Analytical modeling and prediction methods for out-of-plane bending rigidity of diaphragms, design methods for diaphragm plate thickness of steel pipe joints, and steel pipe-diaphragm elastic spring joints

Abstract

To provide an analytical modeling method and a prediction method of the out-of-plane bending stiffness of a diaphragm capable of easily and accurately predicting when joining steel pipes of different dimensions via a through diaphragm.SOLUTION: An analytical modeling method is a method of arranging steel pipes of different dimensions in non-eccentric, one-way eccentric, or two-way eccentric arrangement. The method includes: with respect to joints that are joined through a diaphragm, a step of selecting four or more points in advance on the line of the edge of the diaphragm, on the thickness center line of the upper and lower members, and on the nodes provided inside the upper member in plan view, on the center plane of the thickness of the diaphragm; and a step of segmenting into multiple polygonal elements that consist of multiple right edges connecting the selected nodes, and which are connected so that they can bend to each other via a rotating spring and are considered to be rigid bodies. The prediction method is a method of predicting the out-of-plane bending based on total strain energy, load, and displacement of the rotating spring due to the displacement that occurs when a load is applied to the upper member.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 rigidity of a diaphragm when steel pipes of different dimensions are passed through and joined via a diaphragm, a method for designing the diaphragm plate thickness of a steel pipe joint, and a steel pipe-diaphragm elastic spring connection. [Background technology]

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

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

[0004] As a method for joining columns with different dimensions above and below without using a tapered tube 8, there is a construction method in which a square steel tube of the same dimensions as the lower column 4 is used as the joining panel 3, and columns 1, 4 with different dimensions above and below are joined via diaphragms 2, 5, as shown in Figure 2. If the plate thickness of the upper diaphragm 2 is thin, the upper column 1 may be subjected to bending, causing large out-of-plane deformation in the upper diaphragm 2. In that 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 rigidity of a diaphragm at a joint where upper and lower columns of different diameters are joined with a thickened diaphragm by dividing the diaphragm into multiple polygonal elements, and assuming that each polygonal element is connected by a rotational spring at each boundary edge so that it can elastically bend. 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.

[0006] Patent Document 2 discloses a method for predicting the out-of-plane bending strength of a diaphragm of a joint where upper and lower columns of different diameters are joined with a thickened diaphragm, in which the out-of-plane bending yield strength fMy of the upper through diaphragm 5 when axial force N acts on the upper column is calculated using yield line theory, while reflecting the axial force N of the upper column. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] JP 2015-45211 A [Patent Document 2] JP 2013-28997 A [Non-patent literature]

[0008] [Non-Patent Document 1] Tadahiko Kawai and Kazuo Kondo: Bending collapse analysis of plates using a new discretized model, Autumn lecture of the Society of Naval Architects of Japan, November 1977. Summary of the Invention [Problem to be solved by the invention]

[0009] However, the conventional technology has the following problems. Regarding connections where upper and lower columns of different dimensions are joined with thickened diaphragms, the method described in Patent Document 1 is limited to one-way eccentricity and two-way eccentricity arrangements, and does not describe cases without eccentricity. In addition, the rigidity is calculated for multiple types of stress and deformation, making the calculations somewhat complicated. In addition, the corner dimensions (radius) of the square steel pipes are not taken into consideration, and the corners are assumed to be regular angles, so the calculations may not be applicable depending on the values ​​of the corner dimensions.

[0010] The present invention has been made in consideration of the above circumstances, and aims to provide an analytical modeling method and a prediction method for the out-of-plane bending stiffness of a diaphragm that can easily and accurately predict the out-of-plane bending stiffness of a diaphragm when steel pipes of different dimensions are joined through a diaphragm. In addition, the present invention aims to provide a method for designing the diaphragm plate thickness of a steel pipe joint and a steel pipe-diaphragm elastic spring connection. [Means for solving the problem]

[0011] 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 rigidity of a through diaphragm for a joint 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, 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, the method comprising the steps of: first, in a plan view, providing a plurality of nodes on the center plane of the plate thickness of the through diaphragm; selecting four or more of the nodes; and creating an analytical model of the joint consisting of a plurality of straight sides connecting the selected nodes and the selected nodes, connected to each other by a rotational spring so that they can be bent at one of the sides as a boundary, and divided into a plurality of first polygonal elements which are regarded as rigid bodies against bending forces. [2] A method for creating an analytical model to predict the bending rigidity of a through diaphragm for a joint in which 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 having 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 having 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 having 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 having a diameter shorter than the side of the lower member, wherein the entire outer periphery of the lower member is connected to the entire upper end circumference of the upper member via a through diaphragm, a first member having a first thickness of 100 mm and a second member having a first thickness of 100 mm, and an analytical model of the joint is provided in advance, in a plan view, on the mid-plane of the through diaphragm, on a line passing through the edge of the through diaphragm, on the mid-plane of the flat portion of the lower member, on the mid-plane of the corner of the lower member, on the mid-plane of the flat portion of the upper member, on the mid-plane of the corner of the upper member, and inside the upper member, and four or more of the provided nodes are selected, and the nodes are divided into a plurality of polygonal elements consisting of a plurality of straight sides connecting the selected nodes, connected to each other by rotational springs so that they can be bent at one of the sides as a boundary, and regarded as rigid bodies against bending forces. [3] As an analytical model of the joint, the through diaphragm is divided into a plurality of polygonal elements (I01 to I28), and each of the polygonal elements is, in a plan view, a point on one side of the edge of the diaphragm on the thickness center plane of the through diaphragm, a point on the thickness center line of one of the two corners of the lower member that is closest to A, a point on the thickness center line of the flat part of the lower member that is closest to A, a point on the thickness center line of the corner of the upper member that is closest to B, and a point on one diaphragm edge that is closest to B among the diaphragm edges that are perpendicular to the diaphragm edge including A. A is defined as E, a point on the thickness center line of one flat plate portion closest to B among the flat plate portions of the lower member perpendicular to the diaphragm edge including A is defined as F, a point on the thickness center line of one flat plate portion closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is defined as G, a point inside the upper member is defined as H, a point on the thickness center line of a corner of the upper member close to E and not including D is defined as I, a point on the thickness center line of a corner of the lower member close to E and not including B is defined as J, a point on the edge of the diaphragm facing the diaphragm edge including A is defined as K, and a point on the edge of the diaphragm facing the flat plate portion of the lower member including C is defined as A point on the thickness center line of the flat plate portion of the lower member is designated as L, a point on the thickness center line of another corner portion of the lower member closest to A is designated as M, a point on the thickness center line of the corner portion of the upper member closest to M is designated as N, a point on another diaphragm edge among the diaphragm edges perpendicular to the diaphragm edge including A is designated as O, a point on the thickness center line of another flat plate portion among the flat plate portion of the lower member perpendicular to the diaphragm edge including A is designated as P, a point on the thickness center line of another flat plate portion among the flat plate portion of the upper member perpendicular to the diaphragm edge including A is designated as Q, and a point on the thickness center line of the corner portion of the upper member diagonally opposite the corner including D is designated as R. , B, a polygonal element I01 formed by AB, BC, CA, a polygonal element I02 formed by CD, DH, HC, a polygonal element I03 formed by BC, CD, DB, a polygonal element I04 formed by BE, EF, FB, a polygonal element I05 formed by DF, FG, GD, a polygonal element I06 formed by BD, DF, FB, a polygonal element I07 formed by DG, GH, HD, a polygonal element I08 formed by GH, HI, IG, a polygonal element I09 formed by HI, IL,Polygonal element I09 formed by LH, polygonal element I10 formed by FG, GI, IF, polygonal element I11 formed by IJ, JL, LI, polygonal element I12 formed by FI, IJ, JF, polygonal element I13 formed by EF, FJ, JE, polygonal element I14 formed by JK, KL, LJ, polygonal element I15 formed by CH, HN, NC, polygonal element I16 formed by HN, NQ, QH, polygonal element I17 formed by CM, MN, NC, polygonal element I18 formed by NP, PQ, QN, polygonal element I19 formed by MN, NP, PM, polygonal element I20 formed by AC, CM, MA, MO 1. The analytical modeling method for the out-of-plane bending rigidity of a diaphragm according to claim 2, wherein a total of 28 polygonal elements are: polygonal element I21 formed by OP and PM; polygonal element I22 formed by HQ, QR and RH; polygonal element I23 formed by HL, LR and RH; polygonal element I24 formed by PQ, QR and RP; polygonal element I25 formed by LR, RS and SL; polygonal element I26 formed by PR, RS and SP; polygonal element I27 formed by OP, PS and SO; and polygonal element I28 formed by LK, KS and SL, and each of the polygonal elements is rigid against bending forces and is connected by a rotational spring so as to be bendable at each boundary edge. [4] A method for creating an analytical model to predict the bending rigidity of a through diaphragm for a joint in which 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 method comprising: a combination of a lower member made of a square steel pipe and an upper member made of a square steel pipe having 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 having 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 having 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 having a diameter shorter than that of the side of the lower member, the method comprising: A method for analytical modeling of the out-of-plane bending rigidity of a diaphragm described in 1 above, in which a portion of the outer surface of the lower member and a portion of the outer surface of the upper member are arranged to have a common circumscribing plane, and as an analytical model of the joint, nodes are provided in advance, in a plan view, on the mid-plane of the thickness of the through diaphragm, on a line passing through the edge of the through diaphragm, on the mid-line of the thickness of the lower member, on the mid-line of the thickness of the upper member, and inside the upper member, and four or more of the provided nodes are selected, and the element is divided into a plurality of polygonal elements consisting of a plurality of straight sides connecting the selected nodes, which are mutually connected by rotational springs so that they can be bent at one of the sides, and which are regarded as rigid bodies against bending forces. [5] As an analytical model of the joint, an analytical model in which the through diaphragm is divided into a plurality of polygonal elements (I29 to I42) is set, and each of the polygonal elements is, in a plan view, a point on one side of the diaphragm edge that is on the center plane of the plate thickness of the through diaphragm and perpendicular to the flat plate portion whose outer surface is aligned on a single plane, A, a point on the center line of the plate thickness of the flat plate portion of the lower member that is closest to A, a point on the center line of the plate thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a single plane, of two corners of the lower member that are close to A, C, and a point on the center line of the plate thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a single plane, of two corners of the upper ... The point on the center line of the thickness of the corner farthest from the flat plate portion aligned on a plane is D, the point inside the upper member is E, the point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion whose outer surfaces are aligned on a plane is F, the point on the center line of the thickness of the flat plate portion of the upper member facing the flat plate portion whose outer surfaces are aligned on a plane is G, the point on the edge of the diaphragm closest to G is H, the point on the center line of the thickness of the corner of the upper member closest to H and not including D is I, the point on the center line of the thickness of the corner of the lower member closest to H and not including B is J, and the point on the center line of the thickness of the corner of the lower member facing the flat plate portion of the lower member including B is I. Let K be the point on the center line of the thickness of the flat plate, and L be the point on the diaphragm edge opposite the diaphragm edge including A. Then, I29 is a polygonal element formed by AB, BC, and CA, I30 is a polygonal element formed by BC, CD, and DB, I31 is a polygonal element formed by BD, DE, and EB, I32 is a polygonal element formed by DE, EF, and FD, I33 is a polygonal element formed by DF, FG, and GD, I34 is a polygonal element formed by CD, DG, and GC, I35 is a polygonal element formed by CG, GH, and HC, and I36 is a polygonal element formed by EF, FI, and IE. 5. An analytical modeling method for the out-of-plane bending rigidity of a diaphragm as described in 4 above, in which a total of 14 polygonal elements are defined as follows: polygonal element I37 formed by FG, GI, IF; polygonal element I38 formed by EI, IK, KE; polygonal element I39 formed by IJ, JK, KI; polygonal element I40 formed by GI, IJ, JG; polygonal element I41 formed by GH, HJ, JG; and polygonal element I42 formed by JK, KL, LJ, and each of the polygonal elements is rigid against bending forces and is connected by rotational springs at each boundary edge so that it can be bent. [6] A method for creating an analytical model to predict the bending rigidity of a through diaphragm for a joint formed by using a lower member made of a square steel pipe and an upper member made of a square steel pipe having a side length shorter than that of the lower member, aligning the outer surfaces of adjacent flat plate portions of the lower member and the corresponding outer surfaces of adjacent flat plate portions of the upper member on the same plane, and joining the entire upper end circumference of the lower member and the entire lower end circumference of the upper member via a through diaphragm, wherein the analytical model for the joint is created in advance by forming a through diaphragm on the center plane of the plate thickness of the through diaphragm in a plan view, a line passing through the lower member, a thickness center line of the flat portion of the lower member, a thickness center line of the corner of the lower member, a thickness center line of the flat portion of the upper member, a thickness center line of the corner of the upper member, a center of an arc forming the thickness center line of the corner of the upper member, and inside the upper member; selecting four or more of the provided nodes; and dividing the diaphragm into a plurality of polygonal elements consisting of a plurality of straight sides connecting the selected nodes, connected to each other by rotational springs so as to be able to be bent at one of the sides as a boundary, and regarded as a rigid body against bending forces. [7] As an analytical model of the joint, an analytical model was set in which the through diaphragm was divided into a number of polygonal elements (I43 to I60), and each of the polygonal elements was defined as follows: in a plan view, a point on the diaphragm edge that is on the center plane of the plate thickness of the through diaphragm and is closest to one of the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane is designated as A; a point on the center line of the plate thickness of a corner of the lower member close to A and not 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; a point on the center line of the plate thickness of a corner of the upper member close to A and not 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 thickness center line of the corner that is not sandwiched between the two flat plate portions is designated as C, the point on the diaphragm edge perpendicular to the diaphragm edge including A that is farther from the two flat plate portions where the outer surfaces of the upper and lower components are aligned on the same plane is designated as D, the point on the thickness center line of the flat plate portion of the lower component that is closest to D is designated as E, the point on the thickness center line of the corner of the lower component that is sandwiched between the two flat plate portions where the outer surfaces of the upper and lower components are aligned on the same plane is designated as F, the center point of the arc that forms the thickness center line of the corner of the upper component that is diagonally opposite to the corner including F of the lower component is designated as G, and the point on the thickness center line of the corner of the upper component that is diagonally opposite to the corner including F of the lower component is designated as G. A point on the center line of the thickness of the corner of the lower member located diagonally to the corner including C of the upper member is defined as H, a point on the center line of the thickness of the corner of the upper member diagonally to the corner including C of the upper member is defined as I, a point on the center line of the thickness of the flat plate portion of the lower member having an outer surface that is not in the same plane as the outer surface of the flat plate portion of the upper member that does not include E is defined as J, a point inside the upper member is defined as K, a point on the diaphragm edge facing the diaphragm edge including D is defined as L, a point on the center line of the thickness of the corner of the lower member located diagonally to the corner including B of the lower member is defined as M, and a point on the diaphragm edge facing the diaphragm edge including A is defined as N, then AB, Polygonal element I43 formed by BC and CA, polygonal element I44 formed by AC, CF, FA, polygonal element I45 formed by CF, FK, KC, polygonal element I46 formed by CG, GK, KC, polygonal element I47 formed by BC, CG, GB, polygonal element I48 formed by BE, EG, GB, polygonal element I49 formed by BD, DE, EB, polygonal element I50 formed by DE, EH, HD, polygonal element I51 formed by EG, GH, HE, polygonal element I52 formed by FI, IK, KF, FI,A method for analytically modeling the out-of-plane bending stiffness of a diaphragm according to 6 above, comprising a total of 18 polygonal elements: polygonal element I53 formed by IL and LF, polygonal element I54 formed by GI, IK, KG, polygonal element I55 formed by GI, IM, MG, polygonal element I56 formed by IL, LM, MI, polygonal element I57 formed by GJ, JM, MG, polygonal element I58 formed by JM, MN, NJ, polygonal element I59 formed by GH, HJ, JG, and polygonal element I60 formed by HJ, JN, NH, each of the polygonal elements being rigid against bending forces and connected by rotational springs at each boundary edge in a bendable manner. [8] A method for predicting the bending stiffness of a diaphragm using an analytical model set up by the analytical modeling method described in 1 above, wherein a downward load is applied to one of a pair of opposing locations of the upper member and an equal upward load is applied to the other location, the sum of the strain energies of the rotating spring associated with the displacement that occurs at that time is calculated, and the out-of-plane bending stiffness of the diaphragm is predicted based on the sum of the strain energies, the load, and the displacement associated with the application of the load. [9] A method for predicting the out-of-plane bending rigidity of a diaphragm described in 8 above, using an analytical model set up by the analytical modeling method described in 2 above to predict the bending rigidity of the through diaphragm, the method comprising the steps of: (a) applying a downward load to one of a pair of opposing flat plate portions of the upper member when the upper member is a square steel tube, and applying an equal upward load to the other flat plate portion; or (b) applying a downward load to one end of the circumferential diameter of the upper member when the upper member is a circular steel tube, and applying an equal upward load to the other end; calculating the sum of strain energies of the rotating spring associated with the displacements that occur when these loads are applied; and predicting the out-of-plane bending rigidity of the through diaphragm based on the sum of strain energies, the load, and the displacement associated with the application of the load.

[10] A method for predicting the bending stiffness of the through diaphragm using an analytical model set up by the analytical modeling method described in 3 above, in which a load acting downward on the flat plate portion included in DGI is applied as a load acting on the analytical model, and an equivalent load acting upward on the flat plate portion included in NQR is applied as a load acting on the analytical model, and a displacement δ is generated by this load. The sum of the strain energy stored in each of the rotating springs at this time is calculated, and the out-of-plane bending stiffness of the diaphragm is predicted from the relationship between the load and the displacement δ using this.

[11] A method for predicting the bending rigidity of the through diaphragm using an analytical model set up by the analytical modeling method described in 4 above, the method comprising the steps of: (a) applying a downward load to one flat plate portion of the upper member that faces the one plane when the upper member is a square steel tube, and applying an equivalent upward load to the other flat plate portion of the upper member; or (b) applying a downward load 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 when the upper member is a circular steel tube, and applying an equivalent upward load to the one end; calculating the sum of the strain energies of the rotating spring associated with the displacement that occurs when the above-mentioned cases are met; and predicting the out-of-plane bending rigidity of the through diaphragm based on the sum of the strain energies, the load, and the displacement associated with the application of the load.

[12] A method for predicting the bending stiffness of the through diaphragm using an analytical model set up by the analytical modeling method described in 5 above, in which a load acting downward on the flat plate portion included in DFI as a load acting on the analytical model is applied as an equivalent load acting upward on the flat plate portion of an upper member whose outer surface is aligned in a single plane, and a displacement δ is generated by this load. The sum of the strain energy stored in each of the rotating springs at this time is calculated, and the sum is used to predict the out-of-plane bending stiffness of the diaphragm from the relationship between the load and the displacement δ.

[13] A method for predicting the bending stiffness of the through diaphragm using an analytical model set up by the analytical modeling method described in 6 above, which involves applying a downward load to the center point of an arc forming the plate thickness centerline of a corner of the upper member 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 applying an equal upward load to the corner of the lower member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, calculating the sum of strain energies of the rotating spring associated with the displacement that occurs when this occurs, and predicting the out-of-plane bending stiffness of the through diaphragm based on the sum of strain energies, the load, and the displacement associated with the application of the load.

[14] A method for predicting the bending stiffness of the through diaphragm described in claim 13, which uses an analytical model set up by the analytical modeling method described in claim 7 to predict the bending stiffness of the through diaphragm by applying a downward load to G and an upward load to the corner including F as loads acting on the analytical model, and assuming that a displacement δ occurs due to this load. The sum of the energy stored in each of the rotating springs at this time is calculated, and the sum is used to predict the out-of-plane bending stiffness of the diaphragm from the relationship between the load and the displacement δ.

[15] A method for designing a diaphragm thickness for a steel pipe joint, comprising: determining the out-of-plane bending rigidity of the diaphragm using a method for predicting the out-of-plane bending rigidity of the diaphragm described in any one of items 8 to 14 above; and selecting as the diaphragm material a steel plate having a thickness sufficient to satisfy the required out-of-plane bending rigidity of the diaphragm required when a design load is applied to the upper member from steel plates of multiple standardized thicknesses.

[16] A steel pipe-diaphragm elastic spring 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. Effect of the Invention

[0012] According to the analytical modeling method and prediction method of the out-of-plane bending stiffness of a diaphragm of the present invention, when connecting upper and lower members made of square steel pipes or circular steel pipes of different dimensions with a through diaphragm, the out-of-plane bending stiffness of the diaphragm of the connected joint can be easily and accurately evaluated by taking into account the corner dimensions of the upper and lower members. In particular, when the outer periphery of the lower member is placed outside the upper member, when the outer surfaces of the upper and lower members are aligned on a single plane, and when the outer surfaces of adjacent flat plate parts of the upper and lower members are aligned on the same plane, the out-of-plane bending stiffness of the diaphragm can be easily and accurately predicted by setting an appropriate analytical model for each case. In addition, the prediction method makes it possible to select a steel plate with a thickness sufficient to satisfy the required stiffness. In addition, a steel pipe-diaphragm elastic spring joint can be obtained by using a diaphragm with that thickness. [Brief description of the drawings]

[0013] [Figure 1] FIG. 11 is a schematic diagram showing the configuration of an analytical model for evaluating the out-of-plane bending rigidity of a diaphragm in a joint structure in which square steel pipes of different dimensions are passed through a coaxial arrangement and joined to a diaphragm according to one embodiment of the present invention, where (a) shows a plan view and (b) shows a cross-sectional view taken along the line XX. [Diagram 2] FIG. 2 is a perspective view showing a column-beam joint structure in which the diaphragm according to the embodiment is used as an upper diaphragm; [Diagram 3] FIG. 1 is a perspective view showing a conventional beam-column joint structure in which a tapered tube is used as a joint panel. [Figure 4] 5A and 5B are schematic diagrams showing the configuration of an analytical model for evaluating the out-of-plane bending rigidity 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 in accordance with another embodiment of the present invention, where (a) shows a plan view and (b) shows a cross-sectional view taken along the line XX. [Diagram 5] 10A and 10B are schematic diagrams showing the configuration of an analytical model for evaluating the out-of-plane bending rigidity of a diaphragm in a joint structure in which square steel tubes of different dimensions are passed through a diaphragm in an eccentric arrangement in two directions according to another embodiment of the present invention, where (a) shows a plan view and (b) shows a cross-sectional view taken along the line YY. [Figure 6] 1A and 1B are schematic diagrams illustrating the rotational spring theory, where (a) is a plan view and (b) is a front view. [Figure 7] FIG. 1 is a perspective view showing a joint element of a finite element method (FEM) analysis model. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Hereinafter, the embodiments of the present invention will be described in detail. Note that the drawings are schematic and may differ from the actual ones. The following embodiments are merely examples of equipment and methods for embodying the technical idea of ​​the present invention, and are not intended to limit the configuration to the following. In other words, the technical idea of ​​the present invention can be modified in various ways within the technical scope described in the claims.

[0015] In this embodiment, based on the rotational spring theory described in Non-Patent Document 1, when connecting upper and lower members made of square steel pipes of different dimensions with a through diaphragm, the out-of-plane bending rigidity of the diaphragm of the connected joint is predicted. The through diaphragm is made of a steel plate with a plate 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. Figure 6 shows polygonal elements I1 and I2 composed of nodes o, a, b and nodes o, b, c, respectively. I1 and I2 are connected by a rotational spring 9 inserted between node ob. The rigidity K of this rotational spring 9 can be expressed as the following formula 1 (1) using the distances x and y between the rotational spring 9 and nodes a and c, respectively, and the length l of the rotational spring 9.

[0016]

number

[0017] Here, D is the plate constant, which can be calculated using Young's modulus E, polygonal element plate thickness t, and Poisson's ratio ν as shown in the following formula 2 (2).

[0018]

number

[0019] The angle between polygonal elements I1 and I2, i.e., the rotation angle θ of the rotational spring, can be calculated as follows, assuming that the Cartesian coordinates of each node are o(x0, y0, z0), a(x1, y1, z1), b(x2, y2, z2) and c(x3, y3, z3). The normals of polygon elements I1 and I2 are n A and n B Then, the direction cosine n A (l A , m A , n A ) and n B (l B , m B , n B ) is expressed by the following formulas 3 and 4 (3) and (4).

[0020]

number

number

[0021] Here, the symbols in the above formula are expressed by formulas (5) and (6) in the following formulas 5 and 6.

[0022]

number

[0023]

number

[0024] The direction cosine of the rotational spring vector after deformation C(l C , m C , n C ) is expressed by the following formula (7).

[0025]

number

[0026] Regarding the rotation angle θ of the rotation spring, the relationship of Equation (8) below holds.

[0027]

number

[0028] Therefore, the rotation angle θ of the rotation spring is calculated by the following formula (9).

[0029]

number

[0030] Expanding the right hand side, we obtain equation (10) of the following formula 10.

[0031]

number

[0032] Here, l C is expressed by the following formula (11).

[0033]

number

[0034] The strain energy U stored in the rotation spring 9 is calculated as in Equation 12 (12) below.

[0035]

number

[0036] First Embodiment As a first 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 are used, as shown in Fig. 1, and the outer surfaces of all the flat plate parts of the lower member 3 are arranged outside the outer surfaces of all the flat plate parts of the upper member 1 (non-eccentric arrangement), and a prediction of the bending rigidity of the through diaphragm 2 is considered for a 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. Here, "having a short side length" refers to a comparison of the length of one side if the cross section of the square steel pipe is approximately square, and a comparison of the lengths of the long sides and the 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, forming a so-called coaxial arrangement. In setting up the analytical model, nodes A to S of the polygonal element 10 are defined as follows on the central plane of the plate thickness of the through diaphragm 2 in a plan view. A is a point on one side of the edge of diaphragm 2. A point on the center line of the thickness of one of the two corners of the lower member 3 that is closest to A is designated as B. The point on the center line of the thickness of the flat part of the lower member 3 closest to A is C, The point on the center line of the plate thickness of the corner of the upper part 1 closest to B is D, Among the diaphragm 2 edges perpendicular to the diaphragm 2 edge including A, the point on the diaphragm 2 edge closest to B is called E. Among the flat plate parts of the lower member 3 perpendicular to the edge of the diaphragm 2 including A, the point on the plate thickness center line of the flat plate part closest to B is called F, Among the flat plate parts of the upper member 1 perpendicular to the edge of the diaphragm 2 including A, the point on the center line of the thickness of the flat plate part closest to B is called G, The internal point of the upper member 1 is H. A point on the center line of the plate thickness of the corner of the upper member 1 close to E and not including D is I, A point on the center line of the plate thickness of the corner of the lower member 3 close to E and not including B is J, The point on the edge of diaphragm 2 opposite the edge of diaphragm 2 containing A is K. A point on the center line of the thickness of the flat plate portion of the lower member 3 facing the flat plate portion of the lower member 3 including C is L, The point on the center line of the plate thickness of the other corner of the lower member 3 close to A is M, The point on the center line of the plate thickness of the corner of the upper part 1 closest to M is N, Among the diaphragm 2 edges perpendicular to the diaphragm 2 edge including A, a point on the other diaphragm 2 edge is O, Among the flat plate parts of the lower member 3 perpendicular to the edge of the diaphragm 2 including A, a point on the center line of the plate thickness of the other flat plate parts is P, Among the flat plate parts of the upper member 1 perpendicular to the edge of the diaphragm 2 including A, the point on the center line of the plate thickness of the other flat plate parts is Q, The point on the center line of the plate thickness of the corner of the upper member 1 diagonally opposite the corner including D is R, The point on the center line of the plate thickness of the corner of the lower part 3 diagonally opposite the corner including B is S Let us assume that. Nodes A, C, E, F, G, K, L, O, P, and Q are preferably the midpoints of the sides. Nodes B, D, I, J, M, N, R, and S are preferably the midpoints of the arcs that form the center lines of the plate thickness of the corners. Node H is preferably the axis of the upper member 1.

[0037] The strain energy stored in the sides BC, BD, BF, CD, DG, FG, GH, DF, DH, JF, JI, JL, IF, IG, IL, IH, MC, MN, MP, NC, NP, NQ, NH, PQ, QH, SL, SP, RL, RP, RH, RQ and RS where the rotational spring 9 is located is obtained. The obtained strain energy of the rotational spring is used to calculate the strain energy U stored in all the rotational springs in all the diaphragms, and the following formula (13) is obtained.

[0038]

number

[0039] Therefore, by partially differentiating this with respect to the displacement δ according to Castigliano's theorem, the relationship between the force P' acting on the diaphragm 2 by the upper member 1 and the displacement δ can be obtained as shown in the following equation (14). Km represents the bending stiffness based on the rigid body-spring model.

[0040]

number

[0041] Here, the out-of-plane deformation angle θ of the diaphragm 2 d is expressed by the following formula (15).

[0042]

number

[0043] Bending moment M acting on upper member 1 cu If half the distance between the center of the plate thickness of the opposing flat plate portions of the upper member 1 is B1, then it can be calculated by the following formula (16).

[0044]

number

[0045] Using equations (14) and (15), equation (17) of the following formula 17 is derived.

[0046]

number

[0047] That is, the out-plane bending stiffness Kd of the diaphragm 2 in this embodiment is given by the following formula (18).

[0048]

number

[0049] 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 plate portion of the lower member 3 and the outer surface of one flat plate portion of the upper member 1 are aligned on the same plane, a so-called unidirectional eccentric arrangement, and the bending rigidity of the through diaphragm 2 is 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. In setting up the analytical model, nodes A to L of the polygonal element 10 are defined as follows on the central plane of the plate thickness of the through diaphragm 2 in a plan view. The point A on one side of the diaphragm 2 edge perpendicular to the flat plate part with the outer surface aligned on a plane, The point on the center line of the plate thickness of the flat plate part of the lower member 3 closest to A is B, Of the two corners of the lower member 3 that are close to A, the point on the center line of the plate thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a single plane is called C. Of the two corners of the upper member 1 that are close to A, the point on the center line of the plate thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a plane is D, The internal point of the upper member 1 is E. F is a point on the center line of the thickness of the flat plate portion of the lower member 3 facing the flat plate portion whose outer surface is aligned on a plane, The point on the center line of the plate thickness of the flat plate part of the upper member 1 facing the flat plate part whose outer surface is aligned on a plane is G, The point on the diaphragm 2 edge closest to G is H. A point on the center line of the plate thickness of the corner of the upper member 1 close to H and not including D is I, A point on the center line of the plate thickness of the corner of the lower member 3 close to H and not including B is J, A point on the center line of the thickness of the flat plate portion of the lower member 3 facing the flat plate portion of the lower member 3 including B is K, A point on the edge of diaphragm 2 opposite to the edge of diaphragm 2 containing A is L Let us assume that. Nodes A and L are preferably the intersections of an extension of the thickness center line of the flat portion of the upper member 1, including F, and the edge of the diaphragm 2. Nodes B and K are preferably the intersections of a line passing through the axis of the upper member 1 and parallel to the plane that aligns the outer surfaces of the upper and lower members, and the thickness center line of the flat portion of the lower member 3. Nodes C, D, I, and J are preferably the midpoints of arcs that form the thickness center lines of each corner. Node E is preferably the axis of the upper member 1. Nodes F, G, and H are preferably the midpoints of each side.

[0050] The strain energy stored in the sides BC, BD, CD, CG, DF, EF, DE, FG, DG, KJ, KI, IJ, IG, IE, IF, and JG where the rotational spring 9 is located is obtained. The obtained strain energy of the rotational spring is used to calculate the strain energy U stored in all the rotational springs in all the diaphragms, and the following formula (19) is obtained.

[0051]

number

[0052] By partially differentiating this with respect to the displacement δ from Castigliano's theorem, the relationship between the force P' acting on the diaphragm 2 by the upper member 1 and the displacement δ can be obtained by the following equation (20): Km represents the bending stiffness based on the rigid body-spring model.

[0053]

number

[0054] Here, the out-of-plane deformation angle θ of the diaphragm 2 d is expressed by the following formula (21).

[0055]

number

[0056] Bending moment M acting on upper member 1 cuIf half the distance between the center of the plate thickness of the opposing flat plate portions of the upper member 1 is B1, then it can be calculated by the following formula (22).

[0057]

number

[0058] Using equations (20) and (21), equation (23) of the following formula 23 is derived.

[0059]

number

[0060] That is, the out-plane bending stiffness Kd of the diaphragm 2 of this embodiment is given by the following formula (24).

[0061]

number

[0062] <Third embodiment> As a third 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 5 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, a so-called two-way eccentric arrangement, and the bending rigidity of the through diaphragm 2 is 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. In setting the analytical model, nodes A to N of the polygonal element 10 are defined as follows on the central plane of the plate thickness of the through diaphragm 2 in a plan view. The point on the edge of the diaphragm 2 closest to one of the two flat plate parts where the outer surfaces of the upper and lower members 1 and 3 are aligned on the same plane is called A. A point on the center line of the plate thickness of the corner of the lower member 3 close to A, which is not sandwiched between two flat plate parts whose outer surfaces of the upper and lower members 1 and 3 are aligned on the same plane, is called B. A point on the center line of the plate thickness of the corner of the upper member 1 close to A, which is not sandwiched between two flat plate parts whose outer surfaces of the upper and lower members 1 and 3 are aligned on the same plane, is called C. Among the edges of the diaphragm 2 perpendicular to the edge of the diaphragm 2 including A, the point on the edge of the diaphragm 2 farther from the two flat plate parts where the outer surfaces of the upper and lower members 1 and 3 are aligned on the same plane is called D. The point on the center line of the thickness of the flat part of the lower member 3 closest to D is E, The outer surfaces of the upper and lower members 1 and 3 are aligned on the same plane. The lower member 3 is sandwiched between two flat plate sections, and the point on the center line of the plate thickness of the corner of the lower member 3 is called F. The center point of the arc forming the center line of the plate thickness of the corner of the upper member 1, which is diagonally opposite to the corner of the lower member 3 including F, is G. The point on the center line of the plate thickness of the corner of the lower member 3 diagonally opposite to the corner including F of the lower member 3 is H, The point on the center line of the thickness of the corner of the upper member 1 diagonally opposite to the corner including C of the upper member 1 is I, Among the flat plate portions of the lower member 3 having an outer surface that is not in the same plane as the outer surface of the flat plate portion of the upper member 1, a point on the plate thickness center line of the flat plate portion not including E is designated as J, The internal point of the upper member 1 is K. The point on the edge of the diaphragm 2 opposite the edge of the diaphragm 2 containing D is L, The point on the center line of the plate thickness of the corner of the lower member 3 diagonally opposite to the corner including B of the lower member 3 is M, A point on the edge of diaphragm 2 opposite to the edge of diaphragm 2 containing A is N Let us assume that. Nodes A and L are preferably the intersections of a diagonal of the upper member 1 perpendicular to a diagonal passing through a corner between two flat plate sections whose outer surfaces are aligned on the same plane, and the edge of the diaphragm 2. Nodes B, C, F, H, I and M are preferably the midpoints of arcs forming the center line of the plate thickness of each corner. Nodes D, E, J and N are preferably the midpoints of each side. Node K is preferably the axis of the upper member 1.

[0063] The strain energy stored in the sides BC, BE, BG, CF, CG, CK, EG, EH, FK, GH, GK, MI, MN, MG, IF, IG, IK, JG, JH and JM where the rotational spring 9 is located is obtained. When the strain energy of the obtained rotational spring is used to calculate the strain energy U stored in all the rotational springs in all the diaphragms, the following formula (25) is obtained due to symmetry.

[0064]

number

[0065] By partially differentiating this with respect to the displacement δ from Castigliano's theorem, the relationship between the force P' acting on the diaphragm 2 by the upper member 1 and the displacement δ can be obtained by the following equation (26): Km represents the bending stiffness based on the rigid body-spring model.

[0066]

number

[0067] Here, if GK=a0, FK=b0, and FH=2c0, the out-of-plane deformation angle θ of diaphragm 2 d is expressed by the following formula (27).

[0068]

number

[0069] Bending moment M acting on upper member 1 cu can be calculated using the following formula (28).

[0070]

number

[0071] Using equations (26) and (27), equation (29) of the following formula 29 is derived.

[0072]

number

[0073] That is, the out-plane bending stiffness Kd of the diaphragm 2 of the present embodiment is given by the following formula (30).

[0074]

number

[0075] 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 also be used as the upper and lower members. When using circular steel pipes as the upper and lower members, it is possible to apply the method by taking the nodes on the center plane of the plate thickness of the circular steel pipe at 45° intervals in the circumferential central angle, for example. EXAMPLES

[0076] As shown in Figure 7, an analysis was carried out using the finite element method (FEM) in which a monotonically loaded joint was applied by applying a forced displacement to the top of the upper member 1, targeting the joint where upper and lower members 1 and 3 of different dimensions were connected via a diaphragm 2. A list of analytical models is shown in Table 1. For each of 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 are □-side length x side length x plate thickness, BCR stands for cold roll-formed square steel pipes, BCP stands for cold press-formed square steel pipes, and 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 set to 100 mm, 60 mm, and 45 mm, respectively. The steel standard for diaphragm 2 was TMCP325C, and the diaphragm was a square with a side length 60 mm longer than the side length of the lower member.

[0077] [Table 1]

[0078] Table 2 shows the calculation results using the evaluation formulas 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 the diaphragm out-of-plane bending stiffness obtained from the FEM analysis results can be evaluated with high accuracy by using the diaphragm out-of-plane bending stiffness evaluation formulas of the above embodiments.

[0079] [Table 2] [Industrial Applicability]

[0080] According to the method for predicting the out-of-plane bending stiffness of a diaphragm of the present invention, when connecting upper and lower members made of steel pipes of different dimensions via a through diaphragm, the out-of-plane bending stiffness of the diaphragm of the connected joint can be easily and accurately evaluated by taking into account the corner dimensions of the upper and lower members. In addition, a steel plate with a sufficient plate thickness to satisfy the stiffness obtained by the prediction method can be selected. Furthermore, a steel pipe-diaphragm elastic spring connection can be obtained using a diaphragm of that plate thickness, which is industrially useful. [Explanation of symbols]

[0081] 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 Tube 9 Rotational Spring 10 polygonal elements

Claims

1. A method for creating an analytical model for predicting the bending rigidity 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, the method comprising: a combination of a lower member made of a square steel pipe and an upper member made of a square steel pipe having 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 having 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 having 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 having a diameter shorter than that of the side of the lower member, the method comprising: The lower member is disposed so that all outer circumferences of the lower member are outwardly spaced from all outer circumferences of the upper member; An analytical modeling method for the out-of-plane bending rigidity of a diaphragm, in which, as an analytical model of the joint, nodes are first provided on the mid-plane of the plate thickness of the through diaphragm in a planar view, on a line passing through the edge of the through diaphragm, on the mid-thickness line of the lower member, on the mid-thickness line of the upper member, and inside the upper member, four or more of the provided nodes are selected, and an analytical model of the joint is created which is made up of a plurality of straight edges connecting the selected nodes, is mutually connected by a rotational spring so that it can be bent at one of the edges, and is divided into a plurality of polygonal elements which are regarded as rigid against bending forces.

2. As an analytical model of the joint, the through diaphragm is divided into a plurality of polygonal elements (I01 to I28), Each of the polygonal elements is located on a thickness center plane of the through diaphragm in a plan view, 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, The point on the center line of the thickness of the corner of the upper member closest to B is D, Among the diaphragm edges perpendicular to the diaphragm edge including A, a point on the diaphragm edge closest to B is designated as E. Among the flat plate portions of the lower member perpendicular to the diaphragm edge including A, a point on the plate thickness center line of one flat plate portion closest to B is designated as F, Among the flat plate portions of the upper member perpendicular to the diaphragm edge including A, a point on the plate thickness center line of one flat plate portion closest to B is designated as G, A point inside the upper member is designated as H, A point on the center line of the thickness of the corner of the upper member close to E and not including D is I, A point on the thickness center line of the corner of the lower member close to E and not including B is designated as J, A point on the edge of the diaphragm opposite to the edge of the diaphragm containing A is K, A point on the plate thickness center line of the flat plate portion of the lower member facing the flat plate portion of the lower member including C is L, A point on the center line of the thickness of another corner of the lower member close to A is M, The point on the center line of the thickness of the corner of the upper member closest to M is N, Among the diaphragm edges perpendicular to the diaphragm edge including A, a point on the other diaphragm edge is designated as O, Among the flat plate portions of the lower member perpendicular to the diaphragm edge including A, a point on the plate thickness center line of the other flat plate portions is defined as P, Among the flat plate portions of the upper member perpendicular to the diaphragm edge including A, a point on the plate thickness center line of the other flat plate portions is designated as Q, A point on the center line of the thickness of the corner of the upper member diagonally opposite the corner including D is R, A point on the center line of the thickness of the corner of the lower member diagonally opposite to the corner including B is defined as S When A polygonal element I01 formed by AB, BC, and CA; A polygonal element I02 formed by CD, DH, and HC; A polygonal element I03 formed by BC, CD, and DB; A polygonal element I04 formed by BE, EF, and FB; A polygonal element I05 formed by DF, FG, and GD; A polygonal element I06 formed by BD, DF, and FB; A polygonal element I07 formed by DG, GH, and HD; A polygonal element I08 formed by GH, HI, and IG; A polygonal element I09 formed by HI, IL, and LH; A polygonal element I10 formed by FG, GI, and IF; A polygonal element I11 formed by IJ, JL, and LI, A polygonal element I12 formed by FI, IJ, and JF; A polygonal element I13 formed by EF, FJ, and JE; A polygonal element I14 formed by JK, KL, and LJ; A polygonal element I15 formed by CH, HN, and NC; A polygonal element I16 formed by HN, NQ, and QH; A polygonal element I17 formed by CM, MN, and NC; A polygonal element I18 formed by NP, PQ, and QN; A polygonal element I19 formed by MN, NP, and PM; A polygonal element I20 formed by AC, CM, and MA; A polygonal element I21 formed by MO, OP, and PM; A polygonal element I22 formed by HQ, QR, and RH; A polygonal element I23 formed by HL, LR, and RH; A polygonal element I24 formed by PQ, QR, and RP; A polygonal element I25 formed by LR, RS, and SL; A polygonal element I26 formed by PR, RS, and SP; A polygonal element I27 formed by OP, PS, and SO; Polygonal element I28 formed by LK, KS, and SL A total of 28 polygonal elements are 2. A method for analytically modeling the out-of-plane bending rigidity of a diaphragm as described in claim 1, wherein each of the polygonal elements is assumed to be rigid against bending forces and is connected by rotational springs at each boundary edge so as to be bendable.

3. A method for creating an analytical model for predicting the bending rigidity 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, the method comprising: a combination of a lower member made of a square steel pipe and an upper member made of a square steel pipe having 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 having 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 having 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 having a diameter shorter than that of the side of the lower member, the method comprising: a part of an outer surface of the lower member and a part of an outer surface of the upper member are disposed to have a common circumscribing plane; An analytical modeling method for the out-of-plane bending rigidity of a diaphragm, in which, as an analytical model of the joint, nodes are first provided on the mid-plane of the plate thickness of the through diaphragm in a planar view, on a line passing through the edge of the through diaphragm, on the mid-thickness line of the lower member, on the mid-thickness line of the upper member, and inside the upper member, four or more of the provided nodes are selected, and an analytical model of the joint is created which is made up of a plurality of straight edges connecting the selected nodes, is mutually connected by a rotational spring so that it can be bent at one of the edges, and is divided into a plurality of polygonal elements which are regarded as rigid against bending forces.

4. As an analytical model of the joint, an analytical model in which the through diaphragm is divided into a plurality of polygonal elements (I29 to I42) is set, Each of the polygonal elements is located on a thickness center plane of the through diaphragm in a plan view, A is a point on one side of the diaphragm edge perpendicular to the flat plate part whose outer surface is aligned on a plane, The point on the center line of the thickness of the flat plate portion of the lower member closest to A is B, Of the two corners of the lower member that are close to A, the point on the center line of the plate thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a single plane is C, Of the two corners of the upper member that are close to A, the point on the center line of the thickness of the corner farthest from the flat plate portion whose outer surface is aligned on a single plane is D, A point inside the upper member is E, F is a point on the center line of the thickness of the flat plate portion of the lower member facing the flat plate portion whose outer surface is aligned on a plane, A point on the center line of the thickness of the flat plate portion of the upper member facing the flat plate portion whose outer surface is aligned on a plane is G, The point on the diaphragm edge closest to G is H. A point on the center line of the thickness of the corner of the upper member close to H and not including D is I, A point on the center line of the thickness of the corner of the lower member close to H and not including B 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 of the lower member including B is K, A point on the diaphragm edge opposite the diaphragm edge containing A is L When A polygonal element I29 formed by AB, BC, and CA; A polygonal element I30 formed by BC, CD, and DB; A polygonal element I31 formed by BD, DE, and EB; A polygonal element I32 formed by DE, EF, and FD; A polygonal element I33 formed by DF, FG, and GD; A polygonal element I34 formed by CD, DG, and GC; A polygonal element I35 formed by CG, GH, and HC; A polygonal element I36 formed by EF, FI, and IE; A polygonal element I37 formed by FG, GI, and IF; A polygonal element I38 formed by EI, IK, and KE; A polygonal element I39 formed by IJ, JK, and KI; A polygonal element I40 formed by GI, IJ, and JG; A polygonal element I41 formed by GH, HJ, and JG; A polygonal element I42 formed by JK, KL, and LJ; A total of 14 polygonal elements are 4. A method for analytically modeling the out-of-plane bending rigidity of a diaphragm as described in claim 3, wherein each of the polygonal elements is assumed to be rigid against bending forces and is connected at each boundary edge by a rotational spring so as to be bendable.

5. A method for creating an analytical model to predict the bending rigidity of a through diaphragm for a joint where an entire periphery of the upper end of the lower member and an entire periphery of the lower end of the upper member are joined via a through diaphragm, the method comprising the steps of: using a lower member made of a square steel pipe and an upper member made of a square steel pipe having a side length shorter than that of the lower member; aligning the outer surfaces of adjacent flat plate portions of the lower member and the corresponding outer surfaces of adjacent flat plate portions of the upper member on the same plane; As an analytical model of the joint, in a plan view, nodes are provided on a line passing through an edge of the through diaphragm on a center line of thickness of the flat plate portion of the lower member, on a center line of thickness of the corner portion of the lower member, on a center line of thickness of the flat plate portion of the upper member, on a center line of thickness of the corner portion of the upper member, on a center line of thickness of the corner portion of the upper member, on a center of a circular arc forming the center line of thickness of the corner portion of the upper member, and inside the upper member, and four or more of the provided nodes are selected; A method for analytical modeling of the out-of-plane bending rigidity of a diaphragm, which creates an analytical model of the joint, which consists of selected nodes and a number of straight edges connecting the nodes, which are bendably connected to each other at one of the edges by rotational springs, and which is divided into a number of polygonal elements that are considered to be rigid against bending forces.

6. As an analytical model of the joint, an analytical model in which the through diaphragm is divided into a plurality of polygonal elements (I43 to I60) is set, Each of the polygonal elements is located on a thickness center plane of the through diaphragm in a plan view, A is a point on the edge of the diaphragm that is closest to one of the two flat plate portions where the outer surfaces of the upper and lower members are aligned on the same plane, A point on the center line of the plate thickness of the corner of the lower member that is close to A and is not sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane is called B. A point on the center line of the plate thickness of the corner of the upper member that is close to A and is not sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane is called C, Among the diaphragm edges perpendicular to the diaphragm edge including A, a point on the diaphragm edge farther from the two flat plate portions where the outer surfaces of the upper and lower members are aligned on the same plane is designated as D, The point on the center line of the thickness of the flat plate portion of the lower member closest to D is E, The point on the center line of the plate thickness of the corner portion of the lower member sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane is called F, The center point of the arc forming the plate thickness center line of the corner of the upper member diagonally opposite to the corner including F of the lower member is G, A point on the center line of the thickness of the corner of the lower member diagonally opposite to the corner including F of the lower member is designated as H, A point on the center line of the thickness of the corner of the upper member diagonally opposite to the corner including C of the upper member is designated as I, A point on the center line of the thickness of the flat plate portion of the lower member not including E among the flat plate portions of the lower member having an outer surface that is not in the same plane as the outer surface of the flat plate portion of the upper member is designated as J, A point inside the upper member is designated as K, A point on the diaphragm edge opposite the diaphragm edge including D is L, A point on the center line of the thickness of the corner of the lower member diagonally opposite to the corner including B of the lower member is designated as M, A point on the diaphragm edge opposite the diaphragm edge containing A is called N When A polygonal element I43 formed by AB, BC, and CA; A polygonal element I44 formed by AC, CF, and FA; A polygonal element I45 formed by CF, FK, and KC; A polygonal element I46 formed by CG, GK, and KC; Polygonal element I47 formed by BC, CG, and GB; A polygonal element I48 formed by BE, EG, and GB; A polygonal element I49 formed by BD, DE, and EB; A polygonal element I50 formed by DE, EH, and HD; A polygonal element I51 formed by EG, GH, and HE; A polygonal element I52 formed by FI, IK, and KF; A polygonal element I53 formed by FI, IL, and LF; A polygonal element I54 formed by GI, IK, and KG; A polygonal element I55 formed by GI, IM, and MG; A polygonal element I56 formed by IL, LM, and MI; A polygonal element I57 formed by GJ, JM, and MG; A polygonal element I58 formed by JM, MN, and NJ; A polygonal element I59 formed by GH, HJ, and JG; A polygonal element I60 formed by HJ, JN, and NH; A total of 18 polygonal elements are 6. A method for analytically modeling the out-of-plane bending rigidity of a diaphragm as described in claim 5, wherein each of the polygonal elements is rigid against bending forces and is connected at each boundary edge by a rotational spring so as to be bendable.

7. 2. The analytical model according to claim 1 is used to predict the bending stiffness of the through diaphragm, a) When the upper member is a rectangular steel pipe, a downward load is applied to one of a pair of opposing flat plate portions of the upper member, and an equivalent upward load is applied to the other flat plate portion, or b) In the case where the upper member is a circular steel pipe, a downward load is applied to one end of the circumference of the upper member and an equal upward load is applied to the other end. The sum of the strain energy of the rotating spring caused by the displacement at that time is calculated, and the strain energy a load applied to the diaphragm and a displacement caused by the application of the load, the load being applied to the diaphragm and the displacement caused by the application of the load being applied to the diaphragm.

8. 3. The analytical model set by the analytical modeling method according to claim 2 is used to predict the bending stiffness of the through diaphragm, A method for predicting the out-of-plane bending stiffness of a diaphragm, in which a load acting downward on the flat plate portion included in D-G-I and an equivalent load acting upward on the flat plate portion included in N-Q-R are applied as loads acting on the analysis model, and a displacement δ is generated by this load.The sum of the strain energies stored in each of the rotating springs at this time is calculated, and the sum is used to predict the out-of-plane bending stiffness of the diaphragm from the relationship between the load and the displacement δ.

9. 4. The analytical model set by the analytical modeling method according to claim 3 is used to predict the bending stiffness of the through diaphragm, a) When the upper member applies a downward load to one flat plate portion of the upper member that faces the one plane in the case of the square steel pipe, and applies an equivalent upward load to the other flat plate portion of the upper member, or b) 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 one plane as one end, and an equivalent upward load is applied to the one end, A method for predicting the out-of-plane bending stiffness of a diaphragm, which calculates the sum of the strain energy of the rotating spring associated with the displacement that occurs at that time, and predicts the out-of-plane bending stiffness of the through diaphragm based on the sum of the strain energy, the load, and the displacement associated with the application of the load.

10. 5. The analytical model set by the analytical modeling method according to claim 4 is used to predict the bending stiffness of the through diaphragm, The load acting downward on the flat plate portion included in D-F-I as the load acting on the analysis model is A method for predicting the out-of-plane bending stiffness of a diaphragm, in which an equal load acting upward is applied to the flat plate portion of an upper member whose outer surface is aligned on a single plane, and a displacement δ is generated by this load. The sum of the strain energy stored in each of the rotation springs at this time is calculated, and the out-of-plane bending stiffness of the diaphragm is predicted from the relationship between the load and the displacement δ using this.

11. 6. The analytical model set by the analytical modeling method according to claim 5 is used to predict the bending stiffness of the through diaphragm, When a downward load is applied to the center point of the arc forming the plate thickness centerline of a corner of the upper member diagonally opposite to the corner of the upper member sandwiched between 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 lower member sandwiched between two flat plate portions whose outer surfaces are aligned on the same plane, A method for predicting the out-of-plane bending stiffness of a diaphragm, which calculates the sum of the strain energy of the rotating spring associated with the displacement that occurs at that time, and predicts the out-of-plane bending stiffness of the through diaphragm based on the sum of the strain energy, the load, and the displacement associated with the application of the load.

12. 7. The analytical model set by the analytical modeling method according to claim 6 is used to predict the bending stiffness of the through diaphragm, The load acting on the analysis model in the downward direction of G is Apply an upward load to the corner including F, A method for predicting the out-of-plane bending stiffness of a diaphragm, in which the load causes a displacement δ, the sum of the energy stored in each of the rotation springs at this time is calculated, and the sum is used to predict the out-of-plane bending stiffness of the diaphragm from the relationship between the load and the displacement δ.

13. A method for designing a diaphragm thickness for a steel pipe joint, comprising: determining the out-of-plane bending rigidity of the diaphragm using a method for predicting the out-of-plane bending rigidity of the diaphragm described in any one of claims 7 to 12; and selecting, as the diaphragm material, a steel plate having a thickness sufficient to satisfy the required out-of-plane bending rigidity of the diaphragm required when a design load is applied to an upper member, from steel plates of multiple standardized thicknesses.

14. A steel pipe-diaphragm elastic spring 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 side or diameter shorter than that of the lower member using a diaphragm designed by the diaphragm plate thickness design method described in claim 13.

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