Method for calculating bearing capacity of 360-degree occlusion node of metal roof

Abstract

The invention discloses a method for calculating the bearing capacity of a 360-degree meshing node of a metal roof, and the method comprises the following steps: a, analyzing the damage characteristics of the 360-degree meshing node of the metal roof under the action of wind load, and building a failure judgment criterion of the metal roof; b, establishing a mechanical model of the metal roof according to mechanical characteristics of the metal roof; c, under the assumption of online elasticity and small deformation, substituting the force-displacement relation of the 360-degree occlusion node under the action of the wind load into the failure judgment criterion to obtain the wind pressure bearing capacity of the metal roof within the elastic range; and d, a nonlinear coefficient is introduced to correct the wind pressure bearing capacity of the metal roof within the elastic range, and the wind pressure bearing capacity when the metal roof fails is obtained. The bearing capacity calculation formula is simpler, calculation is convenient, precision is high, and theoretical guidance can be well provided for engineering design.

Description

Technical Field

[0001] The invention relates to the technical field of building structure testing, and in particular to a method for calculating the bearing capacity of a 360-degree bite node of a metal roof. Background Art

[0002] In the construction industry, metal panels are widely used in roofs, walls and other parts due to their good aesthetics and functionality. Panels are connected by bite, which generally has a variety of bite forms, including vertical lock seam bite structure, 360° bite structure, etc. However, with the increase of wind load, the wind resistance of metal panels has become an important issue.

[0003] For 360° interlocking structures, in order to evaluate the wind bearing capacity of metal panels, a three-way decoupled spring model was proposed to simulate the mechanical behavior of the node, that is, the 360° interlocking structure was decoupled into three equivalent springs, including horizontal springs, vertical springs and rotational springs, and the equivalent springs in three directions were used to characterize the mechanical properties of the interlocking node in three directions. According to investigations and studies, the main form of damage for this type of 360° interlocking metal roof is disengagement damage, but the cause of disengagement can be divided into two categories depending on whether the wind pressure is uniform. However, there is currently no method that can reliably determine when the roof panel has disengaged, nor a method for calculating the wind bearing capacity of the roof panel that can be used for engineering design.

[0004] In order to evaluate the wind bearing capacity of 360° interlocking metal roofs, it is necessary to first propose a reliable failure judgment criterion for this type of roof, that is, in what state do we consider the roof to have lost its working ability. After knowing the reliable failure judgment criterion, through theoretical derivation and finite element parametric analysis, a simple wind bearing capacity calculation formula can be proposed to provide certain theoretical guidance for engineering design. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: to provide a method for calculating the bearing capacity of a 360° interlocking node of a metal roof, thereby solving the problem in the prior art of lacking a method for well evaluating the wind bearing capacity of a metal roof.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for calculating the bearing capacity of a 360° snap joint of a metal roof comprises the following steps:

[0008] a. Analyze the failure characteristics of the 360° interlocking nodes of metal roofs under wind loads and establish the failure judgment criteria for metal roofs;

[0009] b. Establish a mechanical model of the metal roof based on its mechanical characteristics;

[0010] c. Under the assumption of linear elasticity and small deformation, the force-displacement relationship of the 360° snap joint under wind load is substituted into the failure judgment criterion to obtain the wind pressure bearing capacity of the metal roof within the elastic range;

[0011] d. Introduce nonlinear coefficients to correct the wind pressure bearing capacity of the metal roof within the elastic range and obtain the wind pressure bearing capacity when the metal roof fails.

[0012] As an optimization, the 360° bite node includes a horizontally arranged panel, and two ends of the panel are bent and extended upward to form a first bite portion and a second bite portion;

[0013] The first engaging portion includes a first vertical plate formed by bending and extending the panel upward, a first flat plate formed by bending and extending to a side away from the panel, a second vertical plate formed by bending and extending downward, a second flat plate formed by bending and extending to a side close to the panel, and a third vertical plate formed by bending and extending upward, and there are gaps between the first vertical plates, between the second vertical plates and the third vertical plates, and between the upper end of the third vertical plate and the first flat plate;

[0014] The second engaging portion includes a fourth vertical plate formed by bending and extending the panel upward, a third flat plate formed by bending and extending toward a side close to the panel, and a fifth vertical plate formed by bending and extending downward;

[0015] When the first engaging portion of the panel engages with the second engaging portion of the adjacent panel, the fifth vertical plate engages in the gap between the second vertical plate and the third vertical plate, the third flat plate engages in the gap between the upper end of the third vertical plate and the first flat plate, and the fourth vertical plate engages in the gap between the first vertical plate and the third vertical plate.

[0016] As an optimization, it also includes a support, which includes a horizontally arranged substrate, and a sixth vertical plate formed by bending and extending one end of the substrate upward, a fourth flat plate formed by bending and extending to a side away from the substrate, a seventh vertical plate formed by bending and extending downward, a fifth flat plate formed by bending and extending to a side close to the substrate, and an eighth vertical plate formed by bending and extending upward. When engaged, the eighth vertical plate is engaged between the third vertical plate and the fifth vertical plate, the seventh vertical plate is engaged between the second vertical plate and the fifth vertical plate, the sixth vertical plate is engaged between the first vertical plate and the fourth vertical plate, and the fourth flat plate is engaged between the first flat plate and the third flat plate.

[0017] As an optimization, in step a, the failure judgment criterion includes that the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°.

[0018] As an optimization, by measuring the relationship between the reaction force of the support of the 360° bite node under wind load and the rotation angle of the first vertical plate or the fourth vertical plate, when the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°, the 360° bite node is disengaged, and the reaction force of the support decreases rapidly, thereby obtaining the failure judgment criterion.

[0019] As an optimization, in step b, the panel is simplified into a beam model according to its one-way plate mechanical characteristics, and is simplified into a three-way spring according to its semi-rigid mechanical characteristics of the 360° bite node, so as to establish a mechanical model of the panel.

[0020] As an optimization, step c, specifically,

[0021] Under the assumption of linear elasticity and small deformation, the vertical displacement formula at the 360° bite node is obtained as follows:

[0022]

[0023] Where y is the vertical displacement of the node, q is the wind pressure, B is the panel width, L is the panel length, and K is v is the vertical spring stiffness of the three-way spring;

[0024] The vertical displacement and the rotation angle of the first vertical plate or the fourth vertical plate have the following geometric relationship:

[0025] y=L R (1-cosα) (2)

[0026] Where, L R is the height of the first vertical board or the fourth vertical board, and α is the turning angle of the first vertical board or the fourth vertical board;

[0027] The failure judgment criterion is expressed as follows:

[0028]

[0029] Combining equations (1) and (2) and substituting them into equation (3) yields the wind pressure bearing capacity of the panel within the elastic range, as follows:

[0030]

[0031] As an optimization, in step d, the nonlinear coefficient k is introduced to represent the influence of nonlinearity through parametric analysis of the finite element model, and the fitting results are obtained:

[0032] k=(0.14t+0.09)(-0.0028B+3.06) (5)

[0033] Where t is the thickness of the panel;

[0034] By correcting equation (4) through equation (5), the wind pressure bearing capacity of the panel when it fails is obtained as:

[0035]

[0036] Compared with the prior art, this application has the following beneficial effects:

[0037] The present invention

[0038] Through experimental research and finite element model simulation, a reasonable failure judgment criterion that can characterize the failure of the bite node is proposed. On the basis of this failure judgment criterion, a simplified model of the panel is established, and the wind pressure bearing capacity formula of the panel within the linear elastic range is derived by combining the force-displacement relationship and the geometric relationship. In order to further improve the scope of application and accuracy of the calculation formula, the nonlinear influence coefficient is introduced for correction to obtain the final wind pressure bearing capacity formula. The bearing capacity calculation formula is simpler, easier to calculate, and has higher accuracy, which can provide theoretical guidance for engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic diagram of establishing the failure judgment criteria in the present invention;

[0040] Figure 2 is a curve of the relationship between the support reaction force of the bite node and the rotation angle of the first vertical plate or the fourth vertical plate in the present invention;

[0041] Figure 3 It is the deformation cloud diagram of the finite element model of the occlusal node in the present invention at various stages;

[0042] Figure 4 It is a simplified model of the panel in the present invention;

[0043] Figure 5 It is a schematic diagram of the calculation of the bending moment of the panel in the present invention;

[0044] Figure 6 It is the fitting curve of the nonlinear influence coefficient in the present invention. DETAILED DESCRIPTION

[0045] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0046] For specific implementation: see Figure 1-6 ,

[0047] A method for calculating the bearing capacity of a 360° snap joint of a metal roof comprises the following steps:

[0048] a. Analyze the failure characteristics of the 360° interlocking nodes of metal roofs under wind loads and establish the failure judgment criteria for metal roofs;

[0049] Specifically, the 360° bite node includes a horizontally arranged panel, and two ends of the panel are bent and extended upward to form a first bite portion and a second bite portion;

[0050] The first engaging portion includes a first vertical plate formed by bending and extending the panel upward, a first flat plate formed by bending and extending to a side away from the panel, a second vertical plate formed by bending and extending downward, a second flat plate formed by bending and extending to a side close to the panel, and a third vertical plate formed by bending and extending upward, and there are gaps between the first vertical plates, between the second vertical plates and the third vertical plates, and between the upper end of the third vertical plate and the first flat plate;

[0051] The second engaging portion includes a fourth vertical plate formed by bending and extending the panel upward, a third flat plate formed by bending and extending toward a side close to the panel, and a fifth vertical plate formed by bending and extending downward;

[0052] When the first engaging portion of the panel engages with the second engaging portion of the adjacent panel, the fifth vertical plate engages in the gap between the second vertical plate and the third vertical plate, the third flat plate engages in the gap between the upper end of the third vertical plate and the first flat plate, and the fourth vertical plate engages in the gap between the first vertical plate and the third vertical plate.

[0053] It also includes a support, which includes a horizontally arranged base plate, and a sixth vertical plate formed by bending and extending upward from one end of the base plate, a fourth flat plate formed by bending and extending to a side away from the base plate, a seventh vertical plate formed by bending and extending downward, a fifth flat plate formed by bending and extending to a side close to the base plate, and an eighth vertical plate formed by bending and extending upward. When engaged, the eighth vertical plate is engaged between the third vertical plate and the fifth vertical plate, the seventh vertical plate is engaged between the second vertical plate and the fifth vertical plate, the sixth vertical plate is engaged between the first vertical plate and the fourth vertical plate, and the fourth flat plate is engaged between the first flat plate and the third flat plate.

[0054] The failure judgment criteria include that the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°. Figure 1 shown.

[0055] Specifically, the present invention proposes a failure judgment criterion under the condition of uniform wind pressure based on experimental research and finite element model simulation. Figure 1 As shown in the figure, α represents the rotation angle of the node web (i.e., the first vertical plate or the fourth vertical plate) under the action of wind load. When the rotation angle exceeds a certain degree, the lock seam formed by the bite is unlocked and the joint failure occurs. After experimental research and finite element model simulation, the relationship curve between the node support reaction force and the rotation angle α is obtained, as shown in Figure 2 As shown, we find that when the rotation angle α is around 110°, the support reaction force decreases rapidly. This is because one of the panels is separated (disengaged) from the node, which means that the node has failed. Figure 3 It is the deformation cloud diagram of the finite element model at each stage, in which it can be found that when the rotation angle is greater than or equal to 110°, the right panel is separated from the node, which means that the node is considered to be failed. In summary, it can be considered that when this type of roof panel is disengaged and damaged, the angle needs to be greater than 110°, that is, when α≥11π / 18(110°), the roof is considered to be failed. That is, by measuring the relationship between the reaction force of the support of the 360° bite node under wind load and the rotation angle of the first vertical plate or the fourth vertical plate, when the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°, the 360° bite node is disengaged, and the reaction force of the support decreases rapidly, and the failure judgment criterion is obtained.

[0056] b. Establish a mechanical model of metal roof based on the mechanical characteristics of metal roof and the theoretical basis of structural mechanics;

[0057] Specifically, the one-way plate mechanical characteristics of the panel are simplified into a beam model, and the semi-rigid mechanical characteristics of the 360° snap joint are simplified into a three-way spring to establish the mechanical model of the panel, such as Figure 4 shown.

[0058] c. Under the assumption of linear elasticity and small deformation, the force-displacement relationship of the 360° snap joint under wind load is substituted into the failure judgment criterion to obtain the wind pressure bearing capacity of the metal roof within the elastic range;

[0059] Specifically, under the assumption of linear elasticity and small deformation, we can calculate its bending moment diagram based on the force method and mechanical model, as follows: Figure 5 As shown, the vertical displacement formula at the 360° occlusal node is as follows:

[0060]

[0061] Where y is the vertical displacement of the node, q is the wind pressure, B is the panel width, L is the panel length, and K is v is the vertical spring stiffness of the three-way spring;

[0062] The vertical displacement and the rotation angle of the first vertical plate or the fourth vertical plate have the following geometric relationship:

[0063] y=L R (1-cosα) (2)

[0064] Where, L R is the height of the first vertical board or the fourth vertical board, and α is the turning angle of the first vertical board or the fourth vertical board;

[0065] The failure judgment criterion is expressed as follows:

[0066]

[0067] Combining equations (1) and (2) and substituting them into equation (3) yields the wind pressure bearing capacity of the panel within the elastic range, as follows:

[0068]

[0069] d. Introduce nonlinear coefficients to correct the wind pressure bearing capacity of the metal roof within the elastic range and obtain the wind pressure bearing capacity when the metal roof fails.

[0070] Specifically, in order to further improve the scope of application and accuracy of the calculation formula, the nonlinear coefficient k is introduced to represent the influence of nonlinearity through parametric analysis of the finite element model. Among them, k is related to the panel thickness and panel width. The fitting result is as follows, and the fitting curve is as follows: Figure 6 As shown,

[0071] k=(0.14t+0.09)(-0.0028B+3.06)(5)

[0072] Where t is the thickness of the panel;

[0073] By correcting equation (4) through equation (5), the wind pressure bearing capacity of the panel when it fails is obtained as:

[0074]

[0075] Through experimental research and finite element model simulation, the present invention proposes a reasonable failure judgment criterion that can characterize the failure of the bite node, and on the basis of this failure judgment criterion, by establishing a simplified model of the panel, and combining the force-displacement relationship and the geometric relationship, the wind pressure bearing capacity formula of the panel within the linear elastic range is derived, and in order to further improve the scope of application and accuracy of the calculation formula, a nonlinear influence coefficient is introduced for correction to obtain the final wind pressure bearing capacity formula. The bearing capacity calculation formula is simpler, convenient to calculate, and has higher accuracy, and can provide theoretical guidance for engineering design.

[0076] Although the embodiments of the present invention have been shown and described, it is apparent to those skilled in the art that various changes, modifications, substitutions and variations may be made to these embodiments without departing from the principles and basis of the present invention. The scope of the present invention is defined by the appended claims and their equivalents. Therefore, the embodiments of the present invention are merely illustrative examples of the present invention. The embodiments of the present invention do not constitute limitations on the present invention from any point of view.

Claims

1. A method for calculating the bearing capacity of a 360° interlocking node of a metal roof, characterized in that: The following steps are included: a. Analyze the failure characteristics of the 360° interlocking nodes of metal roofs under wind loads and establish the failure judgment criteria for metal roofs; b. Establish a mechanical model of the metal roof based on its mechanical characteristics; c. Under the assumption of linear elasticity and small deformation, the force-displacement relationship of the 360° snap joint under wind load is substituted into the failure judgment criterion to obtain the wind pressure bearing capacity of the metal roof within the elastic range; d. Introduce nonlinear coefficients to correct the wind pressure bearing capacity of the metal roof within the elastic range and obtain the wind pressure bearing capacity when the metal roof fails.

2. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 1, characterized in that: The 360° bite node comprises a horizontally arranged panel, and two ends of the panel are bent and extended upward to form a first bite portion and a second bite portion respectively; The first engaging portion includes a first vertical plate formed by bending and extending the panel upward, a first flat plate formed by bending and extending to a side away from the panel, a second vertical plate formed by bending and extending downward, a second flat plate formed by bending and extending to a side close to the panel, and a third vertical plate formed by bending and extending upward, and there are gaps between the first vertical plates, between the second vertical plates and the third vertical plates, and between the upper end of the third vertical plate and the first flat plate; The second engaging portion includes a fourth vertical plate formed by bending and extending the panel upward, a third flat plate formed by bending and extending toward a side close to the panel, and a fifth vertical plate formed by bending and extending downward; When the first engaging portion of the panel engages with the second engaging portion of the adjacent panel, the fifth vertical plate engages in the gap between the second vertical plate and the third vertical plate, the third flat plate engages in the gap between the upper end of the third vertical plate and the first flat plate, and the fourth vertical plate engages in the gap between the first vertical plate and the third vertical plate.

3. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 2, characterized in that: It also includes a support, which includes a horizontally arranged base plate, and a sixth vertical plate formed by bending and extending upward from one end of the base plate, a fourth flat plate formed by bending and extending to a side away from the base plate, a seventh vertical plate formed by bending and extending downward, a fifth flat plate formed by bending and extending to a side close to the base plate, and an eighth vertical plate formed by bending and extending upward. When engaged, the eighth vertical plate is engaged between the third vertical plate and the fifth vertical plate, the seventh vertical plate is engaged between the second vertical plate and the fifth vertical plate, the sixth vertical plate is engaged between the first vertical plate and the fourth vertical plate, and the fourth flat plate is engaged between the first flat plate and the third flat plate.

4. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 3, characterized in that: In step a, the failure judgment criterion includes that the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°.

5. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 4, characterized in that: By measuring the relationship between the reaction force of the support of the 360° bite node under the action of wind load and the rotation angle of the first vertical plate or the fourth vertical plate, when the rotation angle of the first vertical plate or the fourth vertical plate is greater than or equal to 110°, the 360° bite node is disengaged and the reaction force of the support is rapidly reduced, thereby obtaining the failure judgment criterion.

6. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 4, characterized in that: In step b, the panel is simplified into a beam model according to its one-way plate mechanical characteristics, and is simplified into a three-way spring according to its semi-rigid mechanical characteristics of the 360° snap node, so as to establish a mechanical model of the panel.

7. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 6, characterized in that: Step c, specifically, Under the assumption of linear elasticity and small deformation, the vertical displacement formula at the 360° bite node is obtained as follows: Where y is the vertical displacement of the node, q is the wind pressure, B is the panel width, L is the panel length, and K is v is the vertical spring stiffness of the three-way spring; The vertical displacement and the rotation angle of the first vertical plate or the fourth vertical plate have the following geometric relationship: y=L R (1-cosα) (2) Where, L R is the height of the first vertical board or the fourth vertical board, and α is the turning angle of the first vertical board or the fourth vertical board; The failure judgment criterion is expressed as follows: Combining equations (1) and (2) and substituting them into equation (3) yields the wind pressure bearing capacity of the panel within the elastic range, as follows:

8. The method for calculating the bearing capacity of a 360° interlocking node of a metal roof according to claim 6, characterized in that: In step d, through the parametric analysis of the finite element model, the nonlinear coefficient k is introduced to represent the influence of nonlinearity, and the fitting results are obtained: k=(0.14t+0.09)(-0.0028B+3.06) (5)where t is the thickness of the panel; By correcting equation (4) through equation (5), the wind pressure bearing capacity of the panel when it fails is obtained as:

Images