Numerical simulation analysis of wind load on an integral bridge with steel-concrete composite girder based on cloud platform

The integral bridge with steel-concrete composite girder will be affected by wind load in the natural environment, so the buffeting effect of wind on the integral bridge with steel-concrete composite girder cannot be ignored. In order to solve the above problems, the numerical simulation analysis on the wind load on integral bridge with steel-concrete composite girder based on cloud platform is carried out. Before the buffeting analysis of the bridge, the wind environment condition should be calculated. Taking the integral bridge with steel-concrete composite girder as an example, based on empirical formula, the influence of girder size change on static wind load and static wind load under different wind speeds are calculated and analyzed. With the help of Davenport fluctuating wind’s power spectrum, the fluctuating wind field of integral bridge with steel-concrete composite girder under certain wind speed is simulated by harmonic synthesis method, the wind load value of integral bridge with steel-concrete composite girder is simulated, and the structural design of bridge is carried out, in order to ensure the scientificity and safety of bridge design. The numerical simulation can correctly react the test law, and can predict the wind resistance of the structure with the existing model.


Introduction
The integral bridge with steel-concrete composite girder is a flexible structure.In the course of bridge development, steel frame stiffening girder appears earlier, which is a more traditional structural form.The integral bridge with steel-concrete composite girder has been widely used in different areas, and the structural form is also developing.Different from the steel frame stiffening girder, the steel-concrete composite stiffening girder adopts the combination of orthotropic steel deck and lower steel deck.In recent years, the application of steel-concrete composite stiffening girder is gradually increasing [1].Compared with steel frame stiffening girder, steel-concrete composite stiffening girder has the following two advantages: structural characteristics, the stiffness of stiffening girder is greatly improved [2].As a part of the section of the stiffening girder, the steel-concrete deck in the steel-concrete composite stiffening girder forms a more rigid and stable space structure with the main frame.
In the integral bridge with steel-concrete composite girder structure, the vertical, transverse stiffness and flexural torsional stiffness of the stiffening girder are improved.Bridges are lighter.On the one hand, compared with the steel-concrete composite separated stiffening girder, the joint structure of the lower steel frame and the upper deck of the steel-concrete composite girder is greatly simplified and integrated.On the other hand, on the premise of improving the overall stiffness of the stiffening girder, the section size of the components of the lower steel frame structure will be reduced [3].Due to the simplification of the structure of the stiffening girder, the lifting workload has been greatly reduced, and the construction period has been significantly reduced.Due to the direct combination of the bridge deck and the lower structure, there is no need to set the bridge deck support and bridge deck expansion joint, and the maintenance work and cost after operation are reduced.Driving comfort has been improved [4].The support and expansion joint of bridge deck lane are greatly reduced, which improves the stability of driving.
In terms of wind resistance performance, the wind resistance stability of steel frame stiffening girder and steel-concrete composite stiffening girder are quite different, and the aerodynamic control measures need to be adopted are also quite different.It is found that increasing the torsional stiffness of stiffening girder can effectively improve the flutter performance of bridge structure and enhance the critical wind speed of flutter, while the overall stiffness of steel-concrete composite stiffening girder is larger than that of steel frame stiffening girder [5].In the past, the calculation of bridge's wind load focused on the calculation of the three-component coefficient of static wind load, while the research on the parameters affecting static wind load and calculating specific fluctuating wind speed of each section of integral bridge with steel-concrete composite girder was less.Therefore, in this paper, based on cloud platform, the power spectral density matrix is adjusted, and the harmonic is combined to deal with the fluctuating wind speed spectrum.It can provide a reference for buffeting prevention research of wind load numerical simulation machine of integral bridge with steel-concrete composite girder.

Numerical characteristics of wind load
When studying the effect of wind on bridges, the natural wind near the ground is usually treated as mean wind and fluctuating wind.The mean wind is the mean value of wind speed and direction in a certain period of time, while the fluctuating wind is the wind whose speed and intensity change randomly with time.Wind speed includes two processes: long period and short period.The mean wind is usually the product of long period, which is much larger than the natural vibration period of bridge structure.Therefore, the effect of average wind on bridge structure can be considered as static wind load, which is generally determined by ground roughness coefficient and friction coefficient.
Fluctuating wind is a stochastic process of air flow.Because the instability in the initial stage is not considered, the characteristics of fluctuating wind are mostly random in bridge wind engineering [4].The power spectral density function of turbulence is one of the most important parameters in the fluctuating wind characteristics, and it is generally used to express the wind spectrum model.Davenport spectrum, Kaimal spectrum and so on are generally used in the longitudinal fluctuating wind speed spectrum of bridge's wind-resistance design, and the vertical fluctuating wind speed spectrum includes Panofsky spectrum and Lumley spectrum.
The wind force is decomposed and defined by the body axis and wind axis coordinate system of bridge section.In the body axis coordinate system, the three-components are lift F V , resistance F H and torque M r respectively, while in the wind axis coordinate system, the three-components are lift F L , resistance F D and torque M T respectively.Based on this, the three-components of wind load are simulated, as shown in Figure 1.Based on Figure 1, the static wind load on the unit length of the bridge structure is calculated as: Wind load resistance: Where, ρ is the air density, generally 1.293 with the unit of kg / m 3 ; U is the average wind speed, with the unit of m / s; A is the height of the main girder, with the unit of m; B is the width of the main girder, with the unit of m; L is the length of the calculated girder section, with the unit of m; C H , C V and C M are the resistance, lift and torque coefficients under the body shafting.And it further calculates the resistance influence coefficient, lift influence coefficient and torque influence coefficient under the three-component force coefficient, and the calculation formula is as follows： Resistance influence coefficient: Where,  is the angle of attack, D and K are the lift and resistance under the wind shaft system respectively, and the influence coefficient of static wind load can be calculated from the formula, to ensure the accuracy of the research results.

Numerical simulation of wind load on integral bridge with steel-concrete composite girder
For bridge structure, once flutter occurs, it will lead to catastrophic damage of bridge structure.In order to improve the flutter and vortex stability of long-span bridges, structural measures, aerodynamic optimization measures and mechanical measures can be adopted.For long-span steel separated frame bridge, the common aerodynamic measures for flutter stability include the setting of central stabilizer, deflector, wing plate, wind resistant cable, central slotting or sealing slot, optimized nozzle and railing, etc., and the research shows that the combination of multiple aerodynamic optimization measures has a greater effect on improving flutter performance than single aerodynamic optimization measures.The wind load of buildings is related to the shape and scale of buildings.The shape coefficient of wind load is used to reflect the influence of building shape on wind load.In the flow field, the fluid flows into the control body through the control surface, and also flows out of the control body through another part of the control surface.During this period, the fluid quality inside the control body will also change.
According to the law of conservation of mass, the difference between the inflow mass and the outflow mass should be equal to the increment of the mass of the fluid in the control body.The integral form of the continuity equation of fluid flow can be derived as follows:    ( 7 ) Where, d represents control body and n represents control surface.The first term on the left of the equation represents the increment of the internal mass of the control body (x, y, z), and the net flux flowing into the control body through the control surface.According to the Austrian -Gauss formula in mathematics, it can be transformed into differential form in rectangular coordinate system as follows: Where: t is the time, are flow in the x, y, z direction.If the incompressible homogeneous fluid is a constant, then there are: The law of conservation of momentum is the basic law that any flow system must satisfy.It can be expressed as the change rate of fluid momentum to time in the micro element body is equal to the sum of various external forces acting on the micro element body.Neglecting the incompressible flow of mass force f, the tensor form of N-S equations for solving instantaneous variables can be expressed as: ( 1 1 ) According to the principle of statistics, time average, space average and ensemble average are equivalent under ergodic conditions.Among the centralized averaging methods, time averaging is the easiest to implement, which was first proposed by Renault, so it is also called Renault averaging.From this, the continuity equation of mean flow of incompressible flow is obtained.
) Numerical simulation of wind load based on the above algorithm can ensure the accuracy and effectiveness of simulation results, and ensure the safety of bridge building structure.

Analysis of experimental results
In order to verify the effect of numerical simulation analysis of wind load on integral bridge with steelconcrete composite girder based on cloud platform, the finite element model of an integral bridge with steel-concrete composite girder is established by using the finite element analysis software ANSYS, and applied to the subsequent buffeting response analysis.According to the state of completed bridge, the influence of different length of compensation section model on the force test results of out of frame stiffening girder is studied to determine the reasonable length of compensation section model.According to the state of completed bridge and construction, the aerodynamic coefficient of steel-concrete composite stiffening girder is tested under -3 ~ + 3 degree wind attack angle and wind deflection angle of 0 ~ 90 degree (interval of 5 degrees).The specific test conditions are shown in Table 1.
After the installation of the test device, the instrument is calibrated by using 200 g qucode.The results are shown in Table 2.The force measurement result of the balance is close to the actual gravity of qucode, and the maximum error is only 0.255%, which meets the requirements of wind load test.The wind environment of the bridge site is located in the atmospheric boundary layer, and its natural wind has random characteristics.In order to facilitate the analysis, the existing research mainly gives the average wind characteristics and fluctuating wind characteristics of natural wind, and approximately decomposes them into average wind and mean wind.The expression of natural wind is obtained.Among them, Fen represents the natural wind, Kou represents the average wind, and Yun represents the fluctuating wind with an average of 0.

V U v
     (13) According to the above wind speed decomposition method, the static wind force can be obtained through the average wind when calculating the wind load of the bridge, and the buffeting force of the bridge is generated by the fluctuating wind.Therefore, the most important work of buffeting response time history analysis of the integral bridge with steel-concrete composite girder is to obtain the fluctuating wind speed time history of the bridge site.In order to better describe buffeting response of the integral bridge with steel-concrete composite girder under wind action along the bridge, the threedimensional wind field is described as follows； ( , ) ( ) The results of the wind load shape factor under the condition angle are compared and analyzed with the wind load shape factor given in the load code.The full-scale model is used in the numerical calculation, and the SST turbulence model is used.Due to the uniform grid division of the building surface, the overall average wind pressure shape coefficient of the building surface can be obtained according to the formula and compared with the results specified in the code.The comparison results are shown in Table 3.It can be seen from table 3 that there is little difference between the numerical analysis results on the windward side and those specified in the code, and the maximum deviation is about 3% when the wind direction angle is 90 degrees.In the side of 0 degree wind direction, the average deviation of numerical simulation results is 9% compared with the specification, and in the leeward side, the deviation is slightly larger, with 20%.On the side of 90 degree wind direction, the average deviation between the numerical simulation results and the code is 9%.The value of norm is relatively conservative and can meet the needs of engineering.Preliminary analysis of the reasons for the difference shows that the shape factor of wind load specified in the specifications listed in the above table is a result of simplification and mathematical statistics, and the numerical analysis will more or less have some errors, so the results will have some deviations.The results show that the flutter stability of the steel-concrete composite stiffening girder is better than that of the steel frame stiffening girder; the combination of the central sealing groove of the bridge deck and the upper and lower central stabilizing plates can improve the flutter stability of the steel-concrete composite stiffening girder.
The flutter stability of steel frame stiffening girder becomes worse with the change of wind attack angle from + 50 to 50, while the change trend of steel-concrete composite stiffening girder is opposite.In order to study the static wind resistance, lift and torque of the main girder under different wind speeds, the resistance F D , lift F L and torque M T under 23.2m/s and 16m /s wind speeds are calculated, and their changes under different main girder sizes are compared.The results are shown in Figure 2-4.It can be seen from Figure 2-4 that the resistance F D gradually increases with the increase of the height of the main girder, and the lift F L and torque M T gradually increase with the increase of the width of the main girder.The above changes are relatively large, indicating that the height and width of the main girder have a significant impact on the resistance, lift and torque.It can further calculate the shape coefficient of each surface of wind load test and the shape coefficient of each surface calculated by numerical simulation, and make a comparison between the two results, as shown in   4-6 that no matter which operating angle, the calculation results of the wind pressure shape coefficient on the windward side of the numerical simulation are close to the results of the wind load test, and are larger than the results of the wind load test.In general, the results of numerical simulation and wind load test are consistent.

Conclusion
The reliability of numerical simulation method is verified by comparing with wind load test.The drag coefficient of integral cables of steel-concrete composite girder with different inclination and wind deflection angle is measured.The difference between the test value and the calculation of static wind load along the bridge in the code is compared.The buffeting time history analysis method considering only buffeting resistance along the bridge is proposed.The results are compared with those calculated in the code.The numerical simulation can correctly react the test law, and can predict the wind resistance of the structure with the existing model.

Figure 1 .
Figure 1.Three-component action of wind load.

Figure 2 .
Figure 2. Variation of static wind load resistance caused by girder height.

Figure 3 .
Figure 3. Change of static wind load lift caused by girder width.

Figure 4 .
Figure 4. Variation of static wind load torque caused by girder width.

Table 2 .
Calibration results of experimental data.

Table 3 .
Comparative analysis of wind load shape coefficient.

Table 4 .
Comparison of simulation coefficient results of wind load under 0 ° condition angle.

Table 5 .
Comparison of simulation coefficient results of wind load under 90 ° condition angle.

Table 6 .
Comparison of simulation coefficient results of wind load at 180 °condition angle.