CN115470677A - Rapid test and evaluation method for bearing capacity of integral box girder bridge - Google Patents
Rapid test and evaluation method for bearing capacity of integral box girder bridge Download PDFInfo
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Abstract
The invention belongs to the technical field of structural safety detection, and discloses a rapid test and evaluation method for the bearing capacity of an integral box girder bridge, which is used for carrying out rapid static and dynamic test on the box girder bridge; acquiring a box girder bridge bearing capacity evaluation benchmark finite element model; and carrying out structural bearing capacity assessment based on the reference model. The invention utilizes the moving load to rapidly cross the bridge, realizes the rapid test and acquisition of the quasi-influence coefficient and the dynamic characteristic of the bridge structure, and effectively solves the problems of high cost and long time of the traditional load experiment. A bridge bearing capacity evaluation reference finite element model is obtained by using a model correction technology, so that the model can be matched with the overall and local dynamic and static characteristics of an actual bridge at the same time, and the problem of distortion of a single objective function optimization result is solved. In addition, the bearing capacity evaluation method can consider the difference of the bearing capacities of different stressed members, and solves the problem that the traditional detection and calculation coefficient easily causes poor consistency of the bearing capacity evaluation results of different members.
Description
Technical Field
The invention belongs to the technical field of structural safety detection, and particularly relates to a rapid test and evaluation method for bearing capacity of an integral box girder bridge.
Background
In the past decades, bridge construction business has been developed vigorously, and the number of bridges in China has reached hundreds of thousands. The integral box girder bridge is widely applied to the construction of highway bridges due to strong spanning capability and good integral stress performance. The design service life of the bridge is as long as dozens of years or even one hundred years, and during the operation, the environmental influence, the material aging and the long-term action of the vehicle load can bring great threat to the operation safety of the bridge and greatly affect the safe bearing capacity of the bridge. Once a sudden accident happens, the traffic is seriously hindered, and economic loss and casualties are caused. Therefore, in order to ensure the safe operation of the bridge, the regular evaluation of the bearing capacity of the bridge is an essential link in the bridge maintenance and management process.
Box girder bridges are often important traffic hubs and their load carrying capacity is one of the most important properties of box girder bridges. At present, the bearing capacity of a bridge is generally evaluated by combining technical survey, load test and analytical calculation according to the specification JTG J21-2011 and JTG/T J-01-2015. However, carrying capacity assessment by means of load tests requires long-time traffic closure, and renting a large number of heavy trucks to load the bridge so as to make the control section reach a specified value, which is time-consuming and labor-consuming, and has a potential risk of damage to the bridge structure. Therefore, how to develop a rapid test method to replace the traditional load test becomes an urgent problem to be solved in bridge bearing capacity evaluation.
In addition, in the conventional bearing capacity evaluation method, the resistance effect is corrected by using a detection coefficient converted from the result of a load test, and then bearing capacity evaluation is performed. The measure is to reflect the performance difference between the design model and the actual bridge. However, the difference between the real and theoretical performances of the structure is reduced to the same coefficient for consideration, and the degradation conditions of the bridge at different positions and under different limit states are considered to be consistent, which is also deviated from the actual conditions and can cause the evaluation result to be conservative or dangerous. In addition, the load effect calculation and bridge evaluation are based on a design model or simplified model, which is inconsistent with the current bridge performance, and therefore the resistance results need to be corrected by load testing. Therefore, if a model capable of reflecting the real state of the bridge exists, the model can be directly used for comparing the load effect and the resistance effect of the bridge, and whether the bearing capacity of the bridge reaches the standard or not can be accurately evaluated. The model closer to reality means that different positions and different limit states of the bridge can be judged respectively, and the evaluation result that the resistance is corrected through the check calculation coefficient and is conservative or biased to danger is avoided.
Therefore, the method for rapidly testing and evaluating the bearing capacity of the integral box girder bridge is researched, the bridge testing efficiency can be effectively improved, the testing cost is reduced, and the accuracy and the reasonability of the bearing capacity of the bridge can be obviously improved by adopting the corrected finite element model. Therefore, the method has important significance for evaluating the bearing capacity of the integral box girder bridge.
Disclosure of Invention
The invention aims to provide a rapid test and evaluation method for the bearing capacity of an integral box girder bridge, which comprises the following specific steps:
(1.1) obtaining the quasi-influence coefficient by the mobile load test
The quasi-influence coefficient is obtained by acquiring structural vehicle-induced response data generated when one two-axis test vehicle passes through a bridge; the quality of a test vehicle is required to enable the bridge to generate stable response data with high signal-to-noise ratio;
the vehicle loading principle is that a large part of driving areas of the bridge are covered by fewer vehicle driving times; the loading process satisfies the following criteria: 1) The vehicle drives across the bridge at a low speed not exceeding 5km/h, so that the dynamic effect of the vehicle on the structure is reduced as much as possible; 2) The vehicle drives across the bridge on a single lane, and the lane can not be switched in the midway; 3) According to the number of lanes designed for the bridge, the vehicle needs to completely run on each lane at least once;
the structural response to be measured is the strain or deflection of the main beam; in order to improve the signal-to-noise ratio of the structural vehicle-induced response measurement data, the measurement positions are selected from the span center and the quarter span section of the main beam so as to ensure that a larger vehicle-induced response is obtained; when the deflection of the main beam is measured, the deflection is basically consistent in distribution of the whole section, so at least 2 measuring points need to be symmetrically arranged on the bottom surface of the main beam; when the strain of the main beam is measured, the strain measurement values on the same section of the box girder are considered to have larger difference, strain measurement points are uniformly distributed at a bottom plate of the box girder, the number of strain sensors is not less than 2n-1, and n is the number of webs of the vector section, so that the relatively complete strain distribution condition of the bottom plate of the main beam is obtained;
(1.2) obtaining structural dynamic characteristics by dynamic test
Identifying modal parameters of the bridge by collecting acceleration response of a main beam under forced vibration of the bridge structure; adopting wind load as an excitation mode of the bridge, applying unknown excitation in a random environment or applying known excitation artificially, and identifying modal parameters of the excitation;
the dynamic response is mainly measured by acceleration response, and is obtained by an accelerometer arranged on a structure; measuring points are arranged in a net form to obtain the acceleration response of a full bridge and the complete bridge deck vibration mode; in order to obtain a smooth vibration mode of the bridge deck, measuring points of the vibration mode are required to meet certain density arrangement; the arrangement of the longitudinal bridge sensors ensures that the vibration mode curve is smooth, and the arrangement of the transverse bridge sensors is at least two rows or more for identifying the torsional vibration mode of the bridge;
(2.1) a finite element modeling method of the box girder bridge;
the finite element model of the bridge is built by using plate shell units, and the box girder section web, the top plate and the bottom plate are built by the plate shell units with the same actual thickness as the components; adding additional rigidity at the bridge bearing by using a spring unit so as to consider the situation that the constraint condition of the bridge bearing is not ideal and simple;
(2.2) bridge finite element model correction objective function establishment
The initial finite element model of the bridge is different from the actual bridge structure, a model optimization objective function needs to be established, and a finite element model conforming to the actual structure is obtained in a model correction mode; the objective function for optimizing the parameters of the bridge initial finite element model consists of three parts, namely a strain objective function, a frequency objective function and a vibration mode objective function;
establishing a multi-point strain objective function according to the principle that the axial forces of the main beam bottom plate are equal; the strain of the box girder and the transverse position form a cubic function relationship, and the strain obtained by the measuring points is fitted according to the cubic function to obtain the strain distribution of the whole bottom plate; and integrating the strain to obtain the axial force T of the bottom plate, wherein the formula is (1):
T(y j )＝E·t·∫ε(x,y j )dx (1)
wherein: e is the elastic modulus of the main beam bottom plate; t is the thickness of the bottom plate; x is the position coordinate of the strain point of the bottom plate along the transverse bridge direction; y is j The driving position coordinate of the corresponding test vehicle along the longitudinal bridge direction when the strain data is sampled for the jth time; ε (x, y) j ) And the strain of the bottom plate is shown along with the change of the longitudinal bridge position and the transverse bridge position of the bottom plate of the box girder of the test vehicle. Thus, a strain objective function F is established 1 As shown in the following formula:
wherein k is the order of the bridge structure modal frequency participating in model correction; f. of i e And f i a Respectively measuring value and theoretical calculation value of ith order frequency of the structure; phi (phi) of i e And phi i a Respectively measuring and theoretically calculating the ith order vibration mode vector; beta and gamma are weight coefficients, the weight coefficients being taken to be 1;
frequency objective function F 2 And mode shape objective function F 3 As follows:
wherein k is the order of the bridge structure modal frequency participating in model correction; f. of i e And f i a Respectively measuring value and theoretical calculation value of ith order frequency of the structure; phi i e And phi i a Respectively measuring and theoretically calculating the ith order vibration mode vector; beta and gamma are weight coefficients, the weight coefficients being taken to be 1;
when all the response objective functions are combined in a normalized mode, namely the weight factors are set as the reciprocal of the initial value of each objective function, and the final combined bridge finite element model correction objective function is shown as a formula (6):
wherein F i,0 Is a corresponding objective function F of the bridge finite element model before correction i Is started.
(2.3) finite element model correction for box girder bridge bearing capacity evaluation
Before the bridge finite element model is corrected, optimization parameters need to be determined, the parameter determination method is a sensitivity analysis method, the material density, the elastic modulus, the bridge deck pavement thickness and the additional rigidity of the support are selected as alternative optimization parameters, and the optimization parameters are finally determined according to the sensitivity analysis result; the formula for the sensitivity analysis is as follows:
wherein F (θ) is the objective function determined according to equation (6); theta.theta. i For the ith sample point of the candidate optimization parameter for the bridge, Δ θ = 1%. Theta, θ 1 And theta 2 Upper and lower limits for the optimized parameters; selecting the upper limit and the lower limit of the optimized parameters according to the possible variation range of the optimized parameters; the additional rigidity of the support is used as a necessary optimization parameter, and the value range of the additional rigidity is exponentially changed, so that the sensitivity is very small compared with other parameters; therefore, sensitivity comparison is carried out on the groups of the additional stiffness of different supports independently;
after the optimization parameter selection is completed, optimizing the objective function by using a Rosenbrock algorithm, and reducing the error between the bridge finite element model and the actual structure; after the optimization algorithm is executed, a bridge structure finite element model which is in good conformity with an actual bridge structure is obtained, namely, the bridge structure finite element model is used for subsequent bridge bearing capacity evaluation;
After obtaining the corrected bridge structure finite element model, evaluating the load effect according to the formula (8):
wherein, CRF is bridge state evaluation index; gamma ray 0 Is a structural importance coefficient; s is a load effect and is obtained by loading the corrected model according to a design load or a check load; r is the resistance effect of the control section, the bearing capacity provided by the steel bars and the concrete is calculated according to the design specification, and reduction is carried out according to the technical survey result; when CRF is used<And 1.05, judging that the bearing capacity of the bridge meets the requirement.
The invention has the beneficial effects that:
1. the method adopts the moving load to pass the bridge quickly to obtain the strain or deflection standard influence coefficient of the bridge girder, and takes the girder vibration data obtained by the dynamic test as supplement, thereby overcoming the defects of long loading time, more measuring points and more loading vehicles of the traditional bridge load test;
2. a model correction multi-objective function consisting of a space quasi-influence coefficient and structural modal parameters is constructed, the key parameters to be optimized for bridge bearing capacity model correction are determined through sensitivity analysis, a bearing capacity evaluation model is obtained through optimization based on a Rosenbrock method, and the problem of distortion of a single objective function optimization result is solved;
3. the bearing capacity evaluation method based on the corrected bridge model is provided, the load effect of the corrected model is directly used for evaluation, the difference of evaluation of the bearing capacities of different stressed members is considered, and the problem that the consistency of the evaluation results of different members by the bearing capacity detection coefficient in the specification is poor is solved.
Drawings
FIG. 1 is a schematic diagram of a strain and displacement sensor arrangement for the method of the present invention;
FIG. 2 is a flow chart of an implementation of the method employed in the present invention;
FIG. 3 is a two-span continuous box girder bridge in an embodiment of the method of the present invention: (a) a real bridge photo; (b) a general layout; (c) section A-A;
FIG. 4 is a schematic diagram of a moving load test path in an embodiment of the method of the present invention;
FIG. 5 is a diagram of a strain sensor mounting location in an embodiment of the method of the present invention;
FIG. 6 is a graph of strain results in an embodiment of the method of the present invention;
FIG. 7 is a diagram of an acceleration sensor mounting location in an embodiment of the method of the present invention;
FIG. 8 is a graph of frequency and mode results in an embodiment of the method of the present invention: (a) order 1 with a frequency of 6.02Hz; (b) order 2 with a frequency of 7.34Hz; (c) 3 rd order with a frequency of 13.03Hz; (d) order 4 with a frequency of 14.40Hz; (e) order 5 with a frequency of 18.17Hz; (f) order 6 with a frequency of 18.78Hz;
FIG. 9 is a schematic illustration of the loading of a static test in an embodiment of the method of the present invention;
FIG. 10 is a diagram illustrating the results of sensitivity analysis in an embodiment of the method of the present invention: (a) a first set of parameters; (b) a second set of parameters.
Detailed Description
The following further description is made with reference to the drawings and an embodiment.
As shown in FIG. 2, a certain span is 24m +24m, the cross section of the two-span reinforced concrete T-shaped rigid frame bridge adopts a concrete single-box single-chamber variable cross section box girder, the width of the bridge deck is 6m, and the effective pedestrian passing width is 5.5m. The design load is 5.0kN/m of crowd load 2 And C50 concrete is poured for the superstructure and the pier. The bridge was subjected to a moving load test and a dynamic test according to the steps shown in fig. 3, and model correction was completed based on the measured data. In addition, a static test was performed to verify the correctness of the evaluation model correction. And finally, finishing the evaluation work based on the correction model.
(1) Box girder bridge field test
(1.1) moving load test
In the moving load test, a trolley pair carrying a water tank is adopted to slowly run on a bridge, and the loading path is shown in figure 4. The total mass of the trolley and the pushing personnel is about 750kg. The strain sensors are installed on the bottom plate and the web plate of the left midspan section of the bridge, as shown in fig. 5. For data quality reasons, only the strain sensor data on the base plate is used for further model corrections. The strain sensor data is filtered and deshifted as shown in fig. 6.
(1.2) dynamic test
The extraction of the dynamic characteristics is to extract the frequency and the vibration mode of the bridge by measuring the acceleration response attenuation change in the full-bridge range under the excitation of an external load. The bridge deck acceleration sensors are arranged in 54 numbers, the schematic diagram of the sensor arrangement is shown in FIG. 7, and the specific arrangement form is; each span of the bridge is divided into 10 equal parts along the longitudinal direction, 18 sensors are arranged on the two spans, and 3 rows of sensors are arranged on the transverse direction. The method for calculating the frequency and the vibration mode of the acceleration response is a random subspace method, and the obtained 1 st to 6 th order frequency and vibration mode of the bridge structure are shown in fig. 8. Wherein, 1, 2, 4 and 6 orders of vibration mode mainly takes bending as well as 3 and 5 orders mainly takes twisting.
(1.3) confirmatory static load test
In order to verify the correctness of the subsequent optimization result, the bridge is loaded in a water bag loading mode, and the displacement response of the two spans of the bridge is obtained. The water bag loading position is the midspan and quarter span position of the east span of the bridge. The loading scheme is shown in figure 9. And a displacement meter is arranged at the middle position of the two spans and is used for measuring the deflection of the loaded middle span of the water bag.
(2) Assessment model modification
A finite element model of the box girder bridge is built by using the plate shell unit, and the spring unit is added at the support for simulating the situation that the support is not ideal simple support. The model has the optional optimized parameters of mass, elastic modulus of a top plate, a web plate, a bottom plate, a partition plate and piers, bridge deck pavement, translation and rotation additional rigidity of a left support, a right support and a middle pier, and sensitivity analysis is carried out by using a formula (7). The quality, the elastic modulus of the top plate, the web plate, the bottom plate, the partition plate and the bridge pier are sequentially numbered as No. 1-7 as a first group of parameters; the translational additional stiffness of the left support, the right support and the middle pier, and the rotational additional stiffness of the left support, the right support and the middle pier are a second group of parameters which are sequentially numbered as No. 8-13. The results of the sensitivity analysis are shown in FIG. 10. The finally determined optimized parameters include the mass, the elastic modulus of the top plate, the web plate and the bottom plate, and the translational and rotational additional rigidity of the left support and the right support. The model is optimized by using a Rosenbrock algorithm to be closer to the actual condition, the optimization time is about 2 hours, and the upper and lower limits of the optimization parameters and the optimization result are shown in Table 1. The results of model correction were verified using the displacement of the static load test, as shown in table 2. The maximum error is about 10%, and the model is well matched with the measured data. The model can be used for evaluation work of subsequent models.
TABLE 1 results of model corrections
TABLE 2 static test verification results
(3) Load bearing capacity assessment
And applying a check load, namely a design load, on the corrected model according to the worst condition, and calculating the corresponding response of the control section. Taking the bending resistance bearing capacity of the positive section as an example, the control section is positioned near each span, the worst load is applied to the whole bridge floor corresponding to a single span, the combined bending moment caused by the self weight of the control section and the load of people is 4094 kN.m, and the bending resistance bearing capacity of the control section is 8740 kN.m. Then the bridge condition evaluation index can be obtained.
The calculated bending resistance bearing capacity of the box girder bridge completely meets the requirement, and the box girder bridge has larger bearing capacity reserve.
Claims (1)
1. A rapid test and evaluation method for bearing capacity of an integral box girder bridge is characterized by comprising the following steps:
step 1, box girder bridge rapid static power test
(1.1) obtaining the quasi-influence coefficient by the mobile load test
The quasi-influence coefficient is obtained by acquiring structural vehicle-induced response data generated when one two-axis test vehicle passes through a bridge; the quality of a test vehicle is required to enable the bridge to generate stable response data with high signal-to-noise ratio;
the vehicle loading principle is that a large part of driving areas of the bridge are covered by fewer vehicle driving times; the loading process meets the following criteria: 1) The vehicle drives through the bridge at a low speed not exceeding 5km/h, so that the power effect of the vehicle on the structure is reduced as much as possible; 2) The vehicle drives across the bridge on a single lane in a straight line, and the lane can not be switched in the midway; 3) According to the number of lanes designed by the bridge, the vehicle needs to completely run on each lane at least once;
the structural response to be measured is the strain or deflection of the main beam; in order to improve the signal-to-noise ratio of the structural vehicle-induced response measurement data, the measurement positions are selected from the span center and the quarter span section of the main beam so as to ensure that a larger vehicle-induced response is obtained; when the deflection of the main beam is measured, the deflection is basically consistent in distribution of the whole section, so at least 2 measuring points need to be symmetrically arranged on the bottom surface of the main beam; when the strain of the main beam is measured, the strain measurement values on the same section of the box girder are considered to have larger difference, strain measurement points are uniformly distributed at a bottom plate of the box girder, the number of strain sensors is not less than 2n-1, and n is the number of webs of the vector section, so that the relatively complete strain distribution condition of the bottom plate of the main beam is obtained;
(1.2) obtaining structural dynamic characteristics by dynamic test
Identifying modal parameters of the bridge by collecting the acceleration response of the main beam under the forced vibration of the bridge structure; adopting wind load to the excitation mode of the bridge, applying unknown excitation in a random environment or known excitation applied artificially, and identifying modal parameters of the excitation;
the dynamic response is mainly measured by the acceleration response, and is obtained by an accelerometer arranged on the structure; the measuring points are arranged in a net form to obtain the acceleration response of a full bridge and the complete bridge deck vibration mode; in order to obtain a smooth vibration mode of the bridge deck, measuring points of the vibration mode are required to meet certain density arrangement; the arrangement of the longitudinal bridge sensors ensures that the vibration mode curve is smooth, and the arrangement of the transverse bridge sensors is at least two rows or more for identifying the torsional vibration mode of the bridge;
step 2, obtaining an evaluation model of the box girder bridge
(2.1) Box girder bridge modeling method
The finite element model of the bridge is built by using plate shell units, and the box girder section web, the top plate and the bottom plate are built by the plate shell units with the same actual thickness as the components; adding additional rigidity at the bridge bearing by using a spring unit so as to consider the situation that the constraint condition of the bridge bearing is not ideal and simple;
(2.2) bridge finite element model correction objective function establishment
The initial finite element model of the bridge is different from the actual bridge structure, a model optimization objective function needs to be established, and a finite element model which is consistent with the actual structure is obtained in a model correction mode; the objective function for optimizing the parameters of the bridge initial finite element model consists of three parts, namely a strain objective function, a frequency objective function and a vibration mode objective function;
establishing a multi-point strain objective function according to the principle that the axial forces of the main beam bottom plate are equal; the strain of the box girder and the transverse position form a cubic function relationship, and the strain obtained by the measuring points is fitted according to the cubic function to obtain the strain distribution of the whole bottom plate; and integrating the strain to obtain the axial force T of the bottom plate, wherein the formula is (1):
T(y j )＝E·t·∫ε(x,y j )dx (1)
wherein: e is the elastic modulus of the main beam bottom plate; t is the thickness of the bottom plate; x is the position coordinate of the base plate strain point along the transverse bridge direction; y is j The driving position coordinate of the corresponding test vehicle along the longitudinal bridge direction when the strain data is sampled for the jth time; ε (x, y) j ) Representing the baseplate strain along with the change of the longitudinal bridge position and the transverse bridge position of the baseplate of the box girder of the test vehicle; thus, a strain objective function F is established 1 As shown in the following formula:
wherein: m is the number of times of passing the bridge of the test vehicle; n is the total sampling times of the strain of the test vehicle in one-time bridge passing time period; alpha is alpha i Corresponding weight coefficients for the jth bridge crossing of the test vehicle are taken as 1; t is i e And T i a Respectively taking a measured value and a theoretical calculated value of the main beam bottom plate axial force;
frequency objective function F 2 And mode shape objective function F 3 As follows:
wherein k is the order of the bridge structure modal frequency participating in model correction; f. of i e And f i a Respectively measuring value and theoretical calculation value of ith order frequency of the structure; phi i e And phi i a Respectively measuring and theoretically calculating the ith order vibration mode vector; beta and gamma are weight coefficients, the weight coefficients being taken to be 1;
when all the response objective functions are combined in a normalized mode, namely the weight factors are set as the reciprocal of the initial value of each objective function, and the final combined bridge finite element model correction objective function is shown as a formula (6):
wherein, F i,0 Is a corresponding objective function F of the bridge finite element model before correction i An initial value of (1);
(2.3) finite element model correction for box girder bridge bearing capacity evaluation
Before the bridge finite element model is corrected, optimization parameters need to be determined, the parameter determination method is a sensitivity analysis method, the material density, the elastic modulus, the bridge deck pavement thickness and the additional rigidity of the support are selected as alternative optimization parameters, and the optimization parameters are finally determined according to the sensitivity analysis result; the formula for the sensitivity analysis is as follows:
wherein F (θ) is the objective function determined according to equation (6); theta i For the ith sample point of the candidate optimization parameter for the bridge, Δ θ = 1%. Theta, θ 1 And theta 2 Upper and lower limits for the optimized parameters; selecting the upper limit and the lower limit of the optimized parameters according to the possible variation range of the optimized parameters; the additional rigidity of the support is taken as a necessary optimization parameter, and the value range of the additional rigidity is exponentially changed, so that the sensitivity is causedSmall compared to other parameters; therefore, sensitivity comparison is carried out on the groups of the additional stiffness of different supports independently;
after the optimization parameter selection is completed, optimizing the objective function by using a Rosenbrock algorithm, and reducing the error between the bridge finite element model and the actual structure; after the optimization algorithm is executed, a bridge structure finite element model which is in good conformity with an actual bridge structure is obtained, namely the bridge structure finite element model is used for subsequent bridge bearing capacity evaluation;
step 3, evaluating the bearing capacity of the box girder bridge
After obtaining the corrected bridge structure finite element model, evaluating the load effect according to the formula (8):
wherein, CRF is bridge state evaluation index; gamma ray 0 Is a structural importance coefficient; s is a load effect and is obtained by loading the corrected model according to a design load or a check load; r is the resistance effect of the control section, the bearing capacity provided by the steel bars and the concrete is calculated according to the design specification, and reduction is carried out according to the technical survey result; when CRF is used<And 1.05, judging that the bearing capacity of the bridge meets the requirement.
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| CN115828393A (en) * | 2022-12-21 | 2023-03-21 | 广西北投公路建设投资集团有限公司 | Bridge informatization management method and system, electronic equipment and medium |
| CN115855167A (en) * | 2023-02-27 | 2023-03-28 | 济南金曰公路工程有限公司 | Nondestructive testing method for evaluating deflection and strain of single beam of bridge based on mobile sensing |
| CN116720381A (en) * | 2023-06-29 | 2023-09-08 | 西南交通大学 | Power response calculation and evaluation method for highway and railway dual-purpose bridge |
| CN116720381B (en) * | 2023-06-29 | 2024-02-06 | 西南交通大学 | Power response calculation and evaluation method for highway and railway dual-purpose bridge |
| CN117235871A (en) * | 2023-11-13 | 2023-12-15 | 湘潭大学 | Two-stage response surface model correction method for steel-concrete composite beam bridge |
| CN117235871B (en) * | 2023-11-13 | 2024-01-26 | 湘潭大学 | Two-stage response surface model correction method for steel-concrete composite beam bridge |
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