Structure for controlling limited displacement of large-span arch foot foundation of natural foundation and design method thereof

Abstract

The invention relates to a structure for controlling limited displacement of large-span arch foot foundations of a natural foundation and a design method of the structure. The structure comprises two arch foot foundations, and arch feet at the two ends of an arch structure are supported on the two arch foot foundations respectively; the prestressed concrete straining beam comprises a straining beam body and prestressed tendons, the straining beam body is horizontally arranged and located between the two arch foot foundations, the two ends of the straining beam body are connected with the two arch foot foundations respectively, and the prestressed tendons are arranged in the straining beam body and extend in the length direction of the straining beam body. The two ends of the prestressed tendons penetrate through the two arch foot foundations respectively and are anchored to the corresponding arch foot foundations. The prestressed concrete straining beam is arranged between the two arch foot foundations, the prestressed tendons are used for resisting the horizontal thrust resultant force of the arch feet under the load working condition, and the problem that displacement of the arch foot foundations is large under horizontal thrust is solved.

Description

Technical Field

[0001] This invention relates to the technical field of architectural design, specifically to a structure and its design method for controlling the limited displacement of a large-span arch foot foundation on a natural foundation. Background Technology

[0002] Arch structures are widely used in long-span public buildings. The arch abutments of long-span arch structures experience significant horizontal thrust, leading to substantial displacement of the arch abutment foundations. This displacement causes changes in the internal forces of the superstructure, resulting in discrepancies between the actual structure and the design, thus posing significant safety hazards. For projects using pile foundations, the horizontal stiffness of the piles themselves can control the arch abutment foundation displacement. However, for projects using natural ground foundations, the lack of horizontal lateral force resisting members such as piles makes the problem of large displacement of the arch abutment foundation under horizontal thrust more difficult to solve. Summary of the Invention

[0003] Based on the above description, the present invention provides a structure and design method for controlling the limited displacement of large-span arch foot foundations on natural ground, so as to solve the problem of large displacement of arch foot foundations under horizontal thrust.

[0004] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: In a first aspect, this application provides a structure for controlling the limited displacement of a large-span arch foot foundation on natural ground, comprising: The arch structure has two arch foot foundations, with the arch feet at both ends of the arch structure supported on the two arch foot foundations respectively; A prestressed concrete tie beam, comprising a tie beam body and prestressing tendons, wherein the tie beam body is horizontally arranged and located between two arch foot foundations and connected to the two arch foot foundations at both ends, wherein the prestressing tendons are arranged inside the tie beam body and extend along the length of the tie beam body, wherein the two ends of the prestressing tendons pass through the two arch foot foundations and are anchored to the corresponding arch foot foundations.

[0005] Preferably, the prestressing tendon is a bonded prestressed steel strand bundle, comprising multiple prestressed steel strands.

[0006] Preferably, the prestressing tendons are provided in multiple bundles and an even number, with each two bundles of prestressing tendons forming a batch. The two bundles of prestressing tendons in each batch are symmetrically distributed on both sides of the vertical plane where the axis of the main body of the tie beam is located. The multiple bundles of prestressing tendons are distributed sequentially and evenly spaced in a horizontal direction perpendicular to the length direction of the main body of the tie beam. The prestressing tendons are located at the middle position in the height direction of the main body of the tie beam.

[0007] Preferably, the prestressing tendon is fitted with a corrugated metal tube, which is cast inside the main body of the tie beam.

[0008] Preferably, the main body of the tie beam is a reinforced concrete beam.

[0009] Preferably, a sliding layer is provided between the arch foot foundation and the bearing layer of the foundation, and between the main body of the tie beam and the bearing layer of the foundation, and the arch foot foundation and the main body of the tie beam are respectively supported on the corresponding sliding layer.

[0010] Secondly, this application provides a design method for the aforementioned structure controlling the limited displacement of large-span arch foot foundations on natural ground, comprising the following steps: S1: The maximum horizontal thrust resultant force value at the arch foot under quasi-permanent combined load conditions is obtained based on the calculation results of the upper large-span arch structure. N max The displacement calculation results of the arch foot of the upper large-span arch structure under this working condition were obtained. ΔL 0, according to ΔL 0. Determine the displacement limits of the arch foot before and after prestressing tendon tensioning. ΔL ]; S2: According to N max and ΔL 0, the cross-sectional area of ​​the main beam is calculated using Hooke's theorem. A Based on the principle that the width and height of the tie beam body meet the requirements of the natural foundation, the cross-sectional width and height of the tie beam body are obtained. S3: Determine the total number of prestressed steel strands in the actual configuration, and it must be an even number; S4: Calculate the effective prestress based on the total number of prestressed steel strands actually arranged in the prestressed concrete tie beam. N p ; S5: Based on effective prestress N p Under the action of force and structural requirements of axially compressed members, the reinforcement of the main body of the tie beam is determined; S6: Assuming the prestressing tendons are tensioned to the control value in one go, the prestressing tendons are set as two bundles, each bundle of prestressing tendons includes half of the total prestressing steel strands actually arranged, under effective prestressing... N p Under the action of the law, the maximum displacement of the arch foot foundation is calculated according to Hooke's Law. ΔL ,like ΔL ≤[ ΔL If the tensioning method is correct, then this tensioning method should be used; otherwise, the prestressing tendons should be tensioned in batches. When using batch tensioning, the number of prestressing tendons is set to be greater than two bundles and even. Two bundles of prestressing tendons symmetrically distributed on both sides of the vertical plane containing the main axis of the tie beam are prestressing tendons tensioned in the same batch, and the number of prestressing strands in the two bundles of prestressing tendons in the batch is the same. The prestressing tendons are tensioned sequentially from the first batch to the last batch, according to the direction of gradually increasing distance from the vertical plane containing the main axis of the tie beam. The process also includes the following steps: S61: Set the proportion of prestressed steel strands in the first batch of tensioned prestressed tendons to be p1% of the total. Based on the calculation results of the upper large-span arch structure at this time, obtain the horizontal thrust of the arch foot foundation under the quasi-permanent combined load condition. N 1. Calculate the arch foot foundation displacement before the first batch of prestressed tendons are tensioned according to Hooke's Law. ΔL q1 The effective prestress p1% generated by the first batch of tensioned prestressing tendons N p Displacement below ΔL p1 If the first batch of prestressed tendons is tensioned, the displacement of the arch foot foundation... ΔL 1=| ΔL q1 - ΔL p1 |≤[ ΔL If p1% is satisfied, proceed to the next step; otherwise, reduce p1% until the design objective is met. Δ L 1≤[ ΔL ]; S62: Set the timing for tensioning the Xth batch of prestressing tendons, where X>1. Before tensioning the Xth batch of prestressing tendons, obtain the horizontal thrust of the arch foot foundation under the quasi-permanent combined load condition based on the calculation results of the superstructure at this time. N 2. Calculate the value of Hooke's Law in... N Displacement of arch foot foundation under 2 loads ΔL q2 If the displacement of the arch foot foundation before the tensioning of the Xth batch of prestressing tendons is... ΔL 21 =| ΔL q2 - ΔL p1 |≤[ ΔL If the design objective is met, proceed to the next step; otherwise, advance the timing of tensioning the Xth batch of prestressing tendons to reduce the horizontal thrust of the arch foot foundation under quasi-permanent combined load conditions. N 2 until satisfied Δ L 21 ≤[ ΔL ]; S63: Set the proportion of prestressed steel strands in the Xth batch of tensioned prestressed tendons to be p2% of the total, and the proportion of the remaining untensioned prestressed steel strands to be p3% of the total. Calculate the effective prestress (1-p3%) generated from the tensioning of the first batch of tensioned prestressed tendons to the tensioning of the Xth batch of tensioned prestressed tendons after tensioning, based on Hooke's Law. N p Displacement below ΔL p2 , If the arch foundation shifts at this time ΔL 22 =| ΔL q2 - ΔL p2 |>[ ΔL If p2% is satisfied, then decrease p2% until the condition is met. ΔL 22 ≤[ ΔL ]; If the arch foundation shifts at this time ΔL 22 =| ΔL q2 - ΔL p2 |≤[ ΔL If p3% = 0, then the design objective is met. If p3% ≠ 0, then the process ends. If p3% ≠ 0, then repeat steps S62-S63 to tension the next batch of prestressed tendons until p3% = 0.

[0011] Preferably, the determination of the total number of prestressed steel strands, which is an even number, includes: The total number of prestressed steel strands can be initially estimated using the following formula:

[0012] In the formula, N For the tensile force in the main body of the tie beam, f py This represents the design value for the tensile strength of prestressed steel strands. A p1 The cross-sectional area of ​​a single prestressed tendon is... n This represents the total number of prestressed steel strands. Based on the calculated total number of prestressed steel strands, the actual total number of prestressed steel strands is determined to be an even number.

[0013] Compared with the prior art, the technical solution of this application has at least the following beneficial technical effects: 1. This application solves the problem of large displacement of the arch foot foundation under horizontal thrust by setting a prestressed concrete tie beam between the two arch foot foundations and using prestressed tendons to resist the resultant force of the horizontal thrust of the arch foot under load conditions.

[0014] 2. The design method of this application, by adjusting the number of batches of prestressing tendons tensioned and the proportion of each batch, controls the displacement of the arch foot foundation before and after each prestressing tendon tensioning to not exceed the design limit, thereby solving the problem of excessive arch foot displacement in large-span arch structures on natural foundations, which causes safety hazards. Attached Figure Description

[0015] Figure 1 A schematic diagram of a structure for controlling the limited displacement of a large-span arch foot foundation on natural ground, provided in an embodiment of the present invention; Figure 2 for Figure 1 A cross-sectional view along line AA in the middle; Figure 3 for Figure 1 A cross-sectional view along the BB line; Figure 4 for Figure 3 A schematic diagram of the structure with four prestressed tendons as shown in the view.

[0016] Explanation of reference numerals in the attached figures: 1. Arch foot foundation; 2. Arch structure; 21. Arch foot; 3. Main tie beam; 31. Top reinforcement; 32. Bottom reinforcement; 33. Web reinforcement; 34. Stirrups; 4. Prestressed tendons; 5. Corrugated metal pipe; 6. Sliding layer; 7. Plain concrete cushion layer. Detailed Implementation

[0017] To facilitate understanding of this application, a more complete description will be provided below with reference to the accompanying drawings, which illustrate embodiments of the present application. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that the disclosure of this application will be thorough and complete.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0019] It is understood that spatial relation terms such as "below," "under," "below," "below," "above," "above," etc., can be used here to describe the relationship between one element or feature shown in the figure and other elements or features. It should be understood that, in addition to the orientation shown in the figure, spatial relation terms also include different orientations of the device in use and operation. For example, if the device in the figure is flipped, the element or feature described as "below" or "below" of the other element or feature will be oriented "above" the other element or feature. Therefore, the exemplary terms "below" and "below" can include both upper and lower orientations. Furthermore, the device may also include other orientations (e.g., rotated 90 degrees or other orientations), and the spatial descriptive terms used herein will be interpreted accordingly.

[0020] It should be noted that when one element is considered to be "connected" to another element, it can be directly connected to the other element or connected to the other element through an intermediary element. In the following embodiments, "connection" should be understood as "electrical connection," "communication connection," etc., if the connected circuits, modules, units, etc., have the transmission of electrical signals or data between them.

[0021] When used herein, the singular forms of “a,” “an,” and “the” may also include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “comprising,” “including,” or “having,” etc., specify the presence of the stated feature, whole, step, operation, component, part, or combination thereof, but do not preclude the possibility of the presence or addition of one or more other features, wholes, steps, operations, components, parts, or combinations thereof.

[0022] Reference Figure 1 As shown, this application provides a structure for controlling the limited displacement of a large-span arch foot foundation 1 on a natural foundation. The structure includes two arch foot foundations 1 and a prestressed concrete tie beam.

[0023] Reference Figure 2 and Figure 3 As shown, the two arch feet 21 of the upper large-span arch structure 2 are respectively supported on two arch foot foundations 1. Specifically, the upper arch structure 2 can be various forms of steel structure or composite structure, and the arch feet 21 are fixed on the arch foot foundations 1. The prestressed concrete tie beam includes a tie beam body 3 and prestressing tendons 4. The tie beam body 3 is horizontally arranged and located between the two arch foot foundations 1, with both ends connected to the two arch foot foundations 1 respectively. The prestressing tendons 4 are arranged inside the tie beam body 3 and extend along the length of the tie beam body 3. The two ends of the prestressing tendons 4 pass through the two arch foot foundations 1 respectively and are anchored to the corresponding arch foot foundations 1.

[0024] Reference Figure 3As shown, specifically, the prestressed concrete tie beam is located directly below the arch structure 2. The main body 3 of the tie beam is a reinforced concrete beam, with longitudinally arranged top reinforcement 31, bottom reinforcement 32, and web reinforcement 33, as well as transversely arranged stirrups 34. The prestressing tendons 4 are encased in corrugated metal pipes 5, which are cast inside the main body 3 of the tie beam. The prestressing tendons 4 pass through the corrugated metal pipes 5 and emerge from both ends of the tie beam. After passing through the two arch foot foundations 1 respectively, the two ends of the prestressing tendons 4 are anchored to the arch foot foundations 1 through the structural components.

[0025] The prestressing tendon 4 is a bonded prestressed steel strand bundle, which includes multiple prestressed steel strands, each of which is made up of several steel wires twisted together.

[0026] Reference Figure 2 and Figure 3 As shown, to avoid bending moments generated within the prestressed concrete tie beam due to prestress, the prestressing tendons 4 are arranged in multiple even bundles, with each bundle consisting of two tendons. The two bundles of prestressing tendons 4 in each bundle are symmetrically distributed on both sides of the vertical plane containing the axis of the tie beam body 3. The multiple bundles of prestressing tendons 4 are sequentially distributed and evenly spaced in a horizontal direction perpendicular to the length of the tie beam body 3, with the prestressing tendons 4 positioned at the midpoint of the height of the tie beam body 3. Specifically, the number of prestressing strands in the two bundles of prestressing tendons 4 within each bundle is the same. This arrangement ensures that the resultant force of the prestress generated by the prestressing tendons 4 is located at the center of the prestressed concrete tie beam, thereby preventing bending moments generated within the prestressed concrete tie beam. Examples of two and three batches are shown in the figure.

[0027] Reference Figure 1 , Figure 2 and Figure 3 As shown, sliding layers 6 are provided between the arch foot foundation 1 and the bearing stratum of the foundation, and between the main body of the tie beam 3 and the bearing stratum of the foundation. The arch foot foundation 1 and the main body of the tie beam 3 are respectively supported on the corresponding sliding layers 6. Specifically, a plain concrete cushion layer 7 is provided on the bearing stratum of the foundation, and the sliding layer 6 is placed on the plain concrete cushion layer 7. The function of the sliding layer 6 is to reduce the horizontal frictional resistance between the arch foot foundation 1, the main body of the tie beam 3 and the foundation. The specific material of the sliding layer 6 is designed according to the requirements.

[0028] Among them, the characteristic value f of the bearing capacity of the foundation of the bearing layer ak The bearing capacity requirements of the natural foundation must be met. The cross-sections and reinforcement of the prestressed concrete tie beam and arch foot foundation 1 should meet the structural and calculation requirements of the natural foundation. There should be no horizontal lateral stiffness components such as pile foundations under the prestressed concrete tie beam and arch foot foundation 1. The sliding layer 6 is used to eliminate ground friction resistance, ensuring that the displacement of the prestressed concrete tie beam and arch foot foundation 1 under horizontal force is linearly related to the horizontal force. Both the prestressed concrete tie beam and the upper large-span arch structure 2 are linear elastic materials, satisfying Hooke's Law. The formula for calculating Hooke's Law is: 2 ΔL = N 0L / EA In the formula: ΔL For the displacement of the arch foot 21, N 0 represents tension. L It is an arch structure with a span of 2. E The elastic modulus of concrete. A This represents the cross-sectional area of ​​the structure.

[0029] This embodiment also provides a design method for the structure described above that controls the limited displacement of the large-span arch foot foundation 1 on natural ground, including the following steps: S1: Based on the calculation results of the upper large-span arch structure 2, the maximum horizontal thrust of arch foot 21 under the quasi-permanent combination load condition (1.0 × standard value of dead load + 0.5 × standard value of live load) is obtained. N max And the displacement calculation results of the arch foot 21 of the upper large-span arch structure 2 under this working condition were obtained. ΔL 0, according to ΔL 0. Determine the displacement limits of the arch foot 21 before and after tensioning of the prestressing tendons 4. ΔL ].

[0030] Specifically, ΔL [Needs to be based on] ΔL 0 and specific engineering control objectives are determined, taking into account actual engineering design requirements, [ Δ L Usually taken ΔL It is about half of 0, but the specific value will be determined based on the actual requirements of the project.

[0031] S2: According to N max and ΔL 0, the cross-sectional area of ​​the main beam 3 is calculated using Hooke's theorem. A Based on the principle that the width and height of the main body 3 of the tie beam meet the requirements of the natural foundation, the cross-sectional width and height of the main body 3 of the tie beam are obtained.

[0032] S3: Determine the total number of prestressed steel strands to be even.

[0033] Specifically, the upper large-span arch structure 2 is usually an important component. The prestressing tendons 4 are made of bonded prestressed steel strands. Considering a certain proportion (approximately 20%) of prestress loss, the total number of prestressed steel strands is initially estimated using the following formula:

[0034] In the formula, N For the tension force in the main body of the tie beam, take the following value here. N max The value, f py This represents the design value for the tensile strength of prestressed steel strands.A p1 The cross-sectional area of ​​a single prestressed tendon is 4. n This represents the total number of prestressed steel strands.

[0035] Based on the total number of prestressed steel strands n The calculated value, taking into account the structural layout requirements of the actual project, determines the total number of prestressed steel strands to be an even number.

[0036] S4: Calculate the effective prestress based on the total number of prestressed steel strands actually arranged in the prestressed concrete tie beam. N p .

[0037] Specifically, according to the relevant provisions of the "Code for Design of Concrete Structures", the effective prestress is calculated based on the total number of prestressed steel strands actually arranged in the prestressed concrete tie beam. N p In accordance with the relevant provisions of the "Code for Design of Concrete Structures", the dimensions of section 3 of the main tie beam were verified under effective prestressing. N p Whether the stability of the axially compressed member is met under the action is determined. If not, the cross-sectional dimensions of the main body of the tie beam 3 should be increased to ensure that the stability meets the specifications.

[0038] S5: Based on effective prestress N p Under the action of force, the stress and structural requirements of the axially compressed member are met, and the reinforcement of the main body 3 of the tie beam is determined.

[0039] The ratio of the prestressed steel strand to the ordinary longitudinal reinforcement in the main body 3 of the tie beam shall not exceed the limit of 0.75 in the "Code for Design of Concrete Structures". The total longitudinal reinforcement ratio of the prestressed steel strand, converted from the design value of the tensile strength of ordinary steel bars, shall not exceed the limit of 2.5% in the "Code for Design of Concrete Structures" and shall not be less than the minimum reinforcement ratio.

[0040] S6: Assuming the prestressing tendon 4 is tensioned to the control value in one go, then the prestressing tendon 4 is set as two bundles, each bundle of prestressing tendon 4 including half of the actual total prestressing steel strands, in the effective prestress... N p Under the action of the law, the maximum displacement of the arch foot foundation 1 is calculated according to Hooke's Law. ΔL ,like ΔL ≤[ ΔL If the tensioning method is as follows, the prestressed tendon 4 will be tensioned to the control value in one go; otherwise, the prestressed tendon 4 will be tensioned in batches.

[0041] When using batch tensioning, the number of prestressing tendons 4 is set to be greater than two bundles and even. Two bundles of prestressing tendons 4 symmetrically distributed on both sides of the vertical plane containing the axis of the main beam 3 are prestressing tendons 4 tensioned in the same batch. The number of prestressing strands in the two bundles of prestressing tendons 4 in each batch is the same. Following the direction of increasing distance from the vertical plane containing the axis of the main beam 3, the prestressing tendons 4 are tensioned sequentially from the first batch to the last batch. The batch tensioning process includes the following steps: S61: Set the proportion of prestressed steel strands in the first batch of tensioned prestressed tendons 4 to p1% of the total. Based on the calculation results of the upper large-span arch structure 2 at this time, obtain the horizontal thrust of the arch foot foundation 1 under the quasi-permanent combined load condition. N 1. Calculate the displacement of the arch foot foundation 1 before tensioning the first batch of prestressed tendons according to Hooke's Law. ΔL q1 The effective prestress p1% generated by the first batch of tensioned prestressing tendons (4 tensions) N p Displacement below ΔL p1 If the first batch of prestressing tendons 4 are tensioned, the displacement of the arch foot foundation 1 will be... ΔL 1=| ΔL q1 - ΔL p1 |≤[ ΔL If p1% is satisfied, proceed to the next step; otherwise, reduce p1% until the design objective is met. ΔL 1≤[ ΔL ].

[0042] Specifically, when considering the first batch of tensioning of prestressing tendons 4, the upper structure should have a certain rigidity. The tensioning conditions for the first batch of tensioning of prestressing tendons 4 are usually set as follows: the prestressed concrete tie beam and the concrete of the arch foot foundation 1 reach the design strength, the backfill soil on both sides of the arch foot foundation 1 is completed, and the upper large-span arch structure 2 is installed.

[0043] In actual design, the initial p1% is usually set to 50%.

[0044] This step determined that the proportion of prestressed steel strands in the first batch of tensioned prestressed tendons 4 to the total number was p1.

[0045] S62: Set the timing for tensioning the Xth batch of prestressing tendons (4), where X>1. Before tensioning the Xth batch of prestressing tendons (4), based on the calculation results of the superstructure at this time, obtain the horizontal thrust of the arch foot foundation 1 under the quasi-permanent combined load condition. N 2. Calculate the value of Hooke's Law in... N 2. Displacement of the arch foot foundation under action 1 ΔL q2If at this time, the displacement of the arch foot foundation 1 before the tensioning of the Xth batch of prestressed tendons 4 is... ΔL 21 =| ΔL q2 - ΔL p1 |≤[ ΔL If the design objective is met, proceed to the next step; otherwise, advance the timing of tensioning the Xth batch of prestressing tendons 4 to reduce the horizontal thrust of the arch foot foundation 1 under the quasi-permanent combined load condition. N 2 until satisfied ΔL 21 ≤[ ΔL ].

[0046] The specific timing for tensioning the Xth batch of prestressed tendons (4 tensions) should be selected according to the actual project requirements and standards. For example, the timing for tensioning the second batch of prestressed tendons (4 tensions) is set after the main structure construction is completed and the roof structure support is removed.

[0047] S63: Set the proportion of prestressed steel strands in the Xth batch of tensioned prestressed tendons 4 to be p2% of the total, and the proportion of the remaining untensioned prestressed steel strands to be p3% of the total. Calculate the effective prestress (1-p3%) generated by tensioning the first batch of tensioned prestressed tendons 4 to the Xth batch of tensioned prestressed tendons 4 after tensioning the Xth batch of tensioned prestressed tendons 4, based on Hooke's Law. N p Displacement below ΔL p2 .

[0048] If the arch foot foundation 1 displaces at this time ΔL 22 =| ΔL q2 - ΔL p2 |>[ ΔL If p2% is satisfied, then decrease p2% until the condition is met. ΔL 22 ≤[ ΔL ].

[0049] If the arch foot foundation 1 displaces at this time ΔL 22 =| ΔL q2 - ΔL p2 |≤[ ΔL If p3% = 0, then the design objective is met. If p3% ≠ 0, then the process ends. If p3% ≠ 0, then repeat steps S62-S63 to tension the next batch of prestressed tendons 4 until p3% = 0.

[0050] Specifically, taking the second batch as an example, the initial p2% is set to 1-p1%, i.e., p3%=0. If the calculation under this condition yields... ΔL 22 =| ΔL q2 - ΔL p2 |≤[ ΔL If the design objective is met, and p3% = 0, indicating that all prestressed steel strands are tensioned, then the process ends. At this point, the prestressed tendons are tensioned in two batches. If the calculation under these conditions yields... ΔL 22 =| ΔL q2 - ΔL p2 |>[ ΔL If p2% is satisfied, then decrease p2% until the condition is met. ΔL 22 ≤[ ΔL After that, the proportion of the number of prestressed steel strands in the second batch of tensioned prestressed tendons 4 to the total number is determined. However, p3% ≠ 0, indicating that there are still prestressed steel strands that have not been tensioned. Therefore, steps S62-S63 need to be repeated to tension the third batch of prestressed tendons 4 until all prestressed steel strands are tensioned. At this time, the number of tensioning batches of prestressed tendons 4 and the proportion of the number of prestressed steel strands in each batch of tensioned prestressed tendons 4 to the total number are determined.

[0051] In actual design, the prestressing tendons 4 are usually tensioned in two or three batches.

[0052] The following example illustrates the specific implementation process of this design method. The superstructure of this project is a large-span arch structure 2, a 125m span, 35m high steel structure. Due to the large span and height of arch structure 2, there is a significant horizontal thrust at the column bases. Prestressed tendons 4 in the prestressed concrete tie beams are used to balance the horizontal thrust at the arch bases 21. The bearing stratum of the foundation is silty clay, and the characteristic value of the foundation bearing capacity is... f ak With a bearing capacity of 400 kPa, a natural foundation is sufficient to meet the load-bearing requirements of the superstructure. No pile foundations or other horizontally stiffening components are installed beneath the prestressed concrete tie beams and arch foot foundations 1. A sliding layer 6 is installed beneath the prestressed concrete tie beams and column foot foundations to ensure that the prestress is not lost due to ground friction. Both the upper steel arch and the prestressed concrete tie beams are made of linear elastic materials.

[0053] Based on the calculation results of the upper large-span arch structure 2, the maximum horizontal thrust of the arch foot column 21 under the quasi-permanent combined load condition is obtained. N max The displacement calculation results of the two columns of the upper arch structure are 4500kN. ΔL0 is 8mm. In order to control the impact of the displacement of the arch foot 21 on the internal force change of the upper arch structure 2 system, the design goal of this project is set after analysis: to control the displacement limit [ΔL]=5mm of the arch foot foundation 1 before and after each batch of prestressing tendons 4 tensioning by controlling the tensioning sequence of the prestressing tendons 4.

[0054] The main body of the prestressed concrete tie beam in this project is made of C40 concrete. ΔL 0 is 8mm, N max 4500kN L It is 125m. E 3.25x10 4 N / mm 2 According to Hooke's theorem, the cross-sectional area A of the main beam 3 is calculated to be 1081731 mm². 2 Based on the relevant requirements of the natural foundation, the prestressed concrete tie beam has a width of 2000mm and a height of 800mm.

[0055] Based on the span of the prestressed concrete tie beam in this project, the prestressing tendon 4 is tensioned from both ends. Following the principle that the prestressed concrete tie beam is an axially compressed member, the prestressing tendon 4 is selected as a straight line. As this is a critical project, the prestressing tendon 4 uses post-tensioned bonded prestressed steel strand bundles, with each prestressed steel strand being a Ф1860 grade. s 15.2 Steel strands, considering an approximate 20% prestress loss, the number of prestressed steel strands can be preliminarily estimated using the following formula:

[0056] The project is based on N To obtain N max The value is 4500kN. f py 1320 N / mm 2 , A p1 140 mm 2 ,but n The calculated value is 31, but considering the structural layout, we take 40.

[0057] According to the relevant provisions of the "Code for Design of Concrete Structures", the effective prestress of the 40 prestressed steel strands in the prestressed concrete tie beam was calculated. N p The value is 5930 kN. According to the relevant provisions of the "Code for Design of Concrete Structures", the cross-sectional dimensions of the prestressed concrete tie beam are verified within the effective prestress range. N p Under action, it satisfies the stability of the axially compressed member.

[0058] Prestressed concrete tie beams, based on effective prestress N p Reinforcing bars are configured to meet the stress and structural requirements of axially compressed members under a load of 5930 kN. The ratio of the prestressed strength of the prestressed steel strands to the ordinary longitudinal reinforcement in the main body 3 of the tie beam is not greater than the specification limit of 0.75. The total longitudinal reinforcement ratio of the prestressed steel strands, converted from the design value of the tensile strength of ordinary steel bars, is not greater than the specification limit of 2.5% and not less than the minimum reinforcement ratio. The ordinary reinforcement configuration of the prestressed concrete tie beam in this project is as follows: 11 top reinforcement bars of grade III steel with a diameter of 25 mm, 11 bottom reinforcement bars of grade III steel with a diameter of 25 mm, stirrups of grade III steel with a diameter of 12 mm @ 200 (10), and 10 web reinforcement bars of grade III steel with a diameter of 25 mm.

[0059] According to Hooke's Law, if the prestressed concrete tie beams in this project are tensioned at a single tension of 4 to the control value, the effective prestress... N p The maximum displacement of arch foot foundation 1 under a load of 5930kN. ΔL The displacement was 7mm, exceeding the displacement limit before and after four tensioning cycles for each batch of prestressed tendons. ΔL =5mm, therefore the prestressed steel strands in this project are tensioned in batches.

[0060] The tensioning conditions for the first batch of prestressed tendons 4 in this project were as follows: the prestressed concrete tie beam and the concrete of the arch foot foundation 1 reached the design strength, the backfilling on both sides of the arch foot foundation 1 was completed, and the upper large-span arch structure 2 was installed. The proportion of prestressed steel strands in the first batch of prestressed tendons 4 was set at 50% of the total. Based on the calculation results of the superstructure at this time, the horizontal thrust of the arch foot foundation 1 under the quasi-permanent combined load condition was... N 1. The displacement of the arch foot foundation before tensioning of the first batch of prestressed tendons is calculated based on Hooke's Law, which is 900 kN. ΔL q1 To extend 1mm outward from the tie beam. At 50% effective prestress. N p Displacement at 2965 kN ΔL p1 The displacement is 3.5mm outward from the tension beam. Therefore, after the first batch of prestressing tendons 4 are tensioned, the displacement of the arch foot foundation 1 is... ΔL 1=| ΔL q1 - ΔL p1 | 2.5mm to the inside of the tie beam <[ ΔL The diameter is 5mm, which meets the design target.

[0061] The conditions for tensioning the second batch of prestressing tendons (4 tendons) were: completion of the main structure (excluding the roof system) and removal of the roof structure supports. Before tensioning the second batch of prestressing tendons (4 tendons), the horizontal thrust of the arch foot foundation 1 under the quasi-permanent combined load condition was obtained based on the calculation results of the superstructure at that time. N 2 is 1660kN, calculated according to Hooke's Law. N 2. Displacement of the arch foot foundation under action 1 ΔL q2 The displacement is 2mm outward from the tension beam. At this point, the displacement of the arch foot foundation 1 before the second batch of prestressing tendons (4) is... Δ L 21 =| ΔL q2 - ΔL p1 | is 1.5mm towards the inside of the tie beam, less than [ ΔL =5mm, which meets the design target.

[0062] The proportion of prestressed steel strands in the second batch of tensioned prestressed tendons (4) is set at 50% of the total, and the proportion of untensioned prestressed steel strands is set at 0%, meaning the proportion of tensioned prestressed steel strands is 100%. After the second batch of tensioned prestressed tendons (4) is tensioned, according to Hooke's Law, at 100% effective prestress... N p Displacement at 5950 kN ΔL p2 The displacement is 7mm, at which point the arch foot foundation 1 has a displacement of 7mm. ΔL 22 =| ΔL q2 - ΔL p2 | This is 5mm towards the inside of the tension beam, equal to the displacement limit before and after tensioning each batch of prestressed steel strands. ΔL =5mm, meeting the design target, design ends. That is, tensioning is done in two batches, each of the two bundles of prestressing tendons 4 in each batch includes 10 prestressing steel strands.

[0063] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground, characterized in that, include: Two arch foot foundations (1), and the arch feet (21) at both ends of the arch structure (2) are respectively supported on the two arch foot foundations (1); A prestressed concrete tie beam, comprising a tie beam body (3) and prestressing tendons (4), wherein the tie beam body (3) is horizontally arranged, the tie beam body (3) is located between two arch foot foundations (1) and its two ends are respectively connected to the two arch foot foundations (1), the prestressing tendons (4) are arranged inside the tie beam body (3) and extend along the length direction of the tie beam body (3), and the two ends of the prestressing tendons (4) pass through the two arch foot foundations (1) respectively and are anchored to the corresponding arch foot foundations (1).

2. The structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 1, characterized in that: The prestressed tendon (4) is a bonded prestressed steel strand bundle, which includes multiple prestressed steel strands.

3. The structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 2, characterized in that: The prestressing tendons (4) are provided in multiple bundles and in even numbers. Every two bundles of prestressing tendons (4) form a batch. The two bundles of prestressing tendons (4) in a batch are symmetrically distributed on both sides of the vertical plane where the axis of the main body of the tie beam (3) is located. The multiple bundles of prestressing tendons (4) are distributed sequentially and evenly in the horizontal direction perpendicular to the length direction of the main body of the tie beam (3). The prestressing tendons (4) are located at the middle position in the height direction of the main body of the tie beam (3).

4. The structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 2, characterized in that: The prestressed tendon (4) is covered with a metal corrugated pipe (5), which is cast inside the main body of the tie beam (3).

5. The structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 3, characterized in that: The main body of the tie beam (3) is a reinforced concrete beam.

6. The structure for controlling the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 5, characterized in that: A sliding layer (6) is provided between the arch foot foundation (1) and the bearing layer of the foundation, and between the main body of the tie beam (3) and the bearing layer of the foundation. The arch foot foundation (1) and the main body of the tie beam (3) are respectively supported on the corresponding sliding layer (6).

7. The design method for a structure that controls the limited displacement of a large-span arch foot foundation (1) on natural ground as described in claim 6, characterized in that, Includes the following steps: S1: Based on the calculation results of the upper large-span arch structure (2), the maximum horizontal thrust resultant force of the arch foot (21) under the quasi-permanent combined load condition is obtained. N max And the displacement calculation results of the arch foot (21) of the upper large-span arch structure (2) under this working condition are obtained. ΔL 0, according to ΔL 0 Determine the displacement limits of the arch foot (21) before and after tensioning the prestressed tendons (4). ΔL ]; S2: According to N max and ΔL 0, the cross-sectional area of ​​the main body of the tie beam (3) is calculated by Hooke's theorem. A Based on the principle that the width and height of the main body of the tie beam (3) meet the requirements of the natural foundation, the cross-sectional width and height of the main body of the tie beam (3) are obtained; S3: Determine the total number of prestressed steel strands in the actual configuration, and it must be an even number; S4: Calculate the effective prestress based on the total number of prestressed steel strands actually arranged in the prestressed concrete tie beam. N p ; S5: Based on effective prestress N p Under the action of the force and structural requirements of the axially compressed member, the reinforcement of the main body of the tie beam (3) is determined; S6: Assuming the prestressing tendons (4) are tensioned to the control value in one go, the prestressing tendons (4) are set as two bundles, and each bundle of prestressing tendons (4) includes half of the total prestressing steel strands actually arranged, in the effective prestressing N p Under the action of Hooke's Law, the maximum displacement of the arch foot foundation (1) is calculated. ΔL ,like ΔL ≤[ ΔL If the tensioning method is correct, then this tensioning method shall be adopted; otherwise, the prestressed tendons (4) shall be tensioned in batches. When using batch tensioning, the number of prestressing tendons (4) is set to be greater than two bundles and even. Two bundles of prestressing tendons (4) symmetrically distributed on both sides of the vertical plane where the axis of the main body of the tie beam (3) is located are prestressing tendons (4) tensioned in the same batch. The number of prestressing steel strands in the two bundles of prestressing tendons (4) in the batch is the same. According to the direction of gradually moving away from the vertical plane where the axis of the main body of the tie beam (3) is located, the first batch of tensioned prestressing tendons (4) is tensioned to the last batch of tensioned prestressing tendons (4). The following steps are also included: S61: Set the proportion of prestressed steel strands in the first batch of tensioned prestressed tendons (4) to p1% of the total number. Based on the calculation results of the upper large-span arch structure (2) at this time, obtain the horizontal thrust of the arch foot foundation (1) under the quasi-permanent combined load condition. N 1. Calculate the displacement of the first batch of prestressed tendons (4) before tensioning the arch foot foundation (1) according to Hooke's Law. ΔL q1 The effective prestress p1% generated by the first batch of tensioned prestressing tendons (4) N p Displacement below ΔL p1 If the first batch of prestressed tendons (4) is tensioned, the displacement of the arch foot foundation (1) will be... ΔL 1=| ΔL q1 - ΔL p1 |≤[ ΔL If p1% is satisfied, proceed to the next step; otherwise, reduce p1% until the design objective is met. ΔL 1≤[ ΔL ]; S62: Set the timing for tensioning the Xth batch of prestressed tendons (4), where X>1. Before tensioning the Xth batch of prestressed tendons (4), based on the calculation results of the superstructure at this time, obtain the horizontal thrust of the arch foot foundation (1) under the quasi-permanent combined load condition. N 2. Calculate the value of Hooke's Law in... N 2. Displacement of the arch foot foundation under action (1) ΔL q2 If the displacement of the arch foot foundation (1) before the tensioning of the Xth batch of prestressed tendons (4) is... ΔL 21 =| ΔL q2 - ΔL p1 |≤[ ΔL If the design objective is met, proceed to the next step; otherwise, advance the timing of tensioning the Xth batch of prestressed tendons (4) to reduce the horizontal thrust of the arch foot foundation (1) under quasi-permanent combined load conditions. N 2 until satisfied ΔL 21 ≤[ ΔL ]; S63: Set the proportion of prestressed steel strands in the Xth batch of tensioned prestressed tendons (4) to be p2% of the total, and the proportion of the remaining untensioned prestressed steel strands to be p3% of the total. Calculate the effective prestress (1-p3%) generated by tensioning the first batch of tensioned prestressed tendons (4) to the Xth batch of tensioned prestressed tendons (4) after tensioning according to Hooke's Law. N p Displacement below ΔL p2 , If the displacement of the arch foot foundation (1) at this time ΔL 22 =| ΔL q2 - ΔL p2 |>[ ΔL If p2% is satisfied, then decrease p2% until the condition is met. ΔL 22 ≤[ Δ L ]; If the displacement of the arch foot foundation (1) at this time ΔL 22 =| ΔL q2 - ΔL p2 |≤[ ΔL If p3% = 0, then the design goal is met. If p3% ≠ 0, then the process ends. If p3% ≠ 0, then repeat steps S62-S63 to tension the next batch of prestressed tendons (4) until p3% = 0.

8. The design method for a structure that controls the limited displacement of a large-span arch foot foundation (1) on a natural foundation according to claim 7, characterized in that, The determination of the total number of prestressed steel strands, which is an even number, includes: The total number of prestressed steel strands can be initially estimated using the following formula: In the formula, N For the tensile force in the main body of the tie beam (3), f py This represents the design value for the tensile strength of prestressed steel strands. A p1 The cross-sectional area of ​​a single prestressed tendon (4) is... n This represents the total number of prestressed steel strands. Based on the calculated total number of prestressed steel strands, the actual total number of prestressed steel strands is determined to be an even number.

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