Method for quickly evaluating bearing capacity of continuous beam based on arbitrary cross-section bending moment influence line area

Abstract

The present application belongs to the field of bridge and culvert engineering quality detection technology in transportation industry. Based on the method for quickly evaluating the bearing capacity of continuous beam by the area of bending moment influence line of arbitrary section, the method firstly adopts a vehicle with known axle load, axle distance and axle number as a loading vehicle, sets the weight P1 of rear axle I, the weight P2 of rear axle II and the weight P3 of rear axle III; then constructs the effect function of bending moment at arbitrary section x changing with the moving vehicle; finally, the integral value of the effect function of bending moment at section x changing with the moving vehicle under the same condition is taken as the numerator, and n is 0-1; the ratio of the integral value of the effect function of bending moment at section x changing with the moving vehicle under the same condition to the denominator is less than 1, which indicates that the bearing capacity of the bridge meets the requirements. The present application can improve the detection precision and efficiency of existing bridge load and reduce the cost of manpower and material resources.

Description

Technical Field

[0001] This invention belongs to the field of bridge and culvert engineering quality inspection technology in the transportation industry, specifically involving a method for rapidly evaluating the bearing capacity of continuous beams based on the area of ​​the influence line of bending moment at any cross section. Background Technology

[0002] my country is a major bridge-building nation with numerous newly built and existing bridges, most of which are continuous beam bridges. Some of these bridges have been in operation for a long time, resulting in severe material aging and significant reduction in cross-sectional stiffness. Whether old or new, bridges require a precise and effective method to assess their condition and determine their load-bearing capacity. Load testing offers a direct and relatively accurate assessment, but it suffers from drawbacks such as long testing times, traffic closures, numerous measurement points, and substantial time and costs. Furthermore, actual test results often need to be compared with structural model analyses, but different software yields varying theoretical data. Additionally, algorithms based on multiplying the test load by the influence line cannot accurately reflect the actual condition. Traditional load testing calculates the efficiency of the test load within a certain range, applies the load to designated locations on the bridge, and measures parameters such as static displacement and static strain at the test sections to evaluate the bridge's performance and serviceability. Traditional methods require a large number of vehicles, making it difficult to locate them at the test site. The load weight of the loaded vehicle may not fully match the calculated load, and the location of the vehicle load varies depending on different working conditions and times, resulting in too much randomness and low comparability of repeated test data.

[0003] Therefore, how to solve the above-mentioned problems in actual detection and calculation is an important technical issue that urgently needs to be addressed. Summary of the Invention

[0004] This invention overcomes the shortcomings of the above-mentioned technical problems and provides a method for rapidly evaluating the bearing capacity of continuous beams based on the area of ​​the influence line of bending moment at any cross section. This method can improve the detection accuracy and efficiency of existing bridge loads and reduce manpower and material costs.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] 1. A method for rapidly evaluating the bearing capacity of continuous beams based on the area of ​​the influence line of bending moment at any cross-section. When the influence line of the bridge is the influence line of bending moment at any cross-section x of the bridge, the method for evaluating the bearing capacity of continuous beams includes the following steps:

[0007] (1) Using a vehicle with known axle load, wheelbase and number of axles as the loading vehicle, set the weight of rear axle I P1, rear axle II P2 and rear axle III P3 of the loading vehicle.

[0008] (2) Construct the effect function of bending moment at any cross section x as a function of moving vehicle.

[0009] Since a bridge can be divided into two ends, the bridgehead and the bridge abutment, the bridgehead is selected as the origin, and the bridgehead is the end where the loading vehicle enters the bridge. The loading vehicle enters the bridge from the bridgehead and crosses the bridge at a constant speed. The strain value at any cross-section x is collected. The expression of the effect function of the bending moment at any cross-section x as a function of the moving vehicle is obtained by back-calculating the strain value measured on site and the actual stiffness of the control section:

[0010]

[0011] In the formula, Let x be the effect function of bending moment at any cross section x as a function of the moving vehicle; Let X be the expression for the influence line of bending moment at any cross section x, where Z1 is the rear wheelbase, Z2 is the front wheelbase, and X is the cross section x. p To load the distance from the rear axle of the vehicle to the origin;

[0012] (3) The integral of the maximum peak value interval is used as the denominator, where n is 0 to 1; under the same conditions, the integral value of the effect function of bending moment at test section x with the change of moving vehicles is used as the numerator. If the ratio of the numerator to the denominator is less than 1, it indicates that the bridge bearing capacity meets the requirements.

[0013] Furthermore, the continuous beam is a three-span continuous beam with arbitrary cross-section and arbitrary span, which includes spans 1, 2 and 3 of the bridge.

[0014] Furthermore, in step (2), the span of span 1# of the continuous beam is defined as L1, the span of span 2# as L2, and the span of span 3# as L3; the influence factors of the influence line of span 1# are a1 and a2, the influence factors of the influence line of span 2# are b1 and b2, and the influence factors of the influence line of span 3# are c1 and c2; then the expressions for the moment influence line at any section x are ②, ③, and ④:

[0015]

[0016]

[0017]

[0018] In the formula: L is the total span of the three-span continuous beam, i.e., L = L1 + L2 + L3; the influence factors of the influence lines are respectively:

[0019]

[0020]

[0021]

[0022] In the formula,

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. This invention proposes a method for rapidly evaluating the bearing capacity of continuous beams based on the influence line area of ​​bending moment at arbitrary cross-sections. The proposed method for evaluating the bearing capacity of continuous beams presents a simple and easy-to-understand derivation formula for the influence line, directly yielding an analytical solution that is more accurate than software calculations. It allows for adjustments based on changes in measured parameters, making it highly operable. The method derives the analytical formula for the influence line at arbitrary cross-section positions of bridges with different spans and cross-sectional stiffnesses. It incorporates the axle load and wheelbase of the loaded vehicle from the experiment. Based on the method provided by this invention, the change effect function of the bending moment at the control section when a specific loaded vehicle moves from one end of the continuous beam to the other is obtained. The area of ​​a specific interval is obtained through function integration and compared with the measured value. A verification coefficient is used to determine the bearing capacity status of the bridge.

[0030] 2. This invention utilizes the integral area of ​​the bending moment effect function to more comprehensively reflect the actual bearing capacity state of the bridge, breaking through the limitations of the traditional influence line point product theory load.

[0031] 3. This invention can be tested quickly without interrupting traffic. The method and process are simple and easy to implement. The actual test results are obvious. It can improve the detection accuracy and efficiency of existing bridge loads, reduce manpower and material costs, and has great practical engineering application value. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the loading vehicle in Embodiment 1 of the present invention;

[0033] Figure 2 This is a side view of the bridge layout according to Embodiment 1 of the present invention;

[0034] Figure 3 This is a top view of the bridge layout according to Embodiment 1 of the present invention;

[0035] Figure 4 This is a schematic diagram of the cross-sectional structure of the bridge according to Embodiment 1 of the present invention;

[0036] Figure 5 This is a cross-sectional dimension diagram of the bridge according to Embodiment 1 of the present invention;

[0037] Figure 6 This is a diagram showing the arrangement of strain measurement points in Embodiment 1 of the present invention;

[0038] Figure 7 These are the theoretical and measured strain curves of the bridge section bending moment according to Embodiment 1 of the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that the specific embodiments of the present invention are only for the purpose of more clearly describing the technical solution and should not be construed as limiting the scope of protection of the present invention.

[0040] 1. A method for rapidly evaluating the bearing capacity of a continuous beam based on the area of ​​the influence line of bending moment at any cross section, characterized in that, when the influence line of the bridge is the influence line of bending moment at any cross section x of the bridge, the method for evaluating the bearing capacity of the continuous beam includes the following steps:

[0041] (1) Using a vehicle with known axle load, wheelbase and number of axles as the loading vehicle, set the weight of rear axle I P1, rear axle II P2 and rear axle III P3 of the loading vehicle.

[0042] (2) Construct the effect function of bending moment at any cross section x as a function of moving vehicle.

[0043] Since a bridge can be divided into two ends, the bridgehead and the bridge abutment, the bridgehead is selected as the origin, and the bridgehead is the end where the loading vehicle enters the bridge. The loading vehicle enters the bridge from the bridgehead and crosses the bridge at a constant speed. The strain value at any cross-section x is collected. The expression of the effect function of the bending moment at any cross-section x as a function of the moving vehicle is obtained by back-calculating the strain value measured on site and the actual stiffness of the control section:

[0044]

[0045] In the formula, Let x be the effect function of bending moment at any cross section x as a function of the moving vehicle; Let X be the expression for the influence line of bending moment at any cross section x, where Z1 is the rear wheelbase, Z2 is the front wheelbase, and X is the cross section x. p To load the distance from the rear axle of the vehicle to the origin;

[0046] (3) The integral of the maximum peak value interval is used as the denominator, where n is 0 to 1; under the same conditions, the integral value of the effect function of bending moment at test section x with the change of moving vehicles is used as the numerator. If the ratio of the numerator to the denominator is less than 1, it indicates that the bridge bearing capacity meets the requirements.

[0047] Among them, the continuous beam is a three-span continuous beam with arbitrary cross-section and arbitrary span, which includes the bridge's No. 1 span, No. 2 span and No. 3 span.

[0048] In step (2), the span of the continuous beam is defined as L1 for span 1, L2 for span 2, and L3 for span 3; the influence factors of the influence line of span 1 are a1 and a2, the influence factors of the influence line of span 2 are b1 and b2, and the influence factors of the influence line of span 3 are c1 and c2; then the expressions for the moment influence line at any section x are ②, ③, and ④:

[0049]

[0050]

[0051]

[0052] In the formula: L is the total span of the three-span continuous beam, i.e., L = L1 + L2 + L3; the influence factors of the influence lines are respectively:

[0053]

[0054]

[0055]

[0056] In the formula,

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Example 1

[0063] This embodiment evaluates a three-span continuous beam bridge with equal cross-section and equal span. The bridge superstructure consists of 3×30m precast prestressed concrete continuous box girders, installed using precast simple-support construction, followed by cast-in-place continuous joints to form a continuous structure. The bridge substructure uses column piers, column abutments, and bored pile foundations.

[0064] The span is L1 = L2 = L3 = L / 3 = 30m, using C50 concrete with an elastic modulus of 3.45 × 10⁻⁶ m. 4 MPa, the section stiffness is calculated to be EI = 5.02362 × 10 7 kN.m 2 The loading vehicle used in the test was a three-axle heavy-duty vehicle (see attached). Figure 1The rear axle loads are P1 = P2 = 150kN, P3 = 70kN, Z1 = 1.35m, and Z2 = 3.6m. See the attached diagram for bridge layout and cross-sectional dimensions. Figures 5-7 The bridge side view layout is as follows: Figure 2 As shown, the bridge's top-view layout is as follows: Figure 3 As shown in the diagram, the cross-sectional structure of the bridge is as follows: Figure 4 As shown in the figure, the cross-sectional dimensions of the bridge are as follows: Figure 5 As shown in the attached diagram. The arrangement of strain measurement points is also shown. Figure 6 If the span is 20m, the theoretical strain curve is shown below. Figure 7 .

[0065] The method of this invention was used to verify the expression of the bending moment influence line at the mid-span section of span #1. The vehicle was driven slowly and at a constant speed from the bridgehead to the bridge tail to obtain the average strain variation curve of the concrete at mid-span of span #1. The measured strain variation curve is shown below. Figure 7 In actual tests, the same method can be used to obtain the strain average value variation curve. The bearing capacity of span #1 is evaluated by the ratio of the areas of the two curves integrated within an appropriate interval. When the ratio is less than 1, the bearing capacity meets the requirements; when it is greater than 1, the requirements are not met. The specific steps are as follows:

[0066] Find the analytical expression for the influence line of the mid-span section of the side span (x = L1 / 2 = 15m):

[0067]

[0068]

[0069]

[0070] Let x = L1 / 2, the variation law of the bending moment influence line at the mid-span section of the first span can be expressed by an expression.

[0071]

[0072] The formula for the effect function of bending moment at any cross-section x as a function of moving vehicles, derived in this invention, shows good agreement with the calculation results using Midas finite element software, verifying the correctness of the formula. This formula can be used to derive the effect function for any three-span continuous beam with variable cross-section. Multiplying the derived influence line curve by the experimental load yields the curve equation of M(xp), and integrating it gives the area, which can then be compared and evaluated with the measured values. The calculation is simple and clear, and can be well applied in engineering examples.

[0073] This invention presents a method for rapidly evaluating the bearing capacity of continuous beams based on the area of ​​the influence line of bending moment at any cross-section. The derived formula is simple and easy to understand, and can comprehensively reflect the overall state of the bridge. It overcomes the limitations of using the influence line multiplied by the theoretical load as an evaluation algorithm. Furthermore, by arranging one or more strain measurement points at a certain control section without interrupting traffic, a specific test vehicle can drive over the point at a constant speed to measure the response curve, which can then be compared and judged. The method disclosed in this invention is simple, effective, computationally straightforward, and highly accurate, and has broad prospects for engineering applications.

[0074] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for rapidly evaluating the bearing capacity of continuous beams based on the influence line area of ​​bending moment at arbitrary cross-sections, characterized in that, When the influence line of a bridge is the influence line of bending moment at any cross-section x of the bridge, the method for evaluating the bearing capacity of a continuous beam includes the following steps: (1) Using a vehicle with known axle load, wheelbase and number of axles as the loading vehicle, set the weight of rear axle I P1, rear axle II P2 and rear axle III P3 of the loading vehicle. (2) Construct the effect function of bending moment at any cross section x as a function of moving vehicle; Since a bridge can be divided into two ends, the bridgehead and the bridge abutment, the bridgehead is selected as the origin, and the bridgehead is the end where the loading vehicle enters the bridge. The loading vehicle enters the bridge from the bridgehead and crosses the bridge at a constant speed. The strain value at any cross-section x is collected. The expression of the effect function of the bending moment at any cross-section x as a function of the moving vehicle is obtained by back-calculating the strain value measured on site and the actual stiffness of the control section: In the formula, Let x be the effect function of bending moment at any cross section x as a function of the moving vehicle; Let X be the expression for the influence line of bending moment at any cross section x, where Z1 is the rear wheelbase and Z2 is the front wheelbase. p To load the distance from the rear axle of the vehicle to the origin; (3) To The integral of the n-fold maximum peak interval is used as the denominator, where n is 0 to 1; under the same conditions, the integral value of the effect function of bending moment at test section x with the change of moving vehicle is used as the numerator. If the ratio of the numerator to the denominator is less than 1, it indicates that the bridge bearing capacity meets the requirements. The continuous beam is a three-span continuous beam with arbitrary cross-section and arbitrary span. This continuous beam includes spans 1, 2 and 3 of the bridge. In step (2), the span of the continuous beam is defined as L1 for span 1, L2 for span 2, and L3 for span 3; the influence factors of the influence line of span 1 are a1 and a2, the influence factors of the influence line of span 2 are b1 and b2, and the influence factors of the influence line of span 3 are c1 and c2; then the expressions for the moment influence line at any section x are ②, ③, and ④: ： ， : ，③ : ，④ In the formula: L is the total span of the three-span continuous beam. The influence factors of the influence lines are as follows: , ， , ， , ， In the formula, ， ⑤ ， ⑥ ， ⑦ ， ⑧ ⑨ 。

Images