webs is realized. Experiments show that the average evaluation error and time-consuming of this method are 0.41 seconds and 2.71 seconds, respectively. Has more accurate performance and reliability. It can provide certain theoretical basis for bridge construction.

The compression resistance of concrete roof and floor and the shear resistance of corrugated steel web obviously improve the overall shear performance and structural stability of bridge structure. The fuzzy comprehensive evaluation method for its stability proposed in this paper is of great help to the construction of large bridges, and can be used for the analysis of continuous composite box girder bridges with corrugated steel webs, PC composite box girder bridges, long-span composite girder bridges, etc. However, the parameters of this method are mainly studied from the longitudinal stress direction, and the research on prestressed concrete continuous box girder bridge with corrugated steel webs may be slightly insufficient, so it is necessary to further explore its practical applicability. However, in this study, due to the limited time, only natural factors of stroke were considered. In addition, rain and ice and snow are also one of the influencing factors of bridge stability, which will be further analyzed in the future research in order to get more ideal research results.

Footnotes

Acknowledgments

The research is supported by: Natural Science Foundation of Hunan Province, Study on the static mechanical properties and assembly method of composite box girder with multi-cell prefabricated corrugated steel webs (No. 2018JJ5005).

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