CN112858039A - Inverse analysis method for steel fiber concrete stress-crack width constitutive relation - Google Patents

Inverse analysis method for steel fiber concrete stress-crack width constitutive relation Download PDF

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CN112858039A
CN112858039A CN202110123269.9A CN202110123269A CN112858039A CN 112858039 A CN112858039 A CN 112858039A CN 202110123269 A CN202110123269 A CN 202110123269A CN 112858039 A CN112858039 A CN 112858039A
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crack
steel fiber
fiber concrete
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concrete member
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高丹盈
丁冲
庞育阳
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Zhengzhou University
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • G—PHYSICS
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention belongs to the technical field of constitutive relation of building materials; in particular to a reverse analysis method of the steel fiber concrete stress-crack width constitutive relation, which comprises the following steps: selecting a steel fiber concrete component to be tested, carrying out a three-point loading bending test, and drawing a test curve of load and crack opening displacement of the steel fiber concrete component to be tested; obtaining the initial crack load of the steel fiber concrete member on the test curve to obtain the initial crack bending strength of the steel fiber concrete member to be tested; establishing a calculation model of a standardized corner, a standardized bending moment, an external load, crack opening displacement caused by elastic deformation, crack opening displacement caused by initial crack geometric deformation and crack opening total displacement of the steel fiber concrete member to be measured in the bending process according to related parameters; and obtaining a constitutive relation curve of the stress and the crack opening displacement of the steel fiber concrete member through inverse analysis and calculation. The invention can provide theoretical support for the structural design of the steel fiber concrete.

Description

Inverse analysis method for steel fiber concrete stress-crack width constitutive relation
Technical Field
The invention belongs to the technical field of constitutive relation of building materials; in particular to a reverse analysis method of the constitutive relation of the stress-crack width of the steel fiber concrete.
Background
Steel Fiber Reinforced Concrete (FRC) is a building material made by blending short steel fibers distributed disorderly into brittle and easily cracked concrete. Due to its excellent mechanical properties, steel fiber concrete has been widely used in the fields of civil engineering and the like. The steel fiber penetrating through the crack surface of the concrete has strong bridging effect, so that one of the most important characteristics of the steel fiber concrete is excellent post-crack performance. The stress-crack width constitutive relation reflects the function of the steel fiber after the concrete structure is cracked, and is an important parameter in the design of the steel fiber concrete structure, so that the method for obtaining the steel fiber concrete tensile stress-crack constitutive relation by using a proper testing method has important theoretical significance and practical value, and is very necessary to provide a reverse analysis method capable of solving the steel fiber concrete stress-crack constitutive relation.
Disclosure of Invention
The invention aims to provide an inverse analysis method for the stress-crack width constitutive relation of steel fiber concrete, which simplifies the calculation amount of the inverse analysis method, can compile a programmed flow of inverse analysis operation, and can provide theoretical support for the structural design of the steel fiber concrete, wherein the obtained bending stress-crack width constitutive relation of the steel fiber concrete member is closer to an objective condition.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a reverse analysis method of a steel fiber concrete stress-crack width constitutive relation, which comprises the following steps:
step 1, selecting a steel fiber concrete member to be tested, carrying out a three-point loading bending test, and drawing a test curve of load and crack opening displacement of the steel fiber concrete member to be tested;
step 2, obtaining the initial crack load of the steel fiber concrete member on the test curve according to the load of the steel fiber concrete member to be tested and the crack opening displacement test curve, and obtaining the initial crack bending strength of the steel fiber concrete member to be tested;
step 3, according to the width b, the height H, the crack width w and the initial crack bending strength f of the steel fiber concrete member to be detectedtHeight h of non-opening of midspan section, depth a of cut0A net span L, a total crack development height d, a relative crack development height alpha and a nonlinear hinge length s, and establishing a bending process of the steel fiber concrete member to be measuredNormalized rotation angle theta ofiStandardized bending moment mui(theta), external load Fana,iCrack opening displacement w caused by elastic deformationana,i,eCrack opening displacement w caused by initial crack geometric deformationana,i,gFracture opening total displacement CMODana,iThe computational model of (2);
the bending process of the steel fiber concrete member to be tested is divided into a pre-cracking stage, a virtual crack development stage and a real-virtual crack common development stage; in the pre-cracking stage, the normalized bending moment muiThe calculation formula of (θ) is as follows:
μi(θ) ═ θ, (0 < θ < 1) (equation 1);
in the virtual crack development stage, the normalized turning angle thetaiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure BDA0002922821380000021
Figure BDA0002922821380000022
the normalized rotation angle theta is in a real-virtual crack co-development stageiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure BDA0002922821380000023
Figure BDA0002922821380000024
the external load Fana,iThe calculation formula of (a) is as follows:
Figure BDA0002922821380000025
the crack opening displacement w caused by the elastic deformationana,i,eThe calculation formula of (a) is as follows:
Figure BDA0002922821380000031
crack opening displacement w caused by the initial crack geometric deformationana,i,gThe calculation formula of (a) is as follows:
Figure BDA0002922821380000032
the fracture opening total displacement CMODana,iThe calculation formula of (a) is as follows:
CMODana,i＝wi+wana,i,e+wana,i,g(formula 9) of the reaction mixture,
wherein n is the number of bus segments in the stress-crack constitutive relation curve of the steel fiber concrete member, i is the ith line segment in the stress-crack width constitutive relation curve of the steel fiber concrete member, and i is 1,2, …, n; a isiAnd biRespectively represents the slope and intercept of the ith line segment in the constitutive relation curve of the stress-crack width of the steel fiber concrete member,
Figure BDA0002922821380000033
withe crack width w corresponding to the tail end of the ith line segment in the constitutive relation curve of the steel fiber concrete stress-crack width componenti-1The crack width corresponding to the end of the i-1 line segment or the crack width corresponding to the starting point of the i line segment in the constitutive relation curve of the steel fiber concrete stress-crack width member is w when no crack appears0＝0；
Figure BDA0002922821380000034
a0＝H-h；
Figure BDA0002922821380000035
V1(x)＝0.197+17.816x-107.63x2+338.21x3-494.26x4+298.86x5；
Step 4, let i equal to 1, assume the crack width w1Then b is0＝b 11 is ═ 1; suppose a1According to the formula in step 3, obtaining the normalized rotation angle theta1And a standardized bending moment mu1(θ), and the external load F of the inverse analysis process when i is 1 is obtainedana,1Crack opening displacement w caused by elastic deformationana,1,eCrack opening displacement w caused by initial crack geometric deformationana,1,gFracture opening total displacement CMODana,1；
Step 5, reading w from the load and crack opening displacement test curve of the steel fiber concrete member to be tested1Test load of time Fexp,1Judging the test load Fexp,1External load F of inverse analysis processana,1Whether the error precision of (a) meets a set threshold value, if the error precision of (b) is less than the set threshold value, a1The value meets the requirement, if the value is larger than the set threshold value, a is adjusted1Taking values, and repeating the step 4;
step 6, repeating the steps 4 and 5 to obtain Fana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete member;
step 7, according to a1,a2,……,an，b1,b2,……,bnAnd obtaining a constitutive relation curve of the stress of the steel fiber concrete member and the crack opening displacement.
Preferably, the initial crack bending strength f of the steel fiber concrete member to be testedtThe calculation formula of (a) is as follows:
Figure BDA0002922821380000041
wherein, FcrThe initial crack load of the steel fiber concrete member to be detected is measured; l is steel fiber concrete structure that awaits measuringA net span of the piece; b is the width of the steel fiber concrete member to be measured; h is the height of the non-opening of the cross section of the steel fiber concrete member to be measured.
Preferably, the constitutive relation model of the stress and crack opening displacement of the steel fiber concrete member is as follows:
σ＝ft(bi-aiw)，wi-1≤w≤wii is 1,2, … …, n (equation 11).
Preferably, the set threshold in step 5 is 3%.
Compared with the prior art, the invention has the beneficial effects that:
the invention simplifies the operation amount of the inverse analysis method based on the nonlinear hinge model and the expression of the analytical solution of the standardized corner and the standardized bending moment of the whole bending process of the steel fiber concrete member, can compile the programmed flow of inverse analysis operation, and the bending stress-crack width constitutive relation of the obtained steel fiber concrete member is closer to the objective condition, thereby providing theoretical support for the structural design of the steel fiber concrete member. The inverse analysis method can be popularized and applied to the relation between the multi-linear stress and the crack width, and is suitable for the flat steel fibers, the 3D, 4D and 5D end hook steel fibers and other types of fibers; the method is suitable for notched beams and non-notched beams; it is suitable for common concrete, fiber concrete, regenerated concrete, high performance concrete, self-compacting concrete, etc.
Drawings
FIG. 1 is a flow chart of the inverse analysis method of the steel fiber concrete stress-crack width constitutive relation.
Fig. 2 is a test curve and a back analysis curve of the load and crack opening displacement of the 4D steel fiber reinforced concrete beam in the first embodiment of the present invention.
Fig. 3 is a constitutive relation curve of the stress and crack opening displacement of the 4D steel fiber concrete in the first embodiment of the invention.
Fig. 4 is a test curve and a back analysis curve of the load and crack opening displacement of the 5D steel fiber reinforced concrete beam in the second embodiment of the present invention.
Fig. 5 is a constitutive relation curve of 5D steel fiber concrete stress and crack opening displacement in the second embodiment of the present invention.
Detailed Description
The following examples are intended to illustrate the invention, but are not intended to limit the scope of the invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art. The test methods in the following examples are conventional methods unless otherwise specified.
Example one
In the embodiment, the 4D steel fiber doped concrete beam is used for carrying out inverse analysis operation on the nonlinear stress-crack width constitutive relation. The steel fiber type was 4D steel fiber, and the volume content was 1.0% (representing 1 m)378.5kg of steel fiber is added into the concrete), and the test piece size of the steel fiber concrete beam is as follows: length x width x height 550mm x 150mm, i.e. b 150mm, height H150 mm, and the depth a of the cut in the middle of the test piece0The net span L is 500mm at 25mm, and the strength of the concrete is C60. The three-point loading flexural test device adopts a 500kN fatigue testing machine, the acquisition frequency is 5Hz, and a clamp-type extensometer is used for measuring the crack opening displacement (CMOD) of the steel fiber concrete flexural beam in the whole process. Displacement control is adopted, when the opening displacement of the crack mouth is less than 0.1mm, the loading rate is 0.05 mm/min; when the opening displacement of the crack mouth is more than 0.1mm, the loading rate is 0.2 mm/min. The relevant parameters are as follows: the length s of the nonlinear hinge is 75 mm; the height h of the non-opening of the midspan section is 125 mm; the elastic modulus E of the concrete is 38000 MPa.
It is worth noting that the corners of the steel fiber concrete members are calculated during the calculation
Figure BDA0002922821380000051
The conversion equation from the normalized rotation angle θ is as follows:
Figure BDA0002922821380000052
the conversion formula of the bending moment M and the standard bending moment mu (theta) borne by the steel fiber concrete member is as follows:
Figure BDA0002922821380000061
reference is made to the flow chart of the reverse analysis method of the present invention shown in fig. 1. The test curve of the load and crack opening displacement CMOD of the sample subjected to the three-point loading bending test is shown in FIG. 2. Reading the initial crack load F of the point with obvious turning of the slope in the initial stage from the load-CMOD curve graphcrThe initial crack bending strength f of the steel fiber concrete was calculated by the formula (10) under 12.5kNt＝4MPa。
Let i equal to 1 and set w1＝0.05mm，b0＝b1＝1，w 00. Assuming a small value a1Calculating the normalized rotation angle theta of the virtual crack development stage1(equation 2) normalized bending moment μ1(theta) (equation 3), external load Fana,1(equation 6) crack opening displacement w caused by elastic deformationana,1,e(equation 7) crack opening displacement w caused by initial crack geometryana,1,g(equation 8) and fracture propagation Total Displacement CMODana,1(equation 9). Reading w from the load-CMOD test curve1Test load F at 0.05mmexp,1And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased1Until the error precision meets the requirement. The result of the calculation a1＝2.83。
The error calculation formula is as follows:
Figure BDA0002922821380000062
let i equal 2, set w2＝0.1mm，a1＝2.83，b 11. Assuming a small value a2Calculating the normalized rotation angle theta of the virtual crack development stage2(equation 2) normalized bending moment μ2(theta) (equation 3), external load Fana,2(equation 6) crack opening displacement w caused by elastic deformationana,2,e(equation 7) crack opening displacement w caused by initial crack geometryana,2,g(equation 8) and fracture propagation Total Displacement CMODana,2(equation 9). Reading w from the load-CMOD experimental curve2Test load F when 0.1mmexp,2And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased2Until the error precision meets the requirement. The result of the calculation a2When b is 1.66, b is obtained2＝0.94。
Let i equal to 3, set w3When the thickness is 0.2mm, a can be obtained3＝-0.31，b3＝0.74。
Let i be 4,5, … …,32, and let wiThe corresponding a can be obtainediAnd biThe specific process is not shown.
Let i equal 33, set w33＝3.2mm，a1＝2.83，b1＝1，a2＝1.66，b2＝0.94，a3＝-0.31，b3＝0.74，……，a32＝0.10，b321.11, assume a smaller value a33Calculating the normalized rotation angle theta of the virtual crack development stage33(equation 2) normalized bending moment μ33(theta) (equation 3), external load Fana,33(equation 6) crack opening displacement w caused by elastic deformationana,33,e(equation 7) crack opening displacement w caused by initial crack geometryana,33,g(equation 8) and fracture propagation Total Displacement CMODana,33(equation 9). Reading w from the load-CMOD experimental curve33Test load F at 3.2mmexp,33And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased33Until the error precision meets the requirement. The result of the calculation a33When b is 0.10, b is obtained33＝1.11。
From the above inverse analysis operation procedure, F is obtainedana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete beam, as shown in FIG. 2; by contrast, Fana-CMODanaAnd Fexp-CMODexpCurve finding, inverse analysisThe results are well matched with the test results.
According to the obtained a1＝2.83，b1＝1，a2＝1.66，b2＝0.94，a3＝-0.31，b3＝0.74，……，a32＝0.10，b32＝1.11，a33＝0.10，b331.11, obtaining an constitutive relation curve of the 4D steel fiber concrete stress and the crack opening displacement according to the constitutive relation model of the steel fiber concrete stress and the crack opening displacement (formula 11), as shown in fig. 3.
Example two
In the embodiment, the inverse analysis operation of the nonlinear stress-crack width constitutive relation is carried out on the 5D steel fiber doped concrete beam. The steel fiber type was 5D steel fiber, and the volume content was 1.0% (representing 1 m)378.5kg of steel fiber is added into the concrete), and the test piece size of the steel fiber concrete beam is as follows: length x width x height 550mm x 150mm, i.e. b 150mm, height H150 mm, and the depth a of the cut in the middle of the test piece0The net span L is 500mm at 25mm, and the strength of the concrete is C60. The three-point loading flexural beam test device adopts a 500kN fatigue test machine, the acquisition frequency is 5Hz, and a clamp type extensometer is used for measuring the crack opening displacement (CMOD) of the steel fiber concrete flexural beam in the whole process. Displacement control is adopted, when the opening displacement of the crack mouth is less than 0.1mm, the loading rate is 0.05 mm/min; when the opening displacement of the crack mouth is more than 0.1mm, the loading rate is 0.2 mm/min. The relevant parameters are as follows: the length s of the nonlinear hinge is 75 mm; the height h of the non-opening of the midspan section is 125 mm; the elastic modulus E of the concrete is 38000 MPa.
Reference is made to the flow chart of the reverse analysis method of the present invention shown in fig. 1. The test curve of the load and crack opening displacement CMOD of the sample subjected to the three-point loading bending test is shown in FIG. 4. Reading the initial crack load F of the point with obvious turning of the slope in the initial stage from the load-CMOD curve graphcrThe initial crack bending strength f of the steel fiber concrete was calculated by the formula (10) under 12.5kNt＝4MPa。
Let i equal to 1 and set w1＝0.05mm，b0＝b1＝1，w 00. Assuming a small value a1Calculating virtual fracturesNormalized angle of rotation theta of development stage1(equation 2) normalized bending moment μ1(theta) (equation 3), external load Fana,1(equation 6) crack opening displacement w caused by elastic deformationana,1,e(equation 7) crack opening displacement w caused by initial crack geometryana,1,g(equation 8) and fracture propagation Total Displacement CMODana,1(equation 9). Reading w from the load-CMOD test curve1Test load F at 0.05mmexp,1And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased1Until the error precision meets the requirement. The result of the calculation a1＝3.45。
Let i equal 2, set w2＝0.1mm，a1＝2.83，b 11. Assuming a small value a2Calculating the normalized rotation angle theta of the virtual crack development stage2(equation 2) normalized bending moment μ2(theta) (equation 3), external load Fana,2(equation 6) crack opening displacement w caused by elastic deformationana,2,e(equation 7) crack opening displacement w caused by initial crack geometryana,2,g(equation 8) and fracture propagation Total Displacement CMODana,2(equation 9). Reading w from the load-CMOD experimental curve2Test load F when 0.1mmexp,2And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased2Until the error precision meets the requirement. The result of the calculation a21.12, find b2＝0.88。
Let i equal to 3, set w3When the thickness is 0.2mm, a can be obtained3＝-0.77，b3＝0.69。
Let i be 4,5, … …,32, and let wiThen, a can be obtainediAnd biThe specific process is not shown.
Let i equal 33, set w33＝3.2mm，a1＝3.45，b1＝1，a2＝1.12，b2＝0.88，a3＝-0.77，b3＝0.69，……，a32＝0.096，b321.22, assume a smaller value a33Calculating the virtual crack growth orderNormalized angle of rotation theta of the segments33(equation 2) normalized bending moment μ33(theta) (equation 3), external load Fana,33(equation 6) crack opening displacement w caused by elastic deformationana,33,e(equation 7) crack opening displacement w caused by initial crack geometryana,33,g(equation 8) and fracture propagation Total Displacement CMODana,33(equation 9). Reading w from the load-CMOD experimental curve33Test load F at 3.2mmexp,33And checking whether the error precision is less than 3% according to an error calculation formula. If the error accuracy is greater than 3%, a is increased33Until the error precision meets the requirement. The result of the calculation a33When b is 0.097, b is obtained33＝1.23。
From the above inverse analysis operation procedure, F is obtainedana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete beam, as shown in FIG. 4; by contrast, Fana-CMODanaAnd Fexp-CMODexpThe curve shows that the inverse analysis result is well matched with the test result.
According to the obtained a1＝3.45，b1＝1，a2＝1.12，b2＝0.88，a3＝-0.77，b3＝0.69，……，a32＝0.096，b32＝1.22，a33＝0.097，b331.23, obtaining an constitutive relation curve of the stress and the crack opening displacement of the 5D steel fiber concrete according to the constitutive relation model of the stress and the crack opening displacement of the steel fiber concrete (formula 11), as shown in fig. 5.
It should be noted that, a boundary point between the common development stage of the virtual crack and the real-virtual crack is about 15mm, and the actual crack width in the bending process of the 4D steel fiber reinforced concrete beam in the first embodiment and the 5D steel fiber reinforced concrete beam in the second embodiment is not large, and cannot be developed to the common development stage of the real-virtual crack, so that both the two stages are in the virtual crack development stage.
It is worth noting that example one and example 2 are in a reverse analyzerCalculating a in the process of calculating the constitutive relation between the stress of the steel fiber concrete beam and the crack opening displacementiAnd biWhen i ≧ 2, assume wiWhen the inverse analysis method of the invention is popularized to the constitutive relation of stress and crack opening displacement of other steel fiber concrete members, the w can be adjusted according to the actual situation and the precision requirementiAnd carrying out assumed value taking.
The above-mentioned embodiments are merely preferred embodiments of the present invention, which are merely illustrative and not restrictive, and it should be understood that other embodiments may be easily made by those skilled in the art by replacing or changing the technical contents disclosed in the specification, and therefore, all changes and modifications that are made on the principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1. An inverse analysis method for the constitutive relation of the stress-crack width of the steel fiber concrete is characterized by comprising the following steps of:
step 1, selecting a steel fiber concrete member to be tested, carrying out a three-point loading bending test, and drawing a test curve of load and crack opening displacement of the steel fiber concrete member to be tested;
step 2, obtaining the initial crack load of the steel fiber concrete member on the test curve according to the load of the steel fiber concrete member to be tested and the crack opening displacement test curve, and obtaining the initial crack bending strength of the steel fiber concrete member to be tested;
step 3, according to the width b, the height H, the crack width w and the initial crack bending strength f of the steel fiber concrete member to be detectedtHeight h of non-opening of midspan section, depth a of cut0A net span L, a total crack development height d, a relative crack development height alpha and a nonlinear hinge length s, and establishing a standardized corner theta of the steel fiber concrete member to be measured in the bending processiStandardized bending moment mui(theta), external load Fana,iCrack opening displacement w caused by elastic deformationana,i,eCrack opening displacement w caused by initial crack geometric deformationana,i,gCracking of the steelSuture opening total displacement CMODana,iThe computational model of (2);
the bending process of the steel fiber concrete member to be tested is divided into a pre-cracking stage, a virtual crack development stage and a real-virtual crack common development stage; in the pre-cracking stage, the normalized bending moment muiThe calculation formula of (θ) is as follows:
μi(θ)＝θ，(0＜θ＜1)；
in the virtual crack development stage, the normalized turning angle thetaiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure FDA0002922821370000011
Figure FDA0002922821370000012
the normalized rotation angle theta is in a real-virtual crack co-development stageiAnd a standardized bending moment muiThe calculation formula of (θ) is as follows:
Figure FDA0002922821370000021
Figure FDA0002922821370000022
the external load Fana,iThe calculation formula of (a) is as follows:
Figure FDA0002922821370000023
the crack opening displacement w caused by the elastic deformationana,i,eThe calculation formula of (a) is as follows:
Figure FDA0002922821370000024
crack opening displacement w caused by the initial crack geometric deformationana,i,gThe calculation formula of (a) is as follows:
Figure FDA0002922821370000025
the fracture opening total displacement CMODana,iThe calculation formula of (a) is as follows:
CMODana,i＝wi+wana,i,e+wana,i,g，
wherein n is the number of bus segments in the stress-crack constitutive relation curve of the steel fiber concrete member, i is the ith line segment in the stress-crack width constitutive relation curve of the steel fiber concrete member, and i is 1,2, …, n; a isiAnd biRespectively represents the slope and intercept of the ith line segment in the constitutive relation curve of the stress-crack width of the steel fiber concrete member,
Figure FDA0002922821370000026
withe crack width w corresponding to the tail end of the ith line segment in the constitutive relation curve of the steel fiber concrete stress-crack width componenti-1The crack width corresponding to the end of the i-1 line segment or the crack width corresponding to the starting point of the i line segment in the constitutive relation curve of the steel fiber concrete stress-crack width member is w when no crack appears0＝0；
Figure FDA0002922821370000031
a0＝H-h；
Figure FDA0002922821370000032
V1(x)＝0.197+17.816x-107.63x2+338.21x3-494.26x4+298.86x5；
Step 4, let i equal to 1, assume the crack width w1Then b is0＝b11 is ═ 1; suppose a1According to the formula in step 3, obtaining the normalized rotation angle theta1And a standardized bending moment mu1(θ), and the external load F of the inverse analysis process when i is 1 is obtainedana,1Crack opening displacement w caused by elastic deformationana,1,eCrack opening displacement w caused by initial crack geometric deformationana,1,gFracture opening total displacement CMODana,1；
Step 5, reading w from the load and crack opening displacement test curve of the steel fiber concrete member to be tested1Test load of time Fexp,1Judging the test load Fexp,1External load F of inverse analysis processana,1Whether the error precision of (a) meets a set threshold value, if the error precision of (b) is less than the set threshold value, a1The value meets the requirement, if the value is larger than the set threshold value, a is adjusted1Taking values, and repeating the step 4;
step 6, repeating the steps 4 and 5 to obtain Fana,1,Fana,2,……,Fana,nAnd CMODana,1,CMODana,2,……,CMODana,nDrawing a load and crack opening displacement inverse analysis curve of the steel fiber concrete member;
step 7, according to a1,a2,……,an，b1,b2,……,bnAnd obtaining a constitutive relation curve of the stress of the steel fiber concrete member and the crack opening displacement.
2. The reverse analysis method according to claim 1, wherein the initial cracking bending strength f of the steel fiber concrete member to be testedtThe calculation formula of (a) is as follows:
Figure FDA0002922821370000033
wherein, FcrThe initial crack load of the steel fiber concrete member to be detected is measured; l is the clear span of the steel fiber concrete member to be measuredDistance; b is the width of the steel fiber concrete member to be measured; h is the height of the non-opening of the cross section of the steel fiber concrete member to be measured.
3. The inverse analysis method of claim 1, wherein the steel fiber concrete member stress and crack opening displacement constitutive relation model is as follows:
σ＝ft(bi-aiw)，wi-1≤w≤wi,i＝1，2，……,n。
4. a method according to claim 1, wherein the threshold value set in step 5 is 3%.
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