A method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members

Abstract

This invention provides a method for calculating the out-of-plane bearing capacity of unequal-sided angle steel cross-bracing members. An external load is applied to the angle steel, and the resulting compression member is discretized into several micro-segments. The curvature of each micro-segment is calculated, and the internal forces of the micro-segment sections are further calculated. This calculation is iteratively performed until the internal forces and the applied external load satisfy the convergence tolerance. Based on the external load and the matching micro-segment curvature, element stress, and micro-segment section internal forces, the bending moment of the section is obtained by integration. The length and rotation of each micro-segment are then calculated using the moment increment formula and the micro-segment rotation formula, respectively. This iterative calculation continues until the micro-segment rotation is zero. The lengths of each micro-segment are then summed to obtain the member length corresponding to the given external load. This method employs a reverse calculation approach, determining the corresponding bending moment based on the member's buckling shape, and then obtaining the member length, thus filling the gap in the calculation of the out-of-plane bearing capacity of unequal-sided angle steel.

Description

Technical Field

[0001] This invention relates to the field of angle steel bearing capacity calculation, and in particular to a method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members. Background Technology

[0002] To realize the large-scale utilization of new energy sources, long-distance power transmission lines are needed. Power transmission lines are developing towards high voltage, multiple circuits, and large capacity. This is accompanied by larger tower dimensions and longer diagonal members in the tower structure.

[0003] The equilateral angle steel cross bracing currently used has equal moments of inertia in the two bending planes. Due to the auxiliary support, the in-plane stiffness and bearing capacity of the bracing are much greater than those out-of-plane. This makes the out-of-plane bearing capacity verification play a controlling role in the structural stress calculation and material selection. At the same time, there is a large waste of in-plane stiffness, which not only increases the self-weight of the tower but also affects the wind-blocking area of ​​the entire tower.

[0004] Currently, the design calculations in my country's GB50017-2017 "Steel Structure Design Standard" and the power industry standard DL / T 54 86-2020 "Technical Regulations for the Design of Overhead Transmission Line Tower Structures" are mainly based on equilateral angle steel. They do not provide the design methods and parameters that must be considered in the design of iron towers, such as the cross-sectional type of unequal angle steel, the influence of eccentric force on the bearing capacity of unequal angle steel, and the local stability limit of unequal angle steel.

[0005] Although European EC 3 and American ASCE 10 standards include calculation methods for unequal angle steel, these are based on local steel rolling levels and processing conditions. The consideration of the impact of single-sided bolted connections at the ends on the load-bearing capacity of components differs significantly from that in my country's power transmission industry. Currently, 500kV double-circuit and ultra-high-voltage lines are mainly constructed domestically, lacking application experience abroad, and their calculation formulas have not been practically verified. Summary of the Invention

[0006] Since actual compression members contain unknowns such as initial geometric imperfections, initial eccentricity, and residual stress, it is not easy to obtain accurate buckling loads using traditional analytical methods. This invention provides a method for calculating the out-of-plane bearing capacity of unequal angle steel intersecting diagonal members. It adopts an inverse calculation approach, using the buckling shape of the compression member to determine the corresponding bending moment, and then derives the length of the compression member.

[0007] The technical means employed in this invention are as follows:

[0008] A method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members, given an unequal angle steel with an initial curvature of Φ. i＝1 Given an external load P applied to the angle steel, a compression member is obtained. The length L of the compression member corresponding to the external load P is calculated through the following steps:

[0009] S1: Discretize the compression member into several micro-segments, using a given external load P applied to the angle steel and the initial curvature Φ of the angle steel. i＝1 The curvature Φ of each corresponding micro-segment is obtained. i ;

[0010] S2: Divide the cross-section of the angle steel micro-segment in S1 into elements of equal size, and use the curvature Φ of the micro-segment obtained in S1. i The stress σ of each element in the micro-segment section was calculated. i Then, the internal force F of the angle steel section is obtained by integration, and further iterative calculations are performed to ensure that the internal force F and the given external load P satisfy the convergence tolerance δ. tor ;

[0011] S3: Based on the external load P that satisfies the convergence tolerance verification in S2, obtain the micro-segment curvature Φ corresponding to the external load P. i and the stress σ of each element i And further integrate to obtain the corresponding section bending moment M;

[0012] S4: Based on the calculations in S1-S3, the corresponding segment length Δ is further obtained through the moment increment formula between the bottom and top sections of the segment. i ;

[0013] S5: Further based on the micro-segment length Δ obtained in S4 i The rotation angle θ corresponding to the micro-segment can be obtained according to the micro-segment rotation angle formula. i ;

[0014] S6: Continue the calculation of S1-S5 in a loop until the micro-segment rotation angle θ is reached. i =0, the lengths Δ of each obtained micro-segment i The length L of the member corresponding to the given external load P is obtained by summing the results.

[0015] As a preferred embodiment, the curvature calculation formula for each micro-segment of the compression member in S1 is as follows:

[0016]

[0017] In the formula:

[0018] Φ i ,Φ i-1 Let be the curvature of the i-th segment and the (i-1)-th micro-segment;

[0019] P is the given axial pressure;

[0020] Q is the given lateral force;

[0021] Δ i Let i be the length of the i-th micro-segment;

[0022] θ i ,θi-1 This represents the increment of the rotation angle at the bottom and top sections of the member segment;

[0023] EI e This represents the bending stiffness of the elastic portion of the micro-segment cross-section.

[0024] Preferably, the long side of the angle steel section is taken as the y-axis, the short side as the x-axis, and the z-axis as the direction perpendicular to the neutral axis; the strain of each element in the angle steel section of the micro-segment S2 is calculated by the following formula:

[0025]

[0026] In the formula:

[0027] E is the elastic modulus;

[0028] EI x For bending stiffness;

[0029] A is the cross-sectional area of ​​the angle steel;

[0030] M is the bending moment of the section;

[0031] σ ri Residual stress in each cell;

[0032] y is the distance from the edge element to the bending axis of the angle steel section;

[0033] Among them, based on the static relationship of the cross section during bending:

[0034]

[0035] In the formula, ρ is the radius of curvature, and Φ is the curvature;

[0036] In equation (2):

[0037]

[0038] And, when the cell yields, the strain should be:

[0039]

[0040] Its f y The yield strength of the steel;

[0041] as well as:

[0042] When -ε y <ε i <ε y When, stress σ i for:

[0043] σ i =Eε i (6)

[0044] When |ε i |≥ε y When, stress σ i for:

[0045]

[0046] As a preferred embodiment, it is assumed that the length of the long side of the unequal angle steel is b1, the length of the short side is b2, and the origin of the coordinate system is located at the edge of the angle steel; the residual stress σ in equation (2) ri It is calculated using the following formula:

[0047] When y = 0, hour;

[0048] When y = 0, hour;

[0049] When x = 0, hour;

[0050] When x = 0, Time (8)

[0051] In the formula: βf y The given value is a standard value.

[0052] As a preferred embodiment, the internal force F of the angle steel section in S2 is obtained by integrating the following formula:

[0053]

[0054] In the formula: A i This represents the area of ​​each cell on the angle steel cross-section.

[0055] As a preferred option, it can be further verified by the following formula whether the internal force F and the given external load P satisfy the convergence tolerance δ. tor :

[0056] |PF| / P≤δ tor (10)

[0057] If equation (10) is not satisfied, the external load P is adjusted to P' using the following equation:

[0058]

[0059] In equation (11), η is the elastic modulus of the micro-segment cross section, which is calculated using the following formula:

[0060] η = A e / A (12)

[0061] In equation (12), A is the area of ​​the cross-section of the micro-segment. e For ε i <ε y The total area within the elastic range of the micro-segment cross-section obtained by cell integration, which is A e We obtain the following by integration:

[0062]

[0063] Furthermore, after adjusting the external load P to P', the calculation continues until the difference between P and F satisfies equation (10), thus obtaining the external load P that satisfies the convergence tolerance verification.

[0064] As a preferred embodiment, the bending moment M at section S3 is obtained by integrating the following formula:

[0065]

[0066] In the formula:

[0067] A i Let be the area of ​​each cell on the cross-section of the micro-segment;

[0068] Z i This is the distance from the center of each cell in the micro-segment cross section to the bending axis of the angle steel section.

[0069] As a preferred embodiment, the formula for the bending moment increment dM between the bottom and top sections of the micro-segment in S4 is:

[0070]

[0071] Preferably, the rotation angle θ of the micro-segment in S5 is... i It is calculated by the following formula:

[0072] θ i =θ i-1 -Φ i Δ i (16).

[0073] As a preferred method, the calculations of equations (1) to (16) are repeated until the micro-segment rotation angle θ is reached. i =0, and then the length of the member corresponding to the given external load P is obtained by summing the lengths of each micro segment using the following formula:

[0074] L=2∑Δ i (17).

[0075] Compared with existing technologies, the present invention has the following advantages:

[0076] This method is the first to adopt the inverse calculation approach. Based on the buckling form and residual stress distribution of unequal angle steel, the stable bearing capacity is obtained under basic assumptions. The corresponding bending moment is calculated based on the buckling shape of the compression member, and then the length of the compression member is obtained, thus filling the gap in the calculation of the out-of-plane bearing capacity of unequal angle steel. Attached Figure Description

[0077] Figure 1 This is a schematic diagram illustrating the steps of the method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to the present invention.

[0078] Figure 2 For the i-th micro-segment Δ i The coordinate system.

[0079] Figure 3 A schematic diagram showing the division of unequal-sided angle steel section elements and bending axis.

[0080] Figure 4 This is a schematic diagram showing the distribution of residual stress in a coordinate system for a micro-segment cross-section.

[0081] Figure 5 This is a schematic diagram of the peak residual stress in a micro-segment cross section.

[0082] Figure 6 This is a simplified diagram of the experimental setup.

[0083] Figure 7 The stability coefficient of the L90×56×6 component is compared with that of this method.

[0084] Figure 8 The stability coefficient of the L140×90×8 component is compared with that of this method.

[0085] That Figure 6 In the middle: 1. Loading end, 2. Connecting plate, 3. Knife-edge hinge, 4. Experimental platform base. Detailed Implementation

[0086] Combination Figure 1-8 The specific implementation method of this solution is as follows:

[0087] This invention employs an inverse algorithm approach, and based on the buckling mode and residual stress distribution of unequal-sided angle steel diagonal members, it obtains their stable bearing capacity using the following basic assumptions:

[0088] (1) The cross section satisfies the plane section assumption.

[0089] (2) The material is an ideal elastoplastic body.

[0090] like Figure 1 As shown, a method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel is provided. Given an unequal angle steel with an initial curvature of Φ, i＝1Given an external load P applied to the angle steel, a compression member is obtained. The length L of the compression member corresponding to the external load P is calculated through the following steps:

[0091] S1: Discretize the compression bar into several micro-segments, the i-th micro-segment as follows: Figure 2 As shown, given the external load P applied to the angle steel and the initial curvature Φ of the angle steel... i＝1 The curvature Φ of each corresponding micro-segment is obtained. i ;

[0092] S2: Divide the cross-section of the angle steel micro-segment in S1 into elements of equal size, and use the curvature Φ of the micro-segment obtained in S1. i The stress σ of each element in the micro-segment section was calculated. i Then, the internal force F of the angle steel section is obtained by integration, and further iterative calculations are performed to ensure that the internal force F and the given external load P satisfy the convergence tolerance δ. tor ;

[0093] S3: Based on the external load P that satisfies the convergence tolerance verification in S2, obtain the micro-segment curvature Φ corresponding to the external load P. i and the stress σ of each element i And further integrate to obtain the corresponding section bending moment M;

[0094] S4: Based on the calculations in S1-S3, the corresponding segment length Δ is further obtained through the moment increment formula between the bottom and top sections of the segment. i ;

[0095] S5: Further based on the micro-segment length Δ obtained in S4 i The rotation angle θ corresponding to the micro-segment can be obtained according to the micro-segment rotation angle formula. i ;

[0096] S6: Continue the calculation of S1-S5 in a loop until the micro-segment rotation angle θ is reached. i =0, the lengths Δ of each obtained micro-segment i The length L of the member corresponding to the given external load P is obtained by summing the results.

[0097] The formula for calculating the curvature of each micro-segment of the compression member in S1 is as follows:

[0098]

[0099] In the formula:

[0100] Φ i ,Φ i-1 Let be the curvature of the i-th segment and the (i-1)-th micro-segment;

[0101] P is the given axial pressure;

[0102] Q is the given lateral force;

[0103] Δ i Let i be the length of the i-th micro-segment;

[0104] θ i ,θ i-1 This represents the increment of the rotation angle at the bottom and top sections of the member segment;

[0105] EI e This represents the bending stiffness of the elastic portion of the micro-segment cross-section.

[0106] Specifically, based on the deformation characteristics of unequal-sided angle steel diagonal compression members, the following is obtained: Figure 2 The micro-segment deformation shown is expressed by the following formula:

[0107]

[0108]

[0109] In the formula, θ i 'This is an approximate value for the increment of the rod cross-section rotation angle from point O to point B;

[0110] After rearranging formula (1-2), we get:

[0111]

[0112] Differentiating equation (1-3) yields:

[0113]

[0114] In z = Δ i At this point, equation (1-4) is:

[0115]

[0116] Therefore, the end rotation angle of the micro-segment is obtained as follows:

[0117]

[0118] Where θ i for Figure 2 The increment of the rotation angle of the O and B sections of the micro-segment is also the increment of the rotation angle of the bottom and top sections of the micro-segment.

[0119] According to equation (1-6), considering axial pressure and lateral force, the increment of bending moment between the bottom and top sections of the micro-segment can be expressed as:

[0120]

[0121] From the moment-curvature relationship:

[0122] dM=EI e dΦ=EI e (Φi -Φ i-1 (1-8)

[0123] And the curvature calculation formula of equation (1) is obtained from equation (15) and equation (1-8).

[0124] Furthermore, to obtain the bending moments at both ends of the micro-segment, the unequal angle steel section is divided into 1mm × 1mm elements, with the bending axis being mm, as shown below. Figure 3 As shown. First, determine the strain of each element, and then obtain the element stress according to the constitutive relation.

[0125] The residual stress in the cross section is distributed in the coordinate system as follows: Figure 4 As shown. The strain of any element is caused by axial compression, bending deformation, and residual strain; the algebraic sum of these three is the total strain of the element. Figure 3 and Figure 4 As shown, let the long side of the angle steel section be the y-axis, the short side be the x-axis, and the z-axis be the direction perpendicular to the neutral axis; the strain of each element in the angle steel section of the micro-segment S2 is calculated by the following formula:

[0126]

[0127] In the formula:

[0128] E is the elastic modulus;

[0129] EI x For bending stiffness;

[0130] A is the cross-sectional area of ​​the angle steel;

[0131] M is the bending moment of the section;

[0132] σ ri Residual stress in each cell;

[0133] y is the distance from the edge element to the bending axis of the angle steel section;

[0134] Among them, based on the static relationship of the cross section during bending:

[0135]

[0136] In the formula, ρ is the radius of curvature, and Φ is the curvature;

[0137] In equation (2):

[0138]

[0139] And, when the cell yields, the strain should be:

[0140]

[0141] Its fy The yield strength of the steel;

[0142] Because the material is an ideal elastoplastic body, its element stress σ i The upper and lower limits are:

[0143] σ i =-f y When ε i ≤-ε y hour;

[0144] σ i =f y When ε i ≥ε y hour.

[0145] as well as:

[0146] When -ε y <ε i <ε y When, stress σ i for:

[0147] σ i =Eε i (6)

[0148] When |ε i |≥ε y When, stress σ i for:

[0149]

[0150] Wherein, the residual stress σ of each cell ri according to Figure 5 The distribution shown is calculated based on the coordinates of the cell center point. Since the thickness of the angle steel is relatively small compared to its length, σ is not considered. ri Variation in the thickness direction. Assume the length of the long side of the unequal angle steel is b1, the length of the short side is b2, and the origin of the coordinate system is located at the edge of the angle steel; the residual stress σ in equation (2) ri It is calculated using the following formula:

[0151] When y = 0, hour;

[0152] When y = 0, hour;

[0153] When x = 0, hour;

[0154] When x = 0, In equation (8): βfy Given conventional values, such as 0.1, 0.15, etc.

[0155] And, given the external load P, cross-sectional dimensions, and steel material f y Given a curvature Φ, the internal force F of the angle steel section in S2 is obtained by integrating the following formula:

[0156]

[0157] In the formula: A i This represents the area of ​​each cell on the angle steel cross-section.

[0158] Furthermore, the following formula is used to verify whether the internal force F and the given external load P satisfy the convergence tolerance δ. tor :

[0159] |PF| / P≤δ tor (10)

[0160] If satisfied, the given external load P is identified as matching the given curvature Φ. If not satisfied, the external load P is adjusted to P' using the following formula:

[0161]

[0162] In equation (11), η is the elastic modulus of the micro-segment cross section, which is calculated using the following formula:

[0163] η = A e / A (12)

[0164] In equation (12), A is the area of ​​the cross-section of the micro-segment. e For ε i <ε y The total area within the elastic range of the micro-segment cross-section obtained by cell integration, which is A e We obtain the following by integration:

[0165]

[0166] Furthermore, after adjusting the external load P to P', the calculation continues until the difference between P and F satisfies equation (10), thus obtaining the external load P that satisfies the convergence tolerance verification.

[0167] Furthermore, the bending moment M at section S3 is obtained by integrating the following formula:

[0168]

[0169] In the formula:

[0170] A i Let be the area of ​​each cell on the cross-section of the micro-segment;

[0171] Z i This is the distance from the center of each cell in the micro-segment cross section to the bending axis of the angle steel section.

[0172] Furthermore, the formula for the moment increment dM between the bottom and top sections of the micro-segment in S4 is:

[0173]

[0174] And, the rotation angle θ of the micro-segment in S5 i It is calculated by the following formula:

[0175] θ i =θ i-1 -Φ i Δ i (16).

[0176] And, iteratively calculate equations (1) to (16) until the micro-segment rotation angle θ. i =0, and then the length of the member corresponding to the given external load P is obtained by summing the lengths of each micro segment using the following formula:

[0177] L=2∑Δ i (17).

[0178] To verify the above calculation method, tests were conducted on unequal angle steel members with short-side connections. The angle steel used was Q235 with cross-sectional specifications of L90×56×6 and L140×90×8, and slenderness ratios of 30, 40, 60, 90, 120, 150, and 180, with member lengths ranging from 864 mm to 8100 mm.

[0179] In iron towers, unequal-sided angle steel diagonal members are connected to the main members, and are supported by auxiliary members within the plane. When the angle steel is under compression, bending mainly occurs out of plane. Figure 6 The diagram shows a simplified experimental setup. In the experiment, a node plate welded to a knife-edge hinge is connected to an unequal-sided angle steel.

[0180] The stability coefficients obtained from component tests and those calculated using this method are shown in Table 1 below.

[0181] Long side (m) Short side (m) Wall thickness (m) Slenderness ratio Test values This method 0.09 0.056 0.006 30 0.757 0.662 0.09 0.056 0.006 40 0.658 0.659 0.09 0.056 0.006 60 0.570 0.523 0.09 0.056 0.006 90 0.326 0.371 0.09 0.056 0.006 120 0.218 0.269 0.09 0.056 0.006 150 0.154 0.201 0.09 0.056 0.006 180 0.151 0.155 0.14 0.09 0.008 30 0.762 0.662 0.14 0.09 0.008 40 0.691 0.659 0.14 0.09 0.008 60 0.520 0.523 0.14 0.09 0.008 90 0.422 0.371 0.14 0.09 0.008 120 0.259 0.269 0.14 0.09 0.008 150 0.174 0.201 0.14 0.09 0.008 180 0.129 0.155

[0182] Table 1

[0183] Figure 7 , Figure 8 To compare the experimental stability coefficient with that obtained by this method, the average difference between the two types of components was 4.3%, and the results obtained by this method are in good agreement with the experimental results.

Claims

1. A method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members, characterized in that, Given an unequal angle steel with an initial curvature of Φ i＝1 Given an external load P applied to the angle steel, a compression member is obtained. The length L of the compression member corresponding to the external load P is calculated through the following steps: S1: Discretize the compression member into several micro-segments, using a given external load P applied to the angle steel and the initial curvature Φ of the angle steel. i＝1 The curvature Φ of each corresponding micro-segment is obtained. i ; S2: Divide the cross-section of the angle steel micro-segment in S1 into elements of equal size, and use the curvature Φ of the micro-segment obtained in S1. i The stress σ of each element in the micro-segment section was calculated. i Then, the internal force F of the angle steel section is obtained by integration, and further iterative calculations are performed to ensure that the internal force F and the given external load P satisfy the convergence tolerance δ. tor ; S3: Based on the external load P that satisfies the convergence tolerance verification in S2, obtain the micro-segment curvature Φ corresponding to the external load P. i and the stress σ of each element i And further integrate to obtain the corresponding section bending moment M; S4: Based on the calculations in S1-S3, the corresponding segment length Δ is further obtained through the moment increment formula between the bottom and top sections of the segment. i ; S5: Further based on the micro-segment length Δ obtained in S4 i The rotation angle θ corresponding to the micro-segment can be obtained according to the micro-segment rotation angle formula. i ; S6: Continue the calculation of S1-S5 in a loop until the micro-segment rotation angle θ is reached. i =0, the lengths Δ of each obtained micro-segment i The length L of the member corresponding to the given external load P is obtained by summing the results. The curvature calculation formula for each micro-segment of the compression member in S1 is as follows: In the formula: Φ i ,Φ i-1 Let be the curvature of the i-th segment and the (i-1)-th micro-segment; P is the given axial pressure; Q is the given lateral force; Δ i Let i be the length of the i-th micro-segment; θ i ,θ i-1 This represents the increment of the rotation angle at the bottom and top sections of the member segment; EI e This represents the bending stiffness of the elastic portion of the micro-segment cross-section.

2. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 1, characterized in that, Let the long side of the angle steel section be the y-axis, the short side the x-axis, and the z-axis the direction perpendicular to the neutral axis; the strain of each element in the angle steel section of the micro-segment S2 is calculated by the following formula: In the formula: E is the elastic modulus; EI x For bending stiffness; A is the cross-sectional area of ​​the angle steel; M is the bending moment of the section; σ ri Residual stress in each cell; y is the distance from the edge element to the bending axis of the angle steel section; Among them, based on the static relationship of the cross section during bending: In the formula, ρ is the radius of curvature, and Φ is the curvature; In equation (2): And, when the cell yields, the strain should be: Its f y The yield strength of the steel; as well as: When -ε y <ε i <ε y When, stress σ i for: s i =Ee i (6) When |ε i |≥ε y When, stress σ i for:

3. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 2, characterized in that, Assume the length of the longer side of the unequal angle steel is b1, the length of the shorter side is b2, and the origin of the coordinate system is located at the edge of the angle steel; the residual stress σ in equation (2) ri It is calculated using the following formula: When y = 0, hour; When y = 0, hour; When x = 0, hour; When x = 0, Time (8) In the formula: βf y The given value is a standard value.

4. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 3, characterized in that, The internal force F of the angle steel section in S2 is obtained by integrating the following formula: In the formula: A i This represents the area of ​​each cell on the angle steel cross-section.

5. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 4, characterized in that, Further verification is performed using the following formula to determine whether the internal force F and the given external load P satisfy the convergence tolerance δ. tor : |P-F| / P≤δ tor (10) If equation (10) is not satisfied, the external load P is adjusted to P' using the following equation: In equation (11), η is the elastic modulus of the micro-segment cross section, which is calculated using the following formula: n = A e / A (12) In equation (12), A is the area of ​​the cross-section of the micro-segment. e For ε i <ε y The total area within the elastic range of the micro-segment cross-section obtained by cell integration, which is A e We obtain the following by integration: Furthermore, after adjusting the external load P to P', the calculation continues until the difference between P and F satisfies equation (10), thus obtaining the external load P that satisfies the convergence tolerance verification.

6. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 5, characterized in that, The bending moment M at section S3 is obtained by integrating the following formula: In the formula: A i Let be the area of ​​each cell on the cross-section of the micro-segment; Z i This is the distance from the center of each cell in the micro-segment cross section to the bending axis of the angle steel section.

7. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 6, characterized in that, The formula for the bending moment increment dM between the bottom and top sections of the micro-segment in S4 is:

8. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 7, characterized in that, The rotation angle θ of the micro-segment in S5 i It is calculated by the following formula: i i =θ i-1 -F i D i (16)。 9. The method for calculating the out-of-plane bearing capacity of intersecting unequal angle steel members according to claim 8, characterized in that, Repeat equations (1) to (16) until the micro-segment rotation angle θ is reached. i =0, and then the length of the member corresponding to the given external load P is obtained by summing the lengths of each micro segment using the following formula: L=2∑Δ i (17)。

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