Method and system for calculating flexural capacity of cross-shaped steel plate joint of lattice-shaped diaphragm wall

Abstract

The invention relates to the field of foundation pit engineering and hydropower engineering, in particular to a method and a system for calculating flexural capacity of a cross-shaped steel plate joint of a lattice-shaped diaphragm wall. Comprising the following steps: determining a failure mode according to the maximum tensile stress of concrete, the maximum normal cohesion of a web of the cross-shaped steel plate joint and the concrete and the shear strength of a single flange surface of the cross-shaped steel plate joint and a concrete contact surface; calculating a first flexural capacity contributed by the web based on the normal maximum cohesive force of the web and the concrete interface; calculating a second flexural capacity contributed by the flange based on the failure mode, the concrete pressure resultant force, the steel plate-concrete interface normal stress resultant force, the concrete tension and compression resultant force and the tension and compression steel bar force; the sum of the first flexural bearing capacity and the second flexural bearing capacity is the flexural bearing capacity of the cross steel plate joint of the lattice-shaped diaphragm wall. The calculation method is simple, easy to operate, small in calculation deviation and high in precision, and complex equations do not need to be solved.

Description

Technical Field

[0001] The present invention relates to the fields of foundation pit engineering and hydropower engineering, and in particular to a method and system for calculating the bending bearing capacity of cross steel plate joints of a lattice-shaped ground-connected wall. Background Art

[0002] As a key support structure in modern geotechnical engineering, lattice diaphragm walls have achieved technological breakthroughs and widespread application over the past two decades, thanks to their unique spatial grid structure and excellent engineering performance. This three-dimensional lattice retaining structure, composed of reinforced concrete diaphragm wall units, significantly improves overall stability and structural rigidity through spatial synergy. It has established a mature application system in ship locks, ports and docks, deep foundation pit support, and hydraulic anti-seepage, and is gradually expanding into more complex engineering scenarios.

[0003] The cross steel plate joint is a type of joint widely used in underground continuous wall construction. It has a rigid connection and good water-stopping performance. It can effectively transmit shear force and bending moment, enhance the overall stiffness and stability of the underground continuous wall, and effectively prevent groundwater leakage. When the load changes or the foundation settles unevenly, different parts of the ground-connected wall may produce vertical displacement. At the same time, tensile stress may also be generated between different trench sections due to horizontal displacement. However, in current domestic and international standards and specifications, there is no method for calculating the bending bearing capacity when using cross steel plate joints for grid-type ground-connected walls. In the Chinese design specifications, cross steel plates are used as rigid joints. However, compared with conventional ground-connected walls, the force direction of the grid-type ground-connected wall joints has changed. At this time, the cross steel plate joint can no longer be considered a rigid joint. If conventional design is followed, many problems may arise:

[0004] 1. When designing the ground-connected wall, designers have difficulty determining appropriate parameters such as joint size, steel plate thickness, and connection method. This may result in insufficient bending bearing capacity of the joints, and cracks or even fractures may occur at the joints, affecting the overall stability of the ground-connected wall and posing a safety hazard to the project.

[0005] 2. During the construction process, it is difficult for construction workers to grasp the construction quality standards of the cross steel plate joints and cannot strictly control them based on accurate calculation results, which may lead to uneven joint quality and affect the overall performance of the ground-connected wall;

[0006] 3. During project acceptance, there is no accurate calculation method as a basis, making it difficult to determine whether the bending bearing capacity of the cross steel plate joint meets the design requirements through testing means, and potential quality problems cannot be discovered in time;

[0007] 4. When maintaining the ground-connected wall, it is impossible to accurately determine when the joints need to be inspected, repaired, or reinforced. This may lead to missing the best time for maintenance and worsening the problem.

[0008] 5. When the surrounding environment changes or there are new construction projects nearby, it is difficult to accurately evaluate the safety of the ground-connected wall structure based on the actual bending bearing capacity of the cross steel plate joints used in the ground-connected wall and provide a scientific basis for decision-making. Summary of the Invention

[0009] The purpose of this application is to address the deficiencies of the above-mentioned background technology and to provide a method and system for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall.

[0010] The technical solution of this application is: a method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall, comprising:

[0011] The failure mode is determined based on the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange of the cross steel plate joint and the concrete.

[0012] The first bending capacity contributed by the web is calculated based on the maximum normal cohesion between the web and concrete interface;

[0013] The second bending capacity contributed by the flange is calculated based on the failure mode, the resultant concrete pressure, the resultant normal stress of the steel plate-concrete interface, the resultant concrete tension and compression, and the tension and compression reinforcement forces;

[0014] The sum of the first bending bearing capacity and the second bending bearing capacity is the bending bearing capacity of the cross steel plate joint of the lattice ground-connected wall.

[0015] According to a method for calculating the bending bearing capacity of a cross steel plate joint of a lattice diaphragm wall provided in this application, the method for determining the failure mode includes: if the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete meet the following conditions,

[0016] σ t bh0 / 2≤f cs +σ μ bh0

[0017] Where: t ——maximum tensile stress of concrete;

[0018] b——calculated width;

[0019] h0 - height from flange to top of ground-connected wall;

[0020] σ u ——maximum normal cohesion between steel plate and concrete;

[0021] f cs — Shear strength of the contact surface between the flange single surface and concrete;

[0022] The failure mode is determined to be the second mode, otherwise the failure mode is determined to be the first mode.

[0023] According to the method for calculating the bending bearing capacity of the cross steel plate joint of the grid-type ground-connected wall provided in this application, when the failure mode is the first mode, the second bending bearing capacity is calculated according to the following formula:

[0024] M Ⅱ =2(ha cs )f u / 3+(ha cs -x / 3)f cs

[0025] Where: M Ⅱ ——second bending capacity;

[0026] h——thickness of lattice ground wall;

[0027] x——height of compression zone;

[0028] a cs —Distance from flange to bottom of ground-connected wall;

[0029] f u ——the resultant normal stress at the steel plate-concrete interface;

[0030] f cs ——Shear strength of the contact surface between the flange single surface and concrete.

[0031] According to the method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall provided in this application, the normal stress resultant of the steel plate-concrete interface is calculated according to the following formula:

[0032] f u =σ u (hxa cs )b / 2

[0033] Where: f u ——the resultant normal stress at the steel plate-concrete interface;

[0034] b——calculated width;

[0035] x——height of compression zone;

[0036] h——thickness of lattice ground wall;

[0037] a cs —Distance from flange to bottom of ground-connected wall;

[0038] σ u ——The maximum normal cohesion between steel plate and concrete.

[0039] According to a method for calculating the bending bearing capacity of a cross steel plate joint of a lattice-type ground-connected wall provided in this application, when the failure mode is the second mode, the second bending bearing capacity is calculated according to the following formula:

[0040] M Ⅱ =f s (hxa s +(f s '(xa' s )+2f c x / 3) / (f s '+f c ))

[0041] +f cs (h-x+(f s '(xa' s )+2f c x / 3) / (f s '+f c ))+f t (2(hx) / 3

[0042] +(f s '(xa' s )+2f c x / 3) / (f s '+f c ))

[0043] Where: M Ⅱ ——second bending capacity;

[0044] f s — tensile reinforcement force;

[0045] h——thickness of lattice ground wall;

[0046] x——height of compression zone;

[0047] a s - the distance from the tension reinforcement to the bottom of the ground-connected wall;

[0048] f s '——compressive reinforcement force;

[0049] a' s - the distance from the compression reinforcement to the top of the ground-connected wall;

[0050] f c —resultant compressive force on concrete;

[0051] f cs — Shear strength of the contact surface between the flange single surface and concrete;

[0052] f t ——Concrete is subjected to combined tensile force.

[0053] According to the method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall provided in this application, the concrete compressive force and the concrete tensile force are calculated according to the following formula:

[0054] f t =σ t (hx)b / 2

[0055] f c =σ c xb / 2

[0056] Where: f t - Resultant tensile force on concrete;

[0057] f c —resultant compressive force on concrete;

[0058] σ t ——maximum tensile stress of concrete;

[0059] σ c ——maximum compressive stress of concrete;

[0060] h——thickness of lattice ground wall;

[0061] x——height of compression zone;

[0062] b——Calculated width.

[0063] According to the method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall provided in this application, the tensile steel bar force and the compressive steel bar force are calculated according to the following formula:

[0064] f s =nA s ε s E s

[0065] f s '=nA s ε s 'E s

[0066] Where: f s — tensile reinforcement force;

[0067] f s '——compressive reinforcement force;

[0068] n——the number of M-shaped steel bars;

[0069] A s ——cross-sectional area of ​​M-shaped steel bars;

[0070] ε s — strain of tensile reinforcement;

[0071] ε s '——compressive steel bar strain;

[0072] E s ——Elastic modulus of steel bars.

[0073] This application also relates to a system for calculating the bending bearing capacity of cross steel plate joints of lattice-type ground-connected walls, comprising:

[0074] a failure mode determination module, the failure mode determination module being used to determine the failure mode based on the maximum tensile stress of the concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete;

[0075] a first bending capacity calculation module, configured to calculate a first bending capacity contributed by the web according to the maximum normal cohesion of the interface between the web and the concrete;

[0076] A second bending bearing capacity calculation module, the second bending bearing capacity calculation module is used to calculate the second bending bearing capacity contributed by the flange according to the failure mode, the concrete pressure resultant, the steel plate-concrete interface normal stress resultant, the concrete tension and compression resultant, and the tension and compression reinforcement force;

[0077] The joint bending bearing capacity calculation module calculates the sum of the first bending bearing capacity and the second bending bearing capacity as the joint bending bearing capacity.

[0078] The present application also relates to a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall.

[0079] The present application also relates to a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall.

[0080] The advantages of this application are as follows: 1. This application analyzes the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall and provides a detailed calculation method, which solves the problem that there is currently no calculation method for the bending bearing capacity of the cross steel plate joints in the design of the grid-type ground-connected wall; this application analyzes the failure mode of the cross steel plate joints of the ground-connected wall and performs corresponding calculations based on the failure mode, which can accurately calculate the bending bearing capacity of the cross steel plate joints. The calculation is simple and does not require complex variance solutions. The calculation deviation is small and the accuracy is high. It can provide a reference for the design of cross steel plate joints of the grid-type ground-connected wall;

[0081] 2. The method for determining the failure mode in this application is very simple. It only needs to be determined based on the set conditions to accurately obtain the failure mode of the cross steel plate joint of the grid-shaped ground-wall ties, which is convenient for subsequent further calculation and analysis. The calculation and judgment method is easy to operate.

[0082] 3. When the first mode is determined, the second bending capacity is calculated by the resultant normal stress at the steel plate-concrete interface and the shear strength of the contact surface between the flange single surface and the concrete. The calculation method is simple, the force analysis conforms to the force conditions under this mode, and the calculation results are accurate.

[0083] 4. In the first mode, the application can calculate the resultant normal stress at the steel plate-concrete interface by the maximum normal cohesion between the steel plate and the concrete. The calculation method is very simple and does not require solving complex equations.

[0084] 5. When the second mode is determined, the second bending capacity is calculated by the combined tensile and compressive forces of the steel bars and the concrete. The entire calculation method conforms to the mechanical conditions of this failure mode and is simple and accurate.

[0085] 6. In the second mode, the method for calculating the resultant compressive force and the resultant tensile force of concrete is very simple. The constructed formula has minimal calculation amount and is easy to operate.

[0086] 7. In the second mode of this application, the formula for calculating the tensile and compressive reinforcement forces is very simple, easy to operate and implement, and requires little calculation;

[0087] 8. This application also provides a calculation system that can form a calculation program to facilitate analysis, design, and construction personnel to call calculations, thereby greatly improving calculation efficiency.

[0088] The calculation method of the present application is simple and easy to operate, and does not contain a large number of complex calculation formulas or the need to solve complex equations. It fills the gap in the calculation method for the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall. The calculation deviation is small and the accuracy is high, which can provide a reference for the design of the cross steel plate joints of the grid-type ground-connected wall. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 :Schematic diagram of the calculation process of this application;

[0090] Figure 2 : Schematic diagram of the destruction form of the first mode of this application;

[0091] Figure 3 : Schematic diagram of the destruction form of the second mode of this application. DETAILED DESCRIPTION

[0092] The embodiments of the present application are described in detail below, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0093] In the description of this application, it should be understood that the terms "longitudinal", "transverse", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0094] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. Throughout the description of this application, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0095] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0096] This application relates to a method for calculating the bending bearing capacity of a cross steel plate joint of a lattice-type ground-connected wall. The lattice-type ground-connected wall structure of this application is as follows: Figure 2 and 3 As shown, the cross steel plate joint includes a web extending vertically and a flange arranged horizontally. The calculation of the bending bearing capacity of the cross steel plate joint in this application is actually the calculation of the sum of the bending bearing capacity contributed by the web and the bending bearing capacity contributed by the flange. The bending bearing capacity contributed by the web and the bending bearing capacity contributed by the flange are analyzed and calculated based on the stress conditions of the cross steel plate joint when the ground-connected wall is subjected to bending moment. From the perspective of the damage of the cross steel plate joint to the ground-connected wall when the ground-connected wall is subjected to bending moment, there are two modes. One is that the web of the cross steel plate joint is completely detached from the concrete, and the upper and lower surfaces of the flanges of the cross steel plate joint are slipping with the concrete, which is the first mode described in this case. Figure 2 As shown; the other is that the web below the flange of the cross steel plate joint is separated from the concrete, the lower surface of the cross steel plate joint is separated from the concrete but the upper surface is still bonded to the concrete, which is the second mode described in this case, as shown Figure 2 shown.

[0097] Different failure modes have completely different stress conditions, mainly because the calculation methods of the bending bearing capacity contributed by the flange are different. The corresponding calculation methods are used for different failure modes.

[0098] Specifically, such as Figure 1 As shown, the bending bearing capacity of the cross steel plate joint of a lattice-type ground-connected wall in this application is calculated according to the following steps:

[0099] S1. Determine the failure mode based on the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange of the cross steel plate joint and the concrete;

[0100] That is, the judgment and analysis are carried out according to the above failure modes. Only after the specific failure mode is determined can the subsequent calculation be carried out;

[0101] S2. Calculate the first bending capacity contributed by the web based on the maximum normal cohesion between the web and concrete interface;

[0102] The first bending capacity corresponds to the web. Regardless of the failure mode, the first bending capacity contributed by the web can be calculated by the maximum normal cohesion of the interface between the web and concrete.

[0103] S3. Calculate the second bending capacity contributed by the flange based on the failure mode, concrete pressure resultant, normal stress resultant at the steel plate-concrete interface, concrete tension and compression resultant, and tension and compression reinforcement force;

[0104] After the failure mode is determined, the corresponding calculation method can be selected to calculate the second bending bearing capacity. The second bending bearing capacity under the first mode can be calculated by the concrete pressure resultant force and the steel plate-concrete interface normal stress resultant force, and the second bending bearing capacity under the second mode can be calculated by the concrete tension and compression resultant force and the tension and compression reinforcement force.

[0105] S4. The sum of the first bending bearing capacity and the second bending bearing capacity is the bending bearing capacity of the cross steel plate joint of the grid-type ground-connected wall.

[0106] In some embodiments of the present application, this embodiment optimizes the above-mentioned step S1. Specifically, the method for determining the failure mode is: if the maximum tensile stress of the concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete meet the following conditions,

[0107] σ t bh0 / 2≤f cs +σ μ bh0

[0108] Where: t——maximum tensile stress of concrete, unit: N;

[0109] b——calculated width, in mm;

[0110] h0——the height from the flange to the top of the ground-connected wall, in mm;

[0111] σ u ——maximum normal cohesion between steel plate and concrete, unit: N;

[0112] f cs ——shear strength of the contact surface between the flange single surface and concrete, unit: N;

[0113] The failure mode is determined to be the second mode, otherwise the failure mode is determined to be the first mode.

[0114] The calculated width b can be obtained by consulting the design specifications or manuals. The height h0 from the flange to the top of the ground-connected wall can be obtained by consulting the specifications of the ground-connected wall to be calculated and the specifications of the cross-shaped steel plate joint. The maximum normal cohesion between the steel plate and the concrete σ u This can be determined by a semi-embedded three-point bending beam test on a steel plate or a DCB test.

[0115] Shear strength of the contact surface between flange single surface and concrete f cs It can be calculated according to the following formula:

[0116] f cs =A p τ cs +A c τ c

[0117] Where: f cs ——shear strength of the contact surface between the flange single surface and concrete, unit: N;

[0118] A p ——The area of ​​contact between the lower surface of the flange and the concrete, in mm 2 ;

[0119] A c ——flange opening area, in mm 2 ;

[0120] τ cs ——peak shear stress of steel plate-concrete interface, in MPa;

[0121] τ c ——Peak value of concrete shear stress, in MPa.

[0122] The area A where the lower surface of the flange contacts the concrete pThe flange opening area A can be obtained based on the specifications of the ground-connected wall to be calculated and the specifications of the cross-shaped steel plate joint. c According to the specifications of the cross-shaped steel plate joint, the peak shear stress τ at the steel plate-concrete interface is cs The peak shear stress of concrete τ can be obtained through steel plate push-out test. c This can be determined by shear testing.

[0123] In other embodiments of the present application, this embodiment optimizes the above-mentioned step S2. Regardless of the failure mode, the first bending bearing capacity can be calculated according to the following formula:

[0124] M Ι =σ u W

[0125] Where: M Ⅰ ——the first bending bearing capacity, in N*mm;

[0126] σ u ——maximum normal cohesion between steel plate and concrete, unit: N;

[0127] W is the section modulus obtained by the equivalent section method, in mm.

[0128] Maximum normal cohesion between steel plate and concrete σ u It can be determined through a semi-embedded three-point bending beam test of a steel plate or a DCB test. The section modulus W obtained by the equivalent section method can be obtained by integrating the product of the area of ​​each infinitesimal element of the section and the distance from each infinitesimal element to the neutral axis.

[0129] In a further embodiment of the present application, if it is determined to be the first mode, the second bending bearing capacity can be calculated according to the following formula:

[0130] M Ⅱ =2(ha cs )f u / 3+(ha cs -x / 3)f cs

[0131] Where: M Ⅱ ——Second bending bearing capacity, unit: N*mm;

[0132] h——the thickness of the grid-type ground-connected wall, in mm;

[0133] x——height of the compression zone, in mm;

[0134] a cs ——Distance from flange to bottom of ground-connected wall, in mm;

[0135] f u——the resultant normal stress at the steel plate-concrete interface, unit: N;

[0136] f cs ——Shear strength of the contact surface between the flange single surface and concrete, unit: N.

[0137] The thickness h of the grid-shaped ground-connected wall is calculated by querying the specifications of the ground-connected wall to be calculated, and the distance a from the flange to the bottom of the ground-connected wall is cs The height of the compression zone x is obtained by querying the specifications of the diaphragm wall to be calculated and the specifications of the cross-shaped steel plate joints, and the height of the compression zone x is obtained by querying the design structure of the diaphragm wall;

[0138] The normal stress resultant at the steel plate-concrete interface is calculated according to the following formula:

[0139] f u =σ u (hxa cs )b / 2

[0140] Where: f u ——the resultant normal stress at the steel plate-concrete interface, unit: N;

[0141] b——calculated width, in mm;

[0142] x——height of the compression zone, in mm;

[0143] h——the thickness of the grid-type ground-connected wall, in mm;

[0144] a cs ——Distance from flange to bottom of ground-connected wall, in mm;

[0145] σ u ——The maximum normal cohesion between steel plate and concrete, unit: N.

[0146] The calculated width b is obtained based on the design structure of the ground-connected wall and the design structure of the cross-shaped steel plate joint.

[0147] In a preferred embodiment of the present application, the second bending bearing capacity in the second mode is calculated. Specifically, when the failure mode is the second mode, the second bending bearing capacity is calculated according to the following formula:

[0148] M Ⅱ =f s (hxa s +(f s '(xa' s )+2f c x / 3) / (f s '+f c ))

[0149] +f cs(h-x+(f s '(xa' s )+2f c x / 3) / (f s '+f c ))+f t (2(hx) / 3

[0150] +(f s '(xa' s )+2f c x / 3) / (f s '+f c ))

[0151] Where: M Ⅱ ——Second bending bearing capacity, unit: N*mm;

[0152] f s ——tensile reinforcement force, unit: N;

[0153] h——the thickness of the grid-type ground-connected wall, in mm;

[0154] x——height of the compression zone, in mm;

[0155] a s ——Distance from the tension reinforcement to the bottom of the ground-connected wall, in mm;

[0156] f s '——compressive reinforcement force, unit N;

[0157] a' s ——Distance from the compression reinforcement to the top of the ground-connected wall, in mm;

[0158] f c ——resultant compressive force on concrete, unit: N;

[0159] f cs ——shear strength of the contact surface between the flange single surface and concrete, unit: N;

[0160] f t ——resultant tensile force of concrete, unit: N.

[0161] Distance a from the tension reinforcement to the bottom of the ground-connected wall s The distance a' from the compression reinforcement to the top of the ground-connected wall s It can be obtained based on the design structure and specifications of the ground-connected wall.

[0162] The concrete compressive force and concrete tensile force can be calculated according to the following formula:

[0163] f t =σ t (hx)b / 2

[0164] f c =σ c xb / 2

[0165] Where: f t ——resultant tensile force of concrete, unit: N;

[0166] f c ——resultant compressive force on concrete, unit: N;

[0167] σ t ——maximum tensile stress of concrete, unit: N;

[0168] σ c ——maximum compressive stress of concrete, unit: N;

[0169] h——the thickness of the grid-type ground-connected wall, in mm;

[0170] x——height of the compression zone, in mm;

[0171] b——calculated width, unit: mm.

[0172] Maximum tensile stress of concrete σ t It can be calculated through Appendix C of the Code for Design of Concrete Structures, the maximum compressive stress of concrete σ c It can be calculated through Appendix C of the "Code for Design of Concrete Structures".

[0173] The tensile and compressive reinforcement forces can be calculated using the following formula:

[0174] f s =nA s ε s E s

[0175] f s '=nA s ε s 'E s

[0176] Where: f s ——tensile reinforcement force, unit: N;

[0177] f s '——compressive reinforcement force, unit N;

[0178] n——the number of M-shaped steel bars;

[0179] A s ——Cross-sectional area of ​​M-shaped steel bar, in mm 2 ;

[0180] ε s — strain of tensile reinforcement;

[0181] ε s '——compressive steel bar strain;

[0182] E s ——Elastic modulus of steel bar, unit: MPa.

[0183] The number of M-shaped steel bars n can be obtained by consulting the ground-connected wall design manual. The cross-sectional area A of the M-shaped steel bars is s The tensile reinforcement strain ε can be obtained by consulting the ground-connected wall design manual. s Calculated according to the following formula:

[0184] ε s =a s ε cs / (hx)

[0185] Where: ε s — strain of tensile reinforcement;

[0186] a s ——The distance from the tensile reinforcement to the bottom of the ground-connected wall, in mm;

[0187] ε cs —the strain at the interface between the lower surface of the flange and the concrete;

[0188] h——the thickness of the grid-type ground-connected wall, in mm;

[0189] x——height of the compression zone, in mm;

[0190] The strain ε at the interface between the flange lower surface and the concrete is cs It can be calculated by the following formula:

[0191] ε cs =Δ s / l p

[0192] Where: ε cs —the strain at the interface between the lower surface of the flange and the concrete;

[0193] Δ s ——The slip corresponding to the peak shear stress of the steel plate-concrete interface, in mm;

[0194] l p ——flange length, in mm;

[0195] Compressive steel bar strain ε′ s It can be calculated by the following formula:

[0196] ε′ s =(x-a' s )εcs / (hx)

[0197] Where: ε′ s — strain of compressive reinforcement;

[0198] x——height of the compression zone, in mm;

[0199] a' s ——Distance from the compression reinforcement to the top of the ground-connected wall, in mm

[0200] ε cs —the strain at the interface between the lower surface of the flange and the concrete;

[0201] h——the thickness of the grid-type ground-connected wall, in mm;

[0202] Elastic modulus of steel bar E s It can be obtained by looking up the table.

[0203] According to the above method, actual calculation verification is performed:

[0204] Example 1:

[0205] The thickness of the ground-connected wall is h = 400 mm, the height from the flange of the cross-shaped steel plate joint to the top surface of the ground-connected wall is h0 = 200 mm, the calculated width is b = 330 mm, and the flange length is l p =264mm, flange opening area A c =32000mm 2 , the distance a from the tension reinforcement to the bottom of the ground-connected wall s =92mm, the distance a' from the compression reinforcement to the top of the ground-connected wall s =25mm.

[0206] The area A where the lower surface of the flange contacts the concrete p =51424mm 2 , concrete strength grade is C30, peak tensile strength σ t '=2.01MPa. Peak shear stress τ at the steel plate-concrete interface cs It can be determined by steel plate push-out test, taking τ cs =0.27MPa, the slip corresponding to the peak shear stress of the steel plate-concrete interface Δ s =0.14mm.

[0207] Maximum normal cohesion between steel plate and concrete σ u =0.16MPa.

[0208] The shear strength of concrete can be determined by shear tests, τ c =0.21(f′ c ) 2 / 3=0.21×(0.79×30) 2 / 3 =1.73MPa.

[0209] According to the above data and formula, the shear strength f of the contact surface between the flange single surface and the concrete is calculated cs :

[0210] f cs =A p τ cs +A c τ c =32000×1.73+51424×0.27=69244N

[0211] Determine the type of damage:

[0212] σ t 'bh0 / 2=2.01×330×200 / 2=33150≤

[0213] f cs +σ u bh0=69244+0.16×330×200=79804

[0214] Therefore, it is determined that the failure mode is the second mode.

[0215] Calculate the first bending capacity, M Ⅰ =0.16×8800000=1408000N·mm;

[0216] Calculate strain, ε cs =Δ s / l p =0.14 / 264=0.00053;

[0217] Calculate the maximum tensile strain of concrete in the cross section, ε t =(hxh p )ε cs / (hx)=(393-x)*0.00053 / (400-x);

[0218] Calculate the strain of the tensile reinforcement, ε s =a s ε cs / (hx)=92×0.00053 / (400-x);

[0219] Calculate the compressive reinforcement strain, ε′ s =(x-a' s )ε cs / (hx)=(x-25)×0.00053 / (400-x);

[0220] Calculate the maximum compressive strain of concrete in the cross section, ε c =xε cs / (hx)=x×0.00053 / (400-x);

[0221] Calculate the tensile reinforcement force, f s =nA s ε s E s =6×113×206×92×0.00053 / (400-x);

[0222] Calculate the compressive reinforcement force, f s '=nA s ε′ s E s =6×113×206×(x-25)×0.00053 / (400-x).

[0223] The stress-strain relationship of concrete is mature, and it is preferred to use Appendix C of the "Code for Design of Concrete Structures" for calculation.

[0224] σ t =(1-d t )E c ε t

[0225]

[0226] σ c =(1-d c )E c ε c

[0227]

[0228]

[0229] where α t The parameter value of the descending section of the concrete uniaxial tensile stress-strain curve is 1.25; f tr is the uniaxial tensile strength of concrete; ε tr is the peak tensile strain of concrete; E c is the elastic modulus of concrete; α c The parameter value of the descending section of the concrete uniaxial compressive stress-strain curve is 0.74; f cr is the uniaxial tensile strength of concrete; ε cr is the peak tensile strain of concrete.

[0230] Resultant tensile force on concrete f t and the concrete compressive force f c The calculation is as follows:

[0231] f t =σ t (hx)b / 2=σ t (400-x)330 / 2

[0232] f c =σ c xb / 2=σ c x330 / 2

[0233] Combining the above formulas, we can calculate that x = 66.85 mm.

[0234] Substituting x = 66.85 mm into the above formulas for tensile reinforcement force, compressive reinforcement force, concrete tensile force, and concrete compressive force, we can obtain:

[0235] f s =22.78kN, f s '=24.04kN、f t =11.35kN, f c =82kN

[0236] Then substitute the above values ​​into the second bending capacity calculation formula to obtain M Ⅱ =16.65kN·m;

[0237] Calculate the bending bearing capacity M u =16.65+1.41=18.06kN·m.

[0238] Example 2:

[0239] The thickness of the ground-connected wall is h = 400 mm, the height from the flange of the cross-shaped steel plate joint to the top surface of the ground-connected wall is h0 = 200 mm, the calculated width is b = 330 mm, and the flange length is l p =214mm, flange opening area A c =0mm 2 , the distance a from the tension reinforcement to the bottom of the ground-connected wall s =92mm, the distance a' from the compression reinforcement to the top of the ground-connected wall s =25mm.

[0240] The area A where the lower surface of the flange contacts the concrete p =67624mm 2 , concrete strength grade is C30, peak tensile strength σ t '=2.01MPa. Peak shear stress τ at the steel plate-concrete interface cs It can be determined by steel plate push-out test, taking τ cs =0.27Mpa, Δ s =0.14mm.

[0241] Maximum normal cohesion between steel plate and concrete σ u =0.16MPa.

[0242] The shear strength of concrete can be determined by shear tests, τ c =0.21(f c ') 2 / 3 =0.21×(0.79×30) 2 / 3 =1.73MPa.

[0243] According to the above data and formula, the shear strength f of the contact surface between the flange single surface and the concrete is calculated cs :

[0244] f cs =A p τ cs +A c τ c =0×1.73+67624×0.27=18258N

[0245] Determine the type of damage:

[0246] σ t 'bh0 / 2=2.01×330×200 / 2=33150>

[0247] f cs +σ u bh0=18258+0.16×330×200=28818

[0248] Therefore, it is determined that the failure mode is the first mode.

[0249] Calculate the first bending capacity, M Ⅰ =0.16×8800000=1408000N·mm;

[0250] Calculate strain, ε cs =Δ s / l p =0.14 / 214=0.000654;

[0251] Calculate the concrete compressive strain, ε c =xε cs / (ha cs -x)=0.000654x / (400-200-x);

[0252] According to the concrete stress-strain relationship, the maximum compressive stress σ of concrete can be calculated c , Appendix C of the "Code for Design of Concrete Structures" can be used.

[0253] Calculate the resultant compressive force on concrete, fc =σ c xb / 2=330σ c x / 2;

[0254] Calculate the resultant normal stress at the steel plate-concrete interface, f u =σ u (hxa cs )b / 2=0.16×330×(400-200-x) / 2;

[0255] Based on f c 、f u and f cs We can get x = 59.8mm; c 、f u 、f cs And x is substituted into the second bending capacity calculation formula to obtain M Ⅱ =6.98kN·m.

[0256] Calculate M Ⅱ =6.98kN·m,M Ⅰ =0.16×8800000=1.41kN·m The sum of the values ​​is the bending bearing capacity M u =6.98+1.41=8.39kN·m.

[0257] In addition, the present application also relates to a bending bearing capacity calculation system for the cross steel plate joints of a grid-type ground-connected wall, comprising a failure mode determination module, a first bending bearing capacity calculation module, a second bending bearing capacity calculation module and a joint bending bearing capacity calculation module. The failure mode determination module is used to determine the failure mode based on the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete; the first bending bearing capacity calculation module is used to calculate the first bending bearing capacity contributed by the web based on the maximum normal cohesion between the web and the concrete interface; the second bending bearing capacity calculation module is used to calculate the second bending bearing capacity contributed by the flange based on the failure mode, the resultant concrete pressure, the resultant normal stress of the steel plate-concrete interface, the resultant tensile and compressive forces of the concrete, and the tensile and compressive reinforcement forces; the joint bending bearing capacity calculation module calculates the sum of the first bending bearing capacity and the second bending bearing capacity as the joint bending bearing capacity.

[0258] An embodiment of the present invention further provides a non-transitory computer-readable storage medium, which stores a computer program. The computer program includes program instructions, which implement the various steps of the method described in the present invention when executed by a processor, and will not be repeated here.

[0259] The computer-readable storage medium may be the data transmission device provided in any of the aforementioned embodiments or an internal storage unit of a computer device, such as a hard disk or memory of the computer device. The computer-readable storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., provided on the computer device.

[0260] Furthermore, the computer-readable storage medium may include both an internal storage unit of the computer device and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by the computer device. The computer-readable storage medium may also be used to temporarily store data to be output or that has been output.

[0261] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0262] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0263] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0264] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0265] Embodiments of the present invention further provide a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the method for calculating the bending bearing capacity of a cross-shaped steel plate joint in a grid-type ground-connected wall. Matters not described in detail in this specification constitute prior art known to those skilled in the art.

[0266] The above shows and describes the basic principles, main features, and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present application. Various changes and improvements may be made to the present application without departing from the spirit and scope of the present application. Such changes and improvements are intended to fall within the scope of the present application. The scope of protection claimed in this application is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the bending bearing capacity of cross steel plate joints in a lattice-type ground-connected wall, characterized by: include, The failure mode is determined based on the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange of the cross steel plate joint and the concrete. The first bending capacity contributed by the web is calculated based on the maximum normal cohesion between the web and concrete interface; The second bending capacity contributed by the flange is calculated based on the failure mode, the concrete pressure resultant, the normal stress resultant of the steel plate-concrete interface, the concrete tension and compression resultant, and the tension and compression reinforcement force; The sum of the first bending bearing capacity and the second bending bearing capacity is the bending bearing capacity of the cross steel plate joint of the lattice ground-connected wall.

2. The method for calculating the bending bearing capacity of the cross steel plate joints of the grid-type ground-connected wall according to claim 1, characterized in that: The method for determining the failure mode includes: if the maximum tensile stress of concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete meet the following conditions, s t bh0 / 2≤f cs +s μ bh0 Where: t ——maximum tensile stress of concrete; b——calculated width; h0 - height from flange to top of ground-connected wall; σ u ——maximum normal cohesion between steel plate and concrete; f cs — Shear strength of the contact surface between the flange single surface and concrete; The failure mode is determined to be the second mode, otherwise the failure mode is determined to be the first mode.

3. The method for calculating the bending bearing capacity of the cross steel plate joints of the lattice-type ground-connected wall according to claim 2, characterized in that: When the failure mode is the first mode, the second bending bearing capacity is calculated according to the following formula: M Ⅱ =2(h-a cs )f u / 3+(h-a cs -x / 3)f cs Where: M Ⅱ ——second bending capacity; h——thickness of lattice ground wall; x——height of compression zone; a cs —Distance from flange to bottom of ground-connected wall; f u ——the resultant normal stress at the steel plate-concrete interface; f cs ——Shear strength of the contact surface between the flange single surface and concrete.

4. The method for calculating the bending bearing capacity of the cross steel plate joints of the lattice-type ground-connected wall according to claim 3 is characterized by: The normal stress resultant at the steel plate-concrete interface is calculated according to the following formula: f u =s u (hxa cs )b / 2 Where: f u ——the resultant normal stress at the steel plate-concrete interface; b——calculated width; x——height of compression zone; h——thickness of lattice ground wall; a cs —Distance from flange to bottom of ground-connected wall; σ u ——The maximum normal cohesion between steel plate and concrete.

5. The method for calculating the bending bearing capacity of the cross steel plate joints of the lattice-type ground-connected wall according to claim 2, characterized in that: When the failure mode is the second mode, the second bending capacity is calculated according to the following formula: M Ⅱ =f s (h-x-a s +(f s '(x-a' s )+2f c x / 3) / (f s '+f c )) +f cs (h-x+(f s '(x-a' s )+2f c x / 3) / (f s '+f c ))+f t (2(h-x) / 3 +(f s '(x-a' s )+2f c x / 3) / (f s '+f c )) Where: M Ⅱ ——second bending capacity; f s — tensile reinforcement force; h——thickness of lattice ground wall; x——height of compression zone; a s - the distance from the tension reinforcement to the bottom of the ground-connected wall; f s '——compressive reinforcement force; a' s - the distance from the compression reinforcement to the top of the ground-connected wall; f c —resultant compressive force on concrete; f cs — Shear strength of the contact surface between the flange single surface and concrete; f t ——Concrete is subjected to combined tensile force.

6. The method for calculating the bending bearing capacity of the cross steel plate joints of the lattice-type ground-connected wall according to claim 5, characterized in that: The concrete compressive force and concrete tensile force are calculated according to the following formula: f t =s t (hx)b / 2 f c =σ c xb / 2 Where: f t —resultant tensile force on concrete; f c —resultant compressive force on concrete; σ t ——maximum tensile stress of concrete; σ c ——maximum compressive stress of concrete; h——thickness of lattice ground wall; x——height of compression zone; b——Calculated width.

7. The method for calculating the bending bearing capacity of the cross steel plate joints of the lattice-type ground-connected wall according to claim 5, characterized in that: The tensile and compressive reinforcement forces are calculated using the following formula: f s =nA s ε s AND s f s '=nA s ε s 'AND s Where: f s — tensile reinforcement force; f s '——compressive reinforcement force; n——the number of M-shaped steel bars; A s ——cross-sectional area of ​​M-shaped steel bars; ε s — strain of tensile reinforcement; ε s '——compressive steel bar strain; E s ——Elastic modulus of steel bars.

8. A system for calculating the bending bearing capacity of cross steel plate joints in a grid-type ground-connected wall, characterized by: The system performs calculations according to a method for calculating the bending bearing capacity of a cross steel plate joint of a grid-type ground-connected wall as described in any one of claims 1 to 7, including: a failure mode determination module, the failure mode determination module being used to determine the failure mode based on the maximum tensile stress of the concrete, the maximum normal cohesion between the web of the cross steel plate joint and the concrete, and the shear strength of the contact surface between the flange single surface of the cross steel plate joint and the concrete; a first bending capacity calculation module, configured to calculate a first bending capacity contributed by the web according to the maximum normal cohesion of the interface between the web and the concrete; A second bending bearing capacity calculation module, the second bending bearing capacity calculation module is used to calculate the second bending bearing capacity contributed by the flange according to the failure mode, the concrete pressure resultant, the steel plate-concrete interface normal stress resultant, the concrete tension and compression resultant, and the tension and compression reinforcement force; The joint bending bearing capacity calculation module calculates the sum of the first bending bearing capacity and the second bending bearing capacity as the joint bending bearing capacity.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for calculating the bending bearing capacity of the cross steel plate joints of a grid-type ground-connected wall as claimed in any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for calculating the bending bearing capacity of the cross steel plate joints of a grid-type ground-connected wall as described in any one of claims 1 to 7 are implemented.

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