Parallel steel strand stay cable tensioning optimization control method

Abstract

The invention provides a parallel steel strand stay cable tensioning optimization control method. The method comprises the steps that firstly, basic parameters and unstressed cable length of stay cables are determined, wherein the target tensioning control force of the stay cables of a current construction section and the theoretical distance between a main beam anchor point and a bridge tower anchor point after tensioning is completed are determined; based on the parabola theory, considering the sag effect and the elastic elongation of the stay cable, and solving the unstressed cable length of the stay cable; 2, establishing an adjacent strand tensioning force recursive relation based on a structure coupling effect: simplifying a bridge tower and a main beam structure system into a linear elastic system along the axis direction of the stay cable, and obtaining a nonlinear proportional relation between adjacent strand tensioning forces caused by a structure rigidity and cable body flexible coupling effect; 3, calculating a single-strand tensioning force theoretical value of the whole stay cable under the control of a target value; and 4, anchoring loss compensation and final tensioning force optimization: calculating the precise tensioning force of each strand of the whole stay cable to carry out super tensioning, so that the cable force of the whole stay cable is consistent with a design target.

Description

Technical Field

[0001] This invention belongs to the field of building construction technology, and specifically relates to an optimized control method for tensioning of parallel steel strand stay cables. Background Technology

[0002] Due to its economic efficiency and ease of construction, steel strand cable-stayed bridges have become the mainstream cable type for long-span cable-stayed bridges. This system consists of multiple high-strength, low-relaxation steel strands, eliminating the need for factory prefabrication and allowing for flexible on-site material preparation and transportation. Currently, tensioning construction commonly employs single-strand tensioning, with the core control method being the "equivalent tensioning method." However, this traditional method relies on the idealized assumption that "each steel strand within the anchorage experiences equal stress." In actual tensioning, factors such as the deformation of the cable-stayed bridge structure, the interaction between steel strands, and the slippage of the anchorage and wedges all exhibit significant geometric nonlinearity and time-varying characteristics. This causes the tension in the initially tensioned steel strands to decrease non-uniformly and unevenly due to structural deformation caused by subsequent tensioning operations, resulting in deviations in cable force distribution and making it impossible to guarantee the uniformity of the final tension in each strand.

[0003] Therefore, how to provide an optimized control method for tensioning of parallel steel strand stay cables is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] This invention provides an optimized control method for tensioning parallel steel strand stay cables, aiming to overcome the inherent defects of the "equivalent tensioning method" in existing single-strand tensioning techniques for parallel steel strand stay cables. It addresses problems such as uneven cable force distribution and insufficient control precision caused by neglecting factors like the geometric nonlinearity of the stay cable, anchorage retraction losses, and the coupling effects of the structural system. By integrating precise finite element modeling, a more accurate tension force calculation formula and control method are proposed, achieving high-precision and uniform control of the steel strand tension. Ultimately, this achieves one-time tensioning, effectively solving the problem of non-equal cable force attenuation and ensuring that the final tension of the entire cable reaches the design target, thereby improving the overall stress uniformity and service reliability of the stay cable.

[0005] The technical solution of the parallel steel strand cable tension optimization control method of the present invention is as follows:

[0006] A method for optimizing and controlling the tension of parallel steel strand stay cables includes the following steps:

[0007] Step S1, determine the basic parameters of the stay cable and the length of the stress-free cable: Based on the bridge design drawings and simulation calculation analysis, determine the target tension control force of the stay cable in the current construction segment and the theoretical distance between the main beam anchor point and the bridge tower anchor point after tensioning; based on the parabolic theory, considering the sag effect and elastic elongation of the stay cable, solve for the length of the stress-free cable.

[0008] Step S2, establish the recursive relationship of adjacent strand tension based on structural coupling effect: simplify the bridge tower and main beam structural system along the cable axis as a linear elastic system with equivalent stiffness, and obtain the nonlinear proportional relationship between adjacent strand tension caused by the coupling effect of structural stiffness and cable flexibility.

[0009] Step S3: Calculate the theoretical value of the single-strand tension force of the entire stay cable under the control of the target value. The final target of the entire stay cable during the tensioning process is set as follows: after the nth (last) strand is tensioned and anchored, the force values ​​of all n strands reach an ideal uniform state, i.e., F n =F / n;

[0010] Step S4, Anchorage Loss Compensation and Final Tension Optimization: To compensate for the nonlinear prestress loss in the steel strands caused by the retraction of the anchor working wedges during the actual tensioning and anchoring process, the precise tension force of each strand of the entire stay cable is calculated for over-tensioning, so that the cable force of the entire stay cable is consistent with the design target and the stress of each strand of steel strand is uniform.

[0011] Further, in step S1, the formula for calculating the stress-free cable length S0 of the stay cable is:

[0012]

[0013] In the formula, E is the elastic modulus of the stay cable strand, in MPa, and A is the cross-sectional area of ​​the entire stay cable strand, in m². 2 q is the unit weight of the cable strand, in kN / m, and α is the angle between the cable axis and the horizontal direction, in degrees. This formula balances the elastic deformation and geometric deformation of the cable, ensuring the calculation accuracy of the stress-free cable length S0, and providing a reliable benchmark for subsequent mechanical analysis.

[0014] Further, in step S2, the formula for calculating the equivalent stiffness Ke is:

[0015]

[0016] In the formula, δ is the final theoretical displacement between the main beam anchor point and the bridge tower anchor point after the entire steel strand is tensioned, and the unit is m;

[0017] Based on this equivalent model, during single-strand tensioning, when the i-th strand of steel is tensioned, the force balance calculation formula for the system is:

[0018] K e ×δ i =i×F i (3),

[0019] Similarly, after the (i-1)th strand of steel is tensioned, we get:

[0020] K e ×δ i-1 = (i-1)×F i-1 (4),

[0021] In the formula δ i δ i-1 F represents the cumulative displacement between the main beam anchor point and the bridge tower anchor point after the tensioning of the i-th and (i-1)-th steel strands, respectively, in meters (m). i F i-1 These are the tension forces of the i-th and (i-1)-th strands of steel wire, respectively, in kN. Based on formula (1), after the (i-1)-th and i-th strands are tensioned, we get:

[0022]

[0023] In the formula, L i-1 A0 represents the theoretical spacing of the main beam anchor points after the (i-1)th strand of steel wire is tensioned, and A0 is the cross-sectional area of ​​a single strand of steel wire, in m². 2 q0 is the unit weight of a single strand of steel wire, in kN / m;

[0024] Similarly, after the i-th strand of steel is tensioned, we get:

[0025]

[0026] In the formula, L i Given the theoretical distance between the main beam anchor point and the bridge tower anchor point after the i-th steel strand is tensioned, equations (5) and (6) are solved simultaneously. After simplifying the approximation while maintaining engineering accuracy, the following is obtained:

[0027]

[0028] In the formula, n is the total number of steel strands in a single stay cable; during the tensioning of the i-th strand, the internal force of the (i-1)-th strand that has already been tensioned will be reduced from F. i-1 Attenuation to F i The change in internal force causes a change in cable length of δ. i -δ i-1 =L i-1 -L i From formula (7), we can obtain:

[0029]

[0030] The formula for calculating the impact factor β is:

[0031]

[0032] Combining formulas (3), (4), and (8) yields F. i-1 F i The recursive relationship between them is:

[0033]

[0034] Furthermore, in step S3, based on formula (10), the required tension force F of the steel strand to be applied when tensioning the i-th strand is calculated by recursively working backward from the final state i = n. i for:

[0035] Under ideal conditions, tensioning according to formula (11) can achieve the final target F for the cable force of the entire cable.

[0036] Furthermore, by modifying formula (11), the final actual tension control force Fi′ of the i-th strand is obtained:

[0037] In the formula The retraction amount of the working clamp is expressed in meters (m), thus obtaining the control sequence {F1′, F2′, ..., F} of the precise tension force per segment of the entire stay cable. i ′,…,F n-1 ′, F n By loading and anchoring each strand of steel according to this sequence, the cable force of the entire stay cable can be made consistent with the design target F.

[0038] The parallel steel strand stay cable tension optimization control method of the present invention has the following technical effects:

[0039] (1) The parallel steel strand cable tensioning optimization control method of the present invention proposes a compensation algorithm formula, systematically considers the nonlinear geometric influence of the cable and the retraction loss of the anchor wedge, and effectively solves the problem of non-equal attenuation of cable force in the tensioning process of strand by strand through reverse recursion.

[0040] (2) The parallel steel strand cable tensioning optimization control method of the present invention achieves precise control of the construction process by pre-calculating and determining the tensioning sequence, which not only greatly improves the construction efficiency, but also ensures the uniformity of tension of each steel strand in the cable body and significantly improves the stress performance of the cable.

[0041] (3) The parallel steel strand cable tensioning optimization control method of the present invention systematically optimizes and innovates existing tensioning theories and processes to improve tensioning control accuracy and cable formation quality. By constructing an accurate finite element model for cable force prediction, and comprehensively considering the cable length sag effect, the coupling effect of the structural system, and the anchor retraction loss factor, a more accurate tension force calculation formula and control method are proposed, realizing dynamic optimization and precise control of the tensioning process. This method can significantly improve cable force uniformity and cable formation quality, and has important engineering value for enhancing the service performance of cable stays and the lifespan of bridge structures. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the tension optimization control method for parallel steel strand stay cables in one embodiment of the present invention.

[0043] In the picture:

[0044] 1-Main beam, 2-Bridge tower, 3-Cable stay. Detailed Implementation

[0045] The parallel steel strand cable tensioning optimization control method of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0046] Example 1:

[0047] refer to Figure 1 This invention details the optimized control method for tensioning of parallel steel strand stay cables. To improve tension control accuracy and cable quality, it is necessary to systematically optimize and innovate existing tensioning theories and processes. This control method establishes a precise mechanical model to systematically compensate for the non-uniform attenuation of internal forces in the steel strands 3 caused by structural deformation and the prestress loss caused by anchor wedge retraction, thereby achieving high-precision control of the tension force of the stay cables 3. In other words, by constructing a precise finite element model for cable force prediction, comprehensively considering the cable length sag effect, the coupling effect of the structural system, and anchor retraction loss factors, a more accurate tension force calculation formula and control method are proposed, achieving dynamic optimization and precise control of the tensioning process.

[0048] Please continue to refer to this. Figure 1 A method for optimizing and controlling the tensioning of parallel steel strand stay cables includes the following steps:

[0049] Step S1, determine the basic parameters of the stay cable and the length of the stress-free cable: Based on the bridge design drawings and simulation calculation analysis, determine the target tension control force of the stay cable in the current construction segment and the theoretical distance between the anchor point of the main beam 1 and the anchor point of the bridge tower 2 after tensioning; Based on the parabola theory, considering the sag effect and elastic elongation of the stay cable 3, solve for the length of the stress-free cable 3.

[0050] Step S2, establish the recursive relationship of adjacent strand tension based on structural coupling effect: simplify the bridge tower 2 and main beam 1 structural system along the cable 3 axis as a linear elastic system with equivalent stiffness, and obtain the nonlinear proportional relationship between adjacent strand tension caused by the coupling effect of structural stiffness and cable flexibility.

[0051] Step S3: Calculate the theoretical value of the single-strand tension force of the entire stay cable 3 under the control of the target value. The final target of the entire stay cable 3 during the tensioning process is set as follows: after the nth (last) strand is tensioned and anchored, the force values ​​of all n strands reach an ideal uniform state, i.e., F n =F / n;

[0052] Step S4, Anchorage Loss Compensation and Final Tension Optimization: To compensate for the nonlinear prestress loss in the steel strands caused by the retraction of the anchor working wedges during the actual tensioning and anchoring process, the precise tension force of each strand of the entire cable 3 is calculated for over-tensioning, so that the cable force of the entire cable 3 is consistent with the design target, and the stress of each strand of steel strand is uniform.

[0053] In this embodiment, more preferably, in step S1, the formula for calculating the stress-free cable length S0 of the stay cable is:

[0054]

[0055] In the formula, E is the elastic modulus of the stay cable strand, in MPa; A is the cross-sectional area of ​​the entire stay cable strand, in kN / m; q is the unit weight of the stay cable strand, in kN / m; and α is the angle between the cable axis and the horizontal direction, in degrees. This formula balances the elastic deformation and geometric deformation of the stay cable, ensuring the calculation accuracy of the stress-free cable length S0 and providing a reliable benchmark for subsequent mechanical analysis.

[0056] In this embodiment, more preferably, in step S2, the formula for calculating the equivalent stiffness Ke is:

[0057]

[0058] In the formula, δ is the final theoretical displacement between the main beam anchor point and the bridge tower anchor point after the entire steel strand is tensioned, and the unit is m;

[0059] Based on this equivalent model, during single-strand tensioning, when the i-th strand of steel is tensioned, the force balance calculation formula for the system is:

[0060] K e ×δ i =i×F i (3),

[0061] Similarly, after the (i-1)th strand of steel is tensioned, we get:

[0062] K e ×δ i-1 = (i-1)×F i-1 (4),

[0063] In the formula δ i δ i-1 F represents the cumulative displacement between the main beam anchor point and the bridge tower anchor point after the tensioning of the i-th and (i-1)-th steel strands, respectively, in meters (m). i F i-1 These are the tension forces of the i-th and (i-1)-th strands of steel wire, respectively, in kN. Based on formula (1), after the (i-1)-th and i-th strands are tensioned, we get:

[0064]

[0065] In the formula, L i-1 A0 represents the theoretical spacing of the main beam anchor points after the (i-1)th strand of steel wire is tensioned, and A0 is the cross-sectional area of ​​a single strand of steel wire, in m². 2 q0 is the unit weight of a single strand of steel wire, in kN / m;

[0066] Similarly, after the i-th strand of steel is tensioned, we get:

[0067]

[0068] In the formula, L i This represents the theoretical distance between the main beam anchor point and the bridge tower anchor point after the i-th steel strand has been tensioned.

[0069] By combining equations (5) and (6) and simplifying the approximation while maintaining engineering accuracy, we obtain:

[0070]

[0071] In the formula, n is the total number of steel strands in a single stay cable; during the tensioning of the i-th strand, the internal force of the (i-1)-th strand that has already been tensioned will be reduced from F. i-1 Attenuation to F i The change in internal force causes a change in cable length of δ. i -δ i-1 =Li-1 -L i From formula (7), we can obtain:

[0072]

[0073] The formula for calculating the impact factor β is:

[0074]

[0075] Combining formulas (3), (4), and (8) yields F. i-1 F i The recursive relationship between them is:

[0076]

[0077] In this embodiment, more preferably, in step S3, based on formula (10), the required tension force F of the steel strand to be applied when tensioning the i-th strand is calculated by recursively working backward from the final state i = n. i for:

[0078] Under ideal conditions, tensioning according to formula (11) can achieve the final target F for the cable force of the entire cable.

[0079] In this embodiment, more preferably, formula (11) is modified to obtain the final actual tension control force Fi′ of the i-th strand:

[0080] In the formula The retraction amount of the working clamp is expressed in meters (m), thus obtaining the control sequence {F1′, F2′, ..., F} of the precise tension force per segment of the entire stay cable. i ′,…,F n-1 ′, F n By loading and anchoring each strand of steel according to this sequence, the cable force of the entire stay cable can be made consistent with the design target F.

[0081] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A method for optimizing and controlling the tensioning of parallel steel strand stay cables, characterized in that, Includes the following steps: Step S1, determine the basic parameters of the stay cable and the length of the stress-free cable: based on the bridge design drawings and simulation calculation analysis, determine the target tension control force of the stay cable in the current construction segment and the theoretical distance between the main beam anchor point and the bridge tower anchor point after tensioning; Based on parabolic theory, considering the sag effect and elastic elongation of the stay cable, the stress-free cable length of the stay cable is calculated. Step S2, establish the recursive relationship of adjacent strand tension based on structural coupling effect: simplify the bridge tower and main beam structural system along the cable axis as a linear elastic system with equivalent stiffness, and obtain the nonlinear proportional relationship between adjacent strand tension caused by the coupling effect of structural stiffness and cable flexibility. Step S3: Calculate the theoretical value of the single strand tension force of the entire stay cable under the control of the target value; Step S4, Anchorage Loss Compensation and Final Tension Optimization: To compensate for the nonlinear prestress loss in the steel strands caused by the retraction of the anchor working wedges during the actual tensioning and anchoring process, the precise tension force of each strand of the entire stay cable is calculated for over-tensioning, so that the cable force of the entire stay cable is consistent with the design target and the stress of each strand of steel strand is uniform.

2. The control method according to claim 1, characterized in that, In step S1, the formula for calculating the stress-free cable length S0 of the stay cable is: In the formula, E is the elastic modulus of the stay cable strand, in MPa, and A is the cross-sectional area of ​​the entire stay cable strand, in m². 2 q is the unit weight of the cable strand, in kN / m, and α is the angle between the cable axis and the horizontal direction, in °.

3. The control method according to claim 1, characterized in that, In step S2, the formula for calculating the equivalent stiffness Ke is: In the formula, δ is the final theoretical displacement between the main beam anchor point and the bridge tower anchor point after the entire steel strand is tensioned, and the unit is m; Based on this equivalent model, during single-strand tensioning, when the i-th strand of steel is tensioned, the force balance calculation formula for the system is: K e ×δ i =i×F i (3), Similarly, after the (i-1)th strand of steel is tensioned, we get: K e ×δ i-1 =(i-1)×F i-1 (4), In the formula δ i δ i-1 F represents the cumulative displacement between the main beam anchor point and the bridge tower anchor point after the tensioning of the i-th and (i-1)-th steel strands, respectively, in meters (m). i F i-1 These are the tension forces of the i-th and (i-1)-th strands of steel wire, respectively, in kN. Based on formula (1), after the (i-1)-th and i-th strands are tensioned, we get: In the formula, L i-1 A0 represents the theoretical spacing of the main beam anchor points after the (i-1)th strand of steel wire is tensioned, and A0 is the cross-sectional area of ​​a single strand of steel wire, in m². 2 q0 is the unit weight of a single strand of steel wire, in kN / m; Similarly, after the i-th strand of steel is tensioned, we get: In the formula, L i Given the theoretical distance between the main beam anchor point and the bridge tower anchor point after the i-th steel strand is tensioned, equations (5) and (6) are solved simultaneously. After simplifying the approximation while maintaining engineering accuracy, the following is obtained: In the formula, n is the total number of steel strands in a single stay cable; during the tensioning of the i-th strand, the internal force of the (i-1)-th strand that has already been tensioned will be reduced from F. i-1 Attenuation to F i The change in internal force causes a change in cable length of δ. i -δ i-1 =L i-1 -L i From formula (7), we can obtain: The formula for calculating the impact factor β is: Combining formulas (3), (4), and (8) yields F. i-1 F i The recursive relationship between them is:

4. The control method according to claim 3, characterized in that, In step S3, based on formula (10), the required tension force F of the steel strand to be applied when tensioning the i-th strand is calculated by recursively working backward from the final state i = n. i for: Under ideal conditions, tensioning according to formula (11) can achieve the final target F for the cable force of the entire cable.

5. The control method according to claim 4, characterized in that, Formula (11) is modified. The final actual tension control force Fi′ of the i-th steel strand is obtained: In the formula The retraction amount of the working clamp is expressed in meters (m), thus obtaining the control sequence {F1′, F2′, ..., F} of the precise tension force per segment of the entire stay cable. i ′,…,F n-1 ′, F n By loading and anchoring each strand of steel according to this sequence, the cable force of the entire stay cable can be made consistent with the design target F.

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