CN110487496A - Improvement area-moment method based on the strain of long gauge length identifies deflection of bridge span method - Google Patents
Improvement area-moment method based on the strain of long gauge length identifies deflection of bridge span method Download PDFInfo
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Abstract
The invention discloses a kind of improvement area-moment methods based on the strain of long gauge length to identify deflection of bridge span method, comprising the following steps: S1 determines bridge lengthLWith bridge section depth of neutral axish；S2, it is continuous along its length on bridge to arrangemA long gauge length strain transducer, the test long gauge length that each long gauge length strain transducer measures under any load action strain；S3: using the functional relation for improving area-moment method acquisition amount of deflection and strain；S4 is calculated on bridge according to the functional relation of amount of deflection and straintMomentxPoint amount of deflection.The present invention is based on area-moment method is improved, the functional relation of amount of deflection and strain can be derived.The amount of deflection distribution for the amount of deflection distribution and any time flowering structure that any point changes over time in the available structure of strain measured is combined by formula.This method is not influenced by external loads, is suitable for static load and is acted in dynamic loads, measurement accuracy is high, and stability is good, easy to use.
Description
Technical field
The invention belongs to engineering monitoring technical fields, and in particular to a kind of improvement area-moment method based on the strain of long gauge length
Identify deflection of bridge span method.
Background technique
With the rapid development of society, scientific and technical to be constantly progressive, China achieves considerable in terms of bridge construction
Development, national more than 600,000 seat of different types of rridges, but owe thorough due to setting timing considerations, in addition by various in work progress
The influence of indefinite sexual factor and build up that rear maintenance measure is improper and the work of the natural aging of material, overweight vehicle and accidental load
With nearly 1/4 bridge all haves the defects that the hidden danger such as different degrees of, damage and functional failure.Reduce bridge security performance
And normal usage function, lead to catastrophic burst accident.
The continuous generation of bridge security accident, so that the monitoring structural health conditions of bridge just become an essential work
Make.In the health monitoring of bridge, the deformation of structure is the important indicator for evaluating bridge safty and the key of bridge monitoring
Parameter.Amount of deflection can be with the use state and security performance of effective evaluation bridge, therefore to the prison of deflection of bridge span as engineering parameter
Measuring tool is significant.
Currently, mainly being measured with independent measuring device to structural deflection, such as displacement sensor, GPS, laser image
Method, the method for photoelectric imaging, connection tube method etc..
These methods there are the shortcomings that it is as follows:
(1) these measurement methods are only applicable to the short-term measurement of bridge, affected by environment larger, are not suitable for long term monitoring；
(2) there is installation inconvenience in these instruments, time-consuming and laborious, it is difficult to realize the real time on-line monitoring to amount of deflection；
(3) low measurement accuracy, instrument price are more expensive；
(4) independent measuring device increases data volume, increases monitoring cost.
Summary of the invention
It is an object of the invention to overcome deficiency in the prior art, it is curved to propose a kind of improvement based on the strain of long gauge length
Square area-method identifies deflection of bridge span method, solves the problems, such as that prior art measurement deflection of bridge span needs to refer to a little.
In order to solve the above technical problems, the present invention provides a kind of improvement area-moment method identifications based on the strain of long gauge length
Deflection of bridge span method, characterized in that the following steps are included:
S1 determines bridge length L and bridge section depth of neutral axis h；
S2 continuously arranges m long gauge length strain transducers along its length on bridge, tests under any load action
The long gauge length strain that each long gauge length strain transducer measures；
S3: using the functional relation for improving area-moment method acquisition amount of deflection and strain；
S4 calculates t moment x point amount of deflection on bridge according to the functional relation of amount of deflection and strain.
Further, the functional relation of amount of deflection and strain are as follows:
Wherein,The integrating range of n-th of sensor is represented,Indicate i-th long gauge length strain transducer in t
Carve the long gauge length strain measured, LnIndicate the gauge length of n-th long gauge length strain transducer, θA(t) A under t moment is indicated
The corner of point.
Further, when calculating bridge x point amount of deflection according to amount of deflection and the functional relation of strain, need first to judge x point
In which long gauge length sensor footprint domain, ifThen x point is located at i-th long gauge length sensing
In device overlay area；And it defines
Further, the process for obtaining the functional relation of amount of deflection and strain using area-moment method is improved are as follows:
The length for defining bridge is L, and A, C point are the endpoint of bridge, and B point is any point x on beam, and Δ is that A point is scratched and write music
The tangent line of line is at a distance from B point sag curve is on B point vertical direction, the horizontal distance of x A, B point-to-point transmission；
According to area-moment method it follows that
Wherein, M (z) is the corresponding moment of flexure of A, B point-to-point transmission any point z, X1For the distance of B point to micro- section of dz, EI is beam
Bending stiffness；
The amount of deflection of B point can be calculated by geometrical relationship, deflection formula may be expressed as:
Wherein, θAFor the corner of A point；
Similarly, as x=L, vertical deviation delta=θ between the tangent line of A point sag curve and the tangent line of C point sag curveAL can calculate θ based on formula (2)A:
According to additional coefficient, the sectional curvature of any z point is indicated are as follows:
Wherein ε (z), h and 1/ ρ are respectively the strain of z point, bridge section depth of neutral axis and sectional curvature；
In the case where external loads are unknown, the relationship of strain with moment of flexure is established according to sectional curvature, is not knowing outside
The amount of deflection of arbitrary point x is derived in the case where load by strain, relation formula (2) can be converted to:
The method is known as improving area-moment method, can derive any point amount of deflection by strain based on area-moment method is improved
General formulae:
Wherein θA(t), d (x, t) and ε (z, t) is illustrated respectively in the corner of A point under t moment, amount of deflection and z point at x point
The strain at place；
Available by formula 6, t moment x point amount of deflection is expressed as:
Wherein,Represent the integrating range of n-th of sensor；Indicate i-th long gauge length strain transducer in t
Carve the long gauge length strain measured；LnIndicate the gauge length of n-th long gauge length strain transducer, θA(t) the A point under t moment is indicated
Corner, can be found out by formula 3.
Further, the gauge length of m long gauge length strain transducer and it is equal to bridge length, i.e.,Wherein
LiFor the gauge length of i-th long gauge length strain transducer.
Further, long gauge length strain transducer is deployed in the bottom of bridge.
Further, m long gauge length strain transducers are uniformly arranged.
Compared with prior art, the beneficial effects obtained by the present invention are as follows being: the present invention only needs to arrange in the bottom of bridge
Long gauge length strain transducer measures the long gauge length strain-responsive for putting bridge each unit at any time.Based on improvement moment area
Method can derive the functional relation of amount of deflection and strain.It is combined by formula any one in the available structure of strain measured
The amount of deflection distribution of amount of deflection distribution and any time flowering structure that point changes over time.This method is not influenced by external loads,
It is acted on suitable for static load and in dynamic loads, measurement accuracy is high, and stability is good, easy to use.
Detailed description of the invention
Fig. 1 is area-moment method principle；
Fig. 2: (a) being the long gauge length Strain Distribution of simply supported beam each unit；(b) freely-supported beam deflection is distributed；
Fig. 3 is deflection of bridge span identification process schematic diagram；
Fig. 4 is the amount of deflection distribution curve under two kinds of operating conditions.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.Following embodiment is only used for clearly illustrating the present invention
Technical solution, and not intended to limit the protection scope of the present invention.
For the bridge of freely supported structure, by the sag curve and M curve under external force as shown in Figure 1, the length of bridge
Degree direction is x-axis, is y-axis perpendicular to bridge length direction, and the length of bridge is L, and A, C point are the endpoint of bridge, and B point is beam
Upper any point x, Δ are the tangent lines of A point sag curve at a distance from B point sag curve is on B point vertical direction, x A, B two
Horizontal distance between point.
According to area-moment method it follows that
Wherein, M (z) is the corresponding moment of flexure of A, B point-to-point transmission any point z, X1For the distance of B point to micro- section of dz, EI is beam
Bending stiffness.
The amount of deflection of B point can be calculated by geometrical relationship, deflection formula may be expressed as:
Wherein, θAFor the corner of A point.
Similarly, as x=L, vertical deviation delta=θ between the tangent line of A point sag curve and the tangent line of C point sag curveAL can calculate θ based on formula (2)A:
Usual formula (2) is suitable for the situation known to Bending moment distribution.It is described below when Bending moment distribution (or external loads)
How the relationship of amount of deflection and strain is determined under unknown situation.
According to additional coefficient, the sectional curvature of any z point is indicated are as follows:
Wherein ε (z), h and 1/ ρ are respectively the strain of z point, bridge section depth of neutral axis and sectional curvature.
In the case where external loads are unknown, the relationship of strain with moment of flexure is established according to sectional curvature, is not knowing outside
The amount of deflection of arbitrary point x is derived in the case where load by strain.It can be converted to according to this relation formula (2):
The method is known as improving area-moment method, not only has the advantages that area-moment method, but also without the concern for load
Position and load type, be suitable for static load and dynamic loads, based on improve area-moment method by strain can derive
The general formulae of any point amount of deflection:
Wherein θA(t), d (x, t) and ε (z, t) is illustrated respectively in the corner of A point under t moment, at the amount of deflection and z point at x point
Strain.
It is assumed that in bridge bottom continuous installation m long gauge length strain transducers along its length, referring to fig. 2 shown in a, the
The gauge length L of i long gauge length strain transducersiThe long gauge length strain measured in range is denoted asAndWherein
L is the length of bridge.
By taking simply supported beam as an example (Fig. 2 b), simply supported beam can be freely rotated in A point, and A point abscissa is that 0, B point abscissa is
X, available by formula 6, t moment x point amount of deflection is expressed as:
Wherein,Represent the integrating range of n-th of sensor.Indicate i-th long gauge length strain transducer in t moment
The long gauge length strain measured.LnIndicate the gauge length of n-th long gauge length strain transducer, θA(t) the A point under t moment is indicated
Corner, can be found out by formula 3, the meaning of dependent variable is the same as above.
It is found that needing first to judge which long gauge length sensing x point is located at when calculating bridge x point amount of deflection using formula 7
In device overlay area, if therefore definedThen x point is located in the domain of i-th long gauge length sensor footprint.
It is 1 if there is i value, then definesIf this formula definition formula 7 calculating in there is this symbol, it is specified that
Its value is 0.
Based on the above analysis, a kind of improvement area-moment method based on the strain of long gauge length of the invention identifies deflection of bridge span side
Method, including following procedure:
Step 1: determining the depth of neutral axis h in bridge length L and bridge section；
Step 2: continuously m long gauge length strain transducers of arrangement, test are made in Arbitrary Load along its length on bridge
The long gauge length strain measured with lower each long gauge length strain transducer；
Step 3: by long gauge length strain-responsiveThe natural axis h of bridge length L and structural section substitutes into formula (7)
The amount of deflection distribution of bridge is calculated in amount of deflection distribution function d (x, t).
The beneficial effects of the present invention are:
(1) this method does not need the reference point of selected similar displacement sensor, easy to operate, greatlys save human cost；
(2) this method requires no knowledge about position and the type of external loads, while being suitable for static and dynamic loads；
(3) single-sensor need to only be used just to obtain the amount of deflection distribution and any time that structure arbitrary point changes over time
The lower amount of deflection along bridge length is distributed, and stability is good, applied widely.
Embodiment
Amount of deflection inverting is carried out to i-shape steel beam below with the above method, the I-shaped freely-supported steel of a root long degree 8m is set
Beam, sectional dimension are 200 × 120 × 4.5 × 6mm, and depth of neutral axis is 0.1m, apply two-axle car load, vehicle on beam
The weight of load antero posterior axis is 5000N, wheelbase 0.4m.2 kinds of loading conditions are set altogether, are denoted as operating condition D1, operating condition D2, D1 are
Trolley is still at i-shape steel beam span centre position, and D2 is that trolley is travelled with the speed of 18km/h by entire i-shape steel beam.
Fig. 4 (a) is that simply supported beam is distributed along the amount of deflection of beam length under static load；Fig. 4 (b) is to become at any time at simply supported beam span centre position
The amount of deflection of change is distributed.Wherein true value refers to that the deflection value directly extracted in finite element, calculated value are referred to according to the side this paper
The deflection value that method calculates.True value and calculated value worst error are respectively 1.05%, 1.2% under two kinds of operating conditions, and error can be controlled
System has high-precision to guarantee in a small range.D1, D2 display of regime this method are applicable in dynamic static load.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvements and modifications, these improvements and modifications can also be made
Also it should be regarded as protection scope of the present invention.
Claims (7)
1. the improvement area-moment method based on the strain of long gauge length identifies deflection of bridge span method, characterized in that the following steps are included:
S1 determines bridge length L and bridge section depth of neutral axis h；
S2 continuously arranges m long gauge length strain transducers, test each length under any load action along its length on bridge
The long gauge length strain that gauge length strain transducer measures；
S3: using the functional relation for improving area-moment method acquisition amount of deflection and strain；
S4 calculates t moment x point amount of deflection on bridge according to the functional relation of amount of deflection and strain.
2. the improvement area-moment method according to claim 1 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is the functional relation of amount of deflection and strain are as follows:
Wherein,The integrating range of n-th of sensor is represented,Indicate that i-th long gauge length strain transducer is measured in t moment
Long gauge length strain, LnIndicate the gauge length of n-th long gauge length strain transducer, θA(t) turn of the A point under t moment is indicated
Angle.
3. the improvement area-moment method according to claim 2 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is to need first to judge which length x point is located at when calculating bridge x point amount of deflection according to amount of deflection and the functional relation of strain
In the domain of gauge length sensor footprint, ifThen x point is located in the domain of i-th long gauge length sensor footprint；
And it defines
4. the improvement area-moment method according to claim 1 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is, using the process for the functional relation for improving area-moment method acquisition amount of deflection and strain are as follows:
The length for defining bridge is L, and A, C point are the endpoint of bridge, and B point is any point x on beam, and Δ is A point sag curve
Tangent line is at a distance from B point sag curve is on B point vertical direction, the horizontal distance of x A, B point-to-point transmission；
According to area-moment method it follows that
Wherein, M (z) is the corresponding moment of flexure of A, B point-to-point transmission any point z, X1For the distance of B point to micro- section of dz, EI is that the bending resistance of beam is rigid
Degree；
The amount of deflection of B point can be calculated by geometrical relationship, deflection formula may be expressed as:
Wherein, θAFor the corner of A point；
Similarly, as x=L, vertical deviation delta=θ between the tangent line of A point sag curve and the tangent line of C point sag curveAL is based on
Formula (2) can calculate θA:
According to additional coefficient, the sectional curvature of any z point is indicated are as follows:
Wherein ε (z), h and 1/ ρ are respectively the strain of z point, bridge section depth of neutral axis and sectional curvature；
In the case where external loads are unknown, the relationship of strain with moment of flexure is established according to sectional curvature, is not knowing external loads
In the case where the amount of deflection of arbitrary point x is derived by strain, relation formula (2) can be converted to:
The method is known as improving area-moment method, can derive the general of any point amount of deflection by strain based on area-moment method is improved
Formula:
Wherein θA(t), d (x, t) and ε (z, t) is illustrated respectively in the corner of A point under t moment, answering at the amount of deflection and z point at x point
Become；
Available by formula 6, t moment x point amount of deflection is expressed as:
Wherein,Represent the integrating range of n-th of sensor；Indicate that i-th long gauge length strain transducer is measured in t moment
Long gauge length strain；LnIndicate the gauge length of n-th long gauge length strain transducer, θA(t) turn of the A point under t moment is indicated
Angle can be found out by formula 3.
5. the improvement area-moment method according to claim 1 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is, the gauge length of m long gauge length strain transducers and is equal to bridge length, i.e.,Wherein LiFor i-th long mark
Gauge length away from strain transducer.
6. the improvement area-moment method according to claim 1 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is that long gauge length strain transducer is deployed in the bottom of bridge.
7. the improvement area-moment method according to claim 1 based on the strain of long gauge length identifies deflection of bridge span method, special
Sign is that m long gauge length strain transducers are uniformly arranged.
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Cited By (6)
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| CN111413056A (en) * | 2020-03-31 | 2020-07-14 | 广西壮族自治区玉林公路发展中心 | Method for positioning neutral axis of simply supported beam structure with few strain sensors |
| CN111912388A (en) * | 2020-06-30 | 2020-11-10 | 同恩(上海)工程技术有限公司 | Structural upright column inclination monitoring method and system based on fitting inversion and storage medium |
| CN112179264A (en) * | 2020-09-22 | 2021-01-05 | 华东交通大学 | Long gauge length strain-based prestressed carbon fiber plate bridge reinforcing effect monitoring method |
| CN113358048A (en) * | 2021-06-10 | 2021-09-07 | 广西大学 | Method for recognizing beam structure deflection by graph multiplication based on distributed optical fiber |
| CN114323510A (en) * | 2021-11-30 | 2022-04-12 | 河海大学 | Method for rapidly detecting deflection of simply supported beam bridge |
| CN115979551A (en) * | 2022-12-15 | 2023-04-18 | 广西北投交通养护科技集团有限公司 | Continuous beam structure damage identification method based on strain time-course curve |
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Cited By (10)
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| CN111413056A (en) * | 2020-03-31 | 2020-07-14 | 广西壮族自治区玉林公路发展中心 | Method for positioning neutral axis of simply supported beam structure with few strain sensors |
| CN111413056B (en) * | 2020-03-31 | 2022-01-14 | 广西壮族自治区玉林公路发展中心 | Method for positioning neutral axis of simply supported beam structure with few strain sensors |
| CN111912388A (en) * | 2020-06-30 | 2020-11-10 | 同恩(上海)工程技术有限公司 | Structural upright column inclination monitoring method and system based on fitting inversion and storage medium |
| CN112179264A (en) * | 2020-09-22 | 2021-01-05 | 华东交通大学 | Long gauge length strain-based prestressed carbon fiber plate bridge reinforcing effect monitoring method |
| CN112179264B (en) * | 2020-09-22 | 2021-11-19 | 华东交通大学 | Long gauge length strain-based prestressed carbon fiber plate bridge reinforcing effect monitoring method |
| CN113358048A (en) * | 2021-06-10 | 2021-09-07 | 广西大学 | Method for recognizing beam structure deflection by graph multiplication based on distributed optical fiber |
| CN114323510A (en) * | 2021-11-30 | 2022-04-12 | 河海大学 | Method for rapidly detecting deflection of simply supported beam bridge |
| CN114323510B (en) * | 2021-11-30 | 2022-11-29 | 河海大学 | Method for quickly detecting deflection of simply supported beam bridge |
| CN115979551A (en) * | 2022-12-15 | 2023-04-18 | 广西北投交通养护科技集团有限公司 | Continuous beam structure damage identification method based on strain time-course curve |
| CN115979551B (en) * | 2022-12-15 | 2023-09-19 | 广西北投交通养护科技集团有限公司 | Continuous beam structure damage identification method based on strain time curve |
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