A method for calculating the bending moment of the bottom plate node of an integral culvert foundation

By constructing a calculation parameter model for the difference in stiffness between the foundation base plate and the side wall, the comprehensive coefficient is calculated to accurately calculate the node bending moment of the culvert foundation base plate, the problem of inaccurate calculation in the existing technology is solved, and design optimization and cost reduction are achieved.

CN119293938BActive Publication Date: 2025-03-25ANHUI TRANSPORT CONSULTING & DESIGN INST
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Patent Information

Application Number
CN202411823216.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-12
Publication Date
2025-03-25
Estimated Expiration
2044-12-12

AI Technical Summary

Technical Problem

There is a lack of reasonable and accurate method in the prior art to quickly calculate the node bending moment of the integral culvert foundation base plate, resulting in unreasonable design and waste of materials.

Method used

By constructing a calculation parameter model for the difference in stiffness between the foundation base plate and the side wall, the first, second and third bending moment coefficients are calculated, and the comprehensive coefficients are derived based on the linear stiffness ratio to calculate a more accurate node bending moment.

Benefits of technology

This method can more accurately calculate the node bending moment of the foundation base plate, optimize the design, improve structural rationality and economy, and reduce material use and engineering costs.

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Abstract

The present invention discloses a method for calculating the node bending moment of an integral culvert foundation slab, which belongs to the technical field of culvert engineering, and includes: calculating a calculation parameter model of the lower structure of the tunnel body based on the difference in stiffness between the foundation slab and the side wall, calculating and obtaining the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C; calculating and obtaining the linear stiffness ratio of the foundation slab and the side wall, and based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, combining the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C to derive a comprehensive coefficient; based on the comprehensive coefficient, calculating the node bending moment of the foundation slab of the lower structure of the tunnel body. The present invention can more accurately calculate the node bending moment of the foundation slab of the culvert based on the linear stiffness ratio of the foundation slab and the side wall, which will help optimize the design of the culvert and improve the rationality and economy of its structure.
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Description

Technical Field

[0001] The invention relates to the technical field of culvert engineering, and in particular to a method for calculating the bending moment of a node of an integral culvert foundation bottom plate. Background Art

[0002] Culverts are an indispensable part of transportation infrastructure and play a vital role in highway and municipal road construction. With the rapid development of the economy and the continuous expansion of highway engineering, the design and calculation methods of culverts are also constantly improving and becoming more mature and complete.

[0003] At present, the existing culvert design and calculation methods mainly use two methods: theoretical method and finite element method. Although the finite element method has significant advantages in calculation accuracy and applicability, its complex design and calculation process also makes this method more cumbersome and time-consuming in actual operation. In contrast, the theoretical method is simpler and relatively low-cost in the design and calculation process, but it is mainly used in the design of the upper structure of the culvert. These structures are relatively simple and the stress conditions are clear, so the theoretical design and calculation methods are relatively mature. However, the design of the lower structure of the culvert, including the foundation slab and side walls, is more complex and changeable, and the existing theoretical design and calculation methods need to be further improved.

[0004] In the existing technology, the design method of the culvert substructure mainly relies on the finite element method or the theoretical design method recommended by the specification. For example: Article 9.4.5 of the recommended industry standard of the People's Republic of China JTG / T 3365-02-2020 "Highway Culvert Design Specifications" proposes a design method for an integral foundation slab, and provides calculation formulas for mid-span bending moment and node bending moment. However, these methods do not fully consider the impact of the difference in stiffness between the foundation slab and the side wall on the internal force distribution, resulting in the calculation results of the node bending moment being much higher than the actual value. This situation not only affects the rationality of the structural design, but may also lead to waste of materials. The above problems need to be solved urgently. To this end, the present invention proposes a method for calculating the node bending moment of the culvert foundation slab based on the difference in stiffness between the foundation slab and the side wall. Summary of the invention

[0005] The technical problem to be solved by the present invention is: how to solve the problem that there is currently no reasonable and accurate method in the prior art to quickly calculate the node bending moment of the integral culvert foundation bottom plate and that it is economically feasible. A method for calculating the node bending moment of the integral culvert foundation bottom plate is provided. The method can more accurately calculate the node bending moment of the culvert foundation bottom plate based on the linear stiffness ratio of the foundation bottom plate and the side wall, which will help optimize the design of the culvert and improve the rationality and economy of its structure.

[0006] like Figure 6 As shown, the present invention solves the above technical problems through the following technical solutions, and the present invention comprises the following steps:

[0007] Step S1: construct a calculation parameter model of the tunnel lower structure based on the difference in stiffness between the foundation slab and the side wall, and calculate and obtain the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C;

[0008] Step S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation, and the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C are combined to derive the comprehensive coefficient ;

[0009] Step S3: Based on the comprehensive coefficient , calculate the node bending moment of the foundation bottom plate of the tunnel lower structure .

[0010] Furthermore, in the step S1, the calculation parameter model includes the following parameters: the thickness d of the top plate, the thickness t1 of the side wall, the thickness t2 of the foundation bottom plate, the distance H1 from the center point of the top plate to the center point of the foundation bottom plate, the distance L1 from the center points of the two side walls, the calculated span L′1 of the foundation bottom plate, the distance L2 from the center of the side wall to the outermost side of the foundation bottom plate, the lateral earth pressure q1 at the top of the side wall, the lateral earth pressure q2 at the bottom of the side wall, the design compressive stress q of the foundation bottom plate, and the bending moment M transmitted from the top plate to the top of the side wall.

[0011] Furthermore, the integral culvert includes a top plate, two side walls and a foundation bottom plate. The top plate is made of prefabricated components or cast on site. The top plate and the two side walls are connected by overlapping. The two side walls and the foundation bottom plate are cast as a whole, and the foundation bottom plate extends a predetermined distance to the outside of the two side walls.

[0012] Furthermore, in step S1, the calculation formula of the first bending moment coefficient A is as follows:

[0013] ;

[0014] in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, Design compressive stress for the foundation slab. It is the distance from the center of the side wall to the outermost side of the foundation slab.

[0015] Furthermore, in step S1, the calculation formula of the second bending moment coefficient B is as follows:

[0016] ;

[0017] in, is the distance between the center points of the two side walls.

[0018] Furthermore, in step S1, the calculation formula of the third bending moment coefficient C is as follows:

[0019] .

[0020] Furthermore, in step S2, the linear stiffness ratio of the base slab to the side wall is The calculation formula is as follows:

[0021] ;

[0022] in, is the thickness of the side wall, The thickness of the base slab.

[0023] Furthermore, in step S2, the comprehensive coefficient The calculation formula is as follows:

[0024] .

[0025] Furthermore, in step S2, the node bending moment of the foundation bottom plate The calculation formula is as follows:

[0026] ;

[0027] in, The calculated span of the foundation slab.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1. The present invention establishes a method for calculating the bending moment of the culvert foundation slab node based on the stiffness ratio of the foundation slab and the side wall line, and provides a more accurate, easy-to-operate and fast method for calculating the bending moment of the integral culvert foundation slab node.

[0030] 2. By considering the impact of the difference in stiffness between the foundation slab and the side wall on the internal force distribution, the calculation results can be closer to the actual stress state of the structure, thereby improving the reliability of the design.

[0031] 3. The present invention can accurately calculate the node bending moment value of the foundation slab, thereby allowing differentiated and refined reinforcement design at the mid-span and nodes of the foundation slab, avoiding the previous one-size-fits-all approach of uniform reinforcement at the mid-span and nodes that causes excessive reinforcement, reducing unnecessary material usage and significantly reducing engineering costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram of calculation parameters used in the present invention;

[0033] Figure 2 The bending moment diagram of the numerical simulation analysis result of the integral foundation culvert with a structural size of 6m×4.5m (structure net width×structure net height) and a fill height of 2m in the first embodiment of the present invention;

[0034] Figure 3 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 10m in the second embodiment of the present invention;

[0035] Figure 4 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 16m in the third embodiment of the present invention;

[0036] Figure 5 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m in the fourth embodiment of the present invention;

[0037] Figure 6 It is a schematic diagram of the process of the present invention.

[0038] In the figure: 1-top plate; 2-side wall; 3-foundation bottom plate. DETAILED DESCRIPTION

[0039] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0040] Embodiment 1

[0041] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation slab node based on the stiffness ratio of the foundation slab and the side wall line, such as Figure 1-2 As shown, the following steps are included:

[0042] S1: A calculation parameter model of the tunnel lower structure is constructed based on the difference in stiffness between the foundation bottom plate and the side wall. For the first embodiment of this invention, the integral foundation culvert with a structural size of 6m×4.5m and a fill height of 2m, the detailed calculation parameters are shown in Table 1:

[0043] Table 1 Detailed calculation parameters

[0044]

[0045] Calculate and obtain the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C;

[0046] The first bending moment coefficient A is determined by the following formula:

[0047] ;

[0048] in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, The design compressive stress of the foundation slab is obtained by calculating all the upper loads according to the inverted beam method. It is the distance from the center of the side wall to the outermost side of the foundation slab.

[0049] The second bending moment coefficient B is determined by the following formula:

[0050] ;

[0051] in, The distance between the center points of the two side walls.

[0052] The third bending moment coefficient C is determined by the following formula:

[0053] ;

[0054] S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation to derive the comprehensive coefficient .

[0055] Linear stiffness ratio of foundation slab to side wall Determine by the following formula:

[0056] ;

[0057] in, is the thickness of the side wall, The thickness of the base slab.

[0058] Comprehensive coefficient Determine by the following formula:

[0059] ;

[0060] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0061] Mid-span bending moment of foundation slab Determined according to the specification, the node bending moment of the foundation bottom plate Determine as follows:

[0062] ;

[0063] in, The calculated span of the foundation slab can be taken as 1.15 times the clear distance between the walls on both sides, but should not be greater than the center distance between the walls on both sides.

[0064] For this embodiment 1: the structural dimensions are 6m×4.5m (structure net width×structure net height), the fill height is 2m, and the integral foundation culvert is combined with Figure 2 The calculated value of the present invention is compared with the numerical simulation analysis value (obtained by finite element method simulation analysis) and the standard calculated value (obtained by theoretical method calculation). The results are shown in Table 2. It can be found that the error of the calculated value according to the specification is 49.5% compared with the numerical simulation analysis value, and the error of the calculated value according to the present invention is 7.2% compared with the numerical simulation analysis value, which meets the actual engineering accuracy requirements, and the calculated value according to the present invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0065] Table 2 Comparison of results of three methods

[0066]

[0067] In the present invention, if Figure 1 As shown, the culvert includes a top plate 1, two side walls 2 and a foundation bottom plate 3. The top plate 1 can be a prefabricated component or cast on site. The prefabricated top plate 1 and the two side walls 2 are connected by overlapping. The two side walls 2 and the foundation bottom plate 3 are cast as a whole. The foundation bottom plate 3 extends a certain distance outside the two side walls 2 to form a stable support structure.

[0068] In the present invention, the node bending moment value of the foundation bottom plate can be calculated more accurately ( ), thereby allowing differentiated and refined reinforcement design at the mid-span and nodes of the foundation slab, avoiding the previous one-size-fits-all approach of uniform reinforcement at the mid-span and nodes that causes excessive reinforcement, reducing unnecessary material usage and significantly reducing engineering costs.

[0069] Embodiment 2

[0070] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation slab node based on the stiffness ratio of the foundation slab and the side wall line, such as Figure 1 , Figure 3 As shown, the following steps are included:

[0071] S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For the second embodiment, the structure size is 6m×4.5m, and the fill height is 10m for an integral foundation culvert. The detailed calculation parameters are shown in Table 3:

[0072] Table 3 Detailed calculation parameters

[0073]

[0074] Calculate and obtain the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C;

[0075] The first bending moment coefficient A is determined by the following formula:

[0076] ;

[0077] in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, The design compressive stress of the foundation slab is obtained by calculating all the upper loads according to the inverted beam method. It is the distance from the center of the side wall to the outermost side of the foundation slab.

[0078] The second bending moment coefficient B is determined by the following formula:

[0079] ;

[0080] in, The distance between the center points of the two side walls.

[0081] The third bending moment coefficient C is determined by the following formula:

[0082] ;

[0083] S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation to derive the comprehensive coefficient .

[0084] Linear stiffness ratio of foundation slab to side wall Determine as follows:

[0085] ;

[0086] in, is the thickness of the side wall, The thickness of the base slab.

[0087] Comprehensive coefficient Determine by the following formula:

[0088] ;

[0089] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0090] Mid-span bending moment of foundation slab Determined according to the specification, the node bending moment of the foundation bottom plate Determine by the following formula:

[0091] ;

[0092] in, The calculated span of the foundation slab can be taken as 1.15 times the clear distance between the walls on both sides, but should not be greater than the center distance between the walls on both sides.

[0093] For the second embodiment: the structure size is 6m×4.5m (structure net width×structure net height), the fill height is 10m, and the integral foundation culvert is combined with Figure 3 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 4. It can be found that the error of the calculated value according to the specification is 74.4% compared with the numerical simulation analysis value, which is nearly doubled and has a large error. The error of the calculated value according to the present invention is 0.5% compared with the numerical simulation analysis value, which meets the actual engineering accuracy requirements, and the calculated value according to the present invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0094] Table 4 Comparison of results of three methods

[0095]

[0096] Embodiment 3

[0097] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation slab node based on the stiffness ratio of the foundation slab and the side wall line, such as Figure 1 , 4 As shown, the following steps are included:

[0098] S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For Example 3: an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 16m, the detailed calculation parameters are shown in Table 5:

[0099] Table 5 Detailed calculation parameters

[0100]

[0101] Calculate and obtain the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C;

[0102] The first bending moment coefficient A is determined by the following formula:

[0103] ;

[0104] in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, The design compressive stress of the foundation slab is obtained by calculating all the upper loads according to the inverted beam method. It is the distance from the center of the side wall to the outermost side of the foundation slab.

[0105] The second bending moment coefficient B is determined by the following formula:

[0106] ;

[0107] in, The distance between the center points of the two side walls.

[0108] The third bending moment coefficient C is determined by the following formula:

[0109] ;

[0110] S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation to derive the comprehensive coefficient .

[0111] Linear stiffness ratio of foundation slab to side wall Determine by the following formula:

[0112] ;

[0113] in, is the thickness of the side wall, The thickness of the base slab.

[0114] Comprehensive coefficient Determine by the following formula:

[0115] ;

[0116] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0117] Mid-span bending moment of foundation slab Determined according to the specification, the node bending moment of the foundation bottom plate Determine as follows:

[0118] ;

[0119] in, The calculated span of the foundation slab can be taken as 1.15 times the clear distance between the walls on both sides, but should not be greater than the center distance between the walls on both sides.

[0120] For the third embodiment: the integral foundation culvert with a structural dimension of 6m×4.5m (structure net width×structure net height) and a fill height of 16m, combined with Figure 4 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 6. It can be found that the error between the calculated value according to the specification and the numerical simulation analysis value is 98.7%, which is twice as large as the calculated value of the specification. The error between the calculated value of the present invention and the numerical simulation analysis value is 3.1%, which meets the actual engineering accuracy requirements. In addition, the calculated value of the present invention is closer to the actual stress condition of the structure than the calculated value of the specification.

[0121] Table 6 Comparison of results of three methods

[0122]

[0123] Embodiment 4

[0124] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation slab node based on the stiffness ratio of the foundation slab and the side wall line, such as Figure 1 , 5 As shown, the following steps are included:

[0125] S1: Based on the difference in stiffness between the foundation floor and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For Example 4: an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m, the detailed calculation parameters are shown in Table 7:

[0126] Table 7 Detailed calculation parameters

[0127]

[0128] Calculate and obtain the first bending moment coefficient A, the second bending moment coefficient B and the third bending moment coefficient C;

[0129] The first bending moment coefficient A is determined by the following formula:

[0130] ;

[0131] in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, The design compressive stress of the foundation slab is obtained by calculating all the upper loads according to the inverted beam method. It is the distance from the center of the side wall to the outermost side of the foundation slab.

[0132] The second bending moment coefficient B is determined by the following formula:

[0133] ;

[0134] in, The distance between the center points of the two side walls.

[0135] The third bending moment coefficient C is determined by the following formula:

[0136] ;

[0137] S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation to derive the comprehensive coefficient .

[0138] Linear stiffness ratio of foundation slab to side wall Determine by the following formula:

[0139] ;

[0140] in, is the thickness of the side wall, The thickness of the base slab.

[0141] Comprehensive coefficient Determine by the following formula:

[0142] ;

[0143] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0144] Mid-span bending moment of foundation slab Determined according to the specification, the node bending moment of the foundation bottom plate Determine by the following formula:

[0145] ;

[0146] in, The calculated span of the foundation slab can be taken as 1.15 times the clear distance between the walls on both sides, but should not be greater than the center distance between the walls on both sides.

[0147] For the fourth embodiment: the integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m, combined with Figure 5 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 8. It can be found that the error between the calculated value according to the specification and the numerical simulation analysis value is 96.3%, which is twice as large as the calculated value of the standard. The error between the calculated value according to the invention and the numerical simulation analysis value is 0.6%, which meets the actual engineering accuracy requirements. In addition, the calculated value according to the invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0148] Table 8 Comparison of results of three methods

[0149]

[0150] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the bending moment of the bottom plate node of an integral culvert foundation, characterized in that: The following steps are involved: Step S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed to calculate the first bending moment coefficient. A , the second bending moment coefficient B and the third bending moment coefficient C ; Step S2: Calculate the linear stiffness ratio between the foundation slab and the side wall Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to the deformation coordination relationship between the foundation slab and the side wall at the node, the rotation angle of the foundation slab and the side wall at the node is used as the displacement equilibrium equation, combined with the first bending moment coefficient A , the second bending moment coefficient B and the third bending moment coefficient C Derived comprehensive coefficient ; Step S3: Based on the comprehensive coefficient , calculate the node bending moment of the foundation bottom plate of the tunnel lower structure ; In step S1, the first bending moment coefficient A The calculation formula is as follows: ; in, is the lateral earth pressure at the top of the side wall, is the lateral earth pressure at the bottom of the side wall, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the bending moment transmitted from the top plate to the top of the side wall, Design compressive stress for the foundation slab. It is the distance from the center of the side wall to the outermost side of the foundation slab; In step S1, the second bending moment coefficient B The calculation formula is as follows: ; in, is the distance between the center points of the two side walls; In step S1, the third bending moment coefficient C The calculation formula is as follows: ; In step S2, the linear stiffness ratio of the base slab to the side wall is The calculation formula is as follows: ; in, is the thickness of the side wall, is the thickness of the base slab; In step S2, the comprehensive coefficient The calculation formula is as follows: ; In step S2, the node bending moment of the foundation slab The calculation formula is as follows: ;in, The calculated span of the foundation slab.

2. A method for calculating the bending moment of the bottom plate node of an integral culvert foundation according to claim 1, characterized in that: In step S1, the calculation parameter model includes the following parameters: the thickness d of the top plate, the thickness t1 of the side wall, the thickness t2 of the foundation bottom plate, the distance H1 from the center point of the top plate to the center point of the foundation bottom plate, the distance L1 from the center points of the two side walls, the calculated span L′1 of the foundation bottom plate, the distance L2 from the center of the side wall to the outermost side of the foundation bottom plate, the lateral earth pressure q1 at the top of the side wall, the lateral earth pressure q2 at the bottom of the side wall, the design compressive stress q of the foundation bottom plate, and the bending moment M transmitted from the top plate to the top of the side wall.

3. The method for calculating the bending moment of the bottom plate node of an integral culvert foundation according to claim 1 is characterized in that: The integral culvert includes a top plate, two side walls and a foundation bottom plate. The top plate is made of prefabricated components or cast on site. The top plate and the two side walls are connected by overlapping. The two side walls and the foundation bottom plate are cast as a whole, and the foundation bottom plate extends a predetermined distance to the outside of the two side walls.

Citation Information

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  • Method for calculating dynamic response of adjacent culvert pile foundations

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