Method for predicting the out-of-plane bending strength of diaphragms, and method for designing diaphragm thickness for steel pipe joints

Abstract

To provide an analytic modeling method and a prediction method for an out-of-plane bending proof strength of a diaphragm, which can simply and precisely predict when steel pipes having different sizes are joined through a through diaphragm.SOLUTION: For a joint at which steel pipes having different sizes are joined through a through diaphragm by non-eccentric arrangement, one-direction eccentric arrangement or two-direction eccentric arrangement, four or more nodes are previously selected from those provided, in a plane view, on a board thickness center face of the diaphragm, on a line of a marginal part or an apex of the diaphragm, on an inner peripheral surface of a flat plate part of an upper member, on an inner peripheral surface of a corner part of the upper member, on a board thickness center line of a flat plate part of the lower member, on a board thickness center line of a corner part of the lower member, and in the upper member, and an analytic model of the joint having a yield line consisting of a plurality of straight sides connecting the selected nodes is set. When moment and axial force are added to the upper member, an out-of-plane bending proof strength of the diaphragm is predicted based on total sum of strain energy of the yield line associated with displacement occurred at that time and work by an external force.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an analytical modeling method and a prediction method for the out-of-plane bending strength of a diaphragm when steel pipes of different dimensions are joined via a diaphragm, a method for designing the diaphragm plate thickness at steel pipe joints, and a steel pipe-diaphragm connection. [Background technology]

[0002] Conventionally, in column-to-beam joints using square steel pipes where the upper and lower columns have different dimensions, the joint panel is often made up of a truncated pyramidal tapered pipe 8, as shown in Figure 3. A column-to-beam joint using a tapered pipe such as that shown in Figure 3 has the advantage that it is easy to ensure the strength and rigidity of the column-diaphragm connection.

[0003] While it is easy to ensure the rigidity of the joint with this tapered pipe 8, it is expensive and difficult to distribute due to small-scale production. Furthermore, it is difficult to automate the welding of joints using this. In recent years, there has been a demand for labor-saving construction, and the use of tapered pipe 8 is becoming a problem.

[0004] One method for joining columns with different dimensions above and below without using tapered pipes 8 is to use a square steel pipe of the same dimensions as the lower column 4 as the joining panel 3, and join columns 1 and 4 with different dimensions above and below via diaphragms 2 and 5, as shown in Figure 2. If the thickness of the upper diaphragm 2 is thin, bending of the upper column 1 may cause large out-of-plane deformation in the upper diaphragm 2. In this case, the rigidity and strength of the upper diaphragm 2 will decrease, so it is necessary to evaluate the out-of-plane bending rigidity and strength of the diaphragm.

[0005] Patent Document 1 discloses a method for predicting the out-of-plane bending strength of a diaphragm at a joint where upper and lower columns of different diameters are joined by a thickened diaphragm, in which the out-of-plane bending yield strength fMy of the upper through diaphragm 5 when an axial force N acts on the upper column is calculated using yield line theory, while reflecting the axial force N of the upper column.

[0006] Patent Document 2 discloses a method for predicting the out-of-plane bending rigidity of a diaphragm at a joint where upper and lower columns of different diameters are joined by a thickened diaphragm. The method uses an analytical model in which the diaphragm is divided into multiple polygonal elements, and each polygonal element is connected by a rotational spring at each boundary edge so that it can bend elastically. The method adds up the bending deformation and shear deformation in the rotational spring for a given load and determines the rigidity of the diaphragm from the equilibrium conditions. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-28997 [Patent Document 2] Japanese Patent Application Laid-Open No. 2015-45211 Summary of the Invention [Problem to be solved by the invention]

[0008] However, the conventional technology has the following problems. For connections where upper and lower columns of different dimensions are joined with thickened diaphragms, it is possible to calculate the out-of-plane bending strength of the diaphragm and determine the required diaphragm thickness from the strength perspective by using the design formula described in Patent Document 1. However, since the corner dimensions (radius) of the square steel pipe are not taken into consideration and the corners are assumed to be regular rectangles, accuracy may decrease for steel pipes with large corner dimensions.

[0009] The present invention has been made in consideration of the above circumstances, and aims to provide a method for predicting the out-of-plane bending strength of a diaphragm that can be easily and accurately predicted when connecting square steel pipes of different dimensions via a diaphragm, a method for designing the diaphragm plate thickness of a steel pipe joint, and a steel pipe-diaphragm connection. [Means for solving the problem]

[0010] The gist of the present invention, which advantageously solves the above problems, is as follows. [1] A method for creating an analytical model to predict the bending strength of a through diaphragm for a joint where the entire circumference of the upper end of the lower member and the entire circumference of the lower end of the upper member are joined via a through diaphragm, using a lower member made of a square steel pipe or a circular steel pipe and an upper member made of a square steel pipe or a circular steel pipe with a side or diameter shorter than that of the lower member. The method involves first setting multiple nodes on the center plane of the plate thickness of the through diaphragm in a plan view, selecting four or more of the nodes, setting an analytical model of the joint, applying a downward load to one of a pair of opposing points on the upper member, and applying an equal upward load to the other point, and placing a yield line on the line connecting the nodes as each node displaces. This is an analytical modeling method for the out-of-plane bending strength of a diaphragm. [2] A method for creating an analytical model for predicting the bending strength of a through diaphragm at a joint where the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, using a combination of a lower member made of a square steel pipe and an upper member made of a square steel pipe whose side length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a square steel pipe whose diagonal length is shorter than the diameter of the lower member, or a combination of a lower member made of a square steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than the side of the lower member, wherein the entire outer periphery of the lower member is arranged so that all outer peripheries of the lower member are outside all outer peripheries of the upper member, and the analytical model is previously created by forming a joint where the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, in which the entire outer periphery of the lower member is arranged so that all outer peripheries of the lower member are outside Nodes are provided on a line passing through the edge of the lower member, on the center line of the plate thickness of the flat plate part of the lower member, on the center line of the plate thickness of the corner part of the lower member, on the inner peripheral surface of the flat plate part of the upper member, on the inner peripheral surface of the corner part of the upper member, and inside the upper member, and four or more of the provided nodes are selected, and a) if the upper member is the square steel pipe, a downward load is applied to one of a pair of opposing flat plate parts of the upper member, and an equal upward load is applied to the other flat plate part. or b) if the upper member is a circular steel pipe, a downward load is applied to one end of the diameter of the circumference of the upper member and an equal upward load is applied to the other end to apply a moment to the upper member, and a downward load is added to the axis of the upper member to apply an axial force, and in response to the displacement of each node that occurs at that time, a yield line is placed on the line connecting the nodes. [3] In the analysis model, the lower member and the upper member are square steel pipes, and a point on one side of the edge of the diaphragm is designated as A, a point on the center line of the thickness of one of the two corners of the lower member closest to A is designated as B, a point on the center line of the thickness of the flat part of the lower member closest to A is designated as C, a point on the center line of the thickness of the corner of the lower member closest to A that does not include B is designated as D, a point on the inner surface of the corner of the upper member closest to B is designated as E, a point on the inner surface of the flat part of the upper member closest to A is designated as F, and a point on the inner surface of the flat part of the upper member closest to D is designated as E. A point on the inner peripheral surface of the diaphragm edge closest to B among the diaphragm edges perpendicular to the diaphragm edge including A is designated as G, a point on the diaphragm edge closest to B among the flat plate portions of the lower member perpendicular to the diaphragm edge including A is designated as H, a point on the plate thickness center line of the flat plate portion closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is designated as J, a point inside the upper member is designated as K, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including J is designated as L, a point on the plate thickness center line of the flat plate portion of the lower member opposite to the flat plate portion including I is designated as I, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including J is designated as J, a point inside the upper member is designated as K, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including J is designated as L, a point on the plate thickness center line of the flat plate portion of the lower member opposite to the flat plate portion including I is designated as I, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including I is designated as I, a point on the inner peripheral surface of the flat plate portion of the lower member opposite to the flat plate portion including I is designated as I, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including J is designated as I, a point on the inner peripheral surface of the flat plate portion of the upper member opposite to the flat plate portion including I is designated as I, a point on the inner peripheral surface of the flat plate portion of the lower member opposite to the flat plate portion including I ... A point on the thickness center line is M, a point on the diaphragm edge facing the diaphragm edge including H is N, a point on the inner peripheral surface of the corner of the upper member close to J that does not include E is O, a point on the inner peripheral surface of the flat plate portion of the upper member facing the flat plate portion including F is P, a point on the inner peripheral surface of the corner of the upper member close to L that does not include G is Q, a point on the thickness center line of the corner of the lower member close to I that does not include B is R, a point on the thickness center line of the flat plate portion of the lower member facing the flat plate portion including C is S, a point on the corner of the lower member close to M is S. The analytical modeling method for the out-of-plane bending strength of a diaphragm described in 2 above, in which when the point on the center line of the plate thickness of the corner not including D is defined as T and the point on the edge of the diaphragm opposite the diaphragm edge including A is defined as U, the moment and axial force acting on the upper member of the analytical model are applied, causing displacement at each node and resulting in the creation of a total of 24 yield lines: BC, BE, BI, EC, EF, EJ, DC, DG, DM, GC, GF, GL, QL, QP, QS, TM, TQ, TS, OJ, OP, OS, RI, RO, and RS. [4] A method for creating an analytical model for predicting the bending strength of a through diaphragm, using a combination of a lower member made of a square steel pipe and an upper member made of a square steel pipe whose side length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a square steel pipe whose diagonal length is shorter than the diameter of the lower member, or a combination of a lower member made of a square steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than the side of the lower member, for a joint where the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, wherein a part of the outer surface of the lower member and a part of the outer surface of the upper member are arranged to have a common circumscribing plane, and the analytical model is previously created by forming a through diaphragm on the central plane of the plate thickness of the through diaphragm in a plan view, Nodes are provided on a line passing through the edge of the through diaphragm, on the center line of the plate thickness of the flat plate portion of the lower member, on the center line of the plate thickness of the corner portion of the lower member, on the inner peripheral surface of the flat plate portion of the upper member, and on the inner peripheral surface of the corner portion of the upper member, and four or more of the provided nodes are selected, and a) in the case of the square steel pipe, a downward load is applied to one flat plate portion of the upper member facing the one plane, and an equivalent upward load is applied to the other flat plate portion of the upper member, or b) In the case of a circular steel pipe, a downward load is applied to the other end of a diameter having a point on the circumference of the upper member that is in contact with the plane, and an equal upward load is applied to the end to apply a moment to the upper member, and a downward load is added to the axis of the upper member to apply an axial force.In this case, the displacement of each node that occurs at this time causes a yield line to be placed on the line connecting the nodes. [5] As the analytical model, the lower member and the upper member are square steel pipes, and a point on one diaphragm edge perpendicular to the flat plate portion of the upper and lower members aligned on the same plane is A, a point on the center line of the plate thickness of the corner of the lower member closest to A that is closest to the flat plate portion of the lower member aligned on the same plane is B, a point on the center line of the plate thickness of the flat plate portion of the lower member closest to A is C, a point on the center line of the plate thickness of the corner of the lower member closest to A that is far from the flat plate portion of the lower member aligned on the same plane is D, and a point on the center line of the plate thickness of the flat plate of the lower member aligned on the same plane is C. A point on the center line of the thickness of the flat plate portion of the lower member that is aligned on the same plane is designated as E, a point on the inner peripheral surface of the corner of the upper member that is closest to A, a point on the inner peripheral surface of the corner that is closest to A, a point on the edge of the diaphragm that is closest to the flat plate portion of the upper and lower members that are aligned on the same plane is designated as F, a point on the edge of the diaphragm that is closest to the flat plate portion of the upper and lower members that are aligned on the same plane is designated as G, a point on the center line of the thickness of the flat plate portion of the lower member that is aligned on the same plane is designated as H, a point on the inner peripheral surface of the flat plate portion of the upper member that is opposite to the flat plate portion of the upper member that is aligned on the same plane is designated as I, a point on the inner peripheral surface of the flat plate portion of the lower member that is opposite to the flat plate portion of the lower member that is aligned on the same plane is designated as I, A point on the center line of the thickness of the flat plate portion is designated as J, a point on the diaphragm edge perpendicular to the diaphragm edge including A but not including G is designated as K, a point on the center line of the thickness of the flat plate portion of the lower member aligned on the same plane and farther from A than H is designated as L, a point on the inner peripheral surface of a corner of the upper member close to J but not including F is designated as M, a point on the center line of the thickness of a corner close to the flat plate portion of the lower member aligned on the same plane but not including B is designated as N, and a point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion of the lower member including C is designated as O. 10. An analytical modeling method for the out-of-plane bending strength of a diaphragm as set forth in 4 above, in which, when the point on the center line of the plate thickness of the corner of the lower member closest to K that does not include D is defined as P, and the point on the diaphragm edge opposite the diaphragm edge that includes A is defined as Q, the moment and axial force acting on the upper member of the analytical model are applied, causing displacement at each node and resulting in the creation of a total of 20 yield lines: BC, BE, BF, CD, CF, DF, DJ, EF, EH, FI, MI, LM, LH, PM, PJ, ON, OM, NO, NL, and NM. [6] Using a lower member made of a square steel pipe and an upper member made of a square steel pipe with a side length shorter than that of the lower member, the outer surfaces of the adjacent flat plate portions of the lower member and the corresponding outer surfaces of the adjacent flat plate portions of the upper member are aligned on the same plane, and the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm. In order to predict the bending strength of the through diaphragm, the analytical model is previously calculated by calculating the bending strength of the through diaphragm on the central plane of the thickness of the through diaphragm, on the edge and vertex of the edge of the through diaphragm, on the center line of the thickness of the corner of the lower member, on the center line of the thickness of the corner of the upper member, and a node on each of the upper and lower members, and four or more of the nodes are selected to apply a downward load to the center of an arc forming the plate thickness centerline of the corner of the upper member that is diagonally opposite to the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, and apply an equal upward load to the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, thereby applying a moment to the upper member, and also applying a downward load to the axis of the upper member to apply an axial force, and placing a yield line on the line connecting the nodes as each node displaces. [7] As the analytical model, the point on the center line of the thickness of the corner of the lower member connected to one of the two flat plate portions whose outer surfaces are aligned on the same plane and not sandwiched between the two flat plate portions is designated as A, the point on the diaphragm edge closest to A that is closest to the flat plate portion where the outer surfaces of the upper and lower members are aligned on the same plane is designated as B, the point on the center line of the thickness of the flat plate portion of the lower member whose outer surfaces are aligned on the same plane is designated as C, the point on the center line of the thickness of the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane is designated as D, the center point of the arc that forms the center line of the thickness of the corner of the upper member that protrudes into the inside of the lower member is designated as E, and the point on the center line of the thickness of the corner of the upper member that protrudes into the inside of the lower member is designated as E. 10. The analytical modeling method for the out-of-plane bending strength of a diaphragm described in 6 above, wherein the point on the center line of the plate thickness of the corner of the lower member diagonally opposite the corner sandwiched between the two flat plate portions is defined as F, the vertex of the diaphragm edge closest to F is defined as G, the point on the center line of the plate thickness of the flat plate portion of the lower member where the outer surfaces of the upper and lower members are aligned on the same plane, but not including C, is defined as H, the point on the edge of the diaphragm closest to H is defined as I, and the point on the center line of the plate thickness of the corner of the lower member diagonally opposite the corner including A is defined as J. The moment and axial force acting on the upper member of the analytical model are applied, causing displacement at each node and resulting in the creation of a total of 12 yield lines: AC, AE, AF, CD, CE, DE, EF, HE, HD, JF, JE, and JH. [8] A method for predicting the out-of-plane bending strength of a diaphragm using an analytical model set up by the analytical modeling method described in 1 above, which involves calculating the sum of the strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on a predetermined relational equation from the relationship between the sum of the strain energy and the work due to the moment and axial force. [9] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 8, which uses an analytical model set up by the analytical modeling method described in claim 2 to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and axial force, based on equation (1) of the following formula 1.

[10] When predicting the out-of-plane bending strength of a diaphragm using the analytical model set by the analytical modeling method described in 3 above, A method for predicting the out-of-plane bending strength of a diaphragm described in claim 9, which calculates the sum of the strain energy stored in the yield line, and predicts the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of the strain energy and the work due to the moment and the axial force, based on the following equation (1).

[11] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 8, which uses an analytical model set up by the analytical modeling method described in claim 4 to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on equation (2) of Equation 2 below from the relationship between the sum of strain energy and the work due to the moment and axial force.

[12] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 11, which uses an analytical model set up by the analytical modeling method described in claim 5 to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and the axial force, based on the following equation (2).

[13] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 8, which uses an analytical model set up by the analytical modeling method described in claim 6 to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on equation (3) of Equation 3 below from the relationship between the sum of strain energy and the work due to the moment and axial force.

[14] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 13, which uses an analytical model set up by the analytical modeling method described in claim 7 to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and the axial force, based on the following equation (3).

[15] A method for designing the diaphragm thickness of a steel pipe joint, which involves using a method for predicting the out-of-plane bending strength of a diaphragm described in any one of 8 to 14 above to determine the out-of-plane bending strength of the diaphragm, and selecting as the diaphragm material a steel plate having a thickness sufficient to satisfy the required out-of-plane bending strength when a design moment and design axial force are applied to the upper member from steel plates of multiple standardized thicknesses.

[16] A steel pipe-diaphragm connection in which a lower member made of a square steel pipe or a circular steel pipe is joined to an upper member made of a square steel pipe or a circular steel pipe having a shorter side or diameter than the lower member using a diaphragm designed using the diaphragm plate thickness design method described in 15 above.

[0011]

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[0012]

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[0013]

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[0014] The analytical modeling and prediction methods for the out-of-plane bending strength of diaphragms according to the present invention enable simple and accurate evaluation of the out-of-plane bending strength of diaphragms in joints made of square or circular steel pipes of different dimensions, taking into account the corner dimensions of the upper and lower members. In particular, by establishing appropriate analytical models for cases where the outer periphery of the lower member is positioned outside the upper member, the outer surfaces of the upper and lower members are aligned on the same plane, and the outer surfaces of adjacent flat plate portions of the upper and lower members are aligned on the same plane, the out-of-plane bending strength of the diaphragm can be easily and accurately predicted. Furthermore, the prediction method allows the selection of steel plates with sufficient thickness to meet the required strength. Furthermore, a steel pipe-diaphragm connection can be achieved using a diaphragm of that thickness. [Brief explanation of the drawings]

[0015] [Figure 1]1A and 1B are schematic diagrams showing the configuration of an analytical model for evaluating the out-of-plane bending strength of a diaphragm in a joint structure in which square steel pipes of different dimensions are passed through coaxially and joined to a diaphragm according to one embodiment of the present invention, where (a) is a plan view and (b) is a cross-sectional view taken along the line XX. [Figure 2] 10 is a perspective view schematically illustrating a column-beam joint structure in which the diaphragm according to the embodiment is used as an upper diaphragm. FIG. [Figure 3] FIG. 1 is a perspective view schematically showing a conventional beam-column joint structure using tapered pipes as joint panels. [Figure 4] 10A and 10B are schematic diagrams showing the configuration of an analytical model for evaluating the out-of-plane bending strength of a diaphragm in a joint structure in which square steel pipes of different dimensions are passed through in a unidirectional eccentric arrangement and joined to a diaphragm according to another embodiment of the present invention, where (a) is a plan view and (b) is a cross-sectional view taken along the line XX. [Figure 5] 10A and 10B are schematic diagrams showing the configuration of an analytical model for evaluating the out-of-plane bending strength of a diaphragm in a joint structure in which square steel pipes of different dimensions are passed through in a two-way eccentric arrangement and joined to a diaphragm, according to another embodiment of the present invention, where (a) is a plan view and (b) is a YY cross-sectional view. [Figure 6] FIG. 1 is a perspective view showing a connection element of a finite element method (FEM) analysis model. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, embodiments of the present invention will be described in detail. Note that the drawings are schematic and may differ from the actual ones. Furthermore, the following embodiments exemplify equipment and methods for embodying the technical idea of ​​the present invention, and are not intended to limit the configuration to those described below. In other words, the technical idea of ​​the present invention can be modified in various ways within the technical scope described in the claims.

[0017] In this embodiment, the yield line theory is used to predict the out-of-plane bending strength of the diaphragm of the joint when connecting upper and lower members made of square steel pipes of different dimensions with a through diaphragm. The through diaphragm is made of a steel plate with a thickness greater than that of the lower member, and the side length of the edge of the through diaphragm is the same as or longer than that of the lower member. In the yield line theory, the energy U stored at the yield line XY is XY If the moment per unit length of the yield line is dM, the length of the yield line is l, and the rotation angle of the yield line is θ, then it can be expressed by the following equation (4):

[0018]

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[0019] The moment per unit length of the yield line is dM, and the yield stress of the material where the yield line occurs is σ. y , and the plate thickness is t, then in the outermost yield state, dM=(σ y ·t 2 ) / 6, and in the front cross section yield state, dM=(σ y ·t 2 ) / 4.

[0020] When calculating the work E due to an external force for a joint where members with different dimensions are joined at the top and bottom, the work due to the external force can be divided into a bending (moment) component and an axial force component, so the bending component is E M , axial force component E N Then, it can be expressed by the following formula 5 (5).

[0021]

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[0022] Here, for bending, the yield moment is M y , the diaphragm rotation angle is θ d This can be expressed by the following equation (6):

[0023]

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[0024] Regarding the axial force, let the axial force be N d and the diaphragm axial force displacement be δ N Then, it can be expressed by Equation (7) of the following Equation 7.

[0025]

Equation

[0026] <First Embodiment> As a first embodiment, using a lower member 3 made of a rectangular steel pipe and an upper member 1 made of a rectangular steel pipe with a side length shorter than that of the lower member 3, they are arranged (non-eccentric arrangement) such that the outer surfaces of all flat plate portions of the lower member 3 are outside the outer surfaces of all flat plate portions of the upper member 1, and regarding the joint portion where the entire circumference of the upper end of the lower member 3 and the entire circumference of the lower end of the upper member 1 are joined through the continuous diaphragm 2, it is considered to predict the flexural strength of the continuous diaphragm 2. Here, "shorter side length" means that if the cross-section of the rectangular steel pipe is substantially square, it is compared by the side length, and if it is substantially rectangular, it is compared by the lengths of the long sides and the short sides. The same applies hereinafter. In the example of FIG. 1, the axial centers of the lower member 3 and the upper member 1 are made to coincide with each other, that is, a so-called coaxial arrangement is adopted. When setting the analysis model, in plan view, on the plate thickness center plane of the continuous diaphragm 2, the orthogonal coordinates (x, y, z) of the nodes A to U are determined as shown in the following Equation 8. Here, the axial center position is set as the origin (0, 0, 0).

[0027]

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[0028] Here, B cu : Side length of the upper member 1, t cu : Plate thickness of the upper member 1, B cl : Side length of the lower member 3, t cl : Plate thickness of the lower member 3, x: Distance between the bending axis and the axial center of the upper member 1, r u_out : Outer peripheral radius of the corner of the upper member 1, ru_in : inner radius of corner of upper member 1, r l_out : outer radius of the corner of the lower member 3, r l_mid : Radius of the center line of the thickness of the corner of the lower member 3, δ1: Displacement of the tension side node of the upper member 1, δ2: Displacement of the compression side node of the upper member 1, l d : The protrusion length of the through diaphragm 2, and the relationship between δ1 and δ2 and B2 are expressed by the following equations (8) and (9) of Equation 9.

[0029]

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[0030] In this embodiment, the strain energy U due to internal forces is calculated as follows: U is the total strain energy U stored in the line segments BC, BE, BI, EC, EF, EJ, DC, DG, DM, GC, GF, GL, QL, QP, QS, TM, TQ, TS, OJ, OP, OS, RI, RO, and RS, which are the yield line 9. sum This is expressed as the following formula (10) in Equation 10. Note that the element boundary 10 is taken into consideration when calculating the strain energy stored in each yield line 9.

[0031]

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[0032] The work E due to the external force can be calculated using the above equations (5), (6), and (7). However, the diaphragm rotation angle θ d , diaphragm axial force displacement δ N and axial force N d are the following equations (11), (12), and (13), respectively. In the equations, n is the axial force ratio, σ yc : Yield stress of upper member 1, A cu :The cross-sectional area of ​​the upper member 1.

[0033]

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[0034] <Second Embodiment> As a second embodiment, referring to FIG. 4, a lower member 3 made of a rectangular steel pipe and an upper member 1 made of a rectangular steel pipe with a side length shorter than that of the lower member 3 are used. The outer surfaces of one flat plate portion of the lower member 3 and one flat plate portion of the upper member 1 are aligned on one plane to form a so-called one-direction eccentric arrangement. Regarding the joint portion where the entire circumference of the upper end of the lower member 3 and the entire circumference of the lower end of the upper member 1 are joined through a continuous diaphragm 2, it is considered to predict the bending strength of the continuous diaphragm 2. In setting up the analysis model, in plan view, on the center plane of the plate thickness of the continuous diaphragm 2, the orthogonal coordinates (x, y, z) of nodes A to Q are defined as in the following formula (12). Here, the axial center position of the lower member 3 is set as the origin (0, 0, 0).

[0035]

Number

[0036] Here, B cu : Side length of the upper member 1, t cu : Plate thickness of the upper member 1, B cl : Side length of the lower member 3, t cl : Plate thickness of the lower member 3, x: Distance between the bending axis and the axial center of the upper member 1, r u_out : Outer peripheral radius of the corner of the upper member 1, r u_in : Inner peripheral radius of the corner of the upper member 1, r l_out : Outer peripheral radius of the corner of the lower member 3, r l_mid : Radius of the center line of the corner plate thickness of the lower member 3, δ1: Tensile side node displacement of the upper member 1, δ2: Compressive side node displacement of the upper member 1, l d : Projection length of the continuous diaphragm 2, B2 is as in the above formula (9), and the relationship between δ1 and δ2 is expressed by formula (14) of the following formula (13).

[0037]

Number

[0038] In this embodiment, the strain energy U due to internal forces is calculated as the sum of the strain energy stored in the line segments BC, BE, BF, CD, CF, DF, DJ, EF, EH, FI, MI, LM, LH, PM, PJ, ON, OM, NO, NL, and NM, which are the yield line 9, and the axial strain energy of the lower member 3. First, the sum of the strain energy U stored in the yield line 9 is calculated as sum is expressed as the following equation (15) of Equation 14. Note that the element boundary 10 is taken into consideration when calculating the strain energy stored in each yield line 9.

[0039]

number

[0040] On the other hand, as shown in the axial strain region 11 of FIG. 4, the axial strain energy U l is expressed as equation (16) in equation 15 below.

[0041]

number

[0042] Therefore, the total of the internal forces U is given by equation (17) of equation 16 below.

[0043]

number

[0044] The work E due to the external force can be calculated using the above equations (5), (6), and (7). However, the diaphragm rotation angle θ d is the above equation (11), and the axial force N d is the above equation (13), and the diaphragm axial force displacement δ N is the following equation (18) of Equation 17.

[0045]

number

[0046] Third Embodiment As a third embodiment, as shown in Figure 5, a lower member 3 made of a square steel pipe and an upper member 1 made of a square steel pipe with a side length shorter than that of the lower member 3 are used, and the outer surfaces of adjacent flat plate portions of the lower member 3 and the corresponding outer surfaces of adjacent flat plate portions of the upper member 1 are aligned on the same plane, resulting in a so-called two-way eccentric arrangement, and the bending strength of the through diaphragm 2 is considered to be predicted for the joint where the entire upper end circumference of the lower member 3 and the entire lower end circumference of the upper member 1 are joined via the through diaphragm 2. To set up the analytical model, the Cartesian coordinates (x, y, z) of nodes A to G are defined on the central plane of the through diaphragm 2 in plan view as shown in the following formula 18. Here, the axis position of the lower member is set as the origin (0, 0, 0).

[0047]

number

[0048] where B cu : Side length of upper part 1, t cu : Thickness of upper member 1, B cl :Side length of lower member 3, t cl : thickness of lower member 3, x: distance between bending axis and center of axis of upper member 1, r u_out : Corner outer radius of upper member 1, r l_out : outer radius of the corner of the lower member 3, r l_mid : Radius of the center line of the thickness of the corner of the lower member 3, δ1: Displacement of the tension side node of the upper member 1, δ2: Displacement of the compression side node of the upper member 1, l d : is the protruding length of the through diaphragm 2, L cd , L cd1 , L cd2 and δ2 are expressed by the following formulas (19), (20), (21) and (22), respectively.

[0049]

number

[0050] In this embodiment, the strain energy U due to internal forces is calculated as the sum of the strain energy stored in the line segments AC, AE, AF, CD, CE, DE, EF, HE, HD, JF, JE, and JH, which are the yield line 9, and the axial strain energy of the lower member. First, the energy U stored in the yield line is calculated as follows: sum is expressed as Equation (23) of Equation 20 below. Note that the element boundary 10 is taken into consideration when calculating the strain energy stored in each yield line 9.

[0051]

number

[0052] On the other hand, as shown in the axial strain region 11 of FIG. 5, the axial strain energy U l is expressed as equation (24) in Equation 21 below.

[0053]

number

[0054] Therefore, the total strain energy U due to internal forces is given by equation (17) above.

[0055] The work E due to the external force can be calculated using the above equations (5), (6), and (7). However, the diaphragm rotation angle θ d , diaphragm axial force displacement δ N and axial force N d ’ are the following equations (25), (26), and (27) in Equation 22. In the equations, n is the axial force ratio, σ yc : Yield stress of upper member 1, A cu :The cross-sectional area of ​​the upper member 1.

[0056]

number

[0057] <Prediction of diaphragm out-of-plane bending strength> When the yield moment is calculated from the external work E and the strain energy U due to the internal force calculated for each of the shaft arrangement types of the first to third embodiments, E=U, and therefore, In the first and second embodiments, N d ”=N d In the third embodiment, N d ”=N d / 2, The following equation (28) of Equation 23 is derived.

[0058]

number

[0059] However, the distance x between the bending axis and the axis center of the upper member 1 must satisfy the relationship of equation (29) in Equation 24 below.

[0060]

number

[0061] In the above example, square steel pipes are used as the upper and lower members, but circular steel pipes can also be used as the upper and lower members, or a combination of square steel pipes and circular steel pipes can be used as the upper and lower members. When circular steel pipes are used as the upper and lower members, they can be applied by taking measures such as taking nodes on the center plane of the plate thickness or on the inner peripheral surface of the circular steel pipe every 45° in the circumferential central angle, for example. [Example]

[0062] As shown in Figure 6, a finite element method (FEM) analysis was conducted on a joint connecting upper and lower members 1 and 3 of different dimensions via a diaphragm 2, applying a monotonically loaded force by applying a forced displacement to the top of the upper member 1. A list of analytical models is shown in Table 1. For the coaxial, one-way eccentric, and two-way eccentric configurations, square steel pipes of □-350×350×25 (JBCR385), □-450×450×25 (JBCR385), and □-850×850×50 (BCP325) were used for the upper member 1, while square steel pipes of □-500×500×25 (JBCR385) and □-1000×1000×50 (BCP325) were used for the lower member 3. The standard values ​​for the square steel pipes are expressed as □-side length × side length × plate thickness, with JBCR385 having a strength of 385 N / mm. 2 BCP325 stands for cold roll formed square steel pipe, and BCP325 stands for strength 325N / mm 2 The figure represents a cold-press-formed square steel pipe. The difference in side length between the upper member 1 and the lower member 3 was 50 mm or 150 mm. The plate thickness of the diaphragm 2 was 32 mm to 90 mm. The steel standard for the diaphragm was TMCP385C when the upper member 1 and the lower member 3 were JBCR385, and TMCP325C when they were BCP325. Diaphragm 2 was a square with a side length 60 mm longer than the side length of the lower member. The axial force ratios were 0 and 0.3.

[0063] [Table 1]

[0064] Table 2 shows the calculation results using the evaluation formulas for each of the above embodiments and the structural analysis results using the finite element method (FEM) under the conditions of Table 1. In either case, it can be seen that by using the diaphragm out-of-plane bending strength evaluation formulas of the above embodiments, the diaphragm out-of-plane bending strength obtained from the FEM analysis results can be evaluated with high accuracy.

[0065] [Table 2] [Industrial Applicability]

[0066] The analytical modeling and prediction methods for the out-of-plane bending strength of diaphragms of the present invention enable the out-of-plane bending strength of diaphragms in joints made of square steel pipes of different dimensions to be easily and accurately evaluated, taking into account the corner dimensions of the upper and lower members, when connecting them via a through diaphragm. Furthermore, it is possible to select steel plates with a thickness sufficient to satisfy the strength obtained by the prediction method. Furthermore, the method is industrially useful because a steel pipe-diaphragm connection can be obtained using a diaphragm of that thickness. [Explanation of symbols]

[0067] 1 Upper member (upper column) 2 Diaphragm (through diaphragm, upper diaphragm) 3 Lower member (joint panel) 4 Lower pillar 5 Lower diaphragm 6 Beam flange 7 Beam web 8 Tapered pipe 9 Yield line 10 (computational) element boundaries 11 Axial strain area

Claims

1. In a case where a lower member made of a square steel pipe and an upper member made of a square steel pipe with a side length shorter than that of the lower member are used, and the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, an analytical model is used to predict the out-of-plane bending strength of the diaphragm, The lower member is disposed so that all outer peripheries of the lower member are located outside all outer peripheries of the upper member; As the analysis model, in advance, in a plan view, on the plate thickness center plane of the through diaphragm, A point on one side of the edge of the diaphragm is A, A point on the center line of the thickness of one of the two corners of the lower member that is closest to A is designated as B, The point on the center line of the thickness of the flat plate portion of the lower member closest to A is C, A point on the center line of the thickness of the corner of the lower member closest to A, which does not include B, is D, The point on the inner peripheral surface of the corner of the upper member that is closest to B is E, The point on the inner peripheral surface of the flat plate portion of the upper member closest to A is F, The point on the inner peripheral surface of the corner of the upper member that is closest to D is G, Among the diaphragm edges perpendicular to the diaphragm edge including A, the point on the diaphragm edge closest to B is designated as H, Among the flat plate portions of the lower member perpendicular to the diaphragm edge including A, the point on the center line of the plate thickness of the flat plate portion closest to B is designated as I, Among the flat plate portions of the upper member perpendicular to the diaphragm edge including A, the point on the inner peripheral surface of the flat plate portion closest to B is designated as J, A point inside the upper member is designated by K, A point on the inner peripheral surface of the flat plate portion of the upper member facing the flat plate portion including J is L, A point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion including I is M, The point on the diaphragm edge opposite to the diaphragm edge containing H is N, A point on the inner peripheral surface of the corner of the upper member that is closest to J and does not include E is O, A point on the inner peripheral surface of the flat plate portion of the upper member facing the flat plate portion including F is P, A point on the inner peripheral surface of the corner of the upper member that is closest to L and does not include G is designated as Q, A point on the center line of the thickness of the corner of the lower member that is closest to I and does not include B is R, A point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion including C is S, A point on the center line of the thickness of the corner of the lower member closest to M, which does not include D, is designated as T. The point on the edge of the diaphragm opposite to the diaphragm edge containing A is U When the nodes are set as A downward load is applied to one of a pair of opposing flat plate portions of the upper member, and an equal upward load is applied to the other flat plate portion, thereby applying a moment to the upper member, and also applying a downward load to the axis of the upper member to apply an axial force, which causes displacement at each node, Assume that 24 yield lines have occurred: BC, BE, BI, EC, EF, EJ, DC, DG, DM, GC, GF, GL, QL, QP, QS, TM, TQ, TS, OJ, OP, OS, RI, RO, and RS. The sum of the strain energy stored in the yield line is calculated, and the out-of-plane bending strength of the through diaphragm is predicted based on the relationship between the sum of the strain energy and the work due to the moment and axial force, based on the following formula 1 (1): A method for predicting the out-of-plane bending strength of diaphragms. [Equation 1] Here, M ｙ : Through diaphragm out-of-plane bending strength, U ｓｕｍ : the total strain energy stored at the yield line, N ｄ : Axial force acting on the diaphragm, δ Ｎ : Displacement of the diaphragm due to axial force, θ ｄ : Diaphragm rotation angle caused by node displacement Represents.

2. In a case where a lower member made of a square steel pipe and an upper member made of a square steel pipe with a side length shorter than that of the lower member are used, and the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, an analytical model is used to predict the out-of-plane bending strength of the diaphragm, a portion of an outer surface of the lower member and a portion of an outer surface of the upper member are arranged to have a common circumscribing plane; As the analysis model, in advance, in a plan view, on the plate thickness center plane of the through diaphragm, A point on one edge of the diaphragm perpendicular to the flat plate portions of the upper and lower members aligned on the same plane is designated as A, Among the corners of the lower member closest to A, the point on the center line of the thickness of the corner closest to the flat plate portion of the lower member aligned on the same plane is designated as B, The point on the center line of the thickness of the flat part of the lower member closest to A is C, Among the corners of the lower member closest to A, the point on the center line of the thickness of the corner farthest from the flat plate portion of the lower member aligned on the same plane is designated as D, A point E is located near A on the center line of the thickness of the flat plate portion of the lower member aligned on the same plane, Among the corners of the upper member closest to A, a point on the inner peripheral surface of the corner farthest from the flat plate portion of the lower member aligned on the same plane is designated as F, The point on the edge of the diaphragm closest to the flat plate portions of the upper and lower members aligned on the same plane is G, On the center line of the thickness of the flat plate portion of the lower member aligned on the same plane, a point farther from A than E is designated as H, A point on the inner circumferential surface of the flat plate portion of the upper member facing the flat plate portion of the upper member aligned on the same plane is designated as I, A point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion of the lower member aligned on the same plane is designated as J, Among the diaphragm edges perpendicular to the diaphragm edge including A, a point on the diaphragm edge not including G is designated as K, On the center line of the thickness of the flat plate portion of the lower member aligned on the same plane, a point farther from A than H is defined as L, Among the corners of the upper member closest to J, a point on the inner peripheral surface of a corner not including F is designated as M, Among the corners close to the flat plate portion of the lower member aligned on the same plane, the point on the center line of the plate thickness of the corner not including B is N, A point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion of the lower member including C is O, Among the corners of the lower member closest to K, a point on the center line of the thickness of the corner not including D is designated as P, The point on the diaphragm edge opposite the diaphragm edge containing A is Q When the nodes are set as applying a downward load to one flat plate portion of the upper member facing the one plane, and applying an equal upward load to another flat plate portion of the upper member; A moment is applied to the upper member, and a load is added downward to the axis of the upper member to apply an axial force, which causes displacement at each node. Suppose that 20 yield lines have occurred: BC, BE, BF, CD, CF, DF, DJ, EF, EH, FI, MI, LM, LH, PM, PJ, ON, OM, PO, NL, and NM. A method for predicting the out-of-plane bending strength of a diaphragm, which calculates the sum of strain energy stored in the yield line, and predicts the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and axial force, based on equation (2) of Equation 2 below. [Equation 2] Here, M ｙ : Through diaphragm out-of-plane bending strength, U ｓｕｍ : the total strain energy stored at the yield line, U ｌ : axial strain energy of the lower member, N ｄ : Axial force acting on the diaphragm, δ Ｎ : Displacement of the diaphragm due to axial force, θ ｄ : Diaphragm rotation angle caused by node displacement Represents.

3. When a lower member made of a square steel pipe and an upper member made of a square steel pipe with a side length shorter than that of the lower member are used, and the outer surfaces of the adjacent flat plate portions of the lower member and the corresponding outer surfaces of the adjacent flat plate portions of the upper member are aligned on the same plane, and the entire upper end circumference of the lower member and the entire lower end circumference of the upper member are joined via a through diaphragm, an analytical model is used to predict the out-of-plane bending strength of the diaphragm, As the analysis model, in advance, in a plan view, on the plate thickness center plane of the through diaphragm, The outer surfaces of the upper and lower members are connected to one of the two flat plate portions aligned on the same plane, and a point on the center line of the plate thickness of the corner of the lower member that is not sandwiched between the two flat plate portions is designated as A, Among the diaphragm edges closest to A, the point on the diaphragm edge closest to the flat part where the outer surfaces of the upper and lower members are aligned on the same plane is called B. Of the flat plate portions of the lower member in which the outer surfaces of the upper and lower members are aligned on the same plane, the point on the center line of the thickness of the flat plate portion closer to B is designated as C, The point on the center line of the thickness of the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane is D, The center point of the arc forming the center line of the thickness of the corner portion of the upper member protruding into the lower member is E, The point on the center line of the plate thickness of the corner of the lower member, which is located diagonally between the two flat plate portions where the outer surfaces of the upper and lower members are aligned on the same plane, is designated as F, The apex of the diaphragm edge closest to F is G, Among the flat plate portions of the lower member in which the outer surfaces of the upper and lower members are aligned on the same plane, a point on the center line of the thickness of the flat plate portion not including C is designated as H, The point on the diaphragm edge closest to H is I, A point on the center line of the thickness of the corner of the lower member diagonally opposite to the corner including A is J When the nodes are set as A downward load is applied to the center point of the arc forming the plate thickness centerline of the corner of the upper member that is diagonally opposite to the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, and an equal upward load is applied to the corner of the upper member that is sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, thereby applying a moment to the upper member, and also applying an additional downward load to the axis of the upper member to apply an axial force, which causes displacement at each node and results in a total of 12 yield lines, AC, AE, AF, CD, CE, DE, EF, HE, HD, JF, JE, and JH, A method for predicting the out-of-plane bending strength of a diaphragm, which calculates the sum of strain energy stored in the yield line, and predicts the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and axial force, based on equation (3) of Equation 3 below. [Equation 3] Here, M ｙ : Through diaphragm out-of-plane bending strength, U ｓｕｍ : the total strain energy stored at the yield line, U ｌ : axial strain energy of the lower member, N ｄ : Axial force acting on the diaphragm, δ Ｎ : Displacement of the diaphragm due to axial force, θ ｄ : Diaphragm rotation angle caused by node displacement Represents.

4. A method for designing a diaphragm thickness for a steel pipe joint, comprising: determining the out-of-plane bending strength of the diaphragm using a method for predicting the out-of-plane bending strength of a diaphragm described in any one of claims 1 to 3; and selecting, as the material for the diaphragm, a steel plate having a thickness sufficient to satisfy the required out-of-plane bending strength required when a design moment and a design axial force are applied to the upper member, from steel plates of multiple standardized thicknesses.

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