A method for determining the shear bearing capacity of a deep beam based on an improved tension-compression strut model

Abstract

The application discloses a method for determining the shearing bearing capacity of a deep beam based on an improved tension-compression strut model, and belongs to the technical field of structural engineering. The method comprises the following steps: obtaining the geometric parameters and material parameters of the deep beam; constructing the improved tension-compression strut model, wherein vertical tension rods considering the contribution of the web reinforcement are arranged in the model; calculating the first deep beam shearing bearing capacity according to the internal moment balance condition of the shear span region; determining the second deep beam shearing bearing capacity according to the vertical component on the intersection surface of the main compression rod and the CCT node; calculating the tension of the bottom tension rod, and backstepping the vertical height of the CCC node; comparing the CCC node height with the initial CCC node height; if the set condition is met, the deep beam shearing bearing capacity is output; if the set condition is not met, the initial CCC node vertical height is adjusted, and the iterative calculation is carried out. The application overcomes the defect that the traditional tension-compression strut model does not consider the influence of the web reinforcement, and significantly improves the prediction accuracy and reliability of the deep beam shearing bearing capacity by widely considering various factors influencing the shearing of the deep beam component.

Description

Technical Field

[0001] This invention relates to the field of structural engineering technology, and specifically to a method for determining the shear capacity of deep beams based on an improved tension-compression bar model. Background Technology

[0002] Modern buildings, due to their expanded functions, need to bear significantly increased loads. As a result, the height and dimensions of beams, which are the main load-bearing components, are constantly increasing. Simply supported single-span beams with a span-to-depth ratio of less than 2 are called deep beams (as defined in the "Code for Design of Concrete Structures" (GB50010-2010)). Due to their high vertical bearing capacity and high construction efficiency, they are now widely used. Specific examples include transfer floor beams at vertical load discontinuities in high-rise structures, the ground floor beams of frame-supported shear walls, basement walls and wall-type foundation beams, hydraulic structures such as aqueducts, sluice gates, and power plant buildings that bear enormous water pressure and structural weight, as well as the sidewalls of various storage silos or pools. The problems associated with deep beam components in modern architecture have become unavoidable.

[0003] Deep beams, due to their small shear span ratio and the fact that their inclined sections belong to the typical stress disturbance zone (D zone), exhibit complex force mechanisms, numerous influencing factors, and significant brittle failure characteristics. This makes shear problems more prominent, with subtle signs of failure. Once failure occurs, the consequences are often extremely severe, potentially leading to partial or complete structural collapse and catastrophic accidents. Therefore, calculating the shear capacity of deep beams and conducting corresponding model-based shear analysis are crucial aspects of deep beam structural design.

[0004] Regarding the methods for determining the shear capacity of deep beams, the shear models for deep beams adopted by Chinese and American standards are as follows: The calculation method for the shear capacity of deep beams under concentrated loads given in Appendix G of the current Chinese Code for Design of Concrete Structures (GB 50010-2010) is a semi-empirical and semi-theoretical formula obtained by fitting a large amount of experimental data, which lacks obvious mechanical background and theoretical guidance. The calculation results of the formula in the code show that it cannot accurately reflect the influence of shear span ratio and web reinforcement ratio on shear capacity.

[0005] Chapter 23 of the American Concrete Structures Code (ACI) 318-19 provides a method for calculating shear capacity based on a tension-compression bar model. This model equates the complex stress flow within a deep beam to uniaxially stressed bar elements, where the axial forces on the compression and tension bars are compressive and tensile stresses, respectively, and the intersection of the compression and tension bars is the nodal zone. When any element—compression bar, tension bar, or nodal zone—reaches its ultimate strength, the tension-compression bar model fails, and the shear failure mode of the deep beam corresponds to the compressive failure of the compression bar in the model. In the tension-compression bar model, the bar inclination angle reflects the influence of the shear span ratio, the geometry of the bottom nodal reflects the influence of the section height and longitudinal reinforcement ratio, and the compressive strength of the compression bar directly reflects the influence of concrete strength. However, this method of determining shear capacity does not consider the influence of the web reinforcement on shear capacity. Furthermore, the calculation results based on the tension-compression bar model in the American code are overly conservative and have significant dispersion, failing to accurately reflect the influence of key physical parameters such as the web reinforcement ratio and shear span ratio on shear capacity.

[0006] From an engineering perspective, accurately determining the shear capacity of deep beams and comprehensively considering various design parameters are crucial to ensuring the safety of such components and avoiding brittle failure. This stems from the unique mechanical mechanisms of deep beams, the limitations of current design theories, and the severity of failure modes. These three factors collectively determine that any deviation in the shear capacity estimation can directly translate into structural safety hazards or significant economic and safety risks.

[0007] Therefore, there is an urgent need to establish a method for determining the shear bearing capacity of deep beams that fully reflects the main physical parameters of deep beams, has a wider range of applications, and is more accurate and reliable. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, this invention aims to provide a method for determining the shear capacity of deep beams based on an improved tension-compression bar model. This method addresses the problem that existing calculations of the shear capacity of deep beams based on tension-compression bar models are too conservative and have large dispersion, failing to accurately reflect the influence of key physical parameters such as the reinforcement ratio and shear span ratio on the shear capacity. This new method can broadly consider the physical parameters of deep beam members, effectively improving the accuracy of predictions.

[0009] To achieve the above objectives, the present invention provides the following solution: A method for determining the shear capacity of deep beams based on an improved tension-compression bar model, such as... Figure 1 As shown, it includes the following steps: Step 1: Obtain the geometric and material parameters of the deep beam; Step 2: Based on the traditional tension-compression bar model, an improved tension-compression bar model is established by setting a vertical tension bar in the middle of the shear span zone that simultaneously considers the shear contribution of both vertical and horizontal reinforcement bars. The vertical tension bar divides the original concrete compression bar into a main compression bar and a secondary compression bar. The two ends of the main compression bar are CCT nodes (compression-compression-tension nodes), the loading point is a CCC node (compression-compression-compression node), and the bottom node is a CTT node (compression-tension-tension node). Step 3: Calculate the shear capacity of the first deep beam based on the internal moment equilibrium condition of the shear span zone; Step 4: Calculate the vertical tie rod tension used to characterize the shear contribution of the web reinforcement, and calculate the horizontal tie rod tension based on the vertical tie rod tension; calculate the inclination angle of the main compression member using the horizontal tie rod tension, and calculate the control width of the main compression member based on the inclination angle of the main compression member; Step 5: Determine the shear capacity of the second deep beam based on the vertical component on the intersection surface of the main compression member and the CCT node; Step 6: Calculate the bottom tie rod tension based on the shear capacity of the first deep beam and the shear capacity of the second deep beam, and use the bottom tie rod tension to infer the vertical height of the CCC node. Compare the vertical height of the CCC node with the initial vertical height of the CCC node. If they are equal or the difference is less than a preset threshold, the shear capacity of the deep beam is determined as the shear capacity of the first deep beam; otherwise, adjust the initial vertical height of the CCC node and repeat steps 3-6.

[0010] Furthermore, in step 3, the specific calculation formula for the shear bearing capacity of the first deep beam is as follows: ; in, d It is the vertical distance from the resultant point of the tensile longitudinal reinforcement of the cross section to the compression edge of the concrete; a To cut the span length; w c This represents the initial vertical height of the CCC node; T f The horizontal tension of the bottom horizontal tie rod; The horizontal tension of the bottom horizontal tie rod is calculated using the following formula: ; in, F c The pressure of the horizontal compression bar between the loading points. f c 'This refers to the compressive strength of cylindrical concrete.' b The width of the specimen.

[0011] Furthermore, in step 4, the formula for calculating the tension of the vertical tie rod is: ; in, T wv The formula for calculating the contribution of vertical fascia is as follows: ; In the formula, a cl The horizontal distance from the inner edge of the support to the outer edge of the loading plate. f yv For the vertical abdominal muscle yield strain, This refers to the vertical reinforcement ratio of the web reinforcement. T wh The formula for calculating the contribution of the horizontal abdominal muscles is as follows: ; In the formula, s sc For horizontal abdominal muscle stress, f yh The yield strain of the horizontal abdominal muscles. f s The diameter of the horizontal abdominal muscles. l d This refers to the height of the abdominal muscles. n s The number of horizontal fascia within the calculation range; The horizontal tie rod tension is calculated based on the vertical tie rod tension, using the following formula: ; Calculate the inclination angle of the main compression member using the tension of the horizontal tie rod: ; The formula for calculating the control width of the main pressure bar is: ; In the formula, l b1 The width of the CCT node is taken as the width of the support pad. w t This represents the vertical height of the CCT node.

[0012] Furthermore, in step 5, the formula for calculating the shear capacity of the second deep beam is: ; in, F s The compressive bearing capacity at the intersection of the main compression member and the CCT node is calculated using the following formula: ; in, f strut The effective compressive strength of the concrete for the main compression member BE. βs This is the effective coefficient of the concrete compression bar on the intersecting surface.

[0013] Furthermore, in step 6, the formula for calculating the tension of the bottom tie rod is: ; in, l b3 The width of the CTT node. v b The average shear stress within the node.

[0014] Then, the vertical height of the CCC node is calculated by reverse calculation based on the tension of the bottom tie rod, specifically: Based on the bottom pull rod tension Using the calculation formula in step 3 To reverse-calculate the vertical height of the CCC node The specific calculation formula is as follows: ; Then the vertical height of the CCC node Vertical height of the initial CCC node w c Compare; like ,or If the calculation stops, the shear capacity of the deep beam is output as the shear capacity of the first deep beam. V ,in, This is a preset threshold.

[0015] like Then adjust the vertical height of the initial CCC node, making the new initial CCC node vertical height... Repeat steps 3-6 until the calculation stops.

[0016] Compared with the prior art, the present invention discloses the following technical effects: This invention breaks down the single compression member in the commonly used tension-compression member model in the prior art into primary and secondary compression members, and introduces a vertical tie member in the middle of the shear span. This makes the inclination angle of the primary compression member no longer fixed, but dynamically adjusted according to the amount of web reinforcement and the shear span ratio through force balance relationship. For the first time, it realizes a structured expression of the influence of web reinforcement on the force transmission path. At the same time, the shear resistance of horizontal web reinforcement is analogized to the "longitudinal reinforcement dowel mechanism", and it is included together with the vertical web reinforcement in the tensile force calculation of the vertical tie member. This allows the improved tension-compression member model to widely consider various physical parameters of deep beam members, effectively improving the accuracy of predicting the shear bearing capacity of deep beams.

[0017] This invention also addresses the lack of detailed analysis of the bottom CTT node in existing standards by introducing Modified Pressure Field Theory (MCFT) for membrane element stress-strain analysis. This quantifies the cracking behavior and internal force transmission relationship in the node region, significantly improving the rationality of the calculation of the internal forces in the bottom tie rod. Furthermore, to address the issue of inconsistent CCC node height values, this invention proposes an iterative solution scheme. Specific calculation methods based on mechanical principles are provided for key geometric parameters such as the control width of the main compression member and the dimensions of the CTT node, making the method for determining the shear capacity of deep beams in this invention both engineering-operable and widely applicable. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the method for determining the shear bearing capacity of deep beams provided in an embodiment of the present invention; Figure 2 This is a diagram of the original tension / compression bar model provided in an embodiment of the present invention; Figure 3 A model diagram of an improved tension / compression bar for deep beams provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the effective working area of ​​the abdominal muscles provided in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This invention provides a method for determining the shear capacity of deep beams based on an improved tension-compression member model. It decomposes the single compression member in commonly used tension-compression member models into primary and secondary compression members, and introduces a vertical tension member in the middle of the shear span. This decouples the inclination angle of the primary compression member from a fixed angle, allowing it to dynamically adjust based on the amount of web reinforcement and the shear span ratio through force balance relationships. This achieves, for the first time, a structured expression of the influence of web reinforcement on the force transmission path. Simultaneously, it analogizes the shear resistance of horizontal web reinforcement to a "longitudinal reinforcement dowel mechanism" and incorporates it, along with the vertical web reinforcement, into the tensile force calculation of the vertical tension member. This allows the improved tension-compression member model to broadly consider various physical parameters of deep beam members, effectively improving the accuracy of predicting the shear capacity of deep beams. Specifically, it includes: Step 1: Obtain the geometric and material parameters of the deep beam.

[0022] Step 2: Establish an improved tension / compression bar model.

[0023] like Figure 2 As shown, in the traditional tension-compression bar model, the failure of a concrete inclined compression bar represents the shear failure of a deep beam. The bar inclination angle reflects the influence of the shear span ratio, the geometry of node B reflects the influence of the section height and longitudinal reinforcement ratio, and the compressive strength of the bar directly reflects the influence of the concrete strength. However, the influence of the web reinforcement on the shear strength is not considered. In practical applications, web reinforcement is usually used as crack control reinforcement, only structurally meeting the minimum web reinforcement ratio requirement.

[0024] The influence of stirrups on the shear resistance of deep beams cannot be ignored. Therefore, this invention proposes an improved strut-and-tie model (ISTM) to reasonably account for the shear resistance mechanism of stirrups, such as... Figure 3 As shown. Since the geometric dimensions of the vertical tie rod EF are unknown, the inclination angle θ of the main compression member cannot be determined geometrically. Instead, it needs to be determined based on the force balance relationship at the CCT node, thus realizing the variable inclination angle of the main compression member BE. In ISTM, the influence of the stirrups on the shear capacity of the deep beam is considered through the influence of the stirrups on the inclination angle of the main compression member. Furthermore, if the specimen is a deep beam without stirrups, and the inclination angles of the compression members BE and AE are the same, then ISTM degenerates into STM. To simplify the calculation, the following assumptions are made for the proposed ISTM: 1) Considering the shear resistance mechanism of the web reinforcement with vertical tie rods, and since the web reinforcement is mostly orthogonally and uniformly distributed, the shear resistance contribution of the horizontal web reinforcement is calculated using the pin action. Therefore, a single vertical tie rod located in the middle of the shear span can be used to simultaneously consider the shear resistance mechanisms of both horizontal and vertical web reinforcement.

[0025] 2) The vertical tie rod is located in the middle of the shear span zone. It divides the concrete compression bar AB in the original STM into two parts: compression bar BE and compression bar AE. The axial force of compression bar BE is greater than that of compression bar AE. Therefore, compression bar BE is the main compression bar and compression bar AE is the secondary compression bar. Both ends are CCT nodes, the loading point is a CCC node, and the bottom node is a CTT node. The shear failure of the simply supported deep beam is controlled by the intersection of the main compression bar BE and the CCT node. When its nominal shear strength is greater than the effective compressive strength of concrete, it indicates that the deep beam has undergone shear failure.

[0026] Step 3: Calculate the shear capacity of the first deep beam based on the moment equilibrium condition of the shear span: ; in, d It is the vertical distance from the resultant point of the tensile longitudinal reinforcement of the cross section to the compression edge of the concrete; a To cut the span length;w c The initial vertical height of the CCC node is 0.05d in this embodiment. T f The horizontal tension of the bottom horizontal tie rod is obtained from the force balance in the horizontal direction of the shear span. T f = F c ,in F c For the horizontal compression bar between loading points, according to ACI318-19, this bar is a boundary bar, and its effective compressive strength of concrete under continuous compression is taken as 0.85. f c The effective coefficient of the compression member is taken as 1.0. The compression force of the concrete horizontal compression member can be calculated by the following formula: .

[0027] Step 4: ISTM quantifies the effect of the stirrups by using a single vertical tie rod EF at the midpoint of the shear span, considering both vertical and horizontal stirrups. Due to the clamping effect between the loading point and the support, the strain of both vertical and horizontal stirrups is relatively small near the loading point and the support, while reaching its maximum strain at the midpoint of the shear span. Furthermore, only a portion of the vertical stirrups yields. Therefore, this invention proposes the concept of the effective working area of ​​the stirrups, such as... Figure 4 As shown.

[0028] Calculate the vertical tie rod tension used to characterize the shear contribution of the web reinforcement: ; in, T wv The formula for calculating the contribution of vertical fascia is as follows: ; In the formula, a cl The horizontal distance from the inner edge of the support to the outer edge of the loading plate. f yv For the vertical abdominal muscle yield strain, This refers to the vertical reinforcement ratio of the web reinforcement. b The width of the specimen; T wh The formula for calculating the contribution of the horizontal abdominal muscles is as follows: ; In the formula, s sc For horizontal abdominal muscle stress, f yh The yield strain of the horizontal abdominal muscles. fs The diameter of the horizontal abdominal muscles. l d The height of the stirrups is given by σ, where the strain at the highest point of the shear span section can be approximated as half the yield strain of the horizontal stirrups. sc =0.5 f yh And apply that value to 0.5 h cl Horizontal abdominal muscles within the range h cl = h - w t - w c , h Indicates the total height of the specimen. h cl To exclude the range of height of the top compression member and bottom tie member, i.e., the range of action of the horizontal web reinforcement, 0.5 h cl The effective range of action of the horizontal abdominal muscles, abdominal muscle height l d Pick l de / 2, l de This represents the length of the crack in the dowel at the bottom longitudinal reinforcement. n s To simplify the calculation, the number of horizontal stirrups within the calculation range is converted into the horizontal stirrup reinforcement ratio. T wh It can be further simplified to: ; ; ; Where α is the inclination angle along the line from the inner edge of the support plate to the outer edge of the loading plate, and α1 is the original inclination angle of the compression member; Based on the moment balance relationship of the internal forces in the shear span at point A, we can obtain: ; In the formula, T w The tension in the vertical tie rod EF is denoted by s; s is the vertical distance from point A to the main compression rod BE, which is small and can be ignored. Therefore, the tension in the horizontal tie rod BF is... T b It can be calculated using the following formula: ; Since the geometric dimensions of the vertical tie rod EF are unknown, the inclination angle θ of the main compression member cannot be determined through geometric relationships. It needs to be determined based on the force balance relationship at the CCT node, which can be expressed as the shear force V and the tension T of the horizontal tie rod BF.b The functional relationship is as follows: ; Both ends of the main compression member BE are CCT nodes. The width of the intersection surface between the CCT node at the support and the main compression member BE is the control width w of BE. The projected width of the intersection surface in the BE direction is: ; In the formula, l b1 The width of the CCT node is taken as the width of the support pad. w t The vertical height of the CCT node is 2 in this embodiment. h - d ).

[0029] Step 5: Determine the shear capacity of the second deep beam based on the vertical component on the intersection surface of the main compression member and the CCT node. V ': ; The compressive bearing capacity Fs at the intersection of the main compression member BE and the CCT node is: ; in, f strut The effective compressive strength of the concrete for the main compression member BE. β s The effective coefficient of the concrete compression bar at the intersection surface is calculated according to the two-parameter model proposed by Warwick-Foster based on concrete strength and shear span ratio: .

[0030] Step 6: Considering that the CTT node is located in the cracked concrete zone, this invention uses the modified pressure field theory to analyze the stress on the node, treating the CTT node as a reinforced concrete membrane calculation unit. The average stress and strain of the membrane unit should satisfy the geometric compatibility condition, equilibrium condition, and constitutive relation of the cracked concrete. Meanwhile, without considering the influence of the longitudinal reinforcement dowels on the CTT node, the stress in the z-axis direction... f z It can be ignored.

[0031] Based on the MCFT stress equilibrium equation and the Mohr's circle equation for concrete stress in two-dimensional conditions, we can obtain: ; f cy Let be the yield strain of the CTT node in the y direction; For beam members, the compressive force in the y-direction is small and can be ignored. fcy =0.

[0032] Average shear stress within the node v b It can be calculated using the following formula: ; Based on the MCFT constitutive relation, the principal tensile stress perpendicular to the diagonal crack within the node is... f c1 It can be calculated using the following formula: ; In the formula: v ci This refers to the shear stress at the crack. a g The maximum coarse aggregate size is used; if it cannot be measured, it should be calculated as 19mm. Principal tensile stress. f c1 The unit is MPa; w k Given the average crack width, according to the MCFT geometric compatibility conditions, we have: ; Since the effect of the web reinforcement in the nodal region is not considered, the crack spacing perpendicular to the z-direction is relatively large, and cosine can be ignored. i s / s z Due to the influence of this, the average width of the diagonal crack within the node can be simplified as follows: ; In the formula, s x The average spacing of the diagonal cracks is calculated using the following formula: ; In the formula: f eq The equivalent diameter of the bottom longitudinal reinforcement is... r eff The formulas for calculating the longitudinal reinforcement ratio are as follows: ; ; Based on the MCFT geometric compatibility condition, the average principal tensile strain perpendicular to the crack plane in the CTT node region is... e c1 The calculation formula is: ; In the formula, e x For CTT node along x The average strain in the direction can be obtained through the strain of the horizontal tie rods BF and FF' at both ends of the node. e b and e f To simplify the calculation, let e x ≈ e f ; e c2 The principal compressive strain along the crack direction has an absolute value much smaller than e f Therefore, there is e f - e c2 ≈ e f .

[0033] Then, the tension in the bottom tie rod is calculated based on the shear capacity of the first deep beam and the shear capacity of the second deep beam: ; in, l b3 The width of the CTT node. v b The average shear stress within the node; The height of the bottom CTT node of the vertical tie rod is determined according to the effective control crack height defined in EC2, which is the effective tensile concrete zone height, and its expression is: ; CTT node width l b3 Calculate using the following formula: ; In the formula, i s The formula for calculating the inclination angle AF of the compression member is: ; Based on the calculated bottom tie rod tension Using the calculation formula in step 3 To reverse-calculate the vertical height of the CCC node The specific calculation formula is as follows: ; Then the vertical height of the CCC node Vertical height of the initial CCC node w c If a comparison is made, ,or If the calculation stops, the shear capacity of the deep beam is output as the shear capacity of the first deep beam. V ,in, This is a preset threshold. If... Then adjust the vertical height of the initial CCC node, making the new initial CCC node vertical height... Repeat steps 3-6 until the calculation stops.

[0034] This invention addresses the issue of inconsistent CCC node height values ​​by setting an iterative solution scheme. Furthermore, to address the lack of refined analysis of the bottom CTT node in existing standards, this invention introduces Modified Pressure Field Theory (MCFT) for membrane element stress-strain analysis, quantifying the cracking behavior and internal force transmission relationship in the node region, significantly improving the rationality of the bottom tie rod internal force calculation. For key geometric parameters such as the main compression member control width and CTT node dimensions, specific calculation methods based on mechanical principles are provided, enabling the deep beam shear capacity determination method of this invention to better possess engineering operability and broad parameter applicability.

[0035] To better illustrate the advantages of the method for determining the shear bearing capacity of deep beams based on the improved tension-compression bar model of the present invention, the following comparison of the determination method of the present invention with existing determination methods is made in conjunction with specific embodiments.

[0036] The selection criteria for the validation samples include: ① simply supported deep beams under single or two concentrated force loading; ② non-prestressed tendons with ribbed deformable longitudinal reinforcement; ③ the test deep beams fail under shear stress.

[0037] Using the above principles, 97 deep beams without stirrups were selected that simultaneously met the above conditions and were defined as Database I. Their shear span ratio parameters ranged from 0.5 to 2, their cylindrical compressive strength parameters ranged from 13.5 to 97.2 MPa, and their effective height parameters ranged from 180 to 1440 mm. 171 deep beams containing vertical stirrups but without horizontal stirrups simultaneously met the conditions and were defined as Database II. Their shear span ratio parameters ranged from 0.27 to 2, their cylindrical compressive strength parameters ranged from 13.8 to 97.5 MPa, their effective height parameters ranged from 215 to 1000 mm, and their vertical stirrup reinforcement ratio parameters ranged from 0.06% to 1.91%. A total of 39 deep beams with horizontal web reinforcement but no vertical web reinforcement simultaneously meet the following conditions. These are defined as Database III, with shear span ratio parameters ranging from 0.35 to 1.69, cylindrical compressive strength parameters ranging from 19.2 to 86.3 MPa, effective height parameters ranging from 215 to 900 mm, and horizontal web reinforcement ratio parameters ranging from 0.17% to 2.37%. A total of 153 deep beams with both horizontal and vertical web reinforcement simultaneously meet the following conditions. These are defined as Database IV, with shear span ratio parameters ranging from 0.30 to 2, cylindrical compressive strength parameters ranging from 16.1 to 78 MPa, effective height parameters ranging from 215 to 1559 mm, and comprehensive web reinforcement ratio parameters ranging from 0.15% to 3.09%.

[0038] For the above samples, the determination methods specified in Chapter 23 of the current American Concrete Structure Design Code ACI 318-19 and Appendix G of the Chinese Code for Design of Concrete Structures GB50010-2010 are designated as existing determination methods. These methods, along with the determination method of this invention, are used to calculate the values ​​for the above samples. V u Then compared with the experimental values V exp The comparison and error calculation results are shown in Table 1: Table 1: Calculation Error of Shear Capacity of Deep Beams in Databases I-IV Note: x m , x s , x cov These are the calculation errors (experimental values) V exp Compared with calculated values V u The mean, standard deviation, and coefficient of variation of the ratio (to each other); the minimum and maximum values ​​mentioned above are experimental values. V exp Compared with calculated values V u The minimum and maximum values ​​of the ratio.

[0039] Table 1 presents the experimental values ​​of shear capacity of deep beams from databases I to IV. V exp Compared with calculated values V u The comparison results are shown in the table above. It can be seen that the database sample coverage of this embodiment is wide. Compared with existing determination methods, the calculation error (experimental value) of the determination method of this invention is... V exp Compared with calculated values V u The ratio is smaller, resulting in more accurate calculations.

[0040] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for determining the shear capacity of deep beams based on an improved tension-compression bar model, characterized in that, Includes the following steps: Step 1: Obtain the geometric and material parameters of the deep beam; Step 2: Based on the traditional tension-compression bar model, a vertical tension bar is set in the middle of the shear span zone to simultaneously consider the shear contribution of vertical and horizontal reinforcement bars, thus establishing an improved tension-compression bar model; wherein, the vertical tension bar divides the original concrete compression bar into two parts: a main compression bar and a secondary compression bar. Both ends of the main compression bar are CCT nodes, the loading point is a CCC node, and the bottom node is a CTT node; Step 3: Calculate the shear capacity of the first deep beam based on the internal moment equilibrium condition of the shear span zone; Step 4: Calculate the vertical tie rod tension used to characterize the shear contribution of the web reinforcement, and calculate the horizontal tie rod tension based on the vertical tie rod tension; calculate the inclination angle of the main compression member using the horizontal tie rod tension, and calculate the control width of the main compression member based on the inclination angle of the main compression member; Step 5: Determine the shear capacity of the second deep beam based on the vertical component on the intersection surface of the main compression member and the CCT node; Step 6: Calculate the bottom tie rod tension based on the shear capacity of the first deep beam and the shear capacity of the second deep beam, and use the bottom tie rod tension to infer the vertical height of the CCC node. Compare the vertical height of the CCC node with the initial vertical height of the CCC node. If they are equal or the difference is less than a preset threshold, the shear capacity of the deep beam is determined as the shear capacity of the first deep beam; otherwise, adjust the initial vertical height of the CCC node and repeat steps 3-6.

2. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 1, characterized in that, In step 3, the specific calculation formula for the shear bearing capacity of the first deep beam is as follows: ； in, d It is the vertical distance from the resultant point of the tensile longitudinal reinforcement of the cross section to the compression edge of the concrete; a To cut the span length; w c This represents the initial vertical height of the CCC node; T f The horizontal tension of the bottom horizontal tie rod; The horizontal tension of the bottom horizontal tie rod is calculated using the following formula: ； in, F c The pressure of the horizontal compression bar between the loading points. f c 'This refers to the compressive strength of cylindrical concrete.' b The width of the specimen.

3. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 2, characterized in that, In step 4, the formula for calculating the tension of the vertical tie rod is: ； in, T wv The formula for calculating the contribution of vertical fascia is as follows: ； In the formula, a cl The horizontal distance from the inner edge of the support to the outer edge of the loading plate. f yv For the vertical abdominal muscle yield strain, This refers to the vertical reinforcement ratio of the web reinforcement. T wh The formula for calculating the contribution of the horizontal abdominal muscles is as follows: ； In the formula, σ sc For horizontal abdominal muscle stress, f yh The yield strain of the horizontal abdominal muscles. φ s The diameter of the horizontal abdominal muscles. l d This refers to the height of the abdominal muscles. n s This is the number of horizontal abdominal muscles within the calculation range.

4. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 3, characterized in that, In step 4, the horizontal tie rod tension is calculated based on the vertical tie rod tension. The specific calculation formula is as follows: ； Calculate the inclination angle of the main compression member using the tension of the horizontal tie rod: ； The formula for calculating the control width of the main pressure bar is: ； In the formula, l b1 The width of the CCT node is taken as the width of the support pad. w t This represents the vertical height of the CCT node.

5. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 4, characterized in that, In step 5, the formula for calculating the shear capacity of the second deep beam is: ； in, F s The compressive bearing capacity at the intersection of the main compression member and the CCT node is calculated using the following formula: ； in, f strut The effective compressive strength of the concrete for the main compression member BE. β s This is the effective coefficient of the concrete compression bar on the intersecting surface.

6. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 5, characterized in that, In step 6, the formula for calculating the tension of the bottom tie rod is: ； in, l b3 The width of the CTT node. v b The average shear stress within the node.

7. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 6, characterized in that, In step 6, the vertical height of the CCC node is calculated by reverse calculation based on the tension of the bottom tie rod. Specifically: Based on the bottom pull rod tension Using the calculation formula in step 3 To reverse-calculate the vertical height of the CCC node The specific calculation formula is as follows: ； Then the vertical height of the CCC node Vertical height of the initial CCC node w c If a comparison is made, ,or If the calculation stops, the shear capacity of the deep beam is output as the shear capacity of the first deep beam. V ,in, This is a preset threshold.

8. The method for determining the shear bearing capacity of deep beams based on an improved tension-compression bar model according to claim 7, characterized in that, In step 6, if Then adjust the vertical height of the initial CCC node, making the new initial CCC node vertical height... Repeat steps 3-6 until the calculation stops.

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