JP3868858B2 - 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。
【００４４】
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。
【００４５】
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。
【００４６】
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。
【００４７】
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。
【００４８】
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。
【００４９】
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。
【００５０】
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］
【００５１】
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。
【００５２】
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。
【００５３】
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。
【００５４】
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。
【００５５】
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。
【００５６】
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_{ｉ Ｃ}、σ_ｏＬ、σ_ｏＣ）を計算することができる。
【００５７】
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。
【００５８】
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。
【００５９】
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。
【００６０】
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。
【００６１】
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。
【００６２】
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。
【００６３】
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。
【００６４】
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。
【００６５】
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。
【００６６】
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。
【００６７】
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。
【００６８】
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。
【００６９】
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。
【００７０】
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。
【００７１】
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。
【００７２】
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。
【００７３】
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。
【００７４】
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］
【００７５】
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。
【００７６】
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。
【００７７】
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。
【００７８】
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。
【００７９】
次に、図７〜図９を参照しながら、磁気異方性センサを用いた管路の曲管の応力評価について説明する。
まず、磁気異方性センサの動作原理について説明する。
図７は、磁気異方性センサの動作原理を示す図である。
図８は、図７に示した磁気異方性センサの部分的な詳細図である。
【００８０】
磁気異方性センサ７０１は、励磁コア７０２、磁気異方性検出コア７０３等から構成される。測定対象物７０８は、磁気異方性センサ７０１による測定の対象物である。励磁コア７０２と磁気異方性検出コア７０３とは直交状態に配設されている。測定対象物７０８には、Ｘ方向に引張応力σが作用している。測定対象物７０８の透磁率をμ、透磁率μのＸ方向成分をμｘ、Ｙ方向成分をμｙとする。励磁コア７０２は、励磁コイル７０４を有し、磁気異方性検出コア７０３は、磁気異方性検出コイル７０５を有する。
【００８１】
測定対象物７０８に応力（ひずみ）が作用すると、透磁率μに異方性が生じる。測定対象物７０８が図７に示すような応力状態にある場合、引張応力方向であるＸ方向の透磁率μｘがＹ方向の透磁率μｙに比べて相対的に大きくなる。
【００８２】
このとき、励磁コイル７０４に電源７０６により電流を流すと、励磁コア７０２の一方の足の先端から出た磁束の大部分は最短距離で直接他方の足に向かうが、測定対象物７０８に磁気異方性があるために、一部は磁気異方性検出コア７０３の中を経由して、励磁コア７０２の他方の足に向かう。
【００８３】
以上の磁気回路を交流磁界で形成すると、磁気異方性検出コイル７０５に誘導電流が流れ、電圧計７０７により電圧が検出される。この電圧値Ｖは、Ｘ方向の透磁率μｘとＹ方向の透磁率μｙの差、すなわち、（μｘ−μｙ）に比例する。また、透磁率μは、測定対象物７０８の応力（ひずみ）σ（Ｘ方向成分σｘ、Ｙ方向成分σｙ）と比例関係にある。従って、以下の関係式が成り立つ。
【００８４】
Ｖ＝Ｋ０×（μｘ−μｙ） ・・・［６−１］
但し、Ｋ０は、比例定数。
Ｖ＝Ｋ１×（σｘ−σｙ） ・・・［６−２］
但し、Ｋ１は、比例定数。
【００８５】
このように、磁気異方性センサ７０１は、Ｘ方向とＹ方向の応力差（σｘ−σｙ）に比例した電圧値Ｖを検出値として出力する。従って、比例定数Ｋ１が分かれば、式［６−２］により、Ｘ方向とＹ方向の応力差（σｘ−σｙ）を算出することができる。以上が磁気異方性センサによる応力測定の原理である。
【００８６】
次に、Ｋａｒｍａｎの扁平応力理論について説明する。Ｋａｒｍａｎの扁平応力理論は、曲管にモーメントが作用した際の、曲管部に発生する応力の管周方向の分布を理論的に説明するものである。曲管にモーメント（Ｍ）が作用したときの管軸方向応力σ_Ｌ、管周方向応力σ_Ｃ、は、Ｋａｒｍａｎの扁平応力理論によると、次のように表される。
【００８７】
σ_Ｌ（φ）＝ｋＭｒ／Ｉ×｛ｓｉｎφ−６ｓｉｎ^３φ／（５＋６λ^２）＋９νλｃｏｓ２φ／（５＋６λ^２）｝ ・・・［７−１］
σ_Ｃ（φ）＝ｋＭｒ／Ｉ×｛ν（ｓｉｎφ−６ｓｉｎ^３φ／（５＋６λ^２））＋９λｃｏｓ２φ／（５＋６λ^２）｝ ・・・［７−２］
【００８８】
ここで、φ：管の周方向角度（図１、図２参照）、ν：ポアソン比、Ｒ：曲管の曲率半径、ｒ：管半径、ｔ：管厚、Ｉ：管の断面２次モーメント、Ｍ：曲管に作用するモーメント、である。
λは、パイプ係数であり、λ＝ｔＲ／ｒ^２である。
ｋは、たわみ係数であり、ｋ＝（１０＋１２λ^２）／（１＋１２λ^２）である。
【００８９】
また、前述したように、磁気異方性センサの出力は、式［６−２］から分かるように、直交２方向の応力差（σ_Ｌ（φ）−σ_Ｃ（φ））を示すものである。この直交２方向の応力差（σ_Ｌ（φ）−σ_Ｃ（φ））は、次のように表される。
【００９０】
σ_Ｌ（φ）−σ_Ｃ（φ）＝ｋＭｒ／Ｉ×｛（１−ν）ｓｉｎφ−（１＋ν）６ｓｉｎ^３φ／（５＋６λ^２）−（１−ν）９λｃｏｓ２φ／（５＋６λ^２）｝ ・・・［８］
【００９１】
従って、曲管部にモーメントが作用したとき、管表面に発生する応力を磁気異方性センサで測定すると、式［８］の分布形状が得られることになる。以上がＫａｒｍａｎの扁平応力理論の概要である。
【００９２】
図９は、磁気異方性センサによる、曲管の応力分布測定の概略を示す図である。
磁気異方性センサ９０２は、曲管９０１の表面を円周方向に走査しながら、応力分布の測定を行う。磁気異方性センサ９０２は、区間９０３に示すように等間隔に移動しながら、曲管９０１の応力を測定する。最小二乗法等の統計的手法によって、測定結果を式［８］に回帰して（σ_Ｌ（φ）−σ_Ｃ（φ））の分布を求め、さらに、測定結果及びこの（σ_Ｌ（φ）−σ_Ｃ（φ））の分布を式［７−１］、式［７−２］に回帰してσ_Ｌ（φ）、σ_Ｃ（φ）、Ｍ（曲管に作用するモーメント）を推定することができる。
【００９３】
磁気異方性センサは、その原理から、モーメント等の外力による負荷応力のみならず、残留応力も同時に重畳する形で計測する。従って、磁気異方性センサの測定結果から、直接最大応力、最小応力を求めずに、敢えて、式［８］に回帰することにより、残留応力成分を除去する。
【００９４】
残留応力は、マクロ的に見ると管の周方向にランダムに、すなわち、平均的に分布していると考えると、式［８］に回帰することによって残留応力成分が除去され、純粋にモーメントによる負荷応力のみが抽出されることになる。また、残留応力のみならず、管の内部流体の圧力による応力や、管軸方向の単純引張あるいは圧縮等のように管周方向に分布を持たない一定値として現れる応力についても、式［８］に回帰することによって残留応力と同様に除去することが可能である。
【００９５】
このように、磁気異方性センサを曲管の周方向に移動させて応力分布を測定し、この測定値を式［７−１］、式［７−２］、式［８］に回帰分析することによって、当該曲管に発生する応力評価及び作用モーメント推定等を行うことができる。
【００９６】
尚、上記図１〜図６について説明した、扁平量（曲管の断面扁平量）に基づく曲管の応力評価手法（応力評価手法▲１▼）に関しては、降伏応力を超える領域に関しても応力評価が可能である（図５参照）。しかしながら、曲管の径の初期値、すなわち、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）の曲管の外径値、内径値等の記録がない場合、扁平量（外径変化量、内径変化量等）の正確な値が得られず、ひいては、信頼性を有する応力評価を行うことは困難である。
【００９７】
また、上記図７〜図９について説明した、磁気異方性センサを用いた管路の曲管の応力評価手法（応力評価手法▲２▼）に関しては、磁気異方性センサの原理的な制約から管の降伏応力のせいぜい７０％程度が測定限界である。また、曲管おける残留応力は、直管等と比較して大きいことから、測定限界は、さらに制限されると考えられる。
【００９８】
次に、図１０を参照しながら、曲管の径（外径、内径等）の初期値の記録がない場合の曲管の応力評価、あるいは、磁気異方性センサの測定限界を超える領域における曲管の応力評価について説明する。
図１０は、管路１００１の概略構成を示す図である。管路１００１は、曲管１００２〜曲管１００５等を有するものとし、そのうち曲管１００２は、評価対象（応力評価の対象）の曲管Ａとし、その他の曲管１００３等は、曲管Ａと同時期に製造された曲管Ｂであるとする。
【００９９】
曲管Ａ等の径の初期値の記録がない場合、まず、曲管Ａに関して、上記の磁気異方性センサを用いた曲管の応力評価手法▲２▼により応力評価を行う。ここで得られた応力分布が磁気異方性センサの測定限界に近い場合、すなわち、測定限界を超えている可能性がある場合、曲管Ａ近辺（曲管Ａの前後等）の曲管、例えば、曲管１００３（曲管Ｂ）に関して、曲管Ａと同様に、上記の磁気異方性センサを用いた曲管の応力評価手法▲２▼により応力評価を行う。
【０１００】
ここで得られた応力分布が磁気異方性センサの測定範囲内であれば、式［７−１］、式［７−２］、式［８］に関して回帰分析等の処理を行い、曲管Ｂに作用するモーメント（Ｍ_Ｂ）を推定する。さらに、式［３−１］、式［３−２］により、この作用モーメント（Ｍ_Ｂ）に対応する曲管Ｂの扁平量（外径変化量、内径変化量等）（２ｅ_Ｂ）を求める。
【０１０１】
次に、曲管Ｂの外径、内径等（２ｒ_Ｂ’）をノギス、ピグ等を用いて測定し、曲管Ｂの外径、内径等の初期値（２ｒ_Ｂ＝２ｒ_Ｂ’−２ｅ_Ｂ）を求める。評価対象の曲管Ａの外径、内径等の初期値（２ｒ_Ａ）は、曲管Ｂと同時期に製造されているとすれば、曲管Ｂの外径、内径等の初期値（２ｒ_Ｂ）と同等とみなすことができる。
【０１０２】
次に、曲管Ａの外径、内径等（２ｒ_Ａ’）をノギス、ピグ等を用いて測定し、曲管Ａの扁平量（外径変化量、内径変化量等）（２ｅ_Ａ＝２ｒ_Ａ’−２ｒ_Ａ＝２ｒ_Ａ’−２ｒ_Ｂ）を求める。
尚、曲管Ａの扁平量（外径変化量、内径変化量等）２ｅ_Ａは、２ｅ_Ａ＝２ｒ_Ａ’−２ｒ_Ａ＝２ｒ_Ａ’−２ｒ_Ｂ＝（２ｒ_Ａ’−２ｒ_Ｂ’）＋２ｅ_Ｂ、と表すことができる。従って、曲管Ａの扁平量（外径変化量、内径変化量等）（２ｅ_Ａ）は、曲管Ｂの扁平量（２ｅ_Ｂ）に曲管Ａと曲管Ｂの外径、内径等の測定値の差（２ｒ_Ａ’−２ｒ_Ｂ’）を加えて算出してもよい。
【０１０３】
次に、上記図１〜図６について説明した、扁平量（曲管の断面扁平量）に基づく曲管の応力評価手法▲１▼と同様にして、曲管Ａの扁平量（外径変化量、内径変化量等）（２ｅ_Ａ）から式［３−１］、式［３−２］により、曲管Ａに作用するモーメントＭ_Ａを求め、式［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ ＆ Ｇｅｏｒｇｅの理論式）により、曲管Ａに発生している応力を評価する。
【０１０４】
尚、曲管Ａに関して、上記の磁気異方性センサを用いた曲管の応力評価手法▲２▼により応力評価を行い、ここで得られた応力分布が磁気異方性センサの測定範囲内であれば、その値をそのまま曲管Ａの応力評価結果として用いてもよい。
【０１０５】
このように、評価対象の曲管Ａに作用する応力が磁気異方性センサの測定限界を超える場合であっても、また、評価対象の曲管Ａの外径、内径等の初期値に関する記録がない場合であっても、評価対象の曲管Ａ近辺の他の曲管Ｂに関して、磁気異方性センサにより応力分布測定を行い、応力評価手法▲２▼における式［７−１］、式［７−２］、式［８］から曲管Ｂに作用するモーメントを求め、応力評価手法▲１▼における式［３−１］、式［３−２］から曲管Ｂの扁平量（外径変化量、内径変化量等）を求め、曲管Ｂの外径、内径等の測定値から曲管Ｂの外径、内径等の初期値を求め、これを曲管Ａの外径、内径等の初期値として曲管Ａの扁平量を算出し、応力評価手法▲１▼により曲管Ａの応力評価を行うことができる。
【０１０６】
次に、図１１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、応力評価の手順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、磁気異方性センサにより測定した応力値、ノギス等により測定した曲管の外径、内径等、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。
【０１０７】
図１１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。上記図１０に関して説明したのと同様に、曲管Ａは、評価対象（応力評価の対象）の曲管であり、曲管Ａ近辺に設置されている曲管Ｂは、曲管Ａと同時期に製造された曲管であるとする。
【０１０８】
曲管Ａに関して、上記の磁気異方性センサを用いた曲管の応力評価手法▲２▼により得られた応力値をコンピュータに入力する（ステップ１１０１）。
コンピュータは、この応力値が磁気異方性センサの測定限界を超えている可能性があるかどうかを判定する（ステップ１１０２）。
この応力値が磁気異方性センサの測定限界を超えている可能性がある場合（ステップ１１０２のＹＥＳ）、曲管Ａ近辺の他の曲管に関して、上記の磁気異方性センサを用いた曲管の応力評価手法▲２▼により得られた応力値をコンピュータに入力する（ステップ１１０３）。
コンピュータは、この応力値が磁気異方性センサの測定限界を超えている可能性があるかどうかを判定する（ステップ１１０４）。
ステップ１１０３〜ステップ１１０４の処理を繰り返し、測定限界範囲内の応力値を示す曲管を選定し、この曲管を曲管Ｂとする。
【０１０９】
コンピュータは、磁気異方性センサにより得られた応力分布に基づいて、式［７−１］、式［７−２］、式［８］に関して回帰分析等の処理を行い、曲管Ｂに作用するモーメント（Ｍ_Ｂ）を算出する（ステップ１１０５）。
コンピュータは、式［３−１］、式［３−２］により、作用モーメント（Ｍ_Ｂ）に対応する曲管Ｂの扁平量（外径変化量、内径変化量等）（２ｅ_Ｂ）を求める（ステップ１１０６）。
【０１１０】
曲管Ｂの外径、内径等（２ｒ_Ｂ’）をノギス、ピグ等を用いて測定し、この測定値をコンピュータに入力する（ステップ１１０７）。
コンピュータは、曲管Ｂの外径、内径等の初期値（２ｒ_Ｂ＝２ｒ_Ｂ’−２ｅ_Ｂ）を求める（ステップ１１０８）。尚、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。
【０１１１】
次に、曲管Ａの外径、内径等（２ｒ_Ａ’）をノギス、ピグ等を用いて測定し、この測定値をコンピュータに入力する（ステップ１１０９）。
コンピュータは、曲管Ａの扁平量（外径変化量、内径変化量等）（２ｅ_Ａ＝２ｒ_Ａ’−２ｒ_Ａ＝２ｒ_Ａ’−２ｒ_Ｂ）を算出する（ステップ１１１０）。尚、評価対象の曲管Ａの外径、内径等の初期値（２ｒ_Ａ）は、曲管Ｂと同時期に製造されているとすれば、曲管Ｂの外径、内径等の初期値（２ｒ_Ｂ）と同等とみなすことができる。
【０１１２】
コンピュータは、曲管Ａの扁平量（２ｅ_Ａ）の算出値を用いて、式［３−１］、式［３−２］により、曲管Ａに作用するモーメント（Ｍ_Ａ）を算出する（ステップ１１１１）。
コンピュータは、曲管Ａに作用するモーメント（Ｍ_Ａ）の算出値を用いて、［１−１］〜式［１−４］（Ｒｏｄａｂａｕｇｈ ＆ Ｇｅｏｒｇｅの理論）により、応力評価を行う（ステップ１１１２）。
【０１１３】
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、磁気異方性センサにより測定した応力分布、ノギス等により測定した曲管の外径、内径等、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。さらに、評価対象の曲管に作用する応力が磁気異方性センサの測定限界を超える場合であっても、また、評価対象の曲管の外径、内径等の初期値に関する記録がない場合であっても、扁平量（曲管の断面扁平量）に基づく曲管の応力評価手法（応力評価手法▲１▼）及び磁気異方性センサを用いた管路の曲管の応力評価手法（応力評価手法▲２▼）に係る処理を実行することにより、コンピュータは、当該初期値を推定、算出して、評価対象の曲管の応力評価を行うことができる。
【０１１４】
尚、曲管Ａの扁平量（外径変化量、内径変化量等）２ｅ_Ａは、２ｅ_Ａ＝２ｒ_Ａ’−２ｒ_Ａ＝２ｒ_Ａ’−２ｒ_Ｂ＝（２ｒ_Ａ’−２ｒ_Ｂ’）＋２ｅ_Ｂ、と表すことができる。従って、曲管Ａの扁平量（外径変化量、内径変化量等）（２ｅ_Ａ）は、曲管Ｂの扁平量（２ｅ_Ｂ）に曲管Ａと曲管Ｂの外径、内径等の測定値の差（２ｒ_Ａ’−２ｒ_Ｂ’）を加えて算出してもよい。
【０１１５】
また、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。
【０１１６】
この場合、端末装置からネットワークを介して磁気異方性センサにより得られた曲管の応力分布を応力評価サーバに入力（ステップ１１０１、ステップ１１０３）したり、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１１０７、ステップ１１０９）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１１１０〜ステップ１１１２）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。
【０１１７】
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。
【０１１８】
次に、図１２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１２は、管１２０２の応力解放方法の概要図を示す。地盤１２０１には管１２０２が埋設されている。この管１２０２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１２０４を決定する。
【０１１９】
応力解放部１２０４の下部の掘削部１２０５の地盤を掘削し、管１２０２の応力解放部１２０４を応力解放部１２０３の位置に移動させる。そして、掘削部１２０５を再度埋め立て、管１２０２の位置を補修する。
【０１２０】
次に、図１３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１３は、管１３０２の応力解放方法の概要図を示す。地盤１３０１には管１３０２が埋設されている。この管１３０２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１３０３を決定する。応力解放部１３０３の両端付近を切断し、応力解放部１３０３の中央部分を除去する。そして、切断部１３０４と切断部１３０５を接合し、管１３０２の位置を補修する。
【０１２１】
図１２及び図１３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。
【０１２２】
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。
【０１２３】
【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】 磁気異方性センサの動作原理を示す図
【図８】 図７に示した磁気異方性センサの部分的な詳細図
【図９】 磁気異方性センサによる、曲管の応力分布測定の概略を示す図
【図１０】 管路の概略構成を示す図
【図１１】 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１２】 管のメンテナンス及び補修に関する説明図
【図１３】 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
７０１………磁気異方性センサ
７０２………励磁コア
７０３………磁気異方性検出コア
７０４………励磁コイル
７０５………磁気異方性検出コイル
７０６………電源
７０７………電圧計
７０８………測定対象物
９０１………曲管
９０２………磁気異方性センサ
１００１………管路
１００２………評価対象の曲管
１００３、１００４、１００５………曲管[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 relates to a first stress-moment relational expression showing a relationship between a moment acting on a curved pipe constituting the pipe and a distribution of stresses generated in the curved pipe. The step of calculating the moment by regressing the measured value of the stress distribution, and the second stress-moment relational expression indicating the relationship between the moment and the stress distribution are expanded with respect to the displacement in the sectional direction of the curved pipe. A first flat amount calculation step of calculating the flat amount by inputting the moment into a moment-flat amount relational expression showing a relationship between the flat amount of the bent pipe and the moment, derived by It is the stress evaluation method of the curved pipe characterized by comprising.
[0012]
In the stress evaluation method described above, the initial values of the diameters of the first curved pipe and the second curved pipe constituting the pipe are regarded as equivalent, and the first flat amount calculation step calculates the first A second flat amount calculating step of calculating a flat amount of the second bent pipe based on a flat amount of the bent pipe and a measured value of a diameter of the first bent pipe and the second bent pipe; By inputting the flattening amount of the second curved pipe into the moment-flattening relational expression, the moment acting on the second curved pipe is calculated, and this moment is inputted into the second stress-moment relational expression. And calculating the stress distribution of the second bent pipe.
[0013]
In the first invention, the distribution of stress generated in the curved pipe is measured using a magnetic anisotropy sensor or the like, and the regression analysis is performed on the first stress-moment relational expression based on the measured value of the distribution of stress. Thus, the moment acting on the bent pipe is calculated, and the flat amount of the bent pipe is calculated from the moment-flat amount relational expression.
[0014]
In the first invention, the flatness of the first curved pipe calculated by the first flattening amount calculating step is assumed with the initial values of the diameters of the first curved pipe and the second curved pipe constituting the pipe being equivalent. The flat amount of the second bent pipe is calculated based on the amount and the measured values of the diameters of the first bent pipe and the second bent pipe, and the flat amount of the second bent pipe is calculated as a moment-flat amount relationship. The moment acting on the second curved pipe is calculated by inputting into the equation, and this moment is input to the second stress-moment relational expression to calculate the stress distribution of the second curved tube.
[0015]
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.
The “first bent pipe” is manufactured at the same time as the bent pipe subjected to stress evaluation, and is a bent pipe whose initial value of the diameter (inner diameter, outer diameter, etc.) can be regarded as equivalent to the bent pipe subjected to stress evaluation. For example, it is a curved pipe arranged in the vicinity of the curved pipe subject to stress evaluation.
The “second bent pipe” is a bent pipe subjected to stress evaluation.
[0016]
The “sensor” measures stress generated in the curved pipe, and is, for example, a magnetic anisotropy sensor. Incidentally, regarding the stress distribution measurement by the magnetic anisotropy sensor, it is known that the measurement limit is about 70% of the yield stress of the pipe at most because of the fundamental limitation. Moreover, since the residual stress in a curved pipe is large compared with a straight pipe etc., it is thought that a measurement limit is further restrict | limited. Details of the stress measurement by the magnetic anisotropy sensor will be described later.
[0017]
“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. That is, the amount of flatness generated by the external force corresponds to the difference between the initial value of the diameter of the curved pipe and the measured value of the diameter of the curved pipe at the current time.
[0018]
The “first stress-moment relational expression” indicates the relationship between the moment acting on the curved pipe and the stress (tube axial stress, pipe circumferential stress, etc.) generated in the curved pipe. It is a theoretical formula. Karman's theoretical formula theoretically explains the distribution of stress generated in the bent pipe portion when a moment acts on the bent pipe. The details of Karman's theory (Karman's flat stress theory) will be described later.
[0019]
The “second stress-moment relational expression” includes the moment acting on the curved pipe (in-plane bending moment, out-of-plane bending moment, etc.) and the stress generated in the curved pipe (tube axial stress, pipe circumferential stress, etc.) This shows the relationship. Further, this second stress-moment relational expression 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. Desirably, for example, the theoretical formula of Rodabaugh & George. Details of this theoretical formula will be described later.
[0020]
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.
[0021]
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 in the direction of 0 ° in the circumferential direction,
2 x e_oIs the amount of flatness in the direction of 45 ° in the circumferential direction,
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.
[0022]
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.
[0023]
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.
[0024]
In the first invention, the stress distribution of the curved pipe is measured by a sensor such as a magnetic anisotropy sensor, the acting moment of the curved pipe is calculated using Karman's theoretical formula, etc., and the moment-flat amount relational expression is used. Since the flattening amount of the curved pipe is calculated from the acting moment of the curved pipe, the flattening amount of the curved pipe can be calculated even when the initial value of the diameter of the curved pipe is not recorded. It is also possible to calculate the initial value of the diameter of the bent pipe by measuring the diameter of the bent pipe.
[0025]
In the first aspect of the invention, the initial value of the diameter of the predetermined curved pipe is used as the initial value of the diameter of the curved pipe subjected to stress evaluation, thereby calculating the flat amount of the curved pipe subjected to stress evaluation, and the moment-flat amount. The stress distribution of the bent pipe subject to the stress evaluation is calculated by a relational expression, a theoretical equation of Rodabaugh & George, and the like. In this case, even if there is no record of the initial value of the diameter of the bent pipe subjected to stress evaluation, the stress evaluation of the bent pipe can be performed. Moreover, even when the measurement limit of the magnetic anisotropy sensor is exceeded, such as a range exceeding the yield stress of the tube, stress evaluation can be performed.
[0026]
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.
[0027]
According to a second aspect of the present invention, in the first stress-moment relational expression showing the relationship between the moment acting on the curved pipe constituting the pipe and the distribution of the stress generated in the curved pipe, the measured value of the stress distribution by the sensor is obtained. Means for calculating the moment by regression, and a second stress-moment relational expression indicating a relation between the moment and the distribution of the stress, which is derived by developing the sectional displacement of the curved pipe. And a first flat amount calculating means for calculating the flat amount by inputting the moment into a moment-flat amount relational expression indicating a relationship between the flat amount of the pipe and the moment. It is a stress evaluation apparatus of a pipe.
[0028]
Further, the stress evaluation apparatus considers the initial values of the diameters of the first curved pipe and the second curved pipe constituting the pipe as equivalent, and calculates the first flat amount calculation step by the first flat amount calculation step. A second flat amount calculating means for calculating a flat amount of the second bent pipe based on a flat amount of the bent pipe and a measured value of a diameter of the first bent pipe and the second bent pipe; The moment acting on the second curved pipe is calculated by inputting the flat amount of the second curved pipe into the moment-flat quantity relational expression, and this moment is inputted into the second stress-moment relational expression. And a means for calculating the stress distribution of the second bent pipe.
[0029]
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 first stress-moment relational expression, the second stress-moment relational expression, the flatness-moment relational expression, and the like in a memory or a database.
[0030]
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.
[0031]
In this case, the measured value of the diameter of the curved pipe, the measured value of the stress distribution of the curved pipe by the magnetic anisotropy sensor, and the like can be input from the terminal device to the stress evaluation server via the network. The stress evaluation server can calculate the initial value of the diameter of the bent pipe, the flattening amount, the acting moment, the stress distribution, and the like, 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.
[0032]
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.
[0033]
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.
[0034]
The configuration and characteristics of the present invention will be clarified in the embodiments and the accompanying drawings described below.
[0035]
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.
[0036]
First, stress evaluation of a curved pipe based on a flat amount (a cross-sectional flat amount of a curved pipe) will be described with reference to FIGS.
[0037]
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.
[0038]
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.
[0039]
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.
[0040]
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.
[0041]
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]
[0042]
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. λ is a pipe coefficient.
[0043]
F₁(Φ), f₂(Φ), f₃(Φ), f₄Specifically, (φ) is expressed as follows.
[Formula 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.
[0044]
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.
[0045]
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.
[0046]
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.
[0047]
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.
[0048]
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.
[0049]
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.
[0050]
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]
[0051]
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.
[0052]
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].
[0053]
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 °.
[0054]
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 °.
[0055]
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.
[0056]
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_{i C}, Σ_oL, Σ_oC) Can be calculated.
[0057]
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.
[0058]
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.
[0059]
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.
[0060]
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.
[0061]
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.
[0062]
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.
[0063]
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.
[0064]
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.
[0065]
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.
[0066]
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.
[0067]
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).
[0068]
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.
[0069]
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.
[0070]
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.
[0071]
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.
[0072]
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.
[0073]
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).
[0074]
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]
[0075]
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.
[0076]
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.
[0077]
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.
[0078]
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.
[0079]
Next, stress evaluation of a curved pipe in a pipe line using a magnetic anisotropy sensor will be described with reference to FIGS.
First, the operation principle of the magnetic anisotropy sensor will be described.
FIG. 7 is a diagram showing the operating principle of the magnetic anisotropy sensor.
FIG. 8 is a partial detail view of the magnetic anisotropy sensor shown in FIG.
[0080]
The magnetic anisotropy sensor 701 includes an excitation core 702, a magnetic anisotropy detection core 703, and the like. A measurement object 708 is an object to be measured by the magnetic anisotropy sensor 701. The excitation core 702 and the magnetic anisotropy detection core 703 are disposed in an orthogonal state. A tensile stress σ acts on the measurement object 708 in the X direction. The magnetic permeability of the measurement object 708 is μ, the X direction component of the magnetic permeability μ is μx, and the Y direction component is μy. The excitation core 702 has an excitation coil 704, and the magnetic anisotropy detection core 703 has a magnetic anisotropy detection coil 705.
[0081]
When stress (strain) acts on the measurement object 708, anisotropy occurs in the magnetic permeability μ. When the measurement object 708 is in a stress state as shown in FIG. 7, the permeability μx in the X direction, which is the tensile stress direction, is relatively larger than the permeability μy in the Y direction.
[0082]
At this time, when a current is supplied to the exciting coil 704 from the power source 706, most of the magnetic flux emitted from the tip of one leg of the exciting core 702 goes directly to the other leg at the shortest distance. Due to the directivity, a part of the magnetic anisotropy detection core 703 goes to the other leg of the excitation core 702.
[0083]
When the above magnetic circuit is formed by an alternating magnetic field, an induced current flows through the magnetic anisotropy detection coil 705 and a voltage is detected by the voltmeter 707. This voltage value V is proportional to the difference between the magnetic permeability μx in the X direction and the magnetic permeability μy in the Y direction, that is, (μx−μy). The magnetic permeability μ is proportional to the stress (strain) σ (X-direction component σx, Y-direction component σy) of the measurement object 708. Therefore, the following relational expression holds.
[0084]
V = K0 × (μx−μy) [6-1]
However, K0 is a proportional constant.
V = K1 × (σx−σy) [6-2]
However, K1 is a proportional constant.
[0085]
Thus, the magnetic anisotropy sensor 701 outputs the voltage value V proportional to the stress difference (σx−σy) between the X direction and the Y direction as a detection value. Therefore, if the proportionality constant K1 is known, the stress difference (σx−σy) between the X direction and the Y direction can be calculated by the equation [6-2]. The above is the principle of stress measurement using a magnetic anisotropy sensor.
[0086]
Next, Karman's flat stress theory will be described. Karman's flat stress theory theoretically explains the distribution in the pipe circumferential direction of the stress generated in the bent pipe portion when a moment acts on the bent pipe. Pipe axial stress σ when moment (M) acts on the curved pipe_L, Pipe circumferential stress σ_C, Can be expressed as follows according to Karman's flat stress theory.
[0087]
σ_L(Φ) = kmr / I × {sin φ−6 sin³φ / (5 + 6λ²) + 9νλcos2φ / (5 + 6λ)²]} ... [7-1]
σ_C(Φ) = kMr / I × {ν (sin φ−6 sin³φ / (5 + 6λ²)) + 9λcos 2φ / (5 + 6λ)²]} ... [7-2]
[0088]
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: moment acting on the curved pipe.
λ is a pipe coefficient, and λ = tR / r²It is.
k is a deflection coefficient, and k = (10 + 12λ²) / (1 + 12λ²).
[0089]
Further, as described above, the output of the magnetic anisotropy sensor is the stress difference (σ in two orthogonal directions) as can be seen from the equation [6-2]._L(Φ) −σ_C(Φ)). Stress difference between two orthogonal directions (σ_L(Φ) −σ_C(Φ)) is expressed as follows.
[0090]
σ_L(Φ) −σ_C(Φ) = kMr / I × {(1-ν) sinφ− (1 + ν) 6 sin³φ / (5 + 6λ²)-(1-ν) 9λcos 2φ / (5 + 6λ)²]} [8]
[0091]
Therefore, when a moment acts on the curved pipe portion, when the stress generated on the pipe surface is measured by the magnetic anisotropy sensor, the distribution shape of the equation [8] is obtained. The above is an overview of Karman's flat stress theory.
[0092]
FIG. 9 is a diagram showing an outline of the stress distribution measurement of a curved pipe by a magnetic anisotropy sensor.
The magnetic anisotropy sensor 902 measures the stress distribution while scanning the surface of the curved tube 901 in the circumferential direction. The magnetic anisotropy sensor 902 measures the stress of the curved pipe 901 while moving at equal intervals as indicated by a section 903. Using a statistical method such as the least square method, the measurement result is regressed to Equation [8] (σ_L(Φ) −σ_C(Φ)) distribution, and the measurement result and this (σ)_L(Φ) −σ_C(Φ)) is regressed to Equation [7-1] and Equation [7-2] to obtain σ_L(Φ), σ_C(Φ), M (moment acting on the curved pipe) can be estimated.
[0093]
Due to its principle, the magnetic anisotropy sensor measures not only the load stress caused by an external force such as moment but also the residual stress in a superimposed manner. Accordingly, the residual stress component is removed by regressing to the equation [8] without directly obtaining the maximum stress and the minimum stress from the measurement result of the magnetic anisotropy sensor.
[0094]
Considering that the residual stress is distributed randomly in the circumferential direction of the tube from the macro viewpoint, that is, averaged, the residual stress component is removed by regressing to Equation [8], and purely due to the moment. Only the load stress is extracted. In addition to the residual stress, the stress due to the pressure of the internal fluid of the pipe, and the stress appearing as a constant value having no distribution in the pipe circumferential direction, such as simple tension or compression in the pipe axis direction, can be expressed by Equation [8]. It is possible to remove in the same manner as the residual stress by returning to.
[0095]
In this way, the stress distribution is measured by moving the magnetic anisotropy sensor in the circumferential direction of the curved pipe, and the measured values are subjected to regression analysis into the equations [7-1], [7-2], and [8]. By doing so, it is possible to evaluate the stress generated in the bent pipe and estimate the acting moment.
[0096]
In addition, regarding the stress evaluation method (stress evaluation method {circle around (1)}) of the bent pipe based on the flat amount (cross-sectional flat amount of the bent pipe) described with reference to FIGS. Is possible (see FIG. 5). However, if there is no record of the initial diameter value of the curved pipe, that is, the outer diameter value or inner diameter value of the curved pipe in a state where it has not been subjected to cross-sectional deformation due to external force (production, installation, etc.), the flat amount (outside The accurate value of the diameter change amount, the inner diameter change amount, etc.) cannot be obtained, and as a result, it is difficult to perform stress evaluation with reliability.
[0097]
Further, regarding the stress evaluation method (stress evaluation method {circle around (2)}) of the curved pipe of the pipe using the magnetic anisotropy sensor described with reference to FIGS. Therefore, the measurement limit is about 70% of the yield stress of the pipe. Moreover, since the residual stress in a curved pipe is large compared with a straight pipe etc., it is thought that a measurement limit is further restrict | limited.
[0098]
Next, referring to FIG. 10, in a region where the initial value of the diameter (outer diameter, inner diameter, etc.) of the bent pipe is not recorded, or in a region exceeding the measurement limit of the magnetic anisotropy sensor. The stress evaluation of a curved pipe will be described.
FIG. 10 is a diagram illustrating a schematic configuration of the pipe line 1001. The pipe 1001 has curved pipes 1002 to 1005 and the like. Among them, the curved pipe 1002 is a curved pipe A to be evaluated (stress evaluation target), and the other curved pipes 1003 and the like are curved pipe A and the like. It is assumed that the curved pipe B is manufactured at the same time.
[0099]
When the initial value of the diameter of the curved pipe A or the like is not recorded, first, stress evaluation is performed on the curved pipe A by the curved pipe stress evaluation method {circle around (2)} using the magnetic anisotropy sensor. When the stress distribution obtained here is close to the measurement limit of the magnetic anisotropy sensor, that is, when there is a possibility that the measurement limit is exceeded, a curved pipe in the vicinity of the curved pipe A (such as before and after the curved pipe A), For example, with respect to the curved pipe 1003 (curved pipe B), stress evaluation is performed by the curved pipe stress evaluation method {circle around (2)} using the magnetic anisotropy sensor, similarly to the curved pipe A.
[0100]
If the stress distribution obtained here is within the measurement range of the magnetic anisotropy sensor, a process such as regression analysis is performed on the equations [7-1], [7-2], and [8], and the curved pipe Moment acting on B (M_B). Furthermore, the acting moment (M) is obtained by the equations [3-1] and [3-2]._B) Of the curved pipe B corresponding to the outer diameter change amount, the inner diameter change amount, etc. (2e)_B)
[0101]
Next, the outer diameter and inner diameter of the curved pipe B (2r_B′) Is measured using calipers, pigs, etc., and the initial values (2r) of the outer diameter and inner diameter of the bent pipe B are measured._B= 2r_B'-2e_B) Initial value (2r) of outer diameter, inner diameter, etc. of bent pipe A to be evaluated_A) Is an initial value (2r) of the outer diameter, inner diameter, etc. of the bent pipe B if it is manufactured at the same time as the bent pipe B._B).
[0102]
Next, the outer diameter and inner diameter of the curved pipe A (2r_A′) Is measured using calipers, pigs, etc., and the flattened amount (outer diameter change amount, inner diameter change amount, etc.) of the curved pipe A (2e)_A= 2r_A'-2r_A= 2r_A'-2r_B)
In addition, the flat amount of the bent pipe A (outer diameter change amount, inner diameter change amount, etc.) 2e_AIs 2e_A= 2r_A'-2r_A= 2r_A'-2r_B= (2r_A'-2r_B′) + 2e_B,It can be expressed as. Accordingly, the flat amount of the curved pipe A (outer diameter change amount, inner diameter change amount, etc.) (2e_A) Is the flat amount (2e) of the curved pipe B_B) And the difference in measured values of the outer diameter and inner diameter of the curved pipe A and the curved pipe B (2r)_A'-2r_B′) May be added for calculation.
[0103]
Next, in the same manner as the curved pipe stress evaluation method (1) based on the flattening amount (cross-sectional flattening amount of the curved pipe) described with reference to FIGS. , Inner diameter change, etc.) (2e_A) To Eqs. [3-1] and [3-2], the moment M acting on the curved pipe A_AAnd the stress generated in the curved pipe A is evaluated by the equations [1-1] to [1-4] (Rodabaugh & George's theoretical equation).
[0104]
For the curved pipe A, stress evaluation is performed by the curved pipe stress evaluation method (2) using the magnetic anisotropy sensor, and the obtained stress distribution is within the measurement range of the magnetic anisotropy sensor. If there is, the value may be used as the stress evaluation result of the curved pipe A as it is.
[0105]
As described above, even if the stress acting on the bending pipe A to be evaluated exceeds the measurement limit of the magnetic anisotropy sensor, the initial value such as the outer diameter and inner diameter of the bending pipe A to be evaluated is recorded. Even if there is not, the stress distribution measurement is performed with the magnetic anisotropy sensor for the other bent pipe B in the vicinity of the bent pipe A to be evaluated, and the equations [7-1] and [7] in the stress evaluation method (2) are used. The moment acting on the curved pipe B is obtained from [7-2] and [8], and the flat amount of the curved pipe B (outside is calculated from the formula [3-1] and the formula [3-2] in the stress evaluation method (1). Diameter change amount, inner diameter change amount, etc.), and initial values such as the outer diameter and inner diameter of the bent pipe B are obtained from the measured values of the outer diameter and inner diameter of the bent pipe B, and the outer diameter and inner diameter of the bent pipe A are obtained. The flattening amount of the curved pipe A can be calculated as an initial value such as and the stress evaluation of the curved pipe A can be performed by the stress evaluation method (1).
[0106]
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 equations [1-1] to [5-2] and other calculation formulas, procedures for stress evaluation, and the like in the computer, the computer measures the stress value measured by the magnetic anisotropy sensor. When other necessary numerical values such as the outer diameter and inner diameter of the bent pipe measured with calipers are input, the stress evaluation of the bent pipe and the calculation of the stress distribution can be performed.
[0107]
FIG. 11 is a flowchart illustrating a process executed by a computer as a stress evaluation apparatus for a curved pipe. As described above with reference to FIG. 10, the curved pipe A is a curved pipe to be evaluated (stress evaluation target), and the curved pipe B installed in the vicinity of the curved pipe A is in the same period as the curved pipe A. Suppose that it is a curved pipe manufactured in
[0108]
For the curved pipe A, the stress value obtained by the curved pipe stress evaluation method (2) using the magnetic anisotropy sensor is input to the computer (step 1101).
The computer determines whether the stress value may exceed the measurement limit of the magnetic anisotropy sensor (step 1102).
When there is a possibility that this stress value exceeds the measurement limit of the magnetic anisotropy sensor (YES in Step 1102), the bending using the magnetic anisotropy sensor described above is performed for the other bending pipes near the bending pipe A. The stress value obtained by the pipe stress evaluation method (2) is input to the computer (step 1103).
The computer determines whether this stress value may exceed the measurement limit of the magnetic anisotropy sensor (step 1104).
The process from step 1103 to step 1104 is repeated, a curved pipe showing a stress value within the measurement limit range is selected, and this curved pipe is defined as a curved pipe B.
[0109]
Based on the stress distribution obtained by the magnetic anisotropy sensor, the computer performs processing such as regression analysis on the equations [7-1], [7-2], and [8], and acts on the curved pipe B. Moment (M_B) Is calculated (step 1105).
The computer uses the equations [3-1] and [3-2] to calculate the acting moment (M_B) Of the curved pipe B corresponding to the outer diameter change amount, the inner diameter change amount, etc. (2e)_B) Is obtained (step 1106).
[0110]
Outer diameter, inner diameter, etc. of curved pipe B (2r_B′) Is measured using calipers, pigs, etc., and the measured value is input to the computer (step 1107).
The computer uses initial values such as the outer diameter and inner diameter of the curved pipe B (2r_B= 2r_B'-2e_B) Is obtained (step 1108). The initial values are the outer diameter, inner diameter, etc. of the bent pipe in a state where it has not been subjected to cross-sectional deformation due to external force (manufacturing, installation, etc.).
[0111]
Next, the outer diameter and inner diameter of the curved pipe A (2r_A′) Is measured using calipers, pigs, etc., and the measured value is input to the computer (step 1109).
The computer calculates the flat amount of the curved pipe A (outer diameter change amount, inner diameter change amount, etc.) (2e_A= 2r_A'-2r_A= 2r_A'-2r_B) Is calculated (step 1110). In addition, initial values (2r) of the outer diameter and inner diameter of the bent pipe A to be evaluated_A) Is an initial value (2r) of the outer diameter, inner diameter, etc. of the bent pipe B if it is manufactured at the same time as the bent pipe B._B).
[0112]
The computer calculates the flat amount of curved pipe A (2e_A) Using the calculated value, the moment (M) acting on the curved pipe A according to the equations [3-1] and [3-2]._A) Is calculated (step 1111).
The computer uses the moment (M_A), The stress is evaluated according to [1-1] to [1-4] (Rodabaugh & George theory) (step 1112).
[0113]
Through the above process, the computer as the stress evaluation apparatus receives the necessary values such as the stress distribution measured by the magnetic anisotropy sensor and the outer diameter and inner diameter of the curved pipe measured by calipers. Pipe stress evaluation and stress distribution calculation can be performed. In addition, even when the stress acting on the bending pipe to be evaluated exceeds the measurement limit of the magnetic anisotropy sensor, or when there is no record regarding the initial value of the outer diameter and inner diameter of the bending pipe to be evaluated. Even in such a case, a stress evaluation method (stress evaluation method {circle around (1)}) of a curved pipe based on a flat amount (a cross-sectional flat amount of a curved pipe) and a stress evaluation method (stress) of a curved pipe using a magnetic anisotropy sensor. By executing the processing related to the evaluation method (2)), the computer can estimate and calculate the initial value and perform stress evaluation of the bending pipe to be evaluated.
[0114]
In addition, the flat amount of the bent pipe A (outer diameter change amount, inner diameter change amount, etc.) 2e_AIs 2e_A= 2r_A'-2r_A= 2r_A'-2r_B= (2r_A'-2r_B′) + 2e_B,It can be expressed as. Accordingly, the flat amount of the curved pipe A (outer diameter change amount, inner diameter change amount, etc.) (2e_A) Is the flat amount (2e) of the curved pipe B_B) And the difference in measured values of the outer diameter and inner diameter of the curved pipe A and the curved pipe B (2r)_A'-2r_B′) May be added for calculation.
[0115]
Also, the computer as the stress evaluation device is connected to a network such as the Internet as a stress evaluation server, and a terminal device (personal computer, portable information terminal, mobile phone, etc.) can access this server via the network. You can also
[0116]
In this case, the stress distribution of the curved pipe obtained by the magnetic anisotropy sensor from the terminal device via the network is input to the stress evaluation server (step 1101, step 1103), or the measured value of the outer diameter or inner diameter is input to the network. To the stress evaluation server (step 1107, step 1109). 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 1110 to 1112), 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.
[0117]
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.
[0118]
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. 12 shows a schematic diagram of a stress relief method for the tube 1202. A pipe 1202 is embedded in the ground 1201. The stress is calculated for any point (bent tube portion or the like) of the tube 1202 by the method described in the above embodiment, the necessity of stress release is determined, and the stress release portion 1204 is determined.
[0119]
The ground of the excavation part 1205 below the stress release part 1204 is excavated, and the stress release part 1204 of the pipe 1202 is moved to the position of the stress release part 1203. And the excavation part 1205 is refilled again and the position of the pipe | tube 1202 is repaired.
[0120]
Next, the maintenance and repair of the pipe using the stress evaluation method and the stress evaluation apparatus described above will be described with reference to FIG. FIG. 13 shows a schematic diagram of a stress relief method for the tube 1302. A pipe 1302 is embedded in the ground 1301. For any point (bent tube portion or the like) of the tube 1302, 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 1303 is determined. The vicinity of both ends of the stress release portion 1303 is cut, and the central portion of the stress release portion 1303 is removed. Then, the cutting portion 1304 and the cutting portion 1305 are joined to repair the position of the tube 1302.
[0121]
As described with reference to FIGS. 12 and 13, by using the stress evaluation method and the stress evaluation apparatus according to the embodiment of the present invention, the stress at an arbitrary point can be easily calculated at the site, Can be repaired.
[0122]
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.
[0123]
【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 diagram showing the operating principle of a magnetic anisotropy sensor.
FIG. 8 is a partial detail view of the magnetic anisotropy sensor shown in FIG. 7;
FIG. 9 is a diagram showing an outline of stress distribution measurement of a curved pipe by a magnetic anisotropy sensor.
FIG. 10 is a diagram showing a schematic configuration of a pipeline.
FIG. 11 is a flowchart showing processing executed by a computer as a stress evaluation device for a curved pipe;
FIG. 12 is an explanatory diagram related to pipe maintenance and repair.
FIG. 13 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
701: Magnetic anisotropy sensor
702 ... Excitation core
703 ... Magnetic anisotropy detection core
704 ..... Excitation coil
705 ... Magnetic anisotropy detection coil
706 ... …… Power
707 ……… Voltmeter
708 ... Measurement object
901 ......... Tube
902 ... Magnetic anisotropy sensor
1001 .... Pipe line
1002 ......... Tube for evaluation
1003, 1004, 1005 ......... curved pipe

Claims (12)

By regressing the measured value of the stress distribution by the sensor to the first 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, the moment Calculating
The relationship between the flattening amount of the curved pipe and the moment, which is derived by developing the second stress-moment relational expression showing the relation between the moment and the distribution of the stress with respect to the displacement in the sectional direction of the curved pipe, is shown. A first flat amount calculation step of calculating the flat amount by inputting the moment into a moment-flat amount relational expression;
A stress evaluation method for a curved pipe, comprising: The initial values of the diameters of the first bent pipe and the second bent pipe constituting the pipe are regarded as equivalent, and the flat amount of the first bent pipe calculated by the first flat amount calculating step and the first A second flattening amount calculating step for calculating a flattening amount of the second bent pipe based on the measured value of the diameter of the bent pipe and the second bent pipe;
By inputting the flattening amount of the second curved pipe into the moment-flattening relational expression, the moment acting on the second curved pipe is calculated, and this moment is inputted into the second stress-moment relational expression. Calculating the stress distribution of the second bent pipe;
The bent pipe stress evaluation method according to claim 1, comprising: 3. The first stress-moment relational expression is Karman's theoretical expression, and the second stress-moment relational expression is Rodabaugh & George's theoretical expression. The stress evaluation method of the curved pipe as described. The moment-flat amount relational expression is
M _i = η ₁ EI / k _p R × e _i ,
M _o = η ₂ EI / k _p R × e _o ,
The stress evaluation method for a curved pipe according to any one of claims 1 to 3, 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 in the direction of 0 ° in the circumferential direction,
2 × _eo is the amount of flatness 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 4, 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. By regressing the measured value of the stress distribution by the sensor to the first 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, the moment Means for calculating
The relationship between the flattening amount of the curved pipe and the moment, which is derived by developing the second stress-moment relational expression showing the relation between the moment and the distribution of the stress with respect to the displacement in the sectional direction of the curved pipe, is shown. A first flat amount calculating means for calculating the flat amount by inputting the moment into a moment-flat amount relational expression;
A stress evaluation apparatus for a curved pipe, comprising: The initial values of the diameters of the first bent pipe and the second bent pipe constituting the pipe are regarded as equivalent, and the flat amount of the first bent pipe calculated by the first flat amount calculating step and the first A second flat amount calculating means for calculating a flat amount of the second bent pipe based on the curved pipe and a measured value of the diameter of the second bent pipe;
By inputting the flattening amount of the second curved pipe into the moment-flattening relational expression, the moment acting on the second curved pipe is calculated, and this moment is inputted into the second stress-moment relational expression. Means for calculating the stress distribution of the second bent pipe;
The apparatus for evaluating stress of a bent pipe according to claim 6. The first stress-moment relational expression is Karman's theoretical expression, and the second stress-moment relational expression is Rodabaugh & George's theoretical expression. The stress evaluation apparatus of the described curved pipe. The moment-flat amount relational expression 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 any one of claims 6 to 8, 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 in the direction of 0 ° in the circumferential direction,
2 × _eo is the amount of flatness 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 9, 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. The program which makes a computer function as a stress evaluation apparatus in any one of Claims 6-10. A recording medium on which a program for causing a computer to function as the stress evaluation apparatus according to any one of claims 6 to 10 is recorded.

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