A method for calculating the bearing capacity of a bending member of orthogonal laminated wood based on a rolling shear effect

Abstract

The application provides a calculation method of the bearing capacity of a bending member of orthogonal laminated wood based on a rolling shear effect, and comprises the following steps: determining the geometric parameters and material characteristics of the orthogonal laminated wood member; determining calculation parameters alpha and beta; establishing a control equation characterized by rolling shear stress distribution; solving the control equation to obtain the rolling shear stress distribution tau(x); introducing boundary conditions; and determining the bearing capacity of the member. The application establishes a low-order simplified calculation model, obtains an analytical solution of the bearing capacity of the bending member of the orthogonal laminated wood, and effectively solves the problem that high-order differential equations can only be solved in the form of numerical solutions in the conventional solving method. The method can be used as a supplement to the current domestic and foreign wood structure design specifications, realizes the replacement of the design and checking formula of the bending member of the orthogonal laminated wood in the specifications, and is beneficial to the application and popularization of the orthogonal laminated wood heavy wood structure.

Description

Technical Field

[0001] This invention relates to a method for calculating the bearing capacity of orthogonal glued laminated timber bending members, belonging to the field of civil engineering technology. Background Technology

[0002] New-type timber-framed buildings meet green, energy-saving, and low-carbon requirements, and their application has developed rapidly in recent years. As a natural prefabricated building structure, new-type timber-framed buildings use glued laminated timber as the main structural material, connecting structural components into a stable structural system through metal connectors. Compared with traditional building structures, its components are lighter, meet building requirements in terms of strength, and have superior seismic performance. More and more public buildings, civil buildings, large-span structures, bridges, etc. are choosing glued laminated timber as the basic structural material.

[0003] Cross-laminated timber (CLT), a novel timber structural material, possesses excellent shear properties due to its sequential arrangement of longitudinal and transverse veneers glued together, making it commonly used in heavy timber shear walls and floors. However, it is precisely this transverse veneer arrangement, unlike other timber structural materials, that makes the roll-shear effect a unique property of CLT bending members. Therefore, conventional calculation methods cannot accurately calculate the load-bearing capacity of CLT bending members. Currently, the formulas for CLT bending and compression-bending members given in various domestic and international timber structure design codes are all load-bearing capacity verification formulas; the limit state analysis problem of CLT bending members based on the roll-shear effect remains unsolved. Summary of the Invention

[0004] Technical issues:

[0005] This invention provides a method for calculating the bearing capacity of orthogonal glulam (GLA) bending members based on the rolling shear effect. The method analyzes the limit state of the bending member based on the rolling shear stress field of GLA, establishes a bearing capacity calculation model characterized by rolling shear stress, and solves the analytical solution.

[0006] Technical solution:

[0007] This invention relates to a method for calculating the bearing capacity of orthogonal glued laminated timber members under bending based on the rolling shear effect, comprising the following steps:

[0008] (1) Determine the basic dimensions of the component, including the thickness h of the veneer with parallel grain, the thickness t of the veneer with cross grain, and the cross-sectional area A of the veneer with parallel grain; determine the material properties of the component, including the elastic modulus E0 with parallel grain and the shear modulus G with cross grain. r The moment of inertia I of the cross section of the parallel-grained veneer;

[0009] (2) Based on the equilibrium and geometric conditions of the infinitesimal element at point x, determine the calculation parameters α and β, as shown in equations (1) and (2):

[0010]

[0011]

[0012] (3) Establish the governing equation for the roll shear stress distribution, considering the transverse-grained veneer as having a shear stiffness of G between two adjacent parallel-grained veneers. r In a spring-like structure, when the component is subjected to bending, the longitudinally grained veneer is the effective load-bearing unit, while the transversely grained veneer, acting as the connecting unit between adjacent longitudinally grained veneers, provides the main shear stiffness. Based on the equilibrium and geometric conditions of the component's micro-element, the overall deformation δ of the micro-element is obtained. τ for

[0013] (δ N2 -δ N1 )+(δ M1 +δ M2 )=δ τ (3);

[0014] Where δ Ν1 This represents the deformation caused by the axial force N1 acting on the first layer of parallel-grained veneer; δ Ν2 This represents the deformation caused by the axial force N2 acting on the second layer of parallel-grained veneer; δ M1 This represents the deformation caused by the bending moment M1 acting on the first layer of parallel-grooved veneer; δ M2 This indicates the deformation caused by the bending moment M2 on the second layer of parallel-grained veneer;

[0015] Based on the classical basic beam theory, we obtain

[0016]

[0017] dy1 represents the y-direction deformation of the first layer of parallel-grain veneer; dy2 represents the y-direction deformation of the second layer of parallel-grain veneer.

[0018] Furthermore, the deformation of two adjacent parallel-grained veneers caused by shear force is

[0019]

[0020] τ is the rolling shear stress;

[0021] Based on the relationship between infinitesimal element deformation and bending moment in classical elasticity Substituting equations (4) and (5) into equation (3), we derive the governing equation for the rolling shear stress as follows:

[0022]

[0023] Right now

[0024] V is the shear force;

[0025] (4) Solve the governing equations to obtain the rolling shear stress distribution τ(x).

[0026]

[0027] τ0 is the numerical value of the shear strain distribution of the infinitesimal element caused by shear force;

[0028] (5) Introduce boundary conditions: due to the symmetry of shear strain, the shear stress at the mid-span of the member is 0, τ=0, and according to the shear failure mode, τ0=-τ f The shear force on the veneer with parallel grain is

[0029]

[0030] i represents the number of the i-th layer of parallel-grained veneer;

[0031] (6) Determine the load-bearing capacity of the member, that is, the load-bearing capacity of the orthogonal glued laminated timber bending member is the sum of the shear forces on each longitudinal veneer.

[0032] V = ∑V i (10).

[0033] Furthermore, cross-laminated timber (CLT) is a multi-layered composite wood-based panel with an odd number of layers, and CLT boards with different numbers of layers have different stiffnesses; among them, the bending parameters of three-layer CLT members... Parameters of a five-layer orthotropic glued laminated timber bending member

[0034] Furthermore, in step (5), the bearing capacity of the three-layer orthotropic glued laminated timber bending member... 5-layer orthotropic laminated timber bending member bearing capacity b is the width of the bending member.

[0035] Beneficial effects:

[0036] This invention can serve as a supplement to existing domestic and international timber structure design codes and regulations, replacing the design verification formula for orthogonal glued laminated timber bending members in the codes, which is beneficial to the application and promotion of orthogonal glued laminated timber heavy timber structures. Attached Figure Description

[0037] Figure 1 The flowchart shows the method for calculating the bearing capacity of orthogonal glued laminated timber bending members based on the rolling shear effect in this invention.

[0038] Figure 2 This is a schematic diagram of the calculation model;

[0039] Figure 3 This is a diagram of the force analysis of a micro-element. Detailed Implementation

[0040] The technical solution of the present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0041] like Figure 1 As shown, this invention is a method for calculating the bearing capacity of orthogonal glued laminated timber bending members based on the rolling shear effect, comprising the following steps:

[0042] A method for calculating the bearing capacity of orthogonal glued laminated timber members under bending based on the roll-shear effect, characterized by the following steps:

[0043] (1) Determine the basic dimensions of the component, including the thickness h of the veneer with parallel grain, the thickness t of the veneer with cross grain, and the cross-sectional area A of the veneer with parallel grain; determine the material properties of the component, including the elastic modulus E0 with parallel grain and the shear modulus G with cross grain. r The moment of inertia I of the cross section of the parallel-grained veneer;

[0044] (2) Based on the equilibrium and geometric conditions of the infinitesimal element at point x, determine the calculation parameters α and β, as shown in equations (1) and (2):

[0045]

[0046]

[0047] (3) Establish the governing equation for the roll shear stress distribution, considering the transverse-grained veneer as having a shear stiffness of G between two adjacent parallel-grained veneers. r In a spring-like structure, when the component is subjected to bending, the longitudinally grained veneer is the effective load-bearing unit, while the transversely grained veneer, acting as the connecting unit between adjacent longitudinally grained veneers, provides the main shear stiffness. Based on the equilibrium and geometric conditions of the component's micro-element, the overall deformation δ of the micro-element is obtained. τ For (δ) N2 -δ N1 )+(δ M1 +δ M2 )=δ τ (3);

[0048] Where δ Ν1 This represents the deformation caused by the axial force N1 acting on the first layer of parallel-grained veneer; δ Ν2 This represents the deformation caused by the axial force N2 acting on the second layer of parallel-grained veneer; δ M1 This represents the deformation caused by the bending moment M1 acting on the first layer of parallel-grooved veneer; δ M2 This indicates the deformation caused by the bending moment M2 on the second layer of parallel-grained veneer;

[0049] Based on the classical basic beam theory, we obtain

[0050]

[0051] dy1 represents the y-direction deformation of the first layer of parallel-grain veneer; dy2 represents the y-direction deformation of the second layer of parallel-grain veneer.

[0052] Furthermore, the deformation of two adjacent parallel-grained veneers caused by shear force is

[0053]

[0054] τ is the rolling shear stress;

[0055] Based on the relationship between infinitesimal element deformation and bending moment in classical elasticity Substituting equations (4) and (5) into equation (3), we derive the governing equation for the rolling shear stress as follows:

[0056]

[0057] Right now

[0058] V is the shear force;

[0059] (4) Solve the governing equations to obtain the rolling shear stress distribution τ(x).

[0060]

[0061] τ0 is the numerical value of the shear strain distribution of the infinitesimal element caused by shear force;

[0062] (5) Introduce boundary conditions: due to the symmetry of shear strain, the shear stress at the mid-span of the member is 0, τ=0, and according to the shear failure mode, τ0=-τ f The shear force on the veneer with parallel grain is

[0063]

[0064] i represents the number of the i-th layer of parallel-grained veneer;

[0065] (6) Determine the load-bearing capacity of the member, that is, the load-bearing capacity of the orthogonal glued laminated timber bending member is the sum of the shear forces on each longitudinal veneer.

[0066] V = ∑V i (10).

[0067] Furthermore, cross-laminated timber (CLT) is a multi-layered composite wood-based panel with an odd number of layers, and CLT boards with different numbers of layers have different stiffnesses; among them, the bending parameters of three-layer CLT members... Parameters of a five-layer orthotropic glued laminated timber bending member

[0068] Commonly used orthotropic glued laminated timber bending members are 3-layer and 5-layer boards, and their stiffness is represented by the parameter α.

[0069] When using a 5-layer board, the preferred parameter α is... More accurate calculation results can be obtained. It can be understood that this method can be used for five-layer orthogonal laminated timber or any other odd-numbered-layer orthogonal laminated timber. Perform the calculation.

[0070] Furthermore, in step (5), the bearing capacity of the three-layer orthotropic glued laminated timber bending member... 5-layer orthotropic laminated timber bending member bearing capacity b is the width of the bending member.

[0071] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited to the above methods. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the bearing capacity of orthogonal glued laminated timber members under bending based on the rolling shear effect, characterized in that, Includes the following steps: (1) Determine the basic dimensions of the component, including the thickness h of the veneer with parallel grain, the thickness t of the veneer with cross grain, and the cross-sectional area A of the veneer with parallel grain; determine the material properties of the component, including the elastic modulus E0 with parallel grain and the shear modulus G with cross grain. r The moment of inertia I of the cross section of the parallel-grained veneer; (2) Based on the equilibrium and geometric conditions of the infinitesimal element at point x, determine the calculation parameters α and β, as shown in equations (1) and (2): (3) Establish the governing equation for the roll shear stress distribution, considering the transverse-grained veneer as having a shear stiffness of G between two adjacent parallel-grained veneers. r In a spring-like structure, when the component is subjected to bending, the longitudinally grained veneer is the effective load-bearing unit, while the transversely grained veneer, acting as the connecting unit between adjacent longitudinally grained veneers, provides the main shear stiffness. Based on the equilibrium and geometric conditions of the component's micro-element, the overall deformation δ of the micro-element is obtained. τ For (δ) N2 -δ N1 )+(δ M1 +δ M2 )=δ τ (3); Where δ Ν1 This represents the deformation caused by the axial force N1 acting on the first layer of parallel-grained veneer; δ Ν2 This represents the deformation caused by the axial force N2 acting on the second layer of parallel-grained veneer; δ M1 This represents the deformation caused by the bending moment M1 acting on the first layer of parallel-grooved veneer; δ M2 This indicates the deformation caused by the bending moment M2 on the second layer of parallel-grained veneer; Based on the classical basic beam theory, we obtain dy1 represents the y-direction deformation of the first layer of parallel-grain veneer; dy2 represents the y-direction deformation of the second layer of parallel-grain veneer. Furthermore, the deformation of two adjacent parallel-grained veneers caused by shear force is τ is the rolling shear stress; Based on the relationship between infinitesimal element deformation and bending moment in classical elasticity Substituting equations (4) and (5) into equation (3), we derive the governing equation for the rolling shear stress as follows: Right now V is the shear force; (4) Solve the governing equations to obtain the rolling shear stress distribution τ(x). τ0 is the numerical value of the shear strain distribution of the infinitesimal element caused by shear force; (5) Introduce boundary conditions: due to the symmetry of shear strain, the shear stress at the mid-span of the member is 0, τ=0, and according to the shear failure mode, τ0=-τ f The shear force on the veneer with parallel grain is i represents the number of the i-th layer of parallel-grained veneer; (6) Determine the load-bearing capacity of the member, that is, the load-bearing capacity of the orthogonal glued laminated timber bending member is the sum of the shear forces on each longitudinal veneer. V=∑V i (10)。 2. The method for calculating the bearing capacity of orthogonal glued laminated timber bending members based on the rolling shear effect according to claim 1, characterized in that: Cross-laminated timber (CLT) is a multi-layered composite wood-based panel with an odd number of layers. Different numbers of CLT layers result in different stiffnesses. Specifically, the bending parameters of a three-layer CLT member are... Parameters of a five-layer orthotropic glued laminated timber bending member 3. The method for calculating the bearing capacity of orthogonal glued laminated timber bending members based on the rolling shear effect according to claim 1, characterized in that: In step (5), the bearing capacity of the 3-layer orthotropic glued laminated timber bending member. 5-layer orthotropic laminated timber bending member bearing capacity b is the width of the bending member.

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