Calculation method of negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on quasi-design conditions

Abstract

The present invention discloses a method for calculating the negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on a quasi-design state, including the following processes: determining the second-order vertical bending frequency of the bridge; determining the bridge deck roughness grade; and calculating the negative bending moment impact coefficient under the unevenness grade of the bridge deck using the second-order vertical bending frequency of the bridge. Based on the quasi-design state of the bridge, the present invention calculates the impact coefficient using the measured second-order frequency and roughness data of the bridge; at the same time, it can also adjust the impact coefficient assessment standard in a timely manner according to the degree of deterioration of the road surface grade. Therefore, the present invention can realize the evaluation of the negative bending moment impact coefficient of the continuous beam bridge according to the bridge deck condition in different operation periods, and has stronger pertinence and wider applicability.

Description

Technical Field

[0001] The present invention relates to the field of bridge engineering, and in particular to a method for calculating the negative bending moment impact coefficient of a small- and medium-span assembled continuous beam bridge based on a quasi-design state. Background Art

[0002] Vehicle load is one of the most important live loads acting on the bridge structure. Due to the vibration caused by the unevenness of the bridge deck and the interaction between the vehicle and the bridge, the vehicle load will always have a dynamic effect on the bridge structure. In bridge design, the impact coefficient (μ) is usually used to consider the dynamic effect of vehicle loads. This coefficient is defined by the ratio of the maximum dynamic response to the maximum static response. The impact coefficient is a comprehensive coefficient that reflects the dynamic response under the influence of various factors when a vehicle passes through the bridge. Due to the differences in the mechanical properties of each section of the bridge, the impact coefficients of different sections are different. Taking the bending moment effect as an example, it is usually divided into two types of sections: positive bending moment sections and negative bending moment sections. For simply supported beam bridges, there are only positive bending moment sections. For continuous beam bridges, see Figure 1(a) to Figure 1(c) The vibration forms of negative bending moment sections and positive bending moment sections are different, and the dynamic impact mechanisms of vehicle loads on them are different. Existing technologies do not provide reliable statistical data support for the negative bending moment impact coefficient of the support section of continuous beam bridges. The impact coefficient calculation formula in the current "General Specification for Design of Highway Bridges and Culverts" (JTG D60-2015, referred to as the 15 Specification) is obtained through statistical regression analysis of field measured data of simply supported beam bridges. It only considers the fundamental frequency of the bridge structure and does not consider the impact of the important factor of bridge deck roughness grade on the impact coefficient. At the same time, since the frequency spectrum characteristics of continuous beam bridges are different from those of simply supported beam bridges, the applicability of the current 15 Specification impact coefficient calculation formula to continuous beam bridges remains to be discussed:

[0003]

[0004] Where: f is the fundamental frequency of the bridge structure.

[0005] At the same time, the "Highway Bridge Load Test Code" (JTG / T J21-01-2015) stipulates that on-site tests of the static and dynamic characteristics of bridge structures or components by applying loads include static load tests and dynamic load tests. The dynamic load test of a bridge should test the natural frequency and impact coefficient of the bridge span structure. Usually, the impact coefficient is calculated by obtaining a dynamic time history curve obtained by a single vehicle or multiple vehicles passing through the bridge at a constant speed. However, there are the following problems: ① The impact coefficient calculated using the standard is not related to the design load effect value, that is, the impact coefficient in the standard is not the impact coefficient under the quasi-design load state, which leads to a large difference between the measured impact coefficient in the dynamic load test and the calculated result of the standard value (Equation (1)). ② Due to differences in road conditions, the impact coefficient obtained based on actual measurements is significantly different from the standard design value (Equation (1)). The standard design impact coefficient only considers the maximum impact effect value of the bridge under the most unfavorable road conditions, and has not yet considered the impact of road conditions on the impact coefficient. Since the condition of the bridge deck continues to deteriorate over time after completion, even under the action of the same vehicle, the impact coefficient calculation of the same cross-section changes continuously with the bridge deck condition. Currently, there is no existing technology that can evaluate the negative bending moment impact coefficient of continuous beam bridges based on the bridge deck condition and quasi-design load conditions during the operation period. Summary of the Invention

[0006] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a method for calculating the negative bending moment impact coefficient of small and medium-span prefabricated continuous beam bridges based on a quasi-design state. The present invention obtains a calculation formula for the negative bending moment impact coefficient by considering the combined influence of bridge deck unevenness and bridge frequency factors, thereby realizing the evaluation of the negative bending moment impact coefficient of the continuous beam bridge according to the bridge deck condition during the operation period.

[0007] The technical solution adopted in the present invention is as follows:

[0008] The calculation method of the negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on the quasi-design state includes the following steps:

[0009] Determine the second-order vertical bending frequency of the bridge;

[0010] Determine the bridge deck roughness level;

[0011] The second-order vertical bending frequency of the bridge is used to calculate the negative bending moment impact coefficient under the unevenness level of the bridge deck.

[0012] Preferably, when determining the second-order vertical bending frequency of the bridge, a finite element spatial grillage model of the corresponding bridge is established, and the second-order vertical bending frequency of the bridge is extracted through the finite element spatial grillage model of the bridge.

[0013] Preferably, the bridge is a continuous small box girder bridge or a continuous T-girder bridge.

[0014] Preferably, when the bridge is a continuous small box girder bridge, the calculation formula of the negative bending moment impact coefficient μ1 is as follows:

[0015] μ1=α1×(0.0125f2+0.0496)

[0016] in:

[0017]

[0018] Among them, α1 is the bridge deck grade conversion coefficient of the continuous small box girder bridge, and f2 represents the second-order vertical bending frequency of the bridge.

[0019] Preferably, when the bridge is a continuous T-beam bridge, the calculation formula of the negative bending moment impact coefficient μ2 is as follows:

[0020] μ2=α2×(0.0047f2 2 -0.0413f2+0.1681)

[0021] in:

[0022]

[0023] Where α2 is the deck grade conversion coefficient of the continuous T-beam bridge, and f2 represents the second-order vertical bending frequency of the bridge.

[0024] The present invention also provides a calculation system for the negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on a quasi-design state, comprising:

[0025] Input module: used to input the second-order vertical bending frequency of the bridge and the bridge deck roughness level;

[0026] Calculation module: used to calculate the negative bending moment impact coefficient under the unevenness level of the bridge deck using the second-order vertical bending frequency of the bridge.

[0027] Preferably, the calculation module includes a negative bending moment impact coefficient calculation module for a continuous small box girder bridge and / or a negative bending moment impact coefficient calculation module for a continuous T-beam bridge. The negative bending moment impact coefficient calculation module for a continuous small box girder bridge is used to calculate the negative bending moment impact coefficient of the continuous small box girder bridge, and the negative bending moment impact coefficient calculation module for a continuous T-beam bridge is used to calculate the negative bending moment impact coefficient of the continuous T-beam bridge.

[0028] Preferably, the calculation formula of the negative bending moment impact coefficient μ1 of the continuous small box girder bridge is as follows:

[0029] μ1=α1×(0.0125f2+0.0496)

[0030] in:

[0031]

[0032] Among them, α1 is the bridge deck grade conversion coefficient of the continuous small box girder bridge, and f2 represents the second-order vertical bending frequency of the bridge.

[0033] Preferably, the calculation formula of the negative bending moment impact coefficient μ2 of the continuous T-beam bridge is as follows:

[0034] μ2=α2×(0.0047f2 2 -0.0413f2+0.1681)

[0035] in:

[0036]

[0037] Where α2 is the deck grade conversion coefficient of the continuous T-beam bridge, and f2 represents the second-order vertical bending frequency of the bridge.

[0038] The present invention has the following beneficial effects:

[0039] This method calculates the negative bending moment impact coefficient of small- and medium-span prefabricated continuous beam bridges based on a quasi-design state. Based on the bridge's quasi-design state, the impact coefficient is calculated using measured frequency and roughness data. Furthermore, the impact coefficient assessment criteria can be adjusted based on the degree of pavement degradation. Therefore, this method enables a more targeted assessment of the negative bending moment impact coefficient of continuous beam bridges during operation based on bridge deck conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] FIG1(a) is a schematic diagram of a first type of multi-span continuous beam; FIG1(b) is a schematic diagram of a second type of multi-span continuous beam; FIG1(c) is a schematic diagram of a third type of multi-span continuous beam;

[0041] FIG2(a) is a schematic diagram of vehicle loading for a 2×20m continuous small box girder bridge (schematic diagram of bridge cross-section loading) according to an embodiment of the present invention; FIG2(b) is a schematic diagram of vehicle loading for a 2×20m continuous small box girder bridge (schematic diagram of bridge plan loading) according to an embodiment of the present invention;

[0042] Figure 3(a) is a schematic diagram of vehicle loading on a 2×20m continuous T-beam bridge in an embodiment of the present invention (a schematic diagram of bridge cross-section loading); Figure 3(b) is a schematic diagram of vehicle loading on a 2×20m continuous T-beam bridge in an embodiment of the present invention (a schematic diagram of bridge plane loading).

[0043] Figure 4 This is a flow chart of the vehicle-bridge coupling program in an embodiment of the present invention;

[0044] Figure 5 : is the regression curve of the negative bending moment impact coefficient of the continuous small box girder bridge under the Class A bridge deck in the embodiment of the present invention;

[0045] Figure 6 : is the regression curve of the negative bending moment impact coefficient of the continuous small box girder bridge under the Class B bridge deck in the embodiment of the present invention;

[0046] Figure 7 : is the regression curve of the negative bending moment impact coefficient of the continuous small box girder bridge under the C-level bridge deck in the embodiment of the present invention;

[0047] Figure 8 : is the regression curve of the negative bending moment impact coefficient of the continuous T-beam bridge under the Class A bridge deck in the embodiment of the present invention;

[0048] Figure 9 : is the regression curve of the negative bending moment impact coefficient of the continuous T-beam bridge under the Class B bridge deck in the embodiment of the present invention;

[0049] Figure 10 This is the regression curve of the negative bending moment impact coefficient of the continuous T-beam bridge under the C-level bridge deck in the embodiment of the present invention.

[0050] In the figure, 1-continuous small box girder bridge, 2-continuous T-girder bridge. DETAILED DESCRIPTION

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] Bridge deck roughness is a significant factor influencing the bridge impact effect caused by vehicle-bridge coupling. Bridge deck roughness is inherently random, and in practice, its statistical characteristics are often described using power spectral density (PSD). The road surface roughness values ​​specified in the "Method for Representing Road Surface Roughness for Vehicle Vibration Input" (GB / T 7031-86) are similar to those in the ISO SC2 / WG4 standard. The expression is shown in Equation (2). The eight-level road surface classification in GB / T 7031-86 is shown in Table 1:

[0053] Table 1

[0054]

[0055]

[0056] According to the actual conditions of China's roads, Class A, Class B and Class C road surface roughness are considered.

[0057]

[0058] Where: n—spatial frequency; n0—reference spatial frequency; G x (n)—displacement power spectrum density value at spatial frequency n; G x (n0)—road roughness coefficient at spatial frequency n0; ω—frequency index, usually ω=2.

[0059] The bridge frequency can be obtained using finite element software (Midas or ANSYS). Since the vertical impact effect of vehicles on the bridge is greater than the lateral impact effect, only the vertical bending frequency of the bridge is considered.

[0060] This paper takes prefabricated continuous beam bridges (T-beam bridges and small box beam bridges) as research objects. The structural parameters of typical bridges are shown in Table 2:

[0061] Table 2

[0062]

[0063] First, the negative bending moment influence line of the continuous beam bridge is calculated. The lane load arrangement in accordance with the General Specification for Design of Highway Bridges and Culverts (JTG D60-2015) is applied to determine the design value of the negative bending moment of the continuous beam bridge under the design state.

[0064] Based on the calculated value of the design load effect, the vehicle load spectrum is determined according to the principle of equivalent quasi-design load effect. The calculation formula for the load effect equivalent ratio is defined as shown in formula (3):

[0065]

[0066] Where: S S It is the maximum equivalent calculated effect value of the internal force or displacement of a certain control section under the action of the static vehicle load spectrum; S is the most unfavorable effect calculated value of the internal force or displacement of the same control section under the design load (ignoring the impact effect); η is the load effect equivalent ratio, and η is taken as 1.

[0067] According to the specification, the lateral clear distance between vehicles is 1.3m. At the same time, in order to achieve the design load effect as much as possible, the longitudinal clear distance between vehicles is 6m. The vehicles are in the same direction and the vehicle weight is adjusted (the vehicle weight range is 26.15t to 38.3t) to achieve the quasi-design load effect. Taking the 2×20m continuous small box girder bridge and the continuous T-beam bridge as examples, the vehicle space layout is as follows: Figures 2(a) to 3(b) The number of vehicles carried on other bridge spans is shown in Table 3:

[0068] Table 3

[0069]

[0070] The vehicles are loaded in sequence according to the above-mentioned vehicle space loading method. By adjusting the vehicle weight and calculating the negative bending moment equivalent ratio of the continuous small box girder bridge and the continuous T-beam bridge under different span arrangements according to formula (3), the ratio is equal to 1. The calculation results of the quasi-design state of the negative bending moment effect of the continuous beam bridge are shown in Table 4:

[0071] Table 4

[0072]

[0073] The quasi-design negative bending moment effect generated by the control section of each bridge under the action of vehicle load is basically equal to the design state negative bending moment effect, and the equivalent ratio η is all equal to 1.00, which means that the equivalent quasi-design load effect reaches the design state load effect, that is, the negative bending moment effect generated by the test vehicle load is equivalent to the design load standard value.

[0074] Since vehicle speed, deck roughness, and bridge frequency all have a certain impact on the negative bending moment impact coefficient of continuous beam bridges, and since deck roughness is the most sensitive factor causing differences in the negative bending moment impact coefficient of continuous beam bridges, deck roughness is used as the grading standard for evaluating the impact coefficient. Furthermore, while vehicle speed has a certain influence on the negative bending moment impact coefficient of continuous beam bridges, its influence on the negative bending moment impact coefficient of continuous beam bridges is not clearly evident and exhibits a certain degree of randomness. Considering five types of driving speeds (20 km / h, 40 km / h, 60 km / h, 80 km / h and 100 km / h) and three types of bridge deck roughness (Grade A, Grade B and Grade C), the displacement coupling method is used to obtain the time history curves of the negative bending moment dynamic response of the continuous beam bridge under each road surface grade. The impact coefficient of each bridge under different road surface grades is calculated by formula (4), and then the average value (the average value of the impact coefficient obtained under five vehicle speeds under the same road surface grade) is obtained. The calculation results are shown in Tables 5 to 10. Table 5 is the negative bending moment impact coefficient table of the continuous small box beam bridge under Grade A bridge deck, Table 6 is the negative bending moment impact coefficient table of the continuous small box beam bridge under Grade B bridge deck, Table 7 is the negative bending moment impact coefficient table of the continuous small box beam bridge under Grade C bridge deck, Table 8 is the negative bending moment impact coefficient table of the continuous T beam bridge under Grade A bridge deck, Table 9 is the negative bending moment impact coefficient table of the continuous T beam bridge under Grade B bridge deck, and Table 10 is the negative bending moment impact coefficient table of the continuous T beam bridge under Grade C bridge deck. Among them, the dynamic response of the continuous beam bridge with negative bending moment is solved by the modal superposition method. The calculation process of its dynamic response (time history curve) is as follows: Figure 4 As shown, the impact coefficient of each time history curve is calculated using formula (4).

[0075]

[0076] Where: S dmax S is the maximum static response value on the effect time history curve measured under static action of vehicle load; jmax It is the maximum dynamic response value of the vehicle load on the effect time history curve.

[0077] Table 5

[0078]

[0079]

[0080] Table 6

[0081]

[0082] Table 7

[0083]

[0084] Table 8

[0085]

[0086] Table 9

[0087]

[0088]

[0089] Table 10

[0090]

[0091] According to the calculation results of the bridge impact coefficient, the second frequency of the bridge structure is used as the independent variable, and the calculation formula of the negative bending moment impact coefficient of the continuous small box beam bridge is obtained by regression fitting as shown in formula (5), and the calculation formula of the negative bending moment impact coefficient of the continuous T beam bridge is shown in formula (6). Among them, the regression fitting process of calculation formulas (5) to (6) is shown in Figures 5 to 10 .

[0092]

[0093]

[0094] Where: μ A 、μ B and μ C They represent the negative bending moment impact coefficients of bridge deck roughness levels A, B and C respectively; f2 represents the second-order vertical bending frequency of the bridge.

[0095] In order to further simplify the negative bending moment impact coefficient expressions in formulas (5) to (6), the calculation formulas for the negative bending moment impact coefficients of Class B and Class C bridge deck roughness levels are represented by the calculation formula for the negative bending moment impact coefficient of Class A bridge deck roughness. The expression form is shown in formula (7).

[0096] μ=α×μ A (7)

[0097] Where α is the bridge deck grade conversion coefficient.

[0098] Finally, the simplified calculation formulas for the negative bending moment impact coefficient of continuous small box girder bridges are shown in equations (8) to (9). The simplified calculation formulas for the negative bending moment impact coefficient of continuous T-beam bridges are shown in equations (10) to (11).

[0099] μ1=α1×(0.0125f2+0.0496) (8)

[0100]

[0101] μ2=α2×(0.0047f2 2 -0.0413f2+0.1681) (10)

[0102]

[0103] Since the negative bending moment effect of the bridge cannot be directly obtained in actual dynamic load tests, based on the linear elastic assumption, the strain effect is usually used to replace the negative bending moment effect of the bridge.

[0104] Firstly, ANSYS is used to establish the finite element spatial beam grillage model of the corresponding bridge and extract the second-order vertical bending frequency of the bridge.

[0105] According to formula (3), the ANSYS calculation model is used to determine the number of vehicles, vehicle weight and bridge deck space layout under the quasi-design state.

[0106] According to the vehicle layout information obtained above, a dynamic load test is carried out. The vehicles are driven at a constant speed across the bridge deck at 5 different speeds (20km / h, 40km / h, 60km / h, 80km / h and 100km / h) at the specified spacing, and the negative bending moment dynamic strain time history curve and the positive bending moment acceleration time history curve of the bridge are measured. The quasi-static strain curve of the bridge is obtained by the low-pass filtering method, and the right valley value of the first main axis of the amplitude-frequency curve of the time history curve is taken as the filter cutoff frequency. Formula (4) is used to obtain the strain impact coefficient of the negative bending moment zone of the bridge at different speeds. The strain impact coefficients of the 5 speeds are averaged to obtain the measured average impact coefficient of the bridge.

[0107] The acceleration time history curve in the positive bending moment region was transformed by FFT to obtain the bridge's acceleration power spectrum. The measured first two vertical bending frequencies, f1' and f2', were then extracted by comparing them with the theoretically calculated first two vertical bending frequencies, f1 and f2.

[0108] The road surface roughness data is measured using a laser road surface roughness meter or a vehicle-mounted bump accumulation meter. The data is then subjected to power spectrum analysis (see "Mechanical Vibration Road Pavement Spectrum Measurement Data Report" GB / T 7031--2005 / ISO 8608:1995) to determine the bridge deck roughness grade.

[0109] Substitute the measured bridge deck flatness grade and the measured second-order vertical bending frequency f2' of the bridge into formulas (8) to (11) to obtain the bridge impact coefficient evaluation value μ'.

[0110] By comparing the impact coefficient evaluation value μ' and the measured average impact coefficient size, and evaluate the dynamic performance of the bridge. When , it indicates that the vehicle-bridge coupling dynamic performance is good; when When , it indicates that the overall dynamic performance (dynamic stiffness) of the bridge is poor.

Claims

1. The calculation method of negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridge based on quasi-design state is characterized by: The process includes the following: Determine the second-order vertical bending frequency of the bridge; Determine the bridge deck roughness level; The negative bending moment impact coefficient of the bridge deck under the unevenness level is calculated using the second-order vertical bending frequency of the bridge. When the bridge is a continuous small box girder bridge, the negative bending moment impact coefficient μ The calculation formula for 1 is as follows: in: in, α 1 is the bridge deck grade conversion coefficient of continuous small box girder bridge, represents the second-order vertical bending frequency of the bridge; When the bridge is a continuous T-beam bridge, the negative bending moment impact coefficient μ The calculation formula for 2 is as follows: in: in, α 2 is the bridge deck grade conversion coefficient of the continuous T-beam bridge, Represents the second-order vertical bending frequency of the bridge.

2. The method for calculating the negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on quasi-design conditions according to claim 1 is characterized in that: When determining the second-order vertical bending frequency of a bridge, a finite element spatial grillage model of the corresponding bridge is established, and the second-order vertical bending frequency of the bridge is extracted through the finite element spatial grillage model of the bridge.

3. The method for calculating the negative bending moment impact coefficient of small and medium span prefabricated continuous beam bridges based on quasi-design conditions according to claim 1 is characterized in that: The bridge is a continuous small box girder bridge or a continuous T-girder bridge.

4. The negative bending moment impact coefficient calculation system for small and medium span prefabricated continuous beam bridges based on quasi-design conditions is characterized by: include: Input module: used to input the second-order vertical bending frequency of the bridge and the bridge deck roughness level; Calculation module: used to calculate the negative bending moment impact coefficient of the bridge deck under the unevenness level using the second-order vertical bending frequency of the bridge; when the bridge is a continuous small box girder bridge, the negative bending moment impact coefficient μ The calculation formula for 1 is as follows: in: in, α 1 is the bridge deck grade conversion coefficient of the continuous small box girder bridge, represents the second-order vertical bending frequency of the bridge; When the bridge is a continuous T-beam bridge, the negative bending moment impact coefficient μ The calculation formula for 2 is as follows: in: in, α 2 is the bridge deck grade conversion coefficient of the continuous T-beam bridge, Represents the second-order vertical bending frequency of the bridge.

5. The negative bending moment impact coefficient calculation system for small and medium span prefabricated continuous beam bridges based on quasi-design conditions according to claim 4 is characterized in that: The calculation module includes a negative bending moment impact coefficient calculation module for a continuous small box girder bridge and / or a negative bending moment impact coefficient calculation module for a continuous T-beam bridge. The negative bending moment impact coefficient calculation module for a continuous small box girder bridge is used to calculate the negative bending moment impact coefficient of the continuous small box girder bridge, and the negative bending moment impact coefficient calculation module for a continuous T-beam bridge is used to calculate the negative bending moment impact coefficient of the continuous T-beam bridge.

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