JP2004028769A - Stress evaluating method for curved pipe, stress evaluating device, program, and storage medium for the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a stress evaluating method and a stress evaluating device for evaluating a curved pipe for simply and precisely calculating the stress generated in the curved pipe constituting a pipe line. <P>SOLUTION: Regarding the curved pipe A to be evaluated, if a measuring limit is exceeded, the stress evaluation is performed as follows: a distribution of the stress in a curved pipe B being adjacent to the pipe A is measured by a magnetic anisotropy sensor, flatness value of the curved pipe B is obtained from the relational formula of the stress-moment relation and the moment-flatness value, and an initial diameter of the pipe B is obtained from a measure of the diameter of the pipe B. The flatness vale of the pipe A is obtained from the measurement of the diameter of the pipe A considering that the initial value of diameter of the pipe B is equivalent to that of the pipe A, and the distribution of the stress in the curved pipe A is calculated using the relational formula of moment-flatness value and the relational formula of stress-moment. Wherein, the relational formula of moment-flatness value is derived e.g. by developing the theoretical formula of Rodabaugh & George etc., regarding displacement in a sectional direction of the curved pipe. <P>COPYRIGHT: (C)2004,JPO

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]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a pipeline stress evaluation method, a stress evaluation device, and the like. More specifically, the present invention relates to a stress evaluation method, a stress evaluation device, and the like in a curved pipe portion forming a pipe.
[0002]
[Prior art]
In general, when laying a pipeline (line pipe) that supplies gas, etc., stress due to external force due to land subsidence etc. occurs in the pipeline, but in order to absorb displacement due to external force around the common groove and abutment , Curved tubes are often used. In order to safely maintain the pipeline, it is important to know where the maximum stress occurs on the pipeline. In addition, since the maximum stress generally occurs in a curved pipe portion, stress evaluation in the curved pipe section is particularly important. Since the pipeline is in service and the above-mentioned stress evaluation is based on nondestructive diagnosis in principle, it is difficult to use a measuring method with a strain gauge.
[0003]
2. Description of the Related Art Conventionally, the following method is employed for stress evaluation of a pipe such as a curved pipe portion. First, at a plurality of measurement points, the amount of settlement is measured and leveling is performed. The measurement of the settlement amount is performed by a settlement rod or the like installed in the buried portion, and the leveling is performed at a measurement point or the like provided in the support unit in the joint premises. Next, a finite element method (FEM) model considering the shape of the pipeline is created. Then, the measured value of the settlement amount and the measured value of the leveling are input to the finite element method model as the deformation amount of the pipeline, and the analysis is performed, and the stress of the curved pipe portion is evaluated 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 stress in a pipeline using a magnetic anisotropic sensor.
[0005]
The method according to Japanese Patent Publication No. 7-62636 discloses a method in which, when a moment is applied to a straight pipe portion of a pipe, the stress generated on the pipe surface is evaluated mechanically and it is assumed that the cross section of the pipe is not deformed. Focusing on the fact that the stress distribution on the pipeline surface becomes a SIN function with a period of 360 degrees, by regressing the output of the magnetic anisotropy sensor to this 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 the bending.
[0006]
According to the method according to Japanese Patent Publication No. 7-69226, when a moment acts on a straight pipe portion of a pipeline, the pipeline undergoes cross-sectional deformation due to flattening. Evaluation, focusing on the fact that the stress distribution on the pipeline surface becomes a SIN function with a period of 180 degrees, and by regressing the output of the magnetic anisotropy sensor to this SIN function, the amplitude component and phase angle of the SIN function Therefore, the magnitude of the flat stress and the direction of the flat stress are determined from the above.
[0007]
[Problems to be solved by the invention]
However, in order to ensure the accuracy of 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 settlement and leveling. For example, in the case of a pipe having a diameter of 600 mm, measurement data over a minimum of 50 m is required at intervals of about 5 m. For this reason, the cost for measurement increases. Further, since these measurement data are repeatedly analyzed by the finite element method, there is a problem that cost and time are required, and that the presence of a skilled person is indispensable for the work.
[0008]
In the case of a curved tube, it is difficult to directly measure the degree of stress in a non-destructive state. The prior arts described in Japanese Patent Publication No. 7-62636 and Japanese Patent Publication No. 7-69226 are methods for estimating bending stress or flat stress of a straight pipe portion. Therefore, even if the magnetostriction method of measuring the stress in a non-destructive manner by using a magnetic anisotropic sensor is used, the pure bending stress in the straight pipe portion which is not affected by the cross-sectional deformation of the curved pipe is measured, and the finite element method is used. The indirect method of estimating the stress of the curved pipe portion by using the analysis means such as the above is merely performed.
[0009]
Further, the cross-section of the curved pipe that has received the in-plane bending moment has the largest flatness at the central part of the curved pipe, and the flattened end of the curved pipe has about 70% of the central part. The flatness disappears depending on the radius of curvature, but in the case of a radius of curvature of about 1.5 DR, it is about 3D away from the end of the curved pipe. If the target pipe is 750 mm in diameter, a separation of 2 m or more is necessary, and considering that there is almost no room for space inside the sinus (in the common ditch) or around the abutment, There is a problem that the case where the flattening due to the above-mentioned separation can be applied at a position where the flattening has disappeared is extremely limited. On the other hand, even if the magnetostriction method is directly applied to the measurement of stress in a curved tube portion, since considerable distortion during production remains in the portion and its distribution shape is complicated, for example, the sedimentation There is a problem that it is extremely difficult to separate a stress component generated by an external force.
[0010]
The present invention has been made in view of such a problem, and a stress evaluation method, a stress evaluation device, and the like for a curved pipe capable of easily and accurately calculating a stress generated in a curved pipe constituting a pipeline. The purpose is to provide.
[0011]
[Means for Solving the Problems]
In order to achieve the above-described object, a first aspect of the present invention provides a first stress-moment relational expression showing a relationship between a moment acting on a curved pipe constituting a pipe and a distribution of stress generated in the curved pipe by a sensor. Calculating the moment by regressing the measured value of the stress distribution, and developing a second stress-moment relational expression showing a relationship between the moment and the stress distribution with respect to a displacement in a sectional direction of the curved pipe. A first flattening amount calculating step of calculating the flattening amount by inputting the moment into a moment-flattening relational expression indicating a relationship between the flattening amount of the curved pipe and the moment, which is derived by performing A stress evaluation method for a curved pipe, comprising:
[0012]
Further, in the stress evaluation method described above, the first curved pipe and the second curved pipe constituting the pipe are regarded as having the same initial value of the diameter, and the first flattened amount calculated in the first flattening amount calculating step is calculated. A second flatness calculating step of calculating the flatness of the second curved pipe based on the flatness of the curved pipe and the measured values of the diameters of the first curved pipe and the second curved pipe; The flatness of the second curved pipe is input to the moment-flatness relational expression to calculate the moment acting on the second curved pipe, and this moment is input to the second stress-moment relational expression. And calculating the stress distribution of the second curved pipe.
[0013]
In the first invention, the distribution of stress generated in the curved tube is measured using a magnetic anisotropic sensor or the like, and regression analysis is performed on the first stress-moment relational expression based on the measured value of the stress distribution. Thus, the moment acting on the curved pipe is calculated, and the flatness of the curved pipe is calculated from the moment-flatness relational expression.
[0014]
Further, in the first invention, 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 flatness of the first curved pipe calculated in the first flattening amount calculating step is calculated. The flatness of the second curved pipe is calculated based on the amount and the measured value of the diameter of the first curved pipe and the diameter of the second curved pipe, and the flatness of the second curved pipe is defined as a moment-flatness relation. The moment acting on the second curved pipe is calculated by inputting the equation to the equation, and the moment is input to the second stress-moment relational equation to calculate the stress distribution of the second curved pipe.
[0015]
The “pipe” is a pipe (lifeline) for supplying gas, water, and the like, and includes a curved pipe, a straight pipe, and the like.
The “first curved pipe” is manufactured at the same time as the curved pipe to be subjected to the stress evaluation, and the initial value of the diameter (inner diameter, outer diameter, etc.) can be considered to be equivalent to the curved pipe to be subjected to the stress evaluation. For example, curved pipes are disposed near, before and after a curved pipe to be subjected to stress evaluation.
The “second curved pipe” is a curved pipe to be subjected to stress evaluation.
[0016]
The “sensor” measures a stress generated in a curved tube, and is, for example, a magnetic anisotropic sensor. It is known that the measurement limit of the stress distribution measurement by the magnetic anisotropic sensor is at most about 70% of the yield stress of the pipe due to the principle limitation. In addition, since the residual stress in a curved pipe is larger than that in a straight pipe or the like, the measurement limit is considered to be further limited. The details of the stress measurement by the magnetic anisotropic sensor will be described later.
[0017]
"Flatness" refers to the amount of cross-sectional deformation and diameter change (outer diameter change, inner diameter change, etc.) of a curved tube, for example, a state in which it is not subjected to cross-sectional deformation due to external force (at the time of manufacture, installation, etc.). This is the amount of change over time in the diameter (outer diameter, inner diameter, etc.) of the curved pipe with reference to the curved pipe. That is, the flatness caused 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 present time.
[0018]
The “first stress-moment relational expression” indicates a relationship between a moment acting on a curved pipe and a stress (a pipe axial stress, a pipe circumferential stress, and the like) generated in the curved pipe. For example, Karman's It is a theoretical formula. Karman's theoretical formula theoretically describes the distribution of stress generated in the curved pipe portion when a moment acts on the curved pipe. The details of Karman's theory (Karman's flat stress theory) will be described later.
[0019]
The “second stress-moment relational expression” includes a moment acting on a curved pipe (an in-plane bending moment, an out-of-plane bending moment, etc.) and a stress generated on the curved pipe (a pipe axial stress, a pipe circumferential stress, etc.) This shows the relationship. In addition, the second stress-moment relational expression indicates a pipe axial stress and a pipe circumferential stress corresponding to an in-plane bending moment, and a pipe axial stress and a pipe circumferential stress corresponding to an out-of-plane bending moment. Desirably, for example, the theoretical formula of Rodabaughｕ & George. The details of this theoretical formula will be described later.
[0020]
The “moment-flatness relational expression” indicates a relationship between the flatness of a curved pipe constituting the pipe and a moment acting on the curved pipe. For example, the theoretical equation of Rodabaugh && George is expressed by the following equation. This is a relational expression derived by expanding the direction displacement up to a term of a predetermined order.
[0021]
In this case, the moment-flatness relational expression is
M_i= Η₁EI / k_pR × e_i,
M_o= Η₂EI / k_pR × e_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 modulus of elasticity,
I is the second moment of area of the tube;
R is the radius of curvature of the curved tube,
2 × e_iIs the flattening amount in the circumferential direction at an angle of 0 °,
2 × e_oIs the flattening amount in the circumferential direction at an angle of 45 °,
k_pIs the deflection constant,
η1 and η2 are constants determined by the internal pressure of the curved pipe, the radius of curvature, the radius, and the pipe thickness.
[0022]
The “angle in the circumferential direction” indicates the direction of the outer diameter and the inner diameter of the curved pipe, the position on the circumference of the curved pipe, and the like. The angle in the circumferential direction is represented by an angle formed by a predetermined reference radius of a cross section of the curved pipe (a cross section taken on a plane perpendicular to the pipe axis). The definition of the angle in the circumferential direction will be described later. For example, the radius of curvature direction of the curved tube corresponds to the direction of 90 ° (−90 °) in the circumferential direction.
[0023]
Note that k_p, Η₁, Η₂Depends on the order of the term that expands in the stress-moment relational equation. For example, if the term expands to about the third order,
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+ 480 °,
C3 = 37 + 7350λ²+ 2520Ψ
d₁= 3 (C2C3-110.25) / {6.25C3-C1 (C2C3-1100.25)},
d₂= 7.5C3 / {6.25C3-C1 (C2C3-1100.25)},
d₃= 78.75 / {6.25C3-C1 (C2C3-1100.25)},
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 Poisson's ratio.
[0024]
In the first invention, the stress distribution of a curved tube is measured by a sensor such as a magnetic anisotropic sensor, the acting moment of the curved tube is calculated using Karman's theoretical formula, and the like, and the moment-flatness relational expression is used. Since the flatness of the curved pipe is calculated from the acting moment of the curved pipe, the flatness of the curved pipe can be calculated even when the initial value of the diameter of the curved pipe is not recorded. Then, by measuring the diameter of the curved pipe, the initial value of the diameter of the curved pipe can be calculated.
[0025]
In the first aspect, the flatness of the curved pipe to be subjected to stress evaluation is calculated by setting the initial value of the diameter of the predetermined curved pipe to the initial value of the diameter of the curved pipe to be subjected to stress evaluation. The stress distribution of the curved tube to be subjected to the stress evaluation is calculated by a relational expression, a theoretical expression of Rodabaugh && George, and the like. In this case, even if there is no record of the initial value of the diameter of the curved pipe to be subjected to the stress evaluation, the stress evaluation of the curved pipe can be performed. Moreover, even when the measurement limit of the magnetic anisotropic sensor is exceeded, such as a range exceeding the yield stress of the tube, the stress evaluation can be performed.
[0026]
In the first invention, the flatness of the curved pipe (1) in the 0 ° / 180 ° direction, (2) in the 45 ° / -135 ° direction or in the −45 ° / 135 ° direction, that is, in the two directions, The amount of change in the outer diameter) is measured with a general measuring instrument such as a caliper, so that the tube axial stress, pipe circumferential stress, and out-of-plane bending moment corresponding to the in-plane bending moment can be obtained with sufficient accuracy for practical use. Corresponding pipe axial stress and pipe circumferential stress can be calculated.
[0027]
According to a second aspect of the present invention, a first stress-moment relational expression showing a relationship between a moment acting on a curved pipe constituting the pipe and a distribution of stress generated in the curved pipe is used to calculate a measured value of the stress distribution by a sensor. Means for calculating the moment by regression; and a curve obtained by developing a second stress-moment relational expression showing a relation between the moment and the stress distribution with respect to a displacement in a sectional direction of the curved pipe. A first flatness calculating means for calculating the flatness by inputting the moment to a moment-flatness relational expression indicating a relationship between the flatness of the pipe and the moment; This is a pipe stress evaluation device.
[0028]
Further, the stress evaluation device considers the initial values of the diameters of the first curved pipe and the second curved pipe constituting the pipe to be equivalent, and calculates the first flattened amount calculated in the first flattening amount calculating step. Second flatness calculating means for calculating the flatness of the second bent pipe based on the flatness of the bent pipe and the measured values of the diameters of the first bent pipe and the second bent pipe; The flatness of the second curved pipe is input to the moment-flatness relational expression to calculate a moment acting on the second curved pipe, and this moment is input to the second stress-moment relational expression. Means for calculating the stress distribution of the second curved pipe.
[0029]
The second invention is an invention regarding a stress evaluation device according to the stress evaluation method of the first invention. The stress evaluation device stores 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 device such as a computer can be used as the “stress evaluation device”. Also, the stress evaluation device may be connected to a network such as the Internet as a stress evaluation server so that a terminal device (a personal computer, a personal digital assistant, a 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 to the stress evaluation server from the terminal device via the network. The stress evaluation server can calculate the initial value of the diameter of the curved pipe, the flattening amount, the acting moment, the stress distribution, and the like, and can transmit the calculation result to the terminal device via the network. Further, the stress evaluation server can hold, record, and manage the input data and the calculation result in a database so that the stress evaluation server itself or a terminal device can use the database as needed.
[0032]
A third invention is a program that causes a computer to function as the stress evaluation device of the second invention.
A fourth invention is a recording medium that records a program that causes a computer to function as the stress evaluation device of the second invention.
[0033]
The “recording medium” is a CD-ROM, DVD, flexible disk, hard disk, or the like.
The above-described program can be distributed through a network such as the Internet, or a recording medium can be distributed.
[0034]
The configuration and features of the present invention will be clarified in the embodiments described below and the accompanying drawings.
[0035]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, preferred embodiments of a stress evaluation method, a stress evaluation device, and the like according to the present invention will be described in detail with reference to the accompanying drawings. Note that, in the following description and the accompanying drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant description will be omitted.
[0036]
First, with reference to FIGS. 1 to 6, a description will be given of stress evaluation of a curved pipe based on a flattened amount (a cross-sectional flattened amount of a curved pipe).
[0037]
FIG. 1 is a perspective view of a curved tube, and explains the definition of “circumferential angle” (hereinafter, also simply referred to as “angle”) φ. FIG. 2 is a cross-sectional view of a curved tube, and explains the definition of an angle. Note that a description will be given on the assumption that the curved pipe 101 has a circular cross section perpendicular to the pipe axis 102. Further, in the present embodiment, the flat amount and the cross-sectional deformation amount of the curved pipe are mainly described as corresponding to the outer diameter change amount of the curved pipe. There is no problem in accuracy in practical use.
[0038]
The 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 of the circumference of the cross section is defined as a reference radius (angle of 0 ° in the circumferential direction), and the circumferential angle of the pipe is defined as shown in FIGS. I do. When indicating directions such as the outer diameter and the inner diameter of the curved pipe, for example, a direction connecting a position at a circumferential angle of 0 ° and a position at a circumferential angle of 180 ° is referred to as “0 °” in the present specification. / 180 ° direction ”,“ 0 ° direction ”, and the like.
[0039]
When an external force such as settlement is applied to a curved pipe, a bending moment is generated. The direction of the bending moment is divided into in-plane bending and out-of-plane bending. The in-plane bending is bending in a plane direction including the pipe axis of the bent pipe, and the out-of-plane bending is bending in an out-of-plane direction including the pipe axis of the bent pipe.
[0040]
In-plane bending moment (M_i) Acts on the pipe in the axial direction σ_iL, Pipe circumferential stress σ_iC, Out-of-plane bending moment (M_o) Acts on the pipe in the axial direction σ_oL, Pipe circumferential stress σ_oCRodabaugh & George's Theory (Rodabaugh, EC, and Georg, HH, "Effect of Internal Pressing on Flexibility Energy and Strength Investigation Funding and Strengthening Investigation." 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]
Here, φ: circumferential angle of the pipe (see FIGS. 1 and 2), ν: Poisson's ratio, R: radius of curvature of the bent pipe, r: pipe radius, t: pipe thickness, I: secondary moment of area of the pipe , M_i: In-plane bending moment acting on curved pipe, M_o: Out-of-plane bending moment acting on curved pipe, k_p: Deflection coefficient.
Note that λ = tR / r²(1-ν²)^(1/2)And put, k_pIs a function of λ and the internal pressure P. λ is a pipe coefficient.
[0043]
Note that f₁(Φ), f₂(Φ), f₃(Φ), f₄(Φ) is specifically expressed as follows.
(Equation 1)

However, + (plus) in the sign of ± is used when calculating the stress on the outer surface of the tube, and-(minus) is used when calculating the stress on the inner surface.
[0044]
Also, d_nAlso k_pIt becomes a function of λ and the internal pressure P in the same manner. The order in which n should be taken depends on the value of λ. As λ becomes smaller, higher-order terms are required, but if λ = about 0.1, up to 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 (C2C3-1100.25)},
d₂= 7.5C3 / {6.25C3-C1 (C2C3-1100.25)},
d₃= 78.75 / {6.25C3-C1 (C2C3-1100.25)},
However,
Ψ = PR²/ Ert (E: elastic modulus),
C1 = 5 + 6λ²+ 24Ψ,
C2 = 17 + 600λ²+ 480 °,
C3 = 37 + 7350λ²+ 2520Ψ
And
[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),
And
[0047]
In addition, the pipe has an in-plane bending moment M_i, Out-of-plane bending moment M_oThe amount of change in the radius of the pipe when_i, E_oEquations [1-1] to [1-4] (Rodabough & George's theoretical equation) are developed for the displacement in the sectional direction, and M_i, M_oAnd e_i, E_oLooking for a relationship with
M_i= Η₁EI / k_pR × e_i... [3-1]
M_o= Η₂EI / k_pR × e_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: Circumferential angle of 0 ° before external force acts)
(R_i′: Radius at an angle of 0 ° in the circumferential direction after external force is applied)
(R_o0: Circumferential angle of 45 ° before external force acts)
(R_o′: Radius at an angle of 45 ° in the circumferential direction after the external force is applied)
It is.
[0049]
In addition, 2 × e_iIs equivalent to the flat amount (the maximum outer diameter change amount, the maximum inner diameter change amount, the maximum cross-sectional deformation, the maximum flat amount) in the circumferential direction at an angle of 0 °.
Also, 2 × e_oCorresponds to the flattening amount (the maximum outer diameter change amount, the maximum inner diameter change amount, the maximum cross-sectional deformation, the maximum flattening amount) in the 45 ° circumferential direction.
[0050]
Flatness W in in-plane bending and out-of-plane bending_i(Φ), W_o(Φ) can be expressed as follows, respectively. Note that the flattening amount W shown in the following equation_i(Φ), W_o(Φ) is the amount of change in the diameter of the curved tube (the amount of change in radius × 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 a relationship between an in-plane bending moment, an out-of-plane bending moment, and a flat amount (outer diameter change amount) and a circumferential angle when these combined moments act on a curved pipe. The vertical axis indicates the flatness (the amount of change in outer diameter), and the horizontal axis indicates the angle in the circumferential direction.
[0052]
A curve 301 shows the relationship between the flat amount (outer diameter change amount) and the circumferential angle when an in-plane bending moment acts on a curved pipe.
A curve 302 shows the relationship between the flat amount (outer diameter change amount) and the angle in the circumferential direction when an out-of-plane bending moment acts on the curved pipe.
A curve 303 indicates the relationship between the flat amount (outer diameter change amount) and the angle in the circumferential direction when a resultant moment acts on the curved pipe.
The curve 301, the curve 302, and the curve 303 are graphs having a period of 180 °, as can be seen from the equations [4-1] and [4-2].
[0053]
Referring to the curve 301 in FIG. 3, the flatness (outer diameter change amount) in the in-plane bending is maximum in the direction of the angle 0 ° / 180 °, and is 0 ° in the direction of 90 ° / angle−90 °. The sign is opposite to the flat amount (outer diameter change amount) in the 180 ° direction, and the value is small. Further, the flatness (outer diameter change amount) in the in-plane bending is substantially zero at the angles of 45 °, −45 °, 135 °, and −135 °.
[0054]
Referring to the curve 302 in FIG. 3, the flatness (outer diameter change amount) in out-of-plane bending is maximum in the direction of 45 ° / 135 °, and in the direction of 135 ° / −45 °, the angle is 45 °. The sign is opposite to the flat amount (outer diameter change amount) in the direction of ° / angle-135 °. Further, the flatness (outer diameter change amount) in out-of-plane bending is almost 0 at an angle of 0 °, an angle of 180 °, an angle of 90 °, and an angle of −90 °.
[0055]
Therefore, even when both in-plane bending and out-of-plane bending are applied, the flatness (outer diameter variation) 2e in the direction of 0 ° / 180 °_iIs measured, the in-plane bending moment M is calculated by the equation [3-1]._iCan be calculated.
Further, even when both in-plane bending and out-of-plane bending are applied, the flatness (outer diameter change amount) in the direction of 45 ° / 135 ° or 135 ° / −45 °. 2e_oIs measured, the out-of-plane bending moment M is obtained from the equation [3-2]._oCan be calculated.
[0056]
M_i, M_oIs obtained, the stress (σ) at an arbitrary position on the cross section is obtained by Expressions [1-1] to [1-4] (Rodabaugh & George's theoretical expression)._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 a relationship between a flat amount (amount of change in outer diameter) and a maximum circumferential stress. The tube 401, which is a test body, includes a curved tube 402, a straight tube 403, and the like.
[0058]
A monaka elbow (API-X60 standard, wall thickness t = 12.7 mm, outer diameter 2r = 610 mm, radius of curvature R = 1.5 DR, 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 a surface plate via a flange, and the other flange was loaded with a hydraulic jack downward 405 and upward 406 with a hydraulic jack. That is, an in-plane bending moment was applied to the curved tube 402. A load cell (not shown) was provided at the load point so that the applied load could be measured.
[0059]
The measurement position of the flattening amount (outer diameter change amount) was the center cross section 404 of the elbow, and measurement was made in two directions (0 ° / 180 ° direction and 90 ° / 270 ° (−90 °) direction) using calipers. Further, a biaxial strain gauge (not shown) was attached on the periphery of the central cross section 404 at a pitch of 15 degrees at an angle in the circumferential direction for verification, and stress was measured.
[0060]
FIG. 5 is a diagram showing the relationship between the flat amount (the amount of change in outer diameter) 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 flatness (outer diameter variation). The maximum circumferential stress is the largest of the circumferential stresses measured by a biaxial strain gauge provided on the circumference of the central section 404.
Each point indicated by “○” (FIG. 5) indicates a measured value in the 0 ° / 180 ° direction, and each point indicated by “□” (FIG. 5) indicates a measured value in the 90 ° / 270 ° (−90 °) direction. Shows the measured values.
[0061]
A straight line 501 indicates the relationship between the flatness (the amount of change in outer diameter) and the maximum stress in the circumferential direction in the 0 ° / 180 ° direction.
A straight line 502 indicates the relationship between the flatness (the amount of change in outer diameter) 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, in any of the 0 ° / 180 ° direction and the 90 ° / 270 ° (-90 °) direction, between the flat amount (outer diameter change amount) and the circumferential maximum stress. Has a linearity, that is, a proportional relationship.
[0062]
The monaka elbow used in the above experiment was made by welding (seam welding, etc.) vertically (in the direction of the pipe axis) two pieces, so that the direction of 0 ° / 180 ° is 90 ° / 270 °. Deformation is easier than in the ° (-90 °) direction. In addition, as described above with reference to FIG. 3, in the in-plane bending moment, the flatness (outer diameter change amount) in the 0 ° / 180 ° direction is theoretically the 90 ° / 270 ° (−90 °) direction. Be larger.
[0063]
As described above, the flatness (outer diameter variation) has anisotropy, but it is difficult to separate the influence of 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 variation) in the 0 ° / 180 ° direction where the influence of the vertical seam is small.
[0064]
Note that the yield stress of the material of the Monaca elbow is about 410 MPa, but as described above, in the elastic region, linearity (proportional relationship) between flatness (outer diameter change) and circumferential maximum stress is present. Be looked at.
In the upward direction 406 (the direction in which the maximum circumferential stress is negative in FIG. 5), the flat amount (outer diameter change amount) and the circumferential direction are reduced to a range (plastic region) of about 1.5 times the yield stress. There is linearity (proportional relationship) between the maximum stress.
[0065]
Next, a comparison between the above-described stress evaluation method and the above-described experimental results will be described. FIG. 6 is a diagram showing analytical values (analytical values by the above-described stress evaluation method) and experimental values relating to the circumferential and axial stress distributions. The vertical axis indicates stress, and the horizontal axis indicates circumferential angle.
[0066]
In the experimental results shown in FIG. 5, when the flat amount (outer diameter change amount) in the 0 ° / 180 ° direction is 8 mm (FIG. 5: point 503), the maximum circumferential stress is less than 400 MPa.
The moment with respect to the flatness (outer diameter variation) 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, whereby a solid line 601 (circumferential analysis value) and a solid line 602 (axial analysis value) in FIG. 6 are obtained.
[0067]
In the flatness (change in outer diameter) in the 0 ° / 180 ° direction of 8 mm, a measured value of the circumferential stress measured by a biaxial strain gauge provided at a pitch of 15 ° on the circumference of the central cross section 404 is “ Each point (experimental value in the circumferential direction) is indicated by a mark (●), and the measured value of the axial stress is indicated by each point (experimental value in the axial direction) (FIG. 6).
[0068]
Regarding the stress in the circumferential direction, there is a slight difference between the peak positions of 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 with each other, but a slight shift is seen in the stress value. It should be noted that there is no practical problem regarding these slight deviations.
From the comparison and consideration of the above experimental values and analytical values, it can be concluded that it is possible to estimate stress with sufficient accuracy for practical use even with flatness (outer diameter change) measured values with the accuracy of a vernier caliper. I can say.
[0069]
As described above, according to the embodiment of the present invention, the tune is formed in two directions of (1) 0 ° / 180 ° direction, (2) 45 ° / -135 ° direction or -45 ° / 135 ° direction. By measuring the flatness (change in outer diameter) of the pipe with a general measuring tool such as a caliper, it is possible to estimate the stress distribution generated in the curved pipe with sufficient accuracy for practical use.
[0070]
One of the purposes of using a curved pipe is to give flexibility to a normal pipe and reduce stress by deformation. Therefore, three-dimensional piping is often used. This indicates that the probability that the in-plane bending moment and the out-of-plane bending moment simultaneously act as a load 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 when the in-plane bending moment acts 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 during the action of the out-of-plane bending moment is maximum in the 45 ° / −135 ° direction or the −45 ° / 135 ° direction, and is theoretically almost zero in the 0 ° / 180 ° direction.
[0072]
From these facts, (1) the in-plane bending moment (M) can be calculated from the flatness in the 0 ° / 180 ° direction (the amount of change in the outer diameter) by the equation [3-1]._i) Is calculated, and (2) the out-of-plane bending moment (M) is calculated from the flatness (outer diameter change amount) in the 45 ° / -135 ° direction or the −45 ° / 135 ° direction by the equation [3-2]._o) Can be calculated.
[0073]
That is, (1) flatness in 0 ° / 180 ° direction (outer diameter change amount), (2) flatness amount in two directions of 45 ° / -135 ° direction or −45 ° / 135 ° direction (outer diameter change amount) ), The in-plane bending moment (M_i) And out-of-plane bending moment (M_o) Can be calculated separately. Then, these in-plane bending moments (M_i) And out-of-plane bending moment (M_o), The stress distributions due to the bending moments in both directions, the in-plane bending moment and the out-of-plane bending moment, can be calculated by Expressions [1-1] to Expression [1-4] (the theoretical expression of Rodabaugh & George).
[0074]
For the stress (σ) in accordance with ANSI B31.8 adopted in the design, the in-plane bending moment (M_i) And out-of-plane bending moment (M_o), The resultant moment (M) is obtained (see Equation [5-1]), and the result is divided by the section modulus (Z), and then multiplied by the stress concentration coefficient (i) due to the in-plane bending moment (in-plane bending moment and For the out-of-plane bending moment, the former is about 17% larger, so it is evaluated on the safe side), and the stress (σ) of the curved pipe where the outer diameter change (flat) occurs (Equation [5-2]) reference).
M = (M_i ²+ M_o ²)^(1/2)... [5-1]
σ = M · i / Z [5-2]
[0075]
Further, the above-described stress evaluation method can directly evaluate the stress of the curved pipe itself in a non-destructive manner. Further, stress evaluation and stress estimation can be performed in a service state and a use state without requiring measures such as lowering the pressure. Therefore, it is not necessary to take any special measures, such as loading equipment, when performing stress evaluation of a curved pipe.
[0076]
In addition, stress evaluation and stress diagnosis can be performed only by measuring the flatness (change in outer diameter) in two directions in the center section of the curved pipe, and a skilled person is not required for the measurement. Thus, the cost burden can be reduced as compared with the above.
[0077]
In addition, since the mode in which flattening generates stress in the curved 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 values and the analysis values, the stress evaluation described in the present embodiment has sufficient accuracy for practical use.
Further, the present invention can be used not only for a clear deformation mode such as settlement, but also for stress estimation in a state where various external forces such as thermal stress are applied.
[0078]
As for the flatness, the change in the outer diameter of the curved tube is measured by a measuring tool such as a caliper, but the measuring device such as a pig or the inspection tool may be used to measure the change in the inner diameter of the curved tube.
[0079]
Next, with reference to FIGS. 7 to 9, a description will be given of stress evaluation of a curved pipe in a pipeline using a magnetic anisotropic sensor.
First, the operating principle of the magnetic anisotropy sensor will be described.
FIG. 7 is a diagram illustrating the operation principle of the magnetic anisotropy sensor.
FIG. 8 is a partial detailed view of the magnetic anisotropic sensor shown in FIG.
[0080]
The magnetic anisotropy sensor 701 includes an excitation core 702, a magnetic anisotropy detection core 703, and the like. The 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 arranged orthogonally. 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 a stress (strain) acts on the measurement object 708, anisotropy occurs in the magnetic permeability μ. When the object to be measured 708 is in a stress state as shown in FIG. 7, the magnetic permeability μx in the X direction, which is the tensile stress direction, is relatively larger than the magnetic permeability μy in the Y direction.
[0082]
At this time, when a current is supplied from the power supply 706 to the exciting coil 704, 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 anisotropy, a part goes through the magnetic anisotropy detection core 703 to the other leg of the excitation core 702.
[0083]
When the above magnetic circuit is formed by an AC 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]
Here, K0 is a proportional constant.
V = K1 × (σx−σy) [6-2]
Here, K1 is a proportional constant.
[0085]
As described above, the magnetic anisotropy sensor 701 outputs the voltage value V proportional to the stress difference (σx−σy) in the X direction and the Y direction as a detection value. Therefore, if the proportionality constant K1 is known, the stress difference ([sigma] x- [sigma] y) in the X direction and the Y direction can be calculated by equation [6-2]. The above is the principle of the stress measurement by the magnetic anisotropic sensor.
[0086]
Next, Karman's theory of flat stress will be described. Karman's flat stress theory theoretically describes the distribution of stress generated in a curved pipe portion in the pipe circumferential direction when a moment acts on the curved pipe. Pipe axial stress σ when moment (M) acts on a curved pipe_L, Pipe circumferential stress σ_CAccording to Karman's flat stress theory, is expressed as follows.
[0087]
σ_L(Φ) = kMr / I × ｛sinφ-6sin³φ / (5 + 6λ²) + 9νλcos2φ / (5 + 6λ)²)｝ ... [7-1]
σ_C(Φ) = kMr / I × ｛ν (sinφ−6sin³φ / (5 + 6λ²)) + 9λcos2φ / (5 + 6λ)²)｝ ... [7-2]
[0088]
Here, φ: circumferential angle of the pipe (see FIGS. 1 and 2), ν: Poisson's ratio, R: radius of curvature of the bent pipe, r: pipe radius, t: pipe thickness, I: secondary moment of area 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 + 12λ)²) / (1 + 12λ)²).
[0089]
Further, as described above, the output of the magnetic anisotropy sensor indicates the stress difference (σ_L(Φ) -σ_C(Φ)). The stress difference in the 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) 6sin³φ / (5 + 6λ²) − (1−ν) 9λ cos2φ / (5 + 6λ)²)｝ ・ ・ ・ [8]
[0091]
Therefore, when the stress generated on the tube surface when a moment acts on the curved tube portion is measured by the magnetic anisotropy sensor, the distribution shape of Expression [8] is obtained. The above is the outline of Karman's theory of flat stress.
[0092]
FIG. 9 is a diagram showing an outline of measurement of a stress distribution in a curved tube using 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 tube 901 while moving at equal intervals as shown in a section 903. The measurement result is regressed to equation [8] by a statistical method such as the least square method or the like (σ_L(Φ) -σ_C(Φ)) is obtained, 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) and M (moment acting on the curved pipe) can be estimated.
[0093]
Due to its principle, the magnetic anisotropic sensor measures not only a load stress caused by an external force such as a moment, but also a residual stress at the same time. Therefore, the residual stress component is removed by dare to return to the equation [8] without directly obtaining the maximum stress and the minimum stress from the measurement results of the magnetic anisotropy sensor.
[0094]
Assuming that the residual stress is randomly distributed in the circumferential direction of the pipe, that is, averagely distributed, macroscopically, the residual stress component is removed by regressing on the equation [8], and purely due to the moment. Only the applied stress will be extracted. Further, not only the residual stress but also 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, are expressed by the following equation [8]. By returning to the above, it is possible to remove the residual stress as well.
[0095]
In this way, the magnetic anisotropy sensor is moved in the circumferential direction of the curved pipe to measure the stress distribution, and the measured value is regression-analyzed into the equations [7-1], [7-2], and [8]. By doing so, it is possible to evaluate the stress generated in the curved pipe and estimate the acting moment.
[0096]
The stress evaluation method (stress evaluation method {circle around (1)}) for a curved pipe based on the flatness (cross-section flatness of a curved pipe) described with reference to FIGS. (See FIG. 5). However, if there is no record of the initial value of the diameter of the curved pipe, that is, the outer diameter value, inner diameter value, 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.), It is difficult to obtain accurate values of the amount of change in diameter and the amount of change in inner diameter, and it is difficult to perform reliable stress evaluation.
[0097]
Regarding the stress evaluation method (stress evaluation method {circle over (2)}) of a curved pipe in a pipeline using the magnetic anisotropy sensor described with reference to FIGS. The measurement limit is at most about 70% of the yield stress of the pipe. Further, since the residual stress in a bent pipe is larger than that in a straight pipe or the like, the measurement limit is considered to be further limited.
[0098]
Next, referring to FIG. 10, stress evaluation of a curved pipe when there is no record of an initial value of the diameter (outer diameter, inner diameter, etc.) of the curved pipe, or in a region exceeding the measurement limit of the magnetic anisotropy sensor. The evaluation of the stress of a curved pipe will be described.
FIG. 10 is a diagram showing a schematic configuration of the conduit 1001. The pipe 1001 has a curved pipe 1002 to a curved pipe 1005 and the like. The curved pipe 1002 is a curved pipe A to be evaluated (an object of stress evaluation), and the other curved pipes 1003 and the like are curved pipes A. It is assumed that the tube B is manufactured at the same time.
[0099]
When there is no record of the initial value of the diameter of the curved tube A or the like, first, the curved tube A is subjected to stress evaluation by the curved tube stress evaluation method (2) using the magnetic anisotropy sensor. If the obtained stress distribution is close to the measurement limit of the magnetic anisotropy sensor, that is, if there is a possibility that it exceeds the measurement limit, a curved tube near curved tube A (before and after curved tube A, etc.) For example, similarly to the curved tube A, the stress evaluation is performed on the curved tube 1003 (curved tube B) by the curved tube stress evaluation method (2) using the magnetic anisotropy sensor described above.
[0100]
If the obtained stress distribution is within the measurement range of the magnetic anisotropy sensor, a process such as regression analysis is performed with respect to Expressions [7-1], [7-2], and [8], and a curved tube is obtained. Moment acting on B (M_B). Further, according to Expressions [3-1] and [3-2], this acting moment (M_B) (The amount of change in outer diameter, the amount of change in inner diameter, etc.) of the curved tube B (2e)_B).
[0101]
Next, the outer diameter and inner diameter of the curved tube B (2r_B′) Is measured using a caliper, a pig or the like, and the initial values (2r_B= 2r_B'-2e_B). Initial values of the outer diameter and inner diameter of the curved tube A to be evaluated (2r_A) Is the initial value of the outer diameter and inner diameter of the curved tube B (2r_B) Can be considered equivalent.
[0102]
Next, the outer diameter and inner diameter of the curved tube A (2r_A′) Is measured using a caliper, a pig or the like, and the flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, etc.) (2e)_A= 2r_A'-2r_A= 2r_A'-2r_B).
The flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, 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 flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, etc.) (2e_A) Is the flatness of the curved tube B (2e)_B) Shows the difference between the measured values of the outer diameter and inner diameter of the curved pipe A and the curved pipe B (2r_A'-2r_B)).
[0103]
Next, in the same manner as in the stress evaluation method (1) of the curved pipe based on the flatness (the flatness of the curved pipe) described with reference to FIGS. , Change in inner diameter, etc.) (2e_A) From Equations [3-1] and [3-2], the moment M acting on the curved pipe A_AIs calculated, and the stress generated in the curved tube A is evaluated by the formulas [1-1] to [1-4] (Rodabaugh & George's theoretical formula).
[0104]
The curved pipe A was subjected to stress evaluation by the curved pipe stress evaluation method (2) using the magnetic anisotropic sensor described above, and the obtained stress distribution was within the measurement range of the magnetic anisotropic sensor. If there is, the value may be used as it is as the stress evaluation result of the curved pipe A.
[0105]
As described above, even when the stress acting on the curved pipe A to be evaluated exceeds the measurement limit of the magnetic anisotropy sensor, it is also necessary to record the initial value of the outer diameter, the inner diameter, and the like of the curved pipe A to be evaluated. Even if there is no curve, stress distribution measurement is performed on the other curved tube B near the curved tube A to be evaluated by the magnetic anisotropy sensor, 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 the equation [8], and the flatness of the curved pipe B is calculated from the equations [3-1] and [3-2] in the stress evaluation method (1). Diameter change, inner diameter change, etc.), and from the measured values of the outer diameter, inner diameter, etc. of the curved pipe B, the initial values of the outer diameter, inner diameter, etc. of the curved pipe B are obtained, The flatness of the curved tube A is calculated as an initial value, and the stress of the curved tube A can be evaluated by the stress evaluation method (1).
[0106]
Next, a stress evaluation apparatus according to the above-described stress evaluation method will be described with reference to FIG.
By registering and recording the above formulas [1-1] to [5-2] and other calculation formulas, procedures for stress evaluation, and the like in the computer, the computer obtains the stress value measured by the magnetic anisotropy sensor. When other necessary numerical values such as the outer diameter and the inner diameter of the curved pipe measured by a caliper and the like are input, the stress evaluation and the stress distribution of the curved pipe can be performed.
[0107]
FIG. 11 is a flowchart illustrating a process executed by a computer as a stress evaluation device for a curved pipe. As described with reference to FIG. 10 above, the curved tube A is a curved tube to be evaluated (stress evaluation target), and the curved tube B installed near the curved tube A is the same as the curved tube A at the same time. It is assumed that the bent tube is manufactured in the following manner.
[0108]
With respect to the curved tube A, the stress value obtained by the curved tube stress evaluation method (2) using the magnetic anisotropy sensor is input to the computer (step 1101).
The computer determines whether this stress value may have exceeded the measurement limit of the magnetic anisotropy sensor (step 1102).
If there is a possibility that the stress value exceeds the measurement limit of the magnetic anisotropy sensor (YES in step 1102), the curve using the magnetic anisotropy sensor described above is used for other curved pipes near the curved pipe A. The stress value obtained by the pipe stress evaluation method (2) is input to a computer (step 1103).
The computer determines whether this stress value may have exceeded the measurement limit of the magnetic anisotropy sensor (step 1104).
The processing of steps 1103 to 1104 is repeated to select a curved pipe having a stress value within the measurement limit range, and this curved pipe is defined as a curved pipe B.
[0109]
The computer performs processing such as regression analysis on Expressions [7-1], [7-2], and [8] based on the stress distribution obtained by the magnetic anisotropy sensor, and acts on the curved tube B. Moment (M_B) Is calculated (step 1105).
The computer calculates the acting moment (M by using the equations [3-1] and [3-2]._B) (The amount of change in outer diameter, the amount of change in inner diameter, etc.) of the curved tube B (2e)_B) Is obtained (step 1106).
[0110]
Outer diameter, inner diameter, etc. of curved tube B (2r_B') Is measured using a caliper, a pig or the like, and the measured value is input to a computer (step 1107).
The computer calculates the initial values (2r_B= 2r_B'-2e_B) Is obtained (step 1108). Note that the initial values are the outer diameter, the inner diameter, and the like of the curved pipe in a state in which the cross section is not deformed by an external force (at the time of manufacture, installation, and the like).
[0111]
Next, the outer diameter and inner diameter of the curved tube A (2r_A') Is measured using a caliper, a pig or the like, and the measured value is input to a computer (step 1109).
The computer calculates the flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, etc.) (2e_A= 2r_A'-2r_A= 2r_A'-2r_B) Is calculated (step 1110). In addition, the initial value (2r_A) Is the initial value of the outer diameter and inner diameter of the curved tube B (2r_B) Can be considered equivalent.
[0112]
The computer calculates the flatness of the curved tube A (2e_A), The moment (M) acting on the curved pipe A is calculated by the equations [3-1] and [3-2]._A) Is calculated (step 1111).
The computer calculates the moment (M_A)), Stress evaluation is performed by [1-1] to [1-4] (Rodabaugh & George's theory) (step 1112).
[0113]
Through the above process, the computer as the stress evaluation device inputs the stress distribution measured by the magnetic anisotropy sensor, the outer diameter and the inner diameter of the curved tube measured by a caliper, etc., and other necessary numerical values. It is possible to evaluate the stress of the pipe and calculate the stress distribution. Further, even when the stress acting on the curved 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, the inner diameter, etc. of the curved pipe to be evaluated. Even if there is, a stress evaluation method for a curved pipe based on the flatness (a cross-sectional flatness of a curved pipe) (stress evaluation method (1)) and a stress evaluation method for a curved pipe in a pipeline using a magnetic anisotropic sensor (stress By executing the process according to the evaluation method (2)), the computer can estimate and calculate the initial value, and can evaluate the stress of the curved pipe to be evaluated.
[0114]
The flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, 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 flatness of the curved tube A (the amount of change in outer diameter, the amount of change in inner diameter, etc.) (2e_A) Is the flatness of the curved tube B (2e)_B) Shows the difference between the measured values of the outer diameter and inner diameter of the curved pipe A and the curved pipe B (2r_A'-2r_B)).
[0115]
In addition, the computer as the stress evaluation device is connected to a network such as the Internet as a stress evaluation server so that a terminal device (a personal computer, a personal digital assistant, a mobile phone, etc.) can access the 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 the inner diameter is transmitted to the network. (Step 1107, Step 1109). The stress evaluation server may calculate the flatness, the in-plane bending moment, the out-of-plane bending moment, the stress distribution, and the like of the curved pipe (steps 1110 to 1112), and transmit the calculation result to the terminal device via the network. it can. Further, the stress evaluation server may record and manage the input data and the calculation result as a database so that the stress evaluation server itself or the terminal device can use the database as needed.
[0117]
The functions of the computer (including the stress evaluation server, the terminal device, and the like) 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 a DVD-ROM in which the programs are recorded.
[0118]
Next, with reference to FIG. 12, a description will be given of maintenance and repair of a pipe using the above-described stress evaluation method, stress evaluation apparatus, and the like. FIG. 12 shows a schematic diagram of a method for releasing the stress of the tube 1202. A pipe 1202 is embedded in the ground 1201. For an arbitrary point (such as a curved pipe portion) of the pipe 1202, the stress is calculated by the method described in the above-described embodiment, the necessity of stress release is determined, and the stress release section 1204 is determined.
[0119]
The ground of the excavation section 1205 below the stress release section 1204 is excavated, and the stress release section 1204 of the pipe 1202 is moved to the position of the stress release section 1203. Then, the excavated portion 1205 is reclaimed, and the position of the pipe 1202 is repaired.
[0120]
Next, the maintenance and repair of a pipe using the above-described stress evaluation method, the stress evaluation device, and the like will be described with reference to FIG. FIG. 13 shows a schematic diagram of a method for releasing the stress of the tube 1302. A pipe 1302 is buried in the ground 1301. At any point (such as a curved pipe portion) of the pipe 1302, the stress is calculated by the method described in the above embodiment, the necessity of stress release is determined, and the stress release section 1303 is determined. The vicinity of both ends of the stress releasing portion 1303 is cut off, and a central portion of the stress releasing portion 1303 is removed. Then, the cutting portion 1304 and the cutting portion 1305 are joined, and the position of the pipe 1302 is repaired.
[0121]
As described with reference to FIGS. 12 and 13, by using the stress evaluation method, the stress evaluation device, and the like according to the embodiment of the present invention, it is possible to easily calculate the stress at an arbitrary point on site, and perform maintenance of the pipe. Repairs can be made.
[0122]
As described above, the preferred embodiments of the stress evaluation method and the stress evaluation device for a curved pipe according to the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to such examples. It is obvious to those skilled in the art that various changes or modifications can be made within the scope of the technical idea disclosed in the present application, and these naturally belong to the technical scope of the present invention. I understand.
[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 device, and the like for a curved pipe, which can easily and accurately calculate a stress generated in a curved pipe constituting a pipeline. Can be.
[Brief description of the drawings]
FIG. 1 is a perspective view of a curved tube.
FIG. 2 is a sectional view of a curved pipe;
FIG. 3 is a diagram showing a relationship between an in-plane bending moment, an out-of-plane bending moment, and a flat amount (outer diameter change amount) and a circumferential angle when these combined moments act 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 a relationship between a flat amount (a change in outer diameter) and a maximum stress in a circumferential direction.
FIG. 6 is a diagram showing analytical values and experimental values regarding the circumferential and axial stress distributions;
FIG. 7 is a diagram showing the operating principle of a magnetic anisotropic sensor.
FIG. 8 is a partial detailed view of the magnetic anisotropic sensor shown in FIG. 7;
FIG. 9 is a diagram showing an outline of measurement of a stress distribution in a curved pipe by a magnetic anisotropic 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 …… Bent tube
102 .... tube axis
401 ... tube
402 ......... Bent tube
403 ...... Straight pipe
404 ...... Center cross section
701 ... magnetic anisotropy sensor
702 Excitation core
703 ... magnetic anisotropy detection core
704: Excitation coil
705: Magnetic anisotropy detection coil
706 ...... Power supply
707 voltmeter
708 ... Measurement target
901 …… Bent tube
902 ... magnetic anisotropy sensor
1001 ... pipeline
1002 ... Curved tube to be evaluated
1003, 1004, 1005 ... curved pipe

Claims (12)

By regressing the measured value of the stress distribution by a sensor to a 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 moment is obtained. Calculating the
The relation between the flatness of the curved pipe and the moment is shown by deriving a second stress-moment relational expression showing the relation between the moment and the distribution of the stress on the displacement in the sectional direction of the curved pipe. A first flattening amount calculating step of calculating the flattening amount by inputting the moment into a moment-flattening relational expression;
A stress evaluation method for a curved pipe, comprising: 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 flatness of the first curved pipe calculated in the first flattening quantity calculating step and the first flattened pipe are compared with the first curved pipe. A second flattening amount calculating step of calculating the flattening amount of the second curved tube based on the measured value of the diameter of the curved tube and the second curved tube;
The flatness of the second curved pipe is input to the moment-flatness relational expression to calculate the moment acting on the second curved pipe, and this moment is input to the second stress-moment relational expression. Calculating the stress distribution of the second curved pipe by using
The stress evaluation method for a curved pipe according to claim 1, comprising: 3. The method according to claim 1, wherein the first stress-moment relational expression is a Karman theoretical expression, and the second stress-moment relational expression is a Rodabaugh & George theoretical expression. 4. The stress evaluation method of the curved pipe as described. The moment-flatness 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 plane bending moment,
_Mo is the out-of-plane bending moment,
E is the modulus of elasticity,
I is the second moment of area of the tube;
R is the radius of curvature of the curved tube,
2 × e _i is the flatness in the circumferential direction at an angle of 0 °,
2 × _eo is the flatness in the circumferential direction at an angle of 45 °,
k _p is the deflection constant,
η1 and η2 are constants determined by the internal pressure of the curved pipe, the radius of curvature, the radius, and the pipe thickness. The above k _p , η ₁ , 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 + 24 °,
C2 = 17 + 600λ ² + 480 °,
C3 = 37 + 7350λ ² + 2520 °,
_{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 Poisson's ratio. By regressing the measured value of the stress distribution by a sensor to a 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 moment is obtained. Means for calculating
The relation between the flatness of the curved pipe and the moment is shown by deriving a second stress-moment relational expression showing the relation between the moment and the distribution of the stress on the displacement in the sectional direction of the curved pipe. A first flatness calculating means for calculating the flatness by inputting the moment into a moment-flatness relational expression;
A stress evaluation device for a curved pipe, comprising: 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 flatness of the first curved pipe calculated in the first flattening quantity calculating step and the first flattened pipe are compared with the first curved pipe. Second flatness calculating means for calculating the flatness of the second curved pipe based on the measured value of the curved pipe and the diameter of the second curved pipe;
The flatness of the second curved pipe is input to the moment-flatness relational expression to calculate the moment acting on the second curved pipe, and this moment is input to the second stress-moment relational expression. Means for calculating the stress distribution of the second curved pipe by means of:
The stress evaluation device for curved pipes according to claim 6, comprising: 8. The method according to claim 6, wherein the first stress-moment relational expression is a Karman theoretical expression, and the second stress-moment relational expression is a Rodabaugh & George theoretical expression. The stress evaluation device for curved pipes according to the above. The moment-flatness 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 device for a curved pipe according to any one of claims 6 to 8, wherein:
However,
M _i is plane bending moment,
_Mo is the out-of-plane bending moment,
E is the modulus of elasticity,
I is the second moment of area of the tube;
R is the radius of curvature of the curved tube,
2 × e _i is the flatness in the circumferential direction at an angle of 0 °,
2 × _eo is the flatness in the circumferential direction at an angle of 45 °,
k _p is the deflection constant,
η1 and η2 are constants determined by the internal pressure of the curved pipe, the radius of curvature, the radius, and the pipe thickness. The above k _p , η ₁ , 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 device according to claim 9, wherein:
However,
Ψ = PR ² / Ert,
λ = tR / r ² (1-ν ² ) ^(1/2) ,
C1 = 5 + 6λ ² + 24 °,
C2 = 17 + 600λ ² + 480 °,
C3 = 37 + 7350λ ² + 2520 °,
_{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 Poisson's ratio. A program for causing a computer to function as the stress evaluation device according to any one of claims 6 to 10. A recording medium recording a program for causing a computer to function as the stress evaluation device according to claim 6.

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