Crack width calculation method of tensile reinforcement UHPC wall panel

Abstract

This application relates to a method for calculating the crack width of tension-reinforced UHPC wall panels, belonging to the field of UHPC wall panels. It includes establishing a basic parameter system for tension-reinforced UHPC wall panels; determining whether the wall panel is cracked; confirming cracking by calculating the average crack spacing, the stress non-uniformity coefficient of the reinforcing steel, the stress of the reinforcing steel at the crack section, and the maximum crack width based on the three-phase synergistic working mechanism of the reinforcing steel, steel fiber, and UHPC matrix. The crack width calculation method for tension-reinforced UHPC wall panels in this application fully considers the bridging effect of steel fibers in UHPC on the inhibition of crack development. Based on the three-phase synergistic working mechanism of "reinforcing steel, steel fiber, and UHPC matrix," the calculation model has a significantly higher prediction accuracy than traditional reinforced concrete crack width calculation methods. Verification shows that the error between the predicted value and the experimentally measured value can be controlled within 15%.

Description

Technical Field

[0001] This application relates to the field of UHPC wall panels, and in particular to a method for calculating the crack width of tensile-reinforced UHPC wall panels. Background Technology

[0002] UHPC, as a new type of cement-based composite material, has ultra-high strength, high toughness and excellent durability.

[0003] Compared with traditional concrete, UHPC significantly improves the tensile properties of the material by incorporating steel fibers, which makes reinforced UHPC members exhibit the characteristic of "multiple crack development" when under tension. The crack width can be controlled within 0.05mm, and the number of cracks is more than 5 times that of ordinary concrete members, which completely changes the inherent pattern of "one crack and it's ruined" in traditional reinforced concrete.

[0004] Currently, methods for calculating concrete crack width mainly target ordinary concrete members, making it difficult to accurately reflect the tensile mechanical behavior of reinforced UHPC. Furthermore, current research on crack width in reinforced UHPC primarily focuses on axially tensioned and flexural members; existing research has not yet established a dedicated crack width calculation method for tensile-reinforced UHPC wall panels. As thin-walled members, wall panels typically have a small thickness (30-80mm), and their stress mode is primarily in-plane tension. Their crack development patterns differ significantly from those of flexural members such as beams and slabs. Therefore, it is necessary to develop a dedicated crack width calculation method for tensile-reinforced UHPC wall panels to meet the design requirements of UHPC thin-walled members under normal serviceability limits. Summary of the Invention

[0005] To achieve the above objectives, this application provides a method for calculating the crack width of a tension-reinforced UHPC wall panel.

[0006] In one aspect of this disclosure, a method for calculating the crack width of a tension-reinforced UHPC wall panel is proposed, comprising: Establish a basic parameter system for tension-reinforced UHPC wall panels; Determine if the wall panels are cracked; To determine wall panel cracking, the average crack spacing was calculated based on the three-phase synergistic working mechanism of steel reinforcement, steel fiber, and UHPC matrix. Stress non-uniformity coefficient of reinforcing steel Stress in the reinforcing steel at the crack section Maximum crack width ; The calculated maximum crack width Compared with the standard limit Compare the results to complete the crack width verification.

[0007] Preferably, the basic parameter system includes the geometric parameters, material parameters, and reinforcement parameters of the wall panel; The geometric parameters include: the thickness h of the wall panel and the calculated width b; The material parameters include: UHPC axial tensile strength. Elastic modulus steel fiber volume fraction steel fiber aspect ratio ; The reinforcement parameters include: the diameter of the reinforcing bars. Reinforcement ratio Elastic modulus Yield strength Bond characteristic coefficient between steel reinforcement and UHPC ; The bond characteristic coefficient between the reinforcing steel and UHPC The values ​​are determined based on the surface characteristics of the reinforcing bars; for plain round reinforcing bars, the values ​​are... =0.7, for corrugated steel bars =0.8, hot-rolled ribbed steel bars are taken as =1.0.

[0008] Preferably, determining whether the wall panel is cracked includes: Calculate cracking load , ,in, The cross-sectional area of ​​the wall panel. for Standard value; Compare the axial tensile forces borne by the wall panels and cracking load Size; If the wall panel does not crack, then the wall panel will crack.

[0009] Preferably, the average crack spacing The calculation formula is: ; In the formula, For the influence coefficient of UHPC protective layer thickness, 1 1.2, For load form coefficients, =1, The net protective layer thickness of the reinforcing steel. The coefficient representing the influence of rebar diameter is... 0.12, To achieve an effective reinforcement ratio, , The total area of ​​the tensile reinforcement. For the effective tension zone cross-sectional area, The fiber toughening coefficient is 0.05. 0.15.

[0010] Preferred, .

[0011] Preferably, the stress non-uniformity coefficient of the reinforcing steel is... The calculation formula is: In the formula, For the effective tensile strength of UHPC, In the formula, The fiber contribution coefficient is 0.2. 0.4.

[0012] Preferred, .

[0013] Preferably, the stress of the reinforcing steel in the crack section The calculation formula is: .

[0014] Preferably, the maximum crack width The calculation formula is: In the formula, To account for the expansion factor of crack width distribution dispersion, 1.2 1.5.

[0015] Preferably, the calculated maximum crack width Compared with the standard limit The comparison and verification of crack width includes: Sure If the crack width of the wall panel meets the requirements of the normal service limit state; Sure If necessary, adjust the reinforcement parameters and / or wall panel thickness, and recalculate the maximum crack width. Continue until the requirements are met; =0.05mm.

[0016] Beneficial technical effects: 1. The crack width calculation method for tensile reinforced UHPC wall panels in this application fully considers the bridging effect of steel fibers in UHPC on the inhibition of crack development. The calculation model is established based on the three-phase synergistic working mechanism of "steel reinforcement-steel fiber-UHPC matrix". The prediction accuracy is significantly better than the traditional reinforced concrete crack width calculation method. It has been verified that the error between the predicted value and the experimental measured value can be controlled within 15%.

[0017] 2. The crack width calculation method for tension-reinforced UHPC wall panels in this application is specifically designed for this type of thin-walled component, which takes into account the characteristics of small wall panel thickness, low reinforcement ratio, and in-plane tension stress mode, thus solving the problem of poor applicability of existing crack width calculation methods to thin-walled components.

[0018] 3. The crack width calculation method for tensile reinforced UHPC wall panels in this application establishes a complete parameter system, including the steel bond characteristic coefficient, fiber toughening coefficient, fiber contribution coefficient, etc., which can comprehensively reflect the influence of material properties, reinforcement parameters and component geometry on crack width.

[0019] 4. The method for calculating the crack width of tensile-reinforced UHPC wall panels in this application is expressed in a formulaic way with clear steps, and can be directly used for the serviceability limit state design of UHPC wall panels. Detailed Implementation

[0020] The exemplary embodiments will now be described more fully. However, the exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art.

[0021] In one aspect of this disclosure, a method for calculating the crack width of a tension-reinforced UHPC wall panel is provided, comprising: S1. Establish a basic parameter system for tension-reinforced UHPC wall panels, which includes the geometric parameters, material parameters, and reinforcement parameters of the wall panels; Specifically, the geometric parameters include: the thickness h of the wall panel and the calculated width b; The material parameters include: UHPC axial tensile strength. Elastic modulus steel fiber volume fraction steel fiber aspect ratio ; The reinforcement parameters include: the diameter of the reinforcing bars. Reinforcement ratio Elastic modulus Yield strength Bond characteristic coefficient between steel reinforcement and UHPC .

[0022] Wherein, the bond characteristic coefficient between the steel reinforcement and UHPC The values ​​are determined based on the surface characteristics of the reinforcing bars; for plain round reinforcing bars, the values ​​are... =0.7, for corrugated steel bars =0.8, hot-rolled ribbed steel bars are taken as =1.0.

[0023] As can be seen, the crack width calculation method of the tensile-reinforced UHPC wall panel in this embodiment establishes a complete parameter system, including the steel bond characteristic coefficient, fiber toughening coefficient, fiber contribution coefficient, etc., which can comprehensively reflect the influence of material properties, reinforcement parameters and component geometry on crack width.

[0024] S2. Determine if the wall panel is cracked; The judgment method is as follows: S21. Calculate cracking load , The cross-sectional area of ​​the wall panel. for Standard value; As an example, the material properties of C120 grade UHPC can be selected... = 8.5 MPa, of course, in other embodiments, The value can also be obtained from the material testing report.

[0025] When it is known that At that time, it can be done according to the formula Calculate , This is the partial factor for UHPC materials, usually taken as 1.4.

[0026] S22. Compare the axial tensile forces borne by the wall panels. and cracking load Size; S23, If the wall panel does not crack, then the wall panel will crack.

[0027] S3. Determine wall panel cracking and calculate the average crack spacing based on the three-phase collaborative working mechanism of steel reinforcement-steel fiber-UHPC matrix. Stress non-uniformity coefficient of reinforcing steel Stress in the reinforcing steel at the crack section Maximum crack width ; Specifically, the average crack spacing The calculation formula is: ; In the formula, For the influence coefficient of UHPC protective layer thickness, 1 1.2, For load form coefficients, =1, The net protective layer thickness of the reinforcing steel. The coefficient representing the influence of rebar diameter is... 0.12, To achieve an effective reinforcement ratio, , The total area of ​​the tensile reinforcement. , This refers to the number of steel bars within the calculated width b. For the effective tension zone cross-sectional area, The fiber toughening coefficient is 0.05. 0.15, It is positively correlated with fiber volume fraction and aspect ratio.

[0028] In practice, Use this formula to calculate The effect of wall panel thickness h on fiber toughening effect was considered.

[0029] As an example, That is, the effective tensile zone cross-sectional area Take 2.5 times the net protective layer thickness of the reinforcing steel. The cross-sectional area within the specified range.

[0030] Specifically, the stress non-uniformity coefficient of the reinforcing steel The calculation formula is: In the formula, For the effective tensile strength of UHPC, In the formula, The fiber contribution coefficient is 0.2. 0.4.

[0031] It should be noted that when calculated according to the formula... When it is less than 0.2, take =0.2, when calculated according to the formula When it is greater than 1, take =1.

[0032] In practice, .

[0033] Specifically, the stress in the reinforcing steel at the crack section The calculation formula is: .

[0034] Specifically, the maximum crack width The calculation formula is: In the formula, To account for the expansion factor of crack width distribution dispersion, 1.2 1.5.

[0035] In practice, The specific value can be determined according to the crack control level requirements. For example, when a strict requirement is that no cracks should appear, the value should be [value missing]. =1.2, generally required to be taken when no cracks appear. =1.3, allowing for the occurrence of cracks. =1.5.

[0036] As can be seen, the crack width calculation method of the tension-reinforced UHPC wall panel in this embodiment fully considers the bridging effect of steel fibers in UHPC on the inhibition of crack development. The calculation model is established based on the three-phase synergistic working mechanism of "steel bar-steel fiber-UHPC matrix". The prediction accuracy is significantly better than the traditional reinforced concrete crack width calculation method. It has been verified that the error between the predicted value and the experimental measured value can be controlled within 15%.

[0037] S4. Calculate the maximum crack width. Compared with the standard limit Compare the results to complete the crack width verification.

[0038] Specifically, S4, the calculated maximum crack width Compared with the standard limit The comparison and verification of crack width includes: Sure If the crack width of the wall panel meets the requirements of the normal service limit state; Sure If necessary, adjust the reinforcement parameters and / or wall panel thickness, and recalculate the maximum crack width. Continue until the requirements are met; =0.05mm.

[0039] As can be seen, the crack width calculation method for tension-reinforced UHPC wall panels in this embodiment is specifically designed for this type of thin-walled component, which takes into account the characteristics of small wall panel thickness, low reinforcement ratio, and in-plane tension stress mode. It solves the problem of poor applicability of existing crack width calculation methods to thin-walled components. Moreover, it adopts a formulaic expression with clear steps and can be directly used for the serviceability limit state design of UHPC wall panels.

[0040] The following two specific embodiments will be used to provide a detailed explanation of the crack width calculation method for the tension-reinforced UHPC wall panel of this application.

[0041] Example 1: S1. Establish the basic parameter system for tension-reinforced UHPC wall panels.

[0042] Specifically, taking the wall panel thickness h = 50mm, the calculated width b = 1000mm. =50000mm², =8.5MPa, steel fiber volume fraction =2.0%, steel fiber aspect ratio The diameter of the reinforcing bar =8mm, spacing 150mm =335mm², elastic modulus =200GPa, hot-rolled ribbed steel bars are taken as =1.0, net protective layer thickness of reinforcing steel =15mm, axial tensile force borne by the wall panel =150kN, then the reinforcement ratio can be calculated. =0.67%, effective reinforcement ratio =0.00893, fiber toughening coefficient =0.103, fiber contribution coefficient =0.244, effective tensile strength of UHPC =14.0MPa.

[0043] S2. Determine if the wall panel is cracked; Specifically, cracking load Therefore, the wall panels did not crack.

[0044] Example 2: S1. Establish the basic parameter system for tension-reinforced UHPC wall panels.

[0045] Specifically, taking the wall panel thickness h = 50mm, the calculated width b = 1000mm, and the wall panel cross-sectional area... 50000mm², =8.5MPa, steel fiber volume fraction =2.0%, steel fiber aspect ratio The diameter of the reinforcing bar =8mm, spacing 150mm, total area of ​​tensile reinforcement =335mm², elastic modulus =200GPa, hot-rolled ribbed steel bars are taken as =1.0, net protective layer thickness of reinforcing steel =15mm, axial tensile force borne by the wall panel =500kN, then the reinforcement ratio can be calculated. =0.67%, effective reinforcement ratio =0.00893, fiber toughening coefficient =0.103, fiber contribution coefficient =0.244, effective tensile strength of UHPC =14.0MPa.

[0046] S2. Determine if the wall panel is cracked; Specifically, cracking load Therefore, the wall panels cracked.

[0047] S3. Determine wall panel cracking and calculate the average crack spacing based on the three-phase collaborative working mechanism of steel reinforcement-steel fiber-UHPC matrix. = 101.9mm, coefficient of non-uniformity of steel reinforcement stress Stress in the reinforcing steel at the crack section Maximum crack width .

[0048] S4. Calculate the maximum crack width. Compared with the standard limit Compare the results to complete the crack width verification.

[0049] Specifically, =0.05mm, therefore the crack width of the wall panel meets the requirements of normal serviceability limit state.

[0050] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "first," "second," "third," and similar terms used in this application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. The terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "comprising" or "including" and similar terms mean that the elements or objects preceding "comprising" or "including" encompass the elements or objects listed following "comprising" or "including" and their equivalents, and do not exclude other elements or objects. "Above," "below," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0051] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for calculating the crack width of a tension-reinforced UHPC wall panel, characterized in that, include: Establish a basic parameter system for tension-reinforced UHPC wall panels; Determine if the wall panels are cracked; To determine wall panel cracking, the average crack spacing was calculated based on the three-phase synergistic working mechanism of steel reinforcement, steel fiber, and UHPC matrix. Stress non-uniformity coefficient of reinforcing steel Stress in the reinforcing steel at the crack section Maximum crack width ; The calculated maximum crack width Compared with the standard limit Compare the results to complete the crack width verification.

2. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The basic parameter system includes the geometric parameters, material parameters, and reinforcement parameters of the wall panel; The geometric parameters include: the thickness h of the wall panel and the calculated width b; The material parameters include: UHPC axial tensile strength. Elastic modulus steel fiber volume fraction steel fiber aspect ratio ; The reinforcement parameters include: the diameter of the reinforcing bars. Reinforcement ratio Elastic modulus Yield strength Bond characteristic coefficient between steel reinforcement and UHPC ; The bond characteristic coefficient between the reinforcing steel and UHPC The values ​​are determined based on the surface characteristics of the reinforcing bars; for plain round reinforcing bars, the values ​​are... =0.7, for corrugated steel bars =0.8, hot-rolled ribbed steel bars are taken as =1.

0.

3. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The determination of whether the wall panel is cracked includes: Calculate cracking load , ,in, The cross-sectional area of ​​the wall panel. for Standard value; Compare the axial tensile forces borne by the wall panels and cracking load Size; If the wall panel does not crack, then the wall panel will crack.

4. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The average crack spacing The calculation formula is: ; In the formula, For the influence coefficient of UHPC protective layer thickness, 1 1.2, For load form coefficients, =1, The net protective layer thickness of the reinforcing steel. The coefficient representing the influence of rebar diameter is... 0.12, To achieve an effective reinforcement ratio, , The total area of ​​the tensile reinforcement. For the effective tension zone cross-sectional area, The fiber toughening coefficient is 0.

05. 0.

15.

5. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 4, characterized in that: 。 6. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The stress non-uniformity coefficient of the reinforcing steel The calculation formula is: In the formula, For the effective tensile strength of UHPC, In the formula, The fiber contribution coefficient is 0.

2. 0.

4.

7. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 6, characterized in that: 。 8. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The stress in the reinforcing steel at the crack section The calculation formula is: .

9. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The maximum crack width The calculation formula is: , To account for the expansion factor of crack width distribution dispersion, 1.2 1.

5.

10. The method for calculating the crack width of a tension-reinforced UHPC wall panel according to claim 1, characterized in that: The calculated maximum crack width Compared with the standard limit The comparison and verification of crack width includes: Sure If the crack width of the wall panel meets the requirements of the normal service limit state; Sure If necessary, adjust the reinforcement parameters and / or wall panel thickness, and recalculate the maximum crack width. Continue until the requirements are met; =0.05mm。

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