CN111651926A - Method for evaluating stress capacity of mortise and tenon joint of wood structure - Google Patents

Method for evaluating stress capacity of mortise and tenon joint of wood structure Download PDF

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CN111651926A
CN111651926A CN202010505868.2A CN202010505868A CN111651926A CN 111651926 A CN111651926 A CN 111651926A CN 202010505868 A CN202010505868 A CN 202010505868A CN 111651926 A CN111651926 A CN 111651926A
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mortise
tenon
loading
stress
displacement
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姚利宏
张俊
郭宇
宋怡
李英洁
李源河
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Inner Mongolia Agricultural University
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Abstract

The invention discloses an evaluation method for the stress capacity of a mortise and tenon joint of a wood structure, which comprises the following steps of 1, selecting a mortise and tenon joint prototype; step 2, analyzing the stress action of the selected mortise and tenon joint prototype; step 3, establishing a finite element model of the mortise and tenon joint prototype through ANSYS or ABAQUS software according to the actual stress condition of the mortise and tenon joint prototype; step 4, carrying out finite element test on the established finite element model to obtain mechanical property parameters of the mortise and tenon joint, wherein the mechanical property parameters comprise hysteresis performance, rigidity degradation rule, strength degradation rule, energy consumption capability and tenon pulling amount; and 5, carrying out finite element analysis according to the mechanical properties obtained in the step 4, thereby obtaining the influence of different parameter changes on the stress performance of the node. The method can solve the problems of complex boundary conditions, geometric shapes, material materials, nonlinearity and the like; and the method accords with the actual condition of the node, and the analysis result is real and reliable.

Description

Method for evaluating stress capacity of mortise and tenon joint of wood structure
Technical Field
The invention relates to the technical field of timber structure buildings, in particular to an evaluation method for the stress capacity of timber structure mortise and tenon joints.
Background
The wood structure building types in China are various, most of the wood structure buildings in the north are of a beam-lifting type, and bucket-type wood structures in the south are more. Most of the beams and columns of these ancient buildings are built by log, and the timber structure is widely used in ancient China. The wood structure is brought back to the end in the ancient fashion and benefits from good earthquake-resistant performance, according to history records, the whole collapse of the wood structure building in a plurality of large earthquakes is very little, and the main damage forms of the wood structure building are tenon pulling and deformation dislocation of tenon-and-mortise joints, damage of walls and falling of roof components.
The structure form according to tenon fourth of twelve earthly branches node mainly divide into: dovetail joints, straight joints (half joints and through joints), steamed bun joints, cross hoop head joint joints and the like. Of these, dovetails and straight tenons are the two of the most widely used of the above node forms. Different forms of mortise and tenon joints have different stress mechanisms and energy consumption mechanisms, and in order to probe the mechanical properties of the traditional timber structure building, the deep research on the mortise and tenon joint and the mortise and tenon joint timber structure is very necessary. The mechanical property research of the mortise and tenon joint is usually carried out by a method of a pseudo-static force loading test and a computer modeling analysis.
The structure form according to tenon fourth of twelve earthly branches node mainly divide into: dovetail joints, straight joints (half joints and through joints), steamed bun joints, cross hoop head joint joints and the like. Of these, dovetails and straight tenons are the two of the most widely used of the above node forms. Different forms of mortise and tenon joints have different stress mechanisms and energy consumption mechanisms, and in order to probe the mechanical properties of the traditional timber structure building, the deep research on the mortise and tenon joint and the mortise and tenon joint timber structure is very necessary.
Disclosure of Invention
In order to solve the defects in the related field, the invention provides an evaluation method for the stress capacity of the mortise and tenon joint of the wood structure.
The invention discloses an evaluation method for the stress capacity of a mortise and tenon joint of a wood structure, which is realized by the following technical scheme:
a method for evaluating the stress capacity of a mortise and tenon joint of a wood structure comprises the following steps:
step 1, selecting a mortise and tenon joint prototype;
step 2, analyzing the stress action of the prototype of the mortise and tenon joint selected in the step 1;
step 3, establishing a finite element model of the mortise and tenon joint prototype through ANSYS or ABAQUS software according to the actual stress condition of the mortise and tenon joint prototype obtained in the step 2;
step 4, carrying out a finite element test on the finite element model established in the step 3 to obtain mechanical property parameters of the mortise and tenon joint, wherein the mechanical property parameters comprise: hysteresis performance, rigidity degradation rule, strength degradation rule, energy consumption capability and tenon pulling amount;
and 5, carrying out finite element analysis according to the mechanical properties obtained in the step 4, thereby obtaining the influence of different parameter changes on the stress performance of the node.
Further, the step 3 of establishing a finite element model includes:
step a, according to the mortise and tenon joint prototype in the step 1, measuring dovetail joint nodes of a wood structure to obtain the original size and shape of the joint;
b, selecting materials of the finite element model, obtaining the adjusted node size by reducing the prototype proportion of the mortise and tenon node, drawing a virtual digital model stereogram by ABAQUS software, and determining an elastic engineering constant of the finite element model;
the materials comprise second-class materials and third-class materials;
the ratio is 1: 2-5;
step c, setting boundary conditions to be the same as the constraint form of the actual situation of the mortise and tenon joint;
step d, selecting a material constitutive relation model;
step e, according to the stress analysis, determining a loading scheme in the modeling analysis step;
step f, carrying out mesh division by adopting a C3D8R mesh and Hex unit cell mesh division mechanism;
step g, setting a contact friction effect;
step h, detecting whether the simulation result of the finite element model is converged, and if so, directly entering step 4; if not, the check process is carried out to converge and then the step 4 is carried out.
Further, the finite element test comprises a unidirectional loading simulation test and low-cycle reciprocating cyclic loading;
the unidirectional loading simulation test adopts a displacement control method to apply constant-speed horizontal displacement to the ends of the square beams, applies axially uniformly distributed load to the column top local flat square beams, the loading amplitude is 5mm/min, and the test is terminated when the load is applied until the node is damaged or the bearing capacity is reduced to 80% of the limit load, so that the maximum displacement of node yield is obtained;
the low-cycle reciprocating cyclic loading adopts a displacement control method for loading, the control displacement adopted by the loading is the maximum displacement obtained by unidirectional loading, and the top of the column is kept to apply fixed and uniformly distributed axial loads; the low-cycle cyclic reciprocating loading firstly selects and controls the displacement to be 1.25 percent, 2.5 percent, 5 percent and 10 percent of triangular waves of the maximum displacement in sequence for single cycle; and then, performing cyclic loading by using 20%, 40%, 60%, 80% and 100% of the maximum displacement as control displacements, and performing three cycles on each stage of control displacement until the node model is subjected to yield failure and stops loading.
Further, the finite element analysis comprises hysteresis curve analysis, skeleton curve analysis, rigidity degradation analysis, strength degradation analysis, energy consumption capability analysis, tenon pulling amount analysis and node stress analysis;
the central rotation angle theta of the hysteresis curve is taken as an abscissa, and the bending moment M is taken as an ordinate, and the central rotation angle theta and the bending moment M are respectively obtained by the following formula: m is equal to P.H,
Figure BDA0002526513020000041
wherein, Δ -horizontal displacement of the loading point; h-horizontal distance between the loading point and the column end face; p-horizontal load applied at the load point;
the skeleton curve is an envelope curve formed by mutually connecting maximum bending moment value points of the first cycle under each stage of control displacement loading of the hysteresis curve;
the stiffness degradation curve is a change curve of which the stiffness decreases with the increase of the displacement, wherein the secant stiffness of the node under each level of repeated load is represented by K, the forward secant stiffness of the node is Ki +, and the reverse secant stiffness of the node is Ki-, and the stiffness degradation curve is obtained by the following formula:
Figure BDA0002526513020000042
Figure BDA0002526513020000043
in the formula, Mi + is a positive maximum bending moment value of the 1 st cycle loaded by the ith-level control displacement; theta i + is the maximum positive rotation angle of the 1 st cycle of the ith-level control displacement loading; mi-is the reverse maximum bending moment value of the 1 st cycle of the ith-level control displacement loading; theta i-is the reverse maximum rotation angle of the 1 st cycle of the ith-level control displacement loading;
the intensity degradation analysis is performed by observing an intensity degradation coefficient lambdaiReflecting the change of the node strength under different cycles under each stage of displacement loading control, and selecting the ratio of the third cycle bearing capacity P to the first cycle bearing capacity P for calculation, wherein the formula is as follows:
Figure BDA0002526513020000044
in the formula, λiControlling the intensity degradation coefficient under the displacement circulation for the ith level; pi3 is the bearing capacity of the third cycle under the loading of the ith control displacement; pi1 is the bearing capacity of the first cycle under the loading of the ith-stage control displacement;
the energy dissipation capability is represented by an equivalent viscous damping coefficient he, which is obtained by the following formula:
Figure BDA0002526513020000051
in the formula, SABCDIs the hysteresis curve envelope area; s△ODF+S△OCE△ ODF plus △ OCE area;
the tenon pulling amount analysis is realized by observing the change of the tenon pulling amount along with the increase of the corner;
the nodal stress analysis is performed from the stress in the grain-following direction, the stress in the cross grain (chord direction) and the stress in the cross grain (radial direction), respectively.
And furthermore, the boundary conditions in the step b comprise setting boundary conditions that one end of the column in the finite element model is fixedly connected and the other end of the column is hinged, carrying out x-direction and z-direction displacement constraint and y-direction and z-direction rotation constraint on the top part of the column in the finite element model, and carrying out x-direction, y-direction and z-direction displacement constraint and y-direction and z-direction rotation constraint on the column foot until the displacement and the rotation angle are 0.
Further, in the step g, 44mm grids are adopted for dividing the balk, 34mm grids are adopted for dividing the column, and 24mm grids are adopted for dividing the local flat balk.
Further, the contact friction effect comprises tangential and normal effects on the contact surface of the tenon and the mortise;
the setting of the contact friction is realized by the following steps:
selecting a friction model, wherein the friction model is one of a Lagrange friction model, a dynamic friction model, a coulomb friction model and a penalty function model;
step (2), selecting a main surface and a slave surface, wherein the main surface and the slave surface have two selection schemes: one is that at the tenon and mortise part, the mortise of the column end is selected as the tenon of the slave face as the main face; the other is at the contact part of the top end surface of the column and the local flat plate purlin, the top end surface of the main surface is selected from the surface of the column, and the local flat plate purlin is selected from the surface to be in contact with the bottom surface;
step (3), selecting a tracking method, wherein the tracking method is used for judging the contact state of the node; the tracking method includes a small sliding method and a limited sliding method.
Further, the material constitutive relation model comprises a longitudinal grain constitutive relation and a transverse grain constitutive relation;
the texture constitutive relation is assumed to be an ideal elastic-plastic model without original damage of wood, the tensile elastic modulus and the compressive elastic modulus of the texture are both expressed by adopting the relation of strain and stress, and the calculation formula is as follows:
Figure BDA0002526513020000061
in the formula:cuis the grain-following ultimate compressive strain of the wood,c0is the yield strain under compression of the grain of the wood, EcsModulus of elasticity under compression for grain of wood, EtsTensile elastic modulus of wood grain;
the calculation formula of the transverse texture constitutive relation is as follows:
Figure BDA0002526513020000062
in the formula:Lthe transverse striation of the wood is subjected to compressive yield strain,Nis the transverse grain compressive ultimate strain of wood, EL、E1Modulus of the elastic section under compression of the wood grain E2Is a compression elastic mold in the strengthening stage of wood transverse striation.
Further, the stress action comprises a shear force action, a bending moment action and an axial force action.
Furthermore, the mortise and tenon joint is a dovetail joint.
Compared with the prior art, the analysis method has the following beneficial effects:
1) the finite element analysis of the invention can deal with the problems of complex boundary conditions, geometric shapes, material materials, nonlinearity and the like;
2) the ABAQUS analysis software has a strong nonlinear analysis function;
3) according to the invention, a penalty function model is preferably selected, and small-amplitude relative motion, namely 'elastic sliding', can be carried out between contact surfaces of the penalty function model, which are bonded with each other, so that the node loading practical situation is better met;
4) the nonlinear analysis part of the invention is nonlinear analysis of the nonlinear and mortise and tenon joint contact conditions of the wood material;
5) the invention adopts a fixing mode that one end of the node upright post is consolidated and the other end is hinged, which is consistent with the actual situation of the mortise and tenon joint.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a schematic diagram of boundary conditions and load application;
FIG. 2 is a P-Delta curve diagram of unidirectional load loading of mortise and tenon joints according to embodiments 1 to 4;
FIG. 3 is a graph showing M-theta curves of the mortise and tenon joints in examples 1 to 4;
FIG. 4 is a graph showing the skeleton of the mortise and tenon joints according to examples 1 to 4;
fig. 5 is a graph of the skeleton of the mortise and tenon joints of the embodiments 1 and 4;
FIG. 6 is a graph showing the degradation of the rigidity of the mortise and tenon joints according to examples 1 to 4;
FIG. 7 is a graph showing the degradation of the strength of the mortise and tenon joints according to examples 1 to 4;
fig. 8 is a schematic view of the relation between the equivalent viscous damping coefficient of the mortise and tenon joint and the corner in embodiments 1 to 4;
FIG. 9 is a schematic view showing the relationship between the mortise and tenon joint pulling amount and the corner in examples 1 to 4;
FIG. 10 is a schematic view showing the feather and feather directions of the tenon according to embodiments 1 to 4;
FIG. 11 is S11Stress clouds of the mortise and tenon joint of the embodiment 1 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) along the grain direction;
FIG. 12 is S11Stress clouds of the mortise and tenon joint of the embodiment 2 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) along the grain direction;
FIG. 13 is S11Stress clouds of the mortise and tenon joint of the embodiment 3 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) along the grain direction;
FIG. 14 is S11Stress clouds of the mortise and tenon joint of the embodiment 4 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) along the grain direction;
FIG. 15 is S33Stress cloud plots of the mortise and tenon joints of the embodiment 1 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) respectively in the radial direction of the transverse striations;
FIG. 16 is S33Transverse striation in radial direction the tenon of embodiment 2Stress cloud pictures of the mortise node at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) respectively;
FIG. 17 is S33Stress cloud plots of the mortise and tenon joints of the embodiment 3 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right and from top to bottom) respectively in the radial direction of the cross striations;
FIG. 18 is S33Stress cloud plots of the tenon-and-mortise joints of example 4 at 0.15, 0.35, 0.05, 0.65 and 0.08rad (from left to right, from top to bottom) respectively in the radial direction of the striations;
FIG. 19 shows mortise and tenon joints in S of examples 1 to 412Stress cloud pictures of tenons in the direction;
FIG. 20 is a PEEQ stress cloud for the mortise and tenon joint of examples 1-4;
wherein:
YS-1 is expressed as example 1, YS-2 as example 2, YS-3 as example 3 and YS-4 as example 4.
Detailed Description
Example 1
The embodiment provides an evaluation method for the stress capacity of a mortise and tenon joint of a wood structure, which comprises the following steps:
step 1, selecting a mortise and tenon joint prototype, and performing different regulations (the column diameter and the column height are shown in table 2) on relevant components such as columns, purlins, appendices and the like of the dovetail joint in the building method formula, wherein the column height must be smaller than the span of the wood frame, and the column diameter is selected to be 42 minutes as a modeling standard in the embodiment. According to the rule that the two ends of the dovetail joint are arranged on the center of the column, the thickness of the dovetail joint is reduced by half, the two shoulders are respectively killed by four flaps, and the length of each flap is eight minutes, the length of the dovetail joint, the width of the dovetail joint and the width of the dovetail diameter are respectively 10 minutes, 12 minutes and 10 minutes;
step 2, analyzing the stress action of the prototype of the mortise and tenon joint selected in the step 1;
step 3, establishing a finite element model of the mortise and tenon joint prototype through ABAQUS software according to the actual stress condition of the mortise and tenon joint prototype obtained in the step 2;
step 4, carrying out finite element test on the finite element model established in the step 3 to obtain mechanical property parameters of the mortise and tenon joint, wherein the mechanical property parameters comprise;
and 5, carrying out finite element analysis according to the mechanical properties obtained in the step 4, thereby obtaining the influence of different parameter changes on the stress performance of the node.
Further, the step 3 of establishing a finite element model includes:
step a, selecting a pine camphor wood as a research object according to the prototype of the mortise and tenon joint in the step 1, wherein the elastic engineering constant of the pine camphor wood refers to a table 1, and the model proportion is 1:2.2 of a second-class wood;
TABLE 1 Pinus sylvestris elastic engineering constants
Figure BDA0002526513020000091
Note: l-in-line direction; r-transverse striation radial; t-cross grain chord direction; LR-radial cut plane; LT-tangent plane; RT-cross section; e-modulus of elasticity; μ -poisson's ratio; g-shear modulus of elasticity.
B, setting boundary conditions, wherein the boundary conditions are set for the upright columns by adopting the boundary conditions that one end of each upright column is fixedly connected and the other end of each upright column is hinged according to the actual stress condition of the dovetail joint; the top part of the column in the model is subjected to displacement constraint in the x and z directions and rotation constraint in the y and z directions, and the column foot is subjected to displacement constraint in the x, y and z directions and rotation constraint in the y and z directions until the displacement and the rotation angle are 0; the boundary condition definition and loading manner are shown in fig. 1;
step c, selecting a material constitutive relation model;
d, determining a loading scheme according to the stress analysis;
step e, dividing the dovetail joint column and the balk by adopting swept grids, dividing the balk by adopting a 44mm grid, dividing the column by adopting a 34mm grid, and dividing the local flat balk by adopting a 24mm grid;
step f, setting contact friction;
step g, detecting whether the simulation result of the finite element model is converged, and if so, directly entering step 4; if not, the check process is carried out to converge and then the step 4 is carried out.
Further, the finite element test comprises a unidirectional loading simulation test and low-cycle reciprocating cyclic loading;
the unidirectional loading simulation test adopts a displacement control method to apply constant-speed horizontal displacement to the ends of the square beams, applies axially uniformly distributed load to the column top local flat square beams, the loading amplitude is 5mm/min, and the test is terminated when the load is applied until the node is damaged or the bearing capacity is reduced to 80% of the limit load, so that the maximum displacement of node yield is obtained;
the low-cycle reciprocating cyclic loading adopts a displacement control method for loading, the control displacement adopted by the loading is the maximum displacement obtained by unidirectional loading, and the top of the column is kept to apply fixed and uniformly distributed axial loads; the low-cycle cyclic reciprocating loading firstly selects and controls the displacement to be 1.25 percent, 2.5 percent, 5 percent and 10 percent of triangular waves of the maximum displacement in sequence for single cycle; and then, performing cyclic loading by using 20%, 40%, 60%, 80% and 100% of the maximum displacement as control displacements, and performing three cycles on each stage of control displacement until the node model is subjected to yield failure and stops loading.
Further, the finite element analysis comprises hysteresis curve analysis, skeleton curve analysis, rigidity degradation analysis, strength degradation analysis, energy consumption capability analysis, tenon pulling amount analysis and node stress analysis;
the central rotation angle theta of the hysteresis curve is taken as an abscissa, and the bending moment M is taken as an ordinate, and the central rotation angle theta and the bending moment M are respectively obtained by the following formula: m is equal to P.H,
Figure BDA0002526513020000111
in the formula, delta is the horizontal displacement of the loading point; h is the horizontal distance between the loading point and the column end face; p is the horizontal load applied at the loading point;
the skeleton curve is an envelope curve formed by mutually connecting maximum bending moment value points of the first cycle under each stage of control displacement loading of the hysteresis curve;
the rigidity degradation curve is a change curve of rigidity decreasing along with the increase of displacement, wherein the secant rigidity of the node under repeated load of each level is represented by K, and the positive secant rigidity of the node is Ki+The stiffness of the reverse secant is ki-And are respectively obtained by the following formula:
Figure BDA0002526513020000112
Figure BDA0002526513020000113
in the formula, Mi+Loading the positive maximum bending moment value of the 1 st cycle for the ith-level control displacement; theta i + is the maximum positive rotation angle of the 1 st cycle of the ith-level control displacement loading; mi-Loading the reverse maximum bending moment value of the 1 st cycle for the ith-level control displacement; thetai-Loading the reverse maximum rotation angle of the 1 st cycle for the ith-level control displacement;
the intensity degradation analysis is performed by observing an intensity degradation coefficient lambdaiReflecting the change of the node strength under different cycles under each stage of displacement loading control, and selecting the ratio of the third cycle bearing capacity P to the first cycle bearing capacity P for calculation, wherein the formula is as follows:
Figure BDA0002526513020000114
in the formula, λiControlling the intensity degradation coefficient under the displacement circulation for the ith level; pi3The bearing capacity of the third circulation under the loading of the ith-level control displacement is obtained; pi1Loading the bearing capacity of the next first cycle for the ith-stage control displacement;
the energy consumption capability is expressed by an equivalent viscous damping coefficient he, and the equivalent viscous damping coefficient heIs obtained by the following formula:
Figure BDA0002526513020000121
in the formula, SABCDIs the hysteresis curve envelope area; s△ODF+S△OCE△ ODF plus △ OCE area;
the tenon pulling amount analysis is realized by observing the change of the tenon pulling amount along with the increase of the corner;
the nodal stress analysis is performed from the stress in the grain-following direction, the stress in the cross grain (chord direction) and the stress in the cross grain (radial direction), respectively.
And furthermore, the boundary conditions in the step b comprise setting boundary conditions that one end of the column in the finite element model is fixedly connected and the other end of the column is hinged, carrying out x-direction and z-direction displacement constraint and y-direction and z-direction rotation constraint on the top part of the column in the finite element model, and carrying out x-direction, y-direction and z-direction displacement constraint and y-direction and z-direction rotation constraint on the column foot until the displacement and the rotation angle are 0.
Further, in the step g, 44mm grids are adopted for dividing the balk, 34mm grids are adopted for dividing the column, and 24mm grids are adopted for dividing the local flat balk.
Further, the contact friction effect comprises tangential and normal effects on the contact surface of the tenon and the mortise;
the setting of the contact friction is realized by the following steps:
selecting a friction model, wherein the friction model is a penalty function model; the formula of the penalty function is taucμ p, wherein: mu is the anti-slip coefficient, p is the pressure of the contact surface of the mortise and tenon joint, and taucThe critical friction shear stress is related to the normal direction pressure. The prior art shows that the friction coefficient between woods is usually 0.1-0.6, and the anti-slip coefficient of the invention is 0.4.
Step (2), selecting a main surface and a slave surface, wherein the main surface and the slave surface have two selection schemes: one is that at the tenon and mortise part, the mortise of the column end is selected as the tenon of the slave face as the main face; the other is at the contact part of the top end surface of the column and the local flat plate purlin, the top end surface of the main surface is selected from the surface of the column, and the local flat plate purlin is selected from the surface to be in contact with the bottom surface;
step (3), selecting a tracking method, wherein the tracking method is used for judging the contact state of the node; the tracking method is a limited sliding method, and obvious rotation amount and deformation amount can occur when the tenon-and-mortise nodes are subjected to cyclic low-cycle reciprocating loading.
Further, the material constitutive relation model comprises a longitudinal grain constitutive relation and a transverse grain constitutive relation;
the texture constitutive relation is assumed to be an ideal elastic-plastic model without original damage of wood, the tensile elastic modulus and the compressive elastic modulus of the texture are both expressed by adopting the relation of strain and stress, and the calculation formula is as follows:
Figure BDA0002526513020000131
in the formula:cuis the grain-following ultimate compressive strain of the wood,c0is the yield strain under compression of the grain of the wood, EcsModulus of elasticity under compression for grain of wood, EtsTensile elastic modulus of wood grain;
the calculation formula of the transverse texture constitutive relation is as follows:
Figure BDA0002526513020000132
in the formula:Lthe transverse striation of the wood is subjected to compressive yield strain,Nis the transverse grain compressive ultimate strain of wood, EL、E1Modulus of the elastic section under compression of the wood grain E2Is a compression elastic mold in the strengthening stage of wood transverse striation.
Further, the stress action comprises a shear force action, a bending moment action and an axial force action.
Furthermore, the mortise and tenon joint is a dovetail joint.
Further, the problem of non-convergence can be solved by the following scheme:
the mortise and tenon joint can generate larger displacement under the low-cycle reciprocating loading state, so that the problem of geometric nonlinearity is noticed by selecting limited sliding, and the geometric nonlinearity switch of Step is set to be On;
and checking whether the model design and the material plasticity definition are reasonable or not. The attribute should be checked and defined in the attribute, which is based on the constitutive model;
refining the master-slave surface grids, and considering whether the friction contact parameter definition is accurate and reasonable;
and checking whether the local coordinate system of the material is reasonably established. The wood belongs to an orthotropic material, a three-dimensional coordinate system of the wood is constructed, each component of the mortise and tenon joint is assigned with a direction, and assignment is carried out on different directions;
and checking whether the mortise and tenon joint has interference or clearance fit. If the situation exists, setting a reference point as an origin of coordinates, inserting the reference point into a proper position of the mortise and tenon joint column and the square column, measuring displacements in the x direction, the y direction and the z direction, and adjusting to realize seamless fit of the mortise and tenon joint;
if the method cannot be solved, carefully analyzing whether the model has problems, such as rigid body displacement, improper contact definition, over-constraint and the like;
in combination with the convergence problem encountered during simulation of the text, the distance between the surface and the nodes on the surface needs to be set when binding connection is adopted, otherwise, partial data cannot be output. It should also be noted whether model contacts, boundaries, constraints, or load definitions are reasonable.
Example 2
The difference between this embodiment and embodiment 1 is only that the model of this embodiment has two equal materials 1: 3.2.
Example 3
The difference between this embodiment and embodiment 1 is only that the model of this embodiment has two equal materials 1: 4.4.
Example 4
The difference between this embodiment and embodiment 1 is only that the model of this embodiment is scaled by three equal materials 1: 3.2.
Analysis of the results obtained in examples 1-4 above gave the following results:
1. unidirectional loading simulation test
FIG. 2 is a relationship curve of the unidirectional loading displacement load of examples 1-4, and the ultimate bearing capacity of example 1 is 4.1KN and the ultimate displacement is 51.7mm according to analysis; the ultimate bearing capacity of the embodiment 2 is 11.8KN, and the ultimate displacement is 51.9 mm; the ultimate bearing capacity of example 3 is 1.65KN, and the ultimate displacement is 57.9 mm; the ultimate bearing capacity of example 4 was 3.2KN and the ultimate displacement was 46.5 mm.
2. Hysteresis curve analysis
The hysteresis curve refers to the relation between force and node deformation in the cyclic loading process, and can reflect the mechanical properties of the mortise and tenon joint, such as the rigidity, the energy consumption capability, the ductility and the like. The area enveloped by the hysteresis loop is the energy absorbed by the node after each displacement loading control; the slope of the hysteresis loop diagonal represents the stiffness of the node; the fuller the hysteresis loop and the larger the envelope area, the stronger the energy consumption capability and the seismic performance of the node are. The shape of the hysteresis curve is generally classified into four categories: arcuate, fusiform, reverse S-shaped and Z-shaped.
FIG. 3 shows the hysteresis curves of the above-mentioned embodiments 1 to 4, and it can be seen from FIG. 3 that:
1) the hysteresis curves of examples 1-4 are all "Z" in general, and obvious "pinching effect" and slippage occur, which indicates that shear deformation and slippage occur during loading, and the slippage increases with the increase of the rotation angle.
2) The hysteresis loops of the hysteresis curves of examples 1-4 are substantially symmetrical for forward loading and reverse loading, and M is generally less for reverse loading than for forward loading because a partial flat plate column exerts a backpressure on the upper surface of the tenon for reverse loading. The hysteresis loop area is increased along with the increase of the corner, which shows that the energy consumption capacity of the node is higher and higher; under each stage of control displacement, the hysteresis loop area of the first circle is larger than that of the second circle and the third circle in circulation, and the hysteresis loop area of the next stage of circulation loading is larger than that of the previous stage. The hysteresis loop is smaller at the initial loading stage and is in a superposition state; continuously loading the slope of the curve to increase progressively, and indicating that the mutual extruding contact position of the tenon and the mortise enters an elastic deformation stage; when the load is loaded to a certain degree, the slope of the curve is slowly increased or even decreased, the node is converted from an elastic stage to a plastic deformation stage, and the tenon and the mortise of the node can be seen to be extruded and deformed and expanded in different degrees through simulation; the bending moment is almost linearly reduced in the unloading stage, and the contact part of the node has obvious plastic deformation, which indicates that the node is damaged and loses the anti-seismic performance.
(3) Examples 1-3 all show the rule that the bending moment value of the node is reduced along with the increase of the model proportion, and the comparison between example 1 and example 4 shows that when the grade of the equivalent material is reduced, the bending moment of the node is reduced along with the reduction. The forward loading time-delay loop areas of all the nodes are larger than those of the reverse loading, which shows that the energy consumption performance of the nodes is stronger during forward loading.
(4) The unload degradation of example 3 is greatest in magnitude compared to the other nodes, resulting in greater residual distortion. The peak bending moment drop occurs when all the nodes reach the control displacement, which shows that the maximum accumulated plastic strain is reached before the slope of the node curve drops.
2. Skeletal curve analysis
And the envelope curve formed by mutually connecting the maximum bending moment value points of the first cycle under each stage of displacement loading control of the hysteresis curve is a node skeleton curve. Compared with a hysteresis curve, the skeleton curve can be used for analyzing the change condition and the bearing capacity of the rigidity in the elastic stage, the plastic stage and the damage stage in the observation period more intuitively.
As can be seen in FIG. 4, the slope of the forward-reverse curve of the node is high near the origin, indicating that the node has strong horizontal stiffness. Because the axial load evenly distributed on the local flat plate column is transmitted to the column, the column rotates around the column base by the column top transverse force and the column bottom friction force, the column base is in a hinged state, and the column rotation needs to overcome the bending moment added by the axial force, so that the node has higher horizontal rigidity.
Example 1 the elastic stage is approximately before 0.015rad, and the tenon-and-mortise joint is in a sliding state; the yield stage is between 0.015 and 0.05rad, and the node is in a linear elastic state at the moment; when 0.05 rad-0.065 is a strengthening stage, obvious plastic extrusion deformation occurs to the tenon and the mortise of the node; after 0.065rad, the bending moment of the node begins to decline, which indicates that the node enters a limit state and is about to be damaged by tenon pulling or tenon stripping and the like.
In example 2, the elastic stage is approximately before 0.016rad, the yield stage is between 0.016rad and 0.03rad, the strengthening stage is between 0.03rad and 0.065rad, and the node of curve bending moment decline enters the limit state after 0.065 rad.
In example 3, the elastic phase is approximately before 0.017rad, the yield phase is between 0.017rad and 0.03rad, the reinforcement phase is between 0.03rad and 0.075rad, and the curve bending moment decreasing node enters the limit state after 0.075 rad.
Comparing the peak bending moment of the node rotation, 9.3KN for example 2 is 3.5 times and 10.4 times that for example 1 and example 3.
As shown in fig. 5, comparative example 1 and example 4 found that the skeleton curve is similar in the initial stage, and the nodes are in the squeezing and slipping states; the increase speed of the bending moment of the continuously loaded embodiment 1 is obviously higher than that of the embodiment 4, and the rotating bending moment of the embodiment 1 under the same corner is larger
3. Stiffness degradation analysis
FIG. 6 is a graph showing the stiffness degradation curves of examples 1 to 4, from which:
the initial stiffness of the node is large, the forward stiffness and the reverse stiffness are gradually reduced along with the increase of the rotation angle, and the stiffness degradation rate is high before 0.015 rad. After 0.015rad, the rigidity degradation rate of the node gradually approaches to a horizontal state along with the increase of the control displacement in the embodiment 1 and the embodiment 3, but the rigidity degradation rate of the node still decreases obviously after 0.015rad without obvious horizontal trend in the embodiment 2, and the forward and reverse degradation curve of the embodiment 3 is relatively symmetrical.
The stiffness degradation curves of comparative example 1, example 2, example 3, and the initial stiffness of example 2 under forward loading was at most 594kn.m.rad-1, 3.4 and 9.4 times that of example 1 and example 3. The initial rigidity of the second-class material node is in a decreasing rule along with the increase of the model proportion, and the initial rigidity of reverse loading is generally smaller than that of forward loading, which is caused by the structural asymmetry of the dovetail joint.
In comparative example 1 and example 4, the initial stiffness of example 1 is similar to the large forward and reverse degradation trend, and the maximum stiffness of example 1 under forward loading is 1.3 times that of example 4, and the maximum stiffness under reverse loading is 1.4 times that of example 4. Example 1 and example 4 showed approximately the same tendency to degrade after 0.06rad, with a gradual level towards 0. The initial rigidity of the second-class material node with the same model proportion is higher.
4. Intensity degradation analysis
Fig. 7 is the intensity degradation curves of examples 1 to 4, and it can be seen from fig. 7 that the intensity degradation coefficients of the respective nodes are locally increased or decreased. Example 1 before 0.02rad, the strength degradation factor reached 1.03, indicating that the node was mostly in a slip state during the first cycle and did not cause significant crush deformation.
Reverse loading strength degradation factor λ of example 1iThe forward loading strength degradation coefficient is between 0.92 and 1.0, and the forward loading strength degradation coefficient is between 0.92 and 1.04; the reverse loading strength degradation coefficient of the embodiment 2 is between 0.92 and 0.98, and the forward loading strength degradation coefficient is between 0.96 and 1.03; the reverse loading strength degradation coefficient of the embodiment 3 is between 0.94 and 0.98, and the forward loading strength degradation coefficient is between 0.9 and 0.98; reverse Loading of example 4The strength degradation coefficient is between 0.92 and 0.98, and the positive loading strength degradation coefficient is between 0.94 and 1.0.
The average value of the strength degradation coefficients of the forward and reverse loading of the embodiment 1, the embodiment 2 and the embodiment 3 is calculated, the average value of the strength degradation coefficients of the embodiment 1 is 0.97, the average value of the strength degradation coefficients of the embodiment 2 is 0.98, and the average value of the strength degradation coefficients of the embodiment 3 is 0.95, and the average value is gradually reduced along with the increase of the model proportion.
The degradation rule of the forward and reverse loading strength of the embodiment 1 is similar to that of the embodiment 4, and the strength degradation coefficient mean value of the embodiment 4 is 0.96 smaller than that of the embodiment 1, which shows that the higher the strength of the node is, the greater the strength degradation is.
5. Energy consumption capability analysis
FIG. 8 is a graph of the equivalent viscous damping coefficient versus rotation angle of examples 1-4, as can be seen from FIG. 8: the dovetail joint energy consumption capacity is enhanced along with the increase of the corner, because the contact area of the tenon and the mortise becomes larger along with the increase of the corner, the extrusion stress is obviously larger and larger along with the increase of the extrusion strain, and the friction effect of the contact part is stronger and stronger.
Comparing example 1, example 2 and example 3, it can be seen that the initial energy consumption of example 3 is significantly higher than that of example 1 and example 2, the equivalent viscous damping coefficient is 0.144, the equivalent viscous damping coefficients of example 1, example 2 and example 3 at 0.08rad are 0.187, 0.163 and 0.22, respectively, and the equivalent viscous damping coefficient of example 1 and example 2 at 0.04rad is almost the same. Therefore, the larger the node model proportion is, the stronger the energy consumption capability is.
Comparing example 1 with example 4, it can be seen that the initial energy consumption capacity of the two is approximately the same, the growth trend is approximately the same, and he of example 4 at 0.08rad is 0.17 lower than that of the node of example 1 at this corner. The energy consumption capability of the second-grade material node is higher than that of the third-grade material node under the same model proportion.
6. Analysis of tenon pull amount
The node is along with the increase of control displacement, and the extrusion deformation takes place for tenon and mortise mouth and leads to the node not hard up to pull out the mortise mouth gradually, when pulling out tenon volume and surpassing certain limit, can lead to the node to lose bearing capacity and even take off the tenon, seriously influences the stability and the safety of structure.
FIG. 9 is a relationship diagram of tenon pulling amount and corner in examples 1-4, and it can be seen from FIG. 9 that the tenon pulling amount in the initial tenons of examples 1 and 2 is about 1.76mm in comparison with 0.66mm in example 3, which is relatively close to that in example 4. With the continuous increase of the corner, the tenon pulling amount of the dovetail joint is on a growing trend, the tenon pulling amount of the embodiment 2 is obviously larger than that of other nodes, and the tenon pulling amount of the embodiment 3 is obviously smaller than that of other nodes. The tenon pulling amount of the second-grade material node is smaller along with the increase of the model proportion, and the tenon pulling amount of the second-grade material node in the same model proportion is larger than that of the third-grade material node.
7. Nodal stress analysis
As wood is an anisotropic material, a three-dimensional coordinate system of the wood is established, and the longitudinal grain direction and the transverse grain direction of the mortise and tenon joint are defined. The invention specifies S11The stress is along the grain direction, one side of the upper side and the lower side of the tenon is pulled in the direction, and one side is pressed; s22Is the transverse striation (chordwise) stress, S33For the cross-grain (radial) stress, the right upper and left lower diagonal directions of the tenon are subjected to compressive stress from the mortise, as shown in fig. 10.
As shown in FIGS. 11-14, S11In the on-grain direction, S when the node loads to the right11The left side of the direction tenon is pulled, the right side of the direction tenon is pressed, the deeper the color is, the higher the stress value is, and the tensile force and the pressure value are increased along with the increase of the corner. The tensile stress and the compressive stress of example 1 are respectively 9.3MPa and 18.2MPa at 0.08rad, the tensile stress and the compressive stress of example 2 are respectively 10.5MPa and 14.4MPa, the tensile stress and the compressive stress of example 3 are respectively 9.1MPa and 13.6MPa, and the tensile stress and the compressive stress of example 4 are respectively 13.9MPa and 17.8 MPa. When the node is loaded to 0.08rad, the left tenon face of the tenon and the right tenon neck of the tenon are found to be seriously damaged by compression.
As shown in fig. 15-18, in the radial direction of the S33 cross striations, when the node rotates to the right, the stress in the S33 direction is mainly that the left lower part and the right upper part of the tenon are subjected to compressive stress from the radial direction of the mortise cross striation, and the compressive stress and the deformation form increase with the increase of the corner. At 0.08rad, the compressive stresses on the left lower part and the right upper part of the tenon in embodiment 1 are respectively 4Mpa and 6Mpa, the compressive stresses on the left lower part and the right upper part of the tenon in embodiment 2 are respectively 4.7Mpa and 5.8Mpa, the compressive stresses on the left lower part and the right upper part of the tenon in embodiment 3 are respectively 3.5Mpa and 4.1Mpa, and the compressive stresses on the left lower part and the right upper part of the tenon in embodiment 4 are respectively 5Mpa and 4.98 Mpa. Only the stress values of the left lower part and the right upper part of the tenon in the embodiment 3 do not exceed the radial compressive strength (4.55MPa) of the transverse striation of the wood, and the cloud chart can also observe that no obvious plastic deformation occurs in the embodiment 3 along the radial direction of the transverse striation.
Since the shear stress variation law also increases with the increase of the rotation angle, the maximum shear stress at the node 0.08rad is directly taken for comparison. As shown in FIG. 19, the shear stress in the direction S12 is opposite, and the shear forces are greater on both sides of the tenon and the mortise neck. The maximum shear stress of example 1 was 2.54MPa, the maximum shear stress of example 2 was 2.9MPa, the maximum shear stress of example 3 was 1.75MPa, and the maximum shear stress of example 4 was 3.01MPa, and all of them did not exceed the limit shear stress. No shear failure of the wood material was found during loading.
The equivalent plastic strain of the tenon refers to the sum of absolute values of tensile strain and compressive strain borne by the tenon in cyclic control displacement loading, and the sum of absolute values of tensile strain and compressive strain is constantly greater than or equal to 0 in accumulative terms (PEEQ greater than 0 represents yield). As shown in FIG. 20, at 0.08rad, very significant plastic deformation of the dovetail has occurred, and it can be observed during the simulation that as the number of load displacement steps increases, the extrusion and plastic deformation of the dovetail becomes more significant. The PEEQ is strongest at the dovetail, and decreases with increasing distance from the dovetail, with the PEEQ at the dovetail end being the smallest.
8. Conclusion
(1) The tenon-and-mortise joint mainly bears shearing force, and the mechanical property is mainly influenced by density, moisture content, temperature and long-term load. The dovetail joint is a mortise and tenon joint with mixed stress of shearing force, bending moment and axial force, and the damage forms of the dovetail joint are tenon side compression deformation, tenon neck fracture, tenon shearing and mortise opening expansion crack.
(2) The vertical load application values of the top column of the dovetail joint of the second grade material model are respectively 28.8KN, 14.85KN and 7.2KN, the vertical load application values of the top column of the dovetail joint of the first grade material model are respectively 1:2.2, 1:3.2 and 1:4.4, the vertical load application values of the dovetail joint of the third grade material model are respectively 13.5KN, the loading scheme adopts displacement control and circular loading according to a triangular wave curve, and the loading amplitude is 5 mm/min.
(3) The ultimate bearing capacity of the embodiment 2 is 11.8KN which is 2.9 times and 7.2 times of the embodiment 1 and the embodiment 3, and the ultimate bearing capacity of the equal-model-proportion equal-grade node is slightly larger than that of the equal-model-proportion equal-grade node. The node hysteresis curve is Z-shaped, obvious pinching effect appears, and the bending moment peak value of the first circulation under each stage of control displacement is generally larger than the second and third circulations.
(4) Because the horizontal rigidity generated by the rotation of the node upright post and the need of overcoming the additional bending moment of the axial force, the forward and reverse slopes near the origin of the skeleton curve are higher, and the curve has obvious stages of slip strengthening and yield failure. The peak bending moment of the example 2 is 9.3KN which is 3.5 times and 10.4 times of that of the examples 1 and 3, the initial stage trend of the skeleton curve is similar to that of the comparative example 1 and 4, the node is in a state of extrusion in a slip state, and the bending moment of the continuously loaded example 1 is obviously increased faster than that of the example 4.
(5) Example 2 initial stiffness was 594kn. m. rad-1, 3.4 and 9.4 times that of examples 1 and 3, and example 1 initial stiffness was 1.4 times that of example 4. The mean values of the intensity degradation coefficients of example 1, example 2, example 3 and example 4 were 0.97, 0.98, 0.95 and 0.96, respectively. Examples 1, 2, 3 and 4 had a he at 0.08rad of 0.187, 0.163, 0.22 and 0.17, respectively. The result shows that the overall rigidity and the strength degradation coefficient of the node are reduced along with the increase of the model proportion, but the energy consumption capability is enhanced, and the overall rigidity, the strength degradation and the energy consumption capability of the second-class material node under the same model proportion are higher.
(6) The maximum tenon pulling amount in the first-stage control displacement of the embodiment 1, the embodiment 2 and the embodiment 4 is about 1.76mm, but the tenon pulling amount in the embodiment 3 is obviously smaller to 0.66 mm. The maximum tenon pulling amounts of the two-grade node under the same model proportion are larger than that of the three-grade node under the same model proportion, and the tenon pulling amounts of the two-grade node under the last-stage control displacement of the embodiments 1, 2, 3 and 4 are 13.5mm, 17.8mm, 4.85mm and 11 mm.
In conclusion, the 1:2.2 model proportion dovetail joint bending moment, rigidity and strength value are the highest, but the tenon pulling amount is the largest, and the energy consumption capability is the weakest. The 1:4.4 model proportional dovetail joint has the best energy consumption capability, the minimum tenon pulling amount, the minimum bending moment, the minimum rigidity and the minimum strength value, and the maximum residual deformation. In contrast, the 1:3.2 model proportion dovetail joint has better mechanical properties.

Claims (10)

1. A method for evaluating the stress capacity of a mortise and tenon joint of a wood structure is characterized by comprising the following steps:
step 1, selecting a mortise and tenon joint prototype;
step 2, analyzing the stress action of the prototype of the mortise and tenon joint selected in the step 1;
step 3, drawing a node model stereogram through ABAQUS software according to the actual stress condition of the mortise and tenon node prototype obtained in the step 2, and sequentially defining boundary conditions, grid units, friction contact parameters and a loading scheme;
step 4, carrying out a finite element test on the finite element model established in the step 3 to obtain mechanical property parameters of the mortise and tenon joint, wherein the mechanical property parameters comprise: hysteresis performance, rigidity degradation rule, strength degradation rule, energy consumption capability and tenon pulling amount;
and 5, carrying out finite element analysis according to the mechanical properties obtained in the step 4, thereby realizing the evaluation of the stress capacity of the selected mortise and tenon joint prototype.
2. The method for evaluating the stress capacity of the mortise and tenon joints of the wood structure according to claim 1, wherein the step 3 of establishing the finite element model comprises the following steps:
step a, according to the mortise and tenon joint prototype in the step 1, measuring dovetail joint nodes of a wood structure to obtain the original size and shape of the joint;
b, selecting materials of the finite element model, obtaining the adjusted node size by reducing the prototype proportion of the mortise and tenon node, drawing a virtual digital model stereogram by ABAQUS software, and determining an elastic engineering constant of the finite element model;
the materials comprise second-class materials and third-class materials;
the ratio is 1: 2-5;
step c, setting boundary conditions to be the same as the constraint form of the actual situation of the mortise and tenon joint;
step d, selecting a material constitutive relation model;
step e, according to the stress analysis, determining a loading scheme in the modeling analysis step;
step f, carrying out mesh division by adopting a C3D8R mesh and Hex unit cell mesh division mechanism;
step g, setting a contact friction effect;
step h, detecting whether the simulation result of the finite element model is converged, and if so, directly entering step 4; if not, the check process is carried out to converge and then the step 4 is carried out.
3. The method for evaluating the stress capacity of the mortise and tenon joints of the wood structure according to claim 2, wherein the finite element test comprises a unidirectional loading simulation test and low-cycle reciprocating cyclic loading;
the unidirectional loading simulation test adopts a displacement control method to apply constant-speed horizontal displacement to the ends of the square beams, applies axially uniformly distributed load to the column top local flat square beams, the loading amplitude is 5mm/min, and the test is terminated when the load is applied until the node is damaged or the bearing capacity is reduced to 80% of the limit load, so that the maximum displacement of node yield is obtained;
the low-cycle reciprocating cyclic loading adopts a displacement control method for loading, the control displacement adopted by the loading is the maximum displacement obtained by unidirectional loading, and the top of the column is kept to apply fixed and uniformly distributed axial loads; the low-cycle cyclic reciprocating loading firstly selects and controls the displacement to be 1.25 percent, 2.5 percent, 5 percent and 10 percent of triangular waves of the maximum displacement in sequence for single cycle; and then, performing cyclic loading by using 20%, 40%, 60%, 80% and 100% of the maximum displacement as control displacements, and performing three cycles on each stage of control displacement until the node model is subjected to yield failure and stops loading.
4. The method for evaluating the stress capability of the mortise and tenon joints of the wood structure according to claim 3, wherein the finite element analysis comprises hysteresis curve analysis, skeleton curve analysis, rigid degradation analysis, strength degradation analysis, energy consumption capability analysis, tenon pulling amount analysis and node stress analysis;
the central rotation angle theta of the hysteresis curve is taken as an abscissa, and the bending moment M is taken as an ordinate, and the central rotation angle theta and the bending moment M are respectively obtained by the following formula: m is the product of the formula P.H,
Figure FDA0002526513010000031
wherein, Δ -horizontal displacement of the loading point; h-horizontal distance between the loading point and the column end face; p-horizontal load applied at the load point;
the skeleton curve is an envelope curve formed by mutually connecting maximum bending moment value points of the first cycle under each stage of control displacement loading of the hysteresis curve;
the rigidity degradation curve is a change curve of rigidity decreasing along with the increase of displacement, wherein the secant rigidity of the node under repeated load of each level is represented by K, and the positive secant rigidity of the node is Ki+The stiffness of the reverse secant is ki-And are respectively obtained by the following formula:
Figure FDA0002526513010000032
Figure FDA0002526513010000033
in the formula, Mi+Loading the positive maximum bending moment value of the 1 st cycle for the ith-level control displacement; thetai+Loading the positive maximum rotation angle of the 1 st cycle for the ith-level control displacement; mi-Loading the reverse maximum bending moment value of the 1 st cycle for the ith-level control displacement; thetai-Loading the reverse maximum rotation angle of the 1 st cycle for the ith-level control displacement;
the intensity degradation analysis is performed by observing an intensity degradation coefficient lambdaiReflecting the change of the node strength under different cycles under each stage of displacement loading control, and selecting the ratio of the third cycle bearing capacity P to the first cycle bearing capacity P for calculation, wherein the formula is as follows:
Figure FDA0002526513010000034
in the formula, λiControlling the intensity degradation coefficient under the displacement circulation for the ith level; pi3The bearing capacity of the third circulation under the loading of the ith-level control displacement is obtained; pi1Loading the bearing capacity of the next first cycle for the ith-stage control displacement;
the energy dissipation capability is determined by the equivalent viscous damping coefficient heIs expressed by the equivalent viscous damping coefficient heIs obtained by the following formula:
Figure FDA0002526513010000035
in the formula, SABCDIs the hysteresis curve envelope area; sΔODF+SΔOCE△ ODF plus △ OCE area;
the tenon pulling amount analysis is realized by observing the change of the tenon pulling amount along with the increase of the corner;
the nodal stress analysis is performed from the stress in the grain-following direction, the stress in the cross grain (chord direction) and the stress in the cross grain (radial direction), respectively.
5. The method for evaluating the stress capability of the mortise and tenon joints of the wood structure according to claim 2, wherein the boundary conditions in the step b comprise the setting of boundary conditions that one end of the column in the finite element model is fixed and the other end of the column is hinged, the constraint on displacement in the x direction and the z direction and the constraint on rotation in the y direction and the z direction are carried out on the top part of the column in the finite element model, and the constraint on displacement in the x direction, the y direction and the z direction and the constraint on rotation in the y direction and the z direction are carried out on the column foot until the displacement and the rotation angle are both 0.
6. The method for evaluating the stress capacity of the mortise and tenon joints of the wood structure according to claim 2, wherein in the step g, the balk is divided into grids of preferably 44mm, the column is divided into grids of 34mm, and the local flat board balk is divided into grids of 24 mm.
7. The method for evaluating the stress capability of a mortise and tenon joint of a wood structure according to claim 2, wherein the contact friction effect comprises tangential and normal effects on contact surfaces of a tenon and a mortise;
the setting of the contact friction is realized by the following steps:
selecting a friction model, wherein the friction model is one of a Lagrange friction model, a dynamic friction model, a coulomb friction model and a penalty function model;
step (2), selecting a main surface and a slave surface, wherein the main surface and the slave surface have two selection schemes: one is that at the tenon and mortise part, the mortise of the column end is selected as the tenon of the slave face as the main face; the other is at the contact part of the top end surface of the column and the local flat plate purlin, the top end surface of the main surface is selected from the surface of the column, and the local flat plate purlin is selected from the surface to be in contact with the bottom surface;
step (3), selecting a tracking method, wherein the tracking method is used for judging the contact state of the node; the tracking method includes a small sliding method and a limited sliding method.
8. The method for evaluating the stress capability of the mortise and tenon joints of the wood structure according to claim 2, wherein the material constitutive relation model comprises orthomorphic constitutive relations and transverse morphic constitutive relations;
the texture constitutive relation is assumed to be an ideal elastic-plastic model without original damage of wood, the tensile elastic modulus and the compressive elastic modulus of the texture are both expressed by adopting the relation of strain and stress, and the calculation formula is as follows:
Figure FDA0002526513010000051
in the formula:cuis the grain-following ultimate compressive strain of the wood,c0is the compressive yield strain along the grain of the wood,tuis the tensile yield strain in grain of the wood, EcsModulus of elasticity under compression for grain of wood, EtsTensile elastic modulus of wood grain;
the calculation formula of the transverse texture constitutive relation is as follows:
Figure FDA0002526513010000052
in the formula:Lthe transverse striation of the wood is subjected to compressive yield strain,Nis the transverse grain compressive ultimate strain of wood, EL、E1Modulus of the elastic section under compression of the wood grain E2Is a compression elastic mold in the strengthening stage of wood transverse striation.
9. The method for evaluating the stress capacity of the mortise and tenon joints of the wood structure according to claim 1, wherein the stress action comprises a shearing force action, a bending moment action and an axial force action.
10. The method for evaluating the stress capability of a mortise and tenon joint of a wood structure according to any one of claims 1 to 9, wherein the mortise and tenon joint is a dovetail joint.
CN202010505868.2A 2020-06-05 2020-06-05 Method for evaluating stress capacity of mortise and tenon joint of wood structure Pending CN111651926A (en)

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CN113076585A (en) * 2021-04-13 2021-07-06 中南林业科技大学 Method for calculating pin bolt connection bearing capacity of wood structure steel clamping plate
CN113408024A (en) * 2021-05-11 2021-09-17 北京城建设计发展集团股份有限公司 Method for calculating bending resistance and bearing capacity of grouting type mortise joint of assembled underground structure
CN113408024B (en) * 2021-05-11 2023-10-27 北京城建设计发展集团股份有限公司 Method for calculating bending-resistant bearing capacity of grouting tongue-and-groove joint of assembled underground structure
CN113158318A (en) * 2021-05-17 2021-07-23 云南省设计院集团有限公司 Method for designing bearing capacity reinforcement for normal section of shear wall with special-shaped end columns

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