Analytical modeling and prediction methods for out-of-plane bending strength of diaphragms, and design methods for diaphragm thickness in steel pipe joints

Abstract

To provide an analytical modeling method and a prediction method of the out-of-plane bending strength of a diaphragm capable of easily and accurately performing prediction when joining steel pipes of different dimensions via a through diaphragm.SOLUTION: An analytical modeling method includes the steps: concerning joints where steel pipes of different dimensions are joined via a through diaphragm in non-eccentric arrangement, one-way eccentric arrangement, or two-way eccentric arrangement, selecting four or more nodes in advance, in plan view, on the edge line or apex of the diaphragm, on the thickness center line of the flat part of the upper and lower members, on the thickness center line of the corner of the upper and lower members, and inside the upper member, on the thickness center plane of the diaphragm; setting an analytical model for a joint with a yield line consisting of multiple straight sides connecting the selected nodes; and regarding the case where moment and axial force are added to the upper member, predicting the out-of-plane bending strength of diaphragm based on the total strain energy at the yield line due to the displacement generated at that time and the work due to 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, 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. Using other analytical models, the bending deformation and shear deformation in the rotational spring for a given load are added up, and the rigidity of the diaphragm is determined 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 joining steel pipes of different dimensions through 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 for predicting the bending strength of 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 whose side or diameter is shorter than that 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, in which, in a plan view, a line is first drawn on the center plane of the plate thickness of the through diaphragm, passing through the edge of the through diaphragm, and the line of the lower member and the upper member is drawn on the center plane of the plate thickness of the through diaphragm. A method for analytical modeling of the out-of-plane bending strength of a diaphragm, which includes providing a plurality of nodes on the center line of the plate thickness of the flat plate portion, on the center lines of the plate thickness of the corners of the lower and upper members, and on the center of the arc forming the center line of the plate thickness of the corners of the upper member, 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 locations on the upper member and applying an equal upward load to the other location, and placing a yield line on the line connecting the nodes as each node displaces. [2] 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 all outer peripheries of the lower member are arranged outside all outer peripheries of the upper member, 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 ear framing, on the center line of the thickness of the flat plate part of the lower member, on the center line of the thickness of the corner of the lower member, on the center line of the thickness of the flat plate part of the upper member, and on the center line of the thickness of the corner of 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 that is closest to A is designated as B, a point on the center line of the thickness of the flat plate part of the lower member that is closest to A is designated as C, a point on the center line of the thickness of the corner of the lower member that is closest to A but does not include B is designated as D, a point on the center line of the thickness of the corner of the upper member that is closest to B is designated as E, and a point on the center line of the thickness of the corner of the upper member that is closest to A but does not include E is designated as C. The point on the center line of the thickness of the corner is F, the point on the diaphragm edge closest to B among the diaphragm edges perpendicular to the diaphragm edge including A is G, the point on the center line of the thickness of the flat plate portion of the lower member closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is H, the point on the center line of the thickness of the flat plate portion of the upper member closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is I, the point on the center line of the thickness of the flat plate portion of the upper member opposite the flat plate portion including I is J, the point on the center line of the thickness of the lower member opposite the flat plate portion including H The point on the center line of the thickness of the flat plate portion of the side member is K, the point on the edge of the diaphragm facing the edge of the diaphragm including G is L, the point on the center line of the thickness of the corner of the upper member close to G that does not include E is M, the point on the center line of the thickness of the corner of the upper member close to L that does not include F is N, the point on the center line of the thickness of the corner of the lower member close to G that does not include B is O, the 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 P, the point on the center line of the thickness of the corner of the lower member close to L is D 1. An analytical modeling method for the out-of-plane bending strength of a diaphragm as set forth in 2 above, in which when the point on the center line of the plate thickness of the corner not including A is defined as Q and the point on the edge of the diaphragm opposite the diaphragm edge including A is defined as R, 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, BH, EC, EI, DC, DF, DK, FC, FJ, OP, OM, OH, MP, MI, QP, QN, QK, NP, and NJ. [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 center plane of the plate thickness of the through diaphragm in a plan view, a) if the upper member is a square steel pipe, a downward load is applied to one flat plate portion of the upper member that faces the one plane, and an equivalent upward load is applied to the other flat plate portion of the upper member; or b) if the upper member is a square steel pipe, a downward load is applied to one flat plate portion of the upper member that faces the one plane, and an equivalent upward load is applied to the other flat plate portion of the upper member; or In the case where the upper member is 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 as one end, and an equal upward load is applied to the one end to apply a moment to the upper member, and a downward load is also applied to the axis of the upper member to apply an axial force, and in response to the displacement of each node that occurs at this time, a yield line is 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 corner of the upper member closest to A that is far from the flat plate portion of the lower member aligned on the same plane is D. 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 E, the point on the center line of the thickness of the corner of the upper member closest to A that is far from the flat plate portion of the lower member aligned on the same plane is 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, the point on the center line of the thickness of the flat plate portion of the lower member aligned on the same plane is H, the point on the center line of the thickness of the flat plate portion of the upper member facing the flat plate portion of the upper member aligned on the same plane is I, and the point on the center line of the thickness of the flat plate portion of the upper member facing the flat plate portion of the lower member aligned on the same plane is I. A point on the center line of the thickness of the flat plate portion of the lower member facing the diaphragm edge including A is designated J, a point on the diaphragm edge not including G among the diaphragm edges perpendicular to the diaphragm edge including A is designated K, a point on the center line of the thickness of the corner not including E among the corners of the upper member at the flat plate portion of the upper and lower members aligned on the same plane is designated L, a point on the center line of the thickness of the corner not including F among the corners of the upper member close to J is designated M, a point on the center line of the thickness of the corner not including B among the corners close to the flat plate portion of the lower member aligned on the same plane is designated N, a point on the center line of the thickness of the corner not including B facing the flat plate portion of the lower member including C is designated N. 5. An analytical modeling method for the out-of-plane bending strength of a diaphragm as set forth in 4 above, wherein, when a point on the center line of the plate thickness of the flat plate portion of the lower member is defined as O, a point on the center line of the plate thickness of a corner of the lower member close to K that does not include D is defined as P, and a point on the diaphragm edge facing the diaphragm edge including A is defined as Q, the moment and the 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, BH, CD, CF, FD, FI, DJ, NH, OP, OM, MP, MI, and PJ. [6] 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, the bending strength of the through diaphragm is predicted for the joint, and the analytical model is previously calculated in a plan view on the center plane of the thickness of the through diaphragm, on the 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 in the center of the arc that forms the center line of the thickness of the corner of the upper member. A method for analytical modeling of the out-of-plane bending strength of a diaphragm as described in 1 above, in which a node is set on each of the centers of the upper and lower members, four or more of the set nodes are selected, and a downward load is applied to the center point 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 an equal upward load is applied 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 a yield line is placed on the line connecting the nodes as each node displaces. [7] As the analytical model, 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 the point on the center line of the plate thickness of the corner that is not sandwiched between the two flat plate portions is designated as A, the vertex of the diaphragm edge closest to the corner sandwiched between the two flat plate portions whose 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 plate thickness of the corner of the upper member sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane is designated as C, the center point of the arc that forms the center line of the plate thickness of the corner of the upper member that is diagonally opposite to the corner including C is designated as D, and the outer surfaces of the upper and lower members are connected to one of the two flat plate portions whose outer surfaces are aligned on the same plane is designated as B. 10. An analytical modeling method for the out-of-plane bending strength of a diaphragm as described in 6 above, in which when the point on the center line of the plate thickness of the corner of the lower member diagonally positioned between the corner sandwiched between the two flat plate portions aligned on a plane is defined as E, the vertex of the diaphragm edge diagonally positioned as B is defined as F, and the point on the center line of the plate thickness of the corner of the lower member diagonally positioned to the corner including A is defined as G, the moment and axial force acting on the upper member of the analytical model are applied, causing displacement at each node and resulting in a total of eight yield lines: AC, AD, AE, CD, CG, DG, ED, and EG. [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] A method for predicting the out-of-plane bending strength of a diaphragm described in claim 9, which uses an analytical model set up by the analytical modeling method described in claim 3 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 (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 as described in claim 11, wherein, when predicting the out-of-plane bending strength of a diaphragm using an analytical model set up by the analytical modeling method described in 5 above, 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 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 (2) of Equation 2 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 (2).

[15] A method for designing the diaphragm thickness of a steel pipe joint, which uses a method for predicting the out-of-plane bending strength of a diaphragm described in any one of items 8 to 14 above to determine the out-of-plane bending strength of the diaphragm, and selects 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 whose side or diameter is shorter than that of 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] 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]

[0014] [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

[0015] 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.

[0016] 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 (3):

[0017]

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[0018] 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 full cross-section yield state, dM=(σ y·t 2 ) / 4.

[0019] When calculating the work E due to an external force for a joint where members of 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 equation 4 (4).

[0020]

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[0021] Here, for bending, the yield moment is M y , the diaphragm rotation angle is θ d This can be expressed by the following equation (5).

[0022]

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[0023] For axial force, set the axial force to N d , diaphragm axial force displacement is δ N This can be expressed by the following equation (6):

[0024]

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[0025] First Embodiment As a first embodiment, as shown in Figure 1, a lower member 3 made of a square steel pipe and an upper member 1 made of a square steel pipe with a shorter side length than the lower member 3 are used, and the outer surfaces of all flat plate portions of the lower member 3 are arranged outside the outer surfaces of all flat plate portions of the upper member 1 (non-eccentric arrangement). The entire upper end of the lower member 3 is joined to the entire lower end of the upper member 1 via a through diaphragm 2, and the bending strength of the through diaphragm 2 is estimated for the joint. Here, "short side length" refers to the comparison of the length of one side if the cross section of the square steel pipe is approximately square, and the comparison of the lengths of the long sides and short sides if the cross section is approximately rectangular. The same applies below. In the example of FIG. 1, the axes of the lower member 3 and the upper member 1 are aligned with each other, resulting in a so-called coaxial arrangement. To set up the analysis model, the Cartesian coordinates (x, y, z) of nodes A to R are defined on the central plane of the through diaphragm 2 in plan view as shown in the following formula 7. Here, the axis position is set as the origin (0, 0, 0).

[0026]

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[0027] 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 u_mid : Radius of the center line of the thickness of the corner of the 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, δ m : Reference nodal displacement, l d : The protrusion length of the through diaphragm 2, and B1 and B2 are expressed by the following formulas (8) and (9) of Equation 8.

[0028]

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[0029] 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, BH, EC, EI, DC, DF, DK, FC, FJ, OP, OM, OH, MP, MI, QP, QN, QK, NP, and NJ, which are the yield line 9. sum This is expressed as the following Equation (9) in Equation 9. Note that the element boundaries 10 are taken into consideration when calculating the strain energy stored in each yield line 9.

[0030]

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[0031] The work E due to the external force can be calculated using the above equations (4), (5), and (6). However, the diaphragm rotation angle θ d , diaphragm axial force displacement δ N and axial force N d are the following equations (10), (11), and (12) in Equation 10. 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.

[0032]

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[0033] Second Embodiment As a second embodiment, 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, as shown in Figure 4, are used, and the outer surface of one flat portion of the lower member 3 and the outer surface of one flat portion of the upper member 1 are aligned on the same plane, resulting in a so-called unidirectional eccentric arrangement, and the entire upper end circumference of the lower member 3 and the entire lower end circumference of the upper member 1 are joined via a through diaphragm 2, and the bending strength of the through diaphragm 2 is predicted for the joint. To set up the analytical model, the Cartesian coordinates (x, y, z) of nodes A to Q are defined on the central plane of the through diaphragm 2 in plan view as shown in the following formula 11. Here, the axis position of the lower member 3 is set as the origin (0, 0, 0).

[0034]

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[0035] 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 u_mid : Radius of the center line of the thickness of the corner of the 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, δ m : Reference nodal displacement, l d : The protrusion length of the through diaphragm 2, B1 and B2 are expressed by the above formulas (8) and (9), and dB is expressed by formula (13) of the following formula 12.

[0036]

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[0037] In this embodiment, the strain energy U due to the internal force is calculated as the sum of the strain energy stored in the line segments BH, CD, CF, FD, FI, DJ, NH, OP, OM, MP, MI, and PJ, which are the yield line 9, and the axial strain energy of the lower member 3. First, the strain energy U stored in the yield line 9 is calculated as follows: sum is expressed as the following equation (14) of Equation 13. Note that the element boundary 10 is taken into consideration when calculating the strain energy stored in each yield line 9.

[0038]

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[0039] 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 (15) in equation 14 below.

[0040]

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[0041] Therefore, the total internal force U is given by equation (16) of equation 15 below.

[0042]

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[0043] The work E due to the external force can be calculated using the above equations (4), (5), and (6). However, the diaphragm rotation angle θ d is the above equation (10), and the diaphragm axial force displacement δ N and axial force N d is the following equation (17) of Equation 16. In the equation, 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.

[0044]

number

[0045] 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 11. Here, the axis position of the lower member is set as the origin (0, 0, 0).

[0046]

number

[0047] 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 u_mid : Radius of the center line of the thickness of the corner of the 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, δ m : Reference nodal displacement, l d : is the protrusion length of the through diaphragm 2, B1, B2 and dB are expressed by the above equations (8), (9) and (13), and L cd , L cd1 and L cd2 are expressed by the following equations (18), (19), and (20), respectively.

[0048]

number

[0049] In this embodiment, the strain energy U due to the internal force is calculated as the sum of the strain energy stored in the line segments AC, AD, AE, CD, CG, DG, ED, and EG, 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 the following equation (21) of Equation 19. Note that the element boundary 10 is taken into consideration when calculating the strain energy stored in each yield line 9.

[0050]

number

[0051] 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 (22) in Equation 20 below.

[0052]

number

[0053] Therefore, the total strain energy U due to internal forces is given by equation (16) above.

[0054] The work E due to the external force can be calculated using the above equations (4), (5), and (6). However, the diaphragm rotation angle θ d , diaphragm axial force displacement δ N and axial force N d are the following equations (23), (24), and (25) in Equation 21. 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.

[0055]

number

[0056] <Prediction of diaphragm out-of-plane bending strength> When the yield moment is calculated from the external force work E and the strain energy U due to the internal force calculated for each of the shaft arrangement formats of the first to third embodiments, E=U, and therefore equation (26) of Equation 22 below can be derived.

[0057]

number

[0058] However, the distance x between the bending axis and the axis center of the upper member 1 must satisfy the relationship of equation (27) in the following equation 23.

[0059]

number

[0060] In the above embodiment, an example was shown in which square steel pipes were 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, it is possible to apply this by taking measures such as taking nodes on the central plane of the circular steel pipe plate thickness at 45° central angles in the circumferential direction, for example. [Example]

[0061] As shown in Figure 6, an analysis was carried out using the finite element method (FEM) to apply monotonically loaded force by applying a forced displacement to the top of the upper member 1, targeting a joint where upper and lower members 1 and 3 of different dimensions are connected via a diaphragm 2. A list of analytical models is shown in Table 1. For the coaxial, one-way eccentric, and two-way eccentric arrangements, square steel pipes of □-350×350×12 (BCR295) and □-850×850×40 (BCP325) were used for the upper member 1, and square steel pipes of □-500×500×19 (BCR295) and □-1000×1000×40 (BCP325) were used for the lower member 3. Here, the standard values ​​for square steel pipes represent □ - side length x side length x plate thickness, where BCR represents cold-roll-formed square steel pipes and BCP represents cold-press-formed square steel pipes. The following numbers in parentheses represent the lower limit of the yield point in MPa. The difference in side length between upper member 1 and lower member 3 was set to 150 mm. The plate thicknesses of diaphragm 2 were 100 mm, 60 mm, and 45 mm, respectively. The steel standard for the diaphragm was TMCP325C, and diaphragm 2 was a square with a side length 60 mm longer than the side length of the lower member. The axial force ratios used were 0 and 0.3.

[0062] [Table 1]

[0063] 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.

[0064] [Table 2] [Industrial Applicability]

[0065] 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 steel pipes of different dimensions to be easily and accurately evaluated, taking into account the corner dimensions of the upper and lower members. Furthermore, it is possible to select steel plates with a thickness sufficient to satisfy the strength obtained by the prediction method. Furthermore, a steel pipe-diaphragm connection can be obtained using a diaphragm of that thickness, making it industrially useful. [Explanation of symbols]

[0066] 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. A method for creating an analytical model for predicting the bending strength of a through diaphragm at a joint where 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 having a shorter side or diameter than the lower member are joined via a through diaphragm, the method comprising: In advance, in a plan view, a plurality of nodes are provided on the thickness center plane of the through diaphragm, on a line passing through the edge of the through diaphragm, on the thickness center line of the flat plate portion or circumference of the lower member and the upper member, on the thickness center line of the corner portion of the lower member and the upper member, and on the center of the arc forming the thickness center line of the corner portion of the upper member or on the central axis of the upper member, and four or more points including three points that are on different lines and form a triangle are selected from the nodes, and an analytical model of the joint is set; A downward load is applied to one of a pair of opposing portions of the upper member, and an equal upward load is applied to the other portion, When 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, This is an analytical modeling method for the out-of-plane bending strength of a diaphragm, in which a yield line is placed on the line connecting the nodes in accordance with the displacement of each node that occurs at that time.

2. A method for creating an analytical model for predicting the bending strength of a through diaphragm 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, using a combination of 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, a combination of a lower member made of a circular steel pipe and an upper member made of a circular steel pipe with a diameter 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 with a diagonal length 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 with a diameter shorter than that of the side of the lower member, 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, nodes are provided in advance on a line passing through the edge of the through diaphragm in a plan view, on the center line of the thickness of the flat part of the lower member, on the center line of the thickness of the corner of the lower member, on the center line of the thickness of the flat part of the upper member, and on the center line of the thickness of the corner of the upper member, and four or more of the provided nodes are selected. a) When the upper member is the square steel pipe, 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, or b) When the upper member is the 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, When 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, 2. The analytical modeling method for out-of-plane bending strength of a diaphragm according to claim 1, wherein a yield line is placed on a line segment connecting the nodes in accordance with the displacement of each node that occurs at that time.

3. In the analysis model, the lower member and the upper member are square steel pipes, 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 center line of the thickness of the corner of the upper member closest to B is E, A point on the center line of the thickness of the corner of the upper member closest to A that does not include E is F, Among the diaphragm edges perpendicular to the diaphragm edge including A, the point on the diaphragm edge closest to B is called G. Among the flat plate portions of the lower member perpendicular to the diaphragm edge including A, the point on the plate thickness center line of the flat plate portion closest to B is designated as H, Among the flat plate portions of the upper 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, A point on the center line of the thickness of the flat plate portion of the upper member facing the flat plate portion including I is J, A point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion including H is K, The point on the diaphragm edge opposite to the diaphragm edge containing G is L, A point on the center line of the thickness of the corner of the upper member closest to G that does not include E is designated as M, A point on the center line of the thickness of the corner of the upper member that is closest to L and does not include F is designated as N, A point on the center line of the thickness of the corner of the lower member closest to G that does not include B is O, 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 P, A point on the center line of the thickness of the corner of the lower member that is closest to L and does not include D is designated as Q, The point on the edge of the diaphragm opposite to the diaphragm edge containing A is R When the moment and axial force acting on the upper member of the analysis model are given, displacement occurs at each node, 3. An analytical modeling method for the out-of-plane bending strength of a diaphragm as described in claim 2, in which a total of 20 yield lines, namely, BC, BE, BH, EC, EI, DC, DF, DK, FC, FJ, OP, OM, OH, MP, MI, QP, QN, QK, NP, and NJ, are assumed to occur.

4. A method for creating an analytical model for predicting the bending strength of a through diaphragm 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, using a combination of 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, a combination of a lower member made of a circular steel pipe and an upper member made of a circular steel pipe with a diameter 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 with a diagonal length 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 with a diameter shorter than that of the side of the lower member, 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, nodes are provided on a line passing through the edge of the through diaphragm on the plate thickness center line of the flat plate portion of the lower member, on the plate thickness center line of the corner portion of the lower member, on the plate thickness center line of the flat plate portion of the upper member, and on the plate thickness center line of the corner portion of the upper member, and four or more of the provided nodes are selected, a) When the upper member is a 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) When the upper member is the 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 one plane as one end, and an equal upward load is applied to the one end, When 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, 2. The analytical modeling method for out-of-plane bending strength of a diaphragm according to claim 1, wherein a yield line is placed on a line segment connecting the nodes in accordance with the displacement of each node that occurs at that time.

5. In the analysis model, the lower member and the upper member are square steel pipes, 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, Among the corners of the upper 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 defined as E, Among the corners of the upper 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 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, A point on the center line of the thickness of the flat plate portion of the lower member aligned on the same plane is H, A point on the center line of the thickness 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, The point on the center line of the thickness of the corner of the upper member, which does not include E, is L, Among the corners of the upper member closest to J, a point on the center line of the plate thickness 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 moment and axial force acting on the upper member of the analysis model are given, displacement occurs at each node, 5. An analytical modeling method for the out-of-plane bending strength of a diaphragm as described in claim 4, in which a total of 12 yield lines, BH, CD, CF, FD, FI, DJ, NH, OP, OM, MP, MI, and PJ, are assumed to occur.

6. 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 to predict the bending strength of the through diaphragm, As the analysis model, in advance, in a plan view, nodes are provided on the thickness center plane of the through diaphragm, on the vertices of the edges of the through diaphragm, on the thickness center line of the corners of the lower member, on the thickness center line of the corners of the upper member, and on the center of the arc forming the thickness center line of the corners of the upper member, and four or more of the provided nodes are selected, When 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, a moment is applied to the upper member, and a downward load is also applied to the axis of the upper member to apply an axial force, 2. The analytical modeling method for out-of-plane bending strength of a diaphragm according to claim 1, wherein a yield line is placed on a line segment connecting the nodes in accordance with the displacement of each node that occurs at that time.

7. As the analytical model, 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 portion that is not sandwiched between the two flat plate portions is designated as A, The apex of the diaphragm edge closest to the corner 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 B, The outer surfaces of the upper and lower members are aligned on the same plane, and the point on the center line of the plate thickness of the corner of the upper member sandwiched between the two flat plate portions is called C. The center point of the arc forming the center line of the thickness of the corner of the upper member diagonally opposite the corner including C is D, The point on the center line of the plate thickness of the corner of the lower member located diagonally between the two flat plate portions whose outer surfaces are aligned on the same plane as the upper and lower members is defined as E, The apex of the diaphragm edge diagonally opposite B is F, A point on the center line of the thickness of the corner of the lower member diagonally opposite to the corner including A is G When the moment and axial force acting on the upper member of the analysis model are given, displacement occurs at each node, 7. An analytical modeling method for the out-of-plane bending strength of a diaphragm as set forth in claim 6, in which a total of eight yield lines, AC, AD, AE, CD, CG, DG, ED, and EG, are assumed to occur.

8. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 1, A method for predicting the out-of-plane bending strength of a diaphragm, which involves 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 a predetermined relational equation from the relationship between the sum of strain energy and the work due to the moment and axial force.

9. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 2, 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 a diaphragm according to claim 8. [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.

10. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 3, A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 9, 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 equation (1) from the relationship between the sum of strain energy and the work due to the moment and the axial force.

11. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 4, A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 8, 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.

12. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 5, A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 11, 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 equation (2) from the relationship between the sum of strain energy and the work due to the moment and the axial force.

13. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 6, A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 8, 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 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.

14. When predicting the out-of-plane bending strength of a diaphragm using the analytical model established by the analytical modeling method according to claim 7, A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 13, 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 equation (2) from the relationship between the sum of strain energy and the work due to the moment and the axial force.

15. 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 according to any one of claims 8 to 14; and selecting, as the diaphragm material, 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 a plurality of standardized thicknesses.

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