CN113378399A - Parametric analysis method for rapidly acquiring performance of section of component - Google Patents

Parametric analysis method for rapidly acquiring performance of section of component Download PDF

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CN113378399A
CN113378399A CN202110708968.XA CN202110708968A CN113378399A CN 113378399 A CN113378399 A CN 113378399A CN 202110708968 A CN202110708968 A CN 202110708968A CN 113378399 A CN113378399 A CN 113378399A
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reinforced concrete
section
concrete member
area
curve
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CN113378399B (en
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钟剑
倪明
李想
杨涛
魏圆圆
王伟
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Hefei University of Technology
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Abstract

The parametric analysis method for rapidly acquiring the performance of the section of the member, provided by the invention, realizes the continuous processing of the section of the longitudinal bar in the section of the reinforced concrete member by establishing the two-dimensional plane model, and enables the discretely distributed longitudinal bar to be equivalent to a continuous middle casing pipe area, and establishes an integral formula based on the two-dimensional plane model to analyze the performance of the section of the reinforced concrete member. Therefore, the performance analysis of the section of the reinforced concrete member is simplified, and the accuracy and reliability of calculating the performance parameters of the section of the reinforced concrete member through the two-dimensional plane model are ensured through the consistency of the two-dimensional plane model and the actual composition of the section of the reinforced concrete member.

Description

Parametric analysis method for rapidly acquiring performance of section of component
Technical Field
The invention relates to the field, in particular to a parametric analysis method for rapidly acquiring the performance of a member section.
Background
At present, software for calculating the section of a component is mainly developed according to foreign specifications, analysis control parameters, material characteristics and the like have certain differences with domestic regulations, and if the software is used for taking care of the component, larger errors can be generated, and even wrong results can be obtained. And when the information of the conventional concrete-filled steel tube section is processed, the required information cannot be quickly provided. After relevant data are input in daily operation, output data need to be counted and classified one by one, large-scale analysis cannot be carried out, the influence of each variable on the section curvature limit state cannot be summarized, and actual engineering cannot be optimized. Relevant software such as Xtrack and the like analyzes data, then researchers extract the data one by one, and when different section sizes are analyzed, models need to be reconstructed every time of analysis, and the application range of the model is further limited. If the variable to be studied is large, the range of each variation is small, and the mechanical operation is inefficient, and a lot of time and energy are consumed.
In addition, four damage states of a pier section are indispensable to vulnerability analysis and toughness earthquake-resistant calculation, and the current commercial software cannot directly acquire all damage state curvatures, for example, the limit curvature of medium damage cannot be directly acquired by the Xtrack.
Disclosure of Invention
In order to overcome the defects that the component section calculation method in the prior art is complex in operation, low in efficiency, incomplete in extracted parameters and the like, the invention provides a parametric analysis method for rapidly acquiring the performance of the component section.
The invention adopts the following technical scheme:
a parametric analysis method for rapidly acquiring section performance of a member is suitable for a reinforced concrete member, the reinforced concrete member consists of a reinforcing mesh, core layer concrete filled in the reinforcing mesh and protective layer concrete wrapped on the periphery of the reinforcing mesh, and the reinforcing mesh consists of longitudinal bars and stirrups; setting the section of the reinforced concrete member as a section vertical to the longitudinal bars;
the method comprises the following steps:
s1, obtaining the section area A of the reinforced concrete membergIncorporating reinforced concrete elementsCross-sectional area and reinforcement ratio ρ of reinforced concrete memberlCalculating the total area A of the longitudinal bars on the section of the reinforced concrete membersl，Asl＝ρl×Ag；
S2, obtaining a two-dimensional plane model formed by an inner layer area, a middle sleeve area wrapped on the periphery of the inner layer area and an outer sleeve area wrapped on the periphery of the middle sleeve area, wherein the outer sleeve area is superposed with a protective layer concrete area on the section of the reinforced concrete member, and the area of the middle sleeve area is AslThe thickness of the sleeve pipe is equal along the circumferential direction, and the outer edge of the middle sleeve pipe area is superposed with the inner edge of the outer sleeve pipe area; the outer edge of the inner layer area is superposed with the inner edge of the middle sleeve area;
s3, calculating the length value of the inner edge of the outer sleeve area as the perimeter C of the middle sleeve area according to the design parameters of the reinforced concrete memberslCalculating the thickness d of the middle sleeve region0，d0＝Asl/Csl；
S4, establishing a two-dimensional coordinate system on the plane of the two-dimensional plane model, calculating the thickness distribution of the middle sleeve area along the length direction as a steel pipe thickness function T by taking the x-axis direction in the two-dimensional coordinate system as the length direction of the two-dimensional plane modelsCalculating the thickness distribution of the inner layer region along said length direction as a function T of the thickness of the core layerccCalculating the thickness distribution of the outer casing region along the length direction as a function T of the thickness of the protective layeruc；
S5, combining function Ts、Tcc、TucAnd establishing an integral balance formula of the reinforced concrete member section at each position in the direction of the x axis.
Preferably, the integral balance formula obtained in step S5 is a bending moment curvature function M of the reinforced concrete member, that is
Figure BDA0003132577620000021
The curves are shown in the figure, and,
Figure BDA0003132577620000022
is a songRate;
Figure BDA0003132577620000023
wherein σsIndicates the stress of the reinforcement bar, sigma, at the moment when the strain of the longitudinal bar becomes epsilons(x)＝σs；σucDenotes the concrete stress, σ, at which the concrete of the protective layer is strained to εuc(x)＝σuc；σccDenotes the concrete stress, σ, at which the core concrete strain is εcc(x)＝σcc，L0As a function of strain
Figure BDA0003132577620000031
The neutral axis position of (a) of (b),
Figure BDA0003132577620000032
to a design value, L0According to
Figure BDA0003132577620000034
Is obtained by calculation, Ts(x)＝Ts，Tuc(x)＝Tuc，Tcc(x)＝Tcc，L1Thickness of protective layer concrete (2), L2＝L-L1。
Preferably, step S6 is further included after step S5: defining the damage states of the reinforced concrete member by combining a bending moment and curvature function, and obtaining the curvature and bending moment under each damage state;
preferably, in step S6, four damage states are defined, which are:
initial injury: the state of the reinforced concrete member when the longitudinal bars yield for the first time;
moderate injury; practice of
Figure BDA0003132577620000035
Curve and ideal elastoplasticity
Figure BDA0003132577620000036
Reinforced concrete structure with equal area enclosed by curvesThe state of the piece; practice of
Figure BDA0003132577620000037
Curve and ideal elastoplasticity
Figure BDA0003132577620000038
The equal area enclosed by the curves means that: practice of
Figure BDA0003132577620000039
Curve and ideal elastoplasticity
Figure BDA00031325776200000310
The curves are in the same plane coordinate system with the origin of coordinates and the reality
Figure BDA00031325776200000311
Points on the curve
Figure BDA00031325776200000312
Area of rectangle as diagonal vertex and ideal elastic-plastic property with origin of coordinates and real
Figure BDA00031325776200000313
Points on the curve
Figure BDA00031325776200000314
The area of the rectangles which are the diagonal vertexes is equal; practice of
Figure BDA00031325776200000315
The curve is the bending moment curvature function M obtained in step S5;
ultimate damage: the state of the reinforced concrete member when the stress of the core layer concrete reaches the peak value;
collapse and damage: the state of the reinforced concrete member when the core layer concrete strain reaches the peak value;
the severity of the initial injury, the moderate injury, the extreme injury, and the collapse injury increased in order.
Preferably, each damage state is provided with a corresponding curvature precision, and the curvature precision is a numerical digit of the curvature after a decimal point.
Preferably:
Figure BDA0003132577620000033
wherein f iss、fuc、fccRespectively showing the constitutive relation curve of the reinforcing mesh, the constitutive relation curve of the protective layer concrete 2 and the constitutive relation curve of the core layer concrete 3; the constitutive relation is the stress-strain relation of the material, and the constitutive relation curve of the reinforcing mesh combines the material of the reinforcing steel bar and the hoop ratio rhosDetermining;
the resistance of the material under the action of external force is related to the axial compression ratio of the material, and the bending moment of the material is related to the resistance provided by the material; the bending moment of the reinforced concrete member under different states can be calculated according to the axial compression ratio of the reinforced concrete member;
the method further includes step S6: will reinforcement ratio rholAxial pressure ratio RacLength of cross section L and coupling ratio rhosInput device
Figure BDA0003132577620000043
And (5) obtaining the bending moment and curvature of the reinforced concrete member in each damage state.
Preferably, the method is applied to T when the section of the reinforced concrete member is rectangulars、Tcc、TucIs represented as follows:
Figure BDA0003132577620000041
Figure BDA0003132577620000042
Tcc(x)＝W-2c0 L1＜x＜L2；
wherein L is1、L2As a transition parameter, L1＝c0，L2＝L-c0，c0Indicating the thickness of the concrete of the protective layer, i.e. the thickness of the outer casing region, d0Indicating the thickness of the intermediate casing region, L, W indicating the length and width, p, respectively, of the section of the reinforced concrete elementlThe reinforcement ratio of the reinforced concrete member is represented.
The invention has the advantages that:
(1) the invention realizes the continuous processing of the longitudinal bar section in the reinforced concrete member section by establishing the two-dimensional plane model, the longitudinal bar sections which are distributed in a fragmentary mode are equivalent to a continuous middle casing area, and an integral formula is established based on the two-dimensional plane model to analyze the performance of the reinforced concrete member section. Therefore, the performance analysis of the section of the reinforced concrete member is simplified, and the accuracy and reliability of calculating the performance parameters of the section of the reinforced concrete member through the two-dimensional plane model are ensured through the consistency of the two-dimensional plane model and the actual composition of the section of the reinforced concrete member.
(2) The strip method is used for converting a two-dimensional continuous reinforced concrete model, namely a two-dimensional plane model, into a one-dimensional model with thickness information of each part, so that the model is greatly convenient to program and operate, and meanwhile, the applicability of the method to different section shapes is improved.
(3) According to the invention, the performance parameters of the section of the reinforced concrete member are analyzed through an integral formula, so that higher calculation efficiency is realized, and the multi-stage identification of the damage state is realized. In addition, the modeling method of the reinforced concrete member section is simplified, so that more concise and convenient parameter input is realized, and the method is more beneficial to understanding and application.
(4) When the method is used for calculating the limit curvature of each damage state, the calculation efficiency can be improved while the calculation accuracy is ensured by adjusting the curvature accuracy. Thus, the precision can be adjusted according to the curvature requirement corresponding to the damage state, for example, to achieve slight damage curvature (e.g. 2 × 10)-3) Previously, the curvature accuracy could be adjusted to 10-4The calculation accuracy is ensured; and calculating the curvature of the collapse damage (e.g. 8 x 10)-2) When, the curvature accuracy is 10-3To improve the computational efficiency. Thus, the bookThe invention realizes the self-adaptive calculation and simultaneously ensures the calculation efficiency and the calculation precision.
(5) The invention provides a method for rapidly obtaining the bending moment-curvature of the section of a rectangular reinforced concrete member
Figure BDA0003132577620000051
Curves and curvatures of each lesion. By using the method, only 4 key parameters (reinforcement ratio rho) need to be inputlAxial pressure ratio RacLength of cross section L and coupling ratio rhos) Can be calculated to obtain
Figure BDA0003132577620000052
The curves and the corresponding damage curvatures obtain the curvatures of a plurality of damage states through predefined damage state indexes, and sufficient data samples are provided for the functional simulation of the damage state of the reinforced concrete member.
Drawings
FIG. 1(a) is a schematic flow chart of a parametric analysis method for rapidly acquiring section performance of a component
FIG. 1(b) is a flow chart of a parametric analysis method for rapidly obtaining cross-sectional properties of a component;
FIG. 2 is a sectional view of a rectangular reinforced concrete member used in example 1;
FIG. 3 is a two-dimensional planar model diagram corresponding to FIG. 2;
FIG. 3(a) is a schematic size diagram of the two-dimensional planar model shown in FIG. 3;
FIG. 3(a1) is a one-dimensional model diagram corresponding to the middle casing region in FIG. 3 (a);
FIG. 3(a2) is a one-dimensional model diagram corresponding to the outer casing region of FIG. 3 (a);
FIG. 3(a3) is a one-dimensional model diagram corresponding to the inner layer region in FIG. 3 (a);
FIG. 3(b) is a schematic diagram of a hypothetical function of a flat section;
FIG. 4 is a stress-strain relationship diagram of the steel bar; in FIG. 4, EsRepresenting the modulus of elasticity, b representing the ratio of stiffness after yield;
FIG. 5 is a graph of stress-strain relationship for concrete; in FIG. 5,. epsilontRepresenting tensile strain, ε, of the core concretec0Representing the peak compressive strain, ε, of the concrete of the protective layercpShowing the peel strain of the concrete of the protective layer,. epsilonc1Representing the peak strain, epsilon, of the concrete in the core layercuRepresenting the strain of the core layer concrete when a first stirrup in the reinforced concrete member is broken;
FIG. 6 shows a graph containing four lesion states as defined in example 1
Figure BDA0003132577620000061
A curve;
FIG. 7 is a sectional view of a rectangular reinforced concrete member used in example 2;
FIG. 8 shows two kinds of examples 2
Figure BDA0003132577620000062
A graph comparing curves;
FIG. 9 shows two types of examples 3 with different cross-sectional lengths
Figure BDA0003132577620000063
A graph comparing curves;
FIG. 10 shows two kinds of axial compression ratios in example 4
Figure BDA0003132577620000064
A graph comparing curves;
FIG. 11 shows two kinds of reinforcement ratios of example 5
Figure BDA0003132577620000065
The curves are compared with the graph.
The parametric analysis methods in fig. 8 to 11 refer to the method for obtaining the performance of the constructed section provided by the present invention.
The reference numbers in fig. 2, 3, and 7 are as follows:
1. longitudinal ribs; 2. protective layer concrete; 3. core layer concrete; 10. a middle casing region; 20. an outer jacket region; 30. an inner layer region.
Detailed Description
The reinforced concrete member consists of a reinforcing mesh, core layer concrete 3 filled in the reinforcing mesh and protective layer concrete 2 wrapped on the periphery of the reinforcing mesh; the reinforcing mesh consists of longitudinal bars 1 and stirrups. The section of the reinforced concrete member is set to be a section perpendicular to the longitudinal bars 1.
Example 1: method for acquiring rectangular section performance of reinforced concrete member
In this embodiment, the section of the steel mesh used for the reinforced concrete member is a rectangular frame, and in this embodiment, the design parameters of the reinforced concrete member are obtained as follows:
thickness c of protective layer concrete 20Length value L and width value W of section of reinforced concrete member, axial compression ratio RacReinforcement ratio ρl。
In this embodiment, when the rectangular section performance of the reinforced concrete member is calculated, the steps are as follows:
the first step is as follows: obtaining the section area A of the reinforced concrete memberg，AgCombining the cross-sectional area of the reinforced concrete member and the reinforcement ratio ρ of the reinforced concrete memberlCalculating the total area A of the longitudinal bars 1 on the section of the reinforced concrete membersl，Asl＝ρl×Ag＝L×W。
Secondly, obtaining a two-dimensional plane model formed by an inner layer area 30, a middle sleeve area 10 wrapped on the periphery of the inner layer area 30 and an outer layer sleeve area 20 wrapped on the periphery of the middle sleeve area 10, wherein the outer layer sleeve area 20 is overlapped with a protective layer concrete 2 area on the section of the reinforced concrete member, and the area of the middle sleeve area 10 is AslAnd the thickness is equal along the perimeter direction, and the outer edge of the middle sleeve region 10 is overlapped with the inner edge of the outer sleeve region 20; the outer edge of the inner layer region 30 coincides with the inner edge of the intermediate sleeve region 10.
In this embodiment, since the reinforced concrete member has a rectangular cross section, the outer-layer sleeve region 20 and the middle-layer sleeve region 10 are both rectangular tube cross-sectional shapes, and the inner-layer region 30 is rectangular. In this way, the present step corresponds to a continuous treatment of the dots of the longitudinal bars 1 on the cross section of the reinforced concrete member, thereby forming a rectangular steel pipe cross section.
Thirdly, the length value of the inner edge of the outer sleeve area 20 is calculated as the perimeter C of the middle sleeve area 10 by integrating the design parameters of the reinforced concrete memberslCalculating the thickness d of the intermediate sleeve region 100，d0＝Asl/Csl。
I.e. Csl＝2(L-2c0+W-2c0)＝2(L+W-4c0)；
Figure BDA0003132577620000071
Fourthly, establishing a two-dimensional coordinate system on the plane of the two-dimensional plane model, calculating the thickness distribution of the middle sleeve area 10 along the length direction as a steel pipe thickness function T by taking the direction of the x axis in the two-dimensional coordinate system as the length direction of the two-dimensional plane modelsCalculating the thickness distribution of the inner layer region 30 along the length direction as a function T of the thickness of the core layerccCalculating the thickness profile of the outer casing region 20 along said length as a function T of the thickness of the protective layeruc。
In the present embodiment, the first and second electrodes are,
Figure BDA0003132577620000081
it should be noted that in this embodiment, d is used0Takes a small value, so that the function T is calculatedsWhile neglecting d0And the calculation precision is not influenced. Thus, to ensure the calculation accuracy, x may be c0And x ═ L-c0Value, Ts(x)＝d0(W-2c0) (ii) a When c is going to0＜x＜L-c0When taking value Ts(x)＝2d0。
Thus, in the present embodiment, L is set1＝c0,L2＝L-c0Then T iss、Tcc、TucRespectively, as follows:
Figure BDA0003132577620000082
Figure BDA0003132577620000083
Tcc(x)＝W-2c0 L1＜x＜L2 (1)
fifthly, assuming that the resistance provided by the reinforcing mesh when the reinforced concrete member receives the external force is recorded as NsAnd the resistance provided by the protective layer concrete 2 is recorded as NucThe resistance provided by the core layer concrete 3 is recorded as NccThe resistance provided by the whole reinforced concrete member is marked as N, and the formula is as follows:
Figure BDA0003132577620000084
namely, it is
Figure BDA0003132577620000085
Wherein σsIndicates the strain of the longitudinal bar 1 is epsilonsThe stress of the steel bar; sigmaucIndicating the strain of the protective layer concrete 2 to epsilonucConcrete stress in time; sigmaccIndicating the strain epsilon of the core concrete 3ccConcrete stress at the time.
Specifically, the external force applied to the reinforced concrete member can be determined according to the axial compression ratio R of the reinforced concrete memberacThe resistance N provided by the whole reinforced concrete member is equal to the external force through calculation, so that the axial compression ratio R can be obtainedacThe resistance force N provided by the reinforced concrete member is obtained.
And, σs、σuc、σccCan be obtained according to the constitutive relation of the material, and figure 4 shows the constitutive relation of the steel bar, i.e. the strain epsilonsAnd stress sigmasThe corresponding relation of (2) can be written as sigmas(x)＝fs(εs(x) ); the two curves in FIG. 5 represent the core, respectivelyThe constitutive relation of the layer concrete 3 and the protective layer concrete 2. The constitutive relation of the protective layer concrete 2 indicates the strain epsilon of the protective layer concrete 2ucAnd stress sigmaucThe corresponding relation of (2) can be written as sigmauc(x)＝fuc(εuc(x) ); the constitutive relation of the core layer concrete 3 indicates the strain ε of the core layer concrete 3ccAnd stress sigmaccThe corresponding relation of (2) can be written as sigmacc(x)＝fcc(εcc(x))。
That is to say that the first and second electrodes,
Figure BDA0003132577620000091
wherein f iss、fuc、fccThe constitutive relation curve of the reinforcing mesh, the constitutive relation curve of the protective layer concrete 2 and the constitutive relation curve of the core layer concrete 3 are respectively shown.
The stress-strain relationship of the material, i.e. the constitutive relationship, is the characteristic thereof, the stress-strain relationship of the steel bar and the concrete is common knowledge, and in particular, refer to fig. 4 and 5, and the constitutive relationship of the steel bar mesh and the hoop ratio ρsAnd (4) correlating. Specifically, the stress-strain relationship between the steel bars and the concrete can be referred to in fig. 4 and fig. 5, respectively;
in conjunction with the well-known flat section assumption, the formula for strain along the x-axis is as follows:
Figure BDA0003132577620000092
that is to say that the first and second electrodes,
Figure BDA0003132577620000093
wherein the content of the first and second substances,
Figure BDA0003132577620000094
for a given curvature, x is the distance from the origin of coordinates on the L-axis, L0For neutral axis position, it is noted that the L for rebar and concrete is known because the strain function (i.e., strain curve) for rebar and concrete is known0Are also known.
Substituting the above equations (3) and (4) into the present embodiment, the following equation can be obtained:
Figure BDA0003132577620000101
due to the function fs、fcc、fucAre all known functions, curvatures
Figure BDA0003132577620000105
For design value, therefore, the stress at any position x along the length direction on the section of the reinforced concrete member can be obtained by combining the formula (5).
The calculation function of the bending moment M of the reinforced concrete member can be obtained by combining the formula (2) as follows:
Figure BDA0003132577620000102
wherein M issRepresenting the bending moment, M, provided by the longitudinal bars 1ucRepresenting the bending moment provided by the concrete 2 of the protective layer, MccRepresenting the bending moment provided by the core concrete 3, and, Ts(x)＝Ts，Tuc(x)＝Tuc，Tcc(x)＝Tcc。
That is to say that the first and second electrodes,
Figure BDA0003132577620000103
the following formula (7) can be obtained in combination with formulas (5) and (6):
Figure BDA0003132577620000104
due to fs、fcc、fucAre all known curves, L0According to a set curvature
Figure BDA0003132577620000106
Is obtained by calculation, so that, knowing x, the above equation (7) can be regarded as a bending moment-curvature function, i.e.
Figure BDA0003132577620000107
Curve line.
Combining the above equation (7), it can be seen that the reinforced concrete member is being built
Figure BDA0003132577620000108
During the curve, there are four key factors, which are: length L and axial compression ratio R of reinforced concrete member sectionacReinforcement ratio rholAnd a coupling ratio ρs. Specifically, the length L of the section of the reinforced concrete member is a variable of an integral formula (7), and the axial compression ratio RacUsed for calculating the resistance N and the reinforcement ratio rho provided by the reinforced concrete memberlIs Ts(x)Calculated parameter of (d), hoop ratio ρsIs σs(x)、σuc(x)And σcc(x)The parameter (c) of (d).
In the prior art are known
Figure BDA0003132577620000112
In the case of a curve, different loss states may be defined in combination with curve characteristics, and the limit curvatures corresponding to different damage states may be determined. Specifically, in this example, the damage state is defined in 4 shown in table 1 below.
Table 1: 4 Damage status statistical table
Figure BDA0003132577620000111
Practice of
Figure BDA0003132577620000113
Curve and ideal elastoplasticity
Figure BDA0003132577620000114
The equal area enclosed by the curves means that: practice of
Figure BDA0003132577620000115
Curve and ideal elastoplasticity
Figure BDA0003132577620000116
The curves are in the same plane coordinate system with the origin of coordinates and the reality
Figure BDA0003132577620000117
Points on the curve
Figure BDA0003132577620000118
Is the reality of an endpoint
Figure BDA0003132577620000119
Line segment on curve, abscissa and straight line
Figure BDA00031325776200001110
The enclosed area and the area defined by the origin of coordinates and ideal elastoplasticity
Figure BDA00031325776200001111
Points on the curve
Figure BDA00031325776200001112
Ideal elastoplasticity as end point
Figure BDA00031325776200001113
Line segment on curve, abscissa and straight line
Figure BDA00031325776200001114
The enclosed areas are equal; practice of
Figure BDA00031325776200001115
The curve is a bending moment curvature function M obtained by combining the parameters of the section of the reinforced concrete member according to the method.
Example 2
The method is verified below by modeling and comparing the above example 1 with specific parameters by Xtract and matlab, respectively.
In the embodiment, a section of a rectangular reinforced concrete member of 1.4m × 1.4m is modeled, 52 longitudinal bars 1 with the diameter of 24mm are configured on the reinforced concrete member, the distance between stirrups is 100mm, the volume reinforcement ratio of the longitudinal bars 1 is 1.2%, and the reinforced concrete member is made of C40 concrete and HRB400 steel bars. That is, in the present embodiment, L ═ W ═ 1.4m, and the thickness c of the protective layer concrete 20Is 40mm,. rhol1.2%, and the axial compression ratio is Rac＝0.1。
Obtained by XTract according to the above parameters
Figure BDA0003132577620000122
The curve was used as a reference curve and modeled by matlab and the first to fifth steps in example 1 were performed to obtain
Figure BDA0003132577620000123
The curves are actual curves, and a comparison of the reference curves and the actual curves is shown in fig. 8. It can be seen that obtained by Xtrack and matlab
Figure BDA0003132577620000126
The curves are highly coincident, and the reliability of the method for acquiring the performance of the constructed section provided by the invention is proved.
Example 3
In the embodiment, on the basis of the embodiment 2, the lengths L of the sections of the rectangular reinforced concrete members are respectively 1.1 meter, 1.2 meters, 1.3 meters, 1.4 meters and 1.5 meters, and the sections of the reinforced concrete members are obtained through Xtrack
Figure BDA0003132577620000124
The curve was used as a reference curve to be obtained by matlab in combination with the method described in example 1
Figure BDA0003132577620000125
The curve is taken as an actual curve, and the reference curve and the actual curve are shown in fig. 9, so that the actual curve and the reference curve are highly matched under the condition of different lengths L, and the fact that the analysis accuracy of the method on the constructed section is not influenced by the different section lengths is proved.
The curvature in the slightly damaged state and the curvature in the collapsed damaged state corresponding to different lengths in fig. 9 are compared with each other in the following table 2.
Table 2: curvature comparison table under various damage states at different section lengths
Figure BDA0003132577620000121
Example 4
In this example, the axial compression ratio R of the rectangular reinforced concrete member was set to be higher than that of example 2acRespectively taking the values of 0.1, 0.15, 0.2, 0.25 and 0.3, and obtaining the section of the reinforced concrete member through Xtrack
Figure BDA0003132577620000132
The curve was used as a reference curve to be obtained by matlab in combination with the method described in example 1
Figure BDA0003132577620000133
The curve is used as an actual curve, and the reference curve and the actual curve are shown in fig. 10, so that the actual curve and the reference curve are highly matched under the condition of different axial pressure ratios, and the different axial pressure ratios do not influence the accuracy of the method for analyzing the constructed section.
The curvature in the slightly damaged state and the curvature in the collapsed damaged state corresponding to different axial compression ratios in fig. 10 are compared with each other in the following table 3.
Table 3: curvature comparison table under various damage states at different axial compression ratios
Figure BDA0003132577620000131
Example 5
In the embodiment, on the basis of the embodiment 2, the reinforcement ratio rho of the rectangular reinforced concrete memberlTaking the values of 0.01, 0.012, 0.014, 0.016 and 0.018 respectively, and obtaining the section of the reinforced concrete member by Xtrack
Figure BDA0003132577620000134
The curve was used as a reference curve to be obtained by matlab in combination with the method described in example 1
Figure BDA0003132577620000135
The curve is an actual curve, and the reference curve and the actual curve are shown in fig. 11, and it can be seen that the reinforcement ratio ρ is differentlUnder the condition of (1), the actual curve and the reference curve are highly coincident, and the reinforcement ratio rho is differentlThe method does not influence the accuracy of analyzing the constructed section.
Table 4 below shows the reinforcement ratios ρ of FIG. 11lThe corresponding curvature in the slightly damaged state is compared with the curvature in the collapsed damaged state.
Table 3: curvature comparison table under various damage states at different reinforcement ratios
Figure BDA0003132577620000141
As can be seen from the above tables 2-4, in any state, the curvature obtained by the method combined with the Mtalab calculation and the curvature obtained by the Xtrack are very close, and the reliability of parameter analysis on the reinforced concrete member by the method is proved.
The invention is not to be considered as limited to the specific embodiments shown and described, but is to be understood to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (7)

1. A parametric analysis method for rapidly acquiring section performance of a member is suitable for a reinforced concrete member, the reinforced concrete member consists of a reinforcing mesh, core layer concrete (3) filled in the reinforcing mesh and protective layer concrete (2) wrapped on the periphery of the reinforcing mesh, and the reinforcing mesh consists of longitudinal bars (1) and stirrups; setting the section of the reinforced concrete member as a section vertical to the longitudinal bar (1);
the method is characterized by comprising the following steps:
s1, obtaining the section area A of the reinforced concrete membergCombining the cross-sectional area of the reinforced concrete member and the reinforcement ratio rho of the reinforced concrete memberlCalculating the total area A of the longitudinal bars (1) on the section of the reinforced concrete membersl，Asl＝ρl×Ag；
S2, obtaining a two-dimensional plane model formed by an inner layer area (30), a middle sleeve area (10) wrapped on the periphery of the inner layer area (30) and an outer layer sleeve area (20) wrapped on the periphery of the middle sleeve area (10), wherein the outer layer sleeve area (20) is overlapped with a protective layer concrete (2) area on the section of the reinforced concrete member, and the area of the middle sleeve area (10) is AslThe thickness of the sleeve is equal along the circumferential direction, and the outer edge of the middle sleeve area (10) is superposed with the inner edge of the outer sleeve area (20); the outer edge of the inner layer region (30) coincides with the inner edge of the middle sleeve region (10);
s3, calculating the length value of the inner edge of the outer sleeve area (20) as the perimeter C of the middle sleeve area (10) according to the design parameters of the integrated reinforced concrete memberslCalculating the thickness d of the intermediate sleeve region (10)0，d0＝Asl/Csl；
S4, establishing a two-dimensional coordinate system on the plane of the two-dimensional plane model, calculating the thickness distribution of the middle sleeve area (10) along the length direction as a steel pipe thickness function T by taking the x-axis direction in the two-dimensional coordinate system as the length direction of the two-dimensional plane modelsCalculating the thickness profile of the inner layer region (30) along said length direction as a function T of the core layer thicknessccCalculating the thickness profile of the outer casing region (20) along said length as a function T of the thickness of the protective layeruc；
S5, combining function Ts、Tcc、TucAnd establishing an integral balance formula of the reinforced concrete member section at each position in the direction of the x axis.
2. Parameterization for rapidly acquiring section performance of component according to claim 1The analysis method is characterized in that the integral balance formula obtained in the step S5 is a bending moment curvature function M of the reinforced concrete member, namely
Figure FDA0003132577610000021
The curves are shown in the figure, and,
Figure FDA0003132577610000022
is curvature, M is bending moment;
Figure FDA0003132577610000023
wherein σsIndicates the stress of the steel bar when the strain of the longitudinal bar (1) is epsilon, sigmas(x)＝σs；σucRepresents the concrete stress, sigma, at which the concrete (2) of the protective layer is strained to epsilonuc(x)＝σuc；σccRepresents the concrete stress, sigma, at which the core layer concrete (3) is strained to epsiloncc(x)＝σcc，L0As a function of strain
Figure FDA0003132577610000024
The neutral axis position of (a) of (b),
Figure FDA0003132577610000025
to a design value, L0According to
Figure FDA0003132577610000026
Calculating to obtain; t iss(x)＝Ts，Tuc(x)＝Tuc，Tcc(x)＝Tcc，L1Thickness of protective layer concrete (2), L2＝L-L1。
3. The parametric analysis method for rapidly acquiring the section performance of the component as claimed in claim 1, further comprising a step S6 after the step S5: and defining the damage states of the reinforced concrete member by combining the bending moment and curvature functions, and obtaining the curvatures and bending moments in all the damage states.
4. The parametric analysis method for rapidly acquiring the section performance of the component as claimed in claim 3, wherein four damage states are defined in step S6, which are respectively:
initial injury: the state of the reinforced concrete member when the longitudinal bar (1) yields for the first time;
moderate injury; practice of
Figure FDA0003132577610000027
Curve and ideal elastoplasticity
Figure FDA0003132577610000028
The states of the reinforced concrete members when the areas enclosed by the curves are equal; practice of
Figure FDA0003132577610000029
Curve and ideal elastoplasticity
Figure FDA00031325776100000210
The equal area enclosed by the curves means that: practice of
Figure FDA00031325776100000211
Curve and ideal elastoplasticity
Figure FDA00031325776100000212
The curves are in the same plane coordinate system with the origin of coordinates and the reality
Figure FDA00031325776100000213
Points on the curve
Figure FDA00031325776100000214
Area of rectangle as diagonal vertex and ideal elastic-plastic property with origin of coordinates and real
Figure FDA00031325776100000215
Points on the curve
Figure FDA00031325776100000216
The area of the rectangles which are the diagonal vertexes is equal; practice of
Figure FDA00031325776100000217
The curve is the bending moment curvature function M obtained in step S5;
ultimate damage: the state of the reinforced concrete member when the stress of the core layer concrete (3) reaches the peak value;
collapse and damage: the state of the reinforced concrete member when the strain of the core layer concrete (3) reaches the peak value;
the severity of the initial injury, the moderate injury, the extreme injury, and the collapse injury increased in order.
5. The parametric analysis method for rapidly acquiring the section performance of the component as claimed in claim 4, wherein each damage state is provided with a corresponding curvature precision, and the curvature precision is a numerical digit of the curvature after a decimal point.
6. The parametric analysis method for rapidly acquiring the section performance of the component as claimed in claim 4, wherein:
Figure FDA0003132577610000031
wherein f iss、fuc、fccRespectively showing the constitutive relation curve of the reinforcing mesh, the constitutive relation curve of the protective layer concrete 2 and the constitutive relation curve of the core layer concrete 3; the constitutive relation is the stress-strain relation of the material, and the constitutive relation curve of the reinforcing mesh combines the material of the reinforcing steel bar and the hoop ratio rhosDetermining;
the resistance of the material under the action of external force is related to the axial compression ratio of the material, and the bending moment of the material is related to the resistance provided by the material; the bending moment of the reinforced concrete member under different states can be calculated according to the axial compression ratio of the reinforced concrete member;
the method further includes step S6: will reinforcement ratio rholAxial pressure ratio RacLength of cross section L and coupling ratio rhosInput device
Figure FDA0003132577610000032
And (5) obtaining the bending moment and curvature of the reinforced concrete member in each damage state.
7. Parametric analysis method for rapidly obtaining the section properties of a member according to claim 1, characterised in that it is applied to T, when the section of a rectangular reinforced concrete member is crosseds、Tcc、TucIs represented as follows:
Figure FDA0003132577610000033
Figure FDA0003132577610000034
Tcc(x)＝W-2c0 L1＜x＜L2；
wherein L is1、L2As a transition parameter, L1＝c0，L2＝L-c0，c0Represents the thickness of the protective layer concrete (2), i.e. the thickness of the outer jacket region (20), d0Representing the thickness of the intermediate casing region (10), L, W representing the length and width, respectively, of the section of the reinforced concrete element, plThe reinforcement ratio of the reinforced concrete member is represented.
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