A double-layer sliding calculation method for the cross section of a hollow thin steel shell-concrete composite cable tower

Abstract

The present invention proposes a double-layer slip calculation method for a hollow thin steel shell-concrete composite cable tower section, which belongs to the field of bridge engineering technology, and solves the problem of complex slip calculation methods for composite cable towers in the prior art; the present invention first obtains the steel shell strain and concrete strain of the cable tower section under the bending limit state of the section under the conventional axial compression ratio; then obtains the slip strain at the steel shell when slip is considered; then obtains the slip strain differential equation at the steel shell, and solves the two differential equations in general; finally, introduces boundary conditions and obtains the final slip strain expression at the tension side steel shell based on the differential equation after the general solution. In the present invention, different from the traditional method for calculating slip of composite beams, the steel shell in the cross section of the composite cable tower can ignore its own bending due to its small thickness, which simplifies the complexity of the formula and improves the calculation efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a double-layer sliding calculation method for a hollow thin steel shell-concrete composite cable tower section. Background Art

[0002] Steel shell-concrete composite cable tower is a structure that has emerged in bridge engineering in recent years. It has attracted widespread attention from engineers due to its strong bearing capacity and convenient construction performance. With the completion of composite bridge towers such as Nanjing Fifth Bridge and Anluo Yellow River Bridge, the practicality of the concept of hollow steel shell-concrete composite cable tower has withstood the test.

[0003] The steel-concrete composite tower section consists of a thin steel shell and concrete. Figure 1 As shown, the two are connected to each other through shear connectors. When the cable tower is subjected to force, the shear connectors will deform, resulting in slip between the steel and concrete. At present, the calculation method for the slip of the combined cable tower is complicated, and slip is an indispensable consideration in the design of the combined cable tower section. Summary of the invention

[0004] In view of this, the present invention provides a double-layer slip calculation method for the cross-section of a hollow thin steel shell-concrete composite cable tower. According to the design parameters of the cable tower cross-section, the specific slip sizes of the two slip surfaces in the cross-section can be directly calculated to obtain the true bending stiffness of the cable tower when it is actually subjected to force.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A double-layer sliding calculation method for a hollow thin steel shell-concrete composite cable tower section includes the following steps:

[0007] Step 1: Obtain the steel shell strain ε on the tensile side of the tower section under the bending limit state under the conventional axial compression ratio when slip is not considered s , compression side steel shell strain ε n , the strain of the tensile concrete connected to the tensile steel shell ε sc and the concrete strain ε on the compression side connected to the compression side steel shell nc ;

[0008] The step 1 specifically comprises the following steps:

[0009] Step 1.1: Based on the thickness of the steel shell and the width of the combined cable tower section, the axial stiffness ks of the steel shell itself is calculated and expressed as:

[0010] k s =E s bt(I)

[0011] Among them, E Sis the elastic modulus of the steel shell, b is the width of the combined cable tower section, and t is the thickness of the steel shell;

[0012] Step 1.2: Obtain the axial stiffness k of the combined tower section based on the material and size parameters of the combined tower section c and bending stiffness k cI , which is the total stiffness of the cross section including various structures such as steel shell and concrete; its expression is:

[0013]

[0014] Among them, E C is the converted elastic modulus of the combined tower section, h is the height of the combined section, b k is the width of the hollow part of the composite tower section, h k is the height of the hollow part of the composite tower section;

[0015] Step 1.3: Use the axial stiffness k of the combined section in (II) s and bending stiffness k sI , combined with the plane section assumption, the bending limit state of the tower section under the conventional axial compression ratio can be calculated without considering slip. At this time, the corresponding section curvature is φ, and its expression is:

[0016]

[0017] Where M is the ultimate bending moment of the section, I c0 is the actual bending moment of inertia of the cross section under the limit state;

[0018] Step 1.4: Calculate the steel shell strain ε on the tensile side under the bending limit state of the section under the conventional axial compression ratio s , compression side steel shell strain ε n , concrete strain on the tension side ε sc and the concrete strain ε on the compression side nc , with tensile strain as positive and compressive strain as negative, its expression is as follows:

[0019]

[0020] Where N sc is the axial force on the remaining isolation body when the combined cable tower section separates the tensile side steel shell, N nc is the axial force on the remaining isolation body when the combined cable tower section separates the compression side steel shell, T s Tension borne by the steel shell on the tension side, N n is the pressure on the steel shell on the compression side, y s and n are the distances of the tensile and compressive concrete from the neutral axis respectively;

[0021] Step 2: Based on the tensile side steel shell strain ε in step 1 s , compression side steel shell strain ε n , concrete strain on the tension side ε sc and the concrete strain ε on the compression side nc Obtain the slip strain γ of the steel shell on the tension side when considering slip s and the slip strain γ at the compression side steel shell n ;

[0022] The step 2 specifically includes the following steps:

[0023] Step 2.1: Based on the stiffness of the shear connector between the steel shell and the concrete, define the expression for the slip strain γ in the microelement dx as follows:

[0024]

[0025] Among them, τ is the shear stress between the steel shell and the concrete in the microelement dx, and K is the stiffness of the shear connector in the microelement dx;

[0026] Step 2.2: Define the slip strain γ of the steel shell on the tension side in the microelement segment s and the slip strain γ at the compression side steel shell n , the expression is as follows:

[0027]

[0028] where γ s is the slip strain of the steel shell on the tension side, γ n is the slip strain of the steel shell on the compression side.

[0029] Step 3: Obtain the slip strain γ of the steel shell on the tension side s and the slip strain γ at the compression side steel shell n Differential equations, solve the two differential equations respectively;

[0030] The step 3 specifically includes the following steps:

[0031] Step 3.1: According to the equilibrium relationship of the axial force of the composite beam in the micro segment, establish the N nc , T s 、N n and N sc The equilibrium relationships are:

[0032]

[0033] in;

[0034] Step 3.2: Simplify the tower structure into a cantilever beam with one end fixed and the other end subjected to axial force N and horizontal shear force P. Its length is L. With the fixed end as the origin, the curvature of each section on the cantilever beam is expressed as:

[0035]

[0036] Step 3.3: Combine equations (V), (VI), (VII), and (VIII) to obtain the differential equation of slip strain:

[0037]

[0038] Where K s and K n are the shear connector stiffness of the tension and compression side steel shells respectively;

[0039] Step 3.4: Solve the two equations of formula (IX) separately to obtain:

[0040]

[0041] Step 4: Introduce boundary conditions and obtain the final slip strain γ of the steel shell on the tension side based on the two general solutions of the differential equations s and the slip strain γ at the compression side steel shell n expression.

[0042] The step 4 specifically comprises the following steps:

[0043] Step 4.1: Obtain the boundary conditions of the cantilever beam, that is, the section at the point where the shear force P acts is not subject to bending moment, and the shear strain between the steel shell and the concrete should be 0. The expression is as follows:

[0044]

[0045] Step 4.2: Substitute equation (XI) into equation (X) to obtain the complete slip expression for both tension and compression:

[0046]

[0047] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0048] 1. In the present invention, the calculation formula is based on slip strain rather than slip displacement, so that the differential equation is simplified from second order to first order, which is more convenient to solve.

[0049] 2. In the present invention, the cross section of the composite cable tower is different from the common steel-concrete composite beam. There are two slip surfaces in the cross section of the composite cable tower under unidirectional bending state, which will produce a double slip effect. Even under elastic design, it has a significant impact on the bending stiffness of the cable tower. The present invention can specifically derive the impact of slip on the bending stiffness of the cable tower, thereby ensuring the safety of the structural design. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0051] Figure 1 A simplified cable tower structure force diagram of Example 1 provided by the present invention;

[0052] Figure 2 A simplified cross-sectional view of a cable tower according to Embodiment 1 of the present invention;

[0053] Figure 3 A diagram showing the relationship between the bending and curvature of the tower bottom section when the slippage is not considered in Example 1 provided by the present invention;

[0054] Figure 4 This is a comparison diagram of the bending-curvature relationship of the tower bottom section before and after slipping in Example 1 provided by the present invention.

[0055] Reference numerals

[0056] 1- Steel shell on the tensile side; 2- Steel shell on the compressive side; 3- Concrete; 4- Capping platform; 5- Shear studs; 6- Stiffening ribs with holes. DETAILED DESCRIPTION

[0057] 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.

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] Example

[0064] The embodiment of the present invention discloses a double-layer slip calculation method for a hollow thin steel shell-concrete composite cable tower section, comprising the following steps:

[0065] A double-layer sliding calculation method for a hollow thin steel shell-concrete composite cable tower section includes the following steps:

[0066] Step 1: Obtain the steel shell strain ε on the tensile side of the tower section under the bending limit state under the conventional axial compression ratio when slip is not considered s , compression side steel shell strain ε n , the strain of the tensile concrete connected to the tensile steel shell ε sc and the concrete strain ε on the compression side connected to the compression side steel shell nc ;

[0067] The step 1 specifically comprises the following steps:

[0068] Step 1.1: Based on the thickness of the steel shell and the width of the combined cable tower section, the axial stiffness ks of the steel shell itself is calculated and expressed as:

[0069] k s =E s bt(I)

[0070] Among them, E S is the elastic modulus of the steel shell, b is the width of the combined cable tower section, and t is the thickness of the steel shell;

[0071] Step 1.2: Obtain the axial stiffness k of the combined tower section based on the material and size parameters of the combined tower section c and bending stiffness k cI , which is the total stiffness of the cross section including various structures such as steel shell and concrete; its expression is:

[0072]

[0073] Among them, E C is the converted elastic modulus of the combined tower section, h is the height of the combined section, b k is the width of the hollow part of the composite tower section, h k is the height of the hollow part of the composite tower section;

[0074] Step 1.3: Use the axial stiffness k of the combined section in (II) s and bending stiffness k sI , combined with the plane section assumption, the bending limit state of the tower section under the conventional axial compression ratio can be calculated without considering slip. At this time, the corresponding section curvature is φ, and its expression is:

[0075]

[0076] Where M is the ultimate bending moment of the section, I c0 is the actual bending moment of inertia of the cross section under the limit state;

[0077] Step 1.4: Further, the tensile shell strain ε under this limit state is s , compression side steel shell strain ε n and the concrete strain ε on the tensile side of the concrete connected to them sc , concrete on the compression side ε nc It can also be calculated that, with tensile strain as positive and compressive strain as negative, the corresponding expression is:

[0078]

[0079] Where N sc is the axial force on the remaining isolation body when the combined cable tower section separates the tensile side steel shell, N nc is the axial force on the remaining isolation body when the combined cable tower section separates the compression side steel shell, T s Tension borne by the steel shell on the tension side, N n is the pressure on the steel shell on the compression side, y s and n are the distances of the tensile and compressive concrete from the neutral axis respectively;

[0080] Step 2: Based on the tensile side steel shell strain ε in step 1 s , compression side steel shell strain εn , concrete strain on the tension side ε sc and the concrete strain ε on the compression side nc Obtain the slip strain γ of the steel shell on the tension side when considering slip s and the slip strain γ at the compression side steel shell n ;

[0081] The step 2 specifically includes the following steps:

[0082] Step 2.1: When slip is not considered, under the assumption of plane section, the steel shell and the concrete connected to it are isostrained. However, when slip is considered, the stiffness of the shear connector between the two must be considered. The definition of the slip strain γ in the microelement dx is:

[0083]

[0084] Among them, τ is the shear stress between the steel shell and the concrete in the microelement dx, and K is the stiffness of the shear connector in the microelement dx;

[0085] Step 2.2: In the microelement segment, the slip strain should be equal to the strain difference between the steel shell and the concrete, that is:

[0086]

[0087] where γ s is the slip strain of the steel shell on the tension side, γ n is the slip strain of the steel shell on the compression side.

[0088] Step 3: Obtain the slip strain γ of the steel shell on the tension side s and the slip strain γ at the compression side steel shell n Differential equations, solve the two differential equations respectively;

[0089] The step 3 specifically includes the following steps:

[0090] Step 3.1: Further, whether separating the tensile steel shell or the compressive steel shell, the steel shell and the remaining section need to ensure axial force balance, that is, the axial force changes on the steel shell and the remaining section must be balanced with the shear force on the interface between the two, so the following balance formula is obtained:

[0091]

[0092] in;

[0093] Step 3.2: Due to the introduction of the microelement dx, the concept of φ is no longer limited to a single cross-sectional curvature. The cable tower structure can be simplified as a cantilever beam with one end fixed and the other end subjected to axial force N and horizontal shear force P. Its length is L. With the fixed end as the origin, the curvature of each cross section on the cantilever beam is expressed as:

[0094]

[0095] Step 3.3: Combine equations (V), (VI), (VII), and (VIII) to obtain the differential equation of slip strain:

[0096]

[0097] Where K s and K n are the shear connector stiffness of the tension and compression side steel shells respectively;

[0098] Step 3.4: Solve the two equations of formula (IX) separately to obtain:

[0099]

[0100] Step 4: Introduce boundary conditions and obtain the final slip strain γ of the steel shell on the tension side based on the two general solutions of the differential equations s and the slip strain γ at the compression side steel shell n expression.

[0101] The step 4 specifically comprises the following steps:

[0102] Step 4.1: Substitute the boundary conditions of the cantilever beam, that is, the section at the point where the shear force P acts is not subject to bending moment, and the shear strain between the steel shell and the concrete should be 0, that is:

[0103]

[0104] Step 4.2: The final complete slip expression for both tension and compression is:

[0105]

[0106] Example 2

[0107] This embodiment is a specific implementation method. Figure 1 The simplified cable tower structure is subjected to horizontal shear force P and axial force N = 7300 kN at the top. The tower height is L = 4 m. The bottom is a cap (4). The cross-section of the cap is much larger than the tower body and can be regarded as a rigid foundation. The center of the cross-section where the tower bottom and the cap meet is the coordinate origin O, and the x-axis points to the top of the tower. Under the action of load, the outer steel shell is divided into a tensile side steel shell (1) and a compressive side steel shell (2), both of which are connected to the concrete (3) through shear bolts (5) and stiffening ribs with holes (6).

[0108] The cross section is a 1m×1m square with a 0.4m×0.4m hollow area. The steel shell and stiffening ribs are made of Q345 steel with a thickness of 4mm. The stiffening ribs are 120mm wide and arranged throughout the tower height. The concrete is C50 concrete. The shear bolts are 6mm in diameter and 40mm in length. The opening diameter of the stiffening is 50mm, forming a shear tenon with the concrete.

[0109] First, calculate the axial stiffness of each part, where k s =8×10 5 kN,k c =3.47×10 7 kN, and then calculate the stiffness of the shear connector, where the stiffness of the shear stud can be determined by the following formula:

[0110] P=P u (1-e -0.71s ) 0.4 (XIII)

[0111] Where Pu is the ultimate shear force of the shear stud, and s is the shear deformation of the shear stud.

[0112] The stiffness calculation results of the shear studs with a diameter of 6 mm and a length of 40 mm used in this embodiment are:

[0113]

[0114] Secondly, the shear stiffness of the stiffening rib with holes is calculated. Since the stiffness of the concrete tenon is greater than the stiffness of the stiffening rib in this example, the shear stiffness of the weak stiffening rib is taken when the two are connected in series:

[0115]

[0116] The shear bolts on the tensile steel shell are arranged within the 4m tower body height, with 8 bolts arranged at a spacing of 150mm, totaling 26×8=208 bolts. There are 4 stiffening ribs, including stiffening ribs with holes and steel shells on the left and right sides:

[0117]

[0118]

[0119] It should be pointed out that the stiffness of the shear bolts varies with the slip size, and the stiffness of the stiffening ribs is also affected by the yield stress of the steel. These factors must be considered. The embodiment is calculated for the section with x = 0, because this is the part with the largest bending moment of the entire pier body and the area with the largest slip strain. Without considering slip, the section bending moment curvature relationship can be obtained from the section bearing capacity formula in the "Concrete Structure Design Code", such as Figure 3As shown in the figure, the neutral axis position under each bending moment is also determined. Substituting the above parameters into (Ⅻ) can obtain the section bending moment curvature relationship considering slip. Comparing the section bending curvature relationship before and after slip, as shown in Figure 4 As shown in the figure, the curvature of the cross section under the same bending moment after slip is considered increases significantly. When the cross section reaches the limit bending moment, the curvature increases by 31%. Even in the elastic segment, the difference between the two is 16%.

[0120] 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.

[0121] 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.

[0122] 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 double-layer slip calculation method for a hollow thin steel shell-concrete composite cable tower section, characterized in that: The following steps are involved: Step 1: Obtain the steel shell strain ε on the tensile side of the tower section under the bending limit state under the conventional axial compression ratio when slip is not considered s , compression side steel shell strain ε n , the strain of the tensile concrete connected to the tensile steel shell ε sc and the concrete strain ε on the compression side connected to the compression side steel shell nc ; Step 2: Based on the tensile side steel shell strain ε in step 1 s , compression side steel shell strain ε n , concrete strain on the tension side ε sc and the concrete strain ε on the compression side nc Obtain the slip strain γ of the steel shell on the tension side when considering slip s and the slip strain γ at the compression side steel shell n ; Step 3: Obtain the slip strain γ of the steel shell on the tension side s and the slip strain γ at the compression side steel shell n Differential equations, solve the two differential equations respectively; Step 4: Introduce boundary conditions and obtain the final slip strain γ of the steel shell on the tension side based on the two general solutions of the differential equations s and the slip strain γ at the compression side steel shell n expression; The step 1 specifically comprises the following steps: Step 1.1: Based on the thickness of the steel shell and the width of the combined cable tower section, the axial stiffness ks of the steel shell itself is calculated and expressed as: k s =E s bt(I) Among them, E S is the elastic modulus of the steel shell, b is the width of the combined cable tower section, and t is the thickness of the steel shell; Step 1.2: Obtain the axial stiffness k of the combined tower section based on the material and size parameters of the combined tower section c and bending stiffness k cI , whose expression is: Among them, E C is the converted elastic modulus of the combined tower section, h is the height of the combined section, b k is the width of the hollow part of the composite tower section, h k is the height of the hollow part of the composite tower section; Step 1.3: Based on formula (II) and combined with the plane section assumption, calculate the bending limit state of the tower section under the normal axial compression ratio without considering slip, and establish the section curvature φ at this time, which is expressed as: Where M is the ultimate bending moment of the section, I c0 is the actual bending moment of inertia of the cross section under the limit state; Step 1.4: Calculate the steel shell strain ε on the tensile side under the bending limit state of the section under the conventional axial compression ratio s , compression side steel shell strain ε n , concrete strain on the tension side ε sc and the concrete strain ε on the compression side nc , which is expressed as follows: Where N sc is the axial force on the remaining isolation body when the combined cable tower section separates the tensile side steel shell, N nc is the axial force on the remaining isolation body when the combined cable tower section separates the compression side steel shell, T s Tension borne by the steel shell on the tension side, N n is the pressure on the steel shell on the compression side, y s and n are the distances of the tensile and compressive concrete from the neutral axis respectively; The step 2 specifically includes the following steps: Step 2.1: Based on the stiffness of the shear connector between the steel shell and the concrete, define the expression for the slip strain γ in the microelement dx as follows: Among them, τ is the shear stress between the steel shell and the concrete in the microelement dx, and K is the stiffness of the shear connector in the microelement dx; Step 2.2: Define the slip strain γ of the steel shell on the tension side of the microelement segment s and the slip strain γ at the compression side steel shell n , the expression is as follows: where γ s is the slip strain of the steel shell on the tension side, γ n is the slip strain at the steel shell on the compression side; The step 3 specifically comprises the following steps: Step 3.1: According to the equilibrium relationship of the axial force of the composite beam in the micro segment, establish the N nc , T s 、N n and N sc The equilibrium relationships are: Where T s is the tensile force on the steel shell on the tension side; N n Pressure on the steel shell on the compression side; N sc 、N nc are the total axial forces of the cross-section except the tensile and compressive steel shells; τ s , τ n are the interlaminar shear stresses between the steel shell and concrete on the tension and compression sides, respectively; Step 3.2: Simplify the tower structure into a cantilever beam with one end fixed and the other end subjected to axial force N and horizontal shear force P. Its length is L. With the fixed end as the origin, the curvature of each section on the cantilever beam is expressed as: Step 3.3: Combine equations (V), (VI), (VII), and (VIII) to obtain the differential equation of slip strain: Where K s and K n are the shear connector stiffness of the tension and compression side steel shells respectively; Step 3.4: Solve the two equations of formula (IX) separately to obtain: Where C is an arbitrary constant determined by the boundary conditions; The step 4 specifically comprises the following steps: Step 4.1: Obtain the boundary conditions of the cantilever beam, that is, the section at the point where the shear force P acts is not subject to bending moment, and the shear strain between the steel shell and the concrete should be 0. The expression is as follows: Step 4.2: Substitute equation (XI) into equation (X) to obtain the complete slip expression for both tension and compression:

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