CN110286030B - Preparation method of confined square concrete column and masonry column - Google Patents

Preparation method of confined square concrete column and masonry column Download PDF

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CN110286030B
CN110286030B CN201910435786.2A CN201910435786A CN110286030B CN 110286030 B CN110286030 B CN 110286030B CN 201910435786 A CN201910435786 A CN 201910435786A CN 110286030 B CN110286030 B CN 110286030B
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张营营
宋晓光
刘超
秦世朋
赵玉帅
秘星
刘鹏
徐俊豪
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China University of Mining and Technology CUMT
Shandong Provincial Academy of Building Research
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Abstract

The invention discloses a preparation method of a confined square concrete column and a masonry column, belongs to the technical field of building construction, and solves the problems of low prediction accuracy, low practicability and the like of confined concrete compressive strength in the prior art. The preparation method comprises the following steps: s1, establishing a calculation model of the strength of a confined square concrete column-the strength of an unconfined square concrete column:
Figure DDA0002070473110000011
s2, obtaining the compressive strength f 'of the confined square concrete column through a calculation formula of S1'cc(ii) a And S3, determining whether the confined square concrete column is prepared or not according to whether the confined concrete column compressive strength requirement is met or not. The preparation method is suitable for preparing the confined square concrete column and the masonry column.

Description

Preparation method of confined square concrete column and masonry column
Technical Field
The invention belongs to the technical field, and particularly relates to a preparation method of a confined square concrete column and a masonry column.
Background
The current prediction method can overestimate the compressive strength of the confined concrete and underestimate the ultimate strain: the active constraint is that the concrete member is already subjected to lateral constraint before loading, and before the member is not damaged, the maximum main stress (or referred to as ultimate stress) of the concrete member is higher than that of passively-constrained concrete, but the rising trend of a second section curve of the stress-strain relation of the actively-constrained concrete is slower, and even a descending trend exists after the peak value of the curve; for passively-constrained concrete, for example, an FRP material only plays an obvious role when the concrete has large lateral deformation, so that the ultimate stress of the passively-constrained concrete is generally slightly lower, but the slope of the second section of the stress-strain relationship is obviously higher than that of the actively-constrained concrete under the condition of strong lateral constraint. The above assumptions overestimate the stress-strain relationship and compressive strength of FRP-constrained concrete, but the ultimate strain tends to be underestimated.
The method for determining the hoop breaking strain in the existing prediction method has the defects that: tensile breaking strain ε obtained by Material Performance Test (Coupon Test) for strip FRPfActual breaking strain ε of FRP hoopj,uThe value is slightly lower, and the accurate value is difficult to predict, and the actual breaking strain of the FRP is difficult to obtain directly under the general condition.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a method for preparing a confined square concrete column and a masonry column, so as to solve the problems of low accuracy, low practicability, etc. of confined concrete compressive strength prediction in the prior art.
The purpose of the invention is mainly realized by the following technical scheme:
a preparation method of a confined square concrete column and a masonry column comprises the following steps:
s1, establishing a calculation model of the strength of a confined square concrete column-the strength of an unconfined square concrete column:
Figure GDA0002132121680000021
of formula (II) to'ccTo constrain the compressive strength of the concrete column, f'cCompressive strength of unrestrained concrete column, flThe unit is MPa for the constraint force of a nominal lateral term; rho is the influence coefficient of the concrete column corner;
s2, obtaining the compressive strength f 'of the confined square concrete column and the masonry column through a calculation formula of S1'cc；
S3, determining whether a confined square concrete column is prepared or not according to whether the compressive strength requirements of the confined concrete column and the masonry column are met or not;
in step S3, the preparation of the restrained square concrete column and the masonry column includes the following steps:
s3-1, preparing an unconstrained square concrete column and a masonry column;
and S3-2, according to the parameters of the FPR cloth obtained in the S1, wrapping the FPR cloth outside the unrestrained concrete column and the masonry column to finish the preparation of the restrained square concrete column and the masonry column.
Further, in step S1,
fl＝2nftfEfεj,u/B
in the formula, nf、tf、EfAnd εj,uThe number of FRP layers, the single-layer thickness, the elastic modulus and the actual breaking strain of the FRP hoop are respectively shown, and B is the size of the section of the square column.
Further, step S1 includes step S1-1. the relationship between the mean value of the effective coefficients of strain and the calculation model in step S1 is established.
Further, in step S1-1,
Figure GDA0002132121680000031
in the formula (I), the compound is shown in the specification,
Figure GDA0002132121680000032
is the mean value of the effective coefficients of strain, epsilonfThe ultimate tensile strain is measured by an FRP strip tensile test.
Further, in step S1,
ρ＝2rc/B
in the formula, rcThe chamfer radius of the square column is mm, and B is the side length mm of the section of the concrete square column.
Further, the number n of layers of FRPfThe number of layers is 8 or less.
Further, the compressive strength f 'of the unconstrained concrete'cThe range of (A) is 10.0 to 55.2 MPa.
Further, the step S3 includes a step S3-3: and adjusting the parameters which do not meet the requirement of the compressive strength of the confined concrete column, and repeating the step S2 until the requirement of the compressive strength of the confined concrete column is met.
Furthermore, the confined square concrete column comprises a steel reinforcement framework, concrete and FPR cloth, wherein the FPR cloth is made of a fiber reinforced composite material.
Further, step S3-1 includes: s3-11, building a steel bar framework; and S3-12, pouring concrete into the steel reinforcement framework to finish the preparation of the concrete column.
Compared with the prior art, the invention can at least realize one of the following technical effects:
1) compared with other models, the model established by the invention has higher prediction accuracy, and the problems that the compressive strength does not meet the requirement and potential safety hazards exist because the confined concrete column is directly prepared are prevented.
2) In the prior art, the accurate actual breaking strain of FRP is difficult to obtain directly, and the invention adopts the effective strain coefficient k of the FRPεThe actual FRP breaking strain is replaced, and the actual FRP breaking strain does not need to be acquired in the prediction process, so that the theoretical strength model has stronger practicability.
3) The proposed FRP constraint square column strength model covers the range of unconstrained concrete compressive strength of f'cThe number of FRP wrapping layers is 10.0-55.2 MPa, the maximum number of FRP wrapping layers is 8, and the application range of the strength model is wide.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof.
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The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 fitting FRP constraint concrete strength formula;
FIG. 2(a) Shehata model prediction levels;
FIG. 2(b) Campione model prediction levels;
FIG. 2(c) Wu model prediction levels;
FIG. 2(d) model prediction levels of the present invention.
Detailed Description
A method for making a confined square concrete column or masonry column is described in further detail below with reference to specific examples, which are provided for purposes of comparison and explanation only and to which the present invention is not limited.
A preparation method of a confined square concrete column and a masonry column comprises the following steps:
s1, establishing a calculation model of the strength of a confined square concrete column-the strength of an unconfined square concrete column:
coulomb proposed the internal friction theory in 1773, as shown in formula (1), that is, for a material under a complex stress state, when the shearing force applied to the material reaches the maximum shearing stress τ, the material is damaged. Wherein τ is the shear stress, c is the cohesion,
Figure GDA0002132121680000051
is the internal friction angle and σ is the positive stress on the shear plane.
Figure GDA0002132121680000052
The σ - τ relationship for a material in Mohr's strength theory can be represented by the following function:
τ＝F(σ) (2)
mohr strength theory is written as follows, where f'cIs the compressive strength of the unconstrained concrete column, f'tThe uniaxial tensile strength of concrete:
Figure GDA0002132121680000053
wherein the parameters a and b are both f't/f′cIs expressed as a ═ g (f't/f′c)，b＝h(f′t/f′c)。
The envelope expressed by formula (3) is tangent to the Morle circle describing the uniaxial tension of the concrete at sigma/f'cOn-axis (-f't/f′c0) point, will τ/f'c0 and σ/f'c＝-(f′t/f′c) Substituted by formula (3) to obtain
Figure GDA0002132121680000054
Substituting formula (4) for formula (3) to obtain
Figure GDA0002132121680000055
Let n be 2 in equation (5) to obtain equation (6), the derivation process of the theoretical strength model is simplified, and f 'is discussed finally't/f′cThe value of (2). The specific derivation procedure is as follows.
Figure GDA0002132121680000056
For the Mohr circle under uniaxial stress in FIG. 1, the third principal stress σ thereof30, equation form
Figure GDA0002132121680000061
The p-point of equations (6) and (7) in FIG. 1 is derived, and the slopes of the two equations at this point are equal, and the stress at the p-point is expressed as σpThus obtaining
Figure GDA0002132121680000062
Simplified formula (7) to obtain
Figure GDA0002132121680000063
The value of a is substituted for the formula (6) to obtain
Figure GDA0002132121680000064
Substituting equations (8) and (9) for equation (10) to solve σpThen there is
Figure GDA0002132121680000065
Substituting the formula (8) or the formula (9) into the formula (6) to obtain
Figure GDA0002132121680000066
Finally, formula (11) is substituted for formula (12) as
Figure GDA0002132121680000067
Here, the expressions of the parameters a, b are as follows
Figure GDA0002132121680000068
Figure GDA0002132121680000071
The form of the Moire equation in the multiaxial stress state in FIG. 1 is
Figure GDA0002132121680000072
The q-point in fig. 1 is derived for equations (13) and (15), and the slopes of the equations at this point are equal. For confined concrete, the maximum principal stress σ1＝f′ccThird principal stress σ3＝flOf f'ccTo constrain the compressive strength of the concrete, flNominal lateral restraint force, thus:
Figure GDA0002132121680000073
through the test, the average value f 'is taken't/f′cWhen the value is 0.085, the formula (16) becomes
Figure GDA0002132121680000074
Wherein fl is 2nftfEfεj,u/B，nf、tf、EfAnd εj,uThe number of FRP layers, the single-layer thickness, the elastic modulus and the actual tensile strain of the FRP hoop are respectively shown, and B is the side length of the section of the concrete square column.
Model initial form taking into account the influence of shape
Figure GDA0002132121680000075
In the formula, ksIndicating the effect of the square column shape, fl,jthe constraint force of the actual breaking strain of the FRP hoop is expressed, and gamma is a regression coefficient.
The shape coefficient function k of the above two aspectss＝f1(ρ)、fl＝f2(ρ)·fl,jThe combination is written into a functional form, f (rho), which reflects the influence of the square column shape on the compressive strength, and the formula (18) is changed into
Figure GDA0002132121680000081
In the formula (f)lThe calculated restraining force is the ultimate tensile strain measured by the FRP strip tensile test (Coupon test).
Directly substituting the shape function into an equation (17) to obtain an equation form of a constraint square column theoretical strength model:
Figure GDA0002132121680000082
assume the shape function is as follows:
f(ρ)＝ρα (21)
where α is a constant and is obtained by regression from experimental data. Obviously, f (ρ) ═ 0 or 1 corresponds to the case of the non-chamfered square column and the cylindrical column, respectively.
Thus, the formula (20) becomes the following form:
Figure GDA0002132121680000083
through regression of the experimental data, α is calculated to be 0.87, and equation 22 becomes:
Figure GDA0002132121680000084
the expression (23) is an expression of the constraint column, and the constraint force f in the expressionlThe ultimate tensile strain measured by the FRP strip tensile test is calculated, and the use is convenient.
Rho is the influence coefficient of the concrete column corner:
ρ＝2rc/B
in the formula, rcThe radius (mm) of the chamfer angle of the square column is shown, and B is the side length (mm) of the section of the concrete square column.
S2, obtaining the compressive strength f 'of the confined square concrete column through a calculation formula of S1'cc；
S3, determining whether the confined square concrete column is prepared or not according to whether the confined concrete column compressive strength requirement is met or not;
in the step S3, the preparation of the restrained square concrete column includes the following steps:
s3-1, preparing an unconstrained square concrete column;
and S3-2, finishing the preparation of the restrained square concrete column on the unrestrained concrete column and the outer side of the unrestrained concrete column by wrapping the FPR cloth according to the parameters of the FPR cloth obtained in the S1.
Step S3-1 includes: s3-11, building a steel bar framework; and S3-12, pouring concrete into the steel reinforcement framework to finish the preparation of the concrete column.
The step S3 further includes a step S3-3: and adjusting the parameters which do not meet the requirement of the compressive strength of the confined concrete column, and repeating the step S2 until the requirement of the compressive strength of the confined concrete column is met.
In step S1, step S1-1 is included to establish the relationship between the mean value of the effective coefficients of strain and the calculation model in step S1.
The actual breaking strain of the FRP is difficult to obtain directly, so the effective coefficient k of the strain of the FRP is researchedεTherefore, the theoretical strength model has stronger practicability.
In step S1, step S1-1 is included, the relation between the average value of the effective coefficients of strain and the calculation model in step S1 is established:
Figure GDA0002132121680000091
in the formula (I), the compound is shown in the specification,
Figure GDA0002132121680000092
the average value of the effective coefficients of strain is obtained by collecting data of the FRP hoop strain of the confined concrete column and calculating and taking the average value, wherein epsilon isfThe ultimate tensile strain is measured by an FRP strip tensile test.
The data adopted by the model parameter regression covers f'cThe concrete is in the range of 10.0MPa to 55.2 MPa.
Selecting the existing Shehata, Campione and Wu models and comparing the models with the model of the invention, as shown in figures 2(a) to 2(d), and figures 2(a) Shehata and other models; FIG. 2(b) Camperine et al model; FIG. 2(c) Wu et al model; FIG. 2(d) model of the invention; each model was evaluated using 230 test data. In FIGS. 2(a) and 2(b), both Shehata and Campione significantly underestimate the strength test value f'cc(ii) a In fig. 2(c) and 2(d), the prediction values of the models such as Wu with the highest accuracy in the existing models have certain discreteness, but the model of the present invention has a better prediction level and the off-line property of the prediction values is the smallest.
The model established by the invention has higher prediction accuracy compared with other models, and the problems that the compressive strength can not meet the requirement and potential safety hazards exist because the confined concrete column is directly prepared are prevented; generally, the actual breaking strain of the FRP is difficult to obtain directly, and the invention adopts the effective strain coefficient k of the FRPεThe actual FRP breaking strain is replaced, and the actual FRP breaking strain does not need to be acquired in the prediction process, so that the theoretical strength model has stronger practicability. The range of the unconfined concrete strength which can be predicted by the square column strength model is f'cThe number of FRP layers is at most 8, 10.0MPa to 55.2 MPa.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A preparation method of a confined square concrete column and a masonry column is characterized by comprising the following steps:
s1, establishing a calculation model of the strength of a confined square concrete column-the strength of an unconfined square concrete column:
Figure FDA0003120829940000011
of formula (II) to'ccTo constrain the compressive strength of the concrete column, f'cCompressive strength of unrestrained concrete column, flThe unit is MPa for the constraint force of a nominal lateral term; rho is the influence coefficient of the concrete column corner;
s2, obtaining the compressive strength f 'of the confined square concrete column and the masonry column through a calculation formula of S1'cc；
S3, determining whether the confined square concrete column is prepared or not according to whether the confined concrete column and the masonry column compressive strength requirements are met or not;
in the step S3, the preparation of the restrained square concrete column and the masonry column includes the following steps:
s3-1, preparing an unconstrained square concrete column and a masonry column;
s3-2, according to the parameters of the FPR cloth obtained in the S1, wrapping the non-restrained concrete column and the masonry column with the FPR cloth to finish the preparation of a restrained square concrete column and a restrained masonry column;
s3-3: adjusting parameters which do not meet the requirement of the compressive strength of the confined concrete column, and repeating the step S2 until the requirement of the compressive strength of the confined concrete column is met;
the step S3-1 includes: s3-11, building a steel bar framework; and S3-12, pouring concrete into the steel reinforcement framework to finish the preparation of the concrete column.
2. The method for preparing a confined square concrete column or masonry column as claimed in claim 1, wherein in step S1,
fl＝2nftfEfεj,u/B
in the formula, nf、tf、EfAnd εj,uThe number of FRP layers, the single-layer thickness, the elastic modulus and the actual breaking strain of the FRP hoop are respectively shown, and B is the size of the section of the square column.
3. A method for making a confined square concrete column or masonry column according to claim 2, wherein said step S1 includes a step S1-1. the relationship between the mean value of the effective coefficients of strain and the calculation model in step S1 is established.
4. The method for preparing a confined square concrete column or masonry column according to claim 3, wherein in step S1-1,
Figure FDA0003120829940000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003120829940000022
is the mean value of the effective coefficients of strain, epsilonfThe ultimate tensile strain is measured by an FRP strip tensile test.
5. The method for preparing a confined square concrete column or masonry column as claimed in claim 1, wherein in step S1,
ρ＝2rc/B
in the formula, rcThe chamfer radius of the square column is mm, and B is the side length mm of the section of the concrete square column.
6. The method for preparing confined square concrete and masonry columns according to claim 1, wherein the unconstrained concrete compressive strength f'cThe range of (A) is 10.0 to 55.2 MPa.
7. The method for producing a confined square concrete column or masonry column according to claim 2, wherein the number of FRP layers nfThe number of layers is 8 or less.
8. The method for preparing a column and a masonry column according to claim 1, wherein the column comprises a steel reinforcement cage, concrete and FPR cloth, and the FPR cloth is a fiber reinforced composite material.
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