A classification method for the stiffness of modular steel structure joints

Abstract

The present invention discloses a classification method for the stiffness of modular steel structure joints, which is applicable to the classification of rigid connections, semi-rigid connections and hinged connections between and within such structural modules, so as to facilitate modeling in the overall design of the structure, and belongs to the field of modular steel structure design. The classification of joint stiffness is achieved by comparing the stiffness of the joint with a boundary value. The present invention first provides a calculation method for the boundary value of the stiffness of modular steel structure joints, and then compares the stiffness of the actual joint with the boundary values of rigid / semi-rigid and semi-rigid / hinged connections, so as to classify the joints. The present invention solves the problem that the existing specifications lack discriminant criteria for the classification of the stiffness of joints between and within modular steel structure modules, facilitates the classification of joint stiffness and the overall design of the structure, avoids complex non-linear analysis, and a large amount of computational work when adopting envelope design.

Description

Technical Field

[0001] The present invention belongs to the field of modular steel structure design, and specifically relates to a classification method for rigid / semi-rigid and semi-rigid / hinged connections between and within modular steel structure modules in the overall structural design. Background Art

[0002] Determining the joints as rigid connections or hinged connections during the structural design stage is an important content. However, due to the lack of design specifications specifically for the joints between and within modular steel structure modules, structural engineers lack a basis for classifying the stiffness of joints during the overall modeling analysis of modular steel structures. The classification of joint stiffness is achieved by comparing the stiffness of the joint with a boundary value. There is currently no consensus on the boundary values for rigid / semi-rigid and semi-rigid / hinged connections in modular steel structure joints. Although there is a traditional steel structure specification (EN 1993-1-8) stipulating that when the relative stiffness ratio of beam-column joints in a steel frame structure reaches 25, it can be regarded as a rigid joint. However, it is not clear whether this boundary value is applicable to modular steel structures. Designing the stiffness of joints between and within modules in modular steel structures according to the boundary values of traditional steel frame structure specifications will lead to serious risks.

[0003] Currently, a large number of studies have been conducted on the mechanical behavior of joints between and within modular steel structure modules at home and abroad. As shown in Figure 1, it is a diagram of the joint areas between and within modules. Generally, it is considered that to ensure the self-stability of each module during transportation and assembly, the beam-column joints within the module are designed to be rigid. However, the hinged and rigid connection behaviors of the joints between modules need to be specifically classified, and the influence of their axial, shear, and rotational stiffness on the structure needs to be considered. Most of the existing design studies on the stiffness of joints between modular steel structure modules focus on the rotational behavior of the joints, such as Farajian et al. (2021). "The influence of inter-module connections on the effective length of columns in multi-story modular steel frames." Therefore, it is necessary to conduct a comprehensive study on the classification method for rigid and hinged connections between and within modular steel structure modules, and propose a calculation formula for the boundary values of rigid / semi-rigid and semi-rigid / hinged connections, hoping to provide a reference for the stiffness classification of modular steel structure joints and the formulation of relevant design specifications. Summary of the Invention

[0004] To solve the above problems, the present invention discloses a classification method for the stiffness of modular steel structure joints.

[0005] The technical solution of the present invention:

[0006] A classification method for the stiffness of modular steel structure joints is as follows:

[0007] Determine the forms of the joint areas between modules (as shown in Figure 1), including vertical connections between modules, horizontal connections between modules, connections between ceiling beams and columns within modules, and connections between floor beams and columns within modules; select a reference substructure with the least number of joint areas between modules from a multi-story and multi-span modular steel structure (such as Figure 2 ), including bottom columns, second-floor columns, bottom ceiling beams and floor beams, and second-floor floor beams; where the bottom of the bottom columns is hinged, and the right ends of all beams are hinged and the horizontal degrees of freedom are released; determine that the joint stiffness components affecting the reference substructure are the rotational stiffness of vertical connections (S VR ), the shear stiffness of horizontal connections (S HS ), the rotational stiffness of floor beam-column joints (S FR ), and the rotational stiffness of ceiling beam-column joints (S CR ); The classification method for the stiffness of modular steel structure joints of the present invention is applicable to the classification of rigid / semi-rigid and semi-rigid / hinged joints between modules and within modules, and includes the following steps:

[0008] Step 1: Calculate the boundary values between rigid and semi-rigid joints for each joint;

[0009] Calculating the boundary values between rigid and semi-rigid joints for each joint includes the rotational stiffness S VR of vertical connections between modules of modular steel structures, the shear stiffness S HS of horizontal connections between modules, the rotational stiffness S FR of floor beam-column joints, and the rotational stiffness S CR of ceiling beam-column joints;

[0010] The calculation process is as follows:

[0011] 1) Determine the length L, height H of the module, and the cross-sectional dimensions of columns and beams to obtain the parameters i c , i fb , i cb , k c , D H values;

[0012] Among them, i c = EI c / H, i fb = EI fb / L and i cb = EI cb / L are the flexural line stiffnesses of columns, floor beams, and ceiling beams respectively, E is the elastic modulus of steel, I c is the moment of inertia of the column section, I fb is the moment of inertia of the floor beam section, Icb is the moment of inertia of the ceiling beam cross-section; k c = EA c / H is the axial line stiffness of the column, A c is the cross-sectional area of the column; is the relative slenderness ratio when the two ends of the column are rigidly constrained, N p = A c f y is the axial compressive bearing capacity of the column, f y represents the yield strength of the steel, N cr = π 2 EI c / H 2 is the Euler critical load when the two ends of the column are rigidly constrained; D H is half of the distance between the axes of adjacent module columns;

[0013] 2) Calculate the relative rotational restraint stiffness at the column ends as shown in Figure 2 (b);

[0014]

[0015] 3) Calculate the effective length factor K of the column Rigid ;

[0016]

[0017] 4) Calculate the parameters μ r and u r ;

[0018]

[0019]

[0020] 5) Calculate the boundary value for classifying the joint as rigid or semi-rigid;

[0021]

[0022] Step 2: Calculate the boundary value between semi-rigid and hinged joints for each joint;

[0023] Calculating the boundary value between semi-rigid and hinged joints for each joint includes the rotational stiffness S VR of the vertical connection between modular steel structure modules and the boundary value of the shear stiffness S HS of the horizontal connection between modules;

[0024] The calculation process is as follows:

[0025] 1) Determine the length L, height H of the module, and the cross-sectional dimensions of the columns and beams to obtain the parameters i c 、i fb, i cb , k c , D H The value of each parameter is the same as that in step 1;

[0026] 2) Calculate the relative rotational restraint stiffness of the column end as shown in Figure 2 (b);

[0027]

[0028] 3) Calculate the effective length coefficient k of the column Pinned ;

[0029]

[0030] 4) Calculate the parameters μ p and u p ;

[0031]

[0032]

[0033] 5) Calculate the boundary value between joint and semi-rigid connection of the node;

[0034]

[0035] Step 3: Obtain the stiffness of the node;

[0036] Step 4: Compare the stiffness of the node with the boundary value. When it is greater than the boundary value between rigid connection and semi-rigid connection, the node is regarded as a rigid connection; when it is less than the boundary value between semi-rigid connection and hinged connection, the node is regarded as a hinged connection; otherwise, it is regarded as a semi-rigid connection.

[0037] Advantages of the present invention: The present invention provides a classification method for the stiffness of modular steel structure nodes. The classification method includes the calculation formulas for the boundary values between rigid connection / semi-rigid connection and semi-rigid connection / hinged connection of nodes between modules and within modules, making up for the lack of a node stiffness classification standard in the current modular steel structure node design specification and reducing the risk of structural engineers in modular steel structure modeling design. This method can provide convenient, fast, and accurate results for the node stiffness classification of modular steel structures and provide a reference for modular steel structure design. Description of the Drawings

[0038] Figure 1(a) shows the node areas between modules and within modules;

[0039] Figure 1(b) shows the simplified model of Figure 1(a);

[0040] Figure 2Schematic diagram of a modular steel structure and a selected reference substructure, where (a) is a four-story and four-span modular steel structure; (b) is the reference substructure.

[0041] Figure 3 Schematic diagram of the joint connection of a modular steel structure, where (a) is the external connection view; (b) is the internal view of the connection.

[0042] Figure 4 Four ideal modular steel structure joint connection designs, where (a) both the vertical and horizontal connections are rigid; (b) the vertical connection is hinged and the horizontal connection is rigid; (c) the vertical connection is rigid and the horizontal connection is hinged; (d) both the vertical and horizontal connections are hinged.

[0043] In the figure: 1 - bolt, 2 - connecting plate, 3 - column, 4 - floor beam, 5 - ceiling beam, 6 - in-module joint, 7 - inter-module vertical connection joint, 8 - inter-module horizontal connection joint, 9 - installation hole, 10 - diaphragm, 11 - long bolt, 12 - shear key. Detailed implementation mode

[0044] The following further illustrates the detailed implementation mode of the present invention in combination with the accompanying drawings and technical solutions.

[0045] Embodiment

[0046] A classification method for the stiffness of modular steel structure joints is as follows:

[0047] Step 1: Calculate the boundary values between rigid and semi-rigid connections for each joint.

[0048] S VR ,S FR ,S CR and S HS Boundary values between rigidity and semi-rigidity:

[0049] 1) Figure 2 As shown in c 、i fb 、i cb 、k c ,a four-story and four-span modular steel structure, with the height H of each module being 3 m, the length L being 5 m, the vertical distance between adjacent modules being 0.1 m, and the horizontal distance being 0.2 m. The cross-sectional dimensions of the columns are SHS140×8, the cross-sectional dimensions of the floor beams are RHS80×140×8, and the cross-sectional dimensions of the ceiling beams are SHS80×8. The elastic modulus of the steel is 210 GPa, and the nominal yield stress is 355 MPa; by calculation, the parameters i D H = 0.2 / 2 = 0.1 m. The detailed cross-sectional characteristics of these beams and columns are shown in Table 1.

[0050] Table 1. Section properties and related parameters of components

[0051]

[0052] 2) Calculate the relative restraint rotational stiffness at the column ends

[0053]

[0054] 3) Calculate the effective length factor K of the column Rigid ;

[0055]

[0056] K Rigid,VR = 2

[0057] K Rigid,HS = 2

[0058] K Rigid,FR = 1.74

[0059] K Rigid,CR = 4.5

[0060] 4) Calculate the parameters μ r and u r ;

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] 5) Calculate the boundary value between rigid connection and semi-rigid connection of the joints.

[0068]

[0069] Step 2: Calculate the boundary values between semi-rigid connection and hinged connection of each joint; S VR and S HS Boundary value between hinged connection and semi-rigid connection:

[0070] 1) The same as step 1, step 1);

[0071] 2) Calculate the relative restraint rotational stiffness at the column ends

[0072]

[0073] 3) Calculate the effective length coefficient K of the column Pinned ;

[0074]

[0075] It can be calculated that:

[0076] K Pinned,VR = 2.218

[0077] K pinned,HS = 1.677

[0078] 4) Calculate the parameters μ P and u p ;

[0079]

[0080]

[0081]

[0082]

[0083] 5) Calculate the boundary value between pinned and semi-rigid joints of the node.

[0084]

[0085] Step 3: Obtain the stiffness of the node; From the node of the modular steel structure shown in Figure 3 The rotational stiffness S of the vertical inter-module connection of this node has been calculated in previous literature (Heet.al. Effect of inter-module connection on progressive collapse behavior of MiC.2021) VR is 1249 kN·m, the shear stiffness S of the horizontal inter-module connection HS is 50 kN·m, the rotational stiffness S of the floor beam-column joint FR is 1942 kN·m, and the rotational stiffness S of the ceiling beam-column joint CR is 627 kN·m.

[0086] Step 4: Compare the stiffness with the boundary value; It can be calculated from Step 1

[0087] It can be calculated from Step 2 By comparing the stiffness of each node with the boundary value, it can be seen that S VR 、SFR and S CR The stiffnesses are respectively less than and while S VR is greater than Therefore, S VR , S FR and S CR all have semi-rigid connections; S HS is less than Therefore, S HS is a hinged connection.

[0088] In addition, during the design stage, if the connection type of the module to be designed is Figure 4 the situation shown in (a), then the boundary values for all four node parameters to be classified as rigid need to be obtained, that is, calculate When the connection type of the module to be designed is Figure 4 the situation shown in (b), then the boundary value for S VR to be classified as a hinged connection, and the boundary values for S FR , S CR , S HS to be classified as rigid need to be obtained, that is, calculate Similarly, according to the design requirements, the stiffness boundary limits in different situations can be calculated.

Claims

1. A classification method for the stiffness of modular steel structure joints, characterized in that, Determine the forms of the node regions between modules, including vertical connections between modules, horizontal connections between modules, connections between ceiling beams and columns within modules, and connections between floor beams and columns within modules; select a reference substructure with the least number of node regions between modules from a multi-story and multi-span modular steel structure, including bottom columns, second-story columns, bottom ceiling beams and floor beams, and second-story floor beams; where the bottom of the bottom columns is hinged, and the right ends of all beams are hinged and release the horizontal degrees of freedom; determine that the node stiffness components affecting the reference substructure are the rotational stiffness S of the vertical connection VR , the shear stiffness S of the horizontal connection HS , the rotational stiffness S of the floor beam-column joint FR , and the rotational stiffness S of the ceiling beam-column joint CR ; The classification method for the stiffness of modular steel structure joints is applicable to the classification of rigid / semi-rigid and semi-rigid / hinged joints between modules and within modules, and includes the following steps: Step 1: Calculate the boundary values between rigid and semi-rigid joints for each joint; Calculating the boundary values of rigid connections and semi-rigid connections for each node, including the rotational stiffness S of the vertical connections between modular steel structure modules VR , the shear stiffness S of the horizontal connections between modules HS , the rotational stiffness S of the floor beam-column joints FR and the rotational stiffness S of the ceiling beam-column joints CR of the boundary values; The calculation process is as follows: 1) Determine the length L, height H of the module, as well as the cross-sectional dimensions of the columns and beams, and obtain the parameters i c 、i fb 、i cb 、k c 、 D H values; where i c = EI c / H, i fb = EI fb / L, and i cb = EI cb / L are the flexural line stiffnesses of columns, floor beams, and ceiling beams, respectively, E is the elastic modulus of steel, I c is the moment of inertia of the column cross-section, I fb is the moment of inertia of the floor beam cross-section, I cb is the moment of inertia of the ceiling beam cross-section; k c = EA c / H is the axial line stiffness of the column, A c is the cross-sectional area of the column; is the relative slenderness ratio when the two ends of the column are rigidly constrained, N p = A c f y is the axial compressive bearing capacity of the column, f y represents the yield strength of steel, N cr0 = π 2 EI c / H 2 is the Euler critical load when the two ends of the column are rigidly constrained; D H is half of the distance between the axes of adjacent module columns; 2) Calculate the relative rotational restraint stiffness at the column ends 3) Calculate the effective length factor K of the column Rigid ; 4) Calculate the parameter μ r and u r ; 5) Calculate the boundary values between rigid and semi-rigid joints for the joint classification; Step 2: Calculate the boundary values between semi-rigid and hinged joints for each joint; Calculating the boundary values between semi-rigid and hinged connections for each node, including the rotational stiffness S of the vertical connections between modular steel structure modules VR and the boundary values of the shear stiffness S of the horizontal connections between modules HS ; The calculation process is as follows: 1) Determine the length L, height H of the module, and the cross-sectional dimensions of the columns and beams to obtain the parameters i c and i fb and i cb and k c and D H values; 2) Calculate the relative rotational restraint stiffness of the column end 3) Calculate the effective length factor K of the column Pinned ; 4) Calculate the parameter μ p and u p ; 5) Calculate the boundary values between hinged and semi-rigid joints for the joint; Step 3: Obtain the stiffness of the joint; Step 4: Compare the stiffness of the joint with the boundary values. When it is greater than the boundary value between rigid and semi-rigid joints, the joint is regarded as rigid; when it is less than the boundary value between semi-rigid and hinged joints, the joint is regarded as hinged; otherwise, it is regarded as semi-rigid.

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