JP7616519B2

JP7616519B2 - Analytical modeling method and prediction method for out-of-plane bending rigidity of diaphragm, diaphragm plate thickness design method for steel pipe joint, and steel pipe-diaphragm elastic spring joint

Info

Publication number: JP7616519B2
Application number: JP2023070805A
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: 2025-01-17
Anticipated expiration: 2043-04-24
Also published as: JP2023162147A

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剛性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－ダイアフラム弾性ばね仕口に関する。 The present invention relates to a method for analytical modeling and prediction of the out-of-plane bending stiffness 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.

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-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 Figure 3. A column-beam joint using a tapered tube as shown in Figure 3 has the advantage that it is easy to ensure the strength and rigidity of the column-diaphragm joint.

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 it is easy to ensure the rigidity of the joints with this tapered tube 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 tube. In recent years, there has been a demand for labor-saving construction, and the use of tapered tube 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。 As a method for joining columns with different dimensions above and below without using a tapered tube 8, as shown in Figure 2, a square steel pipe 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. If the thickness of the upper diaphragm 2 is thin, bending of the upper column 1 may cause large out-of-plane deformation in the upper diaphragm 2. In 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.

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 1 discloses a method for predicting the out-of-plane bending stiffness of a diaphragm in a joint where upper and lower columns of different diameters are joined by a thickened diaphragm by dividing the diaphragm into multiple polygonal elements, with each polygonal element connected by a rotational spring that allows it to bend elastically at each boundary edge, and using other analytical models to add up the bending deformation and shear deformation in the rotational spring for a given load and determine the stiffness of the diaphragm from the equilibrium conditions.

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 2 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, in which the out-of-plane bending yield strength fMy of the upper through diaphragm 5 is calculated using yield line theory and reflecting the axial force N of the upper column when an axial force N acts on the upper column.

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

川井忠彦、近藤一夫：新しい離散化モデルによる板の曲げ崩壊解析、日本造船学会秋季講演会、１９７７．１１Tadahiko Kawai and Kazuo Kondo: Plate Bending Collapse Analysis Using a New Discretized Model, Autumn Lecture of the Society of Naval Architects of Japan, November 1977.

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に記載の方法は、１方向偏心および２方向偏心配置に限定されており、偏心なしの場合は記載されていない。また、複数種類の応力と変形について剛性を算出しており、やや計算が煩雑である。その他、角形鋼管の角部寸法（半径）を考慮せず、角部を正角として仮定しているため、角部寸法の値によっては計算が適用できない可能性がある。 However, the conventional techniques have the following problems.
Regarding the joint 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 the case of no eccentricity. In addition, the rigidity is calculated for multiple types of stress and deformation, making the calculation somewhat complicated. In addition, the corner dimensions (radius) of the square steel pipe are not taken into consideration, and the corners are assumed to be regular angles, so the calculation may not be applicable depending on the value of the 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剛性の解析モデル化方法および予測方法を提供することを目的とする。加えて、鋼管接合部のダイアフラム板厚設計方法ならびに鋼管－ダイアフラム弾性ばね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 an analytical modeling method and a prediction method for the out-of-plane bending stiffness of a diaphragm that can be easily and accurately predicted when steel pipes of different dimensions are passed through and joined via a diaphragm. In addition, the 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.

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剛性を予測するために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に複数の節点を設け、該節点の４点以上を選択し、選択した節点と該節点を結ぶ複数の直辺からなり、該辺の一を境に相互に回転ばねにて折れ曲がり可能に連結され、かつ、曲げ力に対して剛体とみなされる複数の第一多角形要素に区分された前記接合部の解析モデルを作成する、ダイアフラムの面外曲げ剛性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剛性を予測するために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、前記接合部の解析モデルとして、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、前記上側部材の角部の板厚中央線上、および、前記上側部材の内部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、選択した節点と該節点を結ぶ複数の直辺からなり、該辺の一を境に相互に回転ばねにて折れ曲がり可能に連結され、かつ、曲げ力に対して剛体とみなされる複数の多角形要素に区分する、上記１に記載のダイアフラムの面外曲げ剛性の解析モデル化方法。
［３］前記接合部の解析モデルとして、前記通しダイアフラムを複数の多角形要素（Ｉ０１～Ｉ２８）に分割し、前記各多角形要素は、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、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Ｄ、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に最も近い一のダイアフラム縁上の点をＥ、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に最も近い一の平板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前記上側部材の平板部のうち、Ｂに最も近い一の平板部の板厚中央線上の点をＧ、前記上側部材の内部の点をＨ、Ｅに近い前記上側部材の角部であってＤを含まない角部の板厚中央線上の点をＩ、Ｅに近い前記下側部材の角部であってＢを含まない角部の板厚中心線上の点をＪ、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Ｋ、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Ｌ、Ａに近い前記下側部材の他の角部の板厚中央線上の点をＭ、Ｍに最も近い前記上側部材の角部の板厚中央線上の点をＮ、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、他のダイアフラム縁上の点をＯ、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、他の平板部の板厚中央線上の点をＰ、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、他の平板部の板厚中央線上の点をＱ、Ｄを含む角部の対角位置にある前記上側部材の角部の板厚中央線上の点をＲ、Ｂを含む角部の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Ｓとしたとき、ＡＢ、ＢＣ、ＣＡにより形成される多角形要素Ｉ０１、ＣＤ、ＤＨ、ＨＣにより形成される多角形要素Ｉ０２、ＢＣ、ＣＤ、ＤＢにより形成される多角形要素Ｉ０３、ＢＥ、ＥＦ、ＦＢにより形成される多角形要素Ｉ０４、ＤＦ、ＦＧ、ＧＤにより形成される多角形要素Ｉ０５、ＢＤ、ＤＦ、ＦＢにより形成される多角形要素Ｉ０６、ＤＧ、ＧＨ、ＨＤにより形成される多角形要素Ｉ０７、ＧＨ、ＨＩ、ＩＧにより形成される多角形要素Ｉ０８、ＨＩ、ＩＬ、ＬＨにより形成される多角形要素Ｉ０９、ＦＧ、ＧＩ、ＩＦにより形成される多角形要素Ｉ１０、ＩＪ、ＪＬ、ＬＩにより形成される多角形要素Ｉ１１、ＦＩ、ＩＪ、ＪＦにより形成される多角形要素Ｉ１２、ＥＦ、ＦＪ、ＪＥにより形成される多角形要素Ｉ１３、ＪＫ、ＫＬ、ＬＪにより形成される多角形要素Ｉ１４、ＣＨ、ＨＮ、ＮＣにより形成される多角形要素Ｉ１５、ＨＮ、ＮＱ、ＱＨにより形成される多角形要素Ｉ１６、ＣＭ、ＭＮ、ＮＣにより形成される多角形要素Ｉ１７、ＮＰ、ＰＱ、ＱＮにより形成される多角形要素Ｉ１８、ＭＮ、ＮＰ、ＰＭにより形成される多角形要素Ｉ１９、ＡＣ、ＣＭ、ＭＡにより形成される多角形要素Ｉ２０、ＭＯ、ＯＰ、ＰＭにより形成される多角形要素Ｉ２１、ＨＱ、ＱＲ、ＲＨにより形成される多角形要素Ｉ２２、ＨＬ、ＬＲ、ＲＨにより形成される多角形要素Ｉ２３、ＰＱ、ＱＲ、ＲＰにより形成される多角形要素Ｉ２４、ＬＲ、ＲＳ、ＳＬにより形成される多角形要素Ｉ２５、ＰＲ、ＲＳ、ＳＰにより形成される多角形要素Ｉ２６、ＯＰ、ＰＳ、ＳＯにより形成される多角形要素Ｉ２７、ＬＫ、ＫＳ、ＳＬにより形成される多角形要素Ｉ２８の計２８の多角形要素とし、前記各多角形要素は曲げ力に対して剛体であって、かつ各境界となる辺で折れ曲がり可能に回転ばねで連結されているとする、上記２に記載のダイアフラムの面外曲げ剛性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剛性を予測するために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、前記接合部の解析モデルとして、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、前記下側部材の板厚中央線上、前記上側部材の板厚中央線上、および、前記上側部材の内部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、選択した節点と該節点を結ぶ複数の直辺からなり、該辺の一を境に相互に回転ばねにて折れ曲がり可能に連結され、かつ、曲げ力に対して剛体とみなされる複数の多角形要素に区分する、上記１に記載のダイアフラムの面外曲げ剛性の解析モデル化方法。
［５］前記接合部の解析モデルとして、前記通しダイアフラムを複数の多角形要素（Ｉ２９～Ｉ４２）に分割した解析モデルを設定し、前記各多角形要素は、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、外面を一平面上に揃えた前記平板部に直交するダイアフラム縁の一辺上の点をＡ、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Ｂ、前記下側部材の角部であってＡに近い２つのうち、外面を一平面上に揃えた前記平板部から遠い方の角部の板厚中央線上の点をＣ、前記上側部材の角部であってＡに近い２つのうち、外面を一平面上に揃えた前記平板部から遠い方の角部の板厚中央線上の点をＤ、前記上側部材の内部の点をＥ、外面を一平面上に揃えた前記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Ｆ、外面を一平面上に揃えた前記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Ｇ、Ｇに最も近いダイアフラム縁上の点をＨ、Ｈに近い前記上側部材の角部であってＤを含まない角部の板厚中央線上の点をＩ、Ｈに近い前記下側部材の角部であってＢを含まない角部の板厚中央線上の点をＪ、Ｂ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Ｋ、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Ｌとしたとき、ＡＢ、ＢＣ、ＣＡにより形成される多角形要素Ｉ２９、ＢＣ、ＣＤ、ＤＢにより形成される多角形要素Ｉ３０、ＢＤ、ＤＥ、ＥＢにより形成される多角形要素Ｉ３１、ＤＥ、ＥＦ、ＦＤにより形成される多角形要素Ｉ３２、ＤＦ、ＦＧ、ＧＤにより形成される多角形要素Ｉ３３、ＣＤ、ＤＧ、ＧＣにより形成される多角形要素Ｉ３４、ＣＧ、ＧＨ、ＨＣにより形成される多角形要素Ｉ３５、ＥＦ、ＦＩ、ＩＥにより形成される多角形要素Ｉ３６、ＦＧ、ＧＩ、ＩＦにより形成される多角形要素Ｉ３７、ＥＩ、ＩＫ、ＫＥにより形成される多角形要素Ｉ３８、ＩＪ、ＪＫ、ＫＩにより形成される多角形要素Ｉ３９、ＧＩ、ＩＪ、ＪＧにより形成される多角形要素Ｉ４０、ＧＨ、ＨＪ、ＪＧにより形成される多角形要素Ｉ４１、ＪＫ、ＫＬ、ＬＪにより形成される多角形要素Ｉ４２、の計１４の多角形要素とし、前記各多角形要素は曲げ力に対して剛体であって、かつ各境界となる辺で折れ曲がり可能に回転ばねで連結されているとする、上記４に記載のダイアフラムの面外曲げ剛性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剛性を予測するために解析モデルを作成する方法であって、前記接合部の解析モデルとして、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、前記上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をなす円弧の中心上、および、前記上側部材の内部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、選択した節点と該節点を結ぶ複数の直辺からなり、該辺の一を境に相互に回転ばねにて折れ曲がり可能に連結され、かつ、曲げ力に対して剛体とみなされる複数の多角形要素に区分する、上記１に記載のダイアフラムの面外曲げ剛性の解析モデル化方法。
［７］前記接合部の解析モデルとして、前記通しダイアフラムを複数の多角形要素（Ｉ４３～Ｉ６０）に分割した解析モデルを設定し、前記各多角形要素は、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、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最も近い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であって、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ていない角部の板厚中央線上の点をＢ、Ａに近い前記上側部材の角部であって、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ていない角部の板厚中央線上の点をＣ、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、上下部材の外面が同一平面上に揃えられた前記２つの平板部から遠い方のダイアフラム縁上の点をＤ、Ｄ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Ｅ、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下側部材の角部の板厚中央線上の点をＦ、前記下側部材のＦ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Ｇ、前記下側部材のＦ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Ｈ、前記上側部材の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線上の点をＩ、前記上側部材の平板部の外面と同一平面上にない外面を有する下側部材の平板部のうちＥを含まない平板部の板厚中央線上の点をＪ、前記上側部材の内部の点をＫ、Ｄ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、前記下側部材のＢ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Ｍ、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Ｎとしたとき、ＡＢ、ＢＣ、ＣＡにより形成される多角形要素Ｉ４３、ＡＣ、ＣＦ、ＦＡにより形成される多角形要素Ｉ４４、ＣＦ、ＦＫ、ＫＣにより形成される多角形要素Ｉ４５、ＣＧ、ＧＫ、ＫＣにより形成される多角形要素Ｉ４６、ＢＣ、ＣＧ、ＧＢにより形成される多角形要素Ｉ４７、ＢＥ、ＥＧ、ＧＢにより形成される多角形要素Ｉ４８、ＢＤ、ＤＥ、ＥＢにより形成される多角形要素Ｉ４９、ＤＥ、ＥＨ、ＨＤにより形成される多角形要素Ｉ５０、ＥＧ、ＧＨ、ＨＥにより形成される多角形要素Ｉ５１、ＦＩ、ＩＫ、ＫＦにより形成される多角形要素Ｉ５２、ＦＩ、ＩＬ、ＬＦにより形成される多角形要素Ｉ５３、ＧＩ、ＩＫ、ＫＧにより形成される多角形要素Ｉ５４、ＧＩ、ＩＭ、ＭＧにより形成される多角形要素Ｉ５５、ＩＬ、ＬＭ、ＭＩにより形成される多角形要素Ｉ５６、ＧＪ、ＪＭ、ＭＧにより形成される多角形要素Ｉ５７、ＪＭ、ＭＮ、ＮＪにより形成される多角形要素Ｉ５８、ＧＨ、ＨＪ、ＪＧにより形成される多角形要素Ｉ５９、ＨＪ、ＪＮ、ＮＨにより形成される多角形要素Ｉ６０、の計１８の多角形要素とし、前記各多角形要素は曲げ力に対して剛体であって、かつ各境界となる辺で折れ曲がり可能に回転ばねで連結されているとする、上記６に記載のダイアフラムの面外曲げ剛性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、前記通しダイアフラムの曲げ剛性を予測するにあたり、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、その際に生じる変位に伴う前記回転ばねの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荷重と前記荷重の付加に伴う変位とに基づき算出したダイアフラムの面外曲げ剛性を予測する、ダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、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た場合、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た場合について、その際に生じる変位に伴う前記回転ばねの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荷重と前記荷重の付加に伴う変位とに基づき前記通しダイアフラムの面外曲げ剛性を予測する、上記８に記載のダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、前記解析モデルに対して作用する荷重としてＤ－Ｇ－Ｉに含まれる平板部に下向きに作用する荷重を、Ｎ－Ｑ－Ｒに含まれる平板部に上向きに作用する同等の荷重を与え、この荷重によって変位δが生じたとし、この時前記各回転ばねに蓄えられる歪エネルギーの和を求め、これを用いて前記荷重と前記変位δとの関係からダイアフラム面外曲げ剛性を予測する、上記９に記載のダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、ａ）前記上側部材が前記角形鋼管で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た場合、または、ｂ）前記上側部材が前記円形鋼管で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た場合について、その際に生じる変位に伴う前記回転ばねの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荷重と前記荷重の付加に伴う変位とに基づき前記通しダイアフラムの面外曲げ剛性を予測する、上記８に記載のダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、前記解析モデルに対して作用する荷重としてＤ－Ｆ－Ｉに含まれる平板部に下向きに作用する荷重を、外面を一平面上に揃えた上側部材の平板部に上向きに作用する同等の荷重を与え、この荷重によって変位δが生じたとし、この時前記各回転ばねに蓄えられる歪エネルギーの和を求め、これを用いて前記荷重と前記変位δとの関係からダイアフラム面外曲げ剛性を予測する、上記１１に記載のダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、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下側部材の角部に対して同等の上向き荷重を付加した場合について、その際に生じる変位に伴う前記回転ばねの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荷重と前記荷重の付加に伴う変位とに基づき前記通しダイアフラムの面外曲げ剛性を予測する、上記８に記載のダイアフラムの面外曲げ剛性の予測方法。
［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、前記通しダイアフラムの曲げ剛性を予測するにあたり、前記解析モデルに対して作用する荷重としてＧに下向きに作用する荷重を、Ｆを含む角部に上向きに作用する荷重を与え、この荷重によって変位δが生じたとし、この時前記各回転ばねに蓄えられるエネルギーの和を求め、これを用いて前記荷重と前記変位δとの関係からダイアフラム面外曲げ剛性を予測する、上記１３に記載のダイアフラムの面外曲げ剛性の予測方法。
［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剛性の予測方法を用いて、前記ダイアフラム面外曲げ剛性を求め、上側部材に設計荷重を与えた際に必要とされるダイアフラム面外曲げ剛性に対して、規格化された複数種類の板厚の鋼板から、必要とされる前記剛性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－ダイアフラム弾性ばね仕口。 The gist of the present invention, which advantageously solves the above problems, is as follows.
[1] A method for creating an analytical model 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 having 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 which is made up of a plurality of straight sides connecting the selected nodes to the selected nodes, which are connected to each other by a rotational spring so that they can be bent at one of the sides as a boundary, and which is 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 on the mid-thickness plane of the through diaphragm in a plan view, on a line passing through the edge of the through diaphragm, on the mid-thickness line of the flat portion of the lower member, on the mid-thickness line of the corner of the lower member, on the mid-thickness line of the flat portion of the upper member, on the mid-thickness line 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, which are mutually connected by rotational springs so as to be able to be bent at one of the sides as a boundary, and which are 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 plate portion 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, A point on the diaphragm edge closest to B among the flat plate portions of the lower member perpendicular to the diaphragm edge including A is designated as D, a point on the diaphragm edge closest to B among the flat plate portions of the lower member perpendicular to the diaphragm edge including A is designated as E, a point on the plate thickness center line of the flat plate portion closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is designated as F, a point on the plate thickness center line of the flat plate portion closest to B among the flat plate portions of the upper member perpendicular to the diaphragm edge including A is designated as G, a point inside the upper member is designated as H, and a corner of the upper member close to E and not including D is designated as A point on the thickness center line of the corner of the lower member closest to E and not including B is designated as I, a point on the thickness center line of the corner of the lower member closest to E but not including B is designated as J, a point on the edge of the diaphragm facing the diaphragm edge including A is designated as K, a point on the thickness center line of the flat portion of the lower member facing the flat portion of the lower member including C is designated as L, a point on the thickness center line of another corner of the lower member close to A is designated as M, a point on the thickness center line of the corner of the upper member closest to M is designated as N, and a point on the thickness center line of the diaphragm edge perpendicular to the diaphragm edge including A is designated as K. Among the points on the other diaphragm edge, O is a point on the thickness center line of the other flat plate part of the flat plate part of the lower member perpendicular to the diaphragm edge including A, Q is a point on the thickness center line of the other flat plate part of the flat plate part of the upper member perpendicular to the diaphragm edge including A, R is a point on the thickness center line of the corner part of the upper member diagonally opposite the corner part including D, and S is a point on the thickness center line of the corner part of the lower member diagonally opposite the corner part including B. A polygonal element I01 formed by CD, DH, and HC, a polygonal element I02 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 L A polygonal element I09 formed by H, a polygonal element I10 formed by FG, GI, IF, a polygonal element I11 formed by IJ, JL, LI, a polygonal element I12 formed by FI, IJ, JF, a polygonal element I13 formed by EF, FJ, JE, a polygonal element I14 formed by JK, KL, LJ, a polygonal element I15 formed by CH, HN, NC, a polygonal element I16 formed by HN, NQ, QH, CM, M A polygonal element I17 formed by N 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, and a polygonal element I25 formed by L. 3. An analytical modeling method for the out-of-plane bending rigidity of a diaphragm described in 2 above, in which a total of 28 polygonal elements are defined as polygonal element I25 formed by R, 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 rotational springs at each boundary edge so that it can be bent.
[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 above in 1, 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 center plane of the thickness of the through diaphragm, on a line passing through the edge of the through diaphragm, on the center line of the thickness of the lower member, on the center 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 connected to each other by a rotational spring 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 is set in which the through diaphragm is divided into a plurality of polygonal elements (I29 to I42), 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 ... A point on the center line of the thickness of the corner farthest from the flat plate portion aligned on a plane is designated as D, a point inside the upper member is designated as E, 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 surfaces are aligned on a plane is designated as F, 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 surfaces are aligned on a plane is designated as G, a point on the edge of the diaphragm closest to G is designated as 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 designated as 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 designated as J, and a 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 designated as I. where K is a point on the center line of the thickness of the flat plate portion, and L is a point on the diaphragm edge opposite the diaphragm edge including A, a polygonal element I29 formed by AB, BC, CA, a polygonal element I30 formed by BC, CD, DB, a polygonal element I31 formed by BD, DE, EB, a polygonal element I32 formed by DE, EF, FD, a polygonal element I33 formed by DF, FG, GD, a polygonal element I34 formed by CD, DG, GC, a polygonal element I35 formed by CG, GH, HC, and a polygonal element I36 formed by EF, FI, IE, 5. An analytical modeling method for the out-of-plane bending rigidity of a diaphragm as described above in 4, in which a total of 14 polygonal elements are used: 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 joining the entire upper end circumference of the lower member and the entire lower end circumference of the upper member via a through diaphragm, using a lower member made of a square steel pipe and an upper member made of a square steel pipe with a side length shorter than that of the lower member, 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 connecting 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 center line of thickness of the flat portion of the lower member, a center line of thickness of the corner of the lower member, a center line of thickness of the flat portion of the upper member, a center line of thickness of the corner of the upper member, a center of an arc forming the center line of thickness 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 is set in which the through diaphragm is divided into a plurality of polygonal elements (I43 to I60), and each of the polygonal elements is, in a plan view, defined as A, 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, B, a point on the plate thickness center line of a corner of the lower member close to A that is not sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane, C, a point on the plate thickness center line of a corner of the upper member close to A that is not sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane, D, a point on the plate thickness center line of a corner of the upper member close to A that is not sandwiched between the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane, and C, a point on the plate thickness center line of a corner of the diaphragm edge that is perpendicular to the diaphragm edge including A that is closest to the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane, and D, a point on the plate thickness center line of a corner of the diaphragm edge that is perpendicular to the diaphragm edge including A that is closest to the two flat plate portions whose outer surfaces of the upper and lower members are aligned on the same plane. D is the point on the edge of the diaphragm farthest from the two flat plate portions in which the two flat plate portions are aligned, E is the point on the plate thickness centerline of the flat plate portion of the lower member closest to D, F is the point on the plate thickness centerline of the corner 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, G is the center point of the arc forming the plate thickness centerline of the corner of the upper member diagonally opposite the corner including F of the lower member, H is the point on the plate thickness centerline of the corner of the lower member diagonally opposite the corner including F of the lower member, I is the point on the plate thickness centerline of the corner of the upper member diagonally opposite the corner including C of the upper member, J is the point on the plate thickness centerline of the flat plate portion of the lower member that has an outer surface that is not on the same plane as the outer surface of the flat plate portion of the upper member that does not include E, K is the point inside the upper member, and D is the die including D. When a point on the diaphragm edge facing the aphragm edge is defined as L, a point on the center line of the plate thickness of the corner of the lower member diagonally opposite 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, a polygonal element I43 formed by AB, BC, CA, a polygonal element I44 formed by AC, CF, FA, a polygonal element I45 formed by CF, FK, KC, a polygonal element I46 formed by CG, GK, KC, a polygonal element I47 formed by BC, CG, GB, a polygonal element I48 formed by BE, EG, GB, a polygonal element I49 formed by BD, DE, EB, a polygonal element I50 formed by DE, EH, HD, and a polygonal element I51 formed by EG, GH, HE, 7. The analytical modeling method for the out-of-plane bending rigidity of a diaphragm described above in 6, comprising a total of 18 polygonal elements: polygonal element I52 formed by FI, IK, KF; polygonal element I53 formed by FI, IL, 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, wherein each of the polygonal elements is rigid against bending forces and is connected by rotational springs at each boundary edge so as to be bendable.
[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, in which 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 bending rigidity of the through diaphragm using an analytical model set up by the analytical modeling method described in 2 above, 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 pipe, 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 pipe, and applying an equal upward load to the other end; calculating the sum of strain energies of the rotating spring associated with the displacement that occurs when the above-mentioned cases are performed; 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 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 analytical 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 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 pipe, 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 pipe, 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 at that time, 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 D-F-I is applied as a load acting on the analytical model, and an equivalent load acting upward on the flat plate portion of the upper member whose outer surface is aligned in a single plane is applied, 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, in which a downward load is applied 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 an equal upward load is applied to the corner of the lower member sandwiched between the two flat plate portions whose outer surfaces are aligned on the same plane, the sum of the strain energies of the rotating spring associated with the displacement that occurs at this time is calculated, and the out-of-plane bending stiffness of the through diaphragm is predicted based on the sum of the 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 using an analytical model set up by the analytical modeling method described in 7 above, in which a downward load acting on G and an upward load acting on the corner including F are applied as loads acting on the analytical model, and a displacement δ is generated by 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.

本発明にかかるダイアフラムの面外曲げ剛性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剛性を、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剛性を予測することができる。また、その予測方法により、必要な剛性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－ダイアフラム弾性ばね仕口を得ることができる。 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 or circular steel pipes of different dimensions with a through diaphragm, the out-of-plane bending stiffness of the diaphragm of the connected connection 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 connection can be obtained by 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剛性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。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 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。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; 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 showing a conventional beam-column joint structure in which a tapered tube is used as a joint panel. 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剛性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 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 another embodiment of the present invention, where (a) shows a plan view and (b) shows 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剛性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 rigidity of a diaphragm in a joint structure in which square steel pipes 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 Y-Y direction. 回転ばね理論を説明する模式図であって、（ａ）は平面図を表し、（ｂ）は正面図を表す。1A and 1B are schematic diagrams illustrating the rotational spring theory, in which FIG. 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. 2 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 is a detailed description of the embodiments of the present invention. Note that the drawings are schematic and may differ from the actual ones. The following embodiments are intended to exemplify equipment and methods for embodying the technical ideas of the present invention, and are not intended to specify the configuration as described below. In other words, the technical ideas 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、非特許文献１に記載の回転ばね理論に基づいて、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剛性を予測する。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。図６には、節点ｏ、ａ、ｂおよび節点ｏ、ｂ、ｃでそれぞれ構成された多角形要素Ｉ１とＩ２とを示す。Ｉ１とＩ２とは節点ｏ－ｂ間に挿入された回転ばね９で接続されている。この回転ばね９の剛性Ｋは、回転ばね９と節点ａ、ｃとのそれぞれの距離ｘ、ｙおよび回転ばね９の長さｌを用いて、下記数式１の（１）式のように表せる。 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 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. 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 nodes o and b. 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.

ここで、Ｄは板定数であり、ヤング係数Ｅ、多角形要素板厚ｔ、ポアソン比νを用いて下記数式２の（２）式のように求められる。 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 Equation 2 (2) below.

多角形要素Ｉ１およびＩ２のなす角すなわち回転ばねの回転角θは、各節点の直交座標をｏ（ｘ_０、ｙ_０、ｚ_０）と、ａ（ｘ_１、ｙ_１、ｚ_１）、ｂ（ｘ_２、ｙ_２、ｚ_２）およびｃ（ｘ_３、ｙ_３、ｚ_３）として以下のように求められる。
多角形要素Ｉ１およびＩ２の法線をｎ_Ａおよびｎ_Ｂとすると、その方向余弦ｎ_Ａ（ｌ_Ａ、ｍ_Ａ、ｎ_Ａ）およびｎ_Ｂ（ｌ_Ｂ、ｍ_Ｂ、ｎ_Ｂ）は、下記数式３および４の（３）式および（４）式で表される。 The angle between polygonal elements I1 and I2, i.e., the rotation angle θ of the rotational spring, can be determined 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 ).
If the normals of polygonal elements I1 and I2 are _nA and _nB , the direction cosines _nA ( _lA , _mA , _nA ) and _nB ( _lB , _mB , _nB ) are expressed by equations (3) and (4) of Equations 3 and 4 below.

ここで、上記式中の記号は下記数式５および６の（５）および（６）式で表される。 The symbols in the above formula are expressed by (5) and (6) in the following formulas 5 and 6.

回転ばねのベクトルの変形後の方向余弦Ｃ（ｌ_Ｃ、ｍ_Ｃ、ｎ_Ｃ）は、下記数式７の（７）式で表される。 The direction cosine C ( _lC , _mC , _nC ) of the vector of the rotational spring after deformation is expressed by Equation 7 (7) below.

回転ばねの回転角θについては下記数式８の（８）式の関係が成り立つ。 The relationship in equation 8 (8) below holds for the rotation angle θ of the rotating spring.

したがって、回転ばねの回転角θは下記数式９の（９）式で求められる。 Therefore, the rotation angle θ of the rotating spring can be calculated using the following formula (9):

右辺を展開すると、下記数式１０の（１０）式となる。 Expanding the right hand side gives us equation (10) below.

ここで、ｌ_Ｃは下記数式１１の（１１）式で表される。 Here, _lC is expressed by the following formula (11).

回転ばね９に蓄えられる歪エネルギーＵは下記数式１２の（１２）式のように求められる。 The strain energy U stored in the rotating spring 9 can be calculated using the following formula (12):

＜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の曲げ剛性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、多角形要素１０の節点Ａ～Ｓを以下のように定める。
ダイアフラム２の縁の一辺上の点をＡ、
下側部材３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に最も近い下側部材３の平板部の板厚中央線上の点をＣ、
Ｂに最も近い上側部材１の角部の板厚中央線上の点をＤ、
Ａを含むダイアフラム２縁に直交するダイアフラム２縁のうち、Ｂに最も近い一のダイアフラ２ム縁上の点をＥ、
Ａを含むダイアフラム２縁に直交する下側部材３の平板部のうち、Ｂに最も近い一の平板部の板厚中央線上の点をＦ、
Ａを含むダイアフラム２縁に直交する上側部材１の平板部のうち、Ｂに最も近い一の平板部の板厚中央線上の点をＧ、
上側部材１の内部の点をＨ、
Ｅに近い上側部材１の角部であってＤを含まない角部の板厚中央線上の点をＩ、
Ｅに近い下側部材３の角部であってＢを含まない角部の板厚中心線上の点をＪ、
Ａを含むダイアフラム２縁に対向するダイアフラム２の縁上の点をＫ、
Ｃを含む下側部材３の平板部に対向する下側部材３の平板部の板厚中央線上の点をＬ、
Ａに近い下側部材３の他の角部の板厚中央線上の点をＭ、
Ｍに最も近い上側部材１の角部の板厚中央線上の点をＮ、
Ａを含むダイアフラム２縁に直交するダイアフラム２縁のうち、他のダイアフラム２縁上の点をＯ、
Ａを含むダイアフラム２縁に直交する下側部材３の平板部のうち、他の平板部の板厚中央線上の点をＰ、
Ａを含むダイアフラム２縁に直交する上側部材１の平板部のうち、他の平板部の板厚中央線上の点をＱ、
Ｄを含む角部の対角位置にある上側部材１の角部の板厚中央線上の点をＲ、
Ｂを含む角部の対角位置にある下側部材３の角部の板厚中央線上の点をＳ
とする。
節点Ａ、Ｃ、Ｅ、Ｆ、Ｇ、Ｋ、Ｌ、Ｏ、ＰおよびＱは、各辺の中点であることが好ましい。節点Ｂ、Ｄ、Ｉ、Ｊ、Ｍ、Ｎ、ＲおよびＳは、各角部の板厚中央線をなす円弧の中点であることが好ましい。節点Ｈは、上側部材１の軸心であることが好ましい。 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 the bending rigidity of the through diaphragm 2 is predicted 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, "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 point on one side of the edge of the diaphragm 2 is A,
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 plate 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 member 1 closest to B is D,
Among the edges of the diaphragm 2 perpendicular to the edge of the diaphragm 2 including A, a point on the edge of the diaphragm 2 closest to B is designated as E.
Among the flat plate portions of the lower member 3 perpendicular to the edge of the diaphragm 2 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 1 perpendicular to the edge of the diaphragm 2 including A, the point on the plate thickness center line of the flat plate portion closest to B is designated as G,
A point inside the upper member 1 is H,
A point on the center line of the 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 thickness of the corner of the lower member 3 close to E and not including B is J,
A point on the edge of the diaphragm 2 opposite to the edge of the 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,
A point on the center line of the plate thickness of another 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 member 1 closest to M is N,
Among the edges of the diaphragm 2 perpendicular to the edge of the diaphragm 2 including A, a point on the other edge of the diaphragm 2 is designated as 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 defined as P,
Among the flat plate parts of the upper member 1 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 called Q,
A point on the center line of the thickness of the corner of the upper member 1 diagonally opposite the corner including D is R,
A point on the center line of the plate thickness of the corner of the lower member 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 midpoints of the sides. Nodes B, D, I, J, M, N, R, and S are preferably midpoints of arcs forming the center lines of the plate thickness of the corners. Node H is preferably the axis of the upper member 1.

回転ばね９を配置した辺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およびＲＳに蓄えられる歪エネルギーを求める。得られた回転ばねの歪エネルギーをもちいて全ダイアフラムにおける全回転ばねに蓄えられる歪エネルギーＵを計算すると、下記数式１３の（１３）式が得られる。 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.

したがって、カスティリアーノの定理からこれを変位δで偏微分することで上側部材１がダイアフラム２に作用する力Ｐ’と変位δの関係が下記数式１４の（１４）式のように求められる。Ｋｍは剛体－バネモデルによる曲げ剛性を表す。 Therefore, by partially differentiating this with respect to the displacement δ using 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.

ここで、ダイアフラム２の面外変形角θ_ｄは下記数式１５の（１５）式で表される。 Here, the out-of-plane deformation angle θ _d of the diaphragm 2 is expressed by the following formula (15).

上側部材１に作用する曲げモーメントＭ_ｃｕは上側部材１の対向する平板部の板厚中央間距離の半分をＢ_１とすると、下記数式１６の（１６）式で求められる。 The bending moment M _cu acting on the upper member 1 can be calculated by the following formula (16), where B ₁ is half the center distance between the plate thicknesses of the opposing flat plate portions of the upper member 1.

（１４）式と（１５）式とを用いて、下記数式１７の（１７）式が導かれる。 Using equations (14) and (15), we derive equation (17) in the following equation 17.

すなわち、本実施形態のダイアフラム２の面外曲げ剛性Ｋｄは下記数式１８の（１８）式で与えられる。 In other words, the out-of-plane bending stiffness Kd of the diaphragm 2 in this embodiment is given by the following formula (18):

＜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の曲げ剛性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、多角形要素１０の節点Ａ～Ｌを以下のように定める。
外面を一平面上に揃えた平板部に直交するダイアフラム２縁の一辺上の点をＡ、
Ａに最も近い下側部材３の平板部の板厚中央線上の点をＢ、
下側部材３の角部であってＡに近い２つのうち、外面を一平面上に揃えた平板部から遠い方の角部の板厚中央線上の点をＣ、
上側部材１の角部であってＡに近い２つのうち、外面を一平面上に揃えた平板部から遠い方の角部の板厚中央線上の点をＤ、
上側部材１の内部の点をＥ、
外面を一平面上に揃えた平板部に対向する下側部材３の平板部の板厚中央線上の点をＦ、
外面を一平面上に揃えた平板部に対向する上側部材１の平板部の板厚中央線上の点をＧ、
Ｇに最も近いダイアフラム２縁上の点をＨ、
Ｈに近い上側部材１の角部であってＤを含まない角部の板厚中央線上の点をＩ、
Ｈに近い下側部材３の角部であってＢを含まない角部の板厚中央線上の点をＪ、
Ｂを含む下側部材３の平板部に対向する下側部材３の平板部の板厚中央線上の点をＫ、
Ａを含むダイアフラム２縁に対向するダイアフラム２縁上の点をＬ
とする。
節点ＡおよびＬは、Ｆを含む上側部材１の平板部の板厚中央線の延長線とダイアフラム２縁との交点であることが好ましい。節点ＢおよびＫは、上側部材１の軸心をとおり、上下部材の外面をそろえた平面に平行な線と、下側部材３の平板部の板厚中央線との交点であることが好ましい。節点Ｃ、Ｄ、ＩおよびＪは、各角部の板厚中央線をなす円弧の中点であることが好ましい。節点Ｅは、上側部材１の軸心であることが好ましい。節点Ｆ、ＧおよびＨは、各辺の中点であることが好ましい。 Second Embodiment
As a second embodiment, a lower member 3 made of a square steel pipe and an upper member 1 made of a square steel pipe with a side length shorter than that of the lower member 3 as shown in Figure 4 are used, and the outer surface of one flat portion of the lower member 3 and the outer surface of one flat portion of the upper member 1 are aligned on the same plane, resulting in a so-called unidirectional eccentric arrangement, and the 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.
A is a point on one side of the edge of the diaphragm 2 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 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 single plane is called D.
A point inside 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,
A point on the center line of the thickness of the flat plate portion of the upper member 1 facing the flat plate portion whose outer surface is aligned on a plane is G,
The point on the edge of the diaphragm 2 closest to G is H.
A point on the center line of the 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 the diaphragm 2 opposite the edge of the 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, with 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 a plane that aligns the outer surfaces of the upper and lower members, with 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.

回転ばね９を配置した辺ＢＣ、ＢＤ、ＣＤ、ＣＧ、ＤＦ、ＥＦ、ＤＥ、ＦＧ、ＤＧ、ＫＪ、ＫＩ、ＩＪ、ＩＧ、ＩＥ、ＩＦ、ＪＧに蓄えられる歪エネルギーを求める。得られた回転ばねの歪エネルギーを用いて全ダイアフラムにおける全回転ばねに蓄えられる歪エネルギーＵを計算すると、下記数式１９の（１９）式が得られる。 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 calculated. 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.

カスティリアーノの定理からこれを変位δで偏微分することで上側部材１がダイアフラム２に作用する力Ｐ’と変位δの関係が下記数式２０の（２０）式で求められる。Ｋｍは剛体－バネモデルによる曲げ剛性を表す。 By partially differentiating this with respect to the displacement δ using 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.

ここで、ダイアフラム２の面外変形角θ_ｄは下記数式２１の（２１）式で表される。 Here, the out-of-plane deformation angle θ _d of the diaphragm 2 is expressed by the following formula (21).

上側部材１に作用する曲げモーメントＭ_ｃｕは上側部材１の対向する平板部の板厚中央間距離の半分をＢ_１とすると、下記数式２２の（２２）式で求められる。 The bending moment M _cu acting on the upper member 1 can be calculated by the following formula (22) when half the center distance between the plate thicknesses of the opposing flat plate portions of the upper member 1 is defined as B ₁ .

（２０）式と（２１）式とを用いて、下記数式２３の（２３）式が導かれる。 Using equations (20) and (21), we derive equation (23) in the following equation 23.

すなわち、本実施形態のダイアフラム２の面外曲げ剛性Ｋｄは下記数式２４の（２４）式で与えられる。 In other words, the out-of-plane bending stiffness Kd of the diaphragm 2 in this embodiment is given by the following formula (24):

＜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の曲げ剛性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、多角形要素１０の節点Ａ～Ｎを以下のように定める。
上下部材１、３の外面が同一平面上に揃えられた２つの平板部の一方に最も近いダイアフラム２縁上の点をＡ、
Ａに近い下側部材３の角部であって、上下部材１、３の外面が同一平面上に揃えられた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Ｂ、
Ａに近い上側部材１の角部であって、上下部材１、３の外面が同一平面上に揃えられた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Ｃ、
Ａを含むダイアフラム２縁に直交するダイアフラム２縁のうち、上下部材１、３の外面が同一平面上に揃えられた２つの平板部から遠い方のダイアフラム２縁上の点をＤ、
Ｄに最も近い下側部材３の平板部の板厚中央線上の点をＥ、
上下部材１、３の外面が同一平面上に揃えられた２つの平板部に挟まれた下側部材３の角部の板厚中央線上の点をＦ、
下側部材３のＦを含む角部と対角位置にある、上側部材１の角部の板厚中央線をなす円弧の中心点をＧ、
下側部材３のＦを含む角部と対角位置にある下側部材３の角部の板厚中央線上の点をＨ、
上側部材１のＣを含む角部と対角位置にある上側部材１の角部の板厚中央線線上の点をＩ、
上側部材１の平板部の外面と同一平面上にない外面を有する下側部材３の平板部のうちＥを含まない平板部の板厚中央線上の点をＪ、
上側部材１の内部の点をＫ、
Ｄを含むダイアフラム２縁に対向するダイアフラム２縁上の点をＬ、
下側部材３のＢを含む角部と対角位置にある下側部材３の角部の板厚中央線上の点をＭ、
Ａを含むダイアフラム２縁に対向するダイアフラム２縁上の点をＮ
とする。
節点ＡおよびＬは、上下部材１、３の外面が同一平面上に揃えられた２つの平板部に挟まれた角部をとおる対角線に直交する上側部材１の対角線とダイアフラム２縁との交点であることが好ましい。節点Ｂ、Ｃ、Ｆ、Ｈ、ＩおよびＭは、各角部の板厚中央線をなす円弧の中点であることが好ましい。節点Ｄ、Ｅ、ＪおよびＮは、各辺の中点であることが好ましい。節点Ｋは、上側部材１の軸心であることが好ましい。 Third Embodiment
As a third embodiment, a lower member 3 made of a square steel pipe as shown in Figure 5 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, 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 up 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 portions where the outer surfaces of the upper and lower members 1 and 3 are 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 3 close to A, which is not sandwiched between two flat plate portions 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 portions 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, a point on the edge of the diaphragm 2 farther from the two flat plate portions where the outer surfaces of the upper and lower members 1 and 3 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 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 portions, and a 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 including F of the lower member 3, is G.
A point on the center line of the thickness of the corner of the lower member 3 diagonally opposite to the corner including F of the lower member 3 is designated as H.
A 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,
A point inside the upper member 1 is K,
A point on the edge of the diaphragm 2 opposite to the edge of the diaphragm 2 including D is L,
A point on the center line of the thickness of the corner of the lower member 3 diagonally opposite to the corner including B of the lower member 3 is designated as M.
A point on the edge of the diaphragm 2 opposite to the edge of the diaphragm 2 containing A is called 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 portions 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.

回転ばね９を配置した辺ＢＣ、ＢＥ、ＢＧ、ＣＦ、ＣＧ、ＣＫ、ＥＧ、ＥＨ、ＦＫ、ＧＨ、ＧＫ、ＭＩ、ＭＮ、ＭＧ、ＩＦ、ＩＧ、ＩＫ、ＪＧ、ＪＨおよびＪＭに蓄えられる歪エネルギーを求める。得られた回転ばねの歪エネルギーを用いて全ダイアフラムにおける全回転ばねに蓄えられる歪エネルギーＵを計算すると、対称性から、下記数式２５の（２５）式が得られる。 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 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, the following formula (25) is obtained due to symmetry.

カスティリアーノの定理からこれを変位δで偏微分することで上側部材１がダイアフラム２に作用する力Ｐ’と変位δの関係が下記数式２６の（２６）式で求められる。Ｋｍは剛体－バネモデルによる曲げ剛性を表す。 By partially differentiating this with respect to the displacement δ using 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.

ここで、ＧＫ＝ａ_０、ＦＫ＝ｂ_０、ＦＨ＝２ｃ_０とすると、ダイアフラム２の面外変形角θ_ｄは下記数式２７の（２７）式で表される。 Here, if GK=a ₀ , FK=b ₀ , and FH=2c ₀ , the out-of-plane deformation angle θ _d of the diaphragm 2 is expressed by the following equation (27).

上側部材１に作用する曲げモーメントＭ_ｃｕは、下記数式２８の（２８）式で求められる。 The bending moment M _cu acting on the upper member 1 can be calculated by the following formula (28).

（２６）式と（２７）式とを用いて、下記数式２９の（２９）式が導かれる。 Using equations (26) and (27), we derive equation (29) in the following equation 29.

すなわち、本実施形態のダイアフラム２の面外曲げ剛性Ｋｄは下記数式３０の（３０）式で与えられる。 In other words, the out-of-plane bending stiffness Kd of the diaphragm 2 in this embodiment is given by the following formula (30):

上記実施例では、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 square steel pipes and circular steel pipes can be combined 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 taking nodes on the central plane of the circular steel pipe plate thickness at 45° central angles in the circumferential direction.

図７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２の鋼材規格はＴＭＣＰ３２５Ｃを用い、ダイアフラムは、下側部材の辺長に６０ｍｍ加算した辺長の正方形とした。 As shown in Figure 7, an analysis was carried out using the finite element method (FEM) to apply a monotonically loaded force 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 are joined 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, the upper member 1 used square steel pipes of □-350 x 350 x 12 (BCR295) and □-850 x 850 x 40 (BCP325), and the lower member 3 used square steel pipes of □-500 x 500 x 19 (BCR295) and □-1000 x 1000 x 40 (BCP325). Here, the standard values for square steel pipes represent □-side length x side length x plate thickness, BCR represents cold roll-formed square steel pipes, BCP represents 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 the upper member 1 and the lower member 3 was set to 150 mm. The plate thicknesses of the diaphragm 2 were set to 100 mm, 60 mm, and 45 mm, respectively. The steel standard for the diaphragm 2 was TMCP325C, and the diaphragm was a square with a side length 60 mm added to the side length of the lower member.

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剛性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剛性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 formulas for each of the above embodiments under the conditions in Table 1, and 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 stiffness evaluation formulas of the above embodiments, the diaphragm out-of-plane bending stiffness obtained from the FEM analysis results can be evaluated with high accuracy.

本発明のダイアフラムの面外曲げ剛性の予測方法によれば、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剛性を、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剛性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－ダイアフラム弾性ばね仕口を得ることができるので産業上有用である。 According to the method for predicting the out-of-plane bending stiffness of a diaphragm of the present invention, when joining 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 joined 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 joint can be obtained using a diaphragm of that plate thickness, which is 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回転ばね
１０多角形要素 1 Upper member (upper pillar)
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 tube 9 Rotational spring 10 Polygonal element

Claims

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 located outside 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.

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 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.

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 so as 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.

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 rigid against bending forces and is connected at each boundary edge by a rotational spring so as to be bendable.

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 regarded as rigid against bending forces.

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 by rotational springs at each boundary edge so as to be bendable.

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.
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.

3. The analytical model 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.

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.

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.

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.

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.

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.

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.