STUDY ON SPATIAL STRESS EFFECT OF PC CONTINUOUS THIN-WALLED BOX GIRDER BRIDGE

In order to study the influence of spatial stress effect and shear lag effect on the cracking of PC continuous thin-walled box girder bridge, a spatial model was established by using ANSYS finite element software to analyze the internal stress distribution of the bridge. The test results are compared with the analysis results of spatial model and plane link system model through the load test of real bridge. The results show that the longitudinal stress is evenly distributed along the width direction, which means that the spatial stress effect and the shear lag effect have little influence on the downdeflection of the bridge. The shear lag coefficient at the longitudinal axis of midspan bottom plate and the intersection of bottom plate and web are larger than other positions, which is most likely to produce cracks caused by stress concentration and should be strengthened here in practical engineering. The results of load test show that the results of spatial finite element analysis are more reliable than those of plane link system calculation, and the design and construction based on the results of spatial finite element analysis is safer.


INTRODUCTION
The PC continuous box girder has the advantages of strong span capacity, large structural stiffness, beautiful appearance, smooth deck and easy maintenance, and is widely used in bridge structures with large span [1]. However, the section of box girder belongs to thin-walled structure. According to the investigation, the prestressed continuous thin-walled box girder bridge has cracked in different degrees after a period of operation [2]. Therefore, it needs to be equipped with a lot of structural reinforcement. There are many reasons that affect the crack generation, such as prestress spatial distribution, shear lag effect, prestress loss, overload, etc. Therefore, appropriate space analysis theory of box girder should be adopted to analyze the crack resistance of box girder, focusing on analyzing the spatial stress effect of the structure, so as to reflect the spatial stress effect of box girde. Then we can accurately understand the crack resistance of box girder structure.
The spatial stress analysis methods of PC thin-walled box girder bridges can be divided into two categories: analytical method and numerical method. Based on the analytical method and from different perspectives, some scholars have proposed such approximate calculation methods as energy variation method, generalized coordinate method, analogy beam method and frame analysis method for the calculation and analysis of torsion and distortion of box girder [3][4][5]. The calculation process of these methods is relatively complicated, and the calculation accuracy depends on the numerical solution accuracy of the differential equations. So, they are mostly applied to the research of the box-girder bridge with constant section, as the theoretical analysis results of the shear lag effect of the box girder with variable section are relatively few [6][7]. With the development of electronic computers, finite element method is very common in the analysis of box girder [8][9][10][11][12], such as Midas Civil, Adina, ANSYS and other structural linear and nonlinear finite element analysis software. With the help of computer finite element analysis, all the stresses on the box section, such as longitudinal bending stress, torsional warping stress, distorted warping stress, distorted transverse stress, shear lag and local load stress, can be obtained. By analyzing the data and results, researchers can accurately know the spatial stress distribution, magnitude and structural deformation of the components.
In this paper, a PC continuous thin-walled box girder bridge is selected as the research object. The finite element analysis software ANSYS is used to analyze the effect of spatial stress and shear lag on the deflection and cracking of the bridge. Through load tests, the fitting degree of spatial finite element model, plane beam analysis and test results is compared, so as to further verify the validity of spatial finite element model to analyze the spatial stress effect of PC continuous thin-walled box girder bridge. It provides reference for engineering practice.

BACKGROUND
The span of the bridge is 35 m+60 m+90 m+60 m+35 m, and the width combination is 0.75 m+10.5 m+0.75 m. The box girder is prestressed in longitudinal, horizontal and vertical directions, and the tensioning stress is 1290 MPa. Lateral view of the bridge is shown in Figure 1 and Figure   3507 1500

FINITE ELEMENT MODEL ANALYSIS
Using ANSYS finite element software to establish the space solid finite element model, reinforced concrete structure using 8-node solid element SOLID 65, can well simulate the Williams-Warnke strength theory based on the concrete three-direction force of the nonlinear response. Link8 unit is selected for prestressing tendon. Separate model is used to simulate the prestress in the model, and the longitudinal, vertical and transverse prestress tendons are separately modelled. Since the linear shape of the bottom flange is a quadratic parabola and there are many control nodes, this paper adopts the bottom-up modelling method, namely K-V and K-L modes. Considering the symmetry of the structure and load of the bridge, the model of the semi-full bridge is selected, which cannot only save the number of units and nodes, but also greatly save the calculation time. The model consists of 120,490 units and 165,435 nodes. In the model, X coordinate represents the transverse bridge direction, Y coordinate represents the vertical bridge direction, and Z coordinate direction is the vertical bridge direction. The box girder concrete bulk density is calculated by 26kN/m 3 , the guardrail load is calculated by 24kN/m.
According to the requirements of design specifications [13], the temperature load and the moving load were loaded according to the worst load condition of the mid-span bending moment of the main span. Working load includes deadweight, deck pavement weight, prestress, temperature gradient and moving load. The finite element model is shown in Figure 5.

SHEAR LAG EFFECT
In order to describe the influence of shear lag effect of box girder, the concept of shear lag coefficient is introduced in the project [14][15].

= real stress stress calculated according to elementary beam theory 
Under the effect of shear lag, the shear force transmits lag from the web to the flange slab, resulting in the uneven lateral distribution of normal stress. The actual longitudinal stress of the flange slab near the web is greater than the elementary beam theory calculation, which is called "positive shear lag effect". On the contrary, it is called "negative shear lag effect".

LOAD TEST ANALYSIS
According to the requirements of design specifications [13], the maximum effect of the combination of bending moment and shear force is considered in the test condition. The measuring points arrangement is shown in Figure 23 and Figure 24. The test results are shown in the tables and figures below. It can be seen that the theoretical calculation of longitudinal stress and principal stress have the same law as the test results, and the results are basically consistent with less error. In general, the results of spatial calculation are smaller than those of plane calculation. The maximum longitudinal stress difference is 0.35MPa, and the principal stress is 0.34 MPa. The spatial calculation are closer to the test results, which indicates that the spatial finite element model established in this paper accords with the practice and the theoretical calculation results are reliable. At the same time, the calculation of the spatial model is slightly larger than the test results, so the calculation is somewhat safe.  The stress at the main pier within the webs is abrupt, and it is easy to crack. Due to the influence of shear lag effect, the main stress from the longitudinal axis of the bottom flange to the web gradually decreases, and the stress concentration occurs at this place, where transverse cracks are more likely to occur than both sides. The spatial calculations are closer to the test results than those of plane calculations, the maximum longitudinal stress difference is 0.35MPa, it indicates that the spatial finite element analysis is more practical and reliable. Moreover, the spatial calculations analysis are generally larger than the test results, so it is safe to carry out design and construction according to the spatial finite element analysis.

(e)
The shear lag coefficient reaches its maximum value at the intersection of the top and bottom flange with web, and decreases to both sides. In the design and construction stage, the cracking and bending situation of this position should be fully considered, and the strengthening treatment should be carried out here. And reasonable arrangement of prestressed and structural reinforcement to prevent cracks caused by stress concentration. For bridges that have been cracked and flexed down, external prestress or steel plate can be used to reinforce them. Cracks should be treated before reinforcement. If the number of external prestressing steel strand is numerous, the scheme of dispersed arrangement along the top and bottom flange can be adopted.