A method for predicting elastic stiffness of a bamboo-steel splint bolted connection node

Abstract

The application discloses a kind of elastic rigidity prediction methods of reed-bamboo-steel splint bolt connection node, and it is related to reed bolt connection technical field.The application is based on infinite body elastic foundation beam theory and is simplified, and an elastic rigidity calculation method suitable for reed-bamboo-steel splint bolt connection node is proposed, the method optimizes calculation parameters, so that it is simple in calculation process, so as to simply and quickly predict the elastic rigidity of reed-bamboo-steel splint connection form in the design process, increase the safety of this kind of connection design.The application can well solve the problem that the connection stiffness of steel splint connection form is difficult to calculate, and the connection stiffness can be calculated directly according to the structural design when reed-bamboo-steel splint bolt connection is adopted, which provides a reference for the design of this kind of connection.

Description

Technical Field

[0001] This invention relates to the field of reconstituted bamboo bolt connection technology, specifically to a method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolt connection nodes. Background Technology

[0002] Currently, research and application of reconstituted bamboo bolt connections mainly focus on steel plate bolt connections and steel filler plate bolt connections. Steel plate bolt connections have advantages such as convenient construction and high external stiffness. However, compared to steel plate bolt connections, steel filler plate bolt connections have lower external stiffness, but they are more aesthetically pleasing. Due to the relatively short development cycle of reconstituted bamboo structures in my country, there are still many shortcomings in the research on the connection of its components. Furthermore, no relevant organizations have issued standards or reference materials related to the application of reconstituted bamboo structures in structural engineering. Since bamboo and wood are similar, both being biomass materials, most current research on the connection of reconstituted bamboo components is based on relevant standards for wood structures. However, relevant Chinese standards such as the *Standard for Design of Timber Structures* (GB50005-2017), *General Specification for Timber Structures* (GB55005-2021), and *Technical Specification for Glulam Timber Structures* (GB / T50708-2012) do not provide a method for calculating the elastic stiffness of bolted connections. Although the European timber structure design code Eurocode 5 provides a method for predicting connection stiffness based on wood density and bolt diameter, and foreign scholar Kuenzi applied the elastic foundation beam theory to predict the elastic stiffness of bolted connections in timber structures and demonstrated good applicability, the significant differences in the basic material properties between wood and reconstituted bamboo mean that directly applying relevant design standards for wood structures to reconstituted bamboo structures may produce huge errors. This could not only lead to material waste but also potentially cause safety hazards. It is evident that there are still significant challenges in predicting the stiffness of reconstituted bamboo bolt connections, making it essential to propose a method for predicting the elastic stiffness of bolt connections in reconstituted bamboo structures.

[0003] In summary, current national and industry standards in my country do not mention methods for calculating the stiffness of bolted connections in reconstituted bamboo or wood structures. Among relevant international wood structure design standards, only the European Wood Structure Design Code 5 records methods for calculating the stiffness of bolted connections in wood structures. However, some scholars have already explored methods for calculating the stiffness of bolted connections in timber structures. Wang Xiaoting et al., in their paper "Mechanical Performance Analysis of Bolted Connections in Timber Structures," derived a method for calculating the elastic stiffness of timber-timber bolted connections based on the theory of elastic foundation beams. This method is consistent with the prediction method for the elastic stiffness of bolted connections in timber structures developed by Kuenzi, but it involves too many parameters to calculate, making the calculation process extremely inconvenient. Tao et al., in their paper "Elastic stiffness of timber joints with dowel-type fasteners and slotted-in-steelplate based on the theory of beamon elastic foundation," derived methods for calculating the elastic stiffness of timber-steel filler plate dowels and bolted connections based on the theory of elastic foundation beams. However, the calculation formulas involved in this method are extremely complex, requiring the complete deflection curve equation of the bolts in the connection, making it very inconvenient to use. Lui et al., in their paper "Force-displacement relations of bolted timber joints with...", further explored this method. The article "Slotted-insteelplates parallel to the grain" proposes a method for calculating the elastic stiffness of timber-steel filler plate bolted connections. However, this method involves the connection bearing capacity, so the connection bearing capacity needs to be known in advance during use, which brings great inconvenience to the prediction of connection stiffness. In the article "Experimental and Theoretical Study on Axial Slip Stiffness of Timber-Steel Plate Group Bolted Joints in Timber Reinforced Shells", Sun Xiaoluan et al. proposed a method for calculating the axial slip stiffness of steel filler plate group bolted joints based on the theory of semi-wireless foundation beams. However, the calculation method is relatively complex and its applicability in practical engineering is not strong.

[0004] In summary, current research on the calculation methods for the elastic stiffness of bolted connections in bamboo and wood structures does not cover steel-ply plate connections, mainly focusing on steel-filled plate bolted connections and wood-to-wood connections. However, the stress characteristics of steel-ply plate bolted connections, steel-filled plate bolted connections, and wood-to-wood bolted connections differ significantly. Therefore, the existing methods for calculating the elastic stiffness of steel-filled plate bolted connections and wood-to-wood connections cannot be directly used to predict the elastic stiffness of steel-ply plate bolted connections. Regarding the research on bolted connections in wood structures, the inventors have made progress in calculating the bearing capacity of connection nodes and have applied for Chinese patent CN115270327A. This application proposes a method for calculating the elastic stiffness of steel-ply plate bolted connections based on the simplified infinite-body elastic foundation beam theory, enabling easy prediction of the connection stiffness of steel-ply plate bolted connections. It also discloses a method for predicting the elastic stiffness of reconstructed bamboo-steel-ply plate bolted connection nodes. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the elastic stiffness of bolted joints in reconstituted bamboo-steel plywood, which can effectively solve the problem of difficulty in calculating the connection stiffness of steel plywood joints. Using this invention, the connection stiffness can be directly calculated based on the structural design when using bolted joints in reconstituted bamboo-steel plywood, providing a reference for the design of this type of connection.

[0006] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0007] A method for predicting the elastic stiffness of bolted joints made of reconstituted bamboo-steel plywood includes the following steps:

[0008] S1: Based on the European yielding model, the reconstituted bamboo-steel plywood bolt connection is divided into reconstituted bamboo pin groove bearing yield I, pin single hinge yield III and pin double hinge yield IV, and simplified using the foundation beam model;

[0009] S2: Based on S1, derive the equation of the bolt deflection curve for the steel plate bolt connection according to the boundary conditions of the steel plate bolt connection form;

[0010] S3: Combining the deflection curve equation derived in S2 with the European yield model, the connection stiffness K of the reconstituted bamboo dowel groove bearing yield I, single-hinged dowel yield III, and double-hinged dowel yield IV is derived to obtain the corresponding connection stiffness K. I K III K IV ;

[0011] S4: Select the minimum stiffness K e Predict the elastic stiffness of the connection nodes;

[0012] Where: K e =min{K Ⅰ ,KⅢ ,K Ⅳ}

[0013] Furthermore, the connection stiffness of S3 is derived as follows:

[0014] When the reconstituted bamboo dowel groove yields under pressure I, the connection stiffness K I for:

[0015] K I =ka

[0016] When the pin single hinge yields (III), the connection stiffness K III for:

[0017]

[0018] When the pin-double hinge yields to N, the connection stiffness K IV for:

[0019]

[0020] In the formula, k represents the basic modulus of reconstituted bamboo (N / mm). 2 ), where 'a' represents the thickness of the reconstituted bamboo; EI represents the bending stiffness of the bolt; and β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate;

[0021] The elastic stiffness of the steel clamp bolt connection under different yield models can be expressed as:

[0022]

[0023] In the formula: K Ⅰ K represents the elastic stiffness when the connection exhibits yield mode I. Ⅲ K represents the elastic stiffness when the connection exhibits yield mode III. Ⅳ EI represents the elastic stiffness of the connection when yielding mode IV occurs, EI represents the bending stiffness of the bolt, and β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate.

[0024] Furthermore, the S1 reconstituted bamboo pin groove bearing yield I, pin single hinge yield III, and pin double hinge yield IV;

[0025] In a double shear connection with steel plates as side members:

[0026] Reconstituted bamboo dowel groove bearing yield I: The main component is damaged while the steel plate remains intact and the bolt remains rigid. Since neither the bolt nor the steel plate yields, the bolt is in uniform contact with the hole wall of the reconstituted bamboo board, and the hole wall of the reconstituted bamboo board undergoes uniform extrusion deformation along the entire length of the bolt under load.

[0027] Pin-single hinge yielding III: This type of yielding involves both the main component and the bolt, and it generally occurs in connections where the main component is relatively thick and the bolt is relatively slender. Under load, the bolt will only generate one plastic hinge at each connection surface in the reconstituted bamboo component, while the bolt can rotate in the connection between the bolt and the steel plate.

[0028] Double-hinged yielding IV: This involves the yielding of both the main component and the bolt. When this yielding mode occurs, not only is the main component thicker and the bolt relatively slender, but the side steel plate is also thicker. When the connecting steel plate is a thick steel plate, it will exert a clamping effect on the bolt. Under load, the bolt will not only generate a plastic hinge on a single connection surface of the reconstituted bamboo component, but also generate a plastic hinge at the contact section between the steel plate and the reconstituted bamboo. At this time, the bolt cannot rotate at the end of the thick steel plate.

[0029] The foundation beam model is simplified as follows: the reconstituted bamboo is simplified to the foundation and the bolt is simplified to the foundation beam. According to Winker's assumption, we have y = P / k; where y represents the foundation settlement, k is the foundation elastic coefficient, and P is the pressure intensity per unit area.

[0030] Furthermore, when the reconstituted bamboo dowel groove yields under pressure I, the connection stiffness is determined by the dowel groove bearing stiffness of the reconstituted bamboo. During the elastic deformation stage of the connection, the foundation resists the load applied to the beam. Therefore, from the mechanical equilibrium relationship, we can obtain:

[0031]

[0032]

[0033] Therefore, by combining equations (1) and (2), we can obtain the connection stiffness as shown in equation (3) when the connection undergoes yield mode I:

[0034] K I =ka(3)

[0035] In the formula, k represents the basic modulus of the main component (N / mm²). 2 ), where a represents the length of the main component.

[0036] Furthermore, when the single hinge of the pin yields, the steel clamp only plays the role of concentrated load transfer, and there is no bending moment at the end of the bolt; under the load, the foundation beam will deform near the load end and the deformation at infinity is 0. In order to obtain the deflection equation of the bolt of the steel clamp bolt connection under the load, a small segment of the bolt is taken near the load end for analysis.

[0037] Based on the mechanical equilibrium relationship and combined with Figure 6 When ∑Q=0 and ∑M=0, we can obtain equations (4) and (5):

[0038] Q-(Q+dQ)+kydx=0(4)

[0039]

[0040] By neglecting the higher-order differentials in equation (5) and combining equations (4) and (5), we can obtain:

[0041]

[0042] Based on the small deformation assumption and the plane section assumption (refer to the mechanics of materials textbook) for the approximate solution of the deflection curve, the rotation angle, bending moment, and shear force of the foundation beam at any point in the interval x ≤ a can be expressed as:

[0043]

[0044] Therefore, by combining equations (6) and (7), we can obtain:

[0045]

[0046] The relative stiffness between the foundation beam and the foundation. By combining the method of complex root extraction, the general solution of equation (8) can be further obtained as:

[0047] y = e βx (Asinβx+Bcosβx)+e -βx (Csinβx+Dcosβx)(9)

[0048] Assume that the deflection of the beam is 0 at an infinite distance from the point of application of the load, i.e., y (x→∞) =0, from this equation (9) we can get A=B=0, then equation (9) can be transformed into:

[0049] y = e -βx (Csinβx+Dcosβx)(10)

[0050] Based on the boundary conditions of the foundation beam at this time:

[0051]

[0052] Therefore, by combining equations (7), (10), and (11), we can obtain the deflection equation of the foundation beam in this case as follows:

[0053]

[0054] From equation (12), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows:

[0055]

[0056] During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw. Furthermore, the stiffness of the connection remains constant during this elastic working phase. Therefore, the elastic stiffness of the connection in its working state can be represented by the stiffness at the interface between the steel plate and the bamboo plate.

[0057]

[0058] Furthermore, regarding the double-hinged yielding of the pin: it is assumed that the compressive effect between the steel plate and the reconstituted bamboo is not significant, so the bolt end only moves vertically under the clamping of the steel plate. Therefore, it is assumed that the connection end between the bolt and the steel plate is a sliding support, and the sliding support only supports displacement in the y direction.

[0059] Because the steel plate is relatively thick when yielding mode IV occurs, the load exerted by the steel plate on the bolts is simplified to a uniformly distributed load, and Therefore, at the interface between the steel plywood and the reconstituted bamboo, there are:

[0060]

[0061] Therefore, by combining equations (7), (10), and (15), we can obtain the deflection equation of the foundation beam under this condition:

[0062]

[0063] From equation (16), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows:

[0064]

[0065] During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw. Since the stiffness of the connection remains constant during this elastic phase, the elastic stiffness of the connection in its working state can be represented by the stiffness at the interface between the steel plate and the bamboo plate.

[0066]

[0067] The beneficial effects of this invention are:

[0068] The present invention provides a method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes. Based on the theory of infinite-body elastic foundation beams and simplified thereof, this method proposes an elastic stiffness calculation method applicable to reconstituted bamboo-steel plywood bolted connection nodes. The method optimizes the calculation parameters, making the calculation process simple, so that the connection elastic stiffness of reconstituted bamboo-steel plywood connection can be predicted easily and quickly in the design process, thereby increasing the safety of this type of connection design.

[0069] The method for predicting the elastic stiffness of bolted joints of reconstituted bamboo-steel plywood of the present invention states that when the connection exhibits yield mode I, the connection stiffness is mainly related to the bearing stiffness of the pin groove and the thickness of the reconstituted bamboo; when the connection exhibits yield mode III, the connection stiffness is mainly related to the bearing stiffness of the pin groove and the bolt diameter (EI); when the connection exhibits yield mode IV, the connection stiffness is mainly related to the bearing stiffness of the pin groove, the bolt diameter, and the thickness of the steel plate.

[0070] The present invention provides a method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes. The stiffness calculation model has a very simple calculation formula and a small number of calculation parameters when calculating the connection stiffness of steel plywood bolted connection. Only the relevant design parameters of the connection are needed to evaluate the stiffness of the connection.

[0071] The method for predicting the elastic stiffness of bolted joints of reconstituted bamboo-steel plywood of the present invention can effectively solve the problem of difficulty in calculating the connection stiffness of steel plywood connection. Using the present invention, the connection stiffness can be directly calculated based on the structural design when bolting reconstituted bamboo-steel plywood, providing a reference for the design of this type of connection.

[0072] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0073] Figure 1 This is a flowchart of the method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes according to an embodiment of the present invention;

[0074] Figure 2 This is a schematic diagram of the yield mode of the bolted connection of the reconstituted bamboo-steel plywood according to an embodiment of the present invention;

[0075] Figure 3 This is a simplified model of the steel clamp bolt double shear connection described in the embodiment of the present invention;

[0076] Figure 4 This is a simplified model of yield mode I as described in the embodiments of the present invention;

[0077] Figure 5 This is a simplified model of yield mode III as described in the embodiments of the present invention;

[0078] Figure 6 This is a schematic diagram illustrating the analysis of a bolt micro-segment near the load end as described in an embodiment of the present invention;

[0079] Figure 7 This is a simplified model of yield mode IV as described in the embodiments of the present invention;

[0080] Figure 8 This is a schematic diagram of the pin groove bearing stiffness according to an embodiment of the present invention; Detailed Implementation

[0081] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings.

[0082] A method for predicting the elastic stiffness of bolted joints made of reconstituted bamboo-steel plywood includes the following steps:

[0083] S1: Based on the European yielding model, the reconstituted bamboo-steel plywood bolt connection is divided into reconstituted bamboo pin groove bearing yield I, pin single hinge yield III and pin double hinge yield IV, and simplified using the foundation beam model;

[0084] S2: Based on S1, derive the equation of the bolt deflection curve for the steel plate bolt connection according to the boundary conditions of the steel plate bolt connection form;

[0085] S3: Combining the deflection curve equation derived in S2 with the European yield model, the connection stiffness K of the reconstituted bamboo dowel groove bearing yield I, single-hinged dowel yield III, and double-hinged dowel yield IV is derived to obtain the corresponding connection stiffness K. I K III K IV ;

[0086] S4: Select the minimum stiffness K e Predict the elastic stiffness of the connection nodes;

[0087] Where: K e =min{K Ⅰ ,K Ⅲ ,K Ⅳ}

[0088] The present invention will now be described in conjunction with specific embodiments:

[0089] Example 1

[0090] Reconstituted bamboo-steel plywood bolt connections are classified into yield modes I, III, and IV:

[0091] In this embodiment:

[0092] In a double shear connection with steel plates as side members:

[0093] For example, 2 Figure 2 As shown in (a), yield mode I is considered to be the failure of the main component while the steel plate remains intact and the bolt remains rigid. This yield mode generally occurs in connections where the main component is relatively thin and the bolt is relatively thick. Under this yield mode, since neither the bolt nor the steel plate yields, it is assumed that the bolt is in uniform contact with the hole wall of the reconstituted bamboo board and the hole wall of the reconstituted bamboo board undergoes uniform extrusion deformation along the entire length of the bolt under load.

[0094] Based on the above analysis, in this embodiment:

[0095] The bolted connection of reconstituted bamboo-steel plywood is simplified using a foundation beam model. In the bolted connection of reconstituted bamboo-steel plywood, such as... Figure 4 Figure 3 As shown, the reconstituted bamboo is simplified to a foundation and the bolts are simplified to foundation beams. According to Winker's assumption, we have y = P / k (where y represents the foundation settlement, k is the foundation elastic coefficient, and P is the pressure intensity per unit area). Based on this, we further estimate the connection elastic stiffness of steel plate bolted connections under different yield modes by considering the boundary form of an infinitely long beam with concentrated loads applied at the ends.

[0096] In this embodiment, yield mode I is the reconstituted bamboo slotted bearing yield I. In yield mode I, it can be assumed that the bolt always remains rigid and is tightly fitted to the reconstituted bamboo hole wall along the entire length of the reconstituted bamboo hole thickness. That is, it is assumed that the foundation will undergo uniform settlement under the uniformly distributed load on the beam. Therefore, as Figure 4 Figure 4 The diagram shows a simplified version.

[0097] thus Figure 4 It can be seen that when the connection occurs in yield mode I, the connection stiffness is determined by the bearing stiffness of the dowel groove of the reconstituted bamboo. During the elastic deformation stage of the connection, the foundation resists the load applied to the beam. Therefore, from the mechanical equilibrium relationship, we can obtain:

[0098]

[0099]

[0100] Therefore, by combining equations (1) and (2), we can obtain the connection stiffness as shown in equation (3) when the connection undergoes yield mode I:

[0101] K I =ka(3)

[0102] In the formula, K I This represents the elastic stiffness corresponding to yield mode III, and k represents the basic modulus of the main component (N / mm). 2 ), where a represents the length of the main component.

[0103] In this embodiment, yielding mode III:

[0104] For example, 2 Figure 2 As shown in (b), yield mode III involves the yielding of both the main member and the bolt. This yield mode generally occurs in connections where the main member is relatively thick and the bolt is relatively slender. According to Eurocode 5, the European timber structure design code, when the connecting steel plate is thin, it will not exert a clamping effect on the bolt. Therefore, under load, the bolt will only generate a plastic hinge on each connection surface in the reconstituted bamboo member, while the bolt can rotate in the connection between the bolt and the steel plate.

[0105] In yield mode III, since the thinner steel plate does not clamp the bolt, the steel clamp can be considered to only transfer concentrated loads. Since there is no bending moment at the bolt end, it can be treated as... Figure 5 Figure 5 The diagram simplifies it ( Figure 5 In this context, k represents the foundation modulus, P represents the concentrated load, and δ represents the bolt end displacement.

[0106] like Figure 5 It is known that under load, the foundation beam will deform near the load end while the deformation at infinity is zero. To obtain the deflection equation of the bolts in the steel clamp bolt connection under load, a small segment of the bolt is taken near the load end for analysis. Figure 5 In this context, k represents the foundation modulus, P represents the concentrated load, and δ represents the bolt end displacement. Figure 6 It can be seen that; ( Figure 6 In this context, M represents the bending moment on any infinitesimal segment of the bolt, Q represents the shear force on any infinitesimal segment of the bolt, and σ represents the ground reaction force.

[0107] Based on the mechanical equilibrium relationship and combined with Figure 6 When ∑Q=0 and ∑M=0, we can obtain equations (4) and (5):

[0108] Q-(Q+dQ)+kydx=0(4)

[0109]

[0110] By neglecting the higher-order differentials in equation (5) and combining equations (4) and (5), we can obtain:

[0111]

[0112] Based on the small deformation assumption and the plane section assumption (refer to the mechanics of materials textbook) for the approximate solution of the deflection curve, the rotation angle, bending moment, and shear force of the foundation beam at any point in the interval x ≤ a can be expressed as:

[0113]

[0114] Therefore, by combining equations (6) and (7), we can obtain:

[0115]

[0116] The relative stiffness between the foundation beam and the foundation. By combining the method of complex root extraction, the general solution of equation (8) can be further obtained as:

[0117] y = e βx (Asinβx+Bcosβx)+e -βx (Csinβx+Dcosβx) (9)

[0118] Assume that the deflection of the beam is 0 at an infinite distance from the point of application of the load, i.e., y (x→∞) =0, from this equation (9) we can get A=B=0, then equation (9) can be transformed into:

[0119] y = e -βx (Csinβx+Dcosβx) (10)

[0120] Based on the boundary conditions of the foundation beam at this time:

[0121]

[0122] Therefore, by combining equations (7), (10), and (11), we can obtain the deflection equation of the foundation beam in this case as follows:

[0123]

[0124] From equation (12), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows:

[0125]

[0126] During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw. Furthermore, the stiffness of the connection remains constant during this elastic working phase. Therefore, the elastic stiffness of the connection in its working state can be represented by the stiffness at the interface between the steel plate and the bamboo plate.

[0127]

[0128] In this embodiment, yielding mode IV:

[0129] For example, 2 Figure 2 As shown in (c), yield mode III is the same, and yield mode IV also involves the yielding of the main member and the bolt. When this yield mode occurs, not only is the thickness of the main member large and the bolt relatively slender, but the thickness of the side steel plate is also large. According to the European timber structure design code Eurocode 5, when the connecting steel plate is a thick steel plate, it will have a clamping effect on the bolt. Therefore, under the load, the bolt will not only generate a plastic hinge on a single connection surface of the reconstituted bamboo member, but also generate a plastic hinge at the contact section between the steel plate and the reconstituted bamboo. At this time, the bolt cannot rotate at the thick steel plate end.

[0130] In yield mode IV, the clamping effect of the thick steel plate on the bolt causes a plastic hinge to form at the interface between the steel plate and the reconstituted bamboo. Therefore, unlike yield mode III, it is assumed that the compressive effect between the steel plate and the reconstituted bamboo is not significant. Consequently, the bolt end only undergoes vertical movement under the clamping of the steel plate. Therefore, it is assumed that the connection end between the bolt and the steel plate is a sliding support, and the sliding support only supports displacement in the y-direction. Therefore, it can be processed as follows: Figure 7 The simplification shown. Figure 7 In this context, k represents the foundation modulus, M represents the bolt end bending moment, q represents the uniformly distributed load on the bolt, qt represents the bolt end shear force, t represents the steel plate thickness, and δ represents the bolt end displacement.

[0131] Because the steel plate is relatively thick when yielding mode IV occurs, the load exerted by the steel plate on the bolts is simplified to a uniformly distributed load, and Therefore, at the interface between the steel plywood and the reconstituted bamboo, there are:

[0132]

[0133] Therefore, by combining equations (7), (10), and (15), we can obtain the deflection equation of the foundation beam under this condition:

[0134]

[0135] From equation (16), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows:

[0136]

[0137] In the formula, P represents the load on the connection, EI represents the bending stiffness of the bolt, and β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate.

[0138] During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw. Since the stiffness of the connection remains constant during this elastic phase, the stiffness at the interface between the steel plate and the bamboo plate can be used to represent the elastic stiffness of the connection in its working state.

[0139]

[0140] In the formula, K Ⅳ EI represents the elastic stiffness corresponding to yield mode IV, EI represents the bolt bending stiffness, and β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate.

[0141] In summary, the elastic stiffness of the steel plate bolted connection under different yield models can be expressed as:

[0142]

[0143] In the formula: K Ⅰ K represents the elastic stiffness when the connection exhibits yield mode I. Ⅲ K represents the elastic stiffness when the connection exhibits yield mode III. ⅣEI represents the elastic stiffness of the connection when yielding mode IV occurs, EI represents the bending stiffness of the bolt, and β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate.

[0144] In this embodiment:

[0145] When performing stiffness design calculations for bolted connections made of reconstituted bamboo and steel plywood, the thickness of the steel plate, the thickness of the reconstituted bamboo, and the bolt diameter all have a certain influence on the yield mode of the connection. Therefore, the minimum stiffness of the connection under the three yield modes can be used as the stiffness K of the connection in the elastic stage. e Reference value, i.e.:

[0146] K e =min{K Ⅰ ,K Ⅲ ,K Ⅳ}(19)

[0147]

[0148] As can be seen from the formula, in the bolted connection of reconstituted bamboo and steel plywood, when the connection undergoes yield mode I, the connection stiffness is mainly related to the bearing stiffness of the pin groove and the thickness of the reconstituted bamboo; when the connection undergoes yield mode III, the connection stiffness is mainly related to the bearing stiffness of the pin groove and the bolt diameter (EI); when the connection undergoes yield mode IV, the connection stiffness is mainly related to the bearing stiffness of the pin groove, the bolt diameter and the thickness of the steel plate.

[0149] As can be seen from equations (19)-(20), this stiffness calculation model has a very simple calculation formula and a small number of calculation parameters when calculating the connection stiffness of the steel plate bolt connection. Only the relevant design parameters of the connection are needed to evaluate the stiffness of the connection.

[0150] It is worth noting that in actual engineering applications, both the steel plywood and the reconstituted bamboo beams in the bolted connection are pre-drilled, and the diameter of the pre-drilled holes is usually larger than the bolt diameter. Consequently, initial gaps inevitably exist between the components of the bolted connection. Therefore, when the reconstituted bamboo is relatively thick and the steel plate is also thick, the bolts usually do not exhibit a double-hinge yield mode (yield mode IV) at the initial stage of loading. Instead, as the loading process continues, the bolts first form a plastic hinge in the reconstituted bamboo component, which is the same as yield mode III. Then, with further loading, the initial gaps between the connected components gradually disappear, and the clamping effect of the steel plate on the bolts becomes apparent. However, by this time, the reconstituted bamboo may have already entered the plastic stage, and the stiffness of the connection has decreased. The stiffness improvement brought about by the second plastic hinge formed by the clamping effect of the steel plate on the bolts is no longer significant. Therefore, in bolted connections of reconstituted bamboo and steel plates, when the thickness of the reconstituted bamboo is significantly greater than that of the steel plate, theoretically, if the connection is fully clamped by the steel plate from the initial loading stage and forms a plastic hinge (i.e., yield mode IV), its elastic stiffness should be much higher than that of connections where the thickness of the reconstituted bamboo is greater than that of the steel plate. However, in practical engineering applications, due to processing errors and the provision of bolt holes, this situation is rarely encountered. Therefore, the elastic stiffness calculation model corresponding to yield mode III can almost satisfy the elastic stiffness prediction for this type of connection in most cases. This statement will be verified later.

[0151] Example 2

[0152] Verification of the method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes in this invention:

[0153] In this embodiment:

[0154] In the current timber structure design standards such as NDS, GB50005, Eurocode5, and CSA, there are very few descriptions of bolt connection stiffness. Only Eurocode5 considers timber density and bolt diameter and proposes a formula for calculating bolt connection stiffness, the specific method of which is shown in equation (21).

[0155]

[0156] In the formula: K ser This represents the slip stiffness of bolted connections in timber structures, i.e., elastic stiffness; ρ m d represents the average density of the wood; d represents the bolt diameter.

[0157] Besides Eurocode 5, Kuenzi et al., in "Theoretical Design of Aniledor Bolted Joint Under Lateral Load," used the elastic foundation beam theory to predict the stiffness of bolted connections in timber structures. Wang Xiaoting et al., in their article "Mechanical Performance Analysis of Bolted Connections in Timber Structures," also used this method for verification. The calculation formula for this method is expressed as:

[0158]

[0159] In the formula: K e,BEFT This represents the elastic stiffness of the bolted connection; K1, K2, L1, L2, J1, and J2 are all calculation parameters, and their calculation methods can be found in the relevant explanations in "Mechanical Performance Analysis of Bolted Connections in Timber Structures".

[0160] To verify the applicability of the above two methods to bolted connections of steel plywood and reconstituted bamboo, the inventors conducted bolted connection tests on reconstituted bamboo and steel plywood. Since there are currently no relevant test specifications for reconstituted bamboo connection components, the specimen dimensions and test procedures were based on ASTM D5652. To avoid the specimen dimensions affecting the connection stiffness, the length, width, and height of the specimens were all greater than the minimum length specified in ASTM D5652. The specific test design is shown in Table 1 below:

[0161] Table 1 Design of bolted connection specimens for reconstituted bamboo-steel plywood

[0162]

[0163] Note: When α is 0°, it indicates loading along the grain; when α is 90°, it indicates loading across the grain.

[0164] Because the elastic stiffness K of the connection is calculated using this invention. e The elastic stiffness K is calculated using the elastic foundation beam theory. e,BEFT All of these require a basic modulus k for the bearing capacity of the dowel groove. Therefore, the inventors conducted a bearing capacity test on the reconstituted bamboo dowel groove to obtain the basic modulus k of the bearing capacity of the reconstituted bamboo dowel groove. Given that there is currently no domestic testing method for the bearing capacity of reconstituted bamboo dowel grooves, in this invention, the inventors referred to ASTM D5764 for the design of the specimen and test scheme. To avoid the influence of specimen size and dowel position on the bearing capacity of the dowel groove, the length, width, and height of the specimen are all greater than the minimum length specified in ASTM D5764. The test considers the influence of the bolt diameter and the angle between the loading direction and the bamboo grain direction. Bolt diameters of 12mm, 16mm, and 20mm were selected, and the loading direction was 0°-90° increasing in 15° increments. The specimen design is shown in Table 2.

[0165] Table 2 Design of Reconstituted Bamboo Groove Pressure-Bearing Specimens

[0166]

[0167] The test yielded the load-displacement curve of the reconstituted bamboo dowel groove. The slope of the elastic segment of the load-displacement curve was taken; this slope represents the bearing stiffness of the reconstituted bamboo dowel groove. The bearing stiffness K is divided by the thickness a of the bearing specimen to obtain the bearing modulus of the reconstituted bamboo dowel groove, i.e., k = K / a. A schematic diagram of the method for determining the bearing stiffness of the dowel groove is shown below. Figure 8 As shown.

[0168] The experimental results are shown in Table 3:

[0169] Table 3. Test results of the compressive stiffness of reconstituted bamboo troughs

[0170]

[0171]

[0172] Note: d represents bolt diameter; a represents specimen thickness; n represents number of specimens; K represents pin groove bearing stiffness; k represents basic modulus; CV represents coefficient of variation.

[0173] As can be seen from Table 3, the coefficient of variation of the pressure bearing capacity of the reconstituted bamboo dowel is very small. The coefficient of variation of all experimental groups is less than 10%, indicating that the pressure bearing capacity of the reconstituted bamboo dowel is less discrete and the material properties are relatively stable.

[0174] The bearing modulus of the reconstituted bamboo dowel groove can be obtained through a dowel groove bearing test, which is then used to determine K. e,BEFT Calculations were performed, and finally, the connection stiffness K obtained from the experimental results was used. t The connection stiffness K was calculated using Eurocode5. ser The connection stiffness K obtained from the theoretical calculation of elastic foundation beams e,BEFT In summary, as shown in Table 4, since Eurocode 5 does not specify how to calculate the connection stiffness when the load direction forms a certain angle with the grain direction of the material, K in Table 4... ser Only the results were calculated when the loading direction is parallel to the grain direction.

[0175] Table 4. Results of Stiffness Test and Stiffness Comparison of Steel Clamp Bolted Connections

[0176]

[0177]

[0178] Note: d represents bolt diameter; t represents steel plate thickness; K represents pin groove bearing stiffness; k represents foundation modulus; CV represents coefficient of variation; K t Indicates the experimental results; K ser Indicates the result of Eurocode5 calculation; Ke,BEFT This represents the calculation results for the elastic foundation beam.

[0179] Table 4 shows that the average values ​​of the connection elastic stiffness calculated using Eurocode 5 and the connection elastic stiffness calculated using the elastic foundation beam differ significantly from the experimental values. To further determine the applicability of the connection stiffness calculation methods in Eurocode 5, the elastic foundation beam calculation method, and this invention for predicting the stiffness of reconstituted bamboo-steel plywood bolted connections, the three methods are compared with experimental results, and a verification coefficient is introduced. The errors between different calculation methods and experimental results are shown in Table 5:

[0180] Table 5 Comparison of different calculation methods

[0181]

[0182] Note: K t K represents the stiffness obtained from the bolted connection test of the reconstituted bamboo-steel plywood; e This indicates the bolt connection stiffness result calculated using this invention; K ser This indicates the calculation result obtained using Eurocode 5; K e,BEFT This indicates the results calculated using the elastic foundation beam theory. This represents the average verification coefficient;

[0183] As can be seen from the comparison in Table 5, the method of the present invention (Equations (19)-(20)) has good accuracy in predicting the elastic stiffness of bolted connections of reconstituted bamboo-steel plywood, and its average verification factor is [missing information]. The value is 1.07; however, the result calculated using Eurocode5 has a large error compared to the experimental results, with an average validation factor of 1.07. The value is 0.61, and using Eurocode 5 significantly underestimates the connection elastic stiffness of the reconstituted bamboo-steel plywood bolted connection. The elastic foundation beam theory calculation overestimates the connection elastic stiffness for connections with smaller diameter bolts and underestimates it for connections with larger diameter bolts, although the average validation factor... The value is 1.14, but overall, the actual effect of this invention is better than Eurocode 5 and the elastic foundation beam theory.

[0184] Example 3

[0185] Comparison of the present invention's method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes:

[0186] In this embodiment:

[0187] In addition to the verification conducted by the inventors, the single-bolt connection tests in Li Xiazhen's article "Research on the Performance of Reconstituted Bamboo Bolt Connection Nodes" and Cui Zhaoyan et al.'s article "Experimental Study on the Bearing Capacity of Reconstituted Bamboo Steel Plywood Bolt Connections" were also used for verification. Li Xiazhen and Cui Zhaoyan introduced their reconstituted bamboo steel plywood bolt connection performance tests in their respective articles and obtained relevant experimental data. In their experiments, due to the relatively small diameter of the selected bolts, the bolts exhibited yield mode IV after the connection failed. Theoretically, if yield mode IV is used for calculation, the stiffness of the connection will be very large, but this does not match the actual situation. Therefore, based on the description of Example 1, regardless of whether the bolt exhibits yield mode III or IV after connection failure, the minimum stiffness value calculated under the construction conditions by this invention is used as the elastic stiffness of the connection. The results are shown in Table 6.

[0188] Table 6 Comparison of different calculation methods

[0189]

[0190] Li Xiazhen's "Performance Study of Reconstituted Bamboo Bolt Connection Nodes"

[0191]

[0192] Cui Zhaoyan, "Experimental Study on the Bearing Capacity of Bolted Connections in Reconstituted Bamboo-Steel Plywood"

[0193]

[0194] Note: a represents the thickness of the reconstituted bamboo component; d represents the bolt diameter; K represents the average fundamental modulus; t K represents the connection stiffness obtained from the bolt connection test of the reconstituted bamboo-steel plywood; e This indicates the bolt connection stiffness result calculated using this invention; This represents the average verification coefficient.

[0195] As shown in Table 6, the calculation formula corresponding to bolt yield mode III in this invention also has a good predictive effect on the connection stiffness of the reconstituted bamboo-steel plywood bolted connection tested by Li Xiazhen and Cui Zhaoyan, which to some extent proves the accuracy of the statement in Part 3 in practical applications. In Cui Zhaoyan's experiment, due to the small number of specimens, some specimens may have large dispersion, so the prediction of individual connection stiffness may be less accurate. However, overall, this invention can predict the connection elastic stiffness of the reconstituted bamboo-steel plywood bolted connection test conducted by the two individuals quite well.

[0196] Example 5

[0197] The steps for using this invention are as follows:

[0198] Design of bolted connections for reconstituted bamboo-steel plywood;

[0199] Determine the compressive strength of the reconstituted bamboo trough;

[0200] Based on the design connection parameters, this invention is used to calculate the connection stiffness under yield modes I, III and IV respectively.

[0201] Select the lowest stiffness to predict the stiffness of the designed connection.

[0202] In summary, the research conducted in this invention effectively solves the problem of calculating the connection stiffness of steel plywood connections. Using this invention, the connection stiffness can be directly calculated based on the structural design when reconstructing bamboo-steel plywood bolt connections, providing a reference for this type of connection design. The preferred embodiments of this invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Obviously, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. This invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for predicting the elastic stiffness of bolted joints in reconstituted bamboo-steel plywood, characterized in that, Includes the following steps: S1: Based on the European yielding model, the reconstituted bamboo-steel plywood bolt connection is divided into reconstituted bamboo pin groove bearing yield I, pin single hinge yield III and pin double hinge yield IV, and simplified using the foundation beam model; S2: Based on S1, derive the equation of the bolt deflection curve for the steel plate bolt connection according to the boundary conditions of the steel plate bolt connection form; S3: Combining the deflection curve equation derived in S2 with the European yield model, the connection stiffnesses for bearing yield I, single-hinged yield III, and double-hinged yield IV of the reconstituted bamboo pin groove are derived to obtain the corresponding connection stiffnesses. , , ; S4: Select the minimum stiffness Predict the elastic stiffness of the connection nodes; in: ; The connection stiffness of S3 is derived as follows: When the reconstituted bamboo dowel groove yields under pressure I, the connection stiffness for: When the pin single hinge yields (III), the connection stiffness for: When the pin-double hinge yields to N, the connection stiffness for: In the formula, k represents the basic modulus of reconstituted bamboo (N / mm). 2 ), 'a' represents the thickness of the reconstituted bamboo (mm); EI represents the bending stiffness of the bolt; β represents the relative stiffness between the foundation beam and the foundation. t represents the thickness of the steel plate (mm).

2. The method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes as described in claim 1, characterized in that, The S1 reconstituted bamboo pin groove bearing yield I, pin single hinge yield III and pin double hinge yield IV; In a double shear connection with steel plates as side members: Reconstituted bamboo dowel groove bearing yield I: The main component reconstituted bamboo is damaged while the steel plate remains intact and the bolts remain rigid. Since neither the bolts nor the steel plate yield, the bolts are in uniform contact with the hole wall of the reconstituted bamboo board, and the hole wall of the reconstituted bamboo undergoes uniform extrusion deformation along the entire length of the bolt under load. Single-hinge yielding III: This involves the yielding of both the main component reconstituted bamboo and the bolt. This yielding mode generally occurs in connections where the main component is relatively thick and the bolt is relatively slender. Under load, the bolt will only generate one plastic hinge at each connection surface in the reconstituted bamboo component, while the bolt can rotate in the connection between the bolt and the steel plate. Double hinge yielding IV: This involves the yielding of both the main component reconstituted bamboo and the bolt. When this yielding mode occurs, not only is the main component thicker and the bolt relatively slender, but the side steel plate is also thicker. When the connecting steel plate is a thick steel plate, it will exert a clamping effect on the bolt. Under load, the bolt will not only generate a plastic hinge on a single connection surface of the reconstituted bamboo component, but also generate a plastic hinge at the contact section between the steel plate and the reconstituted bamboo. At this time, the bolt cannot rotate at the end of the thick steel plate. The foundation beam model is simplified as follows: the reconstituted bamboo is simplified to the foundation and the bolts are simplified to foundation beams. According to Winker's assumption, we have... In the formula, y represents the amount of foundation settlement, k is the foundation elastic coefficient, and P is the pressure intensity per unit area.

3. The method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes as described in claim 1, characterized in that, When the reconstituted bamboo dowel groove yields under pressure I, the connection stiffness is determined by the dowel groove bearing stiffness of the reconstituted bamboo. During the elastic deformation stage of the connection, the foundation resists the load applied to the beam. Therefore, from the mechanical equilibrium relationship, we can obtain: （1） （2） Combining equations (1) and (2), we can obtain the compressive yield strength I of the reconstituted bamboo dowel groove. .

4. The method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes as described in claim 1, characterized in that, When the single hinge of the pin yields to III, the steel clamp only plays the role of concentrated load transfer, and there is no bending moment at the end of the bolt. Under the load, the foundation beam will deform near the load end and the deformation at infinity is 0. In order to obtain the deflection equation of the bolt of the steel clamp bolt connection under the load, a small segment of the bolt is taken near the load end for analysis. Based on the mechanical equilibrium relationship and simplified analysis, when , Then, we can obtain equations (4) and (5): （4） （5） By neglecting the higher-order differentials in equation (5) and combining equations (4) and (5), we can obtain: （6） Based on the assumptions of small deformation and plane section, and referring to the approximate solution of the deflection curve in the mechanics of materials textbook, the rotation angle, bending moment, and shear force of the foundation beam at any point in the interval x ≤ a can be expressed as: (7) Therefore, by combining equations (6) and (7), we can obtain: （8） The relative stiffness between the foundation beam and the foundation. By combining the method of complex root extraction, the general solution of equation (8) can be further obtained as follows: （9） Assume that the deflection of the beam is 0 at an infinite distance from the point of application of the load, i.e. At this point, from equation (9), we can obtain A=B=0, so equation (9) can be transformed into: （10） Based on the boundary conditions of the foundation beam at this time: （11） Therefore, by combining equations (7), (10), and (11), we can obtain the deflection equation of the foundation beam under this condition: （12） From equation (12), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows: （13） During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw. Furthermore, the stiffness of the connection remains constant during this elastic working phase. Therefore, the stiffness at the interface between the steel plate and the bamboo plate can be used to represent the elastic stiffness of the connection under working conditions. .

5. The method for predicting the elastic stiffness of reconstituted bamboo-steel plywood bolted connection nodes as described in claim 1, characterized in that, The double hinge yielding of the pin is assumed to be as follows: Assuming that the compressive effect between the steel plate and the reconstituted bamboo is not significant, the bolt end only moves vertically under the clamping of the steel plate. Therefore, it is assumed that the connection end between the bolt and the steel plate is a sliding support, and the sliding support only supports displacement in the y direction. Because the steel plate is relatively thick when yielding mode IV occurs, the load exerted by the steel plate on the bolts is simplified to a uniformly distributed load, and Therefore, at the interface between the steel plywood and the reconstituted bamboo, there are: （15） Therefore, by combining equations (7), (10), and (15), we can obtain the deflection equation of the foundation beam under this condition: （16） From equation (16), the deflection at the contact surface between the steel plate and the reconstituted bamboo component can be obtained as follows: During operation, the connection initially undergoes elastic deformation due to compression between the two sides of the reconstituted bamboo and the screw, and the stiffness of the connection remains constant during this elastic phase. Therefore, the elastic stiffness of the connection in its working state can be represented by the stiffness at the interface between the steel plate and the bamboo plate. .

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