A method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on the influence matrix
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-21
- Publication Date
- 2026-08-11
AI Technical Summary
[0003]然而，现有方法仍存在明显局限性
[0062]本发明综合考虑了锚跨索力与散索鞍倾角的耦合效应、索鞍圆弧对主缆索股受力特性及传递规律的影响，以及实际施工中散索鞍两侧主缆索股受主塔偏位和温度变化等多因素共同作用的情况。该方法在理论上可实现一次调整到位，适用于散索鞍临时支撑拆除后的施工阶段。
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Figure CN122548947A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of suspension bridge construction control technology, specifically to a method for adjusting the construction of suspension bridge anchor span cable strands based on an influence matrix. Background Technology
[0002] With rapid economic development and continuous growth in transportation demand, various long-span bridges spanning rivers, straits, and deep mountain valleys have seen rapid development. Among these bridge types, suspension bridges, with their superior spanning capacity, are widely used in engineering construction. Existing methods for controlling the cable strands in the anchor span of suspension bridges primarily rely on the deviation between measured and theoretical cable forces to determine the cable strand adjustment amount. This is achieved by rotating the anchor nuts to change the effective length of the cable strands, thus bringing the cable force to the design value. Building upon this, some scholars have proposed improved methods that consider the influence of the inclination angle of the cable saddle. These methods have preliminarily considered the coupling effect between the cable strands and the inclination angle of the cable saddle during the anchor span cable strand adjustment process, which can improve adjustment efficiency to some extent. Furthermore, existing technologies have established an explicit relationship between cable force and frequency through regression analysis, established a mechanical model of the anchor span cable strands based on analytical methods, derived a cable force calculation formula considering tie rods, anchor head mass, and bending stiffness based on the energy method, and proposed a unified adjustment method for anchor span cable force using elasticity theory, providing a theoretical basis for the refined control of the anchor span cable strands.
[0003] However, existing methods still have significant limitations. On the one hand, most cable strand adjustment methods are based on the principle of stiffness equivalence to establish mechanical models, which makes it difficult to accurately reflect the influence of the multi-segment circular arc structure of the cable saddle on the force distribution law of the anchor span, resulting in limited calculation accuracy. On the other hand, existing methods are mostly based on the ideal completed bridge state of suspension bridges, lacking systematic consideration of structural geometric deviations and environmental effects during the construction phase. In actual construction, the main cable strands on both sides of the cable saddle are affected by the main tower offset and temperature changes, resulting in corresponding geometric deformation and internal force redistribution. If these are not considered, they will directly affect the accuracy of anchor span cable strand adjustment and the reliability of construction control. In addition, existing methods often require adjusting the anchor span cable force and cable saddle inclination angle separately, which is difficult to achieve in one step and requires multiple rounds of repeated adjustments to control both within the allowable range, resulting in low construction efficiency. Therefore, there is an urgent need for a refined construction control method for anchor span cable strands that can comprehensively consider the influence of cable saddle geometry, structural deviations during construction, and environmental factors. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention provides a method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix.
[0005] To achieve the above technology, the steps include:
[0006] S1. Establish a local mechanical analysis model for the completed stage of a single-span suspension bridge. Establish a global coordinate system with the center of the rocker axis as the origin, define key geometric points and set constraints.
[0007] S2. Based on the model established in S1, collect measured parameters and establish an objective function based on the principle of stress-free length conservation of cable strands, geometric compatibility conditions, and mechanical equilibrium conditions.
[0008] S3. Based on the objective function, derive the influence matrix of the anchor span cable strands, solve for the optimal adjustment amount, and complete the construction adjustment.
[0009] Preferably, the constraints are set as follows: the cable strands are always in the elastic phase and obey Hooke's Law;
[0010] The main cable strands are ideal flexible cables, bearing only axial tension and not subjected to axial compression or bending moment; the cross-sectional area of the main cable strands does not change with tension, and the axial tensile stiffness remains constant; during the adjustment of the anchor span cable strands, there is no relative slippage of the cable strands in the saddle groove; the adjustment of the anchor span cable strands does not cause the main tower to deviate.
[0011] Preferably, step S2 includes:
[0012] S2.1 The measured parameters collected include: main tower offset and cable strand temperature;
[0013] S2.2 Based on measured parameters and the principle of conservation of stress-free strand length, geometric compatibility and mechanical equilibrium conditions are analyzed for the main cable in the side span and the strand in the anchor span, respectively.
[0014] S2.3 Solve the nonlinear equations generated from the analysis results.
[0015] Preferably, step S2.2 includes:
[0016] S2.2.1, Geometric and mechanical analysis of the main cable in the side span, including: establishing a local coordinate system with the point of tangency between the main cable centerline and the main cable saddle in the side span as the origin to obtain the catenary equation; calculating the tangent angle at the main cable saddle and the tangent angle at the cable saddle; establishing the coordinates of key points in the global coordinate system, including the coordinates of the center of the main cable saddle and the center of the cable saddle.
[0017] Through analysis, the stress-free lengths of the side span main cable catenary segment, main cable saddle arc segment, and loose cable saddle arc segment were obtained;
[0018] S2.2.2, Anchor span cable strand geometric and mechanical analysis, including: obtaining the horizontal bending angle of the anchor span cable strand based on geometric relationships; establishing the catenary segment of the anchor span cable strand; calculating the tangent angle of the anchor span cable strand to determine the global coordinates of the vertical bending endpoint; setting the horizontal bending endpoint and the vertical bending endpoint of the cable strand to be located on the same circular arc, and establishing a complete spatial geometric description of the cable strand in the cable saddle under the global coordinate system;
[0019] The stress-free lengths of the suspended section of the anchor span and the arc section of the cable saddle were obtained through analysis.
[0020] S2.2.3 Perform a moment analysis on the cable saddle, including the moment generated by the weight of the main cable in the side span, the cable strands in the anchor span, and the cable saddle itself on the center of the rocker shaft.
[0021] Preferably, calculating the anchor span strand tangent angle to determine the global coordinates of the vertical bend endpoint includes:
[0022] ;
[0023] ;
[0024] ;
[0025] ;
[0026] The four scenarios are represented as follows:
[0027]
[0028]
[0029]
[0030]
[0031] In the above formula, The tangent angle at the starting point of the horizontal bend of the cable strand at the saddle point; The tangent angle of the anchor span cable strand; The angle of inclination of the cable saddle; and The X and Z coordinates of the endpoint of the vertical bend; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; , , as well as This represents the radius of the strand corresponding to the four circles.
[0032] Preferably, the endpoints of the horizontal and vertical bends of the cable strand are both located on the same arc. In establishing a complete spatial geometric description of the cable strand within the saddle in the global coordinate system, the same arc is the fourth arc segment. The complete spatial geometric description includes five spatial curves, represented as follows:
[0033]
[0034]
[0035]
[0036]
[0037]
[0038] In the formula, and The center of the horizontal bend of the cable strand is respectively X and Y coordinates; The starting point of the flat bend in the cable strand The X coordinate; The first dividing point The X coordinate; The second dividing point The X coordinate; The third dividing point The X coordinate; The end point of the flat bend of the cable strand The X coordinate; The end point of the vertical bend in the cable strand The X coordinate; The radius of the horizontal bend corresponding to the horizontal bend arc of the cable strand; This refers to the angle corresponding to the flat bend of the cable strand.
[0039] Preferably, in S2.3, based on the geometric compatibility condition, mechanical equilibrium condition, and the principle of stress-free length conservation, the following closed control equations can be obtained: horizontal direction closed control equation for side span cable strands, height difference closed control equation for side span cable strands, stress-free length conservation control equation for side span cable strands, horizontal bending angle constraint control equation for anchor span cable strands, horizontal direction closed control equation for anchor span cable strands, height difference closed control equation for anchor span cable strands, stress-free length conservation control equation for anchor span cable strands, and moment balance control equation at the cable saddle.
[0040] Based on 4n+4 control equations, where n is the total number of strands;
[0041] For 4n+4 governing equations, by shifting the right-hand side terms of each equation to the left-hand side, we can obtain their error functions. To ensure that each governing equation holds true, its error function should be approximately equal to 0; therefore, the objective function is established as follows:
[0042]
[0043] The nonlinear GRG method is used to solve the objective function. The convergence accuracy of the objective function is set to be less than 10. -9 When the solution is obtained, the reliability and accuracy of the solution can be ensured, and the solution can be stopped.
[0044] Preferably, the method for constructing the anchor span cable strand influence matrix in S3 is as follows:
[0045] First, the stress-free length of the main cable strands is calculated, and the main tower offset and strand temperature are measured. Under the condition that the anchor surface coordinates are taken as design values, based on the geometric compatibility conditions, mechanical equilibrium conditions, and the principle of stress-free length conservation of the strands, the governing equations are established and solved to obtain the initial parameter vector of the strands.
[0046] Subsequently, the coordinates of the m-th anchor strand on the anchor surface are adjusted by the length of one revolution of the anchor nut to simulate the actual adjustment during construction. The adjusted parameter vector is calculated, and the influence vector of the strand is obtained by subtracting the initial parameter vector from the adjusted parameter vector.
[0047] Repeat the above process until m=n, where n is the total number of anchor span strands, to obtain the influence vector of all anchor span strands. Finally, combine the influence vectors of all strands to form the complete anchor span strand influence matrix.
[0048] Preferably, the influence matrix D of the anchor span cable strand is expressed as:
[0049]
[0050] in, and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the first anchor span cable strand; and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the nth anchor span cable strand, respectively.
[0051] Preferably, the constraint conditions for the influence matrix of the anchor span cable strand are:
[0052]
[0053] In the formula, Adjustment amount for anchor span cable strands; This represents the theoretical cable force across the anchor strand; This represents the measured cable force of the anchor strand; This represents the error vector, which includes the error limit for the anchor span cable force and the error limit for the inclination angle of the cable saddle.
[0054] The constraints are transformed into standard form as follows:
[0055]
[0056] In the formula, Represents the transformation matrix. , Represents the transformation vector. ;
[0057] The governing equations are as follows: ;
[0058] By moving the terms on the right side of the governing equation to the left side, we can obtain its error function. To meet the optimization objective, the error function should be approximately equal to 0. The objective function is established as follows:
[0059]
[0060] The objective function can be solved using MATLAB to obtain the anchor span strand adjustment amount that satisfies the constraints. .
[0061] Beneficial effects of the present invention
[0062] This invention comprehensively considers the coupling effect between the anchor span cable force and the inclination angle of the cable saddle, the influence of the cable saddle arc on the force characteristics and transmission law of the main cable strands, and the combined effects of multiple factors such as the main tower offset and temperature changes on both sides of the cable saddle during actual construction. Theoretically, this method can achieve a one-time adjustment and is applicable to the construction stage after the temporary support of the cable saddle has been removed.
[0063] After adjusting the anchor span cable strands, the relative errors between the measured and theoretical values of the anchor span cable force and the inclination angle of the cable saddle are controlled within ±1%, meeting the engineering accuracy requirements. Attached Figure Description
[0064] Figure 1 This is a flowchart of the steps of the present invention;
[0065] Figure 2 This is a schematic diagram of the calculation process for the anchor span strand influence matrix of the present invention;
[0066] Figure 3 This is a schematic diagram of the Baidi City Yangtze River Bridge structure in the embodiment;
[0067] Figure 4 This is a diagram showing the calculation results of the anchor span cable force during the "empty cable" stage of the suspension bridge in the embodiment;
[0068] Figure 5 This is a diagram showing the relative error of the cable force after the anchor strand was adjusted in the embodiment. Detailed Implementation
[0069] The present invention will be further described in detail below with reference to specific embodiments.
[0070] like Figure 1 As shown, a method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix includes the following steps:
[0071] S1. Establish a local mechanical analysis model for the completed stage of a single-span suspension bridge. Establish a global coordinate system with the center of the rocker axis as the origin, define key geometric points and set constraints.
[0072] Key geometric points include: the center of the main cable saddle. Then the center of the first arc of the saddle Inclination angle of the rope saddle Center of the rocker arm With the center of the rocker arm Establish a global coordinate system with the origin, where The axis is horizontal to the left. The axis is vertically upward. Axis perpendicular to Plane pointing outwards, center of main cable saddle The intersection of the vertical line and the strand. The starting point of the flat curve at the cable saddle. , Tangent angle at the starting point of the horizontal curve of the cable strand at the saddle Anchor point of the cable on the front anchor face Due to the intersection point C and the starting point of the bend Since the positions of the main cable saddle and the cable tie saddle remain constant, the cable strands will be... and They are defined as the side span and anchor span cable strands, respectively;
[0073] The constraints include:
[0074] (1) The cable strands are always in the elastic phase and obey Hooke's Law;
[0075] (2) The main cable strand is an ideal flexible cable that only bears axial tension and is not subject to axial compression or bending moment.
[0076] (3) The cross-sectional area of the main cable strand does not change with the tension, and the axial tensile stiffness remains constant;
[0077] (4) During the adjustment of the anchor span cable strands, there was no relative slippage of the cable strands in the saddle groove;
[0078] (5) The main tower shall not be deviated during the adjustment of the anchor span cable strand.
[0079] S2. Based on the model established in S1, collect measured parameters and establish an objective function based on the principle of stress-free length conservation of cable strands, geometric compatibility conditions, and mechanical equilibrium conditions.
[0080] S2.1, The collected measured parameters include: main tower offset. Temperature of the strand;
[0081] S2.2 Based on measured parameters and the principle of conservation of stress-free strand length, geometric compatibility and mechanical equilibrium conditions are analyzed for the main cable in the side span and the strand in the anchor span, respectively.
[0082] The stress-free lengths of the cable strands in the side spans and anchor spans are determined based on the "main cable form finding" method for suspension bridges, and can be denoted as follows: and The stress-free length is the core constraint (conservation principle) for all subsequent governing equations. The specific steps include:
[0083] S2.2.1, Geometric and mechanical analysis of the main cable in the side span;
[0084] First, to simplify the derivation process, we take the point of tangency between the main cable centerline and the main cable saddle at the side span as an example. Establish a local coordinate system with the origin, where The axis is horizontal to the left. The axis is vertically downward; definition The point of tangency between the main cable centerline and the cable saddle in the side span. and The corresponding tangent angles are respectively and ; and These are the radii of the arcs at the main cable saddle and the branch cable saddle, respectively; The angle of inclination of the cable saddle;
[0085] Secondly, the self-weight of the main cable is considered as a uniformly distributed load along the line after force equilibrium is achieved. The segment can be represented by the catenary equation:
[0086]
[0087] In the formula, Indicates the catenary coefficient of the main cable. , and These are the horizontal component of the main cable in the side span (kN) and the linear density (kN / m), respectively. The parameters are those for the side span catenary equation;
[0088] The geometric shape equation of the side span main cable is obtained through the catenary equation to describe the geometric shape of the side span main cable and establish the relationship between force and shape.
[0089] Next, calculate and This provides angle parameters for subsequent coordinate calculations. The calculation formula is as follows:
[0090]
[0091]
[0092] In the formula, For the catenary along The projected length of the axis;
[0093] Furthermore, establish the coordinates of key points in the global coordinate system, including: the center of the main cable saddle. of The coordinates are represented as: ,in, Center of the bridge completion stage of coordinate, To measure the main tower offset, The pre-offset of the main cable saddle; since the vertical offset of the main tower is negligible, the center of the circle... of The coordinates can be approximated as corresponding to the bridge completion stage. Same coordinates: ,in, Center of the bridge completion stage of Coordinates; Center of the saddle in the global coordinate system of and The coordinates can be represented as follows: and ,in, Center To the center of the rocker arm The distance;
[0094] Then the point of tangency arrive The horizontal and vertical distances are respectively:
[0095]
[0096]
[0097] Next, the stress-free length of the main cable in the side span is calculated segment by segment to provide the terms for the subsequent stress-free length conservation equation for the side span, including:
[0098] Catenary segment stress-free length for:
[0099]
[0100] In the formula, and These are the elastic modulus and cross-sectional area of the main cable, respectively.
[0101] Main cable saddle arc section stress-free length Since the frictional force on the main cable has a relatively small impact on the calculation of its stress-free length, it can usually be ignored within the range of manufacturing and construction errors of the main cable strands. It can be represented as:
[0102]
[0103] Main cable of the saddle arc section stress-free length for:
[0104]
[0105] S2.2.2, Geometric and mechanical analysis of anchor strands;
[0106] After the main cable turns and disperses through the cable saddle, it forms multiple independent spatial strands, which are anchored to the anchorages respectively. Therefore, it is necessary to analyze each strand of the anchorage span one by one. In the saddle groove of the cable saddle, except for the middle row of strands, the remaining strands are all spatial curves formed by the intersection of vertical bending and planar bending.
[0107] The cable saddle is composed of multiple vertical curved arcs with different radii. From the side span to the anchor span, the centers of each vertical curved arc are defined as follows: , , as well as The corresponding central angles are respectively , , as well as The radii of the strands are respectively , , as well as The dividing points are as follows: , and The starting and ending points of the cable-stayed flat bend are respectively and The vertical bend of the cable strand ends at... The corresponding tangent angle is To ensure that the cable strands are in a self-stabilizing state within the saddle groove, their horizontal bends must be included within the vertical bends. Let be the center of the horizontal bend arc of the cable strand, and the corresponding horizontal bend radius and horizontal bend angle are respectively and .
[0108] Furthermore, regarding the anchor span strands, based on geometric relationships, we can obtain:
[0109]
[0110] In the formula, and The starting points of the horizontal curves are respectively and anchor points The Y-coordinate; and They are the starting points of the horizontal curves. and the X coordinate of anchor point M, Specifically, it is expressed as follows: The planar bending angle and anchor point coordinates are obtained through geometric relationships, which are used to describe the planar bending geometry of the cable strands within the cable saddle.
[0111] Furthermore, because the anchor span cable strands consist of catenary segments Harmony and the circular arc segment of the saddle Composed of, with the vertical bend of the cable strand at the end point Establish a local coordinate system with the origin, where The angle between the axis and the horizontal direction is , The axis is vertically downward, and the cable strands are... The equation of the catenary can be expressed as:
[0112]
[0113] In the formula, The coefficient of the chain-link suspension is denoted as . , The horizontal component of the anchor cable strand is given in kN. Linear density of the strands / (kN / m); Given the parameters of the catenary equation for the anchor span, then based on geometric relationships, the tangent angle... It can be represented as: ;
[0114] Because the vertical curvature of the cable saddle groove is composed of multiple arcs of different radii, the endpoint of the vertical curvature of the cable strand... They may be located on different arc segments, which can be determined based on the tangent angle. Determine its global coordinates:
[0115] :
[0116]
[0117] :
[0118]
[0119] :
[0120]
[0121] :
[0122]
[0123] In the formula: and The endpoints of the vertical bends X and Z coordinates, and The center of each circle X and Z coordinates; and The center of each circle X and Z coordinates; and The center of each circle X and Z coordinates; and The center of each circle X and Z coordinates;
[0124] The specific relationships among the above parameters are as follows:
[0125]
[0126]
[0127]
[0128]
[0129]
[0130]
[0131] Furthermore, the endpoint of the vertical bend to anchor point The horizontal and vertical distances can be expressed as follows:
[0132]
[0133]
[0134] In the formula, Let M be the Z coordinate of the anchor point.
[0135] Then the catenary segment cable strand stress-free length It can be represented as:
[0136]
[0137] In the formula, For the catenary along The projected length of the axis;
[0138] Set the endpoint of the straight bend. and the end of the vertical bend All are located in the 4th arc segment. In the global coordinate system, the geometric equation of the cable strands within the saddle groove can be expressed as:
[0139]
[0140]
[0141]
[0142]
[0143]
[0144] In the formula, and The center of the horizontal bend of the cable strand is respectively X and Y coordinates; The starting point of the flat bend in the cable strand The X coordinate; Boundary point The X coordinate; Boundary point The X coordinate; Boundary point The X coordinate; The end point of the flat bend of the cable strand The X coordinate; The end point of the vertical bend in the cable strand The X coordinate;
[0145] The specific relationships among the above parameters are as follows:
[0146]
[0147]
[0148]
[0149]
[0150]
[0151] To fully describe the three-dimensional geometric path of the cable strand within the cable saddle;
[0152] Based on the geometric equation representation of the cable strands within the saddle groove, the cable strands of the circular arc segment of the cable saddle... actual length It can be represented in segments as follows:
[0153]
[0154]
[0155]
[0156]
[0157]
[0158] Summing the above equations, we can obtain the result of the formula. actual length Similarly, neglecting the effect of friction, according to Hooke's Law, its elastic elongation can be expressed as: Where A is the cross-sectional area of the anchor span cable strand; therefore, the cable strand stress-free length for: .
[0159] S2.2.3 Perform moment analysis on the cable saddle, including the weight of the main cable in the side span, the cable strands in the anchor span, and the self-weight of the cable saddle relative to the center of the rocker axis. The resulting torques are expressed as follows:
[0160]
[0161]
[0162]
[0163] In the formula, n is the total number of anchor cable strands; and The starting point of the vertical bend of the cable strand. and the end of the vertical bend Vertical force at the location; and The starting points of the vertical bends are respectively To the center of the rocker arm Horizontal and vertical distances; and The endpoints of the vertical bends To the center of the rocker arm Horizontal and vertical distances; From the center of gravity G of the saddle to the center of the rocker shaft Horizontal distance;
[0164] The above parameters are specifically represented as follows:
[0165]
[0166]
[0167]
[0168]
[0169]
[0170]
[0171]
[0172] In the formula: Let X be the coordinate of the center of gravity of the cable saddle.
[0173] S2.3 Solve the nonlinear equations generated by the analysis results;
[0174] The derivation process of S2.1~S2.2 involves 4n+4 basic unknown parameters (n is the total number of strands), as shown in Table 1:
[0175] Table 1: Basic Unknown Parameters
[0176]
[0177] Once the values of these parameters are determined, the influence matrix of the anchor span strands can be obtained;
[0178] Based on the geometric compatibility condition, the mechanical equilibrium condition, and the principle of stress-free length conservation, the following governing equations can be obtained:
[0179] The horizontal direction of the side span cable strands is closed:
[0180]
[0181] Closure of the height difference between the side span cable strands:
[0182]
[0183] The stress-free length of the side span cable strands is conserved.
[0184]
[0185] Anchor span cable strand horizontal bending angle constraint:
[0186]
[0187] Anchor span cable strands are closed in the horizontal direction:
[0188]
[0189] Anchor span cable strand elevation difference closure:
[0190]
[0191] The stress-free length of the anchor strand is conserved.
[0192]
[0193] Torque balance at the cable saddle:
[0194]
[0195] In the above formula, λ is the coefficient of linear expansion of the main cable material / ℃ -1 Δt represents the difference between the actual temperature T and the design temperature. The difference;
[0196] For 4n+4 governing equations, by shifting the right-hand side terms of each equation to the left-hand side, we can obtain their error functions. (1≤j≤4n+4), to ensure that each governing equation holds true, its error function should be as close to 0 as possible; therefore, the objective function is established as follows:
[0197]
[0198] The nonlinear GRG method is used to solve the objective function. The convergence accuracy of the objective function is set to be less than 10. -9 When the solution is obtained, the reliability and accuracy of the solution can be ensured, and the solution can be stopped.
[0199] S3. Based on the objective function, derive the influence matrix of the anchor span cable strands and solve for the optimal adjustment amount;
[0200] like Figure 2As shown, the derivation process includes: First, calculating the stress-free length of the main cable strands and measuring the main tower offset and strand temperature. Under the condition that the anchor surface coordinates are taken as design values, based on the geometric compatibility conditions, mechanical equilibrium conditions, and the principle of stress-free length conservation of the strands, establishing and solving the governing equations to obtain the initial parameter vector of the strands. Then, adjusting the coordinates of the m-th anchor span strand on the anchor surface to simulate the actual adjustment during construction, and calculating the adjusted parameter vector. Subtracting the initial parameter vector from the adjusted parameter vector yields the influence vector of that strand. Repeating the above process until m=n (n is the total number of anchor span strands) yields the influence vectors of all anchor span strands. Finally, combining the influence vectors of all strands forms the complete anchor span strand influence matrix D, expressed as:
[0201]
[0202] in, and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the first anchor span cable strand; and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the nth anchor span cable strand, respectively.
[0203] After obtaining the influence matrix D of the anchor span cable strands, the corresponding constraint equations can be further constructed based on the control requirements for anchor span cable force and cable saddle inclination angle in actual engineering projects.
[0204]
[0205] In the formula: Its component is the adjustment amount of each anchor span cable strand, and the subscript indicates the cable strand number; Let be the theoretical vector, where This represents the theoretical cable force across the anchor strand. This represents the theoretical value of the nth anchor span strand. The theoretical inclination angle of the cable saddle; Let be the measured vector, where This represents the measured cable force of the anchor strand. The measured value of the nth anchor span cable strand. The measured inclination angle of the cable saddle; This represents the error vector, which includes the error limit of the anchor span cable force. Error limit of the inclination angle of the cable saddle ;
[0206] Furthermore, the adjustment volume of the anchor span cable strand. The calculation can be transformed into solving the problem of finding the minimum value of a constrained nonlinear multivariable function. Therefore, the constraints can be further expressed as:
[0207]
[0208] In the formula, Represents the transformation matrix. , Represents the transformation vector. ;
[0209] Under the premise of satisfying the constraints, with the optimization objective of minimizing the relative errors between the adjusted anchor span cable force and the cable saddle inclination angle and their corresponding theoretical values, the governing equations can be constructed as follows:
[0210]
[0211] By moving the terms on the right side of the governing equation to the left side, we can obtain its error function. (1≤j≤n+1). To satisfy the optimization objective, the error function should be as close to 0 as possible. Based on this, the objective function is established as follows:
[0212]
[0213] The objective function can be solved using the fmincon function in MATLAB to obtain the anchor span strand adjustment amount that satisfies the constraints. .
[0214] To verify the present invention, such as Figure 3 As shown, the simulation was carried out using the Baidi City Yangtze River Bridge as the object. The Baidi City Yangtze River Bridge is a double-tower single-span steel box girder suspension bridge with a main span of 916m. On-site data was collected, and the results are shown in Table 3.
[0215] Table 3. Field Measured Data
[0216]
[0217] Based on on-site measured data and following the derivation process of this invention, the anchor span cable force of the suspension bridge during the "empty cable" stage was calculated under the condition that the anchor surface coordinates are the design values. The results are as follows: Figure 4 As shown in the figure, the cable force in the strands within the saddle groove gradually decreases from bottom to top and gradually increases from the center towards both sides, ranging from 302.1 to 488.1 kN. This result is consistent with the distribution pattern of cable force in the anchor span in existing studies, verifying the reliability of the calculation method presented in this paper. Furthermore, the theoretical value of the saddle inclination angle calculated based on measured data is 2.38°.
[0218] As shown in Table 3, the relative error between the measured and theoretical values of the cable saddle inclination angle is -5.9%. Therefore, the anchor span cable strands need to be adjusted to ensure that the stress on each cable strand is uniform in the completed state of the suspension bridge and to ensure that the cable saddle reaches the design position.
[0219] Considering that in actual construction, the adjustment of the anchor strand is usually achieved by rotating the anchor nut, the adjustment amount of the strand is taken as one rotation of the nut (corresponding to 4 mm).
[0220] Figure 5 To adjust the relative error of the anchor span cable force, theoretical calculations show that after adjustment using the method presented in this paper, the anchor span cable force is highly consistent with the theoretical value, and the error is negligible, verifying the theoretical feasibility of this method in achieving a one-time adjustment. The relative error range between the measured and theoretical values of the anchor span cable force is -0.74% to 0.91%, and the relative error of the cable saddle inclination angle is -0.84%. Overall, the relative errors of the anchor span cable force and the cable saddle inclination angle are both controlled within ±1%, meeting the engineering accuracy requirements. Furthermore, the construction procedure of "installing the clamping beam first and then adjusting the anchor span cable strands" effectively prevents slippage of the cable strands during the adjustment process, further verifying the feasibility and effectiveness of the method presented in this paper.
[0221] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, all modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope of the present invention. The technical content for which protection is sought in the present invention has been fully described in the claims.
Claims
1. A method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix, characterized in that, Includes the following steps: S1. Establish a local mechanical analysis model for the completed stage of a single-span suspension bridge. Establish a global coordinate system with the center of the rocker axis as the origin, define key geometric points and set constraints. S2. Based on the model established in S1, collect measured parameters and establish an objective function based on the principle of stress-free length conservation of cable strands, geometric compatibility conditions, and mechanical equilibrium conditions. S3. Based on the objective function, derive the influence matrix of the anchor span cable strands, solve for the optimal adjustment amount, and complete the construction adjustment.
2. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on the influence matrix according to claim 1, characterized in that: The constraints are set as follows: the cable strands are always in the elastic phase and obey Hooke's Law; The main cable strand is an ideal flexible cable, which only bears axial tension and is not subjected to axial compression or bending moment; the cross-sectional area of the main cable strand does not change with tension, and the axial tensile stiffness remains constant; during the adjustment of the anchor span cable strand, there is no relative slippage of the cable strand in the saddle groove. The main tower will not be displaced during the adjustment of the anchor span cable strands.
3. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 1, characterized in that: The steps in S2 include: S2.1 The measured parameters collected include: main tower offset and cable strand temperature; S2.2 Based on measured parameters and the principle of conservation of stress-free strand length, geometric compatibility and mechanical equilibrium conditions are analyzed for the main cable in the side span and the strand in the anchor span, respectively. S2.3 Solve the nonlinear equations generated from the analysis results.
4. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on the influence matrix according to claim 3, characterized in that: Step S2.2 includes: S2.2.1, Geometric and mechanical analysis of the main cable in the side span, including: establishing a local coordinate system with the point of tangency between the main cable centerline and the main cable saddle in the side span as the origin to obtain the catenary equation; calculating the tangent angle at the main cable saddle and the tangent angle at the cable saddle; establishing the coordinates of key points in the global coordinate system, including the coordinates of the center of the main cable saddle and the center of the cable saddle. Through analysis, the stress-free lengths of the side span main cable catenary segment, main cable saddle arc segment, and loose cable saddle arc segment were obtained; S2.2.2, Anchor span cable strand geometric and mechanical analysis, including: obtaining the horizontal bending angle of the anchor span cable strand based on geometric relationships; establishing the catenary segment of the anchor span cable strand; calculating the tangent angle of the anchor span cable strand to determine the global coordinates of the vertical bending endpoint; setting the horizontal bending endpoint and the vertical bending endpoint of the cable strand to be located on the same circular arc, and establishing a complete spatial geometric description of the cable strand in the cable saddle under the global coordinate system; The stress-free lengths of the suspended section of the anchor span and the arc section of the cable saddle were obtained through analysis. S2.2.3 Perform a moment analysis on the cable saddle, including the moment generated by the weight of the main cable in the side span, the cable strands in the anchor span, and the cable saddle itself on the center of the rocker shaft.
5. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 4, characterized in that: The calculation of the anchor span strand tangent angle to determine the global coordinates of the vertical bend endpoint includes: ； ； ； ； The four scenarios are represented as follows: ； ； ； ； In the above formula, The tangent angle at the starting point of the horizontal bend of the cable strand at the saddle point; The tangent angle of the anchor span cable strand; The angle of inclination of the cable saddle; and The X and Z coordinates of the endpoint of the vertical bend; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; and Center X-axis and Z-axis coordinates; , , as well as This represents the radius of the strand corresponding to the four circles.
6. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 5, characterized in that: The setting of the horizontal and vertical bend endpoints of the cable strand being located on the same arc, establishing a complete spatial geometric description of the cable strand within the saddle in the global coordinate system, wherein the same arc is the 4th arc segment; the complete spatial geometric description includes 5 spatial curves, represented as follows: ； ； ； ； ； ； In the formula, and The center of the horizontal bend of the cable strand is respectively X and Y coordinates; The starting point of the flat bend in the cable strand The X coordinate; The first dividing point The X coordinate; The second dividing point The X coordinate; The third dividing point The X coordinate; The end point of the flat bend of the cable strand The X coordinate; The end point of the vertical bend in the cable strand The X coordinate; The radius of the horizontal bend corresponding to the horizontal bend arc of the cable strand; This refers to the angle corresponding to the flat bend of the cable strand.
7. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 1, characterized in that: In S2.3, based on the geometric compatibility condition, mechanical equilibrium condition, and the principle of stress-free length conservation, the following closed control equations can be obtained: horizontal direction closed control equation for side span cable strands, height difference closed control equation for side span cable strands, stress-free length conservation control equation for side span cable strands, horizontal bending angle constraint control equation for anchor span cable strands, horizontal direction closed control equation for anchor span cable strands, height difference closed control equation for anchor span cable strands, stress-free length conservation control equation for anchor span cable strands, and moment balance control equation at the cable saddle. Based on 4n+4 control equations, where n is the total number of strands; For 4n+4 governing equations, by shifting the right-hand side terms of each equation to the left-hand side, we can obtain their error functions. To ensure that each governing equation holds true, its error function should be approximately equal to 0; therefore, the objective function is established as follows: ； The nonlinear GRG method is used to solve the objective function. The convergence accuracy of the objective function is set to be less than 10. -9 When the solution is obtained, the reliability and accuracy of the solution can be ensured, and the solution can be stopped.
8. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 1, characterized in that: The method for constructing the anchor span cable strand influence matrix in S3 is as follows: First, the stress-free length of the main cable strands is calculated, and the main tower offset and strand temperature are measured. Under the condition that the anchor surface coordinates are taken as the design value, the control equations are established and solved based on the geometric compatibility conditions, mechanical equilibrium conditions and stress-free length conservation principle of the strands to obtain the initial parameter vector of the strands. Subsequently, the coordinates of the m-th anchor strand on the anchor surface are adjusted by the length of one revolution of the anchor nut to simulate the actual adjustment during construction. The adjusted parameter vector is calculated, and the influence vector of the strand is obtained by subtracting the initial parameter vector from the adjusted parameter vector. Repeat the above process until m=n, where n is the total number of anchor span strands, to obtain the influence vector of all anchor span strands. Finally, combine the influence vectors of all strands to form the complete anchor span strand influence matrix.
9. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 8, characterized in that: In S3, the influence matrix D of the anchor span strand is expressed as: ； in, and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the first anchor span cable strand; and These represent the changes in cable force and saddle inclination angle of the nth cable strand after adjusting the nth anchor span cable strand, respectively.
10. The method for adjusting the construction of cable strands in the anchor span of a suspension bridge based on an influence matrix according to claim 9, characterized in that: The constraint condition for the influence matrix of the anchor strand is: ； In the formula, Adjustment amount for anchor span cable strands; This represents the theoretical cable force across the anchor strand; This represents the measured cable force of the anchor strand; This represents the error vector, which includes the error limit for the anchor span cable force and the error limit for the inclination angle of the cable saddle. The constraints are transformed into standard form as follows: ； In the formula, Represents the transformation matrix. , Represents the transformation vector. ; The governing equations are as follows: ; By moving the terms on the right side of the governing equation to the left side, we can obtain its error function. To meet the optimization objective, the error function should be approximately equal to 0. The objective function is established as follows: ； The objective function can be solved using MATLAB to obtain the anchor span strand adjustment amount that satisfies the constraints. .