JP7777741B2

JP7777741B2 - Analytical modeling and prediction methods for out-of-plane bending strength of diaphragms, and design methods for diaphragm thickness in steel pipe joints

Info

Publication number: JP7777741B2
Application number: JP2023071036A
Authority: JP
Inventors: 光永山; 陽介金城; 信太郎金崎; 諒介大庭; 宙光森岡
Original assignee: JFE Steel Corp
Current assignee: JFE Steel Corp
Priority date: 2022-04-26
Filing date: 2023-04-24
Publication date: 2025-12-01
Anticipated expiration: 2043-04-24
Also published as: JP2023162148A

Description

本発明は、寸法が異なる鋼管を通しダイアフラムを介して接合する際のダイアフラムの面外曲げ耐力の解析モデル化方法および予測方法、鋼管接合部のダイアフラム板厚設計方法ならびに鋼管－ダイアフラム仕口に関する。 The present invention relates to analytical modeling and prediction methods for the out-of-plane bending strength of diaphragms when joining steel pipes of different dimensions via a diaphragm, a method for designing the diaphragm thickness of steel pipe joints, and steel pipe-diaphragm connections.

従来、上下柱で寸法の異なる角形鋼管の柱梁接合部においては、図３に示すように、截頭角錐状のテーパー管８で接合部パネルを構成することが多い。図３に示すようなテーパー管を用いる柱梁接合部は、柱－ダイアフラム仕口の耐力および剛性を確保しやすいという特徴がある。 Conventionally, in column-to-beam joints using square steel pipes where the upper and lower columns have different dimensions, the joint panel is often constructed using a truncated pyramidal tapered pipe 8, as shown in Figure 3. Column-beam joints using tapered pipes such as those shown in Figure 3 have the advantage of making it easier to ensure the strength and rigidity of the column-diaphragm connection.

このテーパー管８については、接合部の剛性を確保することが容易である一方、高価かつ少量生産で流通に難がある。また、これを利用した接合部の溶接施工の自動化が困難である。近年、施工の省力化が求められるようになり、テーパー管８の使用が問題になりつつある。 While tapered pipes 8 make it easy to ensure the rigidity of the joint, they are expensive and difficult to distribute due to small-scale production. Furthermore, automating welding of joints using tapered pipes 8 is difficult. In recent years, there has been a demand for labor-saving construction, and the use of tapered pipes 8 is becoming problematic.

テーパー管８を用いずに上下で寸法の異なる柱を接合する方法として、図２のように、下柱４と同寸法の角形鋼管を接合パネル３に用い、上下で寸法の異なる柱１、４を、ダイアフラム２、５を介して接合する工法がある。上ダイアフラム２の板厚が薄いと、上柱１が曲げを受けることにより上ダイアフラム２に大きな面外変形が生じる場合がある。その場合、上ダイアフラム２の剛性および耐力が落ちるため、ダイアフラム面外曲げ剛性および耐力の評価が必要である。 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 of 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.

特許文献１では、径の異なる上下柱を増厚ダイアフラムで接合する仕口のダイアフラム面外曲げ耐力を予測するにあたり、上柱に軸力Ｎが作用する場合の、上部通しダイアフラム５の面外曲げ降伏曲げ耐力ｆＭｙを、降伏線理論を用い、上柱の軸力Ｎを反映させて求める方法を開示している。 Patent Document 1 discloses a method for predicting the out-of-plane bending strength of a diaphragm in a joint where upper and lower columns of different diameters are joined by a thickened diaphragm, using yield line theory to determine the out-of-plane bending yield strength fMy of the upper through diaphragm 5 when an axial force N acts on the upper column, while reflecting the axial force N of the upper column.

特許文献２では、径の異なる上下柱を増厚ダイアフラムで接合する仕口のダイアフラム面外曲げ剛性を予測するにあたり、ダイアフラムを複数の多角形要素で分割し、各多角形要素は各境界となる辺で弾性的に折れ曲がり可能に回転バネで連結されているとし他解析モデルを用いて、与えた荷重に対する回転バネにおける曲げ変形とせん断変形を加算し、釣り合い条件からダイアフラムの剛性を求める方法を開示している。 Patent Document 2 discloses a method for predicting the out-of-plane bending stiffness of a diaphragm at a joint where upper and lower columns of different diameters are joined by a thickened diaphragm. The method divides the diaphragm into multiple polygonal elements, and assumes that each polygonal element is connected by a rotational spring at each boundary edge so that it can bend elastically. Using an analytical model, the bending deformation and shear deformation of the rotational spring in response to a given load are added together to determine the diaphragm stiffness from the equilibrium conditions.

特開２０１３－２８９９７号公報JP 2013-28997 A 特開２０１５－４５２１１号公報JP 2015-45211 A

しかしながら、従来技術では、以下のような課題があった。
寸法の異なる上下柱を増厚ダイアフラムで接合する仕口について、特許文献１に記載するような設計式を用いることでダイアフラム面外曲げ耐力を計算し、耐力の面から必要ダイアフラム厚を求めることが可能である。しかし、角形鋼管の角部寸法（半径）を考慮せず、角部が正角の長方形として仮定しているため、角部寸法が大きい鋼管については精度が低下する可能性がある。 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.

本発明は、上記の事情を鑑みてなされたものであって、寸法の異なる鋼管を通しダイアフラムを介して接合する際に簡易にかつ精度よく予測できるダイアフラムの面外曲げ耐力の予測方法、鋼管接合部のダイアフラム板厚設計方法および鋼管－ダイアフラム仕口を提供することを目的とする。 The present invention was 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 via a diaphragm, a method for designing the diaphragm thickness of steel pipe joints, and a steel pipe-diaphragm connection.

上記課題を有利に解決する本発明の要旨は以下のとおりである。
［１］角形鋼管または円形鋼管からなる下側部材と該下側部材より辺または径の長さが短い角形鋼管または円形鋼管からなる上側部材とを用い、通しダイアフラムを介して前記下側部材の上端全周および前記上側部材の下端全周を接合した接合部につき、前記通しダイアフラムの曲げ耐力を予測するための解析モデルを作成する方法であって、あらかじめ、平面視で、前記通しダイアフラムの板厚中央面上であって、前記通しダイアフラムの縁部を通る線上、前記下側部材および前記上側部材の平板部の板厚中央線上、前記下側部材および前記上側部材の角部の板厚中央線上、ならびに、前記上側部材の角部の板厚中央線をなす円弧の中心上に複数の節点を設け、該節点の４点以上を選択し、前記接合部の解析モデルを設定し、前記上側部材の対向する一対の箇所のうち一方の箇所に対して下向き荷重を付加し、他方の箇所に対して同等の上向き荷重を付加し、その際に生じる各節点の変位に伴い、節点間を結ぶ線分上に降伏線を置く、ダイアフラムの面外曲げ耐力の解析モデル化方法。
［２］角形鋼管からなる下側部材と該下側部材より辺の長さが短い角形鋼管からなる上側部材との組み合わせ、円形鋼管からなる下側部材と該下側部材より径の長さが短い円形鋼管からなる上側部材との組み合わせ、円形鋼管からなる下側部材と該下側部材の径より対角線の長さが短い角形鋼管からなる上側部材との組み合わせ、または、角形鋼管からなる下側部材と該下側部材の辺より径の長さが短い円形鋼管からなる上側部材との組み合わせを用い、通しダイアフラムを介して前記下側部材の上端全周および前記上側部材の下端全周を接合した接合部につき、前記通しダイアフラムの曲げ耐力を予測するための解析モデルを作成する方法であって、前記下側部材のすべての外周が前記上側部材のすべての外周より外側になるように配置し、前記解析モデルとして、あらかじめ、平面視で、前記通しダイアフラムの板厚中央面上であって、前記通しダイアフラムの縁部を通る線上、前記下側部材の平板部の板厚中央線上、前記下側部材の角部の板厚中央線上、前記上側部材の平板部の板厚中央線上および前記上側部材の角部の板厚中央線上にそれぞれ節点を設け、設けられた節点の４点以上を選択しａ）前記上側部材が前記角形鋼管の場合は前記上側部材の対向する一対の平板部のうち一方の平板部に対して下向き荷重を付加し、他方の平板部に対して同等の上向き荷重を付加し、または、ｂ）前記上側部材が前記円形鋼管の場合は前記上側部材の円周の直径の一端に下向き荷重を付加し、他端に同等の上向き荷重を付加して、前記上側部材にモーメントを与え、かつ、前記上側部材の軸に対して下向きに荷重を加算して付加して軸力を与えた場合について、その際に生じる各節点の変位に伴い、節点間を結ぶ線分上に降伏線を置く、上記１に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［３］前記解析モデルとして、前記下側部材および前記上側部材を角形鋼管とし、前記ダイアフラムの縁の一辺上の点をＡ、前記下側部材の角部であってＡに近い２つのうちの一の角部の板厚中央線上の点をＢ、Ａに最も近い前記下側部材の平板部の板厚中央線上の点をＣ、Ａに近い前記下側部材の角部のうちのＢを含まない角部の板厚中央線上の点をＤ、Ｂに最も近い前記上側部材の角部の板厚中央線上の点をＥ、Ａに近い前記上側部材の角部のうちのＥを含まない角部の板厚中央線上の点をＦ、Ａを含むダイアフラム縁に直交するダイアフラム縁のうち、Ｂに最も近いダイアフラム縁上の点をＧ、Ａを含むダイアフラム縁に直交する前記下側部材の平板部のうち、Ｂに最も近い平板部の板厚中央線上の点をＨ、Ａを含むダイアフラム縁に直交する前記上側部材の平板部のうち、Ｂに最も近い平板部の板厚中央線上の点をＩ、Ｉを含む平板部に対向する前記上側部材の平板部の板厚中央線上の点をＪ、Ｈを含む平板部に対向する前記下側部材の平板部の板厚中央線上の点をＫ、Ｇを含むダイアフラム縁に対向するダイアフラム縁上の点をＬ、Ｇに近い前記上側部材の角部のうちのＥを含まない角部の板厚中央線上の点をＭ、Ｌに近い前記上側部材の角部のうちのＦを含まない角部の板厚中央線上の点をＮ、Ｇに近い前記下側部材の角部のうちのＢを含まない角部の板厚中央線上の点をＯ、Ｃを含む平板部に対向する前記下側部材の平板部の板厚中央線上の点をＰ、Ｌに近い前記下側部材の角部のうちのＤを含まない角部の板厚中央線上の点をＱ、Ａを含むダイアフラム縁に対向するダイアフラムの縁上の点をＲとしたとき、前記解析モデルの上側部材に作用する前記モーメントおよび前記軸力を与え、これによって各節点に変位が生じ、ＢＣ、ＢＥ、ＢＨ、ＥＣ、ＥＩ、ＤＣ、ＤＦ、ＤＫ、ＦＣ、ＦＪ、ＯＰ、ＯＭ、ＯＨ、ＭＰ、ＭＩ、ＱＰ、ＱＮ、ＱＫ、ＮＰ、ＮＪの計２０本の降伏線が生じたとする、上記２に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［４］角形鋼管からなる下側部材と該下側部材より辺の長さが短い角形鋼管からなる上側部材との組み合わせ、円形鋼管からなる下側部材と該下側部材より径の長さが短い円形鋼管からなる上側部材との組み合わせ、円形鋼管からなる下側部材と該下側部材の径より対角線の長さが短い角形鋼管からなる上側部材との組み合わせ、または、角形鋼管からなる下側部材と該下側部材の辺より径の長さが短い円形鋼管からなる上側部材との組み合わせを用い、通しダイアフラムを介して前記下側部材の上端全周および前記上側部材の下端全周を接合した接合部につき、前記通しダイアフラムの曲げ耐力を予測するための解析モデルを作成する方法であって、前記下側部材の外面の一部と前記上側部材の外面の一部とが共通に外接する一平面を有するように配置し、前記解析モデルとして、あらかじめ、平面視で、前記通しダイアフラムの板厚中央面上であって、前記通しダイアフラムの縁部を通る線上、前記下側部材の平板部の板厚中央線上、前記下側部材の角部の板厚中央線上、前記上側部材の平板部の板厚中央線上、および、前記上側部材の角部の板厚中央線上にそれぞれ節点を設け、設けられた節点の４点以上を選択し、ａ）前記上側部材が前記角形鋼管の場合は前記一平面に対向する前記上側部材の一の平板部に対して下向き荷重を付加し、前記上側部材の他の平板部に対して同等の上向き荷重を付加し、または、ｂ）前記上側部材が前記円形鋼管の場合は前記一平面に接する前記上側部材の円周上の点を一端とする直径の他端に下向き荷重を付加し、前記一端に同等の上向き荷重を付加して、前記上側部材にモーメントを与え、かつ、前記上側部材の軸に対して下向きに荷重を加算して付加して軸力を与えた場合について、その際に生じる各節点の変位に伴い、節点間を結ぶ線分上に降伏線を置く、上記１に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［５］前記解析モデルとして、前記下側部材および前記上側部材を角形鋼管とし、前記一平面上に揃えた上下部材の平板部に直交する一のダイアフラム縁上の点をＡ、Ａに近い前記下側部材の角部のうち、前記一平面上に揃えた前記下側部材の平板部に近い角部の板厚中央線上の点をＢ、Ａに最も近い下側部材の平板部の板厚中央線上の点をＣ、Ａに近い前記下側部材の角部のうち、前記一平面上に揃えた前記下側部材の平板部に遠い角部の板厚中央線上の点をＤ、Ａに近い前記上側部材の角部のうち、前記一平面上に揃えた前記下側部材の平板部に近い角部の板厚中央線上の点をＥ、Ａに近い前記上側部材の角部のうち、前記一平面上に揃えた前記下側部材の平板部に遠い角部の板厚中央線上の点をＦ、前記一平面上に揃えた上下部材の平板部に最も近いダイアフラム縁上の点をＧ、前記一平面上に揃えた前記下側部材の平板部の板厚中央線上の点をＨ、前記一平面上に揃えた前記上側部材の平板部に対向する前記上側部材の平板部の板厚中央線上の点をＩ、前記一平面上に揃えた前記下側部材の平板部に対向する前記下側部材の平板部の板厚中央線上の点をＪ、Ａを含むダイアフラム縁に直交するダイアフラム縁のうち、Ｇを含まないダイアフラム縁上の点をＫ、前記一平面上に揃えた上下部材の平板部に前記上側部材の角部のうち、Ｅを含まない角部の板厚中央線上の点をＬ、Ｊに近い前記上側部材の角部のうち、Ｆを含まない角部の板厚中央線上の点をＭ、前記一平面上に揃えた前記下側部材の平板部に近い角部のうち、Ｂを含まない角部の板厚中央線上の点をＮ、Ｃを含む前記下側部材の平板部に対向する前記下側部材の平板部の板厚中央線上の点をＯ、Ｋに近い前記下側部材の角部のうち、Ｄを含まない角部の板厚中央線上の点をＰ、Ａを含むダイアフラム縁に対向するダイアフラム縁上の点をＱとしたとき、前記解析モデルの上側部材に作用する前記モーメントおよび前記軸力を与え、これによって各節点に変位が生じ、ＢＨ、ＣＤ、ＣＦ、ＦＤ、ＦＩ、ＤＪ、ＮＨ、ＯＰ、ＯＭ、ＭＰ、ＭＩ、ＰＪの計１２本の降伏線が生じたとする、上記４に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［６］角形鋼管からなる下側部材と該下側部材より辺の長さが短い角形鋼管からなる上側部材とを用い、前記下側部材の隣り合う平板部の外面と対応する前記上側部材の隣り合う平板部の外面とをそれぞれ同一の平面上に揃えて、通しダイアフラムを介して前記下側部材の上端全周および前記上側部材の下端全周を接合した接合部につき、前記通しダイアフラムの曲げ耐力を予測するにあたり、前記解析モデルとして、あらかじめ、平面視で、前記通しダイアフラムの板厚中央面上であって、前記通しダイアフラムの縁の頂点上、前記下側部材の角部の板厚中央線上、前記上側部材の角部の板厚中央線上、および、前記上側部材の角部の板厚中央線をなす円弧の中心上にそれぞれ節点を設け、設けられた節点の４点以上を選択して、上下部材の外面が同一平面上に揃えられた前記２つの平板部に挟まれた前記上側部材の角部と対角位置にある前記上側部材の角部の板厚中央線をなす円弧の中心点に対して下向き荷重を付加し上下部材の外面が同一平面上に揃えられた前記２つの平板部に挟まれた前記上側部材の角部に対して同等の上向き荷重を付加して前記上側部材にモーメントを与え、かつ、前記上側部材の軸に対して下向きに荷重を加算して付加して軸力を与えた場合について、その際に生じる各節点の変位に伴い、節点間を結ぶ線分上に降伏線を置く、上記１に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［７］前記解析モデルとして、上下部材の外面が同一平面上に揃えられた前記２つの平板部の一方に接続し、前記２つの平板部に挟まれていない角部の板厚中央線上の点をＡ、上下部材の外面が同一平面上に揃えられた前記２つの平板部に挟まれた角部に最も近いダイアフラム縁の頂点をＢ、上下部材の外面が同一平面上に揃えられた前記２つの平板部に挟まれた上側部材の角部の板厚中央線上の点をＣ、Ｃを含む角部と対角位置にある前記上側部材の角部の板厚中央線をなす円弧の中心点をＤ、上下部材の外面が同一平面上に揃えられた前記２つの平板部に挟まれた角部の対角位置にある下側部材の角部の板厚中央線上の点をＥ、Ｂと対角位置にあるダイアフラム縁の頂点をＦ、Ａを含む角部と対角位置にある前記下側部材の角部の板厚中央線上の点をＧとしたとき、前記解析モデルの上側部材に作用する前記モーメントおよび前記軸力を与え、これによって各節点に変位が生じ、ＡＣ、ＡＤ、ＡＥ、ＣＤ、ＣＧ、ＤＧ、ＥＤ、ＥＧの計８本の降伏線が生じたとする、上記６に記載のダイアフラムの面外曲げ耐力の解析モデル化方法。
［８］上記１に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび軸力による仕事との関係から、所定の関係式に基づき、前記通しダイアフラムの面外曲げ耐力を予測する、ダイアフラムの面外曲げ耐力の予測方法。
［９］上記２に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび軸力による仕事との関係から、下記数式１の（１）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、上記８に記載のダイアフラムの面外曲げ耐力の予測方法。
［１０］上記３に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび前記軸力による仕事との関係から、下記（１）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、上記９に記載のダイアフラムの面外曲げ耐力の予測方法。
［１１］上記４に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび軸力による仕事との関係から、下記数式２の（２）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、上記８に記載のダイアフラムの面外曲げ耐力の予測方法。
［１２］上記５に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび前記軸力による仕事との関係から、下記（２）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、請求項１１に記載のダイアフラムの面外曲げ耐力の予測方法。
［１３］上記６に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび軸力による仕事との関係から、下記数式２の（２）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、上記８に記載のダイアフラムの面外曲げ耐力の予測方法。
［１４］上記７に記載の解析モデル化方法で設定した解析モデルを用いて、ダイアフラムの面外曲げ耐力を予測するにあたり、前記降伏線に蓄えられる歪エネルギーの総和を求め、前記歪エネルギーの総和と前記モーメントおよび前記軸力による仕事との関係から、下記（２）式に基づき前記通しダイアフラムの面外曲げ耐力を予測する、上記１３に記載のダイアフラムの面外曲げ耐力の予測方法。
［１５］上記８～１４のいずれか１項に記載のダイアフラムの面外曲げ耐力の予測方法を用いて、前記ダイアフラム面外曲げ耐力を求め、上側部材に設計モーメントと設計軸力を与えた際に必要とされるダイアフラム面外曲げ耐力に対して、規格化された複数種類の板厚の鋼板から、必要とされる前記耐力を満たすのに十分な板厚の鋼板を前記ダイアフラム材料として選定する、鋼管接合部のダイアフラム板厚設計方法。
［１６］上記１５に記載のダイアフラム板厚設計方法で設計したダイアフラムを用いて、角形鋼管または円形鋼管からなる下側部材と該下側部材より辺または径の長さが短い角形鋼管または円形鋼管からなる上側部材とを接合した、鋼管－ダイアフラム仕口。 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, comprising the steps of: 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; establishing 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 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 whose side length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than that of the lower member, a combination of a lower member made of a circular steel pipe and an upper member made of a square steel pipe whose diagonal length is shorter than the diameter of the lower member, or a combination of a lower member made of a square steel pipe and an upper member made of a circular steel pipe whose diameter length is shorter than the side of the lower member, wherein the entire outer periphery of the lower member is arranged so that all outer peripheries of the lower member are outside all outer peripheries of the upper member, and the analytical model is previously created by forming a 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 portion 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 portion 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 portions of the upper member, and an equal upward load is applied to the other flat plate portion. 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 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 B, a point on the center line of the thickness of the flat plate portion of the lower member that is closest to A is designated 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 D, a point on the center line of the thickness of the corner of the upper member that is closest to B is designated 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 E. A point on the center line of the thickness of the corner is F, of the diaphragm edges perpendicular to the diaphragm edge including A, the point on the diaphragm edge closest to B is G, of the flat plate portions of the lower member perpendicular to the diaphragm edge including A, the point on the center line of the thickness of the flat plate portion closest to B is H, of the flat plate portions of the upper member perpendicular to the diaphragm edge including A, the point on the center line of the thickness of the flat plate portion closest to B is I, of the flat plate portions of the upper member opposite the flat plate portion including I is J, The point on the center line of the thickness of the flat plate portion of the side member is K, the point on the diaphragm edge opposite the diaphragm edge 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 opposite 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. The analytical modeling method for the out-of-plane bending strength of a diaphragm described in 2 above, in which when the point on the center line of the plate thickness of the corner not including 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, which causes displacement at each node, 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 central plane of the plate thickness of the through diaphragm in a plan view, a) when the upper member is the 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) when the upper member is the 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 at 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 added 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.
[5] In the analysis model, the lower member and the upper member are square steel pipes, and a point on one diaphragm edge perpendicular to the flat plate portions of the upper and lower members aligned on the same plane is designated as 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 designated as B, a point on the center line of the plate thickness of the flat plate portion of the lower member closest to A is designated as 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 designated as 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 designated as F. 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 on 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 among the corners facing the flat plate portion of the lower member including C is designated N. 5. The analytical modeling method for the out-of-plane bending strength of a diaphragm described 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. In advance, as the analytical model, in a plan view, on the thickness center plane of the through diaphragm, on the vertex of the edge of the through diaphragm, on the thickness center line of the corner of the lower member, on the thickness center line of the corner of the upper member, and on the center of the thickness center line of the corner of the upper member. A method for analytical modeling of the out-of-plane bending strength of a diaphragm described above in 1, in which a node is set on each center of the diaphragm, 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 a downward load is added 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 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 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 portion 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 portion 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. A method for analytical modeling of 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 to 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 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] A method for predicting the out-of-plane bending strength of a diaphragm described in above 8, which uses an analytical model set up by the analytical modeling method described in above 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 above 9, which uses an analytical model set up by the analytical modeling method described in above 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 above 8, which uses an analytical model set up by the analytical modeling method described in above 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 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.
[12] A method for predicting the out-of-plane bending strength of a diaphragm as described in claim 11, which uses an analytical model set up by the analytical modeling method described in 5 above to predict the out-of-plane bending strength of a diaphragm by calculating the sum of strain energy stored in the yield line, and predicting the out-of-plane bending strength of the through diaphragm based on the relationship between the sum of strain energy and the work due to the moment and the axial force, based on the following equation (2).
[13] A method for predicting the out-of-plane bending strength of a diaphragm described in above 8, which uses an analytical model set up by the analytical modeling method described in above 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 a diaphragm thickness for 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 having a shorter side or diameter than the lower member using a diaphragm designed by the diaphragm plate thickness design method described in 15 above.

ここで、Ｍ_ｙ：通しダイアフラム面外曲げ耐力、
Ｕ_ｓｕｍ：降伏線に蓄えられる歪エネルギーの総和、
Ｎ_ｄ：ダイアフラムに作用する軸力、
δ_Ｎ：軸力によるダイアフラムの変位、
θ_ｄ：節点の変位により生じたダイアフラム回転角
を表す。 where M _y is the out-of-plane bending strength of the through diaphragm,
U _sum : the sum of strain energy stored at the yield line,
_Nd : Axial force acting on the diaphragm,
δ _N : Displacement of the diaphragm due to axial force,
θ _d : represents the diaphragm rotation angle caused by the displacement of the node.

ここで、Ｍ_ｙ：通しダイアフラム面外曲げ耐力、
Ｕ_ｓｕｍ：降伏線に蓄えられる歪エネルギーの総和、
Ｕ_ｌ：下側部材の軸歪エネルギー、
Ｎ_ｄ：ダイアフラムに作用する軸力、
δ_Ｎ：軸力によるダイアフラムの変位、
θ_ｄ：節点の変位により生じたダイアフラム回転角
を表す。 where M _y is the out-of-plane bending strength of the through diaphragm,
U _sum : the sum of strain energy stored at the yield line,
U _l : axial strain energy of the lower member,
_Nd : Axial force acting on the diaphragm,
δ _N : Displacement of the diaphragm due to axial force,
θ _d : represents the diaphragm rotation angle caused by the displacement of the node.

本発明にかかるダイアフラムの面外曲げ耐力の解析モデル化方法および予測方法によれば、通しダイアフラムで寸法の異なる角形鋼管や円形鋼管からなる上下部材を接合するにあたり、接合した仕口のダイアフラムの面外曲げ耐力を、上下部材の角部寸法などを考慮して簡便に精度良く評価することができる。特に、下側部材の外周を上側部材の外側に配置した場合、上下の部材の外面を一平面上に揃えた場合、および、上下の部材の隣り合う平板部の外面をそれぞれ同一の平面上に揃えた場合に、それぞれ適した解析モデルを設定することで簡便に精度よくダイアフラムの面外曲げ耐力を予測することができる。また、その予測方法により、必要な耐力を満たすのに十分な板厚の鋼板を選定することができる。また、その板厚のダイアフラムを用いて、鋼管－ダイアフラム仕口を得ることができる。 The analytical modeling and prediction methods for the out-of-plane bending strength of diaphragms according to the present invention enable easy and accurate evaluation of the out-of-plane bending strength of diaphragms at joints made of square or circular steel pipes of different dimensions when connecting upper and lower members made of a through diaphragm, taking into account factors such as the corner dimensions of the upper and lower members. In particular, by setting up an appropriate analytical model for each of the following cases, the out-of-plane bending strength of diaphragms can be easily and accurately predicted. Furthermore, this prediction method makes it possible to select steel plates with a thickness sufficient to meet the required strength. Furthermore, a steel pipe-diaphragm connection can be obtained using a diaphragm of that thickness.

本発明の一実施形態にかかる寸法の異なる角形鋼管を同軸配置で通しダイアフラムに接合した接合構造のダイアフラム面外曲げ耐力評価のための解析モデルの構成を示す模式図であり、（ａ）は平面図を表し、（ｂ）はＸ－Ｘ視断面図を表す。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 in a coaxial arrangement 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 X-X. 上記実施形態にかかるダイアフラムを上ダイアフラムとした柱梁接合構造を模式的に表す斜視図である。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. テーパー管を接合パネルに用いた従来の柱梁接合構造を模式的に示す斜視図である。FIG. 1 is a perspective view schematically showing a conventional beam-column joint structure using tapered pipes as joint panels. 本発明の他の実施形態にかかる、寸法の異なる角形鋼管を一方向偏心配置で通しダイアフラムに接合した接合構造のダイアフラム面外曲げ耐力評価のための解析モデルの構成を示す模式図であり、（ａ）は平面図を表し、（ｂ）はＸ－Ｘ視断面図を表す。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 X-X. 本発明の別の実施形態にかかる、寸法の異なる角形鋼管を二方向偏心配置で通しダイアフラムに接合した接合構造のダイアフラム面外曲げ耐力評価のための解析モデルの構成を示す模式図であり、（ａ）は平面図を表し、（ｂ）はＹ－Ｙ視断面図を表す。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 cross-sectional view taken along the Y-Y direction. 有限要素法（ＦＥＭ）解析モデルの接合要素を表す斜視図である。FIG. 1 is a perspective view showing a joint element of a finite element method (FEM) analysis model.

以下、本発明の実施の形態について具体的に説明する。なお、各図面は模式的なものであって、現実のものとは異なる場合がある。また、以下の実施形態は、本発明の技術的思想を具体化するための設備や方法を例示するものであり、構成を下記のものに特定するものでない。すなわち、本発明の技術的思想は、特許請求の範囲に記載された技術的範囲内において、種々の変更を加えることができる。 The following describes in detail the embodiments of the present invention. Note that the drawings are schematic and may differ from the actual product. Furthermore, the following embodiments exemplify equipment and methods for embodying the technical concept of the present invention, and are not intended to limit the configuration to that described below. In other words, the technical concept of the present invention can be modified in various ways within the technical scope described in the claims.

本実施形態では、降伏線理論を用いて、通しダイアフラムで寸法の異なる角形鋼管からなる上下部材を接合するにあたり、接合した仕口のダイアフラムの面外曲げ耐力を予測する。通しダイアフラムは下側部材の板厚より大きい板厚の鋼板からなり、通しダイアフラムの縁の辺長は下側部材の辺長と同じか、または、より長いものを用いる。降伏線理論において、降伏線ＸＹに蓄えられるエネルギーＵ_ＸＹは、降伏線の単位長さ当たりのモーメントをｄＭ、降伏線長さをｌ、降伏線の回転角をθとすると、下記数式３の（３）式で表せる。 In this embodiment, yield line theory is used to predict the out-of-plane bending strength of the diaphragm of a 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 edge length of the through diaphragm is the same as or longer than that of the lower member.In yield line theory, the energy _UXY stored in the yield line XY can be expressed by the following equation (3), where dM is the moment per unit length of the yield line, l is the yield line length, and θ is the rotation angle of the yield line.

降伏線の単位長さ当たりのモーメントをｄＭは、降伏線の生じる材料の降伏応力度をσ_ｙ、板厚をｔとすると、最外縁降伏状態ではｄＭ＝（σ_ｙ・ｔ^２）／６、全断面降伏状態ではｄＭ＝（σ_ｙ・ｔ^２）／４である。 The moment per unit length of the yield line is dM, and if the yield stress of the material where the yield line occurs is σ _y and the plate thickness is t, then in the outermost edge yield state, dM = (σ _y · t ² ) / 6, and in the entire cross section yield state, dM = (σ _y · t ² ) / 4.

上下で寸法の異なる部材を接合した接合部について、外力による仕事Ｅを求めると、外力による仕事は曲げ（モーメント）成分と軸力成分に分けられるので、曲げ成分をＥ_Ｍ、軸力成分をＥ_Ｎとすると、下記数式４の（４）式で表せる。 When calculating the work E due to an external force at a joint where components with different dimensions are joined at the top and bottom, the work due to the external force can be divided into a bending (moment) component and an axial force component, so if the bending component is E _M and the axial force component is E _N , it can be expressed as Equation 4 (4) below.

ここで、曲げについては、降伏モーメントをＭ_ｙ、ダイアフラム回転角をθ_ｄとして、下記数式５の（５）式で表せる。 Here, the bending can be expressed by the following formula 5 (5), where M _y is the yield moment and θ _d is the diaphragm rotation angle.

軸力については、軸力をＮ_ｄ、ダイアフラム軸力変位をδ_Ｎとして、下記数式６の（６）式で表せる。 The axial force can be expressed by the following equation 6 (6), where the axial force is N _d and the diaphragm axial force displacement is _δN .

＜第一実施形態＞
第一の実施形態として、図１に示す、角形鋼管からなる下側部材３と下側部材３より辺の長さが短い角形鋼管からなる上側部材１とを用い、下側部材３のすべての平板部の外面が上側部材１のすべての平板部の外面より外側になるように配置（無偏心配置）し、通しダイアフラム２を介して下側部材３の上端全周および上側部材１の下端全周を接合した接合部につき、通しダイアフラム２の曲げ耐力を予測することを検討する。ここで、「辺の長さが短い」とは、角形鋼管の断面が略正方形であれば一辺の長さで比較し、略長方形であれば長辺どうしおよび短辺どうしの長さで比較する。以下におなじ。
図１の例では、下側部材３と上側部材１との軸心を相互に一致させて、いわゆる同軸配置とした。
解析モデルを設定するにあたり、平面視で、通しダイアフラム２の板厚中央面上に、節点Ａ～Ｒの直交座標（ｘ、ｙ、ｚ）を下記数式７のように定める。ここで、軸心位置を原点（０、０、０）と置く。 First Embodiment
In the 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 sides shorter than those of 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, or 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, that is, they are arranged coaxially.
To set up the analytical 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).

ここで、Ｂ_ｃｕ：上側部材１の辺長、ｔ_ｃｕ：上側部材１の板厚、Ｂ_ｃｌ：下側部材３の辺長、ｔ_ｃｌ：下側部材３の板厚、ｘ：上側部材１の曲げ軸－軸芯間距離、ｒ_{ｕ＿ｏｕｔ}：上側部材１の角部外周半径、ｒ_{ｕ＿ｍｉｄ}：上側部材１の角部板厚中央線の半径、ｒ_{ｌ＿ｏｕｔ}：下側部材３の角部外周半径、ｒ_{ｌ＿ｍｉｄ}：下側部材３の角部板厚中央線の半径、δ_ｍ：基準節点変位、ｌ_ｄ：通しダイアフラム２の突出長さであり、Ｂ_１およびＢ_２は、下記数式８の（８）式および（９）式で表される。 Here, B _cu : side length of upper member 1, t _cu : plate thickness of upper member 1, B _cl : side length of lower member 3, t _cl : plate thickness of lower member 3, x : distance between bending axis and axis center of upper member 1, r _{u _out} : outer radius of corner of upper member 1, r _{u _mid} : radius of center line of thickness of corner of upper member 1, r _{l _out} : outer radius of corner of lower member 3, r _{l _mid} : radius of center line of thickness of corner of lower member 3, δ _m : reference node displacement, l _d : protrusion length of through diaphragm 2, and B ₁ and B ₂ are expressed by equations (8) and (9) of equation 8 below.

本実施形態の内力による歪エネルギーＵを求めると、Ｕは降伏線９である線分ＢＣ、ＢＥ、ＢＨ、ＥＣ、ＥＩ、ＤＣ、ＤＦ、ＤＫ、ＦＣ、ＦＪ、ＯＰ、ＯＭ、ＯＨ、ＭＰ、ＭＩ、ＱＰ、ＱＮ、ＱＫ、ＮＰ、ＮＪに蓄えられる歪エネルギーの合計Ｕ_ｓｕｍであり、下記数式９の（９）式となる。なお、各降伏線９に蓄えられる歪エネルギーの計算にあたっては要素境界１０を考慮する。 When calculating the strain energy U due to internal forces in this embodiment, U is the sum U sum of the strain energy 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 lines 9, and is given by the following Equation 9 (9). Note that the element boundaries 10 are taken into consideration when calculating the strain energy stored in each yield line 9.

外力による仕事Ｅは、上記（４）式、（５）式および（６）式で求めることができる。ただし、ダイアフラム回転角θ_ｄ、ダイアフラム軸力変位δ_Ｎおよび軸力Ｎ_ｄは下記数式１０のそれぞれ（１０）式、（１１）式および（１２）式である。式中の、ｎ：軸力比、σ_ｙｃ：上側部材１の降伏応力度、Ａ_ｃｕ：上側部材１の断面積とする。 The work E due to the external force can be calculated using the above formulas (4), (5), and (6). However, the diaphragm rotation angle θ _d , diaphragm axial force displacement δ _N , and axial force N _d are respectively expressed by formulas (10), (11), and (12) in the following formula 10. In the formulas, n is the axial force ratio, σ _yc is the yield stress of the upper member 1, and A _cu is the cross-sectional area of the upper member 1.

＜第二実施形態＞
第二の実施形態として、図４に示す、角形鋼管からなる下側部材３と下側部材３より辺の長さが短い角形鋼管からなる上側部材１とを用い、下側部材３の一の平板部の外面と上側部材１の一の平板部の外面とを一平面上に揃えて、いわゆる一方向偏心配置とし、通しダイアフラム２を介して下側部材３の上端全周および上側部材１の下端全周を接合した接合部につき、通しダイアフラム２の曲げ耐力を予測することを検討する。
解析モデルを設定するにあたり、平面視で、通しダイアフラム２の板厚中央面上に、節点Ａ～Ｑの直交座標（ｘ、ｙ、ｚ）を下記数式１１のように定める。ここで、下側部材３の軸心位置を原点（０、０、０）と置く。 Second Embodiment
As a second embodiment, as shown in Figure 4, 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 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 bending strength 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.
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 axial center position of the lower member 3 is set as the origin (0, 0, 0).

ここで、Ｂ_ｃｕ：上側部材１の辺長、ｔ_ｃｕ：上側部材１の板厚、Ｂ_ｃｌ：下側部材３の辺長、ｔ_ｃｌ：下側部材３の板厚、ｘ：上側部材１の曲げ軸－軸芯間距離、ｒ_{ｕ＿ｏｕｔ}：上側部材１の角部外周半径、ｒ_{ｕ＿ｍｉｄ}：上側部材１の角部板厚中央線の半径、ｒ_{ｌ＿ｏｕｔ}：下側部材３の角部外周半径、ｒ_{ｌ＿ｍｉｄ}：下側部材３の角部板厚中央線の半径、δ_ｍ：基準節点変位、ｌ_ｄ：通しダイアフラム２の突出長さであり、Ｂ_１およびＢ_２は、上記（８）式および（９）式で表され、ｄＢは下記数式１２の（１３）式で表される。 Here, B _cu : side length of the upper member 1, t _cu : plate thickness of the upper member 1, B _cl : side length of the lower member 3, t _cl : plate thickness of the lower member 3, x : distance between the bending axis and the axis center of the upper member 1, r _{u _out} : outer radius of the corner of the 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 node displacement, l _d : protrusion length of the through diaphragm 2, B ₁ and B ₂ are expressed by the above equations (8) and (9), and dB is expressed by equation (13) of equation 12 below.

本実施形態の内力による歪エネルギーＵを求めると、Ｕは降伏線９である線分ＢＨ、ＣＤ、ＣＦ、ＦＤ、ＦＩ、ＤＪ、ＮＨ、ＯＰ、ＯＭ、ＭＰ、ＭＩ、ＰＪに蓄えられる歪エネルギーおよび下側部材３の軸歪エネルギーの合計となる。まず、降伏線９に蓄えられる歪エネルギーＵ_ｓｕｍは、下記数式１３の（１４）式となる。なお、各降伏線９に蓄えられる歪エネルギーの計算にあたっては要素境界１０を考慮する。 When calculating the strain energy U due to internal forces in this embodiment, U is 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 lines 9, and the axial strain energy of the lower member 3. First, the strain energy U _sum stored in the yield lines 9 is given by equation (14) of equation 13 below. Note that the element boundaries 10 are taken into consideration when calculating the strain energy stored in each yield line 9.

一方、図４の軸歪領域１１に示すように、下側部材３の軸歪エネルギーＵ_ｌは下記数式１４の（１５）式となる。 On the other hand, as shown in the axial strain region 11 in FIG. 4, the axial strain energy U ₁ of the lower member 3 is expressed by the following formula (15) of Equation 14.

したがって、内力Ｕの合計は下記数式１５の（１６）式となる。 Therefore, the total internal force U is given by equation (16) of equation 15 below.

外力による仕事Ｅは、上記（４）式、（５）式および（６）式で求めることができる。ただし、ダイアフラム回転角θ_ｄは上記（１０）式とし、ダイアフラム軸力変位δ_Ｎおよび軸力Ｎ_ｄは下記数式１６の（１７）式である。式中の、ｎ：軸力比、σ_ｙｃ：上側部材１の降伏応力度、Ａ_ｃｕ：上側部材１の断面積とする。 The work E due to the external force can be calculated using the above formulas (4), (5), and (6). However, the diaphragm rotation angle θ _d is calculated using the above formula (10), and the diaphragm axial force displacement δ _N and axial force N _d are calculated using the following formula (17) of formula 16. In the formula, n is the axial force ratio, σ _yc is the yield stress of the upper member 1, and A _cu is the cross-sectional area of the upper member 1.

＜第三実施形態＞
第三の実施形態として、図５に示す、角形鋼管からなる下側部材３と下側部材３より辺の長さが短い角形鋼管からなる上側部材１とを用い、下側部材３の隣り合う平板部の外面と対応する上側部材１の隣り合う平板部の外面とをそれぞれ同一の平面上に揃えて、いわゆる二方向偏心配置とし、通しダイアフラム２を介して下側部材３の上端全周および上側部材１の下端全周を接合した接合部につき、通しダイアフラム２の曲げ耐力を予測することを検討する。
解析モデルを設定するにあたり、平面視で、通しダイアフラム２の板厚中央面上に、節点Ａ～Ｇの直交座標（ｘ、ｙ、ｚ）を下記数式１１のように定める。ここで、下側部材の軸心位置を原点（０、０、０）と置く。 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 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).

ここで、Ｂ_ｃｕ：上側部材１の辺長、ｔ_ｃｕ：上側部材１の板厚、Ｂ_ｃｌ：下側部材３の辺長、ｔ_ｃｌ：下側部材３の板厚、ｘ：上側部材１の曲げ軸－軸芯間距離、ｒ_{ｕ＿ｏｕｔ}：上側部材１の角部外周半径、ｒ_{ｕ＿ｍｉｄ}：上側部材１の角部板厚中央線の半径、ｒ_{ｌ＿ｏｕｔ}：下側部材３の角部外周半径、ｒ_{ｌ＿ｍｉｄ}：下側部材３の角部板厚中央線の半径、δ_ｍ：基準節点変位、ｌ_ｄ：通しダイアフラム２の突出長さであり、Ｂ_１、Ｂ_２およびｄＢは、上記（８）式、（９）式および（１３）式で表され、Ｌ_ｃｄ、Ｌ_ｃｄ１およびＬ_ｃｄ２は下記数式１８のそれぞれ（１８）式、（１９）式および（２０）式で表される。 where B _cu is the side length of the upper member 1, t _cu is the plate thickness of the upper member 1, B _cl is the side length of the lower member 3, t _cl is the plate thickness of the lower member 3, x is the distance between the bending axis and the axis center of the upper member 1, r _{u _ out} is the outer circumferential radius of the corner of the upper member 1, r _{u _ mid} is the radius of the center line of the thickness of the corner of the upper member 1, r _{l _ out} is the outer circumferential radius of the corner of the lower member 3, r _{l _ mid} _is the radius of the center line of the thickness of the corner of the lower member 3, δ _m is the reference nodal displacement, l d is the protrusion length of the through diaphragm 2, B ₁ , B ₂ and dB are expressed by the above formulas (8), (9) and (13), and L _cd , L _cd1 and L _cd2 is expressed by the following formulas (18), (19), and (20), respectively.

本実施形態の内力による歪エネルギーＵを求めると、Ｕは降伏線９である線分ＡＣ、ＡＤ、ＡＥ、ＣＤ、ＣＧ、ＤＧ、ＥＤ、ＥＧに蓄えられる歪エネルギーおよび下側部材の軸歪エネルギーの合計となる。まず、降伏線に蓄えられるエネルギーＵ_ｓｕｍは、下記数式１９の（２１）式となる。なお、各降伏線９に蓄えられる歪エネルギーの計算にあたっては要素境界１０を考慮する。 In this embodiment, the strain energy U due to internal forces is calculated as the sum of the strain energy stored in the line segments AC, AD, AE, CD, CG, DG, ED, and EG, which are the yield lines 9, and the axial strain energy of the lower member. First, the energy U _sum stored in the yield lines is given by Equation (21) of Equation 19 below. Note that the element boundaries 10 are taken into consideration when calculating the strain energy stored in each yield line 9.

一方、図５の軸歪領域１１に示すように、下側部材３の軸歪エネルギーＵ_ｌは下記数式２０の（２２）式となる。 On the other hand, as shown in the axial strain region 11 of FIG. 5, the axial strain energy U ₁ of the lower member 3 is expressed by the following formula (22) of Equation 20.

したがって、内力による歪エネルギーＵの合計は上記（１６）式となる。 Therefore, the total strain energy U due to internal forces is given by equation (16) above.

外力による仕事Ｅは、上記（４）式、（５）式および（６）式で求めることができる。ただし、ダイアフラム回転角θ_ｄ、ダイアフラム軸力変位δ_Ｎおよび軸力Ｎ_ｄは下記数式２１のそれぞれ（２３）式、（２４）式および（２５）式である。式中の、ｎ：軸力比、σ_ｙｃ：上側部材１の降伏応力度、Ａ_ｃｕ：上側部材１の断面積とする。 The work E due to the external force can be calculated using the above formulas (4), (5), and (6). However, the diaphragm rotation angle θ _d , diaphragm axial force displacement δ _N , and axial force N _d are respectively calculated using formulas (23), (24), and (25) in the following formula 21. In the formulas, n is the axial force ratio, σ _yc is the yield stress of the upper member 1, and A _cu is the cross-sectional area of the upper member 1.

＜ダイアフラムの面外曲げ耐力の予測＞
外力仕事Ｅと、上記第一～第三の各実施形態それぞれの軸配置形式について計算した内力による歪エネルギーＵから降伏モーメントを求めると、Ｅ＝Ｕであることから、下記数式２２の（２６）式が導かれる。 <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.

ただし、上側部材１の曲げ軸－軸芯間距離ｘについては、下記数式２３の（２７）式の関係を満たすものとする。 However, the bending axis-to-axial distance x of the upper member 1 must satisfy the relationship in equation (27) of Equation 23 below.

上記実施形態では、角形鋼管を上下部材とする例を示したが、円形鋼管を上下部材として、または角形鋼管と円形鋼管を上下部材として組み合わせて用いることもできる。上下部材に円形鋼管を用いる場合は，円形鋼管板厚中央面上の節点を例えば円周方向中心角で４５°ごとに取る等の対応により適用できる。 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 using circular steel pipes as the upper and lower members, this can be achieved by taking measures such as placing nodes on the central plane of the circular steel pipe thickness at 45° circumferential central angles, for example.

図６に示すように、寸法の異なる上下部材１、３を通しダイアフラム２を介して接合した接合部を対象として、上側部材１頂部に強制変位を与えることで単調載荷する有限要素法（ＦＥＭ）を用いた解析を実施した。解析モデルリストを表１に示す。同軸配置、一方向偏心配置および二方向偏心配置のそれぞれについて、上側部材１は□－３５０×３５０×１２（ＢＣＲ２９５）および□－８５０×８５０×４０（ＢＣＰ３２５）の角形鋼管を用い、下側部材３は□－５００×５００×１９（ＢＣＲ２９５）および□－１０００×１０００×４０（ＢＣＰ３２５）の角形鋼管を用いた。ここで、角形鋼管の規格値は、□－辺長×辺長×板厚を表し、ＢＣＲは冷間ロール成形角形鋼管を表し、ＢＣＰは冷間プレス成形角形鋼管を表し、括弧内の続く数値は、降伏点の下限値をＭＰａで表す。上側部材１と下側部材３の辺長差は１５０ｍｍとした。ダイアフラム２の板厚はそれぞれ１００ｍｍ、６０ｍｍおよび４５ｍｍとした。ダイアフラムの鋼材規格はＴＭＣＰ３２５Ｃを用い、ダイアフラム２は、下側部材の辺長に６０ｍｍ加算した辺長の正方形とした。軸力比は、０および０．３を用いた。 As shown in Figure 6, an analysis was conducted 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 joined via a diaphragm 2. A list of analytical models is shown in Table 1. For the coaxial, one-way eccentric, and two-way eccentric configurations, square steel pipes of □-350 x 350 x 12 (BCR295) and □-850 x 850 x 40 (BCP325) were used for the upper member 1, and square steel pipes of □-500 x 500 x 19 (BCR295) and □-1000 x 1000 x 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.

表２に、表１の条件での上記各実施形態の評価式による計算結果と有限要素法（ＦＥＭ）による構造解析結果を示す。いずれの場合でも上記実施形態のダイアフラム面外曲げ耐力評価式を使用することで、ＦＥＭ解析結果から求められたダイアフラム面外曲げ耐力を精度良く評価できていることが分かる。 Table 2 shows the calculation results using the evaluation formula for each of the above embodiments under the conditions in Table 1, as well as the structural analysis results using the finite element method (FEM). In either case, it can be seen that by using the diaphragm out-of-plane bending strength evaluation formula of the above embodiments, the diaphragm out-of-plane bending strength obtained from the FEM analysis results can be accurately evaluated.

本発明のダイアフラムの面外曲げ耐力の解析モデル化方法および予測方法によれば、通しダイアフラムを介して寸法の異なる鋼管からなる上下部材を接合するにあたり、接合した仕口のダイアフラムの面外曲げ耐力を、上下部材の角部寸法を考慮して簡便に精度良く評価することができる。また、その予測方法により得られた耐力を満たすのに十分な板厚の鋼板を選定することができる。また、その板厚のダイアフラムを用いて、鋼管－ダイアフラム仕口を得ることができるので産業上有用である。 The analytical modeling and prediction methods for the out-of-plane bending strength of diaphragms of the present invention enable easy and accurate evaluation of the out-of-plane bending strength of the diaphragm of a joint when connecting upper and lower members made of steel pipes of different dimensions via a through diaphragm, 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.

１上側部材（上柱）
２ダイアフラム（通しダイアフラム、上ダイアフラム）
３下側部材（接合パネル）
４下柱
５下ダイアフラム
６梁フランジ
７梁ウェブ
８テーパー管
９降伏線
１０（計算用の）要素境界
１１軸歪領域 1 Upper member (upper column)
2 Diaphragm (through diaphragm, upper diaphragm)
3 Lower member (joint panel)
4 Lower column 5 Lower diaphragm 6 Beam flange 7 Beam web 8 Tapered pipe 9 Yield line 10 Element boundary (for calculation) 11 Axial strain area

Claims

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.

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, in advance, in a plan view, nodes are provided on the line passing through the edge of the through diaphragm on the center plane of the plate thickness of the through diaphragm, on the center line of the plate thickness of the flat plate portion of the lower member, on the center line of the plate thickness of the corner of the lower member, on the center line of the plate thickness of the flat plate portion of the upper member, and on the center line of the plate 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 portions of the upper member, and an equivalent 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.

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.

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.

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.

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.

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.

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.

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.
where M _y is the out-of-plane bending strength of the through diaphragm,
U _sum : the sum of strain energy stored at the yield line,
_Nd : Axial force acting on the diaphragm,
δ _N : Displacement of the diaphragm due to axial force,
θ _d : represents the diaphragm rotation angle caused by the displacement of the node.

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.

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.
Where, M _y : Out-of-plane bending strength of the through diaphragm,
U _sum : the sum of strain energy stored at the yield line,
U _l : axial strain energy of the lower member,
_Nd : Axial force acting on the diaphragm,
δ _N : Displacement of the diaphragm due to axial force,
θ _d : represents the diaphragm rotation angle caused by the displacement of the node.

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.

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.
Where, M _y : Out-of-plane bending strength of the through diaphragm,
U _sum : the sum of strain energy stored at the yield line,
U _l : axial strain energy of the lower member,
_Nd : Axial force acting on the diaphragm,
δ _N : Displacement of the diaphragm due to axial force,
θ _d : represents the diaphragm rotation angle caused by the displacement of the node.

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.

A diaphragm thickness design method for steel pipe joints, which uses the diaphragm out-of-plane bending strength prediction method described in any one of claims 8 to 14 to determine the diaphragm out-of-plane bending strength, and selects as the diaphragm material from steel plates of multiple standardized thicknesses a steel plate with a thickness sufficient to satisfy the required diaphragm out-of-plane bending strength when a design moment and design axial force are applied to the upper member.