Rectangular-section corrugated steel plate confined concrete constitutive model calculation method based on fiber model method

Abstract

The invention discloses a method for calculating a constitutive model of rectangular-section corrugated steel plate confined concrete based on a fiber model method, which comprises a rectangular-section corrugated steel plate cavity formed by combining transverse corrugated steel plates and corner components, according to the equivalent hoop coefficient theta and the effective constraint coefficient ka of the rectangular cross-section corrugated steel plate cavity and the material strength of concrete, calculating a confined concrete peak strain epsilon o and a confined concrete peak stress sigma o; and according to the calculated x-y normalized curve of the constitutive model of the rectangular-section corrugated steel plate confined concrete, calculating to obtain a sigma-epsilon curve of the constitutive model of the corrugated steel plate confined concrete. According to the calculation method, efficient calculation and analysis of the constitutive model of the rectangular-section corrugated steel plate confined concrete are promoted, the calculation precision is high, and the sigma-epsilon curve obtained through the calculation method can be well matched with a test result curve.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and particularly relates to a calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method. Background Art

[0002] The corrugated steel plate has advantages such as large out-of-plane stiffness and strong buckling resistance. The cavity formed by its effective connection can provide good confinement for concrete. Corrugated steel plate confined concrete composite columns and composite shear walls, as a new type of high-performance structural system, have gradually been applied to engineering practice. However, the lack of a constitutive model for corrugated steel plate confined concrete has become the key restricting the refined analysis of this structure.

[0003] At present, a series of concrete constitutive models based on the fiber model method have been proposed for reinforced concrete and ordinary steel tube confined concrete at home and abroad. However, these models cannot reflect the anisotropic characteristics of the corrugated steel plate. The significant difference between the corrugated steel plate and the ordinary flat steel plate is that it does not bear axial force in the direction perpendicular to the corrugated ribs. Therefore, its mechanism of confining concrete is significantly different from that of the flat steel plate confining concrete, and the traditional constitutive model of flat steel plate confining concrete cannot be applied to the calculation and analysis of corrugated steel plate confined concrete.

[0004] The fiber model method forms the stress-strain relationship of the core concrete by considering the confinement effect of the corrugated steel plate on the core concrete, avoiding the complex mutual contact effect between the corrugated steel plate and the concrete during the calculation process. Therefore, it can be conveniently applied to the full-process analysis of the mechanical properties and bearing capacity calculation of corrugated steel plate composite members. Therefore, in order to promote the efficient calculation and analysis of corrugated steel plate confined concrete structures, it is necessary to propose a calculation method for the constitutive model of corrugated steel plate confined concrete based on the fiber model method. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method in view of the above-mentioned deficiencies of the prior art. The calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method can promote the efficient calculation and analysis of the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section and has high calculation accuracy.

[0006] To solve the above technical problem, the technical solution adopted by the present invention is: a calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method, including a rectangular cross-section corrugated steel plate cavity formed by the combination of transverse corrugated steel plates and corner members. The transverse corrugated steel plates are arranged around the perimeter, and adjacent transverse corrugated steel plates are connected by corner members. The rectangular cross-section corrugated steel plate cavity is filled with concrete. The calculation method includes the following steps:

[0007] Step 1: Calculate the diameter D of the equivalent circle of the corrugated steel plate cavity with a rectangular cross-section.

[0008] Step 2: Calculate the equivalent hoop coefficient θ of the corrugated steel plate cavity with a rectangular cross-section according to the member size and material strength.

[0009] Step 3: Determine the effective confinement coefficient k of the corrugated steel plate cavity with a rectangular cross-section according to the rectangular cross-section size, corner member size, and transverse corrugated steel plate size a 。

[0010] Step 4: Calculate the peak strain ε of the confined concrete a and the peak stress σ of the confined concrete o according to the equivalent hoop coefficient θ and effective confinement coefficient k of the corrugated steel plate cavity with a rectangular cross-section obtained in Steps 2 and 3 o 。

[0011] Step 5: Calculate the x-y normalized curve of the constitutive model of corrugated steel plate-confined concrete based on the fiber model method.

[0012] Step 6: Calculate the σ-ε curve of the constitutive model of corrugated steel plate-confined concrete according to the peak strain ε and peak stress σ of the confined concrete obtained in Step 4 o and the x-y normalized curve of the constitutive model of corrugated steel plate-confined concrete obtained in Step 5. o 。

[0013] Furthermore, in Step 1, the diameter D of the equivalent circle is calculated as follows:

[0014]

[0015] Where:

[0016] b c —— The length of the member cross-section.

[0017] d c —— The width of the member cross-section.

[0018] a w —— The amplitude of the transverse corrugated steel plate.

[0019] q —— The distance between the outer edge of the transverse corrugated steel plate and the outer edge of the corner member parallel to the outer edge of the transverse corrugated steel plate.

[0020] Furthermore, in Step 2, the equivalent hoop coefficient θ is calculated as follows:

[0021]

[0022] Where:

[0023] t w —— Thickness of corrugated steel plate.

[0024] f y —— Yield strength of corrugated steel plate.

[0025] q w —— Wavelength of corrugated steel plate.

[0026] s - Length dimension after a corrugated steel plate with a wavelength is fully unfolded.

[0027] D - Diameter of equivalent circle.

[0028] f ck —— Standard value of axial compressive strength of concrete.

[0029] Furthermore, in step three, the effective confinement coefficient k a is calculated according to the following formula:

[0030]

[0031] In the formula:

[0032] A e —— Effective confinement area of concrete.

[0033] A c,eq —— Average cross - sectional area of concrete.

[0034] Furthermore, in step four, the peak strain ε o of confined concrete and the peak stress σ o of confined concrete are calculated according to the following formula:

[0035]

[0036] In the formula:

[0037] ε cc —— Peak strain of concrete under unidirectional stress.

[0038] f c ' - Compressive strength of concrete cylinder.

[0039] Among them, the peak strain of concrete under unidirectional stress is calculated according to the following formula:

[0040] ε cc =(1300 + 12.5·f c ')×10 -6 .

[0041] Furthermore, in step five, the normalized curve of the constitutive model of corrugated - steel - plate - confined concrete based on the fiber - model method is calculated according to the following formula:

[0042]

[0043] In the formula:

[0044] x—the ratio of the strain of the confined concrete to the peak strain, x = ε / ε0.

[0045] y—the ratio of the stress of the confined concrete to the peak stress, y = σ / σ o .

[0046] ε—the strain of the confined concrete.

[0047] σ—the stress of the confined concrete.

[0048] ε o —the peak strain of the confined concrete.

[0049] σ o —the peak stress of the confined concrete.

[0050] Furthermore, in step five, the calculation methods of the coefficients n, α, and γ are as follows:

[0051]

[0052] Furthermore, in step three, the calculation method of the effective confinement area A e of the concrete is as follows:

[0053]

[0054] In the formula:

[0055] A c,eq —the average cross-sectional area of the concrete;

[0056] b c —the length of the cross-section of the member.

[0057] d c —the width of the cross-section of the member.

[0058] b a —the width of the corner member.

[0059] Furthermore, in step three, the calculation method of the average cross-sectional area A c,eq of the concrete is as follows:

[0060] A c,eq =(A c,max +A c,min ) / 2

[0061]

[0062] In the formula:

[0063] A c,max —— The maximum cross-sectional area of concrete.

[0064] A c,min —— The minimum cross-sectional area of concrete.

[0065] a w —— The amplitude of the transverse corrugated steel plate.

[0066] b w —— The dimension of the corrugated steel plate in the length direction of the component cross-section.

[0067] d w —— The dimension of the corrugated steel plate in the width direction of the component cross-section.

[0068] t w —— The thickness of the transverse corrugated steel plate.

[0069] q —— The distance between the outer edge of the transverse corrugated steel plate and the outer edge parallel to the outer edge of the transverse corrugated steel plate in the corner component.

[0070] Furthermore, the corner component is one of angle steel, square steel pipe, hot-rolled U-shaped steel, polygonal steel pipe, polygonal steel pipe filled with concrete, or polygonal steel bar; the transverse corrugated steel plate is one of trapezoidal corrugated steel plate or sinusoidal corrugated steel plate.

[0071] The present invention has the following beneficial effects:

[0072] 1. The calculation method of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section based on the fiber model method proposed by the present invention can promote the efficient calculation and analysis of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section, with high calculation accuracy. The σ-ε curve obtained by this calculation method can be in good agreement with the test result curve.

[0073] 2. The peak strain of the confined concrete and the peak stress of the confined concrete obtained from the constitutive model of the present invention based on a large number of test data and three-dimensional finite element analysis results can well characterize the influence law of parameters such as corrugated steel plate and cross-section width-thickness ratio on the constitutive model, with high simulation accuracy.

[0074] 3. The calculation method of the equivalent hoop coefficient of the present invention proposes a calculation method for the equivalent circle of the cavity of the corrugated steel plate with rectangular cross-section. This method improves the universality of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section under different width-thickness ratios and improves the accuracy of the constitutive model of corrugated steel plate-confined concrete under rectangular cross-sections with large width-thickness ratios. The equivalent hoop coefficient of the cavity of the corrugated steel plate with rectangular cross-section proposed by the present invention reveals the unique characteristics and confinement essence of the circumferential confinement of concrete by the transverse corrugated steel plate, which is significantly different from the method of defining the hoop coefficient by the ratio of the compressive strength of the steel pipe cross-section to the compressive strength of the core concrete cross-section in traditional concrete-filled steel tubes. Description of the Drawings

[0075] Figure 1 Cross-sectional schematic diagram of a rectangular-section corrugated steel plate confined concrete member applicable to the present invention;

[0076] Figure 2 A - A sectional view of a rectangular-section corrugated steel plate confined concrete member applicable to the present invention;

[0077] Figure 3 Schematic diagram of the cross-sectional form of the corner member;

[0078] Figure 4 Schematic diagram of the trapezoidal corrugated steel plate;

[0079] Figure 5 Schematic diagram of the effective confinement area of the concrete and the equivalent circle of the rectangular-section corrugated steel plate cavity;

[0080] Figure 6 Cross-sectional schematic diagram of an angle steel - corrugated steel plate confined concrete member according to an embodiment of the present invention;

[0081] Figure 7 Comparison diagram of the constitutive model calculation results and test results of the angle steel - corrugated steel plate confined concrete member and the square steel tube - corrugated steel plate confined concrete member according to the embodiment of the present invention;

[0082] In the figure: 1 - corner member; 2 - transverse corrugated steel plate; 3 - concrete; 4 - maximum cross-sectional area of the concrete; 5 - maximum cross-sectional area of the concrete; 6 - equivalent circle; 7 - effective confinement area; 8 - weak confinement area. Detailed Embodiment

[0083] The present invention will be further described in detail below in conjunction with the drawings and specific preferred embodiments.

[0084] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by terms such as "left side", "right side", "upper part", "lower part", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not represent the importance of the components, so they cannot be understood as limitations to the present invention. The specific dimensions adopted in this embodiment are only for illustrating the technical solution and do not limit the protection scope of the present invention.

[0085] As Figure 1As shown in the figure, a calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method includes a corrugated steel plate cavity with a rectangular cross-section formed by a combination of transverse corrugated steel plates and corner members. The transverse corrugated steel plates are arranged around the perimeter, and adjacent transverse corrugated steel plates are connected by corner members. The corrugated steel plate cavity with a rectangular cross-section is filled with concrete.

[0086] Further, as Figure 3 shown, the corner member is one of an angle steel, a square steel pipe, a hot-rolled U-shaped steel, a polygonal steel pipe, a polygonal steel pipe filled with concrete, or a polygonal steel bar; the transverse corrugated steel plate is one of a trapezoidal corrugated steel plate or a sinusoidal corrugated steel plate.

[0087] As Figure 1-2 shown in FIGS. 4-6, the calculation method includes the following steps:

[0088] Step 1: Calculate the diameter D of the equivalent circle of the corrugated steel plate cavity with a rectangular cross-section.

[0089] Further, in Step 1, the diameter D of the equivalent circle is calculated according to the following formula:

[0090]

[0091] In the formula:

[0092] b c —— The length of the member cross-section.

[0093] d c —— The width of the member cross-section.

[0094] a w —— The amplitude of the transverse corrugated steel plate.

[0095] q —— The distance between the outer edge of the transverse corrugated steel plate and the outer edge of the corner member parallel to the outer edge of the transverse corrugated steel plate.

[0096] Step 2: Calculate the equivalent hoop coefficient θ of the corrugated steel plate cavity with a rectangular cross-section according to the member size and material strength.

[0097] Further, in Step 2, the equivalent hoop coefficient θ is calculated according to the following formula:

[0098]

[0099] In the formula:

[0100] t w —— The thickness of the corrugated steel plate.

[0101] f y —— The yield strength of the corrugated steel plate.

[0102] q w——Wavelength of corrugated steel sheet.

[0103] s is the length of one wavelength of corrugated steel plate when fully expanded.

[0104] D – the diameter of the equivalent circle.

[0105] f ck ——Standard value of concrete axial compressive strength.

[0106] Among them, f y and f ck Measured through experiments or selected according to relevant standards.

[0107] Step 3: Determine the effective constraint coefficient k of the rectangular cross-section corrugated steel plate cavity based on the rectangular cross-section dimensions, corner component dimensions, and transverse corrugated steel plate dimensions. a .

[0108] Furthermore, in step 3, the effective constraint coefficient k a Calculate as follows:

[0109]

[0110] Where:

[0111] A e ——Effective restraint area of concrete.

[0112] A c,eq ——Average cross-sectional area of concrete.

[0113] Furthermore, in step 3, the effective restraint area of concrete A e The calculation method is as follows:

[0114]

[0115] Where:

[0116] A c,eq — average cross-sectional area of concrete;

[0117] b c ——The length of the component section.

[0118] d c ——The width of the component section.

[0119] b a ——Width of corner member.

[0120] Furthermore, the average cross-sectional area of concrete A c,eq The calculation method is as follows:

[0121] A c,eq =(A c,max+A c,min ) / 2

[0122]

[0123] In the formula:

[0124] A c,max —— The maximum cross-sectional area of concrete.

[0125] A c,min —— The minimum cross-sectional area of concrete.

[0126] a w —— The amplitude of the transverse corrugated steel plate.

[0127] b w —— The dimension of the corrugated steel plate in the length direction of the component cross-section.

[0128] d w —— The dimension of the corrugated steel plate in the width direction of the component cross-section.

[0129] t w —— The thickness of the transverse corrugated steel plate.

[0130] q —— The distance between the outer edge of the transverse corrugated steel plate and the outer edge parallel to the outer edge of the transverse corrugated steel plate in the corner component.

[0131] Step 4: Calculate the equivalent hoop coefficient θ and effective confinement coefficient k of the rectangular cross-section corrugated steel plate cavity obtained from Steps 2 and 3 a and the material strength of the concrete, and calculate the peak strain ε o of the confined concrete and the peak stress σ o .

[0132] Furthermore, in Step 4, the peak strain ε o of the confined concrete and the peak stress σ o are calculated according to the following formula:

[0133]

[0134] In the formula:

[0135] ε cc —— The peak strain of concrete under unidirectional stress.

[0136] f c ' —— The compressive strength of the concrete cylinder.

[0137] Among them, the peak strain of concrete under unidirectional stress is calculated according to the following formula:

[0138] ε cc =(1300 + 12.5·fc )×10 -6 。

[0139] Step Five: Calculate the x-y normalized curve of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section based on the fiber model method.

[0140] Further, in Step Five, the normalized curve of the constitutive model of corrugated steel plate-confined concrete based on the fiber model method is calculated according to the following formula:

[0141]

[0142] Where:

[0143] x — The ratio of the strain of confined concrete to the peak strain, x = ε / ε o 。

[0144] y — The ratio of the stress of confined concrete to the peak stress, y = σ / σ o 。

[0145] ε — The strain of confined concrete.

[0146] σ — The stress of confined concrete.

[0147] ε o — The peak strain of confined concrete.

[0148] σ o — The peak stress of confined concrete.

[0149] Further, the calculation methods of the coefficients n, α, and γ are as follows:

[0150]

[0151] Step Six: According to the peak strain ε o of the confined concrete calculated in Step Four o and the peak stress σ

[0152] of the confined concrete, as well as the x-y normalized curve of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section calculated in Step Five, calculate the σ-ε curve of the constitutive model of corrugated steel plate-confined concrete. Figure 7 (a) shows that the σ-ε curve obtained by using the calculation method of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section based on the fiber model method proposed by the present invention is in good agreement with the test result curve.

[0153] In one embodiment, the component is an angle steel-corrugated steel plate-confined concrete component. As Figure 7(b), the σ-ε curve obtained by using the calculation method of the constitutive model of corrugated steel plate-confined concrete with rectangular cross-section based on the fiber model method proposed by the present invention shows a good agreement between the calculated curve and the test result curve.

[0154] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0155] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A calculation method for the constitutive model of corrugated steel plate confined concrete with a rectangular cross-section based on the fiber model method, including a corrugated steel plate cavity with a rectangular cross-section formed by the combination of transverse corrugated steel plates and corner members. The transverse corrugated steel plates are arranged around the perimeter, and adjacent transverse corrugated steel plates are connected by corner members. Concrete is filled in the corrugated steel plate cavity with a rectangular cross-section. It is characterized in that: It includes the following steps: Step 1: Calculate the diameter D of the equivalent circle of the corrugated steel plate cavity with a rectangular cross-section; Step 2: Calculate the equivalent hoop coefficient θ of the corrugated steel plate cavity with a rectangular cross-section according to the member size and material strength; Step 3: Determine the effective constraint coefficient k of the corrugated steel plate cavity with a rectangular cross-section according to the dimensions of the rectangular cross-section, the corner member, and the transverse corrugated steel plate a ; Step 4: Calculate the equivalent hooping coefficient θ and effective confinement coefficient k of the corrugated steel plate cavity with rectangular cross-section obtained from Steps 2 and 3 a and the material strength of the concrete to calculate the peak strain ε o and peak stress σ o of the confined concrete; Step 5: Calculate the x-y normalized curve of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method; Step 6: According to the peak strain ε o of the confined concrete calculated in Step 4 and the peak stress σ o of the confined concrete, as well as the x-y normalization curve of the constitutive model of the corrugated steel plate-confined concrete calculated in Step 5, calculate the σ-ε curve of the constitutive model of the corrugated steel plate-confined concrete.

2. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 1, wherein: In Step 1, the diameter D of the equivalent circle is calculated by the following formula: In the formula: b c —— The length of the cross-section of the component; d c —— width of the cross-section of the component; a w —— Amplitude of the transverse corrugated steel plate; q — The distance between the outer edge of the transverse corrugated steel plate and the outer edge parallel to the outer edge of the transverse corrugated steel plate in the corner member.

3. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 2, wherein: In Step 2, the equivalent hoop coefficient θ is calculated by the following formula: In the formula: t w —— Thickness of corrugated steel sheet; f y —— yield strength of corrugated steel sheet; q w —— Wavelength of corrugated steel sheet; s — The length dimension after the complete unfolding of the corrugated steel plate in one wavelength; D — The diameter of the equivalent circle; f ck —— Standard value of concrete axial compressive strength.

4. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 3, wherein: In step 3, the effective constraint coefficient k a is calculated according to the following formula: In the formula: A e —— Effective confined area of concrete; A c,eq —— Average cross-sectional area of concrete.

5. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 4, wherein: In Step 4, the peak strain ε o of the confined concrete and the peak stress σ o of the confined concrete are calculated according to the following formula: In the formula: ε cc ——Peak strain of concrete under unidirectional stress; f c '——Compressive strength of concrete cylinder; Among them, the peak strain of concrete under unidirectional stress is calculated by the following formula: ε cc = (1300 + 12.5·f’ c ) × 10 -6 .

6. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 5, wherein: In Step 5, the normalized curve of the constitutive model of corrugated steel plate-confined concrete based on the fiber model method is calculated by the following formula: In the formula: x—the ratio of the strain of confined concrete to the peak strain, x = ε / ε o ; y—the ratio of the stress of confined concrete to the peak stress, y = σ / σ o ; ε — The strain of confined concrete; σ — The stress of confined concrete; ε o —— Peak strain of confined concrete; σ o —— Peak stress of confined concrete.

7. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 6, wherein: In Step 5, the calculation methods of the coefficients n, α, and γ are as follows:

8. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 4, wherein: In Step 3, the calculation method of the effective confinement area A of concrete is as follows: e ​ In the formula: A c,eq —— average cross-sectional area of concrete; b c —— The length of the cross-section of the component; d c —— Width of the cross-section of the component; b a —— Width of the corner member.

9. The calculation method of the constitutive model of corrugated steel plate-confined concrete with a rectangular cross-section based on the fiber model method according to claim 8, wherein: In Step 3, the average cross-sectional area A of the concrete c,eq is calculated as follows: A c,eq =(A c,max +A c,min ) / 2 In the formula: A c,max —— the maximum cross-sectional area of the concrete; A c,min —— The minimum cross-sectional area of concrete; a w —— amplitude of the transverse corrugated steel sheet; b w —— The dimension of the corrugated steel plate in the length direction of the cross-section of the component; d w —— Dimension of the corrugated steel sheet in the width direction of the component cross-section; t w —— Thickness of the horizontally corrugated steel sheet; q — The distance between the outer edge of the transverse corrugated steel plate and the outer edge parallel to the outer edge of the transverse corrugated steel plate in the corner member.

10. The calculation method of the constitutive model of rectangular-section corrugated steel plate confined concrete based on the fiber model method according to claim 1, wherein: The corner member is one of an angle steel, a square steel pipe, a hot-rolled U-shaped steel, a polygonal steel pipe, a polygonal steel pipe filled with concrete, or a polygonal steel bar; the transverse corrugated steel plate is one of a trapezoidal corrugated steel plate or a sinusoidal corrugated steel plate.

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