CN116105951A - Method for rapidly evaluating bearing capacity of continuous beam based on area of influence line of bending moment of arbitrary section - Google Patents

Method for rapidly evaluating bearing capacity of continuous beam based on area of influence line of bending moment of arbitrary section Download PDF

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CN116105951A
CN116105951A CN202211344788.9A CN202211344788A CN116105951A CN 116105951 A CN116105951 A CN 116105951A CN 202211344788 A CN202211344788 A CN 202211344788A CN 116105951 A CN116105951 A CN 116105951A
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bridge
section
bending moment
span
continuous beam
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郝天之
陈齐风
于孟生
王龙林
杨雨厚
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Guangxi Jiaoke Group Co Ltd
Guangxi Beitou Transportation Maintenance Technology Group Co Ltd
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Guangxi Beitou Transportation Maintenance Technology Group Co Ltd
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Abstract

The invention belongs to the technical field of bridge and culvert engineering quality detection in the transportation industry. A method for quickly evaluating the bearing capacity of continuous beam based on the influence line area of bending moment of arbitrary cross section includes such steps as using the vehicle with known axle weight, axle distance and axle number as loading vehicle, and setting the weight P of the rear axle I of loading vehicle 1 Weight P of rear axle II 2 Weight P of rear axle III 3 The method comprises the steps of carrying out a first treatment on the surface of the Then constructing the effect function of bending moment at any section x along with the change of the moving vehicle
Figure DDA0003916838930000011
Finally to
Figure DDA0003916838930000012
Taking the integral of the maximum peak value interval of n times as a denominator, wherein n is 0-1; under the same condition, the integral value of the effect function of the bending moment at the position x of the test section along with the change of the moving vehicle is used as a molecule, and the ratio of the molecule to the denominator is smaller than 1, so that the bridge bearing capacity meets the requirement. The invention can improve the detection precision and efficiency of the existing bridge load and reduce the cost of manpower and material resources.

Description

Method for rapidly evaluating bearing capacity of continuous beam based on area of influence line of bending moment of arbitrary section
Technical Field
The invention belongs to the technical field of bridge and culvert engineering quality detection in the transportation industry, and particularly relates to a method for rapidly evaluating the bearing capacity of a continuous beam based on the area of an influence line of bending moment of any section.
Background
The method is characterized in that the method is used for evaluating the state of the existing bridge and determining the bearing capacity of the bridge, the state of the bridge can be intuitively evaluated by using a load test, the evaluation result is more accurate and reliable, but the problem of long time required by the load test exists, the whole test process needs to be closed, the number of the arranged measuring points is large, considerable time and detection cost are required, the actual detection result is usually compared with the analysis of a structural model, the theoretical data are calculated by different software to a certain extent, and the actual state cannot be accurately reflected according to the algorithm of influencing the load of the line point multiplication test. The traditional load test is to calculate the test load efficiency under the test load effect within a certain range, apply the test load on the appointed position of the bridge, and measure the static displacement, static strain and other parameters of the test section, so as to evaluate the working performance and the service capacity of the bridge. The traditional method needs more vehicles, the vehicle finding is difficult in a test site, the load of the loaded vehicle cannot completely meet the calculated load, the vehicle load distribution position is changed at different working conditions, the randomness is too high, and the repeated test data has low contrast.
Therefore, how to solve the above problems in actual detection and calculation is an important technical problem to be solved.
Disclosure of Invention
The invention overcomes the defects of the technical problems, provides the method for rapidly evaluating the bearing capacity of the continuous beam based on the influence of any section bending moment on the line area, can improve the detection precision and efficiency of the existing bridge load, and reduces the cost of manpower and material resources.
In order to solve the technical problems, the invention adopts the following technical scheme:
1. the method for rapidly evaluating the bearing capacity of the continuous beam based on the area of the bending moment influence line of any section comprises the following steps of:
(1) The vehicle with known axle weight, axle base and axle number is used as a loading vehicle, and the weight P of the rear axle I of the loading vehicle is set 1 Weight P of rear axle II 2 Weight P of rear axle III 3 ；
(2) Construction of moment-to-moment effect function of any section x along with change of moving vehicle
The bridge can be divided into two ends of a bridge head and a bridge tail, the bridge head is selected as an origin, the bridge head is an upper bridge end of a loading vehicle, the loading vehicle passes through the bridge from the bridge head at a constant speed, the strain value of any section x is collected, and the bending moment of any section x along with the change effect function expression of the moving vehicle is obtained by performing inverse calculation on the actual rigidity of the measured strain value and the control section on site:
Figure SMS_1
in the method, in the process of the invention,
Figure SMS_2
for the effect of the change of bending moment at any section x along with the moving vehicleA function; />
Figure SMS_3
Z is the expression of a bending moment influence line at an arbitrary section x 1 For rear wheelbase, Z 2 X is the front wheelbase p The distance from the rear axle of the loading vehicle to the origin is calculated;
(3) For a pair of
Figure SMS_4
Taking the integral of the maximum peak value interval of n times as a denominator, wherein n is 0-1; under the same condition, the integral value of the effect function of the bending moment at the position x of the test section along with the change of the moving vehicle is used as a molecule, and the ratio of the molecule to the denominator is smaller than 1, so that the bridge bearing capacity meets the requirement.
Further, the continuous beam is a three-span arbitrary-section arbitrary-span continuous beam, and the continuous beam comprises a bridge No. 1 span, a bridge No. 2 span and a bridge No. 3 span.
Further, in the step (2), the 1# span of the continuous beam is defined as L 1 2# span L 2 3# span L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence factors of the 1# crossing influence lines are a respectively 1 、a 2 The influence factors of the No. 2 cross influence lines are b respectively 1 、b 2 The 3# cross-influence line influence factors are c respectively 1 、c 2 The method comprises the steps of carrying out a first treatment on the surface of the The bending moment influence line expression at any section x is (2), (3), (4):
Figure SMS_5
Figure SMS_6
Figure SMS_7
wherein: l is the total span of the three-span continuous beam, i.e. l=l 1 +L 2 +L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence line influence factors are respectively:
Figure SMS_8
Figure SMS_9
Figure SMS_10
in the method, in the process of the invention,
Figure SMS_11
/>
Figure SMS_12
Figure SMS_13
Figure SMS_14
Figure SMS_15
compared with the prior art, the invention has the following beneficial effects:
1. the method for rapidly evaluating the bearing capacity of the continuous beam based on the area of the influence line of the bending moment of any cross section, provided by the invention, has the advantages that the derivation formula of the influence line of the novel method for evaluating the bearing capacity of the continuous beam is simple and easy to understand, the analytic solution is directly obtained, the analytic solution is more accurate than software calculation, the real-time adjustment can be carried out at any time after the actual measurement of each parameter is changed, and the operability is strong; the method is used for deducing the influence line analysis type of any section position of the bridge with different spans and section rigidities, introducing the axle weight and the axle distance of the loading vehicle to be tested, solving the change effect function of the bending moment at the control section when the specific loading vehicle moves from the beam end to the tail of the continuous beam according to the method, solving the specific section area through function integration, comparing with the measured value, and judging the bearing capacity state of the bridge through the checking coefficient.
2. The invention utilizes the integral area evaluation of the bending moment effect function to more comprehensively reflect the bearing capacity state of the actual bridge, and breaks through the limitation of the traditional influence line point multiplied by the theoretical load.
3. The method and the process are simple and feasible, the actual test effect is obvious, the detection precision and efficiency of the existing bridge load can be improved, the cost of manpower and material resources is reduced, and the method and the process have larger actual engineering application value.
Drawings
FIG. 1 is a schematic view of a loading vehicle according to embodiment 1 of the present invention;
FIG. 2 is a side view of the bridge layout of example 1 of the present invention;
FIG. 3 is a top plan view of the bridge of example 1 of the present invention;
FIG. 4 is a schematic cross-sectional view of a bridge according to example 1 of the present invention;
FIG. 5 is a cross-sectional dimension of a bridge according to example 1 of the present invention;
FIG. 6 is a strain gage layout of example 1 of the present invention;
FIG. 7 is a graph of theoretical strain curve and measured strain curve for bridge section bending moment of example 1 of the present invention;
Detailed Description
The invention will be further described with reference to the drawings and examples. It should be noted that the specific embodiments of the present invention are only for describing the technical solution more clearly, and should not be taken as limiting the scope of the present invention.
1. The method for rapidly evaluating the continuous beam bearing capacity based on the area of the bending moment influence line of any section is characterized in that when the bridge influence line is the bending moment influence line of any section x of the bridge, the method for evaluating the continuous beam bearing capacity comprises the following steps:
(1) The vehicle with known axle weight, axle base and axle number is used as a loading vehicle, and the weight P of the rear axle I of the loading vehicle is set 1 Weight P of rear axle II 2 Weight P of rear axle III 3 ；
(2) Construction of moment-to-moment effect function of any section x along with change of moving vehicle
The bridge can be divided into two ends of a bridge head and a bridge tail, the bridge head is selected as an origin, the bridge head is an upper bridge end of a loading vehicle, the loading vehicle passes through the bridge from the bridge head at a constant speed, the strain value of any section x is collected, and the bending moment of any section x along with the change effect function expression of the moving vehicle is obtained by performing inverse calculation on the actual rigidity of the measured strain value and the control section on site:
Figure SMS_16
in the method, in the process of the invention,
Figure SMS_17
the effect function of the bending moment at any section x along with the change of the moving vehicle is as follows; />
Figure SMS_18
Z is the expression of a bending moment influence line at an arbitrary section x 1 For rear wheelbase, Z 2 X is the front wheelbase p The distance from the rear axle of the loading vehicle to the origin is calculated;
(3) For a pair of
Figure SMS_19
Taking the integral of the maximum peak value interval of n times as a denominator, wherein n is 0-1; under the same condition, the integral value of the effect function of the bending moment at the position x of the test section along with the change of the moving vehicle is used as a molecule, and the ratio of the molecule to the denominator is smaller than 1, so that the bridge bearing capacity meets the requirement.
The continuous beam is a three-span continuous beam with any cross section and any span, and comprises a bridge No. 1 span, a bridge No. 2 span and a bridge No. 3 span.
In the step (2), defining the 1# span of the continuous beam as L 1 2# span L 2 3# span L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence factors of the 1# crossing influence lines are a respectively 1 、a 2 The influence factors of the No. 2 cross influence lines are b respectively 1 、b 2 The 3# cross-influence line influence factors are c respectively 1 、c 2 The method comprises the steps of carrying out a first treatment on the surface of the Then any cross sectionThe bending moment influence line expression at x is (2), (3) and (4):
Figure SMS_20
Figure SMS_21
/>
Figure SMS_22
wherein: l is the total span of the three-span continuous beam, i.e. l=l 1 +L 2 +L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence line influence factors are respectively:
Figure SMS_23
Figure SMS_24
Figure SMS_25
in the method, in the process of the invention,
Figure SMS_26
Figure SMS_27
Figure SMS_28
Figure SMS_29
Figure SMS_30
example 1
In the embodiment, a certain three-span constant-section constant-span continuous beam bridge is evaluated, the upper part of the known bridge is a 3X 30m assembled prestressed concrete continuous box girder, a prefabricated simple support is adopted for installation, and then a cast-in-situ continuous joint is formed into a continuous structure. The lower structure of the bridge adopts column piers, column platforms and bored pile foundations.
The span is L 1 ＝L 2 ＝L 3 Concrete c50 with modulus of elasticity 3.45×10 =l/3=30m 4 The cross-sectional stiffness was calculated as ei= 5.02362 ×10 MPa 7 kN.m 2 The test loading vehicle adopts a triaxial loading vehicle shown in figure 1, wherein the rear axle weight P 1 ＝P 2 ＝150kN，P 3 ＝70kN，Z 1 ＝1.35m，Z 2 =3.6m. The bridge type layout and the cross section size are shown in fig. 5-7, wherein the side view layout of the bridge is shown in fig. 2, the top view layout of the bridge is shown in fig. 3, the cross section structure schematic diagram of the bridge is shown in fig. 4, and the cross section size of the bridge is shown in fig. 5. The strain measuring point layout is shown in figure 6. The theoretical strain curve is shown in FIG. 7 when the span is 20 m.
The method provided by the invention is used for verifying the bending moment influence line expression of the cross section of the 1# cross section, driving the vehicle to slowly open from the bridge head to the bridge tail at a uniform speed, and obtaining a strain average value change curve of the concrete of the 1# cross section, wherein the actual measured strain change curve is shown in fig. 7. The actual test adopts the same method to obtain a strain average value change curve, and the 1# cross-bearing capacity condition is evaluated through the ratio of the areas of the two curves integrated in a proper interval range. When the ratio is smaller than 1, the bearing capacity meets the requirement, and when the ratio is larger than 1, the bearing capacity does not meet the requirement. The method comprises the following specific steps:
the influence line analysis formula of the side span midsection (x=l1/2=15m) is obtained:
Figure SMS_31
Figure SMS_32
Figure SMS_33
let x=l 1 And 2, the change rule of the cross-section bending moment influence line of the 1 st span can be expressed by an expression.
Figure SMS_34
The bending moment at any section x deduced by the invention is well matched with the effect function formula of the change of the bending moment along with the moving vehicle and the calculation result by adopting Midas finite element software, thereby verifying the correctness of the formula. The curve equation of M (xp) can be obtained by multiplying the test load by the curve point of the influence line obtained by the formula derivation for any variable-section three-span continuous beam, the obtained area is integrated, and then the obtained area is compared with and evaluated by the measured value. The calculation is simple and clear, and the method can be well applied to engineering examples.
The method for rapidly evaluating the bearing capacity of the continuous beam based on the area of the influence line of the bending moment of any section is simple and easy to understand, the deduction formula can comprehensively reflect the whole state of the bridge, the limitation that the influence line points multiply the theoretical load to serve as an evaluation algorithm is broken through, and the reaction curve can be measured by arranging one to a plurality of strain measuring points on a certain control section under the condition that traffic is not interrupted, and then the comparison and judgment can be carried out by a specific test car running at a constant speed. The method disclosed by the invention is simple and convenient, obvious in effect, simple in calculation, high in accuracy and wide in engineering application prospect.
The foregoing description is directed to the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the invention, and all equivalent changes or modifications made under the technical spirit of the present invention should be construed to fall within the scope of the present invention.

Claims (3)

1. The method for rapidly evaluating the continuous beam bearing capacity based on the area of the bending moment influence line of any section is characterized in that when the bridge influence line is the bending moment influence line of any section x of the bridge, the method for evaluating the continuous beam bearing capacity comprises the following steps:
(1) The vehicle with known axle weight, axle base and axle number is used as a loading vehicle, and the weight P of the rear axle I of the loading vehicle is set 1 Weight P of rear axle II 2 Weight P of rear axle III 3 ；
(2) Constructing a bending moment variation effect function of any section x along with the moving vehicle;
the bridge can be divided into two ends of a bridge head and a bridge tail, the bridge head is selected as an origin, the bridge head is an upper bridge end of a loading vehicle, the loading vehicle passes through the bridge from the bridge head at a constant speed, the strain value of any section x is collected, and the bending moment of any section x along with the change effect function expression of the moving vehicle is obtained by performing inverse calculation on the actual rigidity of the measured strain value and the control section on site:
Figure QLYQS_1
in the method, in the process of the invention,
Figure QLYQS_2
the effect function of the bending moment at any section x along with the change of the moving vehicle is as follows; />
Figure QLYQS_3
Z is the expression of a bending moment influence line at an arbitrary section x 1 For rear wheelbase, Z 2 X is the front wheelbase p The distance from the rear axle of the loading vehicle to the origin is calculated;
(3) For a pair of
Figure QLYQS_4
Taking the integral of the maximum peak value interval of n times as a denominator, wherein n is 0-1; under the same condition, the integral value of the effect function of the bending moment at the position x of the test section along with the change of the moving vehicle is used as a molecule, and the ratio of the molecule to the denominator is smaller than 1, so that the bridge bearing capacity meets the requirement.
2. The method for rapidly evaluating the bearing capacity of the continuous beam based on the area of the influence line of the bending moment of any cross section according to claim 1, wherein the continuous beam is a three-span continuous beam with any cross section and any span, and comprises a bridge 1# span, a bridge 2# span and a bridge 3# span.
3. The method for rapidly evaluating the bearing capacity of a continuous beam based on the area of influence line of bending moment of arbitrary section according to claim 2, wherein in the step (2), the 1# span of the continuous beam is defined as L 1 2# span L 2 3# span L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence factors of the 1# crossing influence lines are a respectively 1 、a 2 The influence factors of the No. 2 cross influence lines are b respectively 1 、b 2 The 3# cross-influence line influence factors are c respectively 1 、c 2 The method comprises the steps of carrying out a first treatment on the surface of the The bending moment influence line expression at any section x is (2), (3), (4):
Figure QLYQS_5
Figure QLYQS_6
/>
Figure QLYQS_7
wherein: l is the total span of the three-span continuous beam, i.e. l=l 1 +L 2 +L 3 The method comprises the steps of carrying out a first treatment on the surface of the The influence line influence factors are respectively:
Figure QLYQS_8
Figure QLYQS_9
Figure QLYQS_10
in the method, in the process of the invention,
Figure QLYQS_11
Figure QLYQS_12
Figure QLYQS_13
Figure QLYQS_14
Figure QLYQS_15
/>
CN202211344788.9A 2022-10-31 2022-10-31 Method for rapidly evaluating bearing capacity of continuous beam based on area of influence line of bending moment of arbitrary section Pending CN116105951A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117554006A (en) * 2024-01-09 2024-02-13 北京云庐科技有限公司 Bridge health assessment method and system based on dynamic strain monitoring

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117554006A (en) * 2024-01-09 2024-02-13 北京云庐科技有限公司 Bridge health assessment method and system based on dynamic strain monitoring
CN117554006B (en) * 2024-01-09 2024-03-29 北京云庐科技有限公司 Bridge health assessment method and system based on dynamic strain monitoring

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