A method for calculating the external pullout force of the steel shell in a composite cable tower after yielding

Abstract

The present invention proposes a method for calculating the external pull-out force of instability after the steel shell in a combined cable tower yields, which belongs to the field of bridge engineering. The method solves the problem in the prior art that in a steel shell-concrete combined cable tower, the buckling of the steel shell in a ductile state may cause the shear connector to be pulled out, and the structure cannot reach the ideal strength index and is destroyed in advance. The present invention first obtains the thin plate large deflection theory to obtain the thin plate large deflection equation of the steel shell, and then obtains the basic expression of the deformation function and the expression of the stress function; and establishes a specific expression of the deflection at the solution of the Galerkin equation; then obtains the expression of the final deformation function based on the specific expression of the deflection; finally, the expression of the final deformation function is substituted into the surface external force equilibrium equation of the thin plate large deflection equation to obtain the distribution function of the pull-out force; in the present invention, the pull-out force that can be generated when the plate shell is buckled can be obtained according to different shear connectors and different plate thicknesses, and then the arrangement requirements of the shear connectors are clarified.

Description

Technical Field

[0001] The invention belongs to the field of bridge engineering, and in particular relates to a method for calculating the instability external pullout force of a steel shell in a combined cable tower after yielding. Background Art

[0002] Since the 21st century, composite structures have been widely used in my country's bridge projects, and steel shell-concrete composite cable towers are one of them. Most of the cable towers are in the form of steel shells wrapped with concrete. Thanks to their light weight and high strength, many similar composite cable towers have been built in China. The steel shell is one of the main sources of the structural bearing capacity of the composite cable tower. In the design of the composite cable tower, while ensuring strength, its stability must also be guaranteed. "No buckling is allowed before the steel shell reaches the yield stress" is the basic principle of structural design. This is because the stiffness of the steel structure will be greatly reduced after yielding, and it is difficult to ensure that it will not buckle. Therefore, the yield of the steel shell is the standard line for structural elastic design.

[0003] However, with the emergence of the concept of seismic resistance of bridge structures, the ductility of bridge structures has also been taken into consideration in engineering design. The tower structure is the main component in the cable-stayed bridge that bears seismic loads. The steel shell of the combined tower will buckle after yielding under compression. At this time, the steel shell no longer maintains the in-plane stress state. The out-of-plane deformation caused by buckling makes the steel shell in a state of out-of-plane stress. The shear connectors connected to the steel shell will bear the out-of-plane pull-out force.

[0004] In the current bridge design, especially in the seismic design considering material nonlinearity, the focus is mostly on strength indicators. For example, the strength indicator in the structural ductility design is the strain of steel bars and concrete. However, in the steel shell-concrete composite cable tower, the buckling of the steel shell in the ductile state may cause the shear connector to be pulled out, and the structure cannot reach the ideal strength indicator and is destroyed prematurely. Summary of the invention

[0005] In view of this, the present invention provides a method for calculating the instability external pullout force after the steel shell yields in a combined cable tower. According to the design parameters of the cable tower, the magnitude of the external pullout force generated after the steel shell buckles can be directly calculated to obtain the pullout resistance requirement of the shear connector of the cable tower under ductile design.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for calculating the external pullout force of the steel shell in a combined cable tower after yielding, characterized by comprising:

[0008] Step 1: Based on the large deflection theory of thin plates, obtain the large deflection equation of the thin plate of the steel shell. The formula is as follows:

[0009]

[0010] Among them, ω is the deformation function of the steel shell plate; F is the stress function of the steel shell; is the cylindrical stiffness of the steel shell; t is the thickness of the steel shell; E is the Young's elastic modulus of the steel; ν is the Poisson's ratio of the material; x and y are the coordinates on the plate;

[0011] Step 2: obtaining a basic expression of the deformation function ω, wherein the independent variable of the basic expression of the deformation function ω includes a maximum deflection value f generated by determining the buckling deformation;

[0012] The step 2 is specifically as follows:

[0013] Based on the large deflection equation of the thin plate, the deformation function ω of the plate is determined, and its basic expression is composed of trigonometric functions:

[0014]

[0015] Among them, f is the maximum deflection value caused by buckling deformation; m is the parameter that determines the deformation shape, which is a positive integer; j, p, k, q are adjustment parameters that meet the plate boundary conditions; a and b are the lengths of the two sides of the plate;

[0016] Step 3: Introduce boundary conditions into the basic expression of the deformation function ω to obtain the expression of the deformation function ω under the boundary conditions; obtain the expression of the stress function F based on Formula I and the deformation function ω with the boundary conditions introduced;

[0017] The step 3 specifically comprises the following steps:

[0018] Step 3.1: According to the different shear connectors used between the steel shell and the concrete, determine whether the boundary condition is a simply supported boundary condition or a fixed boundary condition, and let x = a to obtain the mathematical expressions under the two boundaries:

[0019]

[0020] Step 3.2: Substitute the deformation function ω that satisfies the boundary conditions into the second part of (I), and let j = p = 1, k = q = 0, corresponding to the case of four simple supports, as follows:

[0021]

[0022] Step 3.3: Obtain the special solution of the trigonometric function of the steel shell stress function F, which is in the form of:

[0023]

[0024] Where A and B are arbitrary constants;

[0025] Step 3.4: Substitute the special solution of the above steel shell stress function F into the left side of equation (V), and compare the coefficients on both sides of the equation to obtain the expressions of A and B:

[0026]

[0027] Step 3.5: Obtain the residual solution of the steel shell stress function F, and obtain the final expression of the steel shell stress function F based on the residual solution of the steel shell stress function F and the special solution of the steel shell stress function F;

[0028] The step 3.5 specifically includes the following steps:

[0029] Step 3.51: Supplement the remaining solution of F to satisfy:

[0030]

[0031] Step 3.52: Combined with the stress characteristics of the steel shell in the cable tower, the steel shell can be regarded as a unidirectional compression state under the action of compression and bending load. At this time, the stress should satisfy:

[0032]

[0033] Among them, p x is the axial load in the x direction;

[0034] Step 3.53: Integrate equation (IX) to obtain the remaining solution of F:

[0035]

[0036] Step 3.54: Combining the special solution and the remaining solution, the complete expression of F is:

[0037]

[0038] Step 4: Substitute the expression of the deformation function ω in step 3 and the expression of the stress function F in step 3 into equation (I), and establish a specific expression for the deflection f at the solution of the Galerkin equation;

[0039] The step 4 specifically comprises the following steps:

[0040] Step 4.1: Substitute the above stress function F and deformation function ω into the first part of (I) and establish a specific expression for the deflection f at the solution of the Galerkin equation. The Galerkin equation is:

[0041]

[0042] Step 4.2: Solve after integration. Since m is a positive integer, the integral result can be simplified using the conditions sin(mπ)=0, cos(mπ)=1, and finally we get:

[0043]

[0044] Step 4.4: The second half of (XIII) related to the shell column stiffness D represents the buckling load of the shell under this boundary condition and is defined as P c , the expression of the maximum deflection value f after deformation is:

[0045]

[0046] Step 5: Substitute the specific expression of f in step 4 into the basic expression of the deformation function ω in step 2 to obtain the expression of the final deformation function ω;

[0047] The expression of the final deformation function ω in step 5 is as follows:

[0048]

[0049] In step 6: taking force as the balance condition, the first part of the equation of formula (I) is deformed to obtain the external force balance equation of the large deflection equation of the thin plate, and the expression of the final deformation function ω in step 5 is substituted into the external force balance equation of the large deflection equation of the thin plate to obtain the distribution function of the pull-out force.

[0050] The external force balance equation of the large deflection equation of the thin plate is specifically as follows:

[0051]

[0052] Where N x 、N y and N xy are the axial force and shear force in the x and y directions on the plate respectively;

[0053] Substituting the expression of the final deformation function ω in step 6 into the external force balance equation of the large deflection equation of the thin plate to obtain the distribution function of the pull-out force specifically includes:

[0054] Substitute the complete deformation function ω into the external force equilibrium equation of the thin plate large deflection equation, the first half of the first part of equation (II):

[0055]

[0056] Where Q is the required distribution function of the pull-out force.

[0057] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0058] In the present invention, the pull-out force that can be generated when the plate shell buckles can be obtained according to different shear connectors and different plate thicknesses, and the layout requirements of the shear connectors can be clarified, thereby avoiding the problem of concrete unconstraint caused by the pull-out separation of the steel shell and concrete in the cable tower in the plastic state. In addition, the moment of steel shell buckling in the cable tower is defined after yielding, which also meets the standard of conventional engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0060] Figure 1 This is a diagram showing the effect of the buckling pull-out force of the steel shell according to Embodiment 2 of the present invention;

[0061] Figure 2 A diagram showing the structure of an isolator according to Embodiment 2 of the present invention;

[0062] Figure 3 The extraction force distribution diagram of Example 2 provided by the present invention;

[0063] Figure 4 This is a cross-sectional view of the structure of Example 2 provided by the present invention.

[0064] Reference numerals

[0065] 1-Steel shell; 2-Shear connector; 3-Concrete. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0067] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0069] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0070] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0071] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0072] Example 1

[0073] The embodiment of the present invention discloses a method for calculating the external pullout force of the steel shell in a hollow thin steel shell-concrete composite cable tower after yielding, which includes the following calculation steps.

[0074] 1. The out-of-plane force problem of the plate is based on the large deflection equation of thin plates proposed by Kbrman in 1910:

[0075]

[0076] Among them, ω is the deformation function of the plate; F is the stress function of the steel shell; is the cylindrical stiffness of the steel shell; t is the thickness of the steel shell; E is the Young's elastic modulus of the steel; ν is the Poisson's ratio of the material; x and y are the coordinates on the plate.

[0077] 2. In the derivation process of the large deflection equation of the thin plate, there is an equilibrium equation based on the balance of forces, which is a deformation of the first part of equation (I):

[0078]

[0079] Where N x 、N y and N xy They are the axial force and shear force in the x and y directions acting on the plate, also known as mid-plane force.

[0080] 3. According to the large deflection equation of the thin plate, first determine the deformation function ω of the plate, whose basic expression is composed of trigonometric functions:

[0081]

[0082] Among them, f is the maximum deflection value caused by buckling deformation; m is the parameter that determines the deformation shape and is a positive integer; j, p, k, q are adjustment parameters that meet the plate boundary conditions; a and b are the lengths of the two sides of the plate.

[0083] 4. Further, depending on the different shear connectors used between the steel shell and the concrete, the boundary conditions are also different. When the steel plate is thinner (t≤30mm) or a flexible shear connector such as a shear stud is used, the boundary condition can be considered to be simply supported, while when the steel plate is thicker (t>30mm) and a rigid connector such as a PBL shear connector is used, the boundary condition is fixed. Taking x=a as an example, the mathematical expressions under the two boundaries are:

[0084]

[0085] 5. Substitute the plate deformation function ω that satisfies the boundary conditions into the second part of (I). Due to the existence of high-order partial differential terms, the expression using parameters will be very large. Here, we take j = p = 1, k = q = 0 as an example, corresponding to the case of four simply supported sides, as follows:

[0086]

[0087] 6. It can be seen that the right side of the equation is completely composed of trigonometric functions. This is because the deformation function ω of the steel shell is composed of trigonometric functions. Then F must have a special solution of trigonometric functions, which is in the form of:

[0088]

[0089] Where A and B are arbitrary constants.

[0090] 7. Substituting the above special solution of F into the left side of equation (V), and comparing the coefficients on both sides of the equation, we can get the expressions of A and B:

[0091]

[0092] 8. Further, supplement the remaining solution of F to satisfy:

[0093]

[0094] 9. The physical meaning represented by formula (VIII) is the plane state when the deformation function ω = 0, that is, the steel shell does not buckle. Combined with the stress characteristics of the steel shell in the cable tower, the steel shell can be regarded as a unidirectional compression state under the compression and bending load. At this time, the stress should satisfy:

[0095]

[0096] Among them, p x is the axial load in the x direction.

[0097] 10. Integrate equation (IX) to obtain the remaining solution of F:

[0098]

[0099] 11. Combining the special solution and the remaining solution, the complete expression of F is:

[0100]

[0101] 12. Then substitute the above stress function F and deformation function ω into the first part of (I) and establish the specific expression of the deflection f at the solution of the Galerkin equation. The Galerkin equation is:

[0102]

[0103] 13. Solve after integration. It should be noted that since m is a positive integer, the integral result can be simplified by the conditions sin(mπ)=0,cos(mπ)=1, and finally get

[0104]

[0105] 14. The latter part of the above equation, which is related to the cylindrical stiffness D of the steel shell, represents the buckling load of the steel shell under this boundary condition and is defined as P c , after deformation, the expression of the maximum deflection value f can be obtained:

[0106]

[0107] 15. The complete deformation function ω is:

[0108]

[0109] 16. Substitute the complete deformation function ω into the external force equilibrium equation of the large deflection equation of the thin plate, the first half of the first part of equation (II):

[0110]

[0111] Where Q is the required distribution function of the pull-out force.

[0112] Example 2

[0113] like Figure 1-3 As shown, this embodiment proposes a specific implementation method for calculating the instability external pullout force of the steel shell in a hollow thin steel shell-concrete composite cable tower after yielding;

[0114] Figure 1 The principle of pull-out force on shear connectors when the steel shell buckles is demonstrated. In essence, the force balance of the deformed steel shell changes from two-dimensional to three-dimensional. Figure 2This is a specific structural diagram of Example 1, in which the steel shell in the isolation body has a size of 1m×1m, a thickness of 24mm, a material number of Q345, and is connected to the concrete using shear bolts. The boundary conditions of its four sides can all be regarded as simply supported, so the deflection function can be defined as:

[0115] ω=f sin(mπx)sin(πy) (XVII)

[0116] Substituting the deformation function ω into the large deflection equation of the thin plate, the stress function F is solved as follows:

[0117]

[0118] where p x is the unidirectional pressure load on the boundary of the steel shell. Since the cross section of the cable tower mainly bears the compression and bending load, the steel shell at the edge can be regarded as being subjected to the vertical pressure load. The general solution of this stress function F is based on the stress condition of the cable tower.

[0119] Then substitute the deformation function ω and the stress function F into the large deflection equation of the thin plate to establish the Galerkin equation and solve it to obtain the specific expression of the deflection f:

[0120]

[0121] where p crx is the buckling load of the steel shell (load per unit length, not stress), and its expression is:

[0122]

[0123] Where E is the Young's elastic modulus of the material; ν is the Poisson's ratio of the material; t is the thickness of the steel shell; m is a positive integer that minimizes the buckling load;

[0124] Substituting the parameters of the embodiment into the formula, the minimum value is obtained when m=1, and the buckling load is calculated to be The buckling load is greater than the yield stress of the material, which satisfies the precondition. Although the buckling load is 416.5MPa, this is the result of elastic calculation. In fact, the steel shell will buckle due to the decrease in stiffness after yielding. To simplify the calculation, when calculating the deflection f, if the buckling load is greater than the yield stress, the two can be considered to be consistent, that is,

[0125] Substituting the complete deformation function ω into the out-of-plane force equilibrium equation of the thin plate large deflection equation, the distribution function of the pull-out force is obtained as:

[0126]

[0127] The first half of the amplitude is defined as A, and the distribution of the pull-out force can be plotted as Figure 3As shown, its shape is based on the initially proposed deformation function ω. It should be clear that the above function Q represents the distribution of the pull-out force on the entire plate, which belongs to the stress unit. If you want to get the force in Newton units, you need to integrate it over the entire plate range:

[0128]

[0129] From the above formula, we can see that there are three factors that determine the pull-out force. The first is the properties of the steel shell, including thickness, elastic modulus, etc. The second is the buckling load of the steel shell, which is 345MPa in this case. The third is the unidirectional pressure load that the steel shell can bear. When the steel shell is an ideal elastic-plastic model, its pull-out force will always be 0, so the steel shell must be considered as a strengthened model. In addition, in actual engineering, the concrete is often crushed before the steel shell reaches the ultimate stress, so p x The value of must also take into account the actual bearing capacity of the entire section.

[0130] Figure 4 Take a hollow section with a length, width and thickness of 2m×2m×0.5m as an example. The concrete is C50. When the section reaches the ultimate bearing capacity, the steel shell on the compression side reaches 356MPa, which is an increase of 11MPa after yielding. The corresponding pull-out force is:

[0131]

[0132] The pull-out resistance of shear studs is:

[0133] T=0.6φf t A0 (XXIV)

[0134] Where φ is the reinforcement influence coefficient. Since reinforcement is usually not provided in the cable tower, it is taken as 0.65; f t is the tensile strength of concrete, and the standard value of C50 is 2.64MPa. A0 is the effective projected area of ​​the stud, which depends on the length of the stud.

[0135] If a bolt with a diameter of 18 mm and a length of 100 mm is used, the pull-out force of a single bolt is 32.3 kN. Therefore, using 6 bolts of this size within the range of 1 m × 1 m can meet the pull-out force requirements.

[0136] The basic principles of the present application are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present application are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present application. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, not for limitation, and the above details do not limit the present application to being implemented by adopting the above specific details.

[0137] The block diagrams of the devices, apparatuses, equipment, and systems involved in this application are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0138] It should also be noted that in the apparatus, equipment and method of the present application, each component or each step can be decomposed and / or recombined. These decompositions and / or recombinations should be regarded as equivalent schemes of the present application. The above description of the disclosed aspects is provided to enable any technician in the field to make or use the present application. Various modifications to these aspects are very obvious to those skilled in the art, and the general principles defined here can be applied to other aspects without departing from the scope of the present application. Therefore, the present application is not intended to be limited to the aspects shown here, but according to the widest scope consistent with the principles disclosed here and novel features.

[0139] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present application to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

[0140] The circuits, electronic components and modules involved are all prior art and can be fully implemented by those skilled in the art. Needless to say, the content protected by the present invention does not involve improvements to software and methods.

[0141] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0142] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the external pullout force of the steel shell in a combined cable tower after yielding, characterized in that: include: Step 1: Based on the large deflection theory of thin plates, obtain the large deflection equation of the thin plate of the steel shell. The formula is as follows: Among them, ω is the deformation function of the steel shell plate; F is the stress function of the steel shell; is the cylindrical stiffness of the steel shell; t is the thickness of the steel shell; E is the Young's elastic modulus of the steel; ν is the Poisson's ratio of the material; x and y are the coordinates on the plate; Step 2: obtaining a basic expression of the deformation function ω, wherein the independent variable of the basic expression of the deformation function ω includes a maximum deflection value f generated by determining the buckling deformation; The step 2 is specifically as follows: Based on the large deflection equation of the thin plate, the deformation function ω of the plate is determined, and its basic expression is composed of trigonometric functions: Among them, f is the maximum deflection value caused by buckling deformation; m is the parameter that determines the deformation shape, which is a positive integer; j, p, k, q are adjustment parameters that meet the plate boundary conditions; a and b are the lengths of the two sides of the plate; Step 3: Introduce boundary conditions into the basic expression of the deformation function ω to obtain the expression of the deformation function ω under the boundary conditions; obtain the expression of the stress function F based on Formula I and the deformation function ω with the boundary conditions introduced; The step 3 specifically comprises the following steps: Step 3.1: According to the different shear connectors used between the steel shell and the concrete, determine whether the boundary condition is a simply supported boundary condition or a fixed boundary condition, and let x = a to obtain the mathematical expressions under the two boundaries: Step 3.2: Substitute the deformation function ω that satisfies the boundary conditions into the second part of (I), and let j = p = 1, k = q = 0, corresponding to the case of four simple supports, as follows: Step 3.3: Obtain the special solution of the trigonometric function of the steel shell stress function F, which is in the form of: Where A and B are arbitrary constants; Step 3.4: Substitute the special solution of the above steel shell stress function F into the left side of equation (V), and compare the coefficients on both sides of the equation to obtain the expressions of A and B: Step 3.5: Obtain the residual solution of the steel shell stress function F, and obtain the final expression of the steel shell stress function F based on the residual solution of the steel shell stress function F and the special solution of the steel shell stress function F; Step 4: Substitute the deformation function ω in step 3 and the stress function F in step 3 into equation (I), and establish the Galerkin equation to solve the specific expression of the deflection f; Step 5: Substitute the specific expression of f in step 4 into the basic expression of the deformation function ω in step 2 to obtain the expression of the final deformation function ω; The expression of the final deformation function ω in step 5 is as follows: The external force balance equation of the large deflection equation of the thin plate is specifically as follows: Where N x 、N y and N xy are the axial force and shear force in the x and y directions on the plate respectively; Substituting the expression of the final deformation function ω in step 5 into the external force balance equation of the large deflection equation of the thin plate to obtain the distribution function of the pull-out force specifically includes: Substitute the complete deformation function ω into the external force equilibrium equation of the thin plate large deflection equation, the first half of the first part of equation (II): Where Q is the required distribution function of the pull-out force; In step 6: taking force as the balance condition, the first part of the equation of formula (I) is deformed to obtain the external force balance equation of the large deflection equation of the thin plate, and the expression of the final deformation function ω in step 5 is substituted into the external force balance equation of the large deflection equation of the thin plate to obtain the distribution function of the pull-out force.

2. The method for calculating the external pullout force of the steel shell in a combined cable tower after yielding according to claim 1 is characterized in that: The step 3.5 specifically includes the following steps: Step 3.51: Supplement the remaining solution of F to satisfy: Step 3.52: Combined with the stress characteristics of the steel shell in the cable tower, the steel shell is considered to be in a unidirectional compression state under the action of the compression and bending load. At this time, the stress should satisfy: Among them, p x is the axial load in the x direction; Step 3.53: Integrate equation (IX) to obtain the remaining solution of F: Step 3.54: Combining the special solution and the remaining solution, the complete expression of F is:

3. The method for calculating the external pullout force of the steel shell in a combined cable tower after yielding according to claim 2 is characterized in that: The step 4 specifically comprises the following steps: Step 4.1: Substitute the above stress function F and deformation function ω into the first part of (I), and establish the Galerkin equation to solve the specific expression of deflection f. The Galerkin equation is: Step 4.2: Solve after integration. Since m is a positive integer, the integral result is simplified using the conditions sin(mπ)=0, cos(mπ)=1, and finally obtained: Step 4.4: The second half of (XIII) related to the shell column stiffness D represents the buckling load of the shell under this boundary condition and is defined as P c , the expression of the maximum deflection value f after deformation is:

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