A suspension bridge and a method for calculating the bridge alignment of the main cable of the suspension bridge

Abstract

The present invention relates to the technical field of bridge engineering and discloses a suspension bridge and a method for calculating the bridge alignment of the main cable of the suspension bridge. The method for calculating the bridge alignment of the main cable of the suspension bridge comprises the following steps: S100 preparing calculation parameters; S200 calculating the bridge alignment of the main cable of the main span; S300 calculating the bridge alignment of the main cable of the side span. The suspension bridge is designed based on the method for calculating the bridge alignment of the main cable of the suspension bridge. The method for calculating the bridge alignment of the suspension bridge and the main cable of the suspension bridge effectively reduces the complexity of calculation, avoids a large number of numerical iterative calculations of the commonly used methods, and significantly improves the calculation efficiency. The calculation accuracy of the main cable bridge coordinates can reach mm level, the calculation accuracy of the main cable internal force can reach more than 1 / 10000, and the calculation accuracy of the main cable length can reach more than 1 / 1000000. It is a high-efficiency and high-precision suspension bridge bridge alignment and construction control calculation method.

Description

Technical Field

[0001] The invention relates to the technical field of bridge engineering, and in particular to a suspension bridge and a method for calculating the bridge line shape of a main cable of the suspension bridge. Background Art

[0002] The accurate calculation of the main cable shape of the suspension bridge in its completed state is the key to the construction process control and precise erection of the suspension bridge.

[0003] When the main cable of a suspension bridge is only subjected to its own weight evenly distributed along its arc, the line shape is a catenary. If the weight of the main cable itself is ignored and only the weight of the bridge system evenly distributed in the horizontal direction is considered, the line shape of the main cable is a parabola.

[0004] Since the middle of the 19th century, experts and scholars have begun to seek analytical solutions to the linear shapes of the main cables of suspension bridges under the combined effects of their own weight and the weight of the bridge system and hangers, but no perfect solution has been obtained. Only complex parametric equation solutions have been obtained under the effects of the weight of both the main cable and the bridge system.

[0005] Recently, new progress has been made in the research on the main cable alignment of suspension bridges. For the first time, a high-precision approximate analytical method for the main cable alignment that simultaneously considers the constant load effects of the main cable, the bridge system and the hanger has been proposed. However, the constant load distribution pattern used in this method is still somewhat different from the actual situation of modern suspension bridges, which limits its practical application in engineering.

[0006] At present, the main cable shape calculation methods for suspension bridges in engineering practice mainly include semi-analytical methods such as the segmented parabola method or the segmented catenary method, and numerical calculation methods such as the finite element method. However, these methods have the disadvantages of complex calculation process, long calculation time, low efficiency, and difficulty for general professional and technical personnel to master. Summary of the invention

[0007] The technical problem to be solved by the present invention is that the existing methods for calculating the linear shape of the main cable of a suspension bridge have the disadvantages of complex calculation process, long calculation time, low efficiency and being difficult for general professional and technical personnel to master. The purpose is to provide a method for calculating the linear shape of the main cable of a suspension bridge to solve the above problems.

[0008] The present invention is achieved through the following technical solutions:

[0009] In a first aspect, the present invention provides a method for calculating the bridge line shape of the main cable of a suspension bridge, comprising the following steps:

[0010] S100 prepares calculation parameters;

[0011] S200 main span main cable bridge alignment calculation;

[0012] S300 side span main cable bridge alignment calculation;

[0013] Among them, in the calculation of the completed bridge alignment, based on the approximate alignment of the main span and the actual constant load of the main span, the calculation formula for the completed bridge alignment, internal force and main cable length is constructed.

[0014] In one possible design, the S200 main span main cable bridge alignment calculation includes the following steps:

[0015] S201: Based on the main span and main cable structure model of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦;

[0016] S202: construct a parabola and a catenary with the same span and sag as the main cable main span, and obtain the parabola equation and the catenary equation; based on the catenary equation, obtain the catenary parameter 𝛼 with boundary conditions;

[0017] S203: Calculate the length of the boom based on the parabola equation or the catenary equation, and calculate the weight of the boom based on the length of the boom;

[0018] Based on the arithmetic mean of the maximum and minimum values ​​of the main cable tension 𝑇(𝑥) of the main span, the approximate value of the unit length weight of the main cable after elastic deformation is obtained: ;

[0019] S204: Construct a simply supported beam 𝐴𝐵 with the same span as the main cable of the main span, apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝐴𝐵, and obtain the support reaction of the simply supported beam , shear force distribution along the span direction and bending moment distribution ;

[0020] S205: Based on S201-S204, the bridge-forming linear equation of the main span main cable, the derivative of the bridge-forming linear equation and the calculation formula of the main cable tension 𝑇(𝑥) are obtained;

[0021] S206: Based on the bridge line shape equation of the main cable of the main span, the stressed length of the main cable segment of the main span is obtained; based on the main cable tension 𝑇(𝑥) of the main span, the unstressed length of the main cable segment of the main span is obtained.

[0022] In one possible design, in S201, the origin of the rectangular coordinate system 𝑥𝑜𝑦 is directly below the 𝐴(𝐼𝑃) point on the top of the left tower and is at the same elevation as the lowest point of the main cable of the main span, the 𝑥 coordinate axis is horizontally rightward and the 𝑦 coordinate axis is vertically upward;

[0023] Based on the rectangular coordinate system 𝑥𝑜𝑦, let the span of the main span be 𝐿, the sag be 𝑓, and the unit length weight of the main cable of the main span in the unstressed state is ;

[0024] In S202, the parabola equation (1) and the catenary equation (2) are as follows:

[0025] ;

[0026] ;

[0027] Where cosh represents the hyperbolic cosine function, 𝛼 is the catenary parameter;

[0028] By boundary conditions The iterative calculation formula for 𝛼 is as follows:

[0029] ;

[0030] In the formula, arch represents the inverse hyperbolic cosine function;

[0031] Pick As the initial value, the value of parameter 𝛼 is obtained by iterative calculation using formula (3).

[0032] In one possible design, in S203, based on the main cable bridge structure model of the main span of the suspension bridge in S201, the main cable tension 𝑇(𝑥) at each point of the main cable acts in its tangent direction, the horizontal component of the main cable tension 𝑇(𝑥) is a constant and set to 𝐻, and 𝐻 is the minimum value of 𝑇(𝑥);

[0033] Based on formula (2), the tangent slope of the main cable at the tower top point 𝐼𝑃 is calculated, and the approximate value of the maximum value of 𝑇(𝑥) is obtained as ;

[0034] Based on the arithmetic mean of the maximum and minimum values, the approximate value of the weight per unit length of the main cable after elastic deformation is calculated :

[0035] ;

[0036] Where 𝐻 is the horizontal component of the main cable tension 𝑇(𝑥) at each point of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable.

[0037] In a possible design, S200 further includes a first intermediate derivation, where the first intermediate derivation includes the following steps:

[0038] S1: Based on formula (4), the main cable deadweight is approximately distributed according to formula (2), and the main cable dead load distribution function is obtained:

[0039] ;

[0040] Where cosh represents the hyperbolic cosine function;

[0041] S2: Take the left side of any calculation point 𝑥 on the main cable as the isolated body, and according to the moment balance condition around point 𝑥, we get:

[0042] ;

[0043] In the formula, is the vertical reaction force of the main cable at point 𝐴(𝐼𝑃) of the left tower; 𝑝(𝑥) represents the generalized dead load distribution function of other dead loads except the dead weight of the main cable;

[0044] S3: Based on formula (6), substitute the coordinates of the main cable at the left tower 𝐵(𝐼𝑃) point 𝑥= 𝐿, 𝑦= 𝑓 into formula (6) to obtain formula (7):

[0045] ;

[0046] Based on formula (6), the coordinates of the main cable at the lowest point are Substituting into equation (6), we obtain equation (8):

[0047] ;

[0048] S4: Based on formula (7), substitute formula (5) into formula (7) and simplify to obtain formula (9):

[0049] ;

[0050] In the formula, sinh represents the hyperbolic cosine function, is the support reaction force of the left end point of the virtual simply supported beam with the same span as the main cable under all other dead loads except the main cable dead load;

[0051] S5: Based on formula (8), substitute formula (5) and formula (9) into formula (8) to obtain the horizontal component 𝐻 of the main cable tension 𝑇(𝑥):

[0052] ;

[0053] In the formula, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable;

[0054] S6: Based on formula (10), formula (4) is substituted into formula (10) to obtain the displayed calculation formula (11) for the horizontal component of the main cable tension;

[0055] S7: Based on equation (6), equation (5) and equation (9) are substituted into equation (6) to obtain the bridge line shape equation of the main cable (12);

[0056] S8: Based on formula (12), derive formula (12) to obtain the derivative formula (13) of the bridge linear equation.

[0057] In one possible design, in S205, the horizontal component of the main cable tension 𝑇(𝑥) is a constant and is set to 𝐻. Based on the intermediate derivation, the explicit calculation formula of 𝐻 is obtained:

[0058] ;

[0059] In the formula, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable;

[0060] Based on the intermediate derivation, the bridge line shape equation of the main span main cable is formula (12), and the derivative of the bridge line shape equation is formula (13):

[0061] ;

[0062] ;

[0063] Based on the relationship between the main cable tension 𝑇(𝑥) and its horizontal component 𝐻, the calculation formula of the main cable tension 𝑇(𝑥) is obtained:

[0064] .

[0065] In one possible design, S206: The cable segment between any two adjacent concentrated force application points 𝑖 and 𝑖+ 1 of the main cable is a catenary, and its catenary parameters are , based on formula (13), the derivative of the left endpoint of the cable segment is obtained as:

[0066] ;

[0067] In the formula, Indicates greater than And infinitely close The value of

[0068] The linear equation of the cable segment between two adjacent concentrated force application points 𝑖 and 𝑖+ 1 on the main span is:

[0069] ;

[0070] Where arsh represents the inverse hyperbolic sine function; ;

[0071] Based on formula (16), the stress length of the cable segment between two adjacent concentrated force action points is obtained as:

[0072] ;

[0073] In the formula, ;

[0074] Based on formula (14), the main cable tension at the midpoint of the cable segment is obtained using formula (16): ;

[0075] Taking the main cable tension at the midpoint of the cable segment as the average tension of the cable segment, the stress-free length of the cable segment between two adjacent concentrated force action points is obtained based on the relationship between the main cable tension and the elastic elongation:

[0076] ;

[0077] Based on formula (18), the stress-free length of the main cable of the main span is obtained by summing up the lengths of all cable segments:

[0078] .

[0079] In one possible design, the calculation of the side span main cable bridge alignment includes the following steps:

[0080] S301: Based on the main cable bridge structure model of the side span of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦;

[0081] S302: Taking the main cable tension at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points as the approximate value of the tension at each point, an approximate formula (20) for the weight per unit length of the side span main cable considering the influence of elastic deformation is obtained;

[0082] Construct the catenary equation and obtain the approximate value of the catenary parameter 𝛽; Based on the approximate value of the catenary parameter 𝛽, obtain the catenary equation;

[0083] S303: If a hanger is provided on the side span, the length of the hanger is approximately calculated based on the catenary equation, and the weight of the hanger is calculated based on the length of the hanger;

[0084] S304: Construct a simply supported beam 𝑂𝐴 with the same span as the main cable of the side span, and apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝑂𝐴, and calculate the shear force distribution of the simply supported beam along the span direction and bending moment distribution ;

[0085] S305: Based on the linear shape and internal force analysis method of the main span main cable, the bridge linear shape equation (24) and its derivative (25) of the side span main cable are obtained:

[0086] Based on formula (14), formula (25) is substituted into formula (14) to calculate the tension of the side span main cable;

[0087] S306: Based on formula (25), the stress length of the main cable segment of the side span main cable and formula (27) are obtained; based on formula (27), the stress-free length of the main cable segment of the side span main cable is obtained, and the stress-free length of the side span main cable is obtained by summing the stress-free lengths of all cable segments of the side span.

[0088] In one possible design, in S301, the origin of the rectangular coordinate system 𝑥𝑜𝑦 is the main cable saddle of the side span IP At point , the 𝑥-axis is positive horizontally to the right, and the 𝑦-axis is positive vertically upward;

[0089] Based on the rectangular coordinate system 𝑥𝑜𝑦, let the side span be , from Sanso Saddle IP The theoretical height from point 𝐴(𝐼𝑃) to the top of the tower is , the unit length weight of the side span main cable in the unstressed state is ;

[0090] S302: Taking the main cable tension at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points as the approximate value of the tension at each point, the approximate formula for the unit length weight of the side span main cable considering the influence of elastic deformation is:

[0091] ;

[0092] Construct the catenary equation; evenly distribute all the dead loads acting on the side span main cable on the catenary, and obtain the approximate value of the catenary parameter 𝛽 as:

[0093] ;

[0094] In the formula, It is the sum of all other dead loads acting on the side span main cable except the dead weight of the main cable; It is the horizontal component of the tension of the main cable of the side span, and is equal to the horizontal component of the tension of the main cable of the main span;

[0095] Based on formula (21), the catenary equation is obtained:

[0096] ;

[0097] In the formula, .

[0098] In a possible design, S300 also includes a second intermediate derivation, and the steps of the second intermediate derivation are the same as those of the first intermediate derivation.

[0099] In a possible design, in S305, based on the second intermediate derivation, the bridge line shape equation (24) and its derivative (25) of the side span main cable are obtained:

[0100] ;

[0101] ;

[0102] For the tension of the main cable of the side span, based on formula (14), formula (25) is substituted into formula (14) to calculate the tension of the main cable of the side span.

[0103] In one possible design, in S306: Based on equation (25), for the cable segment between two adjacent concentrated force application points 𝑗 and 𝑗+ 1 on the side span, the derivative of the left end point of the cable segment is:

[0104] ;

[0105] In the formula, Indicates greater than And infinitely close The value of

[0106] Based on formula (26), the stress length of the cable segment between adjacent concentrated force points 𝑗 and 𝑗+ 1 is obtained as:

[0107] ;

[0108] In the formula, , ;

[0109] The stress-free length of the cable segment between adjacent concentrated force application points is:

[0110] ;

[0111] Based on formula (28), the stress-free length of all cable segments is summed up to obtain the stress-free length of the side span main cable:

[0112] .

[0113] In a possible design, the side span includes a left span and a right span, and the calculation methods of the main cable bridge alignment, internal force and length of the side spans of the two are the same, except that the coordinate axis directions of the rectangular coordinate system in S301 are opposite to each other.

[0114] In a possible design, in S100, the calculation parameters include geometric parameters, material property parameters, and dead load parameters.

[0115] In a second aspect, the present invention provides a suspension bridge designed based on the method for calculating the bridge line shape of the main cables of the suspension bridge.

[0116] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0117] The suspension bridge and the main cable of the suspension bridge bridge bridge line shape calculation method effectively reduces the complexity of calculation, avoids a large number of numerical iteration calculations in the current commonly used methods, and significantly improves the calculation efficiency. The calculation accuracy of the main cable bridge coordinates can reach mm level, the calculation accuracy of the main cable internal force reaches more than 1 / 10000, and the calculation accuracy of the main cable length reaches more than 1 / 1000000. It is a high-efficiency and high-precision suspension bridge bridge state line shape and construction control calculation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0119] Figure 1 Schematic diagram of the calculation model for the main span and main cable.

[0120] Figure 2 Schematic diagram of the virtual simply supported beam shear model of the main span and main cable.

[0121] Figure 3 Schematic diagram of the virtual simply supported beam bending moment model for the main span and main cable.

[0122] Figure 4 Schematic diagram of the calculation model for the main cable in the left span.

[0123] Figure 5 Schematic diagram of the virtual simply supported beam shear model of the main cable in the left span.

[0124] Figure 6 Schematic diagram of the virtual simply supported beam bending moment model of the main cable in the left span. DETAILED DESCRIPTION

[0125] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0126] In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is apparent to one of ordinary skill in the art that these specific details are not necessarily employed to practice the present invention. In other embodiments, in order to avoid obscuring the present invention, well-known structures, circuits, materials, or methods are not specifically described.

[0127] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment," "an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. In addition, it will be appreciated by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0128] In the description of the present invention, the directions or positional relationships indicated by terms such as “front”, “rear”, “left”, “right”, “up”, “down”, “vertical”, “horizontal”, “high”, “low”, “inside” and “outside” are based on the directions or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they should not be understood as limiting the scope of protection of the present invention.

[0129] Based on the design drawings, the known parameters for the calculation of the suspension bridge alignment are obtained, including geometric parameters, material performance parameters, and dead load parameters.

[0130] In specific calculation, the method for calculating the bridge line shape of the main cable of the suspension bridge includes the following steps:

[0131] S10 creates a computational model;

[0132] S20 constructs the main cable linear equation based on the main cable span and sag;

[0133] S30 obtains the weight of the boom and the weight per unit length of the main cable after considering elastic deformation based on the main cable linear equation;

[0134] S40 constructs a virtual simply supported beam and calculates the internal forces based on the main cable span;

[0135] S50 is based on S20-S40 to obtain the bridge alignment and internal forces of the main cable;

[0136] S60 obtains the stressed length of the main cable segment based on the bridge alignment of the main cable; and obtains the stress-free length of the main cable segment based on the internal force of the main cable.

[0137] Based on the above design scheme, S20 constructs the linear equation and assumes the completed bridge linear shape by using the approximate calculation method. Based on S20, combined with the prepared known parameters, the basic value and its calculation formula are obtained through S30 and S40. Based on the basic value and its calculation formula, the required suspension bridge linear shape calculation formula is obtained through S50 and S60, and the design value can be obtained by substituting the relevant parameters.

[0138] The following is an example of the calculation of the main span and main cable bridge line shape:

[0139] S201: Based on the main span and main cable structure model of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦;

[0140] S202: construct a parabola and a catenary with the same span and sag as the main cable main span, and obtain the parabola equation and the catenary equation; based on the catenary equation, obtain the catenary parameter 𝛼 with boundary conditions;

[0141] S203: Calculate the length of the boom based on the parabola equation or the catenary equation, and calculate the weight of the boom based on the length of the boom;

[0142] Based on the arithmetic mean of the maximum and minimum values ​​of the main cable tension 𝑇(𝑥) of the main span, the approximate value of the unit length weight of the main cable after elastic deformation is obtained: ;

[0143] S204: Construct a simply supported beam 𝐴𝐵 with the same span as the main cable of the main span, apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝐴𝐵, and obtain the support reaction of the simply supported beam , shear force distribution along the span direction and bending moment distribution ;

[0144] S205: Based on S201-S204, the bridge-forming linear equation of the main span main cable, the derivative of the bridge-forming linear equation and the calculation formula of the main cable tension 𝑇(𝑥) are obtained;

[0145] S206: Based on the bridge line shape equation of the main cable of the main span, the stressed length of the main cable segment of the main span is obtained; based on the main cable tension 𝑇(𝑥) of the main span, the unstressed length of the main cable segment of the main span is obtained.

[0146] like Figure 1-Figure 3 As shown, the structural model of the main span of the suspension bridge and the rectangular coordinate system 𝑥𝑜𝑦 are shown in Figure 1. It has the left tower top 𝐴(𝐼𝑃) point and the right tower top 𝐵(𝐼𝑃) point on both sides, and the lowest point of the main span cable in the middle. Among them, let the main span be 𝐿, the sag be 𝑓, and the unit length weight of the main span cable in the stress-free state be For the rectangular coordinate system 𝑥𝑜𝑦,

[0147] The origin is directly below the 𝐴(𝐼𝑃) point on the top of the left tower and is at the same elevation as the lowest point of the main cable of the main span. The 𝑥-coordinate axis is positive horizontally to the right, and the 𝑦-coordinate axis is positive vertically upward.

[0148] The total dead load acting on the main cable is divided into two parts: the dead weight of the main cable and other dead loads. The dead weight of the main cable is evenly distributed along the length of the main cable. Other dead loads include the force transmitted to the suspender by the bridge system and the weight of the suspender, cable clamps, and auxiliary structures, and can be regarded as a series of concentrated forces acting on different points on the main cable. .

[0149] It is worth noting that among other constant loads, except for the weight of the hanger, the other parameters are generally known before calculating the bridge alignment of the main cable. Since the weight of the hanger is related to its length, it is necessary to know the bridge alignment of the main cable before it can be accurately calculated.

[0150] The above is the preparatory work for the implementation of the method for calculating the bridge line shape of the main cable of the suspension bridge. Now let’s start the calculation:

[0151] Construct a parabola and catenary with the same span and sag as the main cable, where the parabola equation (1) and catenary equation (2) are as follows:

[0152] ;

[0153] ;

[0154] Where cosh represents the hyperbolic cosine function, 𝛼 is the catenary parameter;

[0155] By boundary conditions The iterative calculation formula for 𝛼 is as follows:

[0156] ;

[0157] Where arch represents the inverse hyperbolic cosine function.

[0158] Pick As the initial value, the value of parameter 𝛼 is obtained by iterative calculation using formula (3).

[0159] It is easy to understand that when the main cable shape is unknown, the distribution of the main cable's deadweight along the coordinate axis is also unknown. Although both equations (1) and (2) have the same span and verticality as the main cable, if equations (1) and (2) are used as the main cable shape, it is still difficult to meet the construction control and high-precision erection requirements of long-span suspension bridges. However, if the main cable deadweight is approximately calculated according to equation (1) or (2), the main cable deadweight error and the final main cable shape calculation error will be very small.

[0160] Based on this, the following assumption is adopted in the calculation method of the bridge line shape of the main cable of the suspension bridge: the self-weight of the main cable of the suspension bridge is approximately calculated by distributing on the parabola represented by formula (1) or the catenary represented by formula (2). Furthermore, considering that the use of the catenary equation will greatly simplify the calculation process, the self-weight of the main cable of the suspension bridge is approximately regarded as being distributed on the catenary represented by formula (2).

[0161] In addition, the length of the suspender required for calculating the weight of the suspender is also approximately calculated according to the main cable line shape using formula (1) or formula (2). Because the weight per unit length of the suspender is very small, this approximation will have little effect on the calculation accuracy of the main cable bridge line shape.

[0162] In addition, the main cable is subjected to elastic deformation and its weight per unit length becomes smaller. The change is proportional to the main cable tension 𝑇(𝑥). In modern suspension bridges, the change between the maximum value (at the tower top 𝐼𝑃 point) and the minimum value (at the lowest point of the main cable) of the main cable tension generally does not exceed 10%. Moreover, the change in the unit length of the main cable caused by elastic deformation is very small. Therefore, only the influence of the average value of the main cable tension on its weight per unit length is considered, that is, it is approximately considered that the weight per unit length of the main cable after elastic deformation is It is still a constant. This approximate treatment only ignores the high-order small quantities of the main cable constant load, so the impact on the main cable bridge line shape and internal force calculation is also very small.

[0163] like Figure 1 As shown in the figure, the main cable tension 𝑇(𝑥) at each point of the main cable acts in the tangent direction. The horizontal component of the main cable tension 𝑇(𝑥) is a constant and set to 𝐻, and 𝐻 is the minimum value of 𝑇(𝑥). Based on formula (2), the tangent slope of the main cable at the tower vertex is calculated, and the approximate value of the maximum value of 𝑇(𝑥) is ; Based on the arithmetic mean of the maximum and minimum values, the approximate value of the unit length weight of the main cable after elastic deformation is calculated :

[0164] ;

[0165] Where 𝐻 is the horizontal component of the main cable tension 𝑇(𝑥) at each point of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable.

[0166] Based on formula (4), the main cable deadweight is approximately distributed according to formula (2), and the main cable dead load distribution function 𝜂(𝑥) is approximately expressed as:

[0167]

[0168] Where cosh represents the hyperbolic cosine function.

[0169] For the convenience of description, the concept of generalized function is introduced below, and other dead loads except the dead weight of the main cable are taken as Etc., expressed as the main cable dead load distribution function 𝑝(𝑥).

[0170] As shown in Figure 1, let the vertical reaction force of the main cable at the left tower point 𝐴(𝐼𝑃) be , for any calculation point 𝑥 on the main cable, take its left side as the isolated body, and the moment balance condition around point 𝑥 is obtained:

[0171] ;

[0172] Based on formula (6), substitute the coordinates of the main cable at the left tower 𝐵(𝐼𝑃) point 𝑥= 𝐿, 𝑦= 𝑓 into formula (6) to obtain formula (7):

[0173] ;

[0174] Based on formula (6), the coordinates of the main cable at the lowest point are Substituting into equation (6), we obtain equation (8):

[0175] ;

[0176] Based on formula (7), formula (5) is substituted into formula (7) and simplified to obtain formula (9):

[0177] ;

[0178] In the formula, sinh represents the hyperbolic cosine function, It is the support reaction force at the left end point of a virtual simply supported beam with the same span as the main cable under the action of all other constant loads except the main cable constant load.

[0179] Based on formula (8), formula (5) and formula (9) are substituted into formula (8) to obtain the horizontal component 𝐻 of the main cable tension 𝑇(𝑥):

[0180] ;

[0181] In the formula, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable;

[0182] Based on formula (10), formula (4) is substituted into formula (10) to obtain the explicit calculation formula (11) of the horizontal component 𝐻 of the main cable tension 𝑇(𝑥):

[0183] ;

[0184] In the formula, is the mid-span bending moment of the virtual simply supported beam under all other constant loads except the deadweight of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable.

[0185] Based on the intermediate derivation, the bridge line shape equation of the main span main cable is formula (12), and the derivative of the bridge line shape equation is formula (13):

[0186] ;

[0187] ;

[0188] In the formula, , are the bending moment and shear force of the virtual simply supported beam under all other dead loads except the main cable dead load, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable, see Figures 2 and Figure 3 .

[0189] Based on the relationship between the main cable tension 𝑇(𝑥) and its horizontal component 𝐻, the calculation formula of the main cable tension 𝑇(𝑥) is obtained:

[0190] ;

[0191] Thus, the bridge alignment and internal force of the main span main cable are obtained, and the length of the main span main cable is further calculated as follows:

[0192] As shown in Figure 1, the cable segment between any two adjacent concentrated force points 𝑖 and 𝑖+ 1 of the main cable is a catenary, and its catenary parameters are , based on formula (13), the derivative of the left endpoint of the cable segment is obtained as:

[0193] ;

[0194] In the formula, Indicates greater than And infinitely close The value of

[0195] The linear equation of the cable segment between two adjacent concentrated force application points 𝑖 and 𝑖+ 1 on the main span is:

[0196] ;

[0197] Where arsh represents the inverse hyperbolic sine function; ;

[0198] Based on formula (16), the stress length of the cable segment between two adjacent concentrated force action points is obtained as:

[0199] ;

[0200] In the formula, ;

[0201] Based on formula (14), the main cable tension at the midpoint of the cable segment is obtained using formula (16): ;

[0202] Taking the main cable tension at the midpoint of the cable segment as the average tension of the cable segment, the stress-free length of the cable segment between two adjacent concentrated force action points is obtained based on the relationship between the main cable tension and the elastic elongation:

[0203] ;

[0204] Based on formula (18), the stress-free length of the main cable of the main span is obtained by summing up the lengths of all cable segments:

[0205] .

[0206] Based on the above design scheme, the calculation of the bridge alignment of the main span and main cable of the suspension bridge is completed and the values ​​of relevant parameters are obtained.

[0207] It is worth noting that the "main cable" mentioned above refers specifically to the main cable of the main span of the suspension bridge. The subsequent explanation of the calculation of the bridge alignment of the side span main cable also involves the "main cable", and the "main cable" here specifically refers to the main cable of the side span of the suspension bridge. If the main cable of the main span of the suspension bridge is involved, it will be explained before the main cable to indicate the location of the main cable.

[0208] The following is an explanation of the calculation of the main cable bridge line shape of the side span:

[0209] The calculation of the side span main cable bridge alignment includes the following steps:

[0210] S301: Based on the main cable bridge structure model of the side span of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦;

[0211] S302: Taking the main cable tension at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points as the approximate value of the tension at each point, an approximate formula (20) for the weight per unit length of the side span main cable considering the influence of elastic deformation is obtained;

[0212] Construct the catenary equation and obtain the approximate value of the catenary parameter 𝛽; Based on the approximate value of the catenary parameter 𝛽, obtain the catenary equation;

[0213] S303: If a hanger is provided on the side span, the length of the hanger is approximately calculated based on the catenary equation, and the weight of the hanger is calculated based on the length of the hanger;

[0214] S304: Construct a simply supported beam 𝑂𝐴 with the same span as the main cable of the side span, and apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝑂𝐴, and calculate the shear force distribution of the simply supported beam along the span direction and bending moment distribution ;

[0215] S305: Based on the linear shape and internal force analysis method of the main span main cable, the bridge linear shape equation (24) and its derivative (25) of the side span main cable are obtained:

[0216] Based on formula (14), formula (25) is substituted into formula (14) to calculate the tension of the side span main cable;

[0217] S306: Based on formula (25), the stress length of the main cable segment of the side span main cable and formula (27) are obtained; based on formula (27), the stress-free length of the main cable segment of the side span main cable is obtained, and the stress-free length of the side span main cable is obtained by summing the stress-free lengths of all cable segments of the side span.

[0218] Specifically, as shown in Figures 4 to 6, the left span is used as an example for explanation:

[0219] The structural model of the main cable of the left span of the suspension bridge and the rectangular coordinate system 𝑥𝑜𝑦 are shown in Figure 4, which has the left tower top 𝐴(𝐼𝑃) point on the right and the left span main cable saddle on the left. IP Point, namely 𝑂(𝐼𝑃) point. Among them, let the side span be , from Sanso Saddle IP The theoretical height from point 𝐴(𝐼𝑃) to the top of the tower is , the unit length weight of the side span main cable in the unstressed state is . For the rectangular coordinate system 𝑥𝑜𝑦, its origin is the point 𝑂(𝐼𝑃) of the left span main cable saddle, the 𝑥 coordinate axis is horizontally positive to the right, and the 𝑦 coordinate axis is vertically positive upward.

[0220] Furthermore, according to the principle of mutual balance of horizontal forces on both sides of the tower top, the horizontal component of the tension of the main cable of the side span is equal to the horizontal component of the tension of the main cable of the main span, and The tension of the side span main cable at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points is taken as the approximate value of the tension at each point. The approximate formula for the weight per unit length of the side span main cable considering the influence of elastic deformation is:

[0221] ;

[0222] For the analysis of the dead load at the left span, please refer to the analysis in the calculation of the main span main cable bridge line shape, which will not be repeated here. According to the conclusion of the calculation of the main span main cable bridge line shape, a catenary close to the actual line shape of the left span main cable is first constructed as the basis for approximate calculation of the dead load distribution of the side span main cable. The two end point positions and horizontal component force of the catenary are consistent with the actual situation of the side span main cable. All the dead loads acting on the side span main cable are evenly distributed on the catenary, and the approximate value of the catenary parameter 𝛽 is obtained as:

[0223] ;

[0224] In the formula, It is the sum of all other dead loads acting on the side span main cable except the dead weight of the main cable; It is the horizontal component of the tension of the main cable of the side span, and is equal to the horizontal component of the tension of the main cable of the main span;

[0225] For the other dead loads in the left span except the dead weight of the main cable, refer to the derivation of equations (5) to (11) in the calculation of the bridge line shape of the main span main cable, and combine with equation (21) to obtain the catenary equation:

[0226] ;

[0227] In the formula, .

[0228] Similarly, a method similar to that used in the calculation of the bridge alignment of the main span main cable is used to obtain the bridge alignment equation (24) and its derivative (25) of the side span main cable:

[0229] ;

[0230] ;

[0231] Based on formula (14), formula (25) is substituted into formula (14) to calculate the tension of the side span main cable, that is, the derivative of the side span main cable linear equation is obtained: Then, substitute into formula (14) to calculate the tension of the side span main cable.

[0232] Thus, the bridge alignment and internal force of the left span main cable are obtained, and the length of the left span main cable is further calculated. That is, the steps and related formulas of the second intermediate derivation refer to the first intermediate derivation, and the calculation formula of the left span main cable length can be obtained. Specifically:

[0233] like Figure 4 As shown, based on formula (25), for the cable segment between two adjacent concentrated force application points 𝑗 and 𝑗+ 1 on the side span, the derivative of the left end point of the cable segment is:

[0234] ;

[0235] In the formula, Indicates greater than And infinitely close The value of

[0236] Based on formula (26), the stress length of the cable segment between adjacent concentrated force points 𝑗 and 𝑗+ 1 is obtained as:

[0237] ;

[0238] In the formula, , ;

[0239] The stress-free length of the cable segment between adjacent concentrated force application points is:

[0240] ;

[0241] Based on formula (28), the stress-free length of all cable segments is summed up to obtain the stress-free length of the side span main cable:

[0242] .

[0243] Based on the above design scheme, the calculation of the bridge alignment of the main cable of the left span of the suspension bridge is completed and the values ​​of relevant parameters are obtained.

[0244] It is easy to understand that the side span includes the left span and the right span. The calculation methods of the bridge alignment, internal force and length of the main cables of the two side spans are the same. Only the directions of the 𝑥-coordinate axes of the rectangular coordinate system 𝑥𝑜𝑦 in S301 are opposite to each other.

[0245] Taking the above-mentioned calculation of the main cable bridge shape of the left span as the basis, the direction of the coordinate axis is set to the opposite direction, and the calculation method and formula of the main cable bridge shape, internal force and length of the left span can be applied to complete the calculation of the main cable bridge shape of the right span of the suspension bridge.

[0246] Furthermore, in a suspension bridge, a suspender is provided at the main span, so the weight of the suspender must be calculated in the implementation of the main span main cable bridge alignment calculation. However, for the side span, the suspender can be set selectively, so in the implementation of the side span main cable bridge alignment calculation, whether to calculate the weight of the suspender should be selected according to the actual situation.

[0247] In summary, in the method for calculating the bridge alignment of the main cable of a suspension bridge, a similar calculation method is used for the main span and the side span, that is, the calculation of the bridge alignment includes the following steps:

[0248] S10 creates a computational model;

[0249] S20 constructs the main cable linear equation based on the main cable span and sag;

[0250] S30 obtains the weight of the boom and the weight per unit length of the main cable after considering elastic deformation based on the main cable linear equation;

[0251] S40 constructs a virtual simply supported beam and calculates the internal forces based on the main cable span;

[0252] S50 is based on S20-S40 to obtain the bridge alignment and internal forces of the main cable;

[0253] S60 obtains the stressed length of the main cable segment based on the bridge alignment of the main cable; and obtains the stress-free length of the main cable segment based on the internal force of the main cable.

[0254] Although the main span and side span are slightly different for different parts of the suspension bridge, please refer to the above description of the calculation of the main span main cable bridge alignment and the calculation of the left span main cable bridge alignment, but the methods are basically the same, and the previous calculation is inspiring and reference for the subsequent calculation. For example, the inspiration of the first intermediate derivation to the second intermediate derivation makes the subsequent calculation simpler and more efficient, effectively reduces the complexity of the calculation, avoids the large number of numerical iterative calculations of the commonly used methods, and significantly improves the calculation efficiency. At the same time, the calculation accuracy of the main cable bridge coordinates of the suspension bridge main cable bridge alignment calculation method can reach mm level, the calculation accuracy of the main cable internal force reaches more than 1 / 10000, and the calculation accuracy of the main cable length reaches more than 1 / 1000000. It is a high-efficiency and high-precision suspension bridge bridge alignment and construction control calculation method.

[0255] Furthermore, the present embodiment also provides a suspension bridge, which is designed based on the suspension bridge main cable bridge line shape calculation method.

[0256] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the bridge line shape of the main cable of a suspension bridge, characterized in that: The following steps are involved: S100 prepares calculation parameters; S200 main span main cable bridge alignment calculation; S300 side span main cable bridge alignment calculation; In the calculation of the completed bridge alignment, the calculation formulas for the completed bridge alignment, internal force and main cable length are constructed based on the approximate alignment of the main span and the actual dead load of the main span. The S200 main span main cable bridge alignment calculation includes the following steps: S201: Based on the main span and main cable structure model of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦; S202: construct a parabola and a catenary with the same span and sag as the main cable main span, and obtain the parabola equation and the catenary equation; based on the catenary equation, obtain the catenary parameter 𝛼 with boundary conditions; S203: Calculate the length of the boom based on the parabola equation or the catenary equation, and calculate the weight of the boom based on the length of the boom; Based on the arithmetic mean of the maximum and minimum values ​​of the main cable tension 𝑇(𝑥) of the main span, the approximate value of the unit length weight of the main cable after elastic deformation is obtained: ; S204: Construct a simply supported beam 𝐴𝐵 with the same span as the main cable of the main span, apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝐴𝐵, and obtain the support reaction of the simply supported beam , shear force distribution along the span direction and bending moment distribution ; S205: Based on S201-S204, the bridge-forming linear equation of the main span main cable, the derivative of the bridge-forming linear equation and the calculation formula of the main cable tension 𝑇(𝑥) are obtained; S206: Based on the bridge line shape equation of the main cable of the main span, the stressed length of the main cable segment of the main span is obtained; based on the main cable tension 𝑇(𝑥) of the main span, the unstressed length of the main cable segment of the main span is obtained; The calculation of the side span main cable bridge alignment includes the following steps: S301: Based on the bridge structure model of the side span main cable of the suspension bridge, establish the rectangular coordinate system 𝑥𝑜𝑦; S302: Taking the main cable tension at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points as the approximate value of the tension at each point, an approximate formula for the weight per unit length of the side span main cable considering the influence of elastic deformation is obtained; Construct the catenary equation and obtain the approximate value of the catenary parameter 𝛽; Based on the approximate value of the catenary parameter 𝛽, obtain the catenary equation; S303: If a hanger is provided on the side span, the length of the hanger is approximately calculated based on the catenary equation, and the weight of the hanger is calculated based on the length of the hanger; S304: Construct a simply supported beam 𝑂𝐴 with the same span as the main cable of the side span, and apply all other dead loads except the dead weight of the main cable to the simply supported beam 𝑂𝐴, and calculate the shear force distribution of the simply supported beam along the span direction and bending moment distribution ; S305: Based on the linear shape and internal force analysis method of the main span main cable, the linear shape equation of the side span main cable and its derivative are obtained: Based on the calculation formula of the main cable tension 𝑇(𝑥), the derivative of the bridge linear equation is substituted into the calculation formula of the main cable tension 𝑇(𝑥) to calculate the tension of the side span main cable; S306: Based on the derivative of the bridge linear equation, the stressed length of the main cable segment of the side span main cable is obtained; based on the stressed length of the main cable segment of the side span main cable, the unstressed length of the main cable segment of the side span main cable is obtained, and the unstressed length of the side span main cable is obtained by summing up the unstressed lengths of all cable segments of the side span.

2. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 1 is characterized in that: In S201, the origin of the rectangular coordinate system 𝑥𝑜𝑦 is directly below the 𝐴(𝐼𝑃) point on the left tower top and is at the same elevation as the lowest point of the main cable of the main span. The 𝑥 coordinate axis is positive horizontally to the right, and the 𝑦 coordinate axis is positive vertically upward; Based on the rectangular coordinate system 𝑥𝑜𝑦, let the span of the main span be 𝐿, the sag be 𝑓, and the unit length weight of the main cable of the main span in the unstressed state is ; In S202, the parabola equation (1) and the catenary equation (2) are as follows: ； ； Where cosh represents the hyperbolic cosine function, 𝛼 is the catenary parameter; By boundary conditions The iterative calculation formula for 𝛼 is as follows: ； In the formula, arch represents the inverse hyperbolic cosine function; Pick As the initial value, the value of parameter 𝛼 is obtained by iterative calculation using formula (3).

3. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 2 is characterized in that: In S203, based on the main cable bridge structure model of the main span of the suspension bridge in S201, the main cable tension 𝑇(𝑥) at each point of the main cable acts in its tangent direction, the horizontal component of the main cable tension 𝑇(𝑥) is a constant and set to 𝐻, and 𝐻 is the minimum value of 𝑇(𝑥); Based on formula (2), the tangent slope of the main cable at the tower top point 𝐼𝑃 is calculated, and the approximate value of the maximum value of 𝑇(𝑥) is obtained as ; Based on the arithmetic mean of the maximum and minimum values, the approximate value of the weight per unit length of the main cable after elastic deformation is calculated : ； Where 𝐻 is the horizontal component of the main cable tension 𝑇(𝑥) at each point of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable.

4. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 3 is characterized in that: S200 further includes a first intermediate derivation, which includes the following steps: S1: Based on formula (4), the main cable deadweight is approximately distributed according to formula (2), and the main cable dead load distribution function is obtained: ； Where cosh represents the hyperbolic cosine function; S2: Take the left side of any calculation point 𝑥 on the main cable as the isolated body, and according to the moment balance condition around point 𝑥, we get: ； In the formula, is the vertical reaction force of the main cable at point 𝐴(𝐼𝑃) of the left tower; 𝑝(𝑥) represents the generalized dead load distribution function of other dead loads except the dead weight of the main cable; S3: Based on formula (6), substitute the coordinates of the main cable at the left tower 𝐵(𝐼𝑃) point 𝑥 = 𝐿, 𝑦 = 𝑓 into formula (6) to obtain formula (7): ； Based on formula (6), the coordinates of the main cable at the lowest point are Substituting into equation (6), we obtain equation (8): ； S4: Based on formula (7), substitute formula (5) into formula (7) and simplify to obtain formula (9): ； In the formula, sinh represents the hyperbolic cosine function, is the support reaction force of the left end point of the virtual simply supported beam with the same span as the main cable under all other dead loads except the main cable dead load; S5: Based on formula (8), substitute formula (5) and formula (9) into formula (8) to obtain the horizontal component 𝐻 of the main cable tension 𝑇(𝑥): ； In the formula, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable; S6: Based on formula (10), formula (4) is substituted into formula (10) to obtain the displayed calculation formula (11) for the horizontal component of the main cable tension; S7: Based on equation (6), equation (5) and equation (9) are substituted into equation (6) to obtain the bridge line shape equation of the main cable (12); S8: Based on formula (12), derive formula (12) to obtain the derivative formula (13) of the bridge linear equation.

5. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 4 is characterized in that: In S205, the horizontal component of the main cable tension 𝑇(𝑥) is a constant and is set to 𝐻. Based on the intermediate derivation, the displayed calculation formula of 𝐻 is obtained: ； In the formula, is the mid-span bending moment of the virtual simply supported beam under all other dead loads except the dead weight of the main cable; 𝐸 is the elastic modulus of the main cable; 𝐴 is the calculated cross-sectional area of ​​the main cable; Based on the intermediate derivation, the bridge line shape equation of the main span main cable is formula (12), and the derivative of the bridge line shape equation is formula (13): ； ； Based on the relationship between the main cable tension 𝑇(𝑥) and its horizontal component 𝐻, the calculation formula of the main cable tension 𝑇(𝑥) is obtained: 。 6. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 5 is characterized in that: S206: The cable segment between any two adjacent concentrated force points 𝑖 and 𝑖 + 1 of the main cable is a catenary, and its catenary parameters are , based on formula (13), the derivative of the left endpoint of the cable segment is obtained as: ； In the formula, Indicates greater than And infinitely close The value of The linear equation of the cable segment between two adjacent concentrated force application points 𝑖 and 𝑖 + 1 on the main span is: ； Where arsh represents the inverse hyperbolic sine function; ; Based on formula (16), the stress length of the cable segment between two adjacent concentrated force action points is obtained as: ； In the formula, ; Based on formula (14), the main cable tension at the midpoint of the cable segment is obtained using formula (16): ; Taking the main cable tension at the midpoint of the cable segment as the average tension of the cable segment, the stress-free length of the cable segment between two adjacent concentrated force action points is obtained based on the relationship between the main cable tension and the elastic elongation: ； Based on formula (18), the stress-free length of the main cable of the main span is obtained by summing up the lengths of all cable segments: 。 7. The method for calculating the bridge alignment of the main cable of a suspension bridge according to claim 1, characterized in that: In S301, the origin of the rectangular coordinate system 𝑥𝑜𝑦 is the main cable saddle of the side span IP At point , the 𝑥-axis is positive horizontally to the right, and the 𝑦-axis is positive vertically upward; Based on the rectangular coordinate system 𝑥𝑜𝑦, let the side span be , from Sanso Saddle IP The theoretical height from point 𝐴(𝐼𝑃) to the top of the tower is , the unit length weight of the side span main cable in the unstressed state is ; S302: Taking the main cable tension at the point where the tangent direction of the side span main cable is parallel to the line connecting the two end points as the approximate value of the tension at each point, the approximate formula for the unit length weight of the side span main cable considering the influence of elastic deformation is: ； Construct the catenary equation; evenly distribute all the dead loads acting on the side span main cable on the catenary, and obtain the approximate value of the catenary parameter 𝛽 as: ； In the formula, It is the sum of all other dead loads acting on the side span main cable except the dead weight of the main cable; It is the horizontal component of the tension of the main cable of the side span, and is equal to the horizontal component of the tension of the main cable of the main span; Based on formula (21), the catenary equation is obtained: ； In the formula, .

8. The method for calculating the bridge alignment of the main cable of a suspension bridge according to claim 7, characterized in that: S300 also includes a second intermediate derivation, and the steps of the second intermediate derivation are the same as those of the first intermediate derivation.

9. The method for calculating the bridge alignment of the main cable of a suspension bridge according to claim 8, characterized in that: In S305, based on the second intermediate derivation, the bridge line shape equation (24) and its derivative (25) of the side span main cable are obtained: ； ； For the tension of the main cable of the side span, based on formula (14), formula (25) is substituted into formula (14) to calculate the tension of the main cable of the side span.

10. The method for calculating the bridge line shape of the main cable of a suspension bridge according to claim 9, characterized in that: In S306: Based on equation (25), for the cable segment between two adjacent concentrated force application points 𝑗 and 𝑗 + 1 on the side span, the derivative of the left end point of the cable segment is: ； In the formula, Indicates greater than And infinitely close The value of Based on formula (26), the stress length of the cable segment between adjacent concentrated force points 𝑗 and 𝑗 + 1 is obtained as: ； In the formula, , ; The stress-free length of the cable segment between adjacent concentrated force application points is: ； Based on formula (28), the stress-free length of all cable segments is summed up to obtain the stress-free length of the side span main cable: 。 11. The method for calculating the bridge alignment of the main cable of a suspension bridge according to claim 10, characterized in that: The side span includes the left span and the right span. The calculation methods of the main cable bridge alignment, internal force and length of the side spans are the same, except that the coordinate axis directions of the rectangular coordinate system in S301 are opposite to each other.

12. The method for calculating the bridge line shape of the main cable of a suspension bridge according to any one of claims 7 to 11, characterized in that: In S100, the calculation parameters include geometric parameters, material performance parameters and dead load parameters.

13. A suspension bridge, characterized in that: A method for calculating the bridge line shape of the main cable of a suspension bridge is designed based on any one of claims 1-12.

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