CN114547729A - Quantitative identification method for bending rigidity of steel-concrete composite beam - Google Patents

Quantitative identification method for bending rigidity of steel-concrete composite beam Download PDF

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CN114547729A
CN114547729A CN202210059856.0A CN202210059856A CN114547729A CN 114547729 A CN114547729 A CN 114547729A CN 202210059856 A CN202210059856 A CN 202210059856A CN 114547729 A CN114547729 A CN 114547729A
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满孝卫
陈建勇
黄青松
张扬
陈耀井
刘汉有
洪万
杨才千
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Jiangsu Expressway Engineering Conservation Co ltd
Jiangsu Menglianqiao Technology Co ltd
Jiangsu Suhuaiyan Expressway Management Co ltd
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Abstract

The invention discloses a quantitative identification method for bending rigidity of a steel-concrete composite beam, which belongs to the technical field of engineering monitoring.

Description

Quantitative identification method for bending rigidity of steel-concrete composite beam
Technical Field
The invention belongs to the technical field of engineering monitoring, and relates to a quantitative identification method for flexural rigidity of a steel-concrete composite beam.
Background
Steel-concrete composite beams are increasingly used in bridge engineering and building structures. The steel-concrete composite beam consists of a steel beam, a concrete plate and a shear connector, wherein the shear connector in the steel-concrete composite beam can effectively restrain the concrete plate and the steel beam to form a combined whole, so that the characteristics of high compressive strength of concrete and high tensile strength of the steel beam can be fully exerted, and the strength and the rigidity of a member are obviously improved. The shear connector determines the synergistic force effect of the concrete slab and the steel beam. The shear connector can transfer a longitudinal shear force of an interface of the concrete slab and the steel beam, and can suppress vertical separation of the concrete slab and the steel beam. Steel-composite beams often employ a studded connector, which is typically a flexible connector. In long-term use, due to the influence of various adverse factors such as various loading effects, environmental erosion, material aging, natural disasters and the like, slippage exists between a concrete slab and a steel beam interface, the concrete slab can crack, the steel-concrete composite beam bending rigidity is reduced due to the interface slippage and the concrete cracking, the bearing capacity is reduced, the deformation is obviously increased, catastrophic accidents can even occur in severe cases, and the great property and life loss is caused. Therefore, the method is particularly important for quantitatively identifying the bending rigidity of the steel-concrete composite beam in the service period.
At present, an evaluation method based on acceleration vibration test data is mainly adopted for the bending rigidity of the steel-concrete composite beam, and the principle is as follows: the natural vibration frequency of the structure is identified by measuring the acceleration of the structure and Fourier transform, and the natural vibration frequency and the bending rigidity of the structure have one-to-one correspondence, so that the bending rigidity of the structure is reduced, and the natural vibration frequency is reduced.
Such methods have the following disadvantages: (1) the self-vibration frequency is utilized to identify that the bending rigidity sensitivity of the structure is insufficient, and the nonlinearity of the structure cannot be considered; (2) the self-vibration frequency is utilized to identify the whole bending rigidity of the structure only, and the local bending rigidity of the structure cannot be identified with high precision; (3) whether the whole bending rigidity of the structure is changed or not can be only identified qualitatively by utilizing the natural vibration frequency, but the bending rigidity of the structure cannot be identified quantitatively.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a quantitative identification method for flexural rigidity of a steel-concrete composite beam, aiming at overcoming the defects of the prior art, and the present invention provides the following technical solutions: a quantitative identification method for bending rigidity of a steel-concrete composite beam comprises the following steps:
s1: arranging n long-gauge-length strain sensors at the bottom of the composite beam along the length direction of the composite beam to measure strain, wherein the area of the composite beam covered by one sensor k in the n long-gauge-length strain sensors is represented as a unit k;
s2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, calculating the strain according to the assumed beam neutral axis height and the assumed concrete slab neutral axis height, and calculating the stress of each strip through the material constitutive relation;
s3: calculating the axial force and the bending moment of each strip according to the stress and the strip size, and calculating an error function of the total axial force and an error function of the bending moment;
s4: defining an error index, and when the error index is equal to zero or the error index is minimum, determining the assumed height of the beam neutral axis and the assumed height of the concrete slab neutral axis as the actual height of the neutral axis;
s5: calculating the average curvature of the unit k according to the actual neutral axis height of the steel beam;
s6: and calculating the average bending rigidity of the unit k according to a bending moment curvature equation, and further solving the local bending rigidity of any unit.
Preferably, the step S1 assumes a concrete slab, and the steel beams respectively satisfy the assumption of a flat section, having the same curvature.
Preferably, in step S2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, and calculating the stress of each strip by using formulas (1) and (2) through the material constitutive relation;
εkz1＝-εk0z1/htk+εk0 (1)
wherein epsilonkz1Along the height direction z of the steel beam1Strain at the coordinates; h istkThe neutral axis height assumed for the beam; epsilonk0Measuring the average strain of the unit k for the sensor k at the bottom of the composite beam; z is a radical of1Calculating the distance from the position to the bottom surface of the steel beam;
εkz2＝(hck-z2)εk0/htk (2)
εkz2along the height direction z of the concrete slab2Strain at the location; h isckA neutral shaft height assumed for the concrete slab; epsilonk0/htkIs the curvature of the steel beam; z is a radical of2To calculate the distance of the location to the bottom surface of the concrete slab.
Preferably, in step S3: calculating the axial force and bending moment of each strip according to the stress and the strip size, and calculating the error function e of the total axial forcefError function e of bending momentmThe calculation formula is as follows:
Figure BDA0003477775750000031
wherein the content of the first and second substances,Fg，Fcand FsIs an axial force generated by steel beam, concrete slab and reinforcing steel bartAnd btThe height and the width of the I-shaped steel beam are respectively; t is twAnd tfWeb and flange thicknesses, hcAnd bcRespectively the height and the width of the section of the concrete slab; sigmat(εkz1) The stress of the steel beam; sigmac(εkz2) Stress for a concrete slab; sigmasStress of steel bars in a concrete slab; a. thesThe area of the steel bar in the concrete slab;
Figure BDA0003477775750000032
wherein M isc，MgAnd MsMoment, M, caused by concrete slabs, steel beams and reinforcing bars, respectivelypMoment caused by external load; z is a radical of1Calculating the distance between the point and the bottom surface of the steel beam; z is a radical of2To calculate the distance of the point to the bottom surface of the slab; a issThe distance from the centroid of the steel bar to the bottom surface of the concrete slab;
Figure BDA0003477775750000033
Figure BDA0003477775750000034
preferably, in step S4: to guarantee the assumed htkAnd hckSatisfy the formulas (3) and (4) at the same time, define the error index efm(ii) a When e isfmWhen equal to zero or a minimum is taken, then h is assumedtkAnd hckNamely the actual neutralization shaft height;
Figure BDA0003477775750000035
preferably, in step S5: according to the actual center of the steel beamAnd height h of shafttkCalculating the average curvature of the unit k, and the formula is as follows:
Figure BDA0003477775750000036
wherein the content of the first and second substances,
Figure BDA0003477775750000037
is the average curvature of the cell k.
Preferably, in step S6: calculating the average bending rigidity of the unit k according to a bending moment curvature equation, wherein the formula is as follows:
Figure BDA0003477775750000041
wherein, EIkIs the average bending stiffness of unit k.
Has the advantages that: (1) the method adopts the long-gauge strain sensor which can cover the damaged part of the composite beam, so that the sensitivity is higher than that of an acceleration-based method; (2) the method considers the non-linear factors such as the interface slippage of the steel-concrete composite beam, the cracking of the concrete material and the like, thereby being suitable for the whole stress process of the composite beam; (3) the method can identify the local bending rigidity of each unit, and can combine the local bending rigidity of each unit into the overall structural rigidity, and the method can also be used as a damage identification index because the structural damage is usually local first damage; (4) the method can not only qualitatively judge whether the local bending rigidity of the composite beam is degraded, but also quantitatively identify the local bending rigidity of the composite beam.
Drawings
FIG. 1 is a schematic view of a steel-concrete composite beam;
FIG. 2 is a schematic view of deformation characteristics of a steel-concrete composite beam under an external load;
FIG. 3 is a schematic diagram of the strain analysis of cell k under an external load.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.
In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
Example 1:
referring to fig. 1 to 3, the invention provides a technical solution, and a method for quantitatively identifying flexural rigidity of a steel-concrete composite beam, comprising the following steps:
s1: arranging n long-gauge strain sensors at the bottom of the composite beam along the length direction of the composite beam to measure strain, wherein the area of the composite beam covered by one sensor k in the n long-gauge strain sensors is represented as a unit k;
s2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, calculating the strain according to the assumed beam neutral axis height and the assumed concrete slab neutral axis height, and calculating the stress of each strip through the material constitutive relation;
s3: calculating the axial force and the bending moment of each strip according to the stress and the strip size, and calculating an error function of the total axial force and an error function of the bending moment;
s4: defining an error index, wherein when the error index is equal to zero or is a minimum value, the assumed beam neutral axis height and the assumed concrete slab neutral axis height are the actual neutral axis height;
s5: calculating the average curvature of the unit k according to the actual neutral axis height of the steel beam;
s6: and calculating the average bending rigidity of the unit k according to a bending moment curvature equation, and further solving the local bending rigidity of any unit.
Further, the step S1 assumes a concrete slab, and the steel beams respectively satisfy the assumption of a flat section, having the same curvature.
Further, in the step S2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, and calculating the stress of each strip by using formulas (1) and (2) through the material constitutive relation;
εkz1＝-εk0z1/htk+εk0 (1)
wherein epsilonkz1Along the height direction z of the steel beam1Strain at the coordinates; h istkThe neutral axis height assumed for the beam; epsilonk0Measuring the average strain of the unit k for the sensor k at the bottom of the composite beam; z is a radical of1Calculating the distance from the position to the bottom surface of the steel beam;
εkz2＝(hck-z2)εk0/htk (2)
εkz2along the height direction z of the concrete slab2Strain at the location; h isckA neutral shaft height assumed for the concrete slab; epsilonk0/htkIs the curvature of the steel beam; z is a radical of2To calculate the distance of the location to the bottom surface of the concrete slab.
Further, in the step S3: calculating the axial force and bending moment of each strip according to the stress and the strip size, and calculating the error function e of the total axial forcefError function of bending moment emThe calculation formula is as follows:
Figure BDA0003477775750000061
wherein, Fg，FcAnd FsIs an axial force generated by steel beam, concrete slab and reinforcing steel bartAnd btThe height and the width of the I-shaped steel beam are respectively; t is twAnd tfWeb and flange thicknesses, hcAnd bcRespectively the height of the section of the concrete slabDegree and width; sigmat(εkz1) The stress of the steel beam; sigmac(εkz2) Stress for a concrete slab; sigmasStress of steel bars in a concrete slab; a. thesThe area of the steel bar in the concrete slab;
Figure BDA0003477775750000062
wherein M isc，MgAnd MsRespectively, moment caused by concrete slabs, beams and reinforcements, MpMoment caused by external load; z is a radical of1Calculating the distance between the point and the bottom surface of the steel beam; z is a radical of formula2To calculate the distance of the point to the bottom surface of the slab; a issThe distance from the centroid of the steel bar to the bottom surface of the concrete slab;
Figure BDA0003477775750000063
Figure BDA0003477775750000064
further, in the step S4: to guarantee the assumed htkAnd hckSatisfy the formulas (3) and (4) at the same time, define the error index efm(ii) a When e isfmWhen equal to zero or a minimum is taken, then h is assumedtkAnd hckNamely the actual neutralization shaft height;
Figure BDA0003477775750000065
further, in the step S5: according to the actual neutralization shaft height h of the steel beamtkCalculating the average curvature of the unit k, and the formula is as follows:
Figure BDA0003477775750000066
wherein the content of the first and second substances,
Figure BDA0003477775750000067
is the average curvature of the cell k.
Further, in the step S6: calculating the average bending rigidity of the unit k according to a bending moment curvature equation, wherein the formula is as follows:
Figure BDA0003477775750000071
wherein, EIkIs the average bending stiffness of unit k.
Example 2:
referring to fig. 1-3, on the basis of embodiment 1, the specific calculation process is as follows: the steel-concrete composite beam is shown in figure 1; the concrete slab and the steel beam are connected by ductile shear connectors (studs). The span and height of the composite beam are respectively represented as L and H, assuming that n long gauge length strain sensors are distributed at the bottom of the composite beam, and the section of the composite beam covered by the sensor k is represented as a unit k, as shown in fig. 2, assuming that the rigidity of the shear connector is sufficiently large, it can be considered that there is no interfacial slippage at the interface between the concrete slab and the steel beam, in the actual engineering, since the stud connector and the like are mostly ductile shear connectors and there is relative slippage at the interface between the concrete slab and the steel beam (see fig. 2), the concrete composite beam connected by the shear connector is partially combined, and thus the composite structure does not satisfy the assumption of a flat section. It is reasonable to assume that both the concrete slab and the steel beam satisfy the flat section assumption and that the curvatures of both are the same (see fig. 3).
Taking a steel-concrete combined beam unit k as an example, the height of a neutralization shaft of a steel beam is htkAlong the height direction z of the steel beam1Strain epsilon at coordinatekz1Can be expressed as:
εkz1＝-εk0z1/htk+εk0 (1)
wherein epsilonk0A sensor k at the bottom of the combined beam measures the average strain of the unit k;
z1-calculating the distance of the location to the bottom surface of the steel beam.
If equation (1) is a positive value, it indicates that the steel beam is in tension; if equation (1) is a negative value, it indicates that the steel beam is compressed. The curvature of the steel beam being epsilonk0/htkBased on the previous assumption that the steel beam and the concrete slab have the same curvature, the neutral axis height h of the concrete slab can be assumedckAlong the height direction z of the concrete slab2Strain epsilon at positionkz2Can be expressed as:
εkz2＝(hck-z2)εk0/htk (2)
wherein z is2-calculating the distance of the location to the bottom surface of the concrete slab.
If equation (2) is positive, it indicates that the concrete fiber is in tension; if equation (2) is negative, it indicates that the concrete fiber is compressed. By substituting equations (1) and (2) into the steel and concrete constitutive relations, respectively, the stress distribution along the composite beam in the height direction can be obtained. For steel-concrete composite beam unit k, the total tensile axial force should be equal to the total compressive axial force, assuming F respectivelyg，FcAnd FsIs the axial force generated by steel beams, concrete slabs and reinforcing steel bars. The height and width of the I-shaped steel beam are respectively htAnd btThe thickness of the web and the flange is twAnd tfThe height and the width of the section of the concrete slab are respectively hcAnd bc. Therefore, an axial force balance equation of the steel-concrete composite beam unit k can be obtained:
Figure BDA0003477775750000081
wherein σt(εkz1) -steel beam stress;
σc(εkz2) -concrete slab stress;
σs-stress of steel reinforcement in the concrete slab;
As-the area of reinforcement in the concrete slab.
At the same time, forIn the steel-concrete composite beam unit k, the moment caused by the internal force should be equal to the moment caused by the external force. Hypothesis sum Mc，MgAnd MsThe moment caused by concrete slab, steel beam and steel bar, and the moment caused by external load is MpTherefore, the moment balance equation of the steel-concrete composite beam unit k can be obtained:
Figure BDA0003477775750000082
wherein z is1-calculating the distance of the point to the bottom surface of the steel beam;
z2-calculating the distance of the point to the bottom surface of the slab;
as-the distance of the centroid of the rebar to the bottom surface of the slab.
From equations (3) and (4), the respective neutral axis heights of the steel beam and the concrete slab can be determined. Although it is difficult to solve the above equation directly to obtain htkAnd hckBut can be at each hypothesis htkAnd hckOn the basis of (a), the provisional calculation is performed step by step until the two assumed values satisfy equations (3) and (4). First, the steel beam neutralizes the axle height htkAnd the concrete slab neutral axis height hckShould be varied within certain limits. The composite beam may be cut into strips of constant thickness along the height of the beam, at each assumed htkAnd hckUnder the conditions, the strain of each strip can be obtained by equations (1) and (2). The stress of each strip can then be obtained by calculation of the material constitutive relation. Secondly, the axial force and bending moment of each strip can be found from the stress and the strip size. Thus, the axial forces of each strip can be summed separately to obtain Fg，FcAnd FsRather than by integral calculations. Similarly, Mg，McAnd MsThis can also be achieved by summing the moments of each strip. Finally, the error function for the total axial force can be defined as:
Figure BDA0003477775750000091
similarly, the error function for the total bending moment can be expressed as:
Figure BDA0003477775750000092
wherein efAnd emIs used to evaluate the hypothesistkAnd hckWhether the parameters of equation (3) or (4) are satisfied, respectively. If ef(or e)m) Is equal to 0, represents htkAnd hckEquation (3) (or (4)) is satisfied. To ensure the assumed htkAnd hckBoth equations (3) and (4) are satisfied, and the following index can be defined as:
Figure BDA0003477775750000093
when e isfmWhen the value is zero or the minimum value is obtained from all the assumed neutral shaft heights of the steel beam and the concrete slab, the actual neutral shaft height h of the steel beam can be determinedtkAnd the concrete slab neutral axis height hck。
Shaft height h in steel beam and concrete slab is identifiedtkAnd hckAfter that, the average curvature of the composite beam element k can be expressed as:
Figure BDA0003477775750000094
the average bending stiffness of the unit along the length direction of the steel-concrete composite beam can be expressed as:
Figure BDA0003477775750000095
while the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Within the technical idea of the invention, various equivalent changes can be made to the technical scheme of the invention, and the equivalent changes all belong to the protection scope of the invention.

Claims (7)

1. A quantitative identification method for bending rigidity of a steel-concrete composite beam is characterized by comprising the following steps:
s1: arranging n long-gauge strain sensors at the bottom of the composite beam along the length direction of the composite beam to measure strain, wherein the area of the composite beam covered by one sensor k in the n long-gauge strain sensors is represented as a unit k;
s2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, calculating the strain according to the assumed beam neutral axis height and the assumed concrete slab neutral axis height, and calculating the stress of each strip through the material constitutive relation;
s3: calculating the axial force and the bending moment of each strip according to the stress and the strip size, and calculating an error function of the total axial force and an error function of the bending moment;
s4: defining an error index, and when the error index is equal to zero or the error index is minimum, determining the assumed height of the beam neutral axis and the assumed height of the concrete slab neutral axis as the actual height of the neutral axis;
s5: calculating the average curvature of the unit k according to the actual neutral axis height of the steel beam;
s6: and calculating the average bending rigidity of the unit k according to a bending moment curvature equation, and further solving the local bending rigidity of any unit.
2. The quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 1, wherein: step S1 assumes concrete slabs and steel beams satisfy the assumption of flat sections, respectively, having the same curvature.
3. The quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 2, wherein: in step S2: dividing the composite beam into a plurality of equal-thickness strips along the height direction, and calculating the stress of each strip by using formulas (1) and (2) through the material constitutive relation;
εkz1＝-εk0z1/htk+εk0 (1)
wherein epsilonkz1Along the height direction z of the steel beam1Strain at the coordinates; h istkThe neutral axis height assumed for the beam; epsilonk0Measuring the average strain of the unit k for the sensor k at the bottom of the composite beam; z is a radical of1Calculating the distance from the position to the bottom surface of the steel beam;
εkz2＝(hck-z2)εk0/htk (2)
εkz2along the height direction z of the concrete slab2Strain at the location; h isckA neutral shaft height assumed for the concrete slab; epsilonk0/htkIs the curvature of the steel beam; z is a radical of2To calculate the distance of the location to the bottom surface of the concrete slab.
4. The quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 3, wherein: in step S3: calculating the axial force and bending moment of each strip according to the stress and the strip size, and calculating the error function e of the total axial forcefError function e of bending momentmThe calculation formula is as follows:
Figure FDA0003477775740000021
wherein, Fg，FcAnd FsIs an axial force generated by steel beams, concrete slabs and steel bars, htAnd btThe height and the width of the steel beam are respectively; t is twAnd tfWeb and flange thicknesses, hcAnd bcRespectively the height and the width of the section of the concrete slab; sigmat(εkz1) The stress of the steel beam; sigmac(εkz2) Stress for a concrete slab; sigmasStress of steel bars in a concrete slab; a. thesThe area of the steel bar in the concrete slab;
Figure FDA0003477775740000022
wherein M isc，MgAnd MsRespectively, moment caused by concrete slabs, beams and reinforcements, MpMoment caused by external load; z is a radical of1Calculating the distance between the point and the bottom surface of the steel beam; z is a radical of formula2To calculate the distance of the point to the bottom surface of the slab; a issThe distance from the centroid of the steel bar to the bottom surface of the concrete slab;
Figure FDA0003477775740000023
Figure FDA0003477775740000024
5. the quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 4, wherein: in step S4: to guarantee the assumed htkAnd hckSatisfy the formulas (3) and (4) at the same time, define the error index efm(ii) a When e isfmWhen equal to zero or take a minimum value, then h is assumedtkAnd hckNamely the actual neutralization shaft height;
Figure FDA0003477775740000025
6. the quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 5, wherein: step S5, the following steps: according to the actual neutralization shaft height h of the steel beamtkCalculating the average curvature of the unit k, and the formula is as follows:
Figure FDA0003477775740000031
wherein the content of the first and second substances,
Figure FDA0003477775740000032
is the average curvature of the cell k.
7. The quantitative identification method for the flexural rigidity of the steel-concrete composite beam as claimed in claim 6, wherein: in step S6: calculating the average bending rigidity of the unit k according to a bending moment curvature equation, wherein the formula is as follows:
Figure FDA0003477775740000033
wherein, EIkIs the average bending stiffness of unit k.
CN202210059856.0A 2022-01-19 2022-01-19 Quantitative identification method for bending rigidity of steel-concrete composite beam Pending CN114547729A (en)

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CN115828762A (en) * 2022-12-20 2023-03-21 湘潭大学 Flexural beam material constitutive parameter model correction and discrimination method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115828762A (en) * 2022-12-20 2023-03-21 湘潭大学 Flexural beam material constitutive parameter model correction and discrimination method
CN115828762B (en) * 2022-12-20 2024-01-05 湘潭大学 Method for correcting and judging constitutive parameter model of bent beam material

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