Method for identifying post-crack shear stiffness of reinforced concrete beam

Abstract

The invention relates to a post-crack shear stiffness identification method for a reinforced concrete beam. The method comprises the following steps: S1, acquiring inclined crack distribution, inclined crack width, inclined crack length and development angle data after the concrete beam is cracked; s2, dividing a cracking part of the concrete beam into a plurality of continuous sections according to a construction section, and completing inclined crack grading scale evaluation according to an evaluation standard to obtain a cracking grade gcr, i of each section; s3, calculating a shear stiffness degradation factor lambda i; s4, calculating the shear stiffness Kv, cr of each section after degradation according to gcr, i and lambda i; and S5, correcting the Poisson's ratio of the concrete according to the lambda i, the Kv and the cr so as to correct the shear stiffness of the section of the concrete beam for post-cracking performance evaluation of the concrete structure. The technical problem that the real working state of the concrete beam bridge cannot be obtained due to the fact that traditional concrete beam bridge bearing capacity evaluation is greatly influenced by subjective factors is solved, and the method can be conveniently applied to performance evaluation of the concrete structure after cracking.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and particularly to a method for identifying the post-cracking shear stiffness of reinforced concrete beams. Background Art

[0002] At present, the total number of highway bridges in China has approached 1.1 million, and the number of concrete bridges accounts for more than 90%. Among the large number of concrete bridges, prestressed concrete beam bridges are widely used around the world due to their good structural performance and simple and beautiful appearance, and have become the mainstream bridge type within the range of main spans from 50 to 300 m.

[0003] However, with the increase of service time, large-span prestressed concrete beam bridges generally suffer from diseases such as cracking and deflection. These diseases not only reduce the structural safety, but also affect the durability and applicability of the bridges, becoming a problem that plagues the further development of large-span prestressed concrete beam bridges.

[0004] Therefore, on the one hand, the engineering community has carried out a large number of investigations and statistics on the diagonal cracks in the webs of prestressed concrete continuous beam bridges. At the same time, many scholars have analyzed and discussed the distribution law and formation mechanism of the cracks. Regarding the causal relationship between "cracks" and "deflection", it is generally considered to be concomitant at present. The appearance of "cracks" increases "deflection", and the continuous increase of "deflection" exacerbates "cracks". Objectively speaking, however, there are still great controversies at home and abroad regarding the main influencing factors and formation mechanisms of "cracks" and "deflection".

[0005] Currently, more and more engineering practices and researches have shown that there is a coupling relationship between the occurrence and development of diagonal cracks in the webs of large-span prestressed concrete beam bridges and the long-term mid-span deflection. However, at present, the understanding of the development mechanism of web shear cracks is not deep enough, the quantitative research on the coupling relationship between diagonal cracks and deflection is lacking, and the research on the influence of diagonal cracks on shear stiffness is also very lacking.

[0006] To sum up, for in-service prestressed concrete beams with cracking diseases, there is still a lack of an accurate method for identifying the post-cracking shear stiffness, so that the relationship between the "cracking" and "deflection" diseases commonly existing in large-span prestressed concrete beam bridges cannot be clarified. Therefore, it is very necessary to propose an accurate method for identifying the shear stiffness of cracked concrete beams, and to reasonably predict the performance of beam bridges by combining existing detection means and calculation means, so as to put forward suggestions for the maintenance or reinforcement of bridges. Summary of the Invention

[0007] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for identifying the post-cracking shear stiffness of reinforced concrete beams, including the following steps:

[0008] S1. Obtain the data of the inclined crack distribution, inclined crack width, inclined crack length, and development angle after the concrete beam cracks.

[0009] S2. Divide the cracked part of the concrete beam into several continuous sections according to the construction section, complete the evaluation of the inclined crack grading scale according to the evaluation criteria, and obtain the cracking grade g of each section. cr,i 。

[0010] S3. Calculate the shear stiffness degradation factor λ. i 。

[0011] S4. According to g cr,i and λ i , calculate the shear stiffness K after degradation of each section. v,cr 。

[0012] S5. According to λ i and K v,cr , correct the Poisson's ratio of the concrete, thereby correcting the shear stiffness of the concrete beam section for the evaluation of the post-cracking performance of the concrete structure.

[0013] Further, the evaluation criteria include: if there is no inclined crack, then g cr,i = 1; if the crack length is less than 1 / 3 of the section size, then g cr,i = 2; if the crack length is greater than or equal to 1 / 3 of the section size and less than or equal to 1 / 2 of the section size, then g cr,i = 3; if the crack length is greater than 1 / 2 of the section size and the average spacing is less than 30 cm, then g cr,i = 4; otherwise, g cr,i = 5.

[0014] Further, the calculation formula for the degradation factor λ i is:

[0015]

[0016] In the formula, λ i is the shear stiffness degradation factor of section i; λ y is the shear stiffness degradation factor when the inclined crack develops most severely.

[0017] Further, the calculation formula for λ y is:

[0018]

[0019] In the formula, ρ v is the stirrup ratio of the corresponding section.

[0020] Further, the calculation formula for the shear stiffness K v,cr is:

[0021] Kv,cr = λ i K e,cr

[0022] Wherein, K e,cr is the shear stiffness of the beam before cracking, that is, the shear stiffness of the beam within the elastic range.

[0023] Furthermore, the calculation formula of K e,cr is as follows:

[0024]

[0025] Wherein, G is the shear modulus; A is the shear area; Ec is the elastic modulus of concrete; μ is the initial value of the Poisson's ratio of concrete.

[0026] Furthermore, the correction calculation of the Poisson's ratio is as follows:

[0027]

[0028] Wherein, μ' is the corrected Poisson's ratio.

[0029] Furthermore, the shear stiffness of the concrete beam section in the finite element model is corrected by the corrected Poisson's ratio.

[0030] Furthermore, μ is taken from 0.17 - 0.2.

[0031] Furthermore, each construction section is divided into one section.

[0032] The present invention grades the crack scales of the cracked parts in sections for the reinforced concrete beam with diagonal cracks; based on the relationship between the crack scale and the shear stiffness degradation factor, the effective value of the post-crack shear stiffness is obtained; by correcting the Poisson's ratio of the concrete material, the reduction of the shear stiffness is simulated. The present invention solves the technical problem that the bearing capacity evaluation of the traditional concrete beam bridge is greatly affected by subjective factors and the true working state of the concrete beam bridge cannot be obtained, and can be conveniently applied to the evaluation of the post-crack performance of the concrete structure.

[0033] The present invention obtains the actual degraded shear stiffness of the cracked section under the given crack disease according to the apparent crack parameters of the cracked concrete beam, provides a simple reference formula for identifying the post-crack shear stiffness for the design of the concrete beam, and solves the technical problem of the correlation between the apparent crack disease of the concrete beam and the internal stress state of the structure.

[0034] The present invention proposes a correction method for correcting the shear stiffness of the finite element model for the bridge evaluation method combining field measurement and numerical simulation, breaks through the research barrier of completing the correction of the finite element model according to the apparent cracks of the structure, and provides a theoretical support and method selection for the evaluation of the post-crack performance of the concrete beam.

[0035] The method of the present invention targets the cracked concrete beam, and through sectional evaluation, a precise method for identifying the post-cracking shear stiffness is obtained, which solves the uncertainty and conservativeness in the evaluation of the post-cracking shear stiffness of traditional structures and simplifies the current calculation formula; a method for correcting the shear stiffness of the finite element model is proposed, realizing the organic combination of on-site detection, theoretical model and numerical calculation in structural evaluation, and providing scientific support for the design and maintenance decision-making of a large number of concrete beam bridges. Description of the Drawings

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0037] Figure 1 It is the step block diagram of the method in the present invention;

[0038] Figure 2 It is the schematic elevation layout diagram of the bridge structure in the verification example of the present invention;

[0039] Figure 3 It is the schematic cross-sectional layout diagram of the bridge structure in the verification example of the present invention;

[0040] Figure 4 It is the schematic diagram of the half-structure segment division of the mid-span of the actual bridge in the verification example of the present invention;

[0041] Figure 5 It is the schematic diagram of the side-span structure segment division of the actual bridge in the verification example of the present invention;

[0042] Figure 6 It is the distribution diagram of the left-side inclined cracks outside the web box girder of the concrete beam in the verification example of the present invention;

[0043] Figure 7 It is the distribution diagram of the right-side inclined cracks outside the web box girder of the concrete beam in the verification example of the present invention;

[0044] Figure 8 It is the schematic diagram of the finite element model in the verification example of the present invention;

[0045] Figure 9 It is the comparison diagram of the static load test and the finite element calculation results under working condition 2 in the verification example of the present invention;

[0046] Figure 10 It is the comparison diagram of the static load test and the finite element calculation results under working condition 3 in the verification example of the present invention;

[0047] Figure 11It is a comparison diagram of the static load test and the finite element calculation results under working condition 4 in the verification example of the present invention. Specific implementation mode

[0048] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

[0049] The method for identifying the post-cracking shear stiffness of a reinforced concrete beam provided in this embodiment is as Figures 1 to 11 shown. For a reinforced concrete beam with inclined cracks, the cracking parts are rated for crack scaling in sections, and at the same time, the design parameters of the concrete beam are introduced. According to the relationship between the crack scaling and the shear stiffness degradation factor, the effective value of the post-cracking shear stiffness is obtained. By correcting the Poisson's ratio of the concrete material, the reduction of the shear stiffness is indirectly simulated. The method uses crack parameters as input parameters, and the evaluation process is independent of the load applied to the bridge structure. Therefore, this evaluation method can take into account the post-cracking degraded shear stiffness of the bridge under various load combinations, including but not limited to the dead load, live load, and prestress load of the bridge.

[0050] As Figure 1 shown, the above evaluation method specifically includes but is not limited to the following steps:

[0051] Step 1: Obtain the inclined crack distribution, inclined crack width, inclined crack length, and development angle, etc. after the concrete structure cracks.

[0052] Step 2: Divide the cracked part of the concrete beam into several sections according to the principle that the length is equal to the beam height. In this embodiment, each construction section is divided into one section. In other embodiments, several adjacent construction sections can also be divided into one section, and at the same time, each section needs to be continuous. Complete the grading and scaling evaluation of the inclined cracks according to the given evaluation criteria to obtain the cracking grade g cr,i ; The evaluation method of the cracking grade g cr,i is as follows: The inclined crack cracking degree of the beam section is divided into 5 cracking grades. The larger the cracking grade g cr,i value, the higher the cracking degree. The evaluation criteria include: no inclined crack, then g cr,i =1; the crack length is less than 1 / 3 of the section size, then g cr,i =2; the crack length is greater than or equal to 1 / 3 of the section size and less than or equal to 1 / 2 of the section size, then g cr,i =3; the crack length is greater than 1 / 2 of the section size and the average spacing is less than 30 cm, then g cr,i =4; the rest, then g cr,i =5.

[0053] Step 3: According to the cracking grade g determined in Step 2 cr,i and the stirrup ratio ρ v , calculate the shear stiffness degradation factor λ i .

[0054] Step 4: According to g determined in Step 2 cr,i and λ calculated in Step 3 i , calculate the degraded shear stiffness K of each section v,cr .

[0055] Step 5: λ calculated in Step 3 i and K calculated in Step 4 v,cr , correct the Poisson's ratio of concrete in the finite element model to indirectly correct the elastic shear stiffness of the section.

[0056] Verification example:

[0057] To verify the accuracy of this embodiment, the following verification example was carried out:

[0058] A certain beam bridge is a three-span continuous rigid frame bridge (49.5m + 252m + 145m). The main beam is a single-cell single-chamber variable cross-section box girder, without dividing into lanes. The bridge deck pavement is 8cm C40 steel fiber waterproof concrete + 2.5cm asphalt concrete pavement layer. The lower structure of the main bridge is double thin-wall piers. The basic structural layout of the bridge is shown in Figure 2 , Figure 3 .

[0059] In 2004, during the routine maintenance inspection of this bridge, it was found that there were many diagonal cracks on the inner side of the web of the box girder of this bridge, and pressure grouting and sealing treatment were carried out; thereafter, safety inspections were carried out by three companies in 2007, after the earthquake in 2008, and in 2011 respectively. According to the inspection results in 2011, the diagonal cracking phenomenon of the main span web is the most serious, and even through diagonal cracks appear in some beam segments.

[0060] According to statistics, the cracks in the web of the box girder mainly occur in a total of 24 segments symmetrically on both sides of the mid-span closure section and the closure section. Generally, the number of cracks on the outer side of the web of the box girder (a total of 210) is less than that on the inner side of the box girder (a total of 358). The cracks on the left and right sides of the web in the mid-span box girder are evenly distributed, and are basically symmetrically distributed on the large and small pile number sides; the cracks on the left and right sides of the web outside the mid-span box girder are evenly distributed, but the number of cracks on the short side span side is more than that on the long side span side of the web. The bridge section division is shown in Figure 4 , Figure 5 , and the distribution of diagonal cracks is shown in Figure 6 , Figure 7 .

[0061] Evaluate the concrete beam based on the crack parameters obtained from the inspection and the structural design parameters. The process is as follows:

[0062] According to Step 2, the inclined crack cracking degrees of the box girder are classified by segment. This method mainly qualitatively and quantitatively evaluates the cracking severity from three aspects: the width, spacing, and length of the inclined cracks, and comprehensively determines the cracking grade according to the cracking degrees of the inclined cracks on the left and right side webs of the box girder.

[0063] According to Step 3, for the cracking grade g of each section determined in Step 2 cr,i , the stirrup ratio ρ is obtained according to the design drawings of this bridge v , and the shear stiffness degradation factor λ is calculated i .

[0064] According to Step 4, for g determined in Step 2 cr,i and λ calculated in Step 3 i , the design parameters of the elastic modulus E of concrete c and the cross-sectional area A of each section are introduced to calculate the degraded shear stiffness K of each section v,cr .

[0065] According to Step 5, for λ calculated in Step 3 i and K calculated in Step 4 v,cr , the modified concrete Poisson's ratio μ' is calculated, and the concrete Poisson's ratio is modified in the finite element model. The finite element calculation uses the bridge structure analysis software Midas / civil, and the structure is discretized into 382 beam elements, 822 solid elements, and 1880 nodes. The initial calculation model of this bridge is as Figure 8 shown. The concrete strength grade of the main girder is C60, and the concrete strength grade of the pier is C40. According to the 2012 inspection situation and the actual project, considering that the concrete strength and elastic modulus of the actual bridge are super strong, the elastic modulus of the C60 concrete with the designed strength grade is taken as 45 GPa, and considering the contribution of the paving layer to the section properties of the box girder, the moment of inertia and area of the box girder section are enlarged by 5%. The pier top node is rigidly connected to the No. 0 segment at the pier bottom. According to the classification of the inclined cracks on the webs of this bridge in Step 2, the Poisson's ratio μ is modified by segment in the initial model, and the decrease in shear stiffness has been considered to obtain the finite element model considering the influence of inclined cracks.

[0066] The situation of inclined crack classification evaluation, as well as the calculation results of the shear stiffness degradation factor and the modified Poisson's ratio, are listed in the following table:

[0067]

[0068]

[0069]

[0070]

[0071] Table of Inclined Crack Classification and Shear Stiffness Reduction of Box Girder Web

[0072] Calculations were performed based on the modified finite element model to obtain the responses of the structure. Subsequently, a static load test was conducted on the actual bridge. Using the finite element model considering the modified shear stiffness, the deflections of the bridge under various static load test conditions were calculated to obtain the cracking prediction values, and they were compared with the measured values of the static load test and the design prediction values (without considering the modified shear stiffness). The comparison results are shown in the following table and Figures 9 - 11 .

[0073]

[0074] Comparison Table of Maximum Deformations of Key Sections under Various Conditions (mm)

[0075] It can be seen from the comparison results that the mean square error between the test value and the design value without considering the shear stiffness reduction is 0.158, while after considering the shear stiffness reduction, the mean square error between the test value and the calculated value is 0.093. It shows that when the inclined cracks develop to a certain extent, the method of using crack classification assessment in the present invention and then reducing the shear stiffness of the box girder according to the crack grade can accurately evaluate the post-cracking shear stiffness of the structure and make a safer prediction of the structural deformation.

[0076] In view of the problems encountered in the assessment of the post-cracking performance of in-service concrete bridges according to the background technology, the present invention proposes a method for identifying the post-cracking shear stiffness of reinforced concrete beams. For reinforced concrete beams with inclined cracks, taking the apparent parameters of the inclined cracks as inputs, the cracking parts are rated for crack scaling in sections. Based on the relationship between the crack scaling and the shear stiffness degradation factor, the effective value of the post-cracking shear stiffness is obtained, and accordingly, the remaining shear stiffness of the structure after cracking is quantitatively evaluated, solving the technical problem that the bearing capacity assessment of traditional concrete beam bridges is greatly affected by subjective factors and the true working state of concrete beam bridges cannot be obtained.

[0077] Based on the apparent crack parameters of the cracked concrete beam, the present invention obtains the actual degraded shear stiffness of the cracked section under a given crack disease, providing a simple reference formula for the identification of post-cracking shear stiffness for the design of concrete beam bridges and solving the technical problem of the correlation between the apparent crack disease of the bridge and the internal force state of the structure. In view of the bridge assessment method combining field measurement and numerical simulation, the present invention proposes an indirect correction method for modifying the shear stiffness of the finite element model, breaking through the research barrier of finite element model correction based on the apparent cracks of the structure and providing theoretical support and method selection for the assessment of the post-cracking performance of concrete beams.

[0078] The method of the present invention is directed at a cracked concrete beam. By evaluating in sections, a precise method for identifying the post-cracking shear stiffness is obtained, which solves the uncertainty and conservatism in the evaluation of the post-cracking shear stiffness of traditional structures and simplifies the current calculation formula. A method for correcting the shear stiffness of a finite element model is proposed, realizing the organic combination of on-site detection, theoretical model and numerical calculation in structural evaluation, and providing scientific support for the design and maintenance decision-making of a large number of concrete beam bridges.

[0079] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A method for identifying the post-cracking shear stiffness of a reinforced concrete beam, characterized in that It includes the following steps: S1. Obtain the data of the inclined crack distribution, inclined crack width, inclined crack length and development angle after the concrete beam cracks; S2. Divide the cracked part of the concrete beam into several continuous sections according to the construction section, complete the evaluation of the inclined crack grading scale according to the evaluation standard, and obtain the cracking grade g of each section cr,i ; S3. Calculate the shear stiffness degradation factor λ i ; S4. Calculate the shear stiffness K after degradation of each section according to g cr,i and λ i , v,cr ; S5. According to λ i and K v,cr , correct the Poisson's ratio of concrete, thereby correcting the shear stiffness of the concrete beam section for evaluating the post-cracking performance of concrete structures.

2. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 1, characterized in that The evaluation criteria include: if there are no diagonal cracks, then g cr,i = 1; if the crack length is less than 1 / 3 of the cross-sectional dimension, then g cr,i = 2; if the crack length is greater than or equal to 1 / 3 of the cross-sectional dimension and less than or equal to 1 / 2 of the cross-sectional dimension, then g cr,i = 3; if the crack length is greater than 1 / 2 of the cross-sectional dimension and the average spacing is less than 30 cm, then g cr,i = 4; otherwise, g cr,i = 5.

3. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 1, characterized in that Degeneration factor λ i The calculation formula is as follows: where λ i is the shear stiffness degradation factor of section i; λ y is the shear stiffness degradation factor when the diagonal crack develops most severely.

4. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 3, characterized in that, λ y The calculation formula is as follows: where ρ v is the stirrup ratio of the corresponding section.

5. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 1, characterized in that, Shearing stiffness K v,cr The calculation formula is as follows: K v,cr = λ i K e,cr where K e,cr is the shear stiffness of the beam before cracking, i.e., the shear stiffness of the beam within the elastic range.

6. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 5, characterized in that, K e,cr The calculation formula is as follows: Where G is the shear modulus; A is the shear area; E c is the elastic modulus of concrete; μ is the initial value of the Poisson's ratio of concrete.

7. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 6, characterized in that, The modified calculation of the Poisson's ratio is as follows: In the formula, μ' is the modified Poisson's ratio.

8. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 7, characterized in that, Through the modified Poisson's ratio, the shear stiffness of the concrete beam section in the finite element model is modified.

9. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 7, characterized in that, μ is taken from 0.17 - 0.

2.

10. The method for identifying the post-cracking shear stiffness of a reinforced concrete beam according to claim 1, wherein Each construction section is divided into one section.

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