JP3868849B2 - Bending pipe stress evaluation method, stress evaluation apparatus, program, storage medium - Google Patents

Description

ただし、±の符号における＋（プラス）は管の外表面における応力、−（マイナス）は内表面における応力を計算するときに用いる。
【００３６】
また、ｄ_ｎもｋ_ｐと同様λと内圧Ｐの関数となる。ｎを何次の項まで採ればよいかについては、λの値によって異なり、λが小さくなるほど高次の項まで必要となるが、λ＝０．１程度であれば３次までで十分とされている。この場合、ｄ_ｎ、ｋ_ｐは、次のように表される。
【００３７】
ｄ_１＝３（Ｃ２Ｃ３−１１０．２５）／｛６．２５Ｃ３−Ｃ１（Ｃ２Ｃ３―１１０．２５）｝、
ｄ_２＝７．５Ｃ３／｛６．２５Ｃ３−Ｃ１（Ｃ２Ｃ３―１１０．２５）｝、
ｄ_３＝７８．７５／｛６．２５Ｃ３−Ｃ１（Ｃ２Ｃ３―１１０．２５）｝、
但し、
Ψ＝ＰＲ^２／Ｅｒｔ（Ｅ：弾性係数）、
Ｃ１＝５＋６λ^２＋２４Ψ、
Ｃ２＝１７＋６００λ^２＋４８０Ψ、
Ｃ３＝３７＋７３５０λ^２＋２５２０Ψ、
とした。
【００３８】
ｋ_ｐ＝１／（ｃ４＋ｃ５＋ｃ６＋ｃ７）
但し、
ｃ４＝１＋３ｄ_１＋２．２５ｄ_１ ^２、
ｃ５＝０．２５（ｄ_１ ^２＋３４ｄ_２ ^２＋７４ｄ_３ ^２−１０ｄ_１ｄ_２−４２ｄ_２ｄ_３）、
ｃ６＝λ^２／１２×（３６ｄ_１ ^２＋３６００ｄ_２ ^２＋４４１０ｄ_３ ^２）、
ｃ７＝Ψ（１２ｄ_１ ^２＋２４０ｄ_２ ^２＋１２６０ｄ_３ ^２）、
とした。
【００３９】
また、管に面内曲げモーメントＭ_ｉ、面外曲げモーメントＭ_ｏが作用したときの管の半径変化量をそれぞれｅ_ｉ、ｅ_ｏとし、断面方向変位について式［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ ＆ Ｇｅｏｒｇｅの理論式）を展開して、Ｍ_ｉ、Ｍ_ｏとｅ_ｉ、ｅ_ｏとの関係を求めると、
Ｍ_ｉ＝η_１ＥＩ／ｋ_ｐＲ×ｅ_ｉ ・・・［３−１］
Ｍ_ｏ＝η_２ＥＩ／ｋ_ｐＲ×ｅ_ｏ ・・・［３−２］
である。
【００４０】
ここで、
η_１＝１／｛ｒ（２ｄ_１＋４ｄ_２＋６ｄ_３）｝
η_２＝１／｛ｒ（２ｄ_１−６ｄ_３）｝
ｅ_ｉ＝ｒ_ｉ’−ｒ_ｉ０
ｅ_ｏ＝ｒ_ｏ’−ｒ_ｏ０
（ｒ_ｉ０：外力が作用する前の周方向の角度０°の半径）
（ｒ_ｉ’：外力が作用した後の周方向の角度０°の半径）
（ｒ_ｏ０：外力が作用する前の周方向の角度４５°の半径）
（ｒ_ｏ’：外力が作用した後の周方向の角度４５°の半径）
である。
【００４１】
尚、２×ｅ_ｉは、周方向の角度０°方向における扁平量（最大外径変化量、最大内径変化量、最大断面変形、最大扁平量）に相当する。
また、２×ｅ_ｏは、周方向の角度４５°方向における扁平量（最大外径変化量、最大内径変化量、最大断面変形、最大扁平量）に相当する。
【００４２】
面内曲げ、面外曲げにおける扁平量Ｗ_ｉ（φ）、Ｗ_ｏ（φ）は、それぞれ、次のように表すことができる。尚、次式に示す扁平量Ｗ_ｉ（φ）、Ｗ_ｏ（φ）は、曲管の直径の変化量（半径変化量×２）である。
Ｗ_ｉ（φ）＝２×η_１｛２ｄ_１ｃｏｓ（２φ）＋４ｄ_２ｃｏｓ（４φ）＋６ｄ_３ｃｏｓ（６φ）｝ ・・・［４−１］
Ｗ_ｏ（φ）＝２×η_２｛２ｄ_１ｓｉｎ（２φ）＋４ｄ_２ｓｉｎ（４φ）＋６ｄ_３ｓｉｎ（６φ）｝ ・・・［４−２］
【００４３】
図３は、曲管に、面内曲げモーメント、面外曲げモーメント、これらの合成モーメントが作用した場合の扁平量（外径変化量）と周方向の角度との関係を示す図である。縦軸は、扁平量（外径変化量）を示し、横軸は、周方向の角度を示す。
【００４４】
曲線３０１は、曲管に面内曲げモーメントが作用した場合の扁平量（外径変化量）と周方向の角度との関係を示す。
曲線３０２は、曲管に面外曲げモーメントが作用した場合の扁平量（外径変化量）と周方向の角度との関係を示す。
曲線３０３は、曲管に合成モーメントが作用した場合の扁平量（外径変化量）と周方向の角度との関係を示す。
曲線３０１、曲線３０２、曲線３０３は、式［４−１］、式［４−２］からも分かるように、周期１８０°のグラフとなる。
【００４５】
図３の曲線３０１を参照すると、面内曲げにおける扁平量（外径変化量）は、角度０°／角度１８０°方向で最大であり、角度９０°／角度−９０°方向では、角度０°／角度１８０°方向の扁平量（外径変化量）と比較して符号が反対であり小さな値となる。また、面内曲げにおける扁平量（外径変化量）は、角度４５°、角度−４５°、角度１３５°、角度−１３５°ではほぼ０となる。
【００４６】
図３の曲線３０２を参照すると、面外曲げにおける扁平量（外径変化量）は、角度４５°／角度−１３５°方向で最大であり、角度１３５°／角度−４５°方向では、角度４５°／角度−１３５°方向の扁平量（外径変化量）と比較して符号が反対である。また、面外曲げにおける扁平量（外径変化量）は、角度０°、角度１８０°、角度９０°、角度−９０°ではほぼ０となる。
【００４７】
従って、面内曲げ及び面外曲げの両方の曲げが作用した状態であっても、角度０°／角度１８０°方向の扁平量（外径変化量）２ｅ_ｉを測定すれば、式［３−１］により、面内曲げモーメントＭ_ｉを算出可能である。
また、面内曲げ及び面外曲げの両方の曲げが作用した状態であっても、角度４５°／角度−１３５°方向または角度１３５°／角度−４５°方向の扁平量（外径変化量）２ｅ_ｏを測定すれば、式［３−２］により、面外曲げモーメントＭ_ｏを算出可能である。
【００４８】
Ｍ_ｉ、Ｍ_ｏが得られれば、式［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ＆ Ｇｅｏｒｇｅの理論式）により断面の任意の位置での応力（σ_ｉＬ、σ_ｉＣ、σ_ｏＬ、σ_ｏＣ）を計算することができる。
【００４９】
図４は、扁平量（外径変化量）と最大周方向応力との関係を測定するための実験の概要を模式的に示す図である。試験体である管４０１は、曲管４０２及び直管４０３等から構成される。
【００５０】
曲管４０２としてモナカエルボ（ＡＰＩ−Ｘ６０規格、肉厚ｔ＝１２．７ｍｍ、外径２ｒ＝６１０ｍｍ、曲率半径Ｒ＝１．５ＤＲ、λ＝０．１３８）を用いた。これに直管４０３としての袖管を溶接し、一方をフランジを介して定盤に取り付け、他方のフランジを油圧ジャッキで下方向４０５、上方向４０６に荷重を負荷した。すなわち、曲管４０２に対して面内曲げモーメントを作用させた。荷重点にはロードセル（図示せず）を設け、負荷荷重を測定可能とした。
【００５１】
扁平量（外径変化量）の測定位置はエルボの中央断面４０４とし、ノギスを用いて２方向（０°／１８０°方向、９０°／２７０°（−９０°）方向）について測定した。また、中央断面４０４の周上には検証のため２軸歪ゲージ（図示せず）を周方向の角度にして１５度ピッチで取り付け、応力測定を行った。
【００５２】
図５は、上記の実験結果より得られた、扁平量（外径変化量）と円周方向の最大応力との関係を示す図である。縦軸は、最大周方向応力を示し、横軸は、扁平量（外径変化量）を示す。尚、最大周方向応力は、中央断面４０４の周上に設けられた２軸歪ゲージにより測定された周方向の応力のうち最大のものである。
「○」印（図５）の各点は、０°／１８０°方向に関する測定値を示し、「□」印（図５）の各点は、９０°／２７０°（−９０°）方向に関する測定値を示す。
【００５３】
直線５０１は、０°／１８０°方向における、扁平量（外径変化量）と円周方向の最大応力との関係を示す。
直線５０２は、９０°／２７０°（−９０°）方向における、扁平量（外径変化量）と円周方向の最大応力との関係を示す。
直線５０１、直線５０２が示すように、０°／１８０°方向、９０°／２７０°（−９０°）方向のいずれに関しても、扁平量（外径変化量）と円周方向最大応力との間には、直線性すなわち比例関係がみられる。
【００５４】
上記の実験で用いたモナカエルボは、２つ割のものを縦（管軸方向）に溶接（シーム溶接等）して作られていることから、０°／１８０°方向の方が９０°／２７０°（−９０°）方向よりも変形し易い。また、図３について前述したように、面内曲げモーメントにおいては、理論的にも０°／１８０°方向の扁平量（外径変化量）の方が９０°／２７０°（−９０°）方向より大きくなる。
【００５５】
このように扁平量（外径変化量）には異方性がみられるが、純粋に縦シームの存在による影響を分離するのは困難である。従って、面内曲げモーメントに係る応力評価は、縦シームの影響の少ない０°／１８０°方向の扁平量（外径変化量）を測定することにより行うことが望ましい。
【００５６】
尚、当該モナカエルボの材料の降伏応力は約４１０ＭＰａであるが、上述したように、弾性領域では、扁平量（外径変化量）と円周方向最大応力との間に直線性（比例関係）がみられる。
また、上方向４０６（図５において最大周方向応力が負の方向）についてみると、降伏応力の１．５倍程度の範囲（塑性領域）まで、扁平量（外径変化量）と円周方向最大応力との間に直線性（比例関係）がみられる。
【００５７】
次に、上述した応力評価方法と上記の実験結果との比較について述べる。図６は、周方向及び軸方向の応力分布に関する解析値（上述の応力評価方法による解析値）及び実験値を示す図である。縦軸は、応力を示し、横軸は、周方向の角度を示す。
【００５８】
図５に示す実験結果において、０°／１８０°方向の扁平量（外径変化量）が８ｍｍの場合（図５：点５０３）、最大周方向応力は、４００ＭＰａ弱程度となる。
この０°／１８０°方向の扁平量（外径変化量）８ｍｍに対するモーメントは［３−１］式より、Ｍ_ｉ＝１．７×１０^５Ｎ・ｍとなる。このＭ_ｉを式［１−２］、式［１−１］に代入し、応力分布を計算すると図６の実線６０１（周方向解析値）、実線６０２（軸方向解析値）が得られる。
【００５９】
また、この０°／１８０°方向の扁平量（外径変化量）８ｍｍにおいて、中央断面４０４の周上に１５度ピッチで設けた２軸歪ゲージにより測定した、周方向応力の測定値を「●」印（図６）の各点（周方向実験値）により示し、軸方向応力の測定値を「□」印（図６）の各点（軸方向実験値）により示した。
【００６０】
周方向の応力に関しては、実験値と解析値のピーク位置に若干ずれがみられるが、応力値はほぼ一致している。軸方向の応力に関しては、実験値と解析値のピーク位置は一致するが、応力値には若干のずれがみられる。尚、これらの若干のずれに関しては、実用上問題ないものである。
以上の実験値と解析値の比較及び考察により、ノギスで得られる程度の精度の扁平量（外径変化量）測定値であっても、実用的に十分な精度の応力推定が可能であるといえる。
【００６１】
以上説明したように、本発明の実施の形態によれば、（１）０°／１８０°方向、（２）４５°／−１３５°方向または−４５°／１３５°方向の２方向について、曲管の扁平量（外径変化量）をノギス等の一般的な測定具により測定することにより、実用上十分な精度で当該曲管に生じる応力分布の推定を行うことができる。
【００６２】
曲管を採用する目的の１つは、通常配管にフレキシビリティを付与し、その変形によって応力を低減させることにある。そのため３次元配管となることが多い。このことは、荷重として面内曲げモーメント及び面外曲げモーメントとが同時に作用する確率が高くなることを示している。面内曲げモーメントと面外曲げモーメントの両方のモーメントが作用した状態での断面変形は相当複雑なものとなる。
【００６３】
しかしながら、図３に関して説明したように、面内曲げモーメント作用時の断面変形は、０°／１８０°方向において最大であり、４５°／−１３５°方向及び−４５°／１３５°方向においては理論上は殆ど０となる。一方、面外曲げモーメント作用時の断面変形は、４５°／−１３５°方向または−４５°／１３５°方向において最大であり、０°／１８０°方向においては理論上は殆ど０となる。
【００６４】
これらのことから、（１）０°／１８０°方向の扁平量（外径変化量）から式［３−１］により面内曲げモーメント（Ｍ_ｉ）を算出し、（２）４５°／−１３５°方向または−４５°／１３５°方向の扁平量（外径変化量）から式［３−２］により面外曲げモーメント（Ｍ_ｏ）を算出することができる。
【００６５】
すなわち、（１）０°／１８０°方向の扁平量（外径変化量）、（２）４５°／−１３５°方向または−４５°／１３５°方向の２方向の扁平量（外径変化量）を測定することにより、面内曲げモーメント（Ｍ_ｉ）と面外曲げモーメント（Ｍ_ｏ）とを分離して算出することができる。そして、これらの面内曲げモーメント（Ｍ_ｉ）と面外曲げモーメント（Ｍ_ｏ）から、式［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ ＆ Ｇｅｏｒｇｅの理論式）により、面内曲げモーメントおよび面外曲げモーメントの両方向の曲げモーメントによる応力分布を算出することができる。
【００６６】
設計で採用しているＡＮＳＩ Ｂ３１．８に則した応力（σ）については、面内曲げモーメント（Ｍ_ｉ）及び面外曲げモーメント（Ｍ_ｏ）から合成モーメント（Ｍ）を求め（式［５−１］参照）、断面係数（Ｚ）で除したものに、面内曲げモーメントによる応力集中係数（ｉ）を乗じて（面内曲げモーメントと面外曲げモーメントでは、前者のほうが約１７％ほど大きいため、安全側の評価となる）、外径変化（扁平）が生じている曲管の応力（σ）とする（式［５−２］参照）。
Ｍ＝（Ｍ_ｉ ^２＋Ｍ_ｏ ^２）^{（１／２）} ・・・［５−１］
σ＝Ｍ・ｉ／Ｚ ・・・［５−２］
【００６７】
また、上記の応力評価手法は、非破壊により、直接曲管そのものの応力を評価することができる。さらに、圧力を下げる等の措置を必要とせず、供用状態、使用状態において、応力評価、応力推定を行うことができる。従って、曲管の応力評価を実施するに当たって、機具の投入等、特別の措置を講ずる必要もない。
【００６８】
また、曲管の中央断面における２方向の扁平量（外径変化量）を測るのみで応力評価、応力診断を行うことが可能であり、測定のために熟練者を必要としないので、磁歪法等に比較して費用的負担を軽減することができる。
【００６９】
また、扁平化が曲管に応力を発生させるというモードが分かっていることから、応力評価結果の信頼性が高い。すなわち、上記、実験値と解析値との比較、考察において説明したところであるが、本実施の形態に示した応力評価は、実用上十分な精度を有する。
さらに、沈下等の変形モードが明確なものばかりでなく、熱応力等、諸々の外力が作用した状態における応力推定にも用いることができる。
【００７０】
また、扁平量に関しては、ノギス等の測定具により曲管の外径変化量を測定したが、ピグ等の測定具、検査具により曲管の内径変化量等を測定するようにしてもよい。
【００７１】
次に、図７を参照しながら、上述した応力評価方法に係る応力評価装置について説明する。
上記の式［１−１］〜式［５−２］及びその他の計算式等をコンピュータに登録、記録することで、当該コンピュータは、測定した曲管の扁平量（外径変化量、内径変化量等）やその他の必要数値が入力されると、曲管の応力評価、応力分布の算出を行うことができる。
【００７２】
図７は、曲管の応力評価装置としてのコンピュータが実行する処理を示すフローチャートである。
コンピュータに曲管の外径または内径の初期値を入力する（ステップ７０１）。この初期値は、外力による断面変形を受けていない状態（製作時、設置時等）の曲管の外径、内径等である。
経年後、ノギス等により計測した曲管の外径またはピグ等により計測した曲管の内径を入力する（ステップ７０２）。
【００７３】
コンピュータは、曲管の扁平量（外径変化量または内径変化量）を求める（ステップ７０３）。尚、（扁平量）＝（ステップ７０２において入力された外径または内径）−（ステップ７０１において入力された外径または内径の初期値）である。
コンピュータは、曲管の扁平量から式［３−１］、式［３−２］により、面内曲げモーメントＭ_ｉ及び面外曲げモーメントＭ_ｏを算出する（ステップ７０４）。
コンピュータは、Ｍ_ｉ、Ｍ_ｏから式［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ ＆ Ｇｅｏｒｇｅの理論式）により、σ_ｉＬ（φ）、σ_ｉＣ（φ）、σ_ｏＬ（φ）、σ_ｏＣ（φ）を算出し、応力評価を行う（ステップ７０５）。
【００７４】
以上の過程を経て、応力評価装置としてのコンピュータは、測定した曲管の扁平量（外径変化量、内径変化量等）やその他の必要数値が入力されると、曲管の応力評価、応力分布の算出を行うことができる。
【００７５】
尚、上記の応力評価装置としてのコンピュータを応力評価サーバとしてインターネット等のネットワークに接続し、端末装置（パーソナルコンピュータ、情報携帯端末、携帯電話等）がネットワークを介してこのサーバにアクセスできるようにすることもできる。
【００７６】
この場合、端末装置からネットワークを介して曲管の外径又は内径の初期値を応力評価サーバに入力（ステップ７０１）したり、経年後の外径又は内径の測定値をネットワークを介して応力評価サーバに入力（ステップ７０２）することができる。応力評価サーバは、曲管の扁平量、面内曲げモーメント、面外曲げモーメント、応力分布等を算出（ステップ７０３〜ステップ７０５）し、その算出結果を端末装置にネットワークを介して送信することができる。また、応力評価サーバは、入力データ及び算出結果をデータベースとして記録、管理し、応力評価サーバ自身あるいは端末装置が必要に応じて当該データベースを利用できるようにしてもよい。
【００７７】
また、このコンピュータ（上記の応力評価サーバ、端末装置等を含む）の機能は、すべてソフトウェア、コンピュータプログラムによって実現することが可能である。このため、必要なソフトウェア、コンピュータプログラムは、ネットワークを介して、あるいは、プログラムを記録したＣＤ−ＲＯＭ、ＤＶＤ−ＲＯＭなどの記録媒体によって、流通させることが可能である。
【００７８】
次に、図８を参照しながら、前述の応力評価方法、応力評価装置等を用いた管のメンテナンス及び補修に関して説明する。図８は、管８０２の応力解放方法の概要図を示す。地盤８０１には管８０２が埋設されている。この管８０２の任意の点（曲管部等）について、前述の実施の形態に示す方法で応力を算出して応力解放の必要性を判定し、応力解放部８０４を決定する。
【００７９】
応力解放部８０４の下部の掘削部８０５の地盤を掘削し、管８０２の応力解放部８０４を応力解放部８０３の位置に移動させる。そして、掘削部８０５を再度埋め立て、管８０２の位置を補修する。
【００８０】
次に、図９を参照しながら、前述の応力評価方法、応力評価装置等を用いた管のメンテナンス及び補修に関して説明する。図９は、管９０２の応力解放方法の概要図を示す。地盤９０１には管９０２が埋設されている。この管９０２の任意の点（曲管部等）について、前述の実施の形態に示す方法で応力を算出して応力解放の必要性を判定し、応力解放部９０３を決定する。応力解放部９０３の両端付近を切断し、応力解放部９０３の中央部分を除去する。そして、切断部９０４と切断部９０５を接合し、管９０２の位置を補修する。
【００８１】
図８及び図９に関して説明したように、本発明の実施の形態に係る応力評価方法、応力評価装置等を用いることにより、現場で簡便に任意の点での応力を算出し、管のメンテナンスや補修を行うことができる。
【００８２】
以上、添付図面を参照しながら、本発明にかかる曲管の応力評価方法、応力評価装置等の好適な実施形態について説明したが、本発明はかかる例に限定されない。当業者であれば、本願で開示した技術的思想の範疇内において、各種の変更例または修正例に想到し得ることは明らかであり、それらについても当然に本発明の技術的範囲に属するものと了解される。
【００８３】
【発明の効果】
以上説明したように、本発明によれば、管路を構成する曲管に発生する応力を簡便に精度よく算出することを可能とする曲管の応力評価方法、応力評価装置等を提供することができる。
【図面の簡単な説明】
【図１】 曲管の斜視図
【図２】 曲管の断面図
【図３】 曲管に、面内曲げモーメント、面外曲げモーメント、これらの合成モーメントが作用した場合の扁平量（外径変化量）と周方向の角度との関係を示す図
【図４】 扁平量（外径変化量）と最大周方向応力との関係を測定するための実験の概要を模式的に示す図
【図５】 扁平量（外径変化量）と円周方向の最大応力との関係を示す図
【図６】 周方向及び軸方向の応力分布に関する解析値及び実験値を示す図
【図７】 曲管の応力評価装置としてのコンピュータが実行する処理を示すフローチャート
【図８】 管のメンテナンス及び補修に関する説明図
【図９】 管のメンテナンス及び補修に関する説明図
【符号の説明】
１０１………曲管
１０２………管軸
４０１………管
４０２………曲管
４０３………直管
４０４………中央断面[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a stress evaluation method for a pipe, a stress evaluation apparatus, and the like. Specifically, the present invention relates to a stress evaluation method, a stress evaluation apparatus, and the like in a curved pipe portion that constitutes a pipe line.
[0002]
[Prior art]
In general, when laying pipes (line pipes) that supply gas, etc., stress is generated in the pipes due to external forces due to ground subsidence, etc., but in order to absorb displacement due to external forces before and after the common grooves and abutments A curved pipe is often used. In order to safely maintain and manage the pipeline, it is important to know where the maximum stress occurs on the pipeline. In addition, since the maximum stress is usually generated in the bent pipe portion, stress evaluation in the bent pipe portion is particularly important. Since the pipe line is in service and the stress evaluation described above is based on non-destructive diagnosis, it is difficult to use a measurement method using a strain gauge.
[0003]
Conventionally, the following methods are used for stress evaluation of pipes such as bent pipes. First, subsidence measurement and leveling are conducted at a plurality of measurement points. The amount of settlement is measured with a settlement bar installed in the buried part, and the leveling is carried out at a measurement point provided in the joint premises support part. Next, a finite element method (FEM) model considering the shape of the pipe is created. Then, the measured value of subsidence amount and the measured value of leveling measure are input to the finite element method model as the deformation amount of the pipe, and the analysis is performed. The stress evaluation of the bent pipe portion is performed from the analysis result.
[0004]
Japanese Patent Publication No. 7-62636 and Japanese Patent Publication No. 7-69226 disclose a technique (magnetostriction method) for evaluating the stress of a pipe line using a magnetic anisotropy sensor.
[0005]
The method according to Japanese Examined Patent Publication No. 7-62636 is based on a material mechanical evaluation of the stress generated on the surface of the pipe when a moment acts on the straight pipe section of the pipe, and it is assumed that the cross section of the pipe is not deformed. Note that the stress distribution on the pipe surface becomes a SIN function with a period of 360 degrees, and by returning the output of the magnetic anisotropy sensor to the SIN function, the amplitude component and the phase angle of the SIN function Each seeks the magnitude of the bending stress and the direction of bending.
[0006]
The method according to Japanese Examined Patent Publication No. 7-69226 discloses that when a moment acts on the straight pipe portion of the pipe, the pipe is deformed in cross section due to flatness, and the stress generated on the surface of the pipe at this time is elastically mechanically applied. Evaluating and paying attention to the fact that the stress distribution on the pipe surface becomes a SIN function with a period of 180 degrees, by regressing the output of the magnetic anisotropy sensor to this SIN function, the amplitude component and phase angle of the SIN function Thus, the magnitude of the flat stress and the direction of the flat are respectively determined.
[0007]
[Problems to be solved by the invention]
However, in order to ensure the accuracy of the analysis by the conventional finite element method model, there is a problem that it is necessary to provide a considerably large number of measurement points for subsidence and leveling. For example, in the case of a pipe having a diameter of 600 mm, measurement data covering at least 50 m is required at intervals of about 5 m. For this reason, the cost for measurement increases. Furthermore, since these measurement data are repeatedly analyzed by the finite element method, there is a problem that cost and time are required, and the presence of a skilled person is indispensable for the work.
[0008]
Further, in the case of a curved pipe portion, it is difficult to directly measure the degree of stress in a nondestructive manner. The conventional techniques shown in the above Japanese Patent Publication Nos. 7-62636 and 7-69226 are methods for estimating the bending stress or flat stress of the straight pipe portion. Therefore, even if the magnetostrictive method is used to measure stress non-destructively using a magnetic anisotropy sensor, the pure bending stress is measured at the straight pipe part without the influence of the cross-sectional deformation of the curved pipe, and the finite element method is used. However, the indirect method of estimating the stress of the bent pipe portion with the aid of an analysis means such as the above is only performed.
[0009]
Further, the cross-sectional flatness of the curved pipe subjected to the in-plane bending moment is the largest at the central part of the curved pipe, and flatness of about 70% of the central part occurs at the curved pipe end. Although this flatness disappears depending on the radius of curvature, in the case of a radius of curvature of about 1.5 DR, the flatness disappears from the end of the curved tube by about 3D. If the target tube has a diameter of 750 mm, it means that a distance of 2 m or more is necessary, and considering that there is almost no space in the cave (in the joint groove) or before and after the abutment, There is a problem that the case that can be applied at the position where the flatness due to the separation is eliminated is extremely limited. On the other hand, even if the magnetostriction method is directly applied to the stress measurement of the bent pipe part, since the distortion at the time of manufacturing remains in the part and its distribution shape is complicated, for example, subsidence etc. There is a problem that it is extremely difficult to separate the stress component generated by the external force.
[0010]
The present invention has been made in view of such a problem, and a curved pipe stress evaluation method, a stress evaluation apparatus, and the like that can easily and accurately calculate a stress generated in a curved pipe constituting a pipe line. The purpose is to provide.
[0011]
[Means for Solving the Problems]
In order to achieve the above-mentioned object, the first invention provides a stress-moment relational expression indicating the relationship between the moment acting on the curved pipe constituting the pipe and the distribution of the stress generated in the curved pipe. Calculating the moment by inputting the measured value of the flat amount into a moment-flat amount relational expression indicating the relationship between the flat amount of the bent pipe and the moment, which is derived by developing the displacement; and And a step of inputting a moment to the stress-moment relational expression to obtain the distribution of the stress.
[0012]
In the first invention, the distribution of the moment (in-plane bending moment, out-of-plane bending moment, etc.) acting on the curved pipe constituting the pipe and the stress (tube axial direction stress, pipe circumferential direction stress, etc.) generated in the curved pipe The relationship between the flattening amount of the curved pipe and the moment acting on the curved pipe, which is derived by expanding the stress-moment relational expression indicating the relationship of A measured value of the flattening amount of the curved pipe is inputted into the moment-flattening relational expression to calculate a moment acting on the curved pipe, and a stress distribution in the curved pipe is obtained from the stress-moment relational expression.
[0013]
The “pipe” is a pipe line (life line) for supplying gas, water and the like, and includes a curved pipe, a straight pipe, and the like.
“Flat amount” is the cross-sectional deformation amount and diameter change amount (outer diameter change amount, inner diameter change amount, etc.) of the curved pipe, for example, a state where it has not been subjected to cross-sectional deformation due to external force (production, installation, etc.) It is the amount of secular change of the diameter (outer diameter, inner diameter, etc.) of the bent pipe with reference to the bent pipe.
The “stress-moment relational expression” is the relationship between the moment acting on the curved pipe (in-plane bending moment, out-of-plane bending moment, etc.) and the stress generated on the curved pipe (stress in the pipe axis direction, stress in the pipe circumferential direction, etc.). It is shown. In addition, this stress-moment relational expression desirably indicates the pipe axial stress and pipe circumferential stress corresponding to the in-plane bending moment, and the pipe axial stress and pipe circumferential stress corresponding to the out-of-plane bending moment. , Rodabaugh & George. Details of this theoretical formula will be described later.
[0014]
The “moment-flat amount relational expression” indicates the relationship between the flat amount of the curved pipe constituting the pipe and the moment acting on the curved pipe. For example, the theoretical formula of Rodabaugh & George is expressed by the section of the curved pipe. It is a relational expression derived by expanding the directional displacement to a term of a predetermined order.
[0015]
In this case, the moment-flat amount relational expression is
M_i= Η₁EI / k_pRxe_i,
M_o= Η₂EI / k_pRxe_o,
It can be expressed as.
However,
M_iIs the in-plane bending moment,
M_oIs the out-of-plane bending moment,
E is the elastic modulus,
I is the cross-sectional second moment of the tube,
R is the radius of curvature of the curved pipe,
2 x e_iIs the amount of flatness before and after the external force acts in the direction of the circumferential angle 0 °,
2 x e_oIs the amount of flatness before and after the external force in the direction of 45 ° in the circumferential direction acts,
k_pIs the deflection constant,
η1 and η2 are constants determined by the internal pressure, curvature radius, radius, and pipe thickness of the curved pipe.
[0016]
The “circumferential angle” indicates the outer diameter, the inner diameter direction, the position on the circumference of the curved pipe, and the like. The angle in the circumferential direction is represented by an angle formed with a predetermined reference radius of the cross section when the cross section of the curved pipe (a cross section by a plane perpendicular to the pipe axis) is circular. The definition of the angle in the circumferential direction will be described later. For example, the radius direction of curvature of the curved pipe corresponds to the direction of 90 ° (−90 °) in the circumferential direction.
[0017]
K_p, Η₁, Η₂Depending on the order of the term that develops in the stress-moment relational expression,
k_p= 1 / (c4 + c5 + c6 + c7),
η₁= 1 / {r (2d₁+ 4d₂+ 6d₃)},
η₂= 1 / {r (2d₁-6d₃)},
Can be used.
However,
Ψ = PR²/ Ert,
λ = tR / r²(1-ν²)^(1/2)(Λ: pipe coefficient),
C1 = 5 + 6λ²+ 24Ψ,
C2 = 17 + 600λ²+ 480ψ,
C3 = 37 + 7350λ²+ 2520Ψ,
d₁= 3 (C2C3-110.25) / {6.25C3-C1 (C2C3-110.25)},
d₂= 7.5C3 / {6.25C3-C1 (C2C3-110.25)},
d₃= 78.75 / {6.25C3-C1 (C2C3-110.25)},
c4 = 1 + 3d₁+ 2.25d₁ ²,
c5 = 0.25 (d₁ ²+ 34d₂ ²+ 74d₃ ²-10d₁d₂-42d₂d₃),
c6 = λ²/ 12 × (36d₁ ²+ 3600d₂ ²+ 4410d₃ ²),
c7 = Ψ (12d₁ ²+ 240d₂ ²+ 1260d₃ ²),
P is the internal pressure,
t is the tube thickness,
r is the radius of the tube,
ν is the Poisson's ratio.
[0018]
In the first invention, the measured value of the flattening amount of the curved pipe is input to the above-mentioned moment-flattening relational expression to calculate the moment acting on the curved pipe, and this moment is calculated by the above-mentioned theoretical formula of Rodabaugh & George, etc. Therefore, the stress distribution of the bent pipe can be estimated by measuring the flattening amount of the bent pipe.
[0019]
In the first invention, (1) 0 ° / 180 ° direction, (2) 45 ° / −135 ° direction or −45 ° / 135 ° direction, that is, the flattening amount of the curved pipe ( By measuring the outer diameter change amount with a common measuring instrument such as calipers, the pipe axial stress, pipe circumferential stress, and out-of-plane bending moment corresponding to the in-plane bending moment can be accurately measured with sufficient accuracy. Corresponding pipe axial direction stress and pipe circumferential direction stress can be calculated.
[0020]
The second invention is derived by developing a stress-moment relational expression showing the relationship between the moment acting on the curved pipe constituting the pipe and the distribution of stress generated in the curved pipe with respect to the displacement in the cross-sectional direction of the curved pipe. , Holding means for holding a moment-flat amount relational expression indicating the relationship between the flattening amount of the bent pipe and the moment, and calculating the moment by inputting the measured value of the flattening amount into the moment-flattening relational expression And a means for obtaining the stress distribution by inputting the moment into the stress-moment relational expression.
[0021]
In the second invention, the stress evaluation apparatus includes a moment (in-plane bending moment, out-of-plane bending moment, etc.) acting on a curved pipe constituting the pipe and a stress (tube axial stress, pipe circumferential stress) generated in the curved pipe. Etc.) is derived by expanding the stress-moment relational expression indicating the relationship with the distribution of the curved pipe in the cross-sectional direction of the curved pipe to a term of a predetermined order and the moment acting on the curved pipe. The moment-flat amount relational expression, etc., that indicates the relationship between and is stored in a storage means such as a database in the memory, and the measured value of the flattened amount of the curved pipe is input to the moment-flattening relational expression and acts on the curved pipe The moment to be calculated is calculated, and the stress distribution in the bent pipe is obtained from the stress-moment relational expression.
[0022]
2nd invention is invention about the stress evaluation apparatus which concerns on the stress evaluation method of 1st invention. The stress evaluation apparatus holds the above-described stress-moment relational expression, flatness-moment relational expression, etc. in a memory or database.
[0023]
An information processing apparatus such as a computer can be used as the “stress evaluation apparatus”. In addition, the stress evaluation device may be connected to a network such as the Internet as a stress evaluation server so that a terminal device (personal computer, portable information terminal, mobile phone, etc.) can access the stress evaluation server via the network. it can.
[0024]
In this case, the flattening amount (outer diameter change amount, inner diameter change amount, etc.) of the curved pipe can be input to the stress evaluation server from the terminal device via the network. The stress evaluation server can calculate an in-plane bending moment, an out-of-plane bending moment, a stress distribution, and the like of the curved pipe, and transmit the calculation result to the terminal device via the network. In addition, the stress evaluation server can store, record, and manage input data and calculation results in a database so that the stress evaluation server itself or a terminal device can use the database as necessary.
[0025]
A third invention is a program for causing a computer to function as the stress evaluation apparatus of the second invention.
4th invention is the recording medium which recorded the program which makes a computer function as a stress evaluation apparatus of 2nd invention.
[0026]
The “recording medium” is a CD-ROM, DVD, flexible disk, hard disk, or the like.
The above-described program can be distributed via a network such as the Internet, or a recording medium can be distributed.
[0027]
The configuration and characteristics of the present invention will be clarified in the embodiments and the accompanying drawings described below.
[0028]
DETAILED DESCRIPTION OF THE INVENTION
Exemplary embodiments of a stress evaluation method and a stress evaluation apparatus according to the present invention will be described below in detail with reference to the accompanying drawings. In the following description and the accompanying drawings, the same reference numerals are given to components having substantially the same functional configuration, and redundant description is omitted.
[0029]
FIG. 1 is a perspective view of a curved pipe and explains the definition of “circumferential angle” (hereinafter also simply referred to as “angle”) φ. FIG. 2 is a cross-sectional view of the curved pipe and explains the definition of the angle. In the following description, it is assumed that the vertical cross section of the curved pipe 101 with respect to the pipe axis 102 is circular. Further, in the present embodiment, the flattening amount and the cross-sectional deformation amount of the curved pipe will be described as mainly corresponding to the outer diameter change amount of the bent pipe, but the inner diameter change amount of the bent pipe, etc. instead of the outer diameter change amount, etc. Even if is used, there is no problem in accuracy in practical use.
[0030]
A cross section 201 is a vertical cross section of the curved pipe 101 with respect to the pipe axis 102. In FIG. 2, the radius connecting the center point 202 and the rightmost point 203 on the circumference of the cross section is defined as a reference radius (circumferential angle of 0 °), and the circumferential angle of the tube is defined as shown in FIGS. To do.
When the direction of the outer diameter, inner diameter, etc. of the curved pipe is indicated, for example, the direction connecting the position of the circumferential angle of 0 ° and the circumferential angle of 180 ° is referred to as “0 ° / 180 ° direction ”,“ 0 ° direction ”, and the like.
[0031]
When an external force is applied to the bent pipe due to subsidence, a bending moment is generated. The direction of the bending moment can be divided into in-plane bending and out-of-plane bending. The in-plane bending is a bending in a plane direction including the tube axis of the curved pipe, and the out-of-plane bending is a bending in an out-of-plane direction including the tube axis of the curved pipe.
[0032]
In-plane bending moment (M_i) Stress in the axial direction of the tube when_iL, Pipe circumferential stress σ_iC, Out-of-plane bending moment (M_o) Stress in the axial direction of the tube when_oL, Pipe circumferential stress σ_oCRodabow & George's Theory (Rodabaugh, EC, and George, H. H., "Effect of International Pressure on Flexibility and Stress In W e s e s e e s e e n e n e e n e n e n e n e n e, e, e. 1957, pp. 939-948.), It is expressed as follows.
[0033]
σ_iL(Φ) = k_pM_ir / I (1-ν²) × f₁(Φ) ... [1-1]
σ_iC(Φ) = k_pM_ir / I (1-ν²) × f₂(Φ) ... [1-2]
σ_oL(Φ) = k_pM_or / I (1-ν²) × f₃(Φ) ... [1-3]
σ_oC(Φ) = k_pM_or / I (1-ν²) × f₄(Φ) ... [1-4]
[0034]
Where φ: circumferential angle of the pipe (see FIGS. 1 and 2), ν: Poisson's ratio, R: radius of curvature of the curved pipe, r: pipe radius, t: pipe thickness, I: secondary moment of section of the pipe , M_i: In-plane bending moment acting on the curved pipe, M_o: Out-of-plane bending moment acting on the curved pipe, k_p: Deflection coefficient.
Λ = tR / r²(1-ν²)^(1/2)And k_pIs a function of λ and internal pressure P.
[0035]
F₁(Φ), f₂(Φ), f₃(Φ), f₄Specifically, (φ) is expressed as follows.
[Expression 1]

However, + (plus) in the sign of ± is used for calculating the stress on the outer surface of the tube, and-(minus) is used for calculating the stress on the inner surface.
[0036]
D_nAlso k_pLike λ and the internal pressure P. The number of terms that n should be taken depends on the value of λ, and as λ becomes smaller, higher-order terms are required. However, if λ is about 0.1, the third order is sufficient. ing. In this case, d_n, K_pIs expressed as follows.
[0037]
d₁= 3 (C2C3-110.25) / {6.25C3-C1 (C2C3-110.25)},
d₂= 7.5C3 / {6.25C3-C1 (C2C3-110.25)},
d₃= 78.75 / {6.25C3-C1 (C2C3-110.25)},
However,
Ψ = PR²/ Ert (E: elastic modulus),
C1 = 5 + 6λ²+ 24Ψ,
C2 = 17 + 600λ²+ 480ψ,
C3 = 37 + 7350λ²+ 2520Ψ,
It was.
[0038]
k_p= 1 / (c4 + c5 + c6 + c7)
However,
c4 = 1 + 3d₁+ 2.25d₁ ²,
c5 = 0.25 (d₁ ²+ 34d₂ ²+ 74d₃ ²-10d₁d₂-42d₂d₃),
c6 = λ²/ 12 × (36d₁ ²+ 3600d₂ ²+ 4410d₃ ²),
c7 = Ψ (12d₁ ²+ 240d₂ ²+ 1260d₃ ²),
It was.
[0039]
In-plane bending moment M_i, Out-of-plane bending moment M_oThe amount of change in the radius of the tube when_i, E_oAnd the equations [1-1] to [1-4] (Rodabaugh & George's theoretical equation) are developed for the displacement in the cross-sectional direction, and M_i, M_oAnd e_i, E_oWhen seeking a relationship with
M_i= Η₁EI / k_pRxe_i  ... [3-1]
M_o= Η₂EI / k_pRxe_o  ... [3-2]
It is.
[0040]
here,
η₁= 1 / {r (2d₁+ 4d₂+ 6d₃)}
η₂= 1 / {r (2d₁-6d₃)}
e_i= R_i'-R_i0
e_o= R_o'-R_o0
(R_i0: Radius with an angle of 0 ° in the circumferential direction before external force is applied)
(R_i': Radius of 0 ° in the circumferential direction after external force is applied)
(R_o0: Radius with 45 ° angle in the circumferential direction before external force is applied)
(R_o': Radius of 45 ° in the circumferential direction after external force is applied)
It is.
[0041]
2 × e_iCorresponds to a flattening amount (maximum outer diameter change amount, maximum inner diameter change amount, maximum cross-sectional deformation, maximum flattening amount) in the circumferential angle direction of 0 °.
2xe_oCorresponds to a flattening amount (maximum outer diameter change amount, maximum inner diameter change amount, maximum cross-sectional deformation, maximum flattening amount) in the direction of 45 ° in the circumferential direction.
[0042]
Flatness W in in-plane bending and out-of-plane bending_i(Φ), W_o(Φ) can be expressed as follows. The flattening amount W shown in the following formula_i(Φ), W_o(Φ) is the amount of change in the diameter of the curved pipe (radius change × 2).
W_i(Φ) = 2 × η₁{2d₁cos (2φ) + 4d₂cos (4φ) + 6d₃cos (6φ)} [4-1]
W_o(Φ) = 2 × η₂{2d₁sin (2φ) + 4d₂sin (4φ) + 6d₃sin (6φ)} [4-2]
[0043]
FIG. 3 is a diagram showing the relationship between the amount of flatness (amount of change in outer diameter) and the angle in the circumferential direction when an in-plane bending moment, an out-of-plane bending moment, or a combined moment of these acts on a curved pipe. The vertical axis represents the flattening amount (outer diameter change amount), and the horizontal axis represents the circumferential angle.
[0044]
A curved line 301 shows a relationship between a flattening amount (outer diameter change amount) and an angle in the circumferential direction when an in-plane bending moment is applied to the curved pipe.
A curve 302 shows a relationship between a flattening amount (outer diameter change amount) and an angle in the circumferential direction when an out-of-plane bending moment is applied to the curved pipe.
A curve 303 indicates a relationship between a flattening amount (outer diameter change amount) and a circumferential angle when a synthetic moment acts on the curved pipe.
The curve 301, the curve 302, and the curve 303 are graphs with a period of 180 ° as can be seen from the equations [4-1] and [4-2].
[0045]
Referring to the curve 301 of FIG. 3, the flattening amount (outer diameter change amount) in the in-plane bending is the maximum in the direction of angle 0 ° / angle 180 °, and the angle 0 ° in the direction of angle 90 ° / angle −90 °. / The sign is opposite to that of the flattening amount (outer diameter change amount) in the direction of angle 180 °, which is a small value. Further, the flattening amount (outer diameter change amount) in the in-plane bending is substantially 0 at an angle of 45 °, an angle of −45 °, an angle of 135 °, and an angle of −135 °.
[0046]
Referring to the curve 302 in FIG. 3, the flattening amount (outer diameter change amount) in the out-of-plane bending is the maximum in the direction of angle 45 ° / angle −135 °, and the angle 45 in the direction of angle 135 ° / angle −45 °. Compared with the flattening amount (outer diameter change amount) in the direction of ° / angle -135 °, the sign is opposite. Further, the flattening amount (outer diameter change amount) in the out-of-plane bending is substantially 0 at an angle of 0 °, an angle of 180 °, an angle of 90 °, and an angle of −90 °.
[0047]
Accordingly, even when both in-plane bending and out-of-plane bending are applied, the flatness amount (outer diameter change amount) 2e in the direction of angle 0 ° / angle 180 °._iIs measured, the in-plane bending moment M is obtained by the equation [3-1]._iCan be calculated.
In addition, even when both in-plane bending and out-of-plane bending are applied, the amount of flatness (outer diameter change amount) in the direction of 45 ° / angle-135 ° or 135 ° / 45 ° 2e_oIs measured, the out-of-plane bending moment M is obtained by the equation [3-2]._oCan be calculated.
[0048]
M_i, M_oIs obtained, the stress (σ in an arbitrary position in the cross section can be obtained by the equations [1-1] to [1-4] (Rodabaugh & George's theoretical equation)._iL, Σ_iC, Σ_oL, Σ_oC) Can be calculated.
[0049]
FIG. 4 is a diagram schematically showing an outline of an experiment for measuring the relationship between the flatness (outer diameter change amount) and the maximum circumferential stress. A tube 401 as a test body is composed of a curved tube 402, a straight tube 403, and the like.
[0050]
A Monaca elbow (API-X60 standard, wall thickness t = 12.7 mm, outer diameter 2r = 610 mm, curvature radius R = 1.5DR, λ = 0.138) was used as the curved tube 402. A sleeve tube as a straight tube 403 was welded to this, one was attached to the surface plate via a flange, and the other flange was loaded in a downward direction 405 and an upward direction 406 with a hydraulic jack. That is, an in-plane bending moment was applied to the curved pipe 402. A load cell (not shown) was provided at the load point so that the load load could be measured.
[0051]
The measurement position of the flat amount (outer diameter change amount) was the elbow center cross section 404, and measurement was performed in two directions (0 ° / 180 ° direction, 90 ° / 270 ° (−90 °) direction) using a caliper. Further, for verification, a biaxial strain gauge (not shown) was attached at a circumferential angle of 15 degrees on the circumference of the central section 404, and stress measurement was performed.
[0052]
FIG. 5 is a diagram showing the relationship between the flattening amount (outer diameter change amount) and the maximum stress in the circumferential direction obtained from the above experimental results. The vertical axis indicates the maximum circumferential stress, and the horizontal axis indicates the flattening amount (outer diameter change amount). The maximum circumferential stress is the largest of the stresses in the circumferential direction measured by a biaxial strain gauge provided on the circumference of the central section 404.
Each point of “◯” (FIG. 5) indicates a measurement value in the 0 ° / 180 ° direction, and each point of “□” (FIG. 5) relates to a 90 ° / 270 ° (−90 °) direction. Indicates the measured value.
[0053]
A straight line 501 represents the relationship between the flattening amount (outer diameter change amount) and the maximum stress in the circumferential direction in the 0 ° / 180 ° direction.
A straight line 502 indicates the relationship between the flattening amount (outer diameter change amount) and the maximum stress in the circumferential direction in the 90 ° / 270 ° (−90 °) direction.
As shown by the straight line 501 and the straight line 502, the flat amount (outer diameter change amount) and the circumferential maximum stress are both in the 0 ° / 180 ° direction and the 90 ° / 270 ° (−90 °) direction. Shows a linearity, that is, a proportional relationship.
[0054]
The Monaca elbow used in the above experiment is manufactured by welding two parts vertically (in the direction of the pipe axis) (such as seam welding), so the direction in the 0 ° / 180 ° direction is 90 ° / 270. It is easier to deform than the direction of ° (-90 °). Further, as described above with reference to FIG. 3, in the in-plane bending moment, the flattening amount (outer diameter change amount) in the 0 ° / 180 ° direction is theoretically 90 ° / 270 ° (−90 °) direction. Become bigger.
[0055]
As described above, anisotropy is observed in the flattening amount (outer diameter change amount), but it is difficult to purely separate the influence due to the presence of the vertical seam. Therefore, it is desirable to evaluate the stress related to the in-plane bending moment by measuring the flatness (outer diameter change amount) in the 0 ° / 180 ° direction, which is less affected by the longitudinal seam.
[0056]
The yield stress of the Monaca elbow material is about 410 MPa. As described above, in the elastic region, linearity (proportional relationship) exists between the flattening amount (outer diameter change amount) and the circumferential maximum stress. Be looked at.
Further, in the upward direction 406 (the direction in which the maximum circumferential stress is negative in FIG. 5), the flattening amount (outer diameter change amount) and the circumferential direction are reduced to a range (plastic region) of about 1.5 times the yield stress. Linearity (proportional relationship) is observed with the maximum stress.
[0057]
Next, a comparison between the stress evaluation method described above and the above experimental results will be described. FIG. 6 is a diagram illustrating analysis values (analysis values obtained by the stress evaluation method described above) and experimental values regarding the stress distribution in the circumferential direction and the axial direction. The vertical axis represents stress, and the horizontal axis represents the circumferential angle.
[0058]
In the experimental results shown in FIG. 5, when the flatness (outer diameter change amount) in the 0 ° / 180 ° direction is 8 mm (FIG. 5: point 503), the maximum circumferential stress is about 400 MPa.
The moment with respect to the flatness (outer diameter change amount) of 8 mm in the 0 ° / 180 ° direction is M from the equation [3-1]._i= 1.7 × 10⁵N · m. This M_iIs substituted into equations [1-2] and [1-1] and the stress distribution is calculated, the solid line 601 (circumferential analysis value) and the solid line 602 (axial analysis value) in FIG. 6 are obtained.
[0059]
In addition, the measurement value of the circumferential stress measured by a biaxial strain gauge provided at a pitch of 15 degrees on the circumference of the central section 404 at the flatness (outer diameter change amount) of 8 mm in the 0 ° / 180 ° direction is “ The symbol “●” (FIG. 6) indicates each point (circumferential experimental value), and the measured value of the axial stress is indicated by each symbol “□” (FIG. 6) (axial experimental value).
[0060]
Regarding the stress in the circumferential direction, there is a slight shift in the peak position between the experimental value and the analytical value, but the stress values are almost the same. Regarding the stress in the axial direction, the peak positions of the experimental value and the analytical value coincide, but there is a slight deviation in the stress value. Note that these slight deviations have no practical problem.
By comparing and considering the above experimental values and analytical values, it is possible to estimate the stress with sufficient accuracy for practical use even if the measured flatness (outside diameter change) is accurate enough to be obtained with calipers. I can say that.
[0061]
As described above, according to the embodiment of the present invention, (1) 0 ° / 180 ° direction, (2) 45 ° / −135 ° direction or −45 ° / 135 ° direction By measuring the flattening amount (outer diameter change amount) of the pipe with a general measuring tool such as a caliper, it is possible to estimate the stress distribution generated in the bent pipe with a practically sufficient accuracy.
[0062]
One of the purposes of adopting a curved pipe is to impart flexibility to normal piping and reduce stress by deformation thereof. Therefore, it is often a three-dimensional pipe. This indicates that the probability that the in-plane bending moment and the out-of-plane bending moment simultaneously act as loads increases. The cross-sectional deformation in the state where both the in-plane bending moment and the out-of-plane bending moment are applied becomes considerably complicated.
[0063]
However, as described with reference to FIG. 3, the cross-sectional deformation during the in-plane bending moment is maximum in the 0 ° / 180 ° direction and is theoretical in the 45 ° / −135 ° direction and the −45 ° / 135 ° direction. The top is almost zero. On the other hand, the cross-sectional deformation at the time of the out-of-plane bending moment is maximum in the 45 ° / −135 ° direction or −45 ° / 135 ° direction, and is theoretically almost 0 in the 0 ° / 180 ° direction.
[0064]
From these facts, (1) the in-plane bending moment (M) from the flattening amount (outer diameter change amount) in the 0 ° / 180 ° direction according to the equation [3-1]._i) And (2) the out-of-plane bending moment (M) according to the equation [3-2] from the flatness (outer diameter change amount) in the 45 ° / −135 ° direction or −45 ° / 135 ° direction._o) Can be calculated.
[0065]
That is, (1) flatness in 0 ° / 180 ° direction (outer diameter change amount), (2) flatness in two directions in 45 ° / −135 ° direction or −45 ° / 135 ° direction (outer diameter change amount) ) To measure the in-plane bending moment (M_i) And out-of-plane bending moment (M_o) And can be calculated separately. These in-plane bending moments (M_i) And out-of-plane bending moment (M_o), The stress distribution due to the bending moments in both directions of the in-plane bending moment and the out-of-plane bending moment can be calculated by the equations [1-1] to [1-4] (Rodabaugh & George's theoretical equation).
[0066]
For stress (σ) conforming to ANSI B31.8 adopted in the design, in-plane bending moment (M_i) And out-of-plane bending moment (M_o) To obtain the composite moment (M) (see Equation [5-1]) and multiply by the section modulus (Z) by the stress concentration factor (i) due to the in-plane bending moment (the in-plane bending moment and With respect to the out-of-plane bending moment, the former is about 17% larger, which is an evaluation on the safe side), and is the stress (σ) of the curved pipe in which the outer diameter change (flatness) occurs (formula [5-2] reference).
M = (M_i ²+ M_o ²)^(1/2)    ... [5-1]
σ = M · i / Z [5-2]
[0067]
In addition, the stress evaluation method described above can directly evaluate the stress of the curved pipe itself by nondestructiveness. Furthermore, stress evaluation and stress estimation can be performed in a service state and a use state without requiring measures such as reducing the pressure. Therefore, it is not necessary to take special measures such as turning on the equipment when performing the stress evaluation of the bent pipe.
[0068]
In addition, it is possible to perform stress evaluation and stress diagnosis only by measuring the flattening amount (outer diameter change amount) in the two directions in the central section of the curved pipe, and an expert is not required for the measurement. The cost burden can be reduced compared to the above.
[0069]
Further, since the mode in which flattening generates stress in the bent pipe is known, the reliability of the stress evaluation result is high. That is, as described above in the comparison and consideration between the experimental value and the analysis value, the stress evaluation shown in the present embodiment has a practically sufficient accuracy.
Furthermore, it can be used not only for a clear deformation mode such as subsidence but also for stress estimation in the state where various external forces such as thermal stress are applied.
[0070]
Regarding the flattening amount, the outer diameter change amount of the bent pipe is measured by a measuring tool such as a caliper, but the inner diameter change amount of the bent pipe may be measured by a measuring tool such as a pig or an inspection tool.
[0071]
Next, a stress evaluation apparatus according to the stress evaluation method described above will be described with reference to FIG.
By registering and recording the above formulas [1-1] to [5-2] and other calculation formulas in the computer, the computer can measure the flattening amount (outer diameter change amount, inner diameter change) of the measured curved pipe. When a necessary amount is input, the stress evaluation of the bent pipe and the calculation of the stress distribution can be performed.
[0072]
FIG. 7 is a flowchart showing a process executed by a computer as a stress evaluation apparatus for a curved pipe.
An initial value of the outer diameter or inner diameter of the bent pipe is input to the computer (step 701). This initial value is the outer diameter, inner diameter, etc. of the curved pipe in a state where it is not subjected to cross-sectional deformation due to external force (at the time of manufacture, installation, etc.).
After the lapse of time, the outer diameter of the curved pipe measured with a caliper or the like, or the inner diameter of the curved pipe measured with a pig or the like is input (step 702).
[0073]
The computer obtains the flattening amount (outer diameter change amount or inner diameter change amount) of the curved pipe (step 703). Note that (flatness) = (outer diameter or inner diameter input in step 702) − (initial value of outer diameter or inner diameter input in step 701).
The computer calculates the in-plane bending moment M from the flat amount of the curved pipe by the equations [3-1] and [3-2]._iAnd out-of-plane bending moment M_oIs calculated (step 704).
Computer is M_i, M_oFrom Equations [1-1] to [1-4] (Rodabaugh & George's theoretical equation), σ_iL(Φ), σ_iC(Φ), σ_oL(Φ), σ_oC(Φ) is calculated, and stress evaluation is performed (step 705).
[0074]
After the above process, the computer as the stress evaluation device inputs the measured flattening amount of the bent pipe (outer diameter change amount, inner diameter change amount, etc.) and other necessary numerical values, and the stress evaluation and stress of the bent pipe Distribution can be calculated.
[0075]
The computer as the stress evaluation apparatus is connected as a stress evaluation server to a network such as the Internet so that terminal devices (personal computers, portable information terminals, mobile phones, etc.) can access this server via the network. You can also.
[0076]
In this case, the initial value of the outer diameter or inner diameter of the curved pipe is input to the stress evaluation server from the terminal device via the network (step 701), or the measured value of the outer diameter or inner diameter after the aging is evaluated via the network. Input to the server (step 702). The stress evaluation server may calculate the flattening amount of the curved pipe, the in-plane bending moment, the out-of-plane bending moment, the stress distribution, and the like (steps 703 to 705), and transmit the calculation result to the terminal device via the network. it can. The stress evaluation server may record and manage input data and calculation results as a database so that the stress evaluation server itself or the terminal device can use the database as necessary.
[0077]
All the functions of the computer (including the stress evaluation server and the terminal device described above) can be realized by software and a computer program. Therefore, necessary software and computer programs can be distributed via a network or a recording medium such as a CD-ROM or DVD-ROM in which the program is recorded.
[0078]
Next, the maintenance and repair of the pipe using the above-described stress evaluation method, stress evaluation apparatus, etc. will be described with reference to FIG. FIG. 8 shows a schematic diagram of a stress relieving method for the tube 802. A pipe 802 is embedded in the ground 801. For any point (bent tube portion or the like) of the tube 802, the stress is calculated by the method described in the above embodiment, the necessity of stress release is determined, and the stress release portion 804 is determined.
[0079]
The ground of the excavation part 805 below the stress release part 804 is excavated, and the stress release part 804 of the pipe 802 is moved to the position of the stress release part 803. And the excavation part 805 is refilled again and the position of the pipe | tube 802 is repaired.
[0080]
Next, the maintenance and repair of the pipe using the above-described stress evaluation method, stress evaluation apparatus, etc. will be described with reference to FIG. FIG. 9 shows a schematic diagram of a stress relief method for the tube 902. A pipe 902 is embedded in the ground 901. For any point (bent tube portion or the like) of this tube 902, the stress is calculated by the method shown in the above-described embodiment, the necessity of stress release is determined, and the stress release portion 903 is determined. The vicinity of both ends of the stress release portion 903 is cut, and the central portion of the stress release portion 903 is removed. And the cutting part 904 and the cutting part 905 are joined, and the position of the pipe | tube 902 is repaired.
[0081]
As described with reference to FIGS. 8 and 9, by using the stress evaluation method, the stress evaluation apparatus, and the like according to the embodiment of the present invention, the stress at an arbitrary point can be easily calculated on site, Can be repaired.
[0082]
The preferred embodiments of the curved pipe stress evaluation method and the stress evaluation apparatus according to the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to such examples. It will be apparent to those skilled in the art that various changes or modifications can be conceived within the scope of the technical idea disclosed in the present application, and these are naturally within the technical scope of the present invention. Understood.
[0083]
【The invention's effect】
As described above, according to the present invention, it is possible to provide a stress evaluation method, a stress evaluation apparatus, and the like for a curved pipe that can easily and accurately calculate the stress generated in the curved pipe constituting the pipe. Can do.
[Brief description of the drawings]
FIG. 1 is a perspective view of a curved pipe.
[Fig. 2] Cross section of curved pipe
FIG. 3 is a diagram showing the relationship between the amount of flatness (amount of change in outer diameter) and the angle in the circumferential direction when an in-plane bending moment, an out-of-plane bending moment, or a combined moment of these acts on a curved pipe.
FIG. 4 is a diagram schematically showing an outline of an experiment for measuring a relationship between a flattening amount (outer diameter change amount) and a maximum circumferential stress.
FIG. 5 is a diagram showing the relationship between the flatness (outer diameter change amount) and the maximum stress in the circumferential direction.
FIG. 6 is a diagram showing analytical values and experimental values regarding the stress distribution in the circumferential direction and the axial direction.
FIG. 7 is a flowchart showing processing executed by a computer as a stress evaluation apparatus for a curved pipe.
[Figure 8] Explanatory drawing on pipe maintenance and repair
FIG. 9 is an explanatory diagram related to pipe maintenance and repair.
[Explanation of symbols]
101 ......... Tube
102 ......... Tube shaft
401 ……… Tube
402 .....
403 ……… Straight pipe
404 ……… Cross section

Claims (10)

A flattened shape of the curved pipe derived by developing a stress-moment relational expression showing a relationship between a moment acting on the curved pipe constituting the pipe and a distribution of stress generated in the curved pipe with respect to a displacement in a cross-sectional direction of the curved pipe. A step of calculating the moment by inputting a measured value of the flat amount into a moment-flat amount relational expression indicating a relationship between a quantity and the moment;
Inputting the moment into the stress-moment relation and obtaining the stress distribution;
A stress evaluation method for a curved pipe, comprising: 2. The stress evaluation method for a bent pipe according to claim 1, wherein the stress-moment relational expression is a theoretical expression of Rodabaugh & George. The flatness-moment calculation formula is:
M _i = η ₁ EI / k _p R × e _i ,
M _o = η ₂ EI / k _p R × e _o ,
The bent pipe stress evaluation method according to claim 1, wherein the bent pipe stress is evaluated. However,
M _i is the in-plane bending moment,
_Mo is the out-of-plane bending moment,
E is the elastic modulus,
I is the cross-sectional second moment of the tube,
R is the radius of curvature of the curved pipe,
2 × e _i is the amount of flatness before and after the external force acts in the direction of the circumferential angle 0 °,
2 × _eo is the amount of flatness before and after an external force acts in the direction of 45 ° in the circumferential direction,
k _p is the deflection constant,
η1 and η2 are constants determined by the internal pressure, curvature radius, radius, and pipe thickness of the curved pipe. The k _p , η ₁ and η ₂ are
k _p = 1 / (c4 + c5 + c6 + c7),
η ₁ = 1 / r (2d ₁ + 4d ₂ + 6d ₃ ),
η ₂ = 1 / r (2d ₁ -6d ₃ ),
The stress evaluation method according to claim 3, wherein: However,
Ψ = PR ² / Ert,
λ = tR / r ² (1-ν ² ) ^(1/2)
C1 = 5 + 6λ ² + 24Ψ,
C2 = 17 + 600λ ² + 480ψ,
C3 = 37 + 7350λ ² + 2520Ψ,
d ₁ = 3 (C2C3-110.25) / {6.25C3-C1 (C2C3-110.25)},
d ₂ = 7.5C3 / {6.25C3-C1 (C2C3-110.25)},
d ₃ = 78.75 / {6.25C3-C1 (C2C3-110.25)},
c4 = 1 + 3d ₁ + 2.25d ₁ ² ,
c5 = 0.25 (d ₁ ² + 34d ₂ ² + 74d ₃ ² -10d ₁ d ₂ -42d ₂ d ₃ ),
_{^{c6 = λ 2/12 × (}} 36d 1 2 + 3600d 2 2 + 4410d 3 2),
^{_{c7 = Ψ (12d 1 2 +}} 240d 2 2 + 1260d 3 2),
P is the internal pressure,
t is the tube thickness,
r is the radius of the tube,
ν is the Poisson's ratio. A flattened shape of the curved pipe derived by developing a stress-moment relational expression showing a relationship between a moment acting on the curved pipe constituting the pipe and a distribution of stress generated in the curved pipe with respect to a displacement in a cross-sectional direction of the curved pipe. Holding means for holding a moment-flat amount relational expression indicating the relationship between the amount and the moment;
Means for calculating the moment by inputting a measured value of the flat amount into the moment-flat amount relational expression;
Means for inputting the moment into the stress-moment relation and obtaining the stress distribution;
A stress evaluation apparatus for a curved pipe, comprising: 6. The stress evaluation apparatus for a curved pipe according to claim 5, wherein the stress-moment relational expression is a theoretical expression of Rodabaugh & George. The flatness-moment calculation formula is:
M _i = η ₁ EI / k _p R × e _i ,
M _o = η ₂ EI / k _p R × e _o ,
The bent pipe stress evaluation apparatus according to claim 5 or 6, wherein However,
M _i is the in-plane bending moment,
_Mo is the out-of-plane bending moment,
E is the elastic modulus,
I is the cross-sectional second moment of the tube,
R is the radius of curvature of the curved pipe,
2 × e _i is the amount of flatness before and after the external force acts in the direction of the circumferential angle 0 °,
2 × _eo is the amount of flatness before and after an external force acts in the direction of 45 ° in the circumferential direction,
k _p is the deflection constant,
η1 and η2 are constants determined by the internal pressure, curvature radius, radius, and pipe thickness of the curved pipe. The k _p , η ₁ and η ₂ are
k _p = 1 / (c4 + c5 + c6 + c7),
η ₁ = 1 / r (2d ₁ + 4d ₂ + 6d ₃ ),
η ₂ = 1 / r (2d ₁ -6d ₃ ),
The stress evaluation apparatus according to claim 7, wherein:
However,
Ψ = PR ² / Ert,
λ = tR / r ² (1-ν ² ) ^(1/2)
C1 = 5 + 6λ ² + 24Ψ,
C2 = 17 + 600λ ² + 480ψ,
C3 = 37 + 7350λ ² + 2520Ψ,
d ₁ = 3 (C2C3-110.25) / {6.25C3-C1 (C2C3-110.25)},
d ₂ = 7.5C3 / {6.25C3-C1 (C2C3-110.25)},
d ₃ = 78.75 / {6.25C3-C1 (C2C3-110.25)},
c4 = 1 + 3d ₁ + 2.25d ₁ ² ,
c5 = 0.25 (d ₁ ² + 34d ₂ ² + 74d ₃ ² -10d ₁ d ₂ -42d ₂ d ₃ ),
_{^{c6 = λ 2/12 × (}} 36d 1 2 + 3600d 2 2 + 4410d 3 2),
^{_{c7 = Ψ (12d 1 2 +}} 240d 2 2 + 1260d 3 2),
P is the internal pressure,
t is the tube thickness,
r is the radius of the tube,
ν is the Poisson's ratio. A program that causes a computer to function as the stress evaluation apparatus according to any one of claims 5 to 8. A recording medium recording a program that causes a computer to function as the stress evaluation apparatus according to claim 5.

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