A prestressed steel-wood composite joint stress performance analysis method and device

Abstract

The present application relates to a kind of prestressed steel wood combination node stress performance analysis method and device, method includes the following steps: S1, the key parameter of prestressed steel wood combination node is obtained;S2, based on the direct balance method of beam-column interface and key parameter, wood beam stress balance equation is established, wood beam stress balance equation is solved, the control function of beam end neutral axis height is obtained, control function is the function about beam-column interface opening angle;S3, the parameter of control function of beam end neutral axis height is changed, and the different critical angle in the opening angle change process of beam-column interface is obtained by calculation;S4, based on the control function of beam end neutral axis height, critical angle and node bending moment, bending moment-angle curve is obtained.Compared with prior art, the present application has the advantages of accurate and fast analysis.

Description

Technical Field

[0001] This invention relates to steel-wood joints, and more particularly to a method and apparatus for analyzing the stress performance of prestressed steel-wood composite joints. Background Technology

[0002] Prestressed steel-wood hybrid frame structures are a type of structural system characterized by concentrated epicentral damage and minimal residual displacement after earthquakes. This type of frame achieves good seismic toughness through prestressed steel-wood composite joints. These joints consist of steel-wood composite columns, glued laminated timber beams, energy-dissipating angle steel, and prestressing tendons. Tensile prestressing tendons connect the beams and columns, and then energy-dissipating angle steel is installed at the beam-column interface. Under seismic loading, the joint opens, the prestressing tendons are further stretched, and the energy-dissipating angle steel undergoes plastic deformation to dissipate seismic energy. After the earthquake, the prestressing tendons contract, causing the joint to return to its original position. Post-earthquake, the main beam and column components of the joint remain intact, requiring only the replacement of the energy-dissipating angle steel for repair.

[0003] Accurately predicting the stress performance of prestressed steel-wood composite joints is a crucial step in supporting the engineering application of prestressed steel-wood hybrid frame structures. The beams and columns of these joints are flexibly connected, allowing for significant relative deformation between them. Consequently, traditional analytical methods that consider deformation coordination between components are difficult to apply to the stress analysis of prestressed steel-wood composite joints. To estimate the bending performance of the joint at a given rotation angle, iterative calculations of the neutral axis height at different beam ends are required until the overall stress of the joint reaches equilibrium.

[0004] However, iterative trial-and-error methods are a brute-force approach. Obtaining a feasible solution that meets the mechanical equilibrium tolerance requirements often requires a lengthy iterative calculation process. And this only addresses the nodal performance under a single rotation angle. In refined time-history analysis of structures, the overall moment-rotation curves of the nodes are often required as input. For this, iterative trial-and-error methods will consume a significant amount of time.

[0005] Therefore, there is currently a lack of efficient and robust methods for analyzing the stress performance of prestressed steel-wood composite joints. This not only presents challenges for structural design but also hinders parametric analysis and performance optimization of structures. Summary of the Invention

[0006] The purpose of this invention is to provide an accurate and rapid method and apparatus for analyzing the stress performance of prestressed steel-wood composite joints in order to overcome the defects of the prior art.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A method for analyzing the stress performance of prestressed steel-timber composite joints, the method comprising the following steps:

[0009] S1. Obtain the key parameters of the prestressed steel-wood composite node;

[0010] S2. Based on the direct equilibrium method of the beam-column interface and key parameters, establish the force equilibrium equation of the timber beam, solve the force equilibrium equation of the timber beam, and obtain the control function of the neutral axis height at the beam end. The control function is a function of the open rotation angle of the beam-column interface, and the expression of the control function is:

[0011]

[0012] Where, θ imp Enable cornering on the beam-column interface, k sho To account for the reduction factor that slows down the prestress growth due to axial shortening of the member, λ is the first variable, μ is the second variable, and α... t α represents the secondary stiffness of the tension-dissipating angle steel after yielding. c L represents the secondary stiffness of the compressive energy-dissipating angle steel after yielding. A L is the length of the weakened section of the energy-dissipating angle steel. f h is the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam. b For the height of the glued laminated timber beam, T pt,i F represents the initial prestress level of the node. yt F yc Δ represents the yield strength of the energy-dissipating angle steel on the tension / compression side. yt Δ yc The yield displacement of the energy-dissipating angle steel on the tension / compression side;

[0013] S3. By changing the parameters of the control function for the height of the neutral axis at the beam end, different critical rotation angles are calculated during the change of the opening rotation angle of the beam-column interface.

[0014] S4. The moment-rotation curve is obtained based on the control function of the neutral axis height at the beam end, the critical rotation angle, and the nodal bending moment.

[0015] Furthermore, the critical angles include the pressure relief critical angle, the prestress growth critical angle, the yield critical angle of tension-side energy-dissipating angle steel, the yield critical angle of compression-side energy-dissipating angle steel, and the wood grain crushing critical angle.

[0016] Furthermore, the key parameters include geometric parameters and material parameters.

[0017] Furthermore, the geometric parameters include the height, width, and length of the glued laminated timber beam, the unbonded length of the prestressing tendon, the total cross-sectional area of ​​the prestressing tendon, the conventional thickness of the energy-dissipating angle steel, the thickness of the weakened section of the energy-dissipating angle steel, the width of the energy-dissipating angle steel, the length of one leg of the energy-dissipating angle steel connecting beam, the length of the weakened section of the energy-dissipating angle steel, and the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam.

[0018] Furthermore, the material parameters include the initial prestress level of the node, the elastic modulus of the prestressing tendon, the yield strength of the steel used in the energy-dissipating angle steel, the elastic modulus of the steel used in the energy-dissipating angle steel, the secondary stiffness of the energy-dissipating angle steel after yielding, the compressive strength of the wood along the grain, the compressive elastic modulus of the wood along the grain, and the end effect coefficient of the wood.

[0019] A device for analyzing the stress performance of a prestressed steel-wood composite joint includes a memory and a processor. The memory stores a computer program, and the processor executes the above steps when executing the program.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) The direct balancing method is adopted on the basis of retaining the basic mechanical logic, which avoids the tedious iteration of the iterative trial algorithm. It can be used for fast and accurate analysis and calculation of node performance, which is conducive to the optimization of node performance.

[0022] (2) The key parameters can be changed to complete the node performance analysis under different parameters, thereby assisting in design and optimization. Attached Figure Description

[0023] Figure 1 This is a flowchart of the present invention;

[0024] Figure 2 This is a curve showing the neutral axis height at the beam end according to an embodiment of the present invention.

[0025] Figure 3 This is a bending moment-rotation curve diagram of an embodiment of the present invention;

[0026] Figure 4 This is a graph showing the variation of nodal prestress in an embodiment of the present invention.

[0027] Figure 5 The graph shows the variation of the bending and rotation performance of the node under different prestress losses according to an embodiment of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0029] Example 1:

[0030] This invention provides a method and apparatus for analyzing the stress performance of prestressed steel-wood composite joints. The method includes the following steps:

[0031] S1. Obtain the key parameters of the prestressed steel-wood composite node.

[0032] The key parameters of prestressed steel-timber composite joints include geometric parameters and material parameters. Geometric parameters include: the height h of the glued laminated timber beam. b Glulam beam width b b Glulam beam length L b Unbonded length of prestressed tendons l ub Total cross-sectional area A of prestressed tendons pt Energy-dissipating angle steel standard thickness t1, energy-dissipating angle steel weakened section thickness t r Width b of energy-consuming angle steel s Length L of one leg of the energy-dissipating angle steel connecting beam s Length L of the weakened section of the energy-consuming angle steel A The distance L from the end of the weakened section of the energy-dissipating angle steel to the side of the beam f Material parameters include: initial prestress level T of the node. pt,i Prestressed tendon elastic modulus E pt The yield strength f of the steel used for energy-consuming angle steel y The elastic modulus E of the steel used in the energy-dissipating angle steel, and the secondary stiffness α of the energy-dissipating angle steel after yielding. s Wood compressive strength along the grain f para Wood's compressive modulus of elasticity along the grain, E para and wood end effect coefficient k gap .

[0033] S2. Based on the direct equilibrium method of the beam-column interface and key parameters, establish the force equilibrium equation of the wooden beam, solve the force equilibrium equation of the wooden beam, and obtain the control function of the neutral axis height at the beam end. The control function is a function of the opening angle of the beam-column interface.

[0034] The prestressed steel-timber composite joint connects the steel-timber composite column to the glued laminated timber beam via tensioned prestressing tendons. During the joint opening process, no plastic crushing or indentation occurs on the column surface, allowing the glued laminated timber beam to be used as an isolator for analysis. Using the direct equilibrium method at the beam-column interface, assuming an elastic triangular stress distribution in the compression zone at the glued laminated timber beam end, with prestressing tendons positioned at half the beam height, and considering only the post-yield bearing capacity of the energy-dissipating angle steel on the tension / compression side, the most general force equilibrium equation for the timber beam can be directly established based on key parameters:

[0035]

[0036] Where c is the height of the neutral axis at the beam end; σ(y) is the stress distribution at the bearing end of the wooden beam, and y is the longitudinal distance (along the beam height) from any compressive stress point to the zero compressive stress point; F yt F yc The yield strength of the energy-dissipating angle steel on the tension / compression side; Δ yt Δ yc α represents the yield displacement of the energy-dissipating angle steel on the tension / compression side. t α cLet α be the secondary stiffness of the energy-dissipating angle steel on the tension / compression side after yielding. If the tension and compression angle steels are the same, then α c =α t =α s ;k sho A reduction factor is used to account for the slowdown in prestress growth caused by axial shortening of the component.

[0037] Solve the force equilibrium equations for the wooden beam, and introduce the variable λ = E. pt A pt n gap / l ub μ=k gap E para b b / (2L b Simplifying the expression, we can obtain the control function f1(θ) for the height c of the neutral axis at the beam end. imp The control function for the beam end neutral axis height c is based on the opening angle θ at the beam-column interface. imp For input variables:

[0038]

[0039] Where, θ imp Enable cornering on the beam-column interface, k sho To account for the reduction factor that slows down the prestress growth due to axial shortening of the member, λ is the first variable, μ is the second variable, and α... t α represents the secondary stiffness of the tension-dissipating angle steel after yielding. c L represents the secondary stiffness of the compressive energy-dissipating angle steel after yielding. A L is the length of the weakened section of the energy-dissipating angle steel. f h is the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam. b For the height of the glued laminated timber beam, T pt,i F represents the initial prestress level of the node. yt F yc Δ represents the yield strength of the energy-dissipating angle steel on the tension / compression side. yt Δ yc This represents the yield displacement of the energy-dissipating angle steel on the tension / compression side.

[0040] S3. By changing the parameters of the control function for the height of the neutral axis at the beam end, different critical rotation angles are calculated during the change of the opening rotation angle of the beam-column interface.

[0041] Critical turning angles include: critical decompression turning angle θ d Critical rotation angle θ for prestress growth pt The critical yield rotation angle θ of tension / compression side energy dissipation angle steel ty ,θ cy, And the critical angle of crushing of wood along the grain θ end .

[0042] (1) Calculate the critical decompression angle θ d

[0043] Let f1(θ) imp ) = h b The critical decompression angle θ can be obtained. d :

[0044]

[0045] (2) Calculate the critical yield angle θ of the energy-dissipating angle steel on the compression side. cy

[0046] Let the formula for the internal force of the energy-dissipating angle steel on the compression side be equal to F. yc The critical yield angle θ of the energy-dissipating angle steel on the compression side can be obtained. cy :

[0047]

[0048] (3) Calculate the critical yield rotation angle θ of the energy-dissipating angle steel on the tension side. ty

[0049] Unlike the compression side, the internal force formula of the energy-dissipating angle steel on the tension side is coupled with the height c of the neutral axis at the beam end. Therefore, the internal force formula of the energy-dissipating angle steel on the tension side needs to be combined with f1(θ). imp Decoupling yields the critical yield rotation θ of the energy-dissipating angle steel on the tension side. ty Possible values ​​θ ty1 and θ ty2 :

[0050]

[0051]

[0052]

[0053] C 1t =(2Δ yt ) 2

[0054]

[0055]

[0056]

[0057] C 2t =(2Δ yt ) 2

[0058] According to f1(θ) imp The physical meaning of θ ty The value of can be determined as follows:

[0059] When f1(θ imp =θ ty1 ,α c =F yc / Δ yc ,α t =F yt / Δ yt ,k sho =0)≥0.5h b And f1(θ) imp =θ ty2 ,α c =F yc / Δ yc ,α t =F yt / Δ yt ≥0.5h b When, θ ty =θ ty1 ;

[0060] When f1(θ imp =θ ty1 ,α c =F yc / Δ yc ,α t =F yt / Δ yt ,k sho =0)<0.5h b And f1(θ) imp =θ ty2 ,α c =F yc / Δ yc ,α t =F yt / Δ yt <0.5h b When, θ ty =θ ty2 .

[0061] (4) Calculate the critical rotation angle θ for prestress growth. pt

[0062] Let f1(θ) imp ) = 0.5h b Considering whether the tension and compression angle steel yields, the critical rotation angle θ for prestress growth can be obtained. pt Possible values ​​θ pt1 θ pt2 , and θ pt3 :

[0063]

[0064]

[0065]

[0066] θ pt The value of can be determined as follows:

[0067]

[0068] (5) Calculate the critical angle of wood crushing along the grain θ end

[0069] Critical crushing angle θ of wood along the grain end The formula is:

[0070]

[0071]

[0072]

[0073]

[0074] S4. The moment-rotation curve is obtained based on the control function of the neutral axis height at the beam end, the critical rotation angle, and the nodal bending moment.

[0075] Calculate the beam end pressure, prestressed tendon internal force, tension / compression side energy dissipation angle steel internal force, and beam end neutral axis height under different beam-column interface open rotation angles, and calculate the corresponding nodal bending moments.

[0076] When the beam-column interface opens the rotation angle θ imp Equal to any rotation angle θ i When the nodal bending moment does not need to be iterated, it can be directly calculated using the following formula.

[0077]

[0078] Because the direct equilibrium method was used to derive f1(θ) imp Functional relationship, arbitrary rotation angle θ i The internal force T calculated below pt (θ i ), T s (θ i C s (θ i ) and C t (θ i All of them satisfy the equilibrium equation.

[0079] The moment-rotation curve is obtained based on the control function of the beam end neutral axis height, critical rotation angle, and nodal bending moment. This curve can be used for the analysis and calculation of nodal performance, which is beneficial for nodal performance optimization.

[0080] The prestress variation curve of the node can also be obtained from the moment-rotation curve. If it is necessary to examine the effect of different prestress losses on the bending performance of the node, repeat the above steps and input the initial prestress level considering the prestress loss. When prestress loss occurs in the node during long-term service, this method can also serve as the basis for different service instantaneous analyses.

[0081] Below is a specific example of the calculation:

[0082] The edge node of a prestressed steel-wood composite frame structure has a glued laminated timber beam section dimension b. b ×h b =260×360mm, beam length L b =3600mm. The glued laminated timber is made of Douglas fir, grade Tct28. Two prestressing tendons are installed at half the beam height, each with a cross-sectional area of ​​140mm². 2 The resultant initial tension force T of the two prestressed tendons pt,i =100kN. Two energy-dissipating angle steels are installed at the beam-column interface. The angle steels are made of Q235 steel, and the thickness of the weakened section of the angle steel is 5mm. The model input parameters are shown in Table 1 below.

[0083] Table 1 Input parameters for node examples

[0084]

[0085] Substituting the above parameters into S2 of the analysis method, the control function f1(θ) for the beam end neutral axis height c is obtained. imp At this point, by inputting an increasing angle at the beam-column interface, the height c of the beam end neutral axis can be obtained as the angle θ at the beam-column interface changes. imp The relationship of change, such as Figure 2 As shown.

[0086] Subsequently, based on the formula in S3, the values ​​of different critical rotation angles were calculated, as shown in Table 2.

[0087] Table 2 Values ​​of different critical rotation angles

[0088] <![CDATA[θ d (mrad)]]> <![CDATA[θ pt (mrad)]]> <![CDATA[θ end (mrad)]]> <![CDATA[θ ty (mrad)]]> <![CDATA[θ cy (mrad)]]> 2.57 10.68 86.63 5.03 10.34

[0089] As shown in Table 2, the node opens when the rotation angle reaches 2.57 mrad; subsequently, the energy-dissipating angle steel on the tension side begins to deform and yields at a rotation angle of 5.03 mrad; the energy-dissipating angle steel on the compression side, being close to the rotation center, deforms less and yields only when the node rotation angle reaches 10.34 mrad; subsequently, the prestressing tendons used in the node are further stretched when the rotation angle reaches 10.68 mrad, and the internal force of the prestressing tendons begins to increase; the corresponding compressive stress at the end of the timber beam also begins to increase, reaching the longitudinal compressive strength of 16.9 MPa for Tct28 glued laminated timber at a rotation angle of 86.63 mrad.

[0090] Combining the control function obtained from S2 and the critical rotation angle obtained from S3, the nodal moment formula from S4 can be used to calculate the nodal moment-rotation curve, as shown below. Figure 3 As shown, the prestress variation curve of the node can be obtained at the same time. Figure 4 As shown, when the initial prestress of the node is reduced by 80%, the bending-rotation bearing capacity of the node at 0.03 rad will decrease by 30%, as... Figure 5 As shown.

[0091] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for analyzing the mechanical behavior of a prestressed steel-wood composite joint, characterized in that, The method includes the following steps: S1. Obtain the key parameters of the prestressed steel-wood composite node; S2. Based on the direct equilibrium method of the beam-column interface and key parameters, establish the force equilibrium equation of the timber beam, solve the force equilibrium equation of the timber beam, and obtain the control function of the neutral axis height at the beam end. The control function is a function of the open rotation angle of the beam-column interface, and the expression of the control function is: Where, θ imp Enable cornering on the beam-column interface, k sho To account for the reduction factor that slows down the prestress growth due to axial shortening of the member, λ is the first variable, μ is the second variable, and α... t α represents the secondary stiffness of the tension-dissipating angle steel after yielding. c L represents the secondary stiffness of the compressive energy-dissipating angle steel after yielding. A L is the length of the weakened section of the energy-dissipating angle steel. f h is the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam. b For the height of the glued laminated timber beam, T pt,i F represents the initial prestress level of the node. yt F yc Δ represents the yield strength of the energy-dissipating angle steel on the tension / compression side. yt Δ yc The yield displacement of the energy-dissipating angle steel on the tension / compression side; S3. By changing the parameters of the control function for the height of the neutral axis at the beam end, different critical rotation angles are calculated during the change of the opening rotation angle of the beam-column interface. S4. The moment-rotation curve is obtained based on the control function of the neutral axis height at the beam end, the critical rotation angle, and the nodal bending moment.

2. The method for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 1, characterized in that, The critical turning angles include the pressure relief critical turning angle, the prestress growth critical turning angle, the yield critical turning angle of tension side energy dissipation angle steel, the yield critical turning angle of compression side energy dissipation angle steel, and the wood grain crushing critical turning angle.

3. The method for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 1, characterized in that, The key parameters include geometric parameters and material parameters.

4. The method for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 3, characterized in that, The geometric parameters include the height, width, and length of the glued laminated timber beam, the unbonded length of the prestressing tendon, the total cross-sectional area of ​​the prestressing tendon, the conventional thickness of the energy-dissipating angle steel, the thickness of the weakened section of the energy-dissipating angle steel, the width of the energy-dissipating angle steel, the length of one leg of the energy-dissipating angle steel connecting beam, the length of the weakened section of the energy-dissipating angle steel, and the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam.

5. The method for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 3, characterized in that, The material parameters include the initial prestress level of the node, the elastic modulus of the prestressing tendon, the yield strength of the steel used in the energy-dissipating angle steel, the elastic modulus of the steel used in the energy-dissipating angle steel, the secondary stiffness of the energy-dissipating angle steel after yielding, the compressive strength of the wood along the grain, the compressive elastic modulus of the wood along the grain, and the end effect coefficient of the wood.

6. A prestressed steel-wood composite joint mechanical behavior analysis device, comprising a memory and a processor, the memory having a computer program stored thereon, characterized in that, When the processor executes the program, it performs the following steps: S1. Obtain the key parameters of the prestressed steel-wood composite node; S2. Based on the direct equilibrium method of the beam-column interface and key parameters, establish the force equilibrium equation of the timber beam, solve the force equilibrium equation of the timber beam, and obtain the control function of the neutral axis height at the beam end. The control function is a function of the open rotation angle of the beam-column interface, and the expression of the control function is: Where, θ imp Enable cornering on the beam-column interface, k sho To account for the reduction factor that slows down the prestress growth due to axial shortening of the member, λ is the first variable, μ is the second variable, and α... t α represents the secondary stiffness of the tension-dissipating angle steel after yielding. c L represents the secondary stiffness of the compressive energy-dissipating angle steel after yielding. A L is the length of the weakened section of the energy-dissipating angle steel. f h is the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam. b For the height of the glued laminated timber beam, T pt,i F represents the initial prestress level of the node. yt F yc Δ represents the yield strength of the energy-dissipating angle steel on the tension / compression side. yt Δ yc The yield displacement of the energy-dissipating angle steel on the tension / compression side; S3. By changing the parameters of the control function for the height of the neutral axis at the beam end, different critical rotation angles are calculated during the change of the opening rotation angle of the beam-column interface. S4. The moment-rotation curve is obtained based on the control function of the neutral axis height at the beam end, the critical rotation angle, and the nodal bending moment.

7. The device for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 6, characterized in that, The critical turning angles include the pressure relief critical turning angle, the prestress growth critical turning angle, the yield critical turning angle of tension side energy dissipation angle steel, the yield critical turning angle of compression side energy dissipation angle steel, and the wood grain crushing critical turning angle.

8. The device for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 6, characterized in that, The key parameters include geometric parameters and material parameters.

9. The device for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 8, characterized in that, The geometric parameters include the height, width, and length of the glued laminated timber beam, the unbonded length of the prestressing tendon, the total cross-sectional area of ​​the prestressing tendon, the conventional thickness of the energy-dissipating angle steel, the thickness of the weakened section of the energy-dissipating angle steel, the width of the energy-dissipating angle steel, the length of one leg of the energy-dissipating angle steel connecting beam, the length of the weakened section of the energy-dissipating angle steel, and the distance from the end of the weakened section of the energy-dissipating angle steel to the side of the beam.

10. The device for analyzing the mechanical behavior of a prestressed steel-wood composite joint according to claim 8, characterized in that, The material parameters include the initial prestress level of the node, the elastic modulus of the prestressing tendon, the yield strength of the steel used in the energy-dissipating angle steel, the elastic modulus of the steel used in the energy-dissipating angle steel, the secondary stiffness of the energy-dissipating angle steel after yielding, the compressive strength of the wood along the grain, the compressive elastic modulus of the wood along the grain, and the end effect coefficient of the wood.

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