A method for selecting size parameters of anchor webs in cable hoisting systems

Abstract

The present invention provides a method for selecting the size parameters of the anchor web of a cable hoisting system. The method simplifies the force calculation of the anchor web into a plane stress problem, constructs a total stress function using a binary polynomial, obtains stress component expressions through partial differentiation, and then substitutes the compatibility equations and boundary conditions to solve the undetermined coefficients in the stress component expressions, thereby obtaining the distribution of the stress field within the plane of the anchor web, thereby providing a basis for selecting design size parameters such as the length and height of the anchor web. Compared with previous methods for calculating the force of anchors, this method can obtain a more accurate calculation structure for the anchor structure, enabling localized and refined design. At the same time, the calculation formula only needs to include the preset length and height of the anchor web to determine whether the anchor web under the preset size meets the construction requirements. Therefore, the method has general applicability and applicability.

Description

Technical Field

[0001] The invention relates to a cable hoisting system for a steel tube arch bridge, in particular to a method for selecting size parameters of a ground anchor web of the cable hoisting system. Background Art

[0002] Cable hoisting systems are used in the construction of concrete-filled steel tube (CFST) arch bridges. Ground anchors are a crucial component of these systems, stabilizing the system's main cables and caulking cables. The safety of ground anchors during construction directly impacts the safety of CFST arch bridges. In previous designs, ground anchors were calculated using a global force calculation. This involves applying classical mechanics theory to consider the equilibrium relationship between the caulking cable tension, the anchor weight, and the front wall earth pressure, thereby determining the anchor weight and determining the anchor dimensions. Since the caulking cable tension and the front wall earth pressure act directly on the front and rear ends of the anchor web, the anchor web is the primary load-bearing component. Therefore, the dimensional parameters of the anchor web significantly impact the anchor's load. Improper dimensionality can reduce the anchor's safety factor. However, existing techniques typically only calculate the overall load of the anchor, failing to analyze the local load conditions, such as those on the anchor web. Consequently, this approach fails to provide a basis for selecting design parameters such as the length, height, and width of the anchor web. Summary of the Invention

[0003] The present invention aims to solve the technical problems raised in the above-mentioned background technology and provide a method for selecting the size parameters of the ground anchor web of a cable lifting system, which can calculate the stress of the ground anchor web and thus formulate the design size parameters such as the length, height, and width of the ground anchor web.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for selecting size parameters of a ground anchor web of a cable hoisting system comprises the following steps:

[0006] Since the length and height of the anchor web are much greater than its thickness, the stress law of the anchor web belongs to a plane stress problem. A rectangular coordinate system is established with one of the vertices of the anchor web as the origin, with the longitudinal bridge direction as the x direction and the vertical bridge direction as the z direction.

[0007] Assume that the range of the force exerted by the cable force on the anchor web is s, and the force exerted by the cable force on the anchor web is decomposed into the horizontal cable force load q and the vertical cable force load q′. The force on the anchor web is regarded as the superposition of the effects of three working conditions: horizontal cable force load, vertical cable force load, and earth pressure load. Therefore, the stress function Φ under the horizontal cable force load, the stress function Φ′ under the vertical cable force load, and the stress function Φ″ under the earth pressure load are constructed using two-variable multinomials respectively.

[0008] The stress component expression σ with unknown coefficients is obtained by partial differentiation of the stress function Φ under the horizontal cable load. x , σ z and τ xz , the stress function Φ′ under the vertical cable load is partially differentiated to obtain the stress component expression σ with unknown coefficients x ′、σ z ′ and τ xz ′, perform partial differentiation on the stress function Φ″ under the action of earth pressure load to obtain the stress component expression σ with unknown coefficients x ″、σ z ″ and τ xz ″;

[0009] Substitute the stress function Φ under the horizontal cable load, the stress function Φ′ under the vertical cable load, and the stress function Φ″ under the earth pressure load into the compatibility equation respectively, introduce the size boundary conditions of the anchor web into the corresponding stress component expressions, and solve the undetermined coefficients in the corresponding stress component expressions to obtain the stress component expressions in the plane of the anchor web.

[0010] Summarize the stress component expressions σ under the three working conditions of horizontal cable force load, vertical cable force load and earth pressure load x总 , σ z总 and τ xz总 ;

[0011] Substitute a preset anchor web length and height value into the formula σ x总 , σ z总 and τ xz总 In the calculation, the stress of the anchor web under three working conditions is obtained: if the calculated σ x总 , σ z总 and τ xz总 If the values ​​of are within the set stress range, it means that the preset anchor web length and height values ​​meet the construction requirements; if the calculated σ x总 , σ z总 and τ xz总 If any value of is outside the set stress range, the length and height of the anchor web are reset until the calculated σ x总 , σ z总 and τ xz总 The values ​​are all within the set stress range.

[0012] Furthermore, a bivariate polynomial is used as the stress function, and the highest order is set to 4.

[0013] Furthermore, the stress function Φ under the horizontal cable force load constructed by a binary multivariate formula is:

[0014] Φ=k1x 2 +k2z 2 +k3xz 2 +k4x 3 +k5z 3 +k6x 2 z+k7x 2 z 2 +k8x 4 +k9z 4 +k 10 x 3 z

[0015] +k 11 xz 3

[0016] Where, k1~k 11 is the coefficient to be determined;

[0017] The stress component expression is obtained by partial differentiation of the stress function under the horizontal cable load:

[0018]

[0019]

[0020]

[0021] From the compatibility equation we can know that:

[0022]

[0023]

[0024] Substituting the stress function Φ into the compatibility equation, we get:

[0025]

[0026] Therefore:

[0027] 3k8+k7+3k9=0 ①

[0028] The steps to introduce boundary conditions into the stress component expressions are:

[0029] Assume the anchor web length is L and height is H.

[0030] (1) Examining the x=0 boundary, σ x and σ y It is approximately a quadratic function that is symmetric at z = H / 2, and both are 0 at the origin (0, 0), so:

[0031]

[0032] Right now

[0033] At the same time, in the area near the external load application, there are:

[0034]

[0035] Where s is the range of force exerted by the cable force on the anchor web, f l is the horizontal component of the cable force;

[0036] Substitute σ x Functional expressions are:

[0037]

[0038]

[0039] Combining ② and ④, we get:

[0040]

[0041]

[0042] (2) Consider the boundary x = L. There is no external load here, so the relationship is:

[0043]

[0044] Since k2=0; k 11 =0, substitute σ x Functional expressions are:

[0045]

[0046] 2LHk3+3H 2 k5+2L 2 Hk7+4H 3 k9=0 ⑤

[0047] (3) Consider the boundary z = 0, which is the constrained end and is subject to shear force and bending moment, so the relationship is:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] L 2 k6+L 3 k 10 =f l s ⑧

[0057] (4) Considering the boundary z = H, there is no external load, so the relationship is:

[0058]

[0059]

[0060] 2Lk1+3L 2 k4+2HLk6+2H 2 Lk7+4L 3 k8+3HL 2 k 10 =0 ⑨

[0061] (5) Combining equations ①-9, we can obtain:

[0062]

[0063] The expressions of the stress components under the action of horizontal cable force are obtained as follows:

[0064]

[0065] Furthermore, the stress function Φ′ under the vertical cable force load constructed by a binary multivariate equation is:

[0066] Φ′=k1′x 2 +k2′z 2 +k3′xz 2 +k4′x 3 +k5′z 3 +k6′x 2 z+k7′z 4 +k8′x 4 +k9′x 3 z+k 10 ′xz 3

[0067] Where, k1′~k 10 ′ is the unknown coefficient;

[0068] The stress component expression is obtained by partial differentiation of the stress function under the vertical cable load:

[0069]

[0070]

[0071]

[0072] From the compatibility equation we can know that:

[0073]

[0074]

[0075] Substituting the stress function Φ' into the compatibility equation, we get:

[0076]

[0077] Therefore:

[0078] k7′+k8′=0 (a)

[0079] Introducing boundary conditions into the corresponding stress component expressions, the method for solving the undetermined coefficients in the corresponding stress component expressions is:

[0080] (1) Examining the x=0 boundary

[0081]

[0082] 2k2′H+3k5′H 2 +4k7′H 3 =0 (b)

[0083]

[0084] -(k3′H 2 +k 10 'H 3 )=f v s (c)

[0085] (2) Examining the x=L boundary

[0086]

[0087] 2k1′H+6k4′LH+k6′H 2 +12k8′L 2 H+3k9′LH 2 =0 (d)

[0088]

[0089] Where s is the range of force exerted by the cable force on the anchor web, f v is the vertical component of the cable force;

[0090] -(k3′H 2 +2k6′LH+3k9′L 2 H+k 10 'H 3 )=0 (e)

[0091] (3) Examining the z=0 boundary

[0092]

[0093] 2k1′L+3k4′L 2 +4k8′L 3 =f v s (f)

[0094]

[0095]

[0096]

[0097] -(k6′L 2 +k9′L 3 )=0 (h)

[0098] (4) Examining the z=H boundary

[0099]

[0100] 2k2′L+k3′L 2 +6k5′HL+12k7′H 2 L+3k 10 'L 2 H=0 (i)

[0101]

[0102] -(2k3′HL+k6′L 2 +k9′L 3 +3k 10 'H 2 L)=0 (j)

[0103] (5) Combining equations (a)-(j), we get:

[0104]

[0105] Solve for the coefficients

[0106] The expressions of the stress components under the vertical cable load are obtained:

[0107]

[0108] Furthermore, the stress function Φ″ under the action of earth pressure load constructed by binary multivariate equation is:

[0109] Since the entire cross-section is subjected to horizontal load at x = L, the vertical stress can be ignored under this working condition, that is, σ z =0, so the stress function under the action of earth pressure load is Φ″:

[0110] Φ″=k1″z 2 +k2″xz+k3″xz 2 +k4″z 3

[0111]

[0112]

[0113]

[0114] In the formula, k1"~k4" are unknown coefficients;

[0115] From the compatibility equation we can know that:

[0116]

[0117]

[0118] Substituting the stress function Φ″ into the compatibility equation, we get:

[0119]

[0120] The steps to introduce boundary conditions into the stress component expressions are:

[0121] (1) Examining the x=L boundary

[0122]

[0123] Where q″ is the earth pressure load;

[0124] So the corresponding relationship is:

[0125]

[0126]

[0127] Where γ is the bulk density of soil, is the internal friction angle of the soil;

[0128] (2) Examining the x=0 boundary

[0129]

[0130] 2k1″+3k4″H 2 =0(C)

[0131] (3) Examining the z=0 boundary

[0132]

[0133]

[0134] (4) Combining equations (A) and (D), we get:

[0135]

[0136] Solve for each coefficient

[0137] The expressions of each component under the action of earth pressure load are obtained:

[0138]

[0139] Furthermore, the stress component expressions under the three working conditions are summarized according to the following formula:

[0140]

[0141]

[0142]

[0143] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0144] The present invention simplifies the force calculation of the anchor web into a plane stress problem. It constructs a total stress function using a binary polynomial, obtains stress component expressions through partial differentiation, and then substitutes the compatibility equations and boundary conditions to solve for the undetermined coefficients in the stress component expressions, thereby obtaining the distribution of the stress field within the plane of the anchor web. This, in turn, provides a basis for selecting design parameters such as the length, height, and width of the anchor web. Compared with previous methods for calculating the force on the anchor web, this method can obtain a more accurate calculation structure for the anchor structure, enabling localized and refined design. Furthermore, the calculation formula only requires the preset length, width, and height of the anchor web to determine whether the anchor web meets construction requirements, thus demonstrating its general applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] Figure 1 It is a structural diagram of a ground anchor in the prior art;

[0146] Figure 2 This is a schematic diagram of the mechanics of the anchor web;

[0147] Figure 3 This is a flow chart of a method for selecting size parameters of a ground anchor web for a cable hoisting system according to a preferred embodiment of the present invention;

[0148] Description of main component symbols

[0149] 1. Soil; 2. Cable stays; 3. Ground anchor weight; 4. Ground anchor web; 5. Shoulder pole beam. DETAILED DESCRIPTION

[0150] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0151] It should be noted that when a component is referred to as being "fixed to" another component, it may be directly on the other component or there may also be a central component. When a component is considered to be "connected to" another component, it may be directly connected to the other component or there may also be a central component. When a component is considered to be "set on" another component, it may be directly set on the other component or there may also be a central component. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0152] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0153] See Figures 1 to 3A preferred embodiment of the present invention provides a method for selecting the size parameters of the ground anchor web of a cable hoisting system, which is used to calculate the stress of the ground anchor web 4, thereby formulating the design size parameters of the ground anchor web, such as the length and height. In the working state, the inclined buckle system transmits the cable force of the inclined buckle cable 2 to the rear end of the ground anchor web 4 through the shoulder beam 5. At the same time, the front end of the ground anchor web 4 contacts the soil 1 and is subjected to the soil pressure. Therefore, the ground anchor web 4 is the main load-bearing component of the ground anchor, and it is meaningful and necessary to perform a stress analysis on it. The method for selecting the size parameters of the ground anchor web of the cable hoisting system includes the following steps:

[0154] S1. Since the length and height of the ground anchor web 4 are much greater than its thickness, the force law of the ground anchor web 4 belongs to a plane stress problem. A rectangular coordinate system is established with one of the vertices of the ground anchor web 4 as the origin, and the longitudinal bridge direction is designed as the x direction, the transverse bridge direction is designed as the y direction, and the vertical bridge direction is designed as the z direction.

[0155] Since the thickness of the anchor web 4 in the y direction of the transverse bridge is relatively thin, the force in the y direction can be ignored, and the actual three-dimensional problem is simplified to a two-dimensional plane stress problem in x and z.

[0156] S2, assuming the range of the force exerted by the cable force on the anchor web 4 is s, decompose the force exerted by the cable force on the anchor web 4 into the horizontal cable force load q and the vertical cable force load q′. The force on the anchor web 4 is considered to be the superposition of the effects of three working conditions: the horizontal cable force load, the vertical cable force load, and the earth pressure load. Therefore, the stress function Φ under the horizontal cable force load, the stress function Φ′ under the vertical cable force load, and the stress function Φ″ under the earth pressure load are constructed using a two-variable multinomial formula respectively;

[0157] S3, perform partial differentiation on the stress function Φ under the horizontal cable load to obtain the stress component expression σ with unknown coefficients x , σ z and τ xz , the stress function Φ′ under the vertical cable load is partially differentiated to obtain the stress component expression σ with unknown coefficients x ′、σ z ′ and τ xz ′, perform partial differentiation on the stress function Φ″ under the action of earth pressure load to obtain the stress component expression σ with unknown coefficients x ″、σ z ″ and τ xz ″;

[0158] S4, respectively, substitute the stress function Φ under the horizontal cable force load, the stress function Φ′ under the vertical cable force load, and the stress function Φ″ under the earth pressure load into the compatibility equation, introduce the dimensional boundary conditions of the anchor web 4 into the corresponding stress component expressions, and solve for the undetermined coefficients in the corresponding stress component expressions, thereby obtaining the stress component expressions in the plane of the anchor web 4;

[0159] S5, summarize the stress component expressions σ under the three working conditions of horizontal cable force load, vertical cable force load and earth pressure load x总 , σ z总 and τ xz总 ;

[0160] S6, substitute a preset anchor web length and height value into the formula σ x总 , σ z总 and τ xz总 In the calculation, the stress of the anchor web under three working conditions is obtained: if the calculated σ x总 , σ z总 and τ xz总 If the values ​​of are within the set stress range, it means that the length and height of the preset anchor web 4 meet the construction requirements; if the calculated σ x总 , σ z总 and τ xz总 If any value of is outside the set stress range, the length and height of the anchor web 4 are revalued until the calculated σ x总 , σ z总 and τ xz总 The values ​​are all within the set stress range.

[0161] In this embodiment, a bivariate polynomial is used as the stress function, and the highest term is 4, where:

[0162] (a) The stress function Φ under the horizontal cable load constructed using a two-variable multinomial is:

[0163] Φ=k1x 2 +k2z 2 +k3xz 2 +k4x 3 +k5z 3 +k6x 2 z+k7x 2 z 2 +k8x 4 +k9z 4 +k 10 x 3 z

[0164] +k 11 xz3

[0165] Where, k1~k 11 is the coefficient to be determined;

[0166] The stress component expression is obtained by partial differentiation of the stress function under the horizontal cable load:

[0167]

[0168]

[0169]

[0170] From the compatibility equation we can know that:

[0171]

[0172]

[0173] Substituting the stress function Φ into the compatibility equation, we get:

[0174]

[0175] Therefore:

[0176] 3k8+k7+3k9=0

[0177] The steps to introduce boundary conditions into the stress component expressions are:

[0178] Assume the anchor web length is L and height is H.

[0179] (1) Examining the x=0 boundary, σ x and σ y It is approximately a quadratic function that is symmetric at z = H / 2, and both are 0 at (0, 0), so:

[0180]

[0181] Right now

[0182] At the same time, in the area near the external load application, that is, the area where the cable force acts on the anchor web 4, there are:

[0183]

[0184] Where s is the range of force applied by the cable to the anchor web 4, and f l is the horizontal component of the cable force;

[0185] Substitute σ xFunctional expressions are:

[0186]

[0187]

[0188] Combining ② and ④, we get:

[0189]

[0190]

[0191] (2) Consider the boundary x = L. There is no external load here, so the relationship is:

[0192]

[0193] Since k2=0; k 11 =0, substitute σ x Functional expressions are:

[0194]

[0195] 2LHk3+3H 2 k5+2L 2 Hk7+4H 3 k9=0 ⑤

[0196] (3) Consider the boundary z = 0, which is the constrained end and is subject to shear force and bending moment, so the relationship is:

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205] L 2 k6+L 3 k 10 =f l s ⑧

[0206] (4) Considering the boundary z = H, there is no external load, so the relationship is:

[0207]

[0208]

[0209] 2Lk1+3L 2 k4+2HLk6+2H 2 Lk7+4L 3 k8+3HL 2 k 10 =0 ⑨

[0210] (5) Combining equations ①-9, we can obtain:

[0211]

[0212] The expressions of each component under the action of horizontal cable force are obtained as follows:

[0213]

[0214] (b) The stress function Φ′ under the vertical cable force load constructed by a two-variable multinomial is:

[0215] Φ′=k1′x 2 +k2′z 2 +k3′xz 2 +k4′x 3 +k5′z 3 +k6′x 2 z+k7′z 4 +k8′x 4 +k9′x 3 z+k 10 ′xz 3

[0216] Where, k1′~k 10 ′ is the unknown coefficient;

[0217] The stress component expression is obtained by partial differentiation of the stress function under the vertical cable load:

[0218]

[0219]

[0220]

[0221] From the compatibility equation we can know that:

[0222]

[0223]

[0224] Substituting the stress function Φ' into the compatibility equation, we get:

[0225]

[0226] Therefore:

[0227] k7′+k8′=0 (a)

[0228] Introducing boundary conditions into the corresponding stress component expressions, the method for solving the undetermined coefficients in the corresponding stress component expressions is:

[0229] (1) Examining the x=0 boundary

[0230]

[0231] 2k2′H+3k5′H 2 +4k7′H 3 =0 (b)

[0232]

[0233] -(k3′H 2 +k 10 'H 3 )=f v s (c)

[0234] Where s is the range of force exerted by the cable force on the anchor web, f v is the vertical component of the cable force;

[0235] (2) Examining the x=L boundary

[0236]

[0237] 2k1′H+6k4′LH+k6′H 2 +12k8′L 2 H+3k9′LH 2 =0 (d)

[0238]

[0239] -(k3′H 2 +2k6′LH+3k9′L 2 H+k 10 'H 3 )=0 (e)

[0240] (3) Examining the z=0 boundary

[0241]

[0242] 2k1′L+3k4′L 2 +4k8′L 3 =f v s (f)

[0243]

[0244]

[0245]

[0246] -(k6′L 2 +k9′L 3 )=0 (h)

[0247] (4) Examining the z=H boundary

[0248]

[0249] 2k2′L+k3′L 2 +6k5′HL+12k7′H 2 L+3k 10 'L 2 H=0 (i)

[0250]

[0251] -(2k3′HL+k6′L 2 +k9′L 3 +3k 10 'H 2 L)=0 (j)

[0252] (5) Combining equations (a)-(j), we get:

[0253]

[0254] Solve for the coefficients

[0255] The expressions of the stress components under the vertical cable load are obtained:

[0256]

[0257] (c) The stress function Φ″ under the action of earth pressure load constructed by a two-variable multinomial is:

[0258] Since the entire cross-section is subjected to horizontal load at x = L, the vertical stress can be ignored under this working condition, that is, σ z =0, so the stress function under the action of earth pressure load is Φ″:

[0259] Φ″=k1″z 2 +k2″xz+k3″xz 2 +k4″z 3

[0260]

[0261]

[0262]

[0263] In the formula, k1"~k4" are unknown coefficients;

[0264] From the compatibility equation we can know that:

[0265]

[0266]

[0267] Substituting the stress function Φ″ into the compatibility equation, we get:

[0268]

[0269] The steps to introduce boundary conditions into the stress component expressions are:

[0270] (1) Examining the x=L boundary

[0271]

[0272] Where q″ is the earth pressure load;

[0273] So the corresponding relationship is:

[0274]

[0275]

[0276] Where γ is the bulk density of soil, is the internal friction angle of the soil;

[0277] (2) Examining the x=0 boundary

[0278]

[0279] 2k1″+3k4″H 2 =0 (C)

[0280] (3) Examining the z=0 boundary

[0281]

[0282]

[0283] (4) Combining equations (A) and (D), we get:

[0284]

[0285] Solve for each coefficient

[0286] The expressions of each component under the action of earth pressure load are obtained:

[0287]

[0288] The stress component expressions under the three working conditions are summarized as follows:

[0289]

[0290]

[0291]

[0292] This method simplifies the anchor web force calculation into a plane stress problem. It constructs a total stress function using a binary polynomial, obtains stress component expressions through partial differentiation, and then substitutes the compatibility equations and boundary conditions to solve for the undetermined coefficients in the stress component expressions. This method then obtains the stress field distribution within the anchor web plane, providing a basis for selecting design parameters such as the length and height of the anchor web. Compared with previous anchor force calculation methods, this method can obtain a more accurate calculation structure for the anchor structure, enabling localized and refined design. Furthermore, the calculation formula only requires the preset anchor web length and height dimensions to determine whether the anchor web meets construction requirements, making it generally applicable.

[0293] The above description is a detailed description of the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the patent application of the present invention. Any equivalent changes or modifications completed under the technical spirit suggested by the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for selecting size parameters of a ground anchor web for a cable hoisting system, characterized in that: The following steps are involved: A rectangular coordinate system is established with one vertex of the anchor web as the origin, with the longitudinal bridge direction being designated as the x direction and the vertical bridge direction being designated as the z direction; Assuming the range of the force exerted by the cable force on the anchor web is s, the force exerted by the cable force on the anchor web is decomposed into the horizontal cable force load q and the vertical cable force load q′. The force on the anchor web is regarded as the superposition of the effects of three working conditions: horizontal cable force load, vertical cable force load, and earth pressure load. Therefore, the stress function Φ under the horizontal cable force load, the stress function Φ′ under the vertical cable force load, and the stress function Φ” under the earth pressure load are constructed using two-variable multinomial equations: Φ=k1x 2 +k2z 2 +k3xz 2 +k4x 3 +k5z 3 +k6x 2 z+k7x 2 z 2 +k8x 4 +k9z 4 +k 10 x 3 z+k 11 xz 3 , where k1~k11 are unknown coefficients; Φ′=k1′x 2 +k2′z 2 +k3'xz 2 +k4′x 3 +k5′z 3 +k6′x 2 z+k7'z 4 +k8'x 4 +k9'x 3 z+k 10 'xz 3 In the formula, k1'~k 10 ' is the coefficient to be determined; Φ”=k1”z 2 +k2”xz+k3”xz 2 +k4”z 3 , where k1"~k4" are unknown coefficients; The stress component expression σ with unknown coefficients is obtained by partial differentiation of the stress function Φ under the horizontal cable load. x , σ z and τ xz , the stress function Φ′ under the vertical cable load is partially differentiated to obtain the stress component expression σ with unknown coefficients x ′、σ z ′ and τ xz ', perform partial differentiation on the stress function Φ" under the action of earth pressure load to obtain the stress component expression σ with unknown coefficients x ”、σ z ” and τ xz ”; Substitute the stress function Φ under the horizontal cable load, the stress function Φ' under the vertical cable load, and the stress function Φ" under the earth pressure load into the compatibility equation respectively, introduce the size boundary conditions of the anchor web into the corresponding stress component expressions, and solve the undetermined coefficients in the corresponding stress component expressions to obtain the stress component expressions in the plane of the anchor web; Summarize the stress component expressions σ under the three working conditions of horizontal cable force load, vertical cable force load and earth pressure load x总 , σ z总 and σ xz总 ; Substitute a preset anchor web length and height value into the formula σ x总 , σ z总 and τ xz总 In the calculation, the stress of the anchor web under three working conditions is obtained: if the calculated σ x总 , σ z总 and τ xz总 If the values ​​of are within the set stress range, it means that the preset anchor web length and height values ​​meet the construction requirements; if the calculated σ x总 , σ z总 and σ xz总 If any value of is outside the set stress range, the length and height of the anchor web are reset until the calculated σ x总 , σ z总 and τ xz总 The values ​​are all within the set stress range.

2. The method for selecting size parameters of the anchor web of the cable hoisting system according to claim 1, characterized in that: A bivariate polynomial is used as the stress function, and the highest order is 4.

3. The method for selecting size parameters of the anchor web of the cable hoisting system according to claim 2, characterized in that: The stress component expression is obtained by partial differentiation of the stress function under the horizontal cable load: From the compatibility equation we can know that: Substituting the stress function Φ into the compatibility equation, we get: Therefore: 3k8+k7+3k9=0 ① The steps to introduce boundary conditions into the stress component expressions are: Assume the anchor web length is L and height is H. (1) Examining the x=0 boundary, σ x and σ y It is approximately a quadratic function that is symmetric at z = H / 2, and both are 0 at the origin (0, 0), so: k1=0;k2=0;k 11 =0; Right now At the same time, in the area near the external load application, there are: Where s is the range of force exerted by the cable force on the anchor web, f l is the horizontal component of the cable force; Substitute σ x Functional expressions are: Combining ② and ④, we get: (2) Consider the boundary x = L. There is no external load here, so the relationship is: Since k2=0; k 11 =0, substitute σ x Functional expressions are: <h2 style=";text-align:left;direction:ltr">2LHk3+3H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> k5+2L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> Hk7+4H<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> k9=0 ⑤ (3) Consider the boundary z = 0, which is the constrained end and is subject to shear force and bending moment, so the relationship is: L 2 k6+L 3 k 10 =f l s ⑧ (4) Considering the boundary z = H, there is no external load, so the relationship is: <h2 style=";text-align:left;direction:ltr">2Lk1+3L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> k4+2HLk6+2H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> Lk7+4L<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> k8+3HL<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> k<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> =0 ⑨ (5) Combining equations ①-9, we can obtain: The expressions of the stress components under the action of horizontal cable force are obtained as follows:

4. The method for selecting size parameters of the anchor web of the cable hoisting system according to claim 3, characterized in that: The stress component expression is obtained by partial differentiation of the stress function under the vertical cable load: From the compatibility equation we can know that: Substituting the stress function Φ' into the compatibility equation, we get: Therefore: k7′+k8′=0 (a) Introducing boundary conditions into the corresponding stress component expressions, the method for solving the undetermined coefficients in the corresponding stress component expressions is: (1) Examining the x=0 boundary (2) Examining the x=L boundary Where s is the range of force exerted by the cable force on the anchor web, f v is the vertical component of the cable force; <h2 style=";text-align:left;direction:ltr">-(k3'H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2k6'LH+3k9'L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> H+k<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> 'H<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> )=0 (e) (3) Examining the z=0 boundary (4) Examining the z=H boundary (5) Combining equations (a)-(j), we get: Solve for the coefficients The expressions of the stress components under the vertical cable load are obtained:

5. The method for selecting size parameters of the anchor web of the cable hoisting system according to claim 4, characterized in that: From the compatibility equation we can know that: Substituting the stress function Φ" into the compatibility equation, we get: The steps to introduce boundary conditions into the stress component expressions are: (1) Examining the x=L boundary Where q'' is the earth pressure load; So the corresponding relationship is: Where γ is the bulk density of soil, is the internal friction angle of the soil; (2) Examining the x=0 boundary (3) Examining the z=0 boundary (4) Combining equations (A) and (D), we get: Solve for each coefficient The expressions of each component under the action of earth pressure load are obtained:

6. The method for selecting size parameters of the anchor web of the cable hoisting system according to claim 4, characterized in that: The stress component expressions under the three working conditions are summarized as follows:

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