Method for calculating rotational stiffness of multi-limb composite steel support node around weak axis

Abstract

The application discloses a kind of multi-limb combined steel support node rotation stiffness calculation methods around weak axis, it is related to the technical field of deep foundation pit engineering and fabricated steel structure;The application decomposes the complex node structure into end plate, connecting plate, bolt group and other mechanical behavior clear core components, and calculates the stiffness of each component by using the component method, and then combines in series and parallel according to the classical mechanics principle, to achieve the technical effect of accurate physical modeling of the semi-rigid characteristics of the node and significantly improving the calculation efficiency.The method avoids complex nonlinear contact analysis, and the calculation formula is clear and easy to program.The calculation results of the method are compared with the full-scale model test results and the fine three-dimensional entity finite element analysis results, which achieves the technical effect of verifying that the calculation error of the method is within the acceptable range of engineering, and proves its reliability, solving the problem of insufficient accuracy of traditional empirical simplified method.

Description

Technical Field

[0001] This invention relates to the fields of deep foundation pit engineering and prefabricated steel structure technology, and in particular to a method for calculating the rotational stiffness of a multi-limb composite steel support node about a weak axis. Background Technology

[0002] As urban underground spaces expand to greater depths, prefabricated multi-limb composite steel support structures are widely used in large-scale deep foundation pit projects due to their advantages such as high load-bearing capacity, rapid construction, and recyclability. This structural system is composed of standardized steel components spliced ​​together at nodes, and its overall stability is highly dependent on the connection performance of these nodes.

[0003] Currently, in engineering design, splicing joints between struts and joints with embedded hydraulic jacks are often simplified to completely rigid or ideally hinged connections around the weak axis of the cross-section. However, actual engineering failure cases and studies show that the rotational resistance of such joints along the weak axis is significantly lower than that along the strong axis, exhibiting typical "semi-rigid" characteristics. This oversimplification of the design model prevents calculations from accurately reflecting the adverse effects of joint rotational deformation on the redistribution of internal forces and overall stability of the support structure, posing a potential safety hazard to the foundation pit support system. Therefore, developing a method to accurately quantify the rotational stiffness of the weak axis of multi-limb composite steel support joints is crucial for achieving refined design of the support system and accurately assessing its stability. Summary of the Invention

[0004] This invention provides a method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis, which solves the technical problem of the lack of an accurate and efficient method for calculating the rotational stiffness of the weak axis of a multi-limb composite steel support node in the prior art.

[0005] To solve the above-mentioned technical problems, the present invention provides a method for calculating the rotational stiffness of a multi-limb composite steel support node, comprising the following steps:

[0006] S1. Determine the rotation center position of the node: Based on the force state of the node, determine the rotation center position of the node about the weak axis;

[0007] S2. Identify the core components of the node: Identify the core components that contribute to the rotational stiffness of the node, wherein the core components include at least: end plates, connecting plates, and groups of high-strength bolts;

[0008] S3. Calculate the stiffness of the core component: Abstract the core component into independent spring units and calculate the stiffness value of each spring unit;

[0009] S4. Overall stiffness of the composite node: Based on the position of the rotation center, spring units located at the same lever arm height and connected in series according to the series connection rule are combined to achieve stiffness. Then, spring units located at different lever arm heights are grouped together and combined in parallel using deformation compatibility conditions, bending moment equivalence conditions, and resultant force equivalence conditions to calculate and output the overall initial rotational stiffness of the node.

[0010] Preferably, in step S1, for a strut node spliced ​​by connecting plates and end plates, the rotation center of the node is located on the neutral axis of the end plate in the plane in which the node bends about the weak axis.

[0011] Preferably, in step S3, the formula for calculating the stiffness of the high-strength bolt group is: ;in, This refers to the number of bolts. The elastic modulus of the bolt; This represents the cross-sectional area of ​​the bolt. This is the effective length of the screw.

[0012] Preferably, in step S3, the stiffness of the end plate is calculated, and the calculation includes the following steps:

[0013] S31. Divide the end plate into multiple rectangular sub-plates with three sides fixed and one side free in the mechanical model;

[0014] S32. Based on the position of each rectangular sub-plate in the overall node, determine the stress zone to which each rectangular sub-plate belongs. For rectangular sub-plates located in the tension zone of the node, treat them as members subjected to concentrated forces at the center and calculate their stiffness; for rectangular sub-plates located in the compression zone of the node, treat them as members subjected to uniformly distributed pressure and calculate their stiffness.

[0015] Preferably, in step S3, the stiffness of the connecting plate is calculated using the following formula: ;in, To improve the rigidity of the connecting plate assembly, For the number of connecting plates, For the elastic modulus of the connecting plates, This refers to the equivalent cross-sectional area of ​​the tension or compression zone of the connecting plate. This is the effective calculated length of the connecting plates.

[0016] Preferably, the series connection rule is specifically as follows: the equivalent stiffness of the spring units connected in series along the force path is calculated as the reciprocal of the sum of their reciprocals of stiffness.

[0017] Preferably, the deformation coordination condition is specifically: when the node rotates around the rotation center position... At that time, the linear displacement generated at the endpoints of each spring unit With corner and the lever arm of the spring unit Satisfies geometric relations: .

[0018] Preferably, the bending moment equivalence condition is as follows: the external bending moment M resisted by multiple parallel spring units is equal to the sum of the bending moments contributed by each spring unit, that is: ;in, and The first The stiffness and lever arm of each spring unit This is the node's corner.

[0019] Preferably, the resultant force equivalence condition is as follows: the resultant force on all parallel spring units should be equal to the resultant force of their equivalent system; that is: ;in, and The first The stiffness and lever arm of each spring unit.

[0020] Preferably, the parallel connection rule is as follows: Step 1: Apply the deformation compatibility condition, that is, the displacement of the endpoints of each spring unit. With node corner satisfy: Step 2: Apply the moment equivalence condition and the resultant force equivalence condition to establish and solve for the equivalent stiffness. With equivalent arm The system of equations.

[0021] Compared with related technologies, the rotational stiffness calculation method for a multi-limb composite steel support node provided by this invention has the following advantages:

[0022] This invention provides a method for calculating the rotational stiffness of multi-limb composite steel support nodes. By decomposing the complex node structure into core components with clear mechanical behaviors, such as end plates, connecting plates, and bolt groups, and calculating the stiffness of each component separately using a component-based method, and then combining them in series and parallel according to classical mechanics principles, this method achieves accurate physical modeling of the semi-rigid characteristics of the node and significantly improves computational efficiency. This method avoids complex nonlinear contact analysis, has clear calculation formulas, and is easy to implement in programming.

[0023] By comparing the calculation results of the method of the present invention with the test results of full-scale model and the results of fine three-dimensional solid finite element analysis, the present invention has achieved the technical effect of verifying that the calculation error of the method of the present invention is within the acceptable range of engineering, proving its reliability, and solving the problem of insufficient accuracy of traditional empirical simplification methods.

[0024] This invention achieves the technical effect of a highly efficient direct analysis method by incorporating the nodal rotational stiffness values ​​calculated in this invention as properties of spring elements into the beam-bar system calculation model of the support structure. This allows designers to significantly simplify the calculation model while ensuring accuracy, and quickly evaluate the overall stability and stress performance of multi-limb combined steel supports and even the entire foundation pit support system, providing key technical support for optimized design and ensuring construction safety. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the structure of Embodiment 1 of the present invention;

[0026] Figure 2 This is a schematic diagram of the force exerted on the cover plate according to Embodiment 1 of the present invention;

[0027] Figure 3 This is a schematic diagram of the force applied to the end plate according to Embodiment 1 of the present invention;

[0028] Figure 4 This is a schematic diagram of the spring stiffness of the component in Embodiment 1 of the present invention;

[0029] Figure 5 This is a schematic diagram of the overall stiffness of Embodiment 1 of the present invention;

[0030] Figure 6 This is a schematic diagram of the tension end plate according to Embodiment 1 of the present invention;

[0031] Figure 7 This is a schematic diagram of the pressure-bearing end plate according to Embodiment 1 of the present invention;

[0032] Figure 8 This is a schematic diagram of the structure of Embodiment 2 of the present invention;

[0033] Figure 9 This is a schematic diagram of the dimensions of the channel steel protective sleeve according to Embodiment 2 of the present invention.

[0034] The following are labeled in the diagram: 1. Standard steel section; 2. Cover plate; 3. High-strength bolt group; 4. End plate; 5. Channel steel protective sleeve; 6. Jack. Detailed Implementation

[0035] The above-mentioned and other technical features and advantages of the present invention will be described in more detail below with reference to the accompanying drawings.

[0036] Example 1

[0037] like Figure 1The diagram shows an application of the present invention to a strut splicing node. Two HW400 standard steel parts 1 (material Q355B) are joined together via end plates 4 (20mm thick, material Q355B). The connecting plates are specifically a rectangular cover plate 2 (16mm thick, material Q355B) used on the outer side of the steel flange and a group of 8.8 grade M22 high-strength bolts 3. The cover plate 2 is 16mm thick, and the end plate 4 is 20mm thick.

[0038] The initial rotational stiffness of the node about the weak axis (i.e., the axis perpendicular to the plane of cover plate 2) is calculated using the method of this embodiment.

[0039] The general principles for determining the rotation center and identifying the core components in this embodiment are as follows:

[0040] (a) General principles for determining the center of rotation

[0041] The rotation center of a node refers to the instantaneous center around which it rotates slightly about its weak axis. The location of this center is determined based on the internal force balance and deformation characteristics of the node under bending moment. Typically, the rotation center is located between the resultant force points of the node's main tensile components (such as the high-strength bolt group 3) and the resultant force points of the main compressive components (such as the bearing surface of the end plate 4). For structurally symmetrical nodes, the rotation center can be simplified to be located on its axis of symmetry. The specific location can be determined by analyzing the force flow path of the node or by referring to a simplified mechanical model. In this embodiment, the neutral axis specifically refers to the axis formed by the set of points where the normal stress within the end plate cross-section is zero when the node bends about its weak axis. For the symmetrical node, this can be simplified to the vertical geometric axis of symmetry of the end plate cross-section.

[0042] (ii) General principles for identifying core components

[0043] Core components are those that provide the main stiffness contribution to a node's resistance to rotation about its weak axis. During identification, components that generate the main internal forces and corresponding elastic deformations under bending moment should be selected along the force flow transmission path of the node. These components typically include:

[0044] 1. Plate areas that directly bear tensile or compressive forces (such as the tension / compression zone of end plate 4, cover plate 2);

[0045] 2. Fastener groups that withstand shear and tensile forces to prevent component separation (such as high-strength bolt groups 3);

[0046] 3. Other critical connectors specifically designed to transmit bending moments.

[0047] Minor components that contribute little to stiffness (such as non-critical parts of certain stiffeners) can be disregarded in simplified analysis.

[0048] (III) Definition of Key Terms and Combination Rules

[0049] To clearly illustrate the stiffness combination steps, the key terms and rules used in this invention are defined as follows:

[0050] 1. Spring Element: A mechanical model that simplifies the complex force-deformation relationship of a node's core components into an ideal linear spring with stiffness in only a single direction. Its stiffness value... It represents the force required to produce a unit deformation.

[0051] 2. Lever arm height: refers to the vertical distance from the point of application of the resultant force of the spring unit of the component to the rotation center O of the node (for rotation about the weak axis, that is, the distance along the height direction of the node section).

[0052] 3. Force path: refers to the chain of components through which external loads are transmitted from the node to the foundation. If two components are resisting the same external force, the force must pass through them sequentially, then they are on the same force path.

[0053] 4. Equivalent: In parallel combinations, this specifically refers to replacing multiple spring units with different lever arms with a single fictitious spring unit that produces the same rotation angle at the nodes. When, the bending moment resisted The resultant force acting on it is exactly the same as that of the original system.

[0054] 5. Series Rule: For spring units that are on the same force path and have the same lever arm height (e.g., with stiffnesses of respectively...), , ), and the overall stiffness after combination Calculated according to the mechanical rules of spring units connected in series:

[0055] ;

[0056] Its physical meaning is: when the deformations of the two are added together, the forces they bear are the same.

[0057] 6. Parallel Connection Rule: For two or more component spring units that jointly resist the same bending moment but have different lever arm heights, their combination must follow the parallel connection rule, which is a two-step solution process:

[0058] Step 1: Apply deformation compatibility conditions, i.e., the displacement of the endpoints of each spring element. With node corner satisfy: ;

[0059] Step 2: Apply the moment equivalence condition and the resultant force equivalence condition to establish and solve for the equivalent stiffness. With equivalent arm The system of equations.

[0060] Based on the above principles, the following explanation will take the strut splicing node as an example.

[0061] The specific steps are as follows:

[0062] Step S1: Determine the rotation center O.

[0063] Under bending moment about the weak axis, the internal forces of a node must form a couple to balance the external bending moment. These internal forces consist of the resultant force of the compressive force in the compression zone and the resultant force of the tensile force in the tension zone. In the node:

[0064] ① The pressure in the pressure zone is mainly transmitted through the contact between the upper half of the end plate 4.

[0065] ② The tensile force in the tension zone is mainly borne by the rod body of the high-strength bolt group 3 that penetrates the end plate 4.

[0066] The point of application of the resultant compressive force is located near the centroid of the compressed area of ​​end plate 4, while the point of application of the resultant tensile force is located near the center of the tensile bolt group. To ensure force balance at the node, the lines of action of this pair of tensile and compressive forces must be symmetrical about a certain point, and this point must be located between the points of application of the compressive and tensile forces. For this symmetrical node structure, the center of rotation O is located at the center of symmetry of the lines of action of this pair of forces. Based on the symmetrical arrangement of end plate 4 and the high-strength bolt group 3, determining the center of rotation O on the vertical central axis of the cross-section of end plate 4 is a reasonable simplification consistent with its force mechanism.

[0067] Step S2: Identify core components.

[0068] Based on the node structure and the force transmission path described above, the core components contributing to the rotational stiffness of the weak axis are identified as follows:

[0069] Tension zone components: high-strength bolt group 3, tension zone portion of end plate 4, and tension zone portion of cover plate 2.

[0070] Pressure zone assembly: the pressure zone portion of end plate 4 and the pressure zone portion of cover plate 2.

[0071] Among them, the high-strength bolt group 3 located in the compression zone contributes little to the rotational stiffness, and its stiffness contribution is already included in the calculation of the end plate compression zone assembly in this simplified model. The bolts connecting the two end plates 4 mainly bear shear force to transmit axial force, and their direct influence on the rotational stiffness of the weak axis is not considered separately in the component method simplified model described in this embodiment.

[0072] Step S3: Calculate the stiffness of each component's spring unit.

[0073] ① Stiffness of high-strength bolt group 3 :

[0074] All high-strength bolts in the tension zone of a node are treated as an equivalent spring element located at the center of that zone. Its stiffness is calculated using the following formula:

[0075] ;

[0076] In the formula, n is the number of tension bolts. Each of the two cover plates 2 has 16 bolts in the tension zone, so in this example there are 32 bolts. Let the elastic modulus of the bolt material be taken as... ; The cross-sectional area of ​​a single bolt is approximately 380 mm². The effective calculated length of the screw is the sum of the thicknesses of the two clamped end plates 4, which is 40mm.

[0077] ② End plate assembly stiffness:

[0078] like Figure 6 and Figure 7 As shown, end plate 4 is divided into four smaller rectangular regions by the steel web and reinforcing ribs. Its stiffness is calculated based on the deflection calculation method for three sides fixed and one side free.

[0079] The three-sided fixed support corresponds to the three boundaries tightly constrained by the strut web, stiffening ribs, or bolt groups; the one-sided free support corresponds to the boundary facing the node center. Figure 6 Taking the sub-plate shown as an example, its short side length 'a' is taken as the horizontal spacing between the two rows of bolts, and its long side length 'b' is taken as the net length of the sub-plate in the vertical direction. The coordinates x and y are the positions of the calculation points, and ξ and η are the positions of the points of application of the tensile force on the bolts, which are approximately considered as a concentrated force. In this example, the center point of the sub-plate is taken.

[0080] Tension zone stiffness The bolt tension is simplified to a concentrated force P acting on the tension zone. Based on the deflection calculation method for a plate with three sides fixed and one side free, the stiffness calculation formula is as follows:

[0081] ;

[0082] Stiffness of the compression zone :

[0083] ;

[0084] In the formula: D is the cylindrical stiffness of the plate. ; The thickness of end plate 2; denoted as Poisson's ratio; a and b are the calculated lengths of the short and long sides of the rectangular plate, respectively; x and y are the ranges of the horizontal and vertical coordinates starting from the center point of the rectangular plate, respectively; ζ and η are the distances of the concentrated force moment along the y-axis and x-axis, respectively.

[0085] ③ Stiffness of the tension zone of cover plate 2 and the stiffness of the compression zone :

[0086] like Figure 3 As shown, cover plate 2 mainly bears axial tension or axial compression. Dividing it into two spring units—one under tension and one under compression—according to the center of rotation, the calculation formula within the elastic range is:

[0087] ;

[0088] In the formula, m is the number of cover plates 2, which is 2 in this example; Let the elastic modulus of the cover material be taken as... ; The cross-sectional area of ​​a single cover plate in the tension zone (or compression zone) is calculated based on the position of the rotation center O, taking the portion of the cover plate's cross-sectional height from point O to the edge of the cover plate. The effective calculated length of the cover plate is the horizontal distance from the center of the outermost bolt hole to the rotation center O.

[0089] Step S4: Combine the overall stiffness.

[0090] The core of this step is to combine the stiffness of each component based on deformation compatibility conditions, bending moment equivalence conditions, and resultant force equivalence conditions.

[0091] The deformation compatibility condition refers to the condition where a small rotation angle occurs at the node around the rotation center O. At that time, the displacement generated at the endpoints of all connected component spring units must be related to the rotation angle. The determined geometric relationships are consistent.

[0092] When the node rotates slightly around the rotation center O At that time, the linear displacement generated at the endpoints of each parallel spring unit It must be with the corner and its lever arm Satisfying geometric compatibility, that is:

[0093] .

[0094] The bending moment equivalence condition refers to the external bending moment resisted by multiple spring units connected in parallel. , should be equal to the sum of the bending moments contributed by each spring element. That is, for the first spring element... One spring unit (stiffness is...) The lever arm is ), at the corner The force generated below is Its contributing bending moment is Therefore, the total bending moment is:

[0095] .

[0096] The aforementioned resultant force equivalence condition means that the resultant force on all parallel spring units should be equal to the resultant force of their equivalent system. That is:

[0097] .

[0098] If these spring units are equivalent to a stiffness of... Lever arm is If the equivalent spring is such that the equivalent spring resists the same bending moment, then the equivalent spring should resist the same bending moment. ,Right now:

[0099] ;

[0100] Combining the two equations, we can obtain the relationship between the equivalent stiffness and the equivalent service arm:

[0101] ;

[0102] At the same time, according to the force balance at the nodes, the resultant force on the equivalent spring should be equal to the resultant force of each spring element, that is:

[0103] ;

[0104] Simplified to:

[0105] ;

[0106] System of simultaneous equations:

[0107] ;

[0108] It can be solved and .

[0109] Based on the above principles, the overall stiffness is combined according to the following steps:

[0110] ① Stiffness combination of components in the tension zone

[0111] For spring unit combinations, those with the same lever arm are connected in series, while those with different lever arms are connected in parallel. Therefore, we first consider the series combination of the tension bolt and the tension end plate. Due to the left-right symmetry of the nodes, the equivalent spring stiffness of the end plate bolt combination under tension is... Calculation formula:

[0112] ;

[0113] Considering the parallel connection of the flange cover plate tension spring unit and the end plate bolt combination tension spring unit, the equivalent spring stiffness in the tension zone is formed. With equivalent tension arm The calculation formula is:

[0114] ;

[0115] ;

[0116] In the formula: Z1 and Z2 are the distances from the equivalent spring of the end plate bolt combination and the tension spring unit of the flange cover plate to the center of rotation, respectively. Pick This is based on simplifying and positioning the point of application of the tensile resultant force of the four bolts on the end plate at the height of the tension zone. The midpoint. Pick This is based on simplifying the tensile stress in the tension zone of cover plate 2 into a triangular distribution (maximum stress at the root, zero stress at the edge), with the resultant force applied at a point a distance from the center of rotation. Among them This represents the height of the tension zone at the node. For example... Figure 7 As shown.

[0117] ② Stiffness combination of components in the compression zone

[0118] The stiffness of the compression zone component is determined by the compressive stiffness of the two compression zone end plates. The series connection has the following equivalent stiffness:

[0119] ;

[0120] equivalent stiffness Then, the flange cover plate compression spring unit Parallel connection forms an equivalent compression spring The formula for its calculation is:

[0121] ;

[0122] Furthermore, based on the equivalent conditions for bending moment and resultant force, the equivalent compression arm can be obtained. The formula for its calculation is:

[0123] ;

[0124] In the formula: Z3 and Z4 are the distances from the equivalent spring of the compressed end plate assembly and the compressed spring unit of the flange cover plate to the center of rotation, respectively, and are respectively taken as and ,in This represents the height of the node's pressure zone. For example... Figure 7 As shown.

[0125] ③ Initial rotational stiffness of nodes

[0126] like Figure 5 As shown, the equivalent stiffness of the tension region component is determined based on the node rotation center. Equivalent stiffness of the component in the compression zone By combining the results, the rotational stiffness of the nodes can be obtained. The calculation formula is:

[0127] ;

[0128] The initial rotational stiffness of the spliced ​​joints in the specimen was calculated. for .

[0129] Step S5: Verify the calculation results.

[0130] To verify the accuracy of the method of the present invention, the following was performed on the same node:

[0131] Full-scale model test: Through static loading tests, the moment-rotation curves were obtained, and the experimental values ​​of the initial rotational stiffness of the nodes were calculated. ;

[0132] Three-dimensional solid finite element analysis: A refined finite element model is established for numerical simulation to calculate the finite element values ​​of the initial rotational stiffness of the nodes. .

[0133] The comparison results show that the calculated value by the method of the present invention is Compared with test values The relative error is -8.89%, which is consistent with the finite element value. The relative error is -9.11%. All errors are within a reasonable range acceptable for engineering applications, fully verifying the accuracy and reliability of the calculation method proposed in this invention.

[0134] Example 2

[0135] like Figure 8 The diagram shows the application of the present invention to a jack embedding node. A hydraulic jack 6 is embedded between a 3.0m long HW400 steel standard part 1 and a 2.1m long HW400 steel standard part 1, with the connecting plate specifically being a channel steel protective sleeve 5. The two are connected by an end plate 4 (20mm thick, Q355B material), a channel steel protective sleeve 5 (12.5mm thick, Q355B material), and a group of 8.8 grade M22 high-strength bolts 3, forming an embedding node where prestress can be applied and adjusted.

[0136] The initial rotational stiffness of the node about the weak axis is calculated using the method of this invention. The specific steps are as follows.

[0137] Step S1: Determine the rotation center O.

[0138] Under bending moment about the weak axis, the internal forces of the node are balanced by a pair of couples. In this node:

[0139] The pressure in the pressure zone is mainly transmitted by the upper half of the two end plates 4 that are in contact with each other.

[0140] The tension in the tension zone is mainly borne by the rod body, which is made up of a group of high-strength bolts 3 that run through the two end plates 4.

[0141] Given that the node structure is symmetrical about the vertical central axis of end plate 4, and the points of application of the compressive and tensile forces are approximately symmetrical about this axis, determining the rotation center O of the node on the vertical central axis of the cross-section of end plate 4 is a reasonable simplification consistent with its force mechanism.

[0142] Step S2: Identify core components.

[0143] Based on the node structure and force transmission path, the core components contributing to the rotational stiffness of the weak axis are identified as follows:

[0144] Tension zone components: high-strength bolt group 3, tension zone portion of end plate 4, and tension zone portion of channel steel protective sleeve 5.

[0145] Pressure zone components: the pressure zone portion of end plate 4 and the pressure zone portion of channel steel protective sleeve 5.

[0146] Step S3: Calculate the stiffness of each component's spring unit.

[0147] ① Stiffness of the high-strength bolt group 3 components :

[0148] The calculation method is the same as in Example 1, and the parameter values ​​are the same.

[0149] ② End plate assembly stiffness and :

[0150] The calculation method is the same as in Example 1. The end plate 4 is divided into tension and compression sub-plates. The stiffness of each sub-plate is calculated as a rectangular plate with three sides fixed and one side free, under concentrated force (tension zone) or uniform pressure (compression zone).

[0151] ③ Rigidity of the 5-component channel steel protective sleeve , :

[0152] The channel steel protective sleeve 5 mainly bears axial force, and its stiffness calculation formula is consistent with the cover plate stiffness formula in Example 1:

[0153] ;

[0154] In the formula, m represents the number of channel steel protective sleeves 5, which is 2 in this example; The elastic modulus of the channel steel protective sleeve 5 material is taken as... ; The equivalent cross-sectional area of ​​the channel steel protective sleeve 5 in the tension zone (or compression zone) is taken as the cross-sectional area of ​​one side flange; The effective calculated length of the channel steel protective sleeve 5 represents its equivalent length that participates in bearing forces.

[0155] In this embodiment, for the channel steel protective sleeve 5, its effective calculated length is obtained through parametric finite element analysis. The empirical formula for how the thickness t (unit: mm) varies with the thickness t (unit: mm) is as follows:

[0156] ;

[0157] In the formula, t is the thickness of the channel steel protective sleeve 5, and in this example, t is taken as 12.5mm.

[0158] Step S4: Combine the overall stiffness.

[0159] The principle and formula of stiffness combination are the same as step S4 in Embodiment 1, except that the relevant parameters of the cover plate are replaced with the parameters of the channel steel protective sleeve in this embodiment.

[0160] The initial rotational stiffness of the spliced ​​joints in the specimen was calculated. for .

[0161] Step S5: Verify the calculation results.

[0162] To verify the accuracy of the calculation method in this embodiment, a verification process similar to that in Embodiment 1 was conducted.

[0163] Full-scale model test verification: Specimens were fabricated according to the node structure of this embodiment and subjected to static loading tests. The moment-rotation curve was obtained, and the initial rotational stiffness of the node was calculated as a test value. .

[0164] Finite element numerical simulation verification: A refined three-dimensional solid finite element model was established for analysis, and the initial rotational stiffness finite element value of the node was obtained. .

[0165] Comparative analysis:

[0166] Calculated values ​​in this embodiment Compared with test values The relative error is -11.2%, and the calculated value in this embodiment is... With finite element value The relative error is -3.2%. All errors are within a reasonable range acceptable for engineering applications, fully verifying the accuracy and reliability of the calculation method proposed in this invention.

[0167] The results demonstrate that the component-based calculation method provided by this invention is also applicable to the jack embedded node. By introducing an empirical formula for the effective calculation length of the channel steel protective sleeve 5, its rotational stiffness can be accurately calculated.

Claims

1. A method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis, characterized in that, Includes the following steps: S1. Determine the rotation center position of the node: Based on the force state of the node, determine the rotation center position of the node about the weak axis; S2. Identify the core components of the node: Identify the core components that contribute to the rotational stiffness of the node, wherein the core components include at least: end plates, connecting plates, and groups of high-strength bolts; S3. Calculate the stiffness of the core component: Abstract the core component into independent spring units and calculate the stiffness value of each spring unit; S4. Overall stiffness of the composite node: Based on the position of the rotation center, spring units located at the same lever arm height and connected in series according to the series connection rule are combined to achieve stiffness. Then, spring units located at different lever arm heights are grouped together and combined in parallel using deformation compatibility conditions, bending moment equivalence conditions, and resultant force equivalence conditions to calculate and output the overall initial rotational stiffness of the node.

2. The method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis according to claim 1, characterized in that, In step S1, for the strut node spliced ​​by connecting plate and end plate, the rotation center of the node is located on the neutral axis of the end plate in the plane in which the node bends about the weak axis.

3. The method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis according to claim 1, characterized in that, In step S3, the formula for calculating the stiffness of the high-strength bolt group is as follows: ； in, This refers to the number of bolts. The elastic modulus of the bolt; This represents the cross-sectional area of ​​the bolt. This is the effective length of the screw.

4. The method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis according to claim 1, characterized in that, In step S3, the stiffness of the end plate is calculated, and the calculation includes the following steps: S31. Divide the end plate into multiple rectangular sub-plates with three sides fixed and one side free in the mechanical model; S32. Based on the position of each rectangular sub-plate in the overall node, determine the stress zone to which each rectangular sub-plate belongs. For rectangular sub-plates located in the tension zone of the node, treat them as members subjected to concentrated forces at the center and calculate their stiffness. For a rectangular subplate located in the compression zone of a node, it is considered as a component bearing uniformly distributed pressure and its stiffness is calculated.

5. The method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis according to claim 1, characterized in that, In step S3, the stiffness of the connecting plate is calculated using the following formula: ； in, To improve the rigidity of the connecting plate assembly, For the number of connecting plates, For the elastic modulus of the connecting plates, This refers to the equivalent cross-sectional area of ​​the tension or compression zone of the connecting plate. This is the effective calculated length of the connecting plates.

6. The method for calculating the rotational stiffness of a multi-limb composite steel support node about a weak axis according to claim 1, characterized in that, The series connection rule is as follows: the equivalent stiffness of spring units connected in series along the force path is calculated as the reciprocal of the sum of their reciprocals of stiffness.

7. The method for calculating the rotational stiffness of a multi-limb composite steel support node about its weak axis according to claim 1, characterized in that, The deformation coordination condition is specifically: when the node rotates around the rotation center position... At that time, the linear displacement generated at the endpoints of each spring unit With corner and the lever arm of the spring unit Satisfies geometric relations: 。 8. The method for calculating the rotational stiffness of a multi-limb composite steel support node about a weak axis according to claim 1, characterized in that, The bending moment equivalence condition is specifically: the external bending moment M resisted by multiple parallel spring units is equal to the sum of the bending moments contributed by each spring unit, that is: ； in, and The first The stiffness and lever arm of each spring unit This is the node's corner.

9. The method for calculating the rotational stiffness of a multi-limb composite steel support node about a weak axis according to claim 1, characterized in that, The specific condition for the equivalent resultant force is: the resultant force on all parallel spring units should be equal to the resultant force of their equivalent system; that is: ； in, and The first The stiffness and lever arm of each spring unit.

10. The method for calculating the rotational stiffness of a multi-limb composite steel support node about a weak axis according to claim 1, characterized in that, The parallel connection rule is as follows: Step 1: Apply deformation compatibility conditions, i.e., the displacement of the endpoints of each spring element. With node corner satisfy: ; Step 2: Apply the moment equivalence condition and the resultant force equivalence condition to establish and solve for the equivalent stiffness. With equivalent arm The system of equations.

Images