㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠਛ᧛޿ߕߺ㧖࡮ᄢ⼱┨ੳ㧖㧖࡮⊕㠽ᱜ᮸㧖㧖㧖

Study on Estimation Method of Seismic Safety Marginof Aged Piping System and Equipment***
Izumi NAKAMURA*, Akihito OTANI****, and Masaki SHIRATORI**** National Research Institute for Earth Science and Disaster Prevention, Japan** Ishikawajima-Harima Heavy Industries Co., Ltd., Japan*** Yokohama National University, Japan

Abstract
In order to clarify the behavior of degraded pipes under seismic events, cyclic four-point bending tests on straight pipe and shaking table
tests using piping system models were conducted. The degradation used in this study were wall thinning or cracks, which were considered
to be caused in piping systems due to the effects of aging. Cyclic bending tests were conducted on straight pipe elements to investigate therelation between the failure mode and degradation condition. Shaking table tests were also conducted to investigate the influence ofdegradation on piping system behavior and clarify the failure mode of degraded piping systems. Through these tests, the failure modes ofaged piping were obtained under varying loading and degradation conditions.
In addition to these experiments, elastic-plastic FEM analysis using ABAQUS were conducted on pipe elements with wall thinning ora crack. It has been found that the failure modes observed in the tests were well simulated by this analysis. With this analysis, the strain
concentrated point could be predicted and the cause of its generation could be explained by the simulated deformation behavior of the pipe.
In order to predict the piping system’s maximum response under elastic-plastic response, a simple response prediction method was
proposed in this report. This method takes account of the dissipation energy caused by plastic deformation. It has been found that thisprediction method provided a conservative value compared with the test results, but not too conservative a value as an elastic response
analysis.
Key Words : Aging effect, Piping, Cracks, Wall thinning, Shaking table test, Failure mode, FEM analysis,
Simple elastic-plastic response prediction method‫ޓޓ‬㧖㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫✚ޓ‬ว㒐ἴ⎇ⓥㇱ㐷⍹Ꮉፉ᠞⏴㊀Ꮏᬺᩣᑼળ␠‫ޓ‬ේሶജ੐ᬺㇱ㧖㧖㧖ᮮᵿ࿖┙ᄢቇᄢቇ㒮‫ޓ‬Ꮏቇ⎇ⓥ㒮
‫ޓ‬㧖㧖

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1.ߪߓ߼ߦ  4
1.1⢛᥊  4
1.2ߎࠇ߹ߢߦⴕࠊࠇߚ⎇ⓥߩ⃻⁁  4
1.3ᧄ⎇ⓥߩ⋡⊛  5
2.ታ㛎ᣇᴺ  6
2.1ⷐ⚛⹜㛎  6
2.1.1⹜㛎૕ߩ᭎ⷐ  6
2.1.2タ⩄᧦ઙ  7
2.1.3⸘᷹  8
2.2㈩▤♽ᝄേ⹜㛎  11
2.2.1ᐔ㕙㈩▤♽ᝄേ⹜㛎  11
2.2.1.1⹜㛎૕ߩ᭎ⷐ  11
2.2.1.2タ⩄᧦ઙ  11
2.2.1.3⸘᷹  12
2.2.2┙૕㈩▤♽ᝄേ⹜㛎  14
2.2.2.1⹜㛎૕ߩ᭎ⷐ  14
2.2.2.2タ⩄᧦ઙ  15
2.2.2.3⸘᷹  15
3.ታ㛎⚿ᨐ  17
3.1ⷐ⚛⹜㛎  17
3.1.1߈ⵚઃ߈㈩▤  17
3.1.1.1⎕៊⁁ᴫ  17
3.1.1.2߈ⵚઃ߈㈩▤ߩ⩄㊀ᄌᒻ․ᕈ  17
3.1.1.3SCC ߈ⵚߣ EDM ߈ⵚߩ⎕៊ኼ๮Ყセ  19
3.1.1.4⎕㕙⸃ᨆ  19
3.1.2ᷫ⡺㈩▤߅ࠃ߮ஜో㈩▤  21
3.1.2.1⎕៊⁁ᴫ  21
3.1.2.2ᷫ⡺㊂ߣ࡜࠴ࠚ࠶࠻ᄌᒻ㊂ߩ㑐ଥ  23
3.1.2.3ᷫ⡺㊂ߣ⹜㛎૕෻ജߩ㑐ଥ  24
3.1.2.4ஜో⹜㛎૕ߩ⩄㊀ᄌᒻ․ᕈ  24
3.2㈩▤♽⹜㛎  25
3.2.1ᐔ㕙㈩▤♽⹜㛎  25
3.2.1.1⎕៊⁁ᴫ  25
3.2.1.2ᝄേᢙߩᄌൻ  28
3.2.1.3ഠൻ᧦ઙߣᔕ╵୯ߩ㑐ଥ  29
3.2.1.4⹜㛎૕ߩᄖᓘᄌൻ  30
3.2.2┙૕㈩▤♽⹜㛎  31
3.2.2.1⎕៊⁁ᴫ  31
3.2.2.2ഠൻ᧦ઙߣᔕ╵୯ߩ㑐ଥ  34
3.2.2.3ࠛ࡞ࡏߩᄖᓘᄌൻ  35
4.㈩▤ⷐ⚛ߦኻߔࠆ⹦⚦⸃ᨆ  36
4.1ᧄ┨ߩ⋡⊛߅ࠃ߮᭴ᚑ  36
4.2ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⸃ᨆ⊛∋ഭ⹏ଔ1㧔⋥▤㧕 36
4.2.1ታ㛎᭎ⷐ  36
4.2.2⸃ᨆࡕ࠺࡞ߣ᧦ઙ  36
4.2.3ታ㛎⚿ᨐߣ⸃ᨆ⚿ᨐߩᲧセ  37
4.2.4ᷫ⡺㈩▤ߩ߈ⵚ⊒↢ࡔࠞ࠾࠭ࡓߣ⎕უ᜼േ  39
4.2.5⚥Ⓧ∋ഭ៊்ೣࠍ↪޿ߚኼ๮⹏ଔ  42

4.2.6Shellࡕ࠺࡞ߦࠃࠆ◲ᤃ⸃ᨆᚻᴺ  44
4.2.7࡜ࡦ࠳ࡓᝄ᏷ᵄߩ⩄㊀ጁᱧߦኻߔࠆ∋ഭኼ๮⹏ଔ  46
4.3ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⸃ᨆ2㧔ᦛ▤㧕 47
4.3.1⸃ᨆࡕ࠺࡞ߣ᧦ઙ  47
4.3.2ࠛ࡞ࡏ㈩▤ߩ߈ⵚ⊒↢ࡔࠞ࠾࠭ࡓߣ⎕უ᜼േ  49
4.3.3Shellࡕ࠺࡞ߦࠃࠆ◲ᤃ⸃ᨆᚻᴺ  51
4.4⴫㕙߈ⵚઃ߈㈩▤ߩૐࠨࠗࠢ࡞∋ഭ߈ⵚㅴዷ⹏ଔ  53
4.4.1࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ࠍ↪޿ߚ߈ⵚㅴዷ⸃ᨆ  53
4.4.1.1࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛  53
4.4.1.2➅ࠅ㄰ߒ J Ⓧಽ▸࿐ ∆ J ߩ⹏ଔ  53
4.4.1.3߈ⵚㅴዷೣ  53
4.4.1.4߈ⵚㅴዷߩ⹏ଔᚻ㗅  53
4.4.2⸃ᨆࡕ࠺࡞ߣ᧦ઙ  54
4.4.3⸃ᨆ⚿ᨐߣ⠨ኤ  55
4.5ᧄ┨ߩ߹ߣ߼  59
5.㈩▤♽ߩേ⊛ᔕ╵ߦኻߔࠆ⹏ଔ  60
5.1᭎ⷐ  60
5.2ᒢ႟ᕈᔕ╵੍᷹ᚻᴺߩ᭎ᔨ  60
5.3 ᒢ႟ᕈᔕ╵੍᷹ᚻᴺߩ⸘▚ߩ⹦⚦  61
5.3.1ᶖᢔࠛࡀ࡞ࠡࠍ᳞߼ࠆߚ߼ߩ FEM ⸃ᨆ  61
5.3.2ᝄേࡕ࡯࠼⸃ᨆ  62
5.3.3ᝄേᔕ╵⸃ᨆ  63
5.3.4╬ଔᷫ⴮Ყ෸߮ᦨᄢᔕ╵㊂ߩ⸘▚  65
5.4ᒢ႟ᕈᔕ╵੍᷹⚿ᨐ  65
6.߹ߣ߼  67
7.޽ߣ߇߈  67㧨⻢ㄉ㧪  67㧨ෳ⠨ᢥ₂㧪  68㧨㑐ㅪ⊒⴫⺰ᢥ㧪  70ⷐ‫ޓ‬ᣦ  71㧨ᷝઃ1 㧪‫ޟޓ‬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޠ‬ታ㛎ታᣉᆔຬળ‫ޓ‬ฬ★  72
㧨ᷝઃ2 㧪‫ޓ‬ታ㛎⚿ᨐ╬ࠞ࡜࡯࿑ ‫  ޓ‬73‫ޣ‬ၫ╩ᜂᒰ‫ޤ‬╙ 1 ┨‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬╙ 2 ┨‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬╙3┨
3.1‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬3.2.1 ⍹Ꮉፉ᠞⏴㊀Ꮏᬺ‫ޓޓ‬ᄢ⼱‫┨ޓ‬ੳ‫ޓ‬3.2.2 㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬╙ 4 ┨‫ޓ‬ᮮᵿ࿖┙ᄢቇ‫⊕ޓޓޓޓ‬㠽‫ޓ‬ᱜ᮸
╙ 5 ┨‫ޓ‬⍹Ꮉፉ᠞⏴㊀Ꮏᬺ‫ޓޓ‬ᄢ⼱‫┨ޓ‬ੳ
╙ 6 ┨‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬╙ 7 ┨‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ߪߓ߼ߦ
⢛᥊
‫ޓ‬ᚒ߇࿖ߢߪ 1960 ᐕߦ⊒㔚↪ේሶἹߩㆇォ߇ᆎ߹ࠅ㧘1970 ᐕߦ໡ᬺ↪ේሶἹ߇Ⓙ௛ࠍ㐿ᆎߒߚ㧚੹ᣣߢߪ 2001
ᐕ4᦬⃻࿷ߢ51ၮߩ໡ᬺ↪ේሶജ⊒㔚ᚲ߇Ⓙ௛ߒߡ߅ࠅ㧘ේሶജߦࠃࠆ⊒㔚㊂ߪ✚⊒㔚㊂ߩ 3 ഀએ਄ࠍභ߼ߡ޿ࠆ㧚৻ᣇ㧘ේሶജ⊒㔚ᚲߩㆇ↪㐿ᆎᐕߏߣߩේሶἹၮᢙߪ࿑
ߩࠃ߁ߦߥࠅ㧘ㆇ↪㐿ᆎ߆ࠄ20ᐕએ਄⚻ㆊߒߡ޿ࠆᣉ
⸳ߪ 20 ၮߣߥࠆ߇㧘⃻࿷ේሶജ⊒㔚ᣉ⸳ߩᣂⷙᑪ⸳ߪ෩
ߒ޿ᖱ൓ߢ޽ࠅ㧘ᣢሽߩᣉ⸳ࠍ⛽ᜬ଻ోߒߟߟ⛮⛯ߒߡ૶↪ߔࠆᔅⷐ߇޽ࠆ㧚ේሶജ⊒㔚ᣉ⸳ߩ⠴↪ᐕᢙߪᓥ᧪
30 ᐕߣߐࠇߡ߈ߚ߇㧘1999 ᐕߦㅢ↥⋭࡮⾗Ḯࠛࡀ࡞ࠡ࡯
ᐡߪㆇォ㐿ᆎᓟ 30 ᐕㄭߊࠍ⚻ߚේሶജ⊒㔚ᣉ⸳ 3 ၮߦߟ޿ߡ㧘60 ᐕࠍⷞ㊁ߦ౉ࠇߚ㐳ᦼㆇォ߇ᛛⴚ⊛ߦน⢻ߣߔࠆႎ๔ᦠ 1) ࠍឭ಴ߒߚ㧚ߒ߆ߒ㧘㐳ᦼߦࠊߚߞߡ૶↪ߐࠇߚᣉ⸳ߦߪ㜞⚻ᐕൻߦ઻޿᭴ᚑᯏེ࡮㈩▤ߩഠൻ߇⊒↢ߔࠆߣ⠨߃ࠄࠇࠆߎߣ߆ࠄ㧘㐳ኼ๮ൻࠍታ⃻ߔࠆߚ߼ߦ
ߪ㧘ㆡಾߥ▤ℂࠍⴕ޿㧘㜞⚻ᐕൻࡊ࡜ࡦ࠻ߩᡷㅧᎿ੐ࠍ฽
߼ߚ⚻ᐕൻኻ╷ࠍ⻠ߓ㧘቟ోᕈࠍ⏕଻ߔࠆᔅⷐ߇޽ࠆ㧚‫ߦ⥸৻ޓ‬㧘ࡊ࡜ࡦ࠻ߦ߅ߌࠆਥⷐ᭴ᚑⷐ⚛ߩ৻ߟߢ޽ࠆ
㈩▤♽ߦߪ‫ޔ‬㜞⚻ᐕൻߦࠃࠅㅢᏱߩᾲ∋ഭߛߌߢߥߊ‫ޔ‬ᔕജ⣣㘩ഀࠇ߿⣣㘩࡮უ㘩ߥߤߦࠃࠆᷫ⡺ߣ޿ߞߚഠൻ߇
⊒↢ߔࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ㧚㊀ⷐᐲߩ㜞޿㈩▤♽ߦ⎕უ߇↢ߓߚ႐ว㧘ࠪࠬ࠹ࡓో૕ߦᵄ෸ߔࠆᓇ㗀߇ᄙᄢߢ޽ࠆߎߣ߆ࠄ㧘ߘߩஜోᕈࠍ⛽ᜬߔࠆߎߣߪ㊀ⷐߢ޽ࠆ㧚․ߦᣣᧄߪ࿾㔡࿖ߢ޽ࠆߚ߼㧘ഠൻࠍᗐቯߒߚ㜞⚻ᐕࡊ࡜ࡦ࠻ߩ቟ోᕈߪᄢ࿾㔡ᤨߦ߅޿ߡ߽චಽ⏕଻ߐࠇߥߌ
ࠇ߫ߥࠄߥ޿㧚㈩▤♽ߦ⊒↢ߔࠆᷫ⡺߿߈ⵚߩࠃ߁ߥഠ
ൻߩ⸵ኈഠൻၮḰߩᬌ⸛ߦ߅޿ߡߪ㧘ታ㛎߿⸃ᨆߦၮߠ
ߊวℂ⊛ߥᬌ⸽࠺࡯࠲ࠍ⫾Ⓧߔࠆᔅⷐ߇޽ࠆ㧚߹ߚ㧘ᣣᧄߪ࿾㔡࿖ߢ޽ࠆߚ߼㧘ߘߩࠃ߁ߥഠൻ߇ᬌ಴ߐࠇߚ႐ว

ߩ㊀ⷐߥ໧㗴ߩ৻ߟߣߒߡ㧘ᒰ⹥ഠൻ⁁ᴫ߇⠴㔡਄⸵ኈߐࠇࠆ߆ߤ߁߆ߩ⹏ଔ߇ᔅⷐߢ޽ࠆ㧚ߘߩߚ߼ߦߪߎߩ
ࠃ߁ߥഠൻㇱ߇㈩▤♽ߩേ⊛᜼േ߅ࠃ߮⠴㔡቟ో⵨ᐲߦ
ਈ߃ࠆᓇ㗀ࠍ᣿ࠄ߆ߦߒ㧘࿾㔡േࠍฃߌࠆ⚻ᐕഠൻ㈩▤ߩ᜼േࠍวℂ⊛ߦ⹏ଔߔࠆᚻᴺ߇ᔅⷐߣߥࠆ㧚ߎࠇ߹ߢߦⴕࠊࠇߚ⎇ⓥߩ⃻⁁‫ޓ‬ഠൻㇱࠍ᦭ߔࠆ㈩▤♽ߩஜోᕈ⹏ଔ߿⠴㔡቟ో⵨ᐲߦ
㑐ߔࠆ⎇ⓥߣߒߡߪ㧘ߎࠇ߹ߢߦ߈ⵚઃ߈㈩▤ࠍኻ⽎ߣߒߡ㧘ᄙߊߩ⎇ⓥ߇ⴕࠊࠇߡ߈ߚ㧚ᣣᧄේሶജ⎇ⓥᚲߢߪ㧘1ᰴ಄ළ㈩▤ߦߟ޿ߡ᭴ㅧᒝᐲ਄ߩା㗬ᕈࠍታ㛎⊛ߦᬌ⸽ߔࠆߎߣࠍ⋡⊛ߣߒߡ㧘1975 ᐕ߆ࠄ 1992 ᐕߦ߆ߌߡ
㈩▤ା㗬ᕈታ⸽⹜㛎߇ታᣉߐࠇߚ 2)㧚ߎߩ⹜㛎⎇ⓥߢߪ㧘ਥߦ߈ⵚઃ߈㈩▤ࠍኻ⽎ߣߒߡ㧘㈩▤∋ഭ⹜㛎㧘ਇ቟ቯ⎕უ⹜㛎㧘⎕ᢿ⹜㛎㧘⸃ᨆ⹏ଔ߇ታᣉߐࠇߚ㧚߹ߚ㧘⎇ⓥᦼ
㑆ਛߩ1986ᐕߦ☨࿖Surryේሶജ⊒㔚ᚲߢᷫ⡺ࠛ࡞ࡏߩ⎕ᢿ੐᡿߇⊒↢ߒߚ 3) ߚ߼㧘ᷫ⡺㈩▤ߩ⎕უ㒢⇇ࠍ᳞߼ࠆ⹜
㛎߽ታᣉߐࠇߚ㧚߹ߚ㧘㔚ജਛᄩ⎇ⓥᚲߢߪࠕࡔ࡝ࠞේሶ
ജⷙ೙ᆔຬળ㧔NRC㧕߇ਥ௅ߒߚ࿖㓙౒ห⎇ⓥߢ޽ࠆ߈ⵚઃ߈㈩▤ߩஜోᕈ⹏ଔᚻᴺࠍ⏕┙ߔࠆߚ߼ߩ⎇ⓥ
㧔IPIRG㧕4) ߦෳടߒ㧘ᣣᧄ࿖ౝߩ὇⚛㍑㈩▤ߦኻߔࠆታᢿ
㕙ᔕജၮḰߩㆡ↪ᕈߩᬌ⸛㧘േ⊛➅ࠅ㄰ߒ⩄㊀ਅߦ߅ߌࠆ߈ⵚㅴዷ⹏ଔߥߤߩ⎇ⓥࠍታᣉߒߚ 5)㧚
ᷫ⡺ߩࠃ߁ߥ㕖߈ⵚ⁁ᰳ㒱ߩஜోᕈ⹏ଔߦኻߒߡߪ㧘ᄢቇ߿᳃㑆ડᬺߦࠃࠅᷫ⡺ࠍᮨᡆߒߚ㈩▤ߩ⚳ዪᒝᐲ߿⎕უᒻᘒࠍᓧࠆታ㛎⎇ⓥ߇ታᣉߐࠇᆎ߼ 6)-8)㧘ഠൻᒻ⁁ߣ⎕៊᧦ઙߣߩ㑐ㅪߠߌ߇ⴕࠊࠇߡ޿ࠆ㧚߹ߚ㧘ේሶജ⊒㔚ᛛⴚᯏ᭴㧔NUPEC㧕ߢߪ㧘ᐔᚑ 12 ᐕᐲࠃࠅᐔᚑ 17 ᐕᐲ߹ߢߩ੍ቯߢ㧘ᷫ⡺㈩▤ߩ⠴㔡ታ⸽⹜㛎ࠍታᣉߒߡ޿ࠆ 9)㧚
ߒ߆ߒ㧘ో૕ߣߒߡߪഠൻ᧦ઙߣߒߡᷫ⡺ࠍኻ⽎ߣߒߚ㈩▤ߩ⠴㔡቟ోᕈ⹏ଔߦ㑐ߔࠆ⎇ⓥߪ߹ߛᢙ߇ዋߥ޿㧚

6

4

Closed2

Closed51

3

1

Comercial Operation Year࿑  ᣣᧄߦ߅ߌࠆ໡ᬺ↪ේሶἹߩㆇ↪㐿ᆎᐕߏߣߩၮᢙ
Fig.1-1 Numbers of Nuclear Power Plants in commercial operation (Japan).

− 4

−

1999

1996

1993

1990

1987

1984

1981

1978

1975

1972

1969

1966

1963

0
1960

Number of NPP

5ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ᄢ࡟ࡌ࡞ߩ࿾㔡ࠍᗐቯߒߚ㈩▤♽ߩᒢ႟ᕈᔕ╵ߦ㑐ߔࠆ⎇ⓥߪ㧘ஜో㈩▤ࠍኻ⽎ߣߒߚ߽ߩ߇ਥߢ޽ࠅ㧘ഠൻ㈩▤ߦ߅ߌࠆ⚳ዪᒝᐲ߿⎕៊ᒻᘒࠍኻ⽎ߣߒߚ߽ߩߪ㧘਄⸥
ߩNUPECߢ੹ᓟታᣉߔࠆ੍ቯߩ⎇ⓥ⺖㗴એᄖߦߪ߶ߣࠎ
ߤ⷗ฃߌࠄࠇߥ޿㧚ஜో㈩▤♽ࠍኻ⽎ߣߒߚ߽ߩߣߒߡ
ߪ㧘1971 ᐕ㨪 1973 ᐕߦታᣉߐࠇߚ㧘࿾㔡ᤨߦ߅ߌࠆේሶ
ജᣉ⸳ߩ㒢⇇⸳⸘ߦ㑐ߔࠆ⹜㛎⎇ⓥ㧔ᣣᧄ㔚᳇දળ㧕10)㧘
㈩▤⠴㔡⸳⸘ၮḰߩวℂൻ⎇ⓥ㧔㔚ജ౒ㅢ⎇ⓥ㧕11) ߿㧘
NUPECߦࠃࠅታᣉߐࠇߡ޿ࠆ㈩▤ߩ⚳ዪᒝᐲ⠴㔡ታ⸽⹜㛎 12) ߇᜼ߍࠄࠇࠆ㧚߹ߚ㧘ᶏᄖߢⴕࠊࠇߡ޿ࠆ⎇ⓥߣߒߡ㧘☨࿖ߩ EPRI ߢታᣉߐࠇߚ㈩▤ߩേ⊛ା㗬ᕈ⹏ଔߦ㑐ߔࠆ⎇ⓥࡊࡠࠣ࡜ࡓ㧔PFDRP㧕13) ߇޽ࠅ㧘ߎߩታ㛎⚿ᨐ߿⸃ᨆ⚿ᨐ߆ࠄ㧘㈩▤♽ߩ⚳ዪ⎕៊ᒻᘒ߿⸳⸘ၮḰᄌᦝߦ㑐ߔࠆ⼏⺰߇ⴕࠊࠇߡ޿ࠆ 14)㧚߹ߚ㧘ࡈ࡜ࡦࠬߢߪේሶ
ജᐡ㧔CEA㧕ߦࠃࠅ㧘ၮḰߩ✭๺ࠍ⋡⊛ߣߒߡ㧘ታⷙᮨߩ㈩▤ࠍ↪޿ߚᝄേ⎕უታ㛎ߣ㧘◲ᤃ⸃ᨆࠦ࡯࠼ߩ㐿⊒߇ⴕࠊࠇߚ 15)㧚
ᧄ⎇ⓥߩ⋡⊛⢛᥊ߢㅀߴߚࠃ߁ߦ㧘㜞⚻ᐕ㈩▤♽ߩᄢ࿾㔡ᤨߦ߅ߌࠆ቟ో⵨ᐲࠍวℂ⊛ߦ⹏ଔߔࠆߚ߼ߦߪ㧘ߘߩࠃ߁ߥ㈩▤♽ߩ㒢⇇ᒝᐲ߿ᦨ⚳⎕៊ᒻᘒࠍᛠីߔࠆᔅⷐ߇޽ࠆ㧚ߒ߆ߒ㧘߈ⵚ߿ᷫ⡺ߣ޿ߞߚ᭴ㅧഠൻ߇޽ࠆ㈩▤♽ߩ㕒⊛⩄㊀ਅߦ߅ߌࠆ㒢⇇ᒝᐲߦ㑐ߔࠆ⎇ⓥ㧘޽ࠆ޿ߪஜో
㈩▤♽ߩᒢ႟ᕈᔕ╵ߦ㑐ߔࠆ⎇ⓥߪᢙᄙߊߥߐࠇߡ޿ࠆ
߇㧘᭴ㅧഠൻ߇޽ࠆ㈩▤♽ߢ࿾㔡⩄㊀ࠍኻ⽎ߣߒ㧘㒢⇇ᒝᐲ߿ᒢ႟ᕈᔕ╵ࠍኻ⽎ߣߒߚ⹜㛎⎇ⓥߪ߶ߣࠎߤߥߐࠇ
ߡ޿ߥ޿㧚ߘߎߢ㧘㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲߢߪ㧘ᮮᵿ࿖┙ᄢቇ㧘⍹Ꮉፉ᠞⏴㊀Ꮏᬺߣߩਃ⠪౒หߢ㧘࿾㔡േࠍฃߌࠆ⚻ᐕഠൻ㈩▤ߩേ⊛᜼േ߅ࠃ߮⎕៊ᒻᘒࠍታ㛎⊛ߦ᣿ࠄ߆ߦߒ㧘⚻ᐕഠൻ㈩▤ߩ⠴㔡ᕈࠍวℂ⊛ߦ⹏ଔߔࠆᚻᴺࠍ
ᬌ⸛ߔࠆߎߣࠍ⋡⊛ߣߒߡ㧘ᐔᚑ 8 ᐕᐲ߆ࠄᐔᚑ 12 ᐕᐲߦ߆ߌߡ㧘ේሶജ቟ో⎇ⓥ‫ޟ‬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻
߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ࠍޠ‬ታᣉߒߚ㧚ᧄ⎇ⓥߢߪ㧘⚻ᐕᄌൻࠍᗐቯߒߚ‫ޔ‬ᒝᐲ⊛ߦ෩ߒ޿ᒻ

− 5⁁ߩ߈ⵚ߹ߚߪᷫ⡺ࠍ㈩▤ࡕ࠺࡞ߦዉ౉ߒታ㛎ࠍⴕ߁ߎߣߦࠃࠅ㧘ഠൻᒻ⁁ߦࠃࠆ⎕៊ᒻᘒߩ㆑޿㧘ഠൻㇱߩ᦭ήߦࠃࠆ㈩▤♽ߩ࿾㔡ᔕ╵ߩᄌൻ╬ࠍ᣿ࠄ߆ߦߔࠆߎߣࠍ
⋡⊛ߣߒߚ㧚ߎߩߚ߼㧘ታ㛎ߢߪ⚻ᐕഠൻࠍᮨᡆߒߚ⋥▤ࠍ↪޿ߡ➅ࠅ㄰ߒ4ὐᦛߍ⹜㛎ࠍⴕ߁ⷐ⚛⹜㛎ߣ㧘ഠൻㇱಽࠍ᦭ߔࠆ㈩▤♽ߦኻߒߡᝄേบࠍ↪޿ߡടᝄࠍⴕ߁㈩▤♽ᝄേ⹜㛎ࠍታᣉߒߚ㧚߹ߚ㧘ߎࠇࠄߩታ㛎࠺࡯࠲ߦၮ
ߠ߈㧘⹦⚦⸃ᨆߦࠃࠆ⎕៊ࡔࠞ࠾࠭ࡓߩ⠨ኤ߿ᒢ႟ᕈᔕ
╵ᄌ૏ߩ◲ᤃ੍᷹ᴺߩᬌ⸛ࠍⴕߞߚ㧚ᧄႎ๔ᦠߪ5ࡩᐕߦࠊߚࠅታᣉߒߚታ㛎ౝኈߣ⸃ᨆ⹏ଔߦߟ޿ߡߣࠅ߹ߣ߼
ߚ߽ߩߢ޽ࠆ㧚╙2 ┨ߢߪ㧘ᧄ⎇ⓥߢታᣉߒߚታ㛎ߩ᭎ⷐࠍ㧘╙ 3 ┨ߢߪታ㛎⚿ᨐߩ᭎⇛ࠍㅀߴࠆ㧚╙ 4 ┨߅ࠃ߮╙
5┨ߢߪ㧘ߎࠇࠄߩታ㛎⚿ᨐࠍ〯߹߃ਃᯏ㑐߇ߎࠇ߹ߢታ
ᣉߒߚ⸃ᨆ⹏ଔߦߟ޿ߡㅀߴࠆ㧚ߎࠇࠄߩ⸃ᨆ⹏ଔߪฦ
ᯏ㑐߇ߘࠇߙࠇߩⷞὐ߆ࠄታᣉߒߚ߽ߩߦߟ޿ߡ㧘ᧄႎ๔ᦠࠍߣࠅ߹ߣ߼ߚᤨὐߦ߅ߌࠆᬌ⸛⁁ᴫࠍㅀߴߚ߽ߩ
ߢ޽ࠅ㧘⃻⁁ߢߪᔅߕߒ߽⋧੕ߦㅪ៤ߩߣࠇߚ⛔৻ᕈߩ޽ࠆౝኈߣߪߥߞߡ޿ߥ޿㧚⸃ᨆߦ߅ߌࠆⷞὐߩ⛔৻ߣ
⹏ଔᴺ߳ߩឭ᩺ߦߟ޿ߡߪᐔᚑ 13ᐕᐲࠃࠅታᣉߔࠆᰴᦼ
ේሶജ቟ో⎇ⓥ㧘‫ޟ‬࿾㔡⩄㊀ࠍฃߌࠆᷫ⡺㈩▤ߩ⎕უㆊ⒟⸃᣿ߦ㑐ߔࠆ⎇ⓥ‫ߩޠ‬ਛߢ⛮⛯ߒߡ޿ߊߎߣߣߒߡ޿ࠆ㧚ߥ߅㧘ᧄ⎇ⓥߪේሶജ቟ో⎇ⓥᐕᰴ⸘↹㧔ᐔᚑ8ᐕᐲ㨪ᐔᚑ 12 ᐕᐲ㧘ේሶജ቟ోᆔຬળ╷ቯ㧕16) ߦၮߠ޿ߡ߅ࠅ㧘⑼ቇᛛⴚᐡ࿖┙ᯏ㑐ේሶജ⹜㛎⎇ⓥ⾌ࠍゲߦ㧘ฦᯏ㑐⁛⥄ߩ⎇ⓥ⾌߽೑↪ߒߡታᣉߐࠇߚ߽ߩߢ޽ࠆ㧚߹ߚ㧘ᧄ⎇ⓥߩታᣉߦ޽ߚࠅ㧘ታ㛎ታᣉᆔຬળ㧔એਅ AP ᆔຬળ㧘ᆔຬ㐳㧦⊕㠽ᱜ᮸ᮮᵿ࿖┙ᄢቇᢎ᝼㧕ࠍ⚵❱ߒ㧘ታ㛎ߩታᣉ㧘⸃ᨆ⹏ଔߦߟ޿ߡ⼏⺰ࠍⴕߞߚ㧚ᧄ⎇ⓥߢߪ࿾㔡ߦࠃࠆ㈩▤ߩᒢ႟ᕈᔕ╵߆ࠄ㈩▤ߩ⎕៊ߦ⥋ࠆ߹ߢߩ㗔ၞࠍኻ⽎ߣߒߚߚ߼㧘⎕უജቇߣᝄേᔕ╵ߩਔಽ㊁ߩኾ㐷ኅ߆ࠄߥࠆᆔຬળߣߒߚ㧚߹ߚ㧘ታോ⊛ߥⷰὐ߆ࠄߩᗧ⷗ࠍ޿
ߚߛߊߚ߼㧘㔚ജળ␠෸߮ࡊ࡜ࡦ࠻ࡔ࡯ࠞ࡯߽߳ᆔຬߩᵷ㆜ࠍଐ㗬ߒߚ㧚ᷝઃ 1 ߦ AP ᆔຬળᆔຬฬ★ࠍ␜ߔ㧚−㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ⷐ⚛⹜㛎⹜㛎૕ߩ᭎ⷐ‫⹜⚛ⷐޓ‬㛎ߢߪ㧘ഠൻᒻ⁁߿タ⩄ጁᱧߦࠃࠆ⎕៊ᒻᘒߩ㆑޿ࠍ⏕⹺ߔࠆߎߣࠍ⋡⊛ߣߒߡഠൻㇱࠍ᦭ߔࠆ⋥▤ࠍ↪޿ߚᄌ૏೙ᓮߩ 4 ὐᦛߍ⹜㛎ࠍⴕߞߚ㧚ᐔᚑ 8 ᐕᐲߦߪタ⩄ⵝ⟎ߩ⵾૞ࠍⴕ޿㧘ᐔᚑ 9 ᐕᐲ㨪ᐔᚑ 12 ᐕᐲߦ߆ߌߡタ⩄⹜㛎ࠍታᣉߒߚ㧚‫⹜⚛ⷐޓ‬㛎ߢዉ౉ߒߚഠൻ᧦ઙߪ㧘ᔕജ⣣㘩ഀࠇ㧔SCC㧕㧘᡼㔚ടᎿ㧔EDM㧕߈ⵚ㧘߹ߚߪᷫ⡺ߩ޿ߕࠇ߆ߣߒߚ㧚߹ߚ㧘ᷫ⡺⹜㛎૕ߣหߓ᧚⾰ߢஜో⡺ෘߩ⹜㛎૕ߦߟ޿ߡ߽タ⩄ࠍⴕ޿㧘⩄㊀ᄌᒻ․ᕈߩᲧセࠍⴕߞߚ㧚㈩▤ߩ᧚⾰ߪ㧘SCC ⹜㛎૕߅ࠃ߮ EDM ߈ⵚઃ߈⹜㛎૕㧔એਅ EDM
⹜㛎૕㧕ߢߪࠬ࠹ࡦ࡟ࠬ㍑ SUS304 ࠍ㧘ᷫ⡺⹜㛎૕߅ࠃ߮ஜో⹜㛎૕ߢߪ὇⚛㍑ STS410 ࠍ૶↪ߒߚ㧚ߥ߅㧘ᧄ⎇ⓥߢߪ⚻ᐕᄌൻߦ઻߁᧚⾰ᄌൻߩᓇ㗀ߪ⠨ᘦߒߡ޿ߥ޿㧚ଏ⹜ㇱߩ㈩▤ߪ100A㧘sch80㧔ᄖᓘ㧦114.3mm㧘⡺ෘ㧦8.6mm㧕
ߣߒߚ㧚߹ߚ㧘4 ὐᦛߍ⹜㛎ⵝ⟎ߩᡰὐㇱಽߦ߅ߌࠆዪㇱᄌᒻࠍ㒐ᱛߔࠆߚ߼㧘⵬ᒝ▤ߣߒߡ⹜㛎૕ㇱಽߩ㈩▤ߩਔ┵ߦ 100A㧘sch160㧔ᄖᓘ㧦114.3mm㧘⡺ෘ㧦13.5mm㧕ߩ㈩▤ࠍṁធߒߚ㧚⹜㛎૕ㇱಽߩ㈩▤㐳ߐߪ 400mm ߹ߚߪ

100
SCC induced area

8.6

400
400

Ǿ114.313.5

࿑  EDM ⹜㛎૕ߩᒻ⁁Fig.2.1-3 Geometry of the specimens with an EDM notch.

200

200

200
EDM notch

200Ǿ114.38.6

8.6(a) SC01 - SC04, SC07, SC08.
400400(1) SCC⹜㛎㈩▤ߦṁធࠍᣉߒߡᒁᒛᱷ⇐ᔕജࠍዉ౉ߒ㧘㜞᷷㜞࿶ਅߩࠝ࡯࠻ࠢ࡟࡯ࡉౝߦ200ᤨ㑆㨪800ᤨ㑆⒟ᐲ
ᩰ⚊ߒ㧘SCCࠍ↢ᚑߐߖߚ㧚↢ᚑߒߚSCCߩ߈ⵚ૏⟎ߣᷓߐߪታ㛎೨ߦᶐㅘត்㧔PT㧕ᬌᩏߢ⺞ᩏߒ㧘ᦨ߽ᄢ߈޿ߣᕁࠊࠇࠆ߈ⵚ૏⟎߇ᦨᄢᦛߍᣇะߦ৻⥌ߔࠆࠃ߁⹜㛎૕ߩ⸳⟎૏⟎ࠍ⺞ᢛߒߚ㧚‫ޓ‬SCC ⹜㛎૕ߪ⹜㛎⚳ੌᓟ㧘⎕㕙ᬌᩏࠍⴕߞߡೋᦼ
SCC ᒻ⁁ࠍ᷹ቯߒߚ㧚࿑  ߦ⹜㛎૕ߩᒻ⁁ࠍ㧘࿑ߦSCCㇱಽߢ߈ⵚ߇⽾ㅢߒߚ⹜㛎૕ߩೋᦼSCCᒻ⁁ࠍ␜ߔ㧚
(2) EDM ߈ⵚ᡼㔚ടᎿߦࠃࠅ㈩▤ౝ㕙ߦ߈ⵚࠍዉ౉ߒߚ㧚߈ⵚᒻ⁁ߪ㧘ౝⷺ 360q߈ⵚᷓߐ 4.3mm㧔⡺ෘߩ 50%㧕ߩో๟߈ⵚࠍᜬߟ⹜㛎૕ࠍ4૕㧘ౝⷺ90qᷓߐ4.3mmߩ⍱ᒻ߈ⵚࠍᣉߒߚ߽ߩࠍ2૕㧘SCC߈ⵚࠍᮨᡆߒߚඨᬦ౞
߈ⵚࠍᣉߒߚ߽ߩࠍ 3 ૕⵾૞ߒߚ㧚ߎߎߢ㧘SCC ߈ⵚࠍᮨᡆߒߚ EDM ߈ⵚઃ߈⹜㛎૕ߪ㧘SCC ߩࠃ߁ߥ⥄ὼ߈ⵚߣEDM߈ⵚߩࠃ߁ߥੱᎿᰳ㒱ߣߩ⎕៊ኼ๮ߩ
8.6

8.6

100

Ǿ114.3

8.6

13.5

200

200mm ߣߒ㧘ṁធߔࠆ⵬ᒝ▤ߩ㐳ߐࠍ⺞▵ߒߡో૕ߩ㐳ߐࠍ 3010mm ߣߒߚ㧚‫⹜ޓ‬㛎૕ߪ㧘SCC ⹜㛎૕ 8 ૕㧘EDM ⹜㛎૕ 9 ૕㧘ᷫ⡺⹜㛎૕ 9 ૕㧘ஜో⹜㛎૕ 2 ૕ߩ⸘ 28 ૕ࠍ⵾૞ߒߚ㧚ฦഠൻߩ
ዉ౉ᣇᴺߣഠൻᒻ⁁ߪએਅߩㅢࠅߢ޽ࠆ㧚

13.5

ታ㛎ᣇᴺ  

SCC induced area(b) SC05, SC06.

90q

࿑ ‫ޓ‬SCC ⹜㛎૕ߩᒻ⁁Fig.2.1-1 Geometry of the specimens with SCC.

8.6 114.3 4.3(a) EM01 - EM04.

6.5q(a) Initial SCC in SC01.

(b) EM05, EM09.

37q(b) Initial SCC in SC03.

13q

Loading direction
Semieliptical
EDM notch
Depth : 4.25 mm
Width : 21.8 mm(c) Initial SCC in SC07.

(c) EM06.

(d) Initial SCC in SC08.

Semieliptical
EDM notch
Depth : 4.2 mm
Width : 12.6 mm(d) EM07.

Semieliptical
EDM notch
Depth : 2.9 mm
Width : 14.1 mm(e) EM08.

࿑  EDM ⹜㛎૕ߩೋᦼ߈ⵚᒻ⁁Fig.2.1-4 Initial crack shapes of EDM notched pipe specimens.

࿑ SCC ⹜㛎૕ߩೋᦼ SCC ߈ⵚᒻ⁁Fig.2.1-2 Initial shape of SCC in SCC specimens.

− 6−ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆㆑޿ࠍ⏕⹺ߔࠆߚ߼ߦታᣉߒߚ㧚⹜㛎૕ߦዉ౉ߒߚ߈
ⵚߪ SCC ⹜㛎૕ߩ⎕ᢿ㕙ߦ޽ࠆೋᦼ SCC ᒻ⁁ࠍ㧘╬ଔߥᷓߐߣᢿ㕙Ⓧࠍᜬߟඨᬦ౞ᒻ⁁ߩEDM߈ⵚߢᮨᡆߒߚ㧚࿑  ߦ⹜㛎૕ߩᒻ⁁ࠍ㧘࿑  ߦዉ౉ߒߚ߈ⵚᒻ⁁ࠍ␜ߔ㧚(3) ᷫ⡺ᯏ᪾ടᎿߦࠃࠅ㈩▤ߩ⡺ෘࠍૐᷫߒߚ㧚ᷫ⡺ߪో๟ᷫ
⡺ߣߒ㧘ᷫ⡺㊂ߪ⡺ෘߩ 50%㧔⡺ෘ 4.3mm㧕ߩ߽ߩࠍ6 ૕㧘75% ߩ߽ߩ㧔⡺ෘ 2.15mm㧕㧘60% ߩ߽ߩ㧔⡺ෘ
3.44mm㧕㧘25% ߩ߽ߩ㧔⡺ෘ 6.45mm㧕ࠍฦ 1 ૕⵾૞ߒߚ㧚࿑  ߦ⹜㛎૕ߩᒻ⁁ࠍ␜ߔ㧚タ⩄᧦ઙ‫ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲᚲ᦭ߩ৻ᰴరᄢဳᝄേบࠍ↪޿㧘ᝄേบߣၮ␆ߣߩ⋧ኻᄌ૏ࠍ೑↪ߒߚᄌ૏೙ᓮߩ➅ࠅ㄰
ߒ 4 ὐᦛߍ⹜㛎ࠍⴕߞߚ㧚⴫  ߦᄢဳᝄേบߩၮᧄᕈ
⢻ࠍ㧘࿑  ߦ 4 ὐᦛߍ⹜㛎ⵝ⟎ࠍ␜ߔ㧚4 ὐᦛߍ⹜㛎ⵝ⟎ߩᡰᜬὐࠬࡄࡦߪ 2,400mm㧘⽶⩄ὐࠬࡄࡦߪ 800mm
ߢ޽ࠆ㧚タ⩄ጁᱧߪቯᏱᝄ᏷ߦࠃࠆタ⩄ߣ࡜ࡦ࠳ࡓᝄ᏷ߦࠃࠆタ⩄ߩ⎕უߦ෸߷ߔᓇ㗀ࠍᛠីߔࠆߚ߼ߦ㧘ᝄ᏷⴫ 
ᝄേบ⻉రTable 2.1-1 Specification of the shaking table.

15.0 m  14.5 m
Weight: 160 ton
Electro – hydraulicservo control s ystem

Table‫ߚ߹ޓ‬㧘ߎߩઁߦஜో⹜㛎૕ࠍ2 ૕૞ᚑߒߚ㧚ஜో⹜㛎૕ߩᒻ⁁ࠍ࿑  ߦ␜ߔ㧚

Driving s ystem

13.5

8.6

4.3

400

100

62.5

62.5

㱂114.3

R200

100

37.5

(a) 50% thinned wall specimen (EC01 - EC06).

A ctuators

360 tonM ax. model weight

500 tonM ax. a mplituder 220 mm

M ax. velocit y

75 cm/sec

M ax. a cceleration

0.55G (wit h 500-ton model)/ 2.2G (without m odel)

Frequency range

DC – 50 Hz

Input wa ve t yp es

Sinusoida l wa ve
Random wa ve
Earthquake wave

13.5

8.6

2.15

400

100

62.8

62.8

㱂114.3

R200

100

37.2

Anchor(b) 75% thinned wall specimen (EC07).

Shaking Table

Ǿ114.3



6.45

13.5

Load
Cell
Load
Cell

400

R200

Displacement meter

62.5
37.5

62.5

80
0

R200

80
0

Loading Direction
Ǿ114.3

8.6

13.5

400
3.45

Specimen

800(c) 25% thinned wall specimen (EC08).

62.5

࿑  4 ὐᦛߍ⹜㛎ⵝ⟎
Fig.2.1-7 Four-point bending test equipment.
Disp.[mm]

62.5
37.5

(d) 60% thinned wall specimen (EC09).
࿑  ᷫ⡺⹜㛎૕ߩᒻ⁁Fig.2.1-5 Geometry of the specimens with wall thinning.













Time[sec]













(a) Sinusoidal wave.
Disp.[mm]Ǿ114.3

13.5

8.6

400
8.6

(90 ton  4)













Time[sec](b) Random amplitude wave.

࿑ ‫ޓ‬ஜో⹜㛎૕ߩᒻ⁁㧔EA01 ߅ࠃ߮ EA02㧕
Fig.2.1-6 Geometry of the specimens without wall thinning(EA01 & EA02).

࿑  ౉ജᄌ૏ᵄᒻ
Fig.2.1-8 Time histories of input displacement.

− 7−㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬߇৻ቯߢ޽ࠆᱜᒏᵄߣථ⿧ᝄേᢙ߇ 1Hz ߢ޽ࠆ࡜ࡦ࠳ࡓ
ᝄ᏷ᵄࠍ૶↪ߒߚ㧚ᱜᒏᵄߪቯᏱㇱಽߩᵄᢙ߇26ᵄߢ㧘⹜㛎૕ߦㆊᄢߥടㅦᐲ߇૞↪ߔࠆߩࠍ㒐ᱛߔࠆߚ߼㧘೨ᓟ
10 ⑽㑆ߦᝄ᏷ߩẋჇ࡮ẋᷫㇱࠍㅊടߒߡ޿ࠆ㧚࡜ࡦ࠳ࡓᝄ᏷ᵄߪේሶജᑪደߩᐥᔕ╵ࠍ㈩▤♽ߦ౉ജߒߡᓧࠄࠇ
ߚᔕ╵ᄌ૏ᵄᒻࠍථ⿧ᝄേᢙ߇ 1Hz ߣߥࠆࠃ߁ᤨ㑆ゲࠍ⺞ᢛߔࠆߎߣߦࠃࠅ૞ᚑߒߚ㧚࡜ࡦ࠳ࡓᝄ᏷ᵄߦ฽߹ࠇ
ࠆᵄᢙߪ 46 ࠨࠗࠢ࡞ߢ޽ࠆ㧚࿑  ߦߎࠇࠄߩタ⩄ᵄᒻࠍ␜ߔ㧚‫⹜ޓ‬㛎૕ߦߪᏱ᷷᳓ߢౝ࿶ࠍ⽶⩄ߒߚ㧚ౝ࿶ߪ㧘SCC⹜㛎૕ߣ EDM ⹜㛎૕ߢ 8MPa㧘ᷫ⡺⹜㛎૕ߣஜో⹜㛎૕ߢ
11MPa ߣߒߚ㧚ߚߛߒ㧘ᷫ⡺⹜㛎૕ߩ߁ߜ 1 ૕ߦߟ޿ߡ
ߪ㧘ౝ࿶߇⎕៊ᒻᘒߦਈ߃ࠆᓇ㗀ࠍᛠីߔࠆߚ߼ߦ㧘ౝ࿶߅ࠃ߮ౝㇱ᳓ߥߒߢ⹜㛎ࠍⴕߞߚ㧚ᐔᚑ 12 ᐕᐲߦታᣉߒ
ߚ⹜㛎૕㧔SC07㧘SC08㧘EM08㧘EM09㧘EC08㧘EC09㧕ߦߟ޿ߡߪౝㇱ᳓ߩṳᵨࠍ⏕⹺ߒߚᤨὐߢタ⩄ࠍ⚳ੌߐߖߚ߇㧘ߘߩઁߩ⹜㛎૕ߢߪ߈ⵚ⽾ㅢᓟ㧘࿑ ߦ␜ߒߚ
౉ജᄌ૏ᵄᒻ߇⚳ੌߔࠆ߹ߢタ⩄ࠍ⛮⛯ߒߚ㧚ታ㛎ߢ૶↪ߒߚ⹜㛎૕ߩฬ⒓㧘ഠൻ᧦ઙ㧘ౝ࿶᧦ઙࠍ߹ߣ߼ߡ⴫  ߦ␜ߔ㧚⸘᷹
‫ޓ‬ታ㛎ߢߪએਅߩ㗄⋡ࠍ⸘᷹ߒߚ㧚(1)⹜㛎૕߳ߩ౉ജᄌ૏
(2)෻ജ
(3)ౝ࿶
(4)⹜㛎૕ᄖ⴫㕙ߩゲᣇะ߅ࠃ߮๟ᣇะ߭ߕߺ
(5)⹜㛎૕ౝ㕙ߩゲᣇะ߅ࠃ߮๟ᣇะ߭ߕߺ㧔ஜో⹜㛎૕ߣᷫ⡺⹜㛎૕ߩ৻ㇱ㧕(6)߈ⵚ㐿ญᄌ૏㧔EDM ⹜㛎૕ߩߺ㧕‫ޓ‬࿑      ߦฦ⹜㛎૕ߩ⸘᷹ὐࠍ␜ߔ㧚ߎࠇࠄߪోߡ
500Hzߩࠨࡦࡊ࡝ࡦࠣ๟ᵄᢙߢ෼㍳ߒߚ㧚߹ߚ㧘ᷫ⡺⹜㛎૕߅ࠃ߮ஜో⹜㛎૕ߢߪ㧘ߎߩઁߦ⹜㛎ߩ೨ᓟߦ߅޿ߡ
㈩▤ᄖᓘࠍ᷹ቯߒߚ㧚⴫ 
ⷐ⚛⹜㛎‫⹜ޓ‬㛎૕৻ⷩ
Table 2.1-2 Specifications for pipe element tests.

Name

Material

Sy
[MPa]

Su
[MPa]

Sm
[MPa]

SC01
SC02
SC03
SC04
SC05
SC06
SC07
SC08

SUS304

311

617

206

EM01
EM02
EM03
EM04
EM05
EM06
EM07
EM08
EM09
EC01
EC02
EC03
EC04
EC05
EC06
EC07
EC08
EC09
EA01
EA02

SUS304

311

617

206

Type ofdefectCondition of defectFull angle incircumference [deg.]

SCC

Natural crack

Natural
Crack

360

0.5 t

90
25.73 *1
14.87 *2
16.64 *390

0.5 t
0.49 t *1
0.49 t *2
0.34 t *3
0.5 t

EDM

Depth ofdefect *0.5 tSTS410STS410

312

312

470

470

157

157

Wall
thinning

8

11

0

No
defect0*2 Same size as SCC in SC03
− 8

8

360
0.75 t0.25 t
0.6 t

11

0

11

* ‘t’ denotes the normal pipe thickness*1 Same size as SCC in SC01

Internal pressure(P) [MPa]−*3 Same size as SCC in SC07

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆

B

A

P01

P02
South

A
L01
D01
A01

B

A : Accelerometer
L : Load Cell
P : Pressure Gauge
D : Displacement
S : Strain Gauge(Hoop & Axial at each position)

50 50

0㫦(Top)S11

Ground0㫦(Top)
S21

S12

S18
270㫦S17

S13 90㫦

270㫦S24

S22 90㫦

S14

S16

S15

180㫦(Bottom)

S23
180㫦(Bottom)

A-A

B-B

(a) Measurement points of SCC specimens.

A C B

P01

South

P02
A 㪚 B

L01
D01
A0
Ground50 50

0 (Top)
S21

S11
S12

S18

S13

S17
S16

S15

S24
S22

S14

S23
180 (Bottom)

A-A

C01

A : Accelerometer
L : Load Cell
P : Pressure Gauge
D : Displacement
S : Strain Gauge(Hoop & Axial at each position)
C : Crip Gauge(2ch for EM01 - EM04 and EM06,
1ch for EM05, EM07 - EM09)

B-B

C-C

(b) Measurement points of EDM specimens.
࿑  ⷐ⚛⹜㛎૕⸘᷹ὐ㧔1/2㧕
Fig.2.1-9 Measurement points of specimens for pipe element tests (1/2).

− 9−㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

A

B C D

E

P01

P02
㪈

South
S51
S52

S54

L01
D01
A01

S53

S44

A-A

Ground

S41

S43
B-B

A

B C D

150

30 30 150

E

S17

S13

S16 S15

S14

S02

S31

S21

0 (Top)
S11S42
S12 S24
S18

S22

S34

S23
D-D

S32
S33
E-E

S01

180(Bottom)
C-C* S01 & S02 are measured only for EC05, EC06 and EC07

A : Accelerometer
L : Load Cell
P : Pressure Gauge
D : Displacement
S : Strain Gauge(Hoop & Axial at each position)(c) Measurement points of EC01 - EC07.

S74

S64
100

G-G

100

F-F
A G B C D F E

P02

P01
A G B C D F E

South
S51
S54

L01
D01
A01
Ground

150

S52
S53
A-A

30 30 150

S41
S42
S18

S44
S43
B-B

S31

S21
0(Top
S11

S24
S13

S17
S16
S02

S34

S12

S15

S14

S32

S22
S23

S33

D-D

E-E

S01
180 (Bottom)
C-C

A : Accelerometer
L : Load Cell
P : Pressure Gauge
D : Displacement
S : Strain Gauge(Hoop & Axial at each position)(d) Measurement points of EC08, EC09, EA01 and EA02.
࿑  ⷐ⚛⹜㛎૕⸘᷹ὐ㧔2/2㧕
Fig.2.1-9 Measurement points of specimens for pipe element tests (2/2).

− 1100 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆

㈩▤♽ᝄേ⹜㛎㈩▤♽⹜㛎ߢߪ㧘ᝄേบ਄ߦഠൻㇱಽࠍ᦭ߔࠆ㈩▤♽ࠍ⸳⟎ߒടᝄታ㛎ࠍⴕߞߚ㧚⹜㛎ߩ⋡⊛ߪഠൻㇱಽ߇ሽ࿷ߔࠆ㈩▤♽ߩᝄേ․ᕈߣ⎕៊᜼േࠍ⏕⹺ߔࠆߎߣߢ޽
ࠆ㧚⹜㛎૕ߦߪᐔ㕙Zဳߩᐔ㕙㈩▤♽ߣ㧘┙ߜ਄߇ࠅㇱࠍᜬߟ┙૕ Z ဳߩ┙૕㈩▤♽ߩ 2 ⒳㘃ࠍ૶↪ߒߚ㧚ᐔ㕙㈩▤♽ᝄേ⹜㛎⹜㛎૕ߩ᭎ⷐ‫ޓ‬ᐔ㕙㈩▤♽ᝄേ⹜㛎ߪᐔᚑ 10 ᐕᐲߦታᣉߒߚ㧚࿑  ߦ⹜㛎૕ߩᒻ⁁ࠍ␜ߔ㧚⹜㛎૕ߪഠൻࠍዉ౉ߔࠆㇱಽ㧔ㇱಽ A㧕ߣ㧘ഠൻࠍዉ౉ߒߥ޿ㇱಽ㧔ㇱಽ B㧕ߦಽ߆ࠇ㧘ࡈ࡜ࡦࠫߢធวߒߚ㧚ߚߛߒធวㇱಽߩࡈ࡜ࡦࠫߪ㐽ᱛߒߡ޽ࠅ㧘ㇱಽAߣㇱಽBߩ㈩▤⚻〝ߪಽ㔌ߒߡ޿ࠆ㧚ᐔ㕙㈩▤♽⹜㛎ߢዉ౉ߒߚഠൻ᧦ઙߪ⋥▤ㇱᷫ⡺߅ࠃ߮ࠛ࡞ࡏㇱᷫ⡺ߩ2 ⒳㘃ߣߒߚ㧚߹ߚ㧘Ყセߩߚ߼ߦഠൻㇱಽ

Thinned wall
Thinnedwallpart
partofofB01
2D_B01760

2900Part AThinnedpart of C01
Thinned wall
partwallof 2D_C01(Elbow1)

10
14

10
42
,S
0A
10

20
ch1

߇ߥ޿ஜో㈩▤♽⹜㛎૕ߦߟ޿ߡ߽ടᝄታ㛎ࠍⴕߞߚ㧚૶↪ߒߚ㈩▤ߩ᧚⾰ߪోߡ὇⚛㍑ STPT370 ߢ㧘㈩▤ญᓘߪⷐ⚛⹜㛎ߣห᭽ 100A ߣߒߚ㧚⡺ෘߪ㧘⹜㛎૕ㇱಽߢ޽ࠆㇱಽ A ߢߪⷐ⚛⹜㛎ߣห᭽ sch80㧔⡺ෘ 8.6mm㧕㧘ㇱಽ B
ߢߪ sch120㧔⡺ෘ 11.1mm㧕ߣߒߚ㧚ㇱಽ B ߪߔߴߡߩ⹜
㛎ߢ౒ㅢߦ૶↪ߒߚ㧚⹜㛎૕ߩฬ⒓ߣዉ౉ഠൻ᧦ઙߪએ
ਅߩㅢࠅߢ޽ࠆ㧚(1)‫⹜ޓ‬㛎૕ฬ㧦2D_A01
ഠൻ᧦ઙ㧦ഠൻߥߒ
(2)‫⹜ޓ‬㛎૕ฬ㧦2D_B01
ഠൻ᧦ઙ㧦⋥▤ㇱᷫ⡺࿑ߦ␜ߒߚ૏⟎ߩ⋥▤ㇱಽߩ⡺ෘࠍᯏ᪾ട
ᎿߦࠃࠅㅢᏱ⡺ෘߩ 50% ߦૐᷫߒ㧘ో๟ᷫ⡺ࠍᮨᡆߒߚ㧚(3)‫⹜ޓ‬㛎૕ฬ㧦2D_C01
ഠൻ᧦ઙ㧦ࠛ࡞ࡏㇱᷫ⡺࿑  ߦ␜ߒߚࠛ࡞ࡏ 1 ࠍ sch40 ߩࠛ࡞ࡏߣߔ
ࠆߎߣߦࠃࠅో๟ᷫ⡺ࠍᮨᡆߒߚ㧚sch40 ߩࠛ࡞ࡏߩ⡺ෘߪ౏⒓ 6.0mm ߢ޽ࠅ㧘ᷫ⡺㊂ߪ 30% ߣ
ߥࠆ㧚

0A
10

,S

‫⹜ߦ⴫ޓ‬㛎૕ߩ․ᕈࠍ߹ߣ߼ߡ␜ߔ㧚߹ߚ㧘࿑
ߦ࿕᦭୯⸃ᨆߢ᳞߼ߚ2D_A01ߩ࿕᦭ᝄേᢙߣᝄേࡕ࡯
࠼ࠍ␜ߔ㧚⹜㛎૕ߩ1ᰴ࿕᦭ᝄേࡕ࡯࠼ߢᡰ㈩⊛ߥᄌᒻߪࠛ࡞ࡏ 1㧘2㧘3 ߩ㕙ౝᄌᒻߢ޽ࠅ㧘ஜో⁁ᘒߩ႐ว㧘ᦨᄢᔕജ߇⊒↢ߔࠆߩߪࠛ࡞ࡏ 1 ߣߥࠆ߇㧘ࠛ࡞ࡏ 2 ߩᔕജ߽߶߷ห⒟ᐲߢ޽ߞߚ㧚0
ch8

Elbow2

Weight (200kg)

on
cti
ire
D
g

Elbow3
Part BinakShタ⩄᧦ઙ‫ޓ‬㈩▤♽ࡕ࠺࡞ߦኻߒߡ㧘㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲᚲ᦭ߩ৻
ᰴరᄢဳᝄേบࠍ↪޿ߡടᝄታ㛎ࠍⴕߞߚ㧚ടᝄᵄᒻߪ
⹜㛎૕ߩ 1 ᰴ࿕᦭ᝄേࡕ࡯࠼ߩߺࠍബ⿠ߔࠆߚ߼㧘2.5Hz
㨪3.5Hzߩ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄࠍ૞ᚑߒߡ૶↪ߒߚ㧚࿑
ߦ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄߩടㅦᐲᤨೞᱧᵄᒻߣᔕ╵ࠬࡍࠢ࠻࡞ࠍ␜ߔ㧚ታ㛎ߪߎߩ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄߩ౉ജ࡟ࡌ࡞ࠍ

427

0࿑  ᐔ㕙㈩▤♽⹜㛎‫⹜ޓ‬㛎૕ᒻ⁁
Fig.2.2-1 2-D piping model for piping system test.

⴫  ᐔ㕙㈩▤♽⹜㛎‫⹜ޓ‬㛎૕৻ⷩ
Table 2.2-1 Specimens for 2-D piping system tests.

Name

Material

S y *1[MPa]

S u *1[MPa]

S m *1[MPa]

Internalpressure(P)[MPa]

2D_A01

2D_B01

STPT370

302

473

158

Condition of defectType

Configuration

Defected partNo defect

---

---

Full circumferential
thinning
Depth : 0.5 t *Straight pipenear the anchor(See Fig. 2.2-1)

Full circumferential
thinning
Depth : 0.3 t *Elbow 111
Wallthinning

2D_C01* ‘t’ denotes the normal pipe thickness− 1111 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

Shaking direction
1st mode : 3.2Hz

2nd mode : 5.7Hz

3rd mode : 14.3Hz

ᒢᕈ࡟ࡌ࡞߆ࠄᦨᄢ1600Gal⒟ᐲ߹ߢჇടߐߖ㧘ฦ౉ജ࡟ࡌ࡞ߢߩᔕ╵ᕈ⁁ࠍᓧࠆߣߣ߽ߦᦨᄢ࡟ࡌ࡞ߢ⹜㛎૕߇

Acc.[Gal]࿑ ‫ޓ‬ᐔ㕙㈩▤♽⹜㛎૕ߩᝄേࡕ࡯࠼
Fig.2.2-2 The vibration mode of the 2-D piping model.

100 0
500
0

-500
-100 0⎕៊ߔࠆ߹ߢ౉ജࠍ➅ࠅ㄰ߒߚ㧚ஜో㈩▤♽⹜㛎૕ߦߟ޿ߡߪฦടᝄ࡟ࡌ࡞ߢ5࿁ߕߟടᝄࠍⴕ޿㧘ᔕ╵ᕈ⁁ࠍᓧߚߩߺߢ⎕៊ߐߖߕߦ⹜㛎ࠍ⚳ੌߐߖߚ㧚‫⹜ޓ‬㛎૕ߩㇱಽ A ߦߪᏱ᷷᳓ࠍḩߚߒ㧘ౝ࿶ࠍ⽶⩄ߒߚ㧚ౝ࿶ߪߔߴߡߩ⹜㛎૕ߢ 11MPa ߣߒߚ㧚ㇱಽ B ߪౝ࿶ߥߒ㧔ౝㇱ᳓ߥߒ㧕ߢ⹜㛎ࠍⴕߞߚ㧚⹜㛎ߢߪ㧘⹜㛎૕߇៊்ߒౝㇱ᳓ߩṳᵨࠍ⋡ⷞ⏕⹺ߒߚᤨὐߢᝄേบߩ౉ജࠍ
⚳ੌߐߖߚ㧚

05Time[s] 1 5

20

25

30

(a) Time history of input acceleration.
M agnification of Response Acc.[Gal/Gal]

20⸘᷹
‫ޓ‬ታ㛎ߢߪએਅߩ㗄⋡ࠍ⸘᷹ߒߚ㧚(1) ᝄേบടㅦᐲ
(2) ⹜㛎૕ߩᔕ╵ടㅦᐲ(3) ਛᄩㇱᔕ╵ᄌ૏(4) ౝ࿶
(5) ⹜㛎૕ᄖ⴫㕙ߩゲᣇะ߅ࠃ߮๟ᣇะ߭ߕߺ

h= 0.0 05
15

h= 0.01h =0.0210
h= 0.05h =0.155h =0.10h= 0.20h =0.25

0

0

1

2
3
Frequency [Hz]45(b) Response spectrum (h: damping ratio).

‫ޓ‬࿑ߦ⹜㛎૕ߩ⸘᷹ὐࠍ␜ߔ㧚ߎࠇࠄߪోߡ 500Hz
ߩࠨࡦࡊ࡝ࡦࠣ๟ᵄᢙߢ෼㍳ߒߚ㧚߹ߚ㧘ߎߩઁߦ㧘⹜㛎ߩ೨ᓟߦ߅޿ߡࠛ࡞ࡏㇱಽ߅ࠃ߮ᷫ⡺ዉ౉ㇱಽߩ㈩▤ᄖᓘࠍ᷹ቯߒߚ㧚10࿑     ‫ޓ‬ᐔ㕙㈩▤♽⹜㛎ߢ૶↪ߒߚ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄ
Fig.2.2-3 Narrow band random wave used for the piping systemtest of the 2-D piping model.

− 1122 −

S096

S097

S098

S106

S107

S108

S116

S117

S118

S095

S094

S093

S092

S104

S103

S102

S114

S113

S112

S091

S105

S101

S115

S111

A-A

S084

S083

S081

A002

− 1133 −
S065

S061

S033

S031

S043

S041

S064

D011

S032

S042

S063

S062

P01

S073

S024
S023

A011

S051

S022

S053

S021

S054

A012

A013

S072

S052

S014

࿑ ‫ޓ‬ᐔ㕙㈩▤♽⹜㛎૕‫⸘ޓ‬᷹ὐ
Fig.2.2-4 Measurement points of the 2-D piping model.

S034

S044

S066

S082 S067

S068

㪉㪐㪇㪇

S074

S071

S013

S011

S012

A001

Strain gauge (Axial direction)
Strain gauge (Hoop direction)

Displacement(Shaking direction and vertical direction)

Accelerometerᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ߚ㧚‫ޓ‬㈩▤ߩ᧚⾰ߪၮᧄ⊛ߦᐔ㕙㈩▤♽ߣห᭽㧘὇⚛㍑
STPT370ߣߒߚ߇㧘ᷫ⡺ࠛ࡞ࡏߪ὇⚛㍑㈩▤FSGPࠛ࡞ࡏߢઍ↪ߒߚߚ߼ࠛ࡞ࡏㇱᷫ⡺⹜㛎૕ߢߪᷫ⡺ࠛ࡞ࡏㇱಽߩߺ᧚⾰߇⇣ߥߞߡ޿ࠆ㧚߹ߚ㧘EDM ߈ⵚઃ߈⹜㛎૕ߢߪ߈ⵚዉ౉ㇱಽߩ㈩▤ߦࠬ࠹ࡦ࡟ࠬ㍑ SUS304 ࠍ૶↪ߒߚ㧚㈩▤ญᓘߪ 100A㧘sch80 ߣߒߚ㧚⹜㛎૕ߩฬ⒓ߣዉ౉
ഠൻ᧦ઙߪએਅߩㅢࠅߢ޽ࠆ㧚(1) ⹜㛎૕ฬ㧦3D_A01
ഠൻ᧦ઙ㧦ഠൻߥߒ
(2)‫⹜ޓ‬㛎૕ฬ㧦3D_C01
ഠൻ᧦ઙ㧦ࠛ࡞ࡏ 1 ߅ࠃ߮ࠛ࡞ࡏ 2 ᷫ⡺࿑  ߦ␜ߒߚࠛ࡞ࡏ 1 ߅ࠃ߮ࠛ࡞ࡏ 2 ㇱಽࠍ
FSGPࠛ࡞ࡏߣߔࠆߎߣߦࠃࠅో๟ᷫ⡺ࠍᮨᡆߒߚ㧚FSGP ࠛ࡞ࡏߩ⡺ෘߪ౏⒓ 4.5mm ߢ޽ࠅ㧘ᷫ⡺㊂ߪ 48% ߣߥࠆ㧚
(3)‫⹜ޓ‬㛎૕ฬ㧦3D_C02
ഠൻ᧦ઙ㧦ࠛ࡞ࡏ 1 ᷫ⡺ࠛ࡞ࡏ1ࠍFSGPࠛ࡞ࡏߣߔࠆߎߣߦࠃࠅᷫ⡺㊂
48% ߩో๟ᷫ⡺ࠍᮨᡆߒߚ㧚(4)‫⹜ޓ‬㛎૕ฬ㧦3D_C03
ഠൻ᧦ઙ㧦ࠛ࡞ࡏ 2 ᷫ⡺
ࠛ࡞ࡏ2ࠍFSGPࠛ࡞ࡏߣߔࠆߎߣߦࠃࠅᷫ⡺㊂
48% ߩో๟ᷫ⡺ࠍᮨᡆߒߚ㧚(5)‫⹜ޓ‬㛎૕ฬ㧦3D_D01
ഠൻ᧦ઙ㧦EDM ߈ⵚ㧔ㇱಽ߈ⵚ㧕࿑ߦ␜ߔࠛ࡞ࡏ1ㄭறߩ⋥▤ㇱಽߦඨᬦ౞
ᒻ⁁ߩ EDM ߈ⵚࠍዉ౉ߒߚ㧚ዉ౉ߒߚ EDM ߈ⵚߩᒻ⁁ߪ㧘࿑  ߦ␜ߒߚⷐ⚛⹜㛎૕ EM07
ߣห৻ᒻ⁁ߣߒ㧘ᦨᄢ߈ⵚᷓߐࠍᦛߍࡕ࡯ࡔࡦ

┙૕㈩▤♽ᝄേ⹜㛎⹜㛎૕ߩ᭎ⷐ‫ޓ‬ᐔᚑ 11 ᐕᐲ߅ࠃ߮ᐔᚑ 12 ᐕᐲߦ㧘┙૕㈩▤♽⹜㛎૕ࠍ↪޿ߚടᝄታ㛎ࠍታᣉߒߚ㧚࿑ߦ⹜㛎૕ߩᒻ⁁ࠍ␜ߔ㧚⹜㛎૕ߪࠛ࡞ࡏ 1 ࠍ฽߻ㇱಽ㧔ㇱಽ A㧕㧘ࠛ࡞ࡏ 2 ࠍ฽߻ㇱಽ㧔ㇱಽ B㧕㧘ࠛ࡞ࡏ 3 ࠍ฽߻ㇱಽ㧔ㇱಽ C㧕ߩ 3 ߟ߆ࠄᚑࠅ㧘ࡈ࡜ࡦࠫߢធวߒߚ㧚┙૕㈩▤♽⹜㛎૕ߪㇱಽ
A㧘B㧘C ߇ߟߥ߇ࠅ৻ߟߩ㈩▤⚻〝ߣߥߞߡ޿ࠆ㧚┙૕
㈩▤♽ߢዉ౉ߒߚഠൻ᧦ઙߪ㧘ࠛ࡞ࡏㇱᷫ⡺߹ߚ EDM ߈
ⵚߩ2 ⒳㘃ߣߒߚ㧚ᐔ㕙㈩▤♽⹜㛎ߣห᭽㧘ഠൻㇱಽߩߥ޿ஜో㈩▤♽⹜㛎૕ߦߟ޿ߡ߽ടᝄታ㛎ࠍⴕߞߚ㧚⸳ቯߔࠆഠൻ᧦ઙߦᓥ޿ㇱಽ A ߹ߚߪㇱಽ B ߩ㈩▤ߩ৻ㇱߦഠൻࠍዉ౉ߒߚ㧚ㇱಽ C ߪోߡߩ⹜㛎૕ߢ౒ㅢߦ૶↪ߒ
Elbow2

260
0

0
300
Weight (200kg + 60kg)
Elbow3

3000
Elbow1260
0Crack induced position(for 3D_D01 & 3D_D02)

Shaking direction࿑  ┙૕㈩▤♽⹜㛎‫⹜ޓ‬㛎૕ᒻ⁁
Fig.2.2-5 3-D piping model for piping system test.

⴫   ┙૕㈩▤♽⹜㛎‫⹜ޓ‬㛎૕৻ⷩ
Table 2.2-2 Specimens for 3-D piping system tests.
Name
3D_A01

3D_C01

3D_C02

3D_C03

3D_D01

3D_D02

Material
STPT370
FSGP Elbow(Elbow 1 & Elbow 2)/ STPT370(Ordinary part)
FSGP Elbow(Elbow 1)/ STPT370(Ordinary part)
FSGP Elbow(Elbow 2)/ STPT370(Ordinary part)
SUS304 (Part A)/ STPT370(Part B & Part C)
SUS304(Part A & Part B)/ STPT370(Part C)S y *1[MPa]

S u *1[MPa]

S m *1
[MPa]

302

473

158

351

452

151

351

452

151

351

452

151

311

617

206

Internalpressure(P) [MPa]
10

Condition of defectType

Configuration

Defected partNo
defect-----Elbow 1
andElbow 210Wallthinning

617

Elbow 1

Elbow 2

Partial EDM notch
Depth : 0.49 t *2
Full crack angle : 14.87[deg.]8311

Full circumferential thinning
Depth : 0.48 t *2

EDM
Full circumferential EDM notch
Depth : 0.5 t *2
Full crack angle : 360[deg.]206*1 Value at defected part*2 ‘t’ denotes the normal pipe thickness− 1144 −Straight pipenear Elbow 1(See Fig. 2.2-5)

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆

+Z
+Y
+X

Shaking direction
1st mode: 2.58Hz

3rd mode: 8.39Hz

2nd mode: 6.26Hz

1000
500
0
-500
-1000
0

10

15

20

25

30

35

Time[s]

40

45

50

55

60

65

25

‫⹜ߦ⴫ޓ‬㛎૕ߩ․ᕈࠍ߹ߣ߼ߡ␜ߔ㧚߹ߚ㧘࿑
ߦ࿕᦭୯⸃ᨆߢ᳞߼ߚ3D_A01ߩ࿕᦭ᝄേᢙߣᝄേࡕ࡯
࠼ࠍ␜ߔ㧚⹜㛎૕ߩ1ᰴ࿕᦭ᝄേࡕ࡯࠼ߢᡰ㈩⊛ߥᄌᒻߪࠛ࡞ࡏ 1 ߅ࠃ߮ 2 ߩ㕙ౝᄌᒻߢ޽ࠆ㧚ஜో⁁ᘒߩ႐ว㧘ᦨᄢᔕജ߇⊒↢ߔࠆߩߪࠛ࡞ࡏ 1 ߢ޽ࠅ㧘ࠛ࡞ࡏ 2 ߩᔕജߪࠛ࡞ࡏ 1 ߦᲧߴ 14% ⒟ᐲૐ޿୯ߣߥߞߚ㧚タ⩄᧦ઙ‫ޓ‬೨㗄ߦ᜼ߍߚ㈩▤♽ࡕ࠺࡞ߦኻߒߡ㧘৻ᰴరᄢဳᝄേ
บࠍ↪޿ߡടᝄታ㛎ࠍⴕߞߚ㧚ടᝄᵄᒻߪ⹜㛎૕ߩᰴ࿕
᦭ᝄേࡕ࡯࠼ߩߺࠍബ⿠ߔࠆߚ߼㧘1.5Hz 㨪 3.0Hz ߩ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄࠍ૞ᚑߒߡ૶↪ߒߚ㧚࿑ߦታ㛎ߢ↪޿ߚ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄߩടㅦᐲᤨೞᱧᵄᒻߣᔕ╵ࠬࡍࠢ࠻࡞ࠍ␜ߔ㧚ታ㛎ߪߎߩ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄߩ౉ജ࡟ࡌ࡞ࠍ
ᒢᕈ࡟ࡌ࡞߆ࠄᦨᄢ1800Gal⒟ᐲ߹ߢჇടߐߖ㧘ฦ౉ജ࡟ࡌ࡞ߢߩᔕ╵ᕈ⁁ࠍᓧࠆߣߣ߽ߦᦨᄢ࡟ࡌ࡞ߢ⹜㛎૕߇⎕៊ߔࠆ߹ߢ౉ജࠍ➅ࠅ㄰ߒߚ㧚‫⹜ޓ‬㛎૕ߦߪᏱ᷷᳓ࠍḩߚߒߡౝ࿶ࠍ⽶⩄ߒߚ㧚ౝ࿶୯ߪ㧘ஜో⹜㛎૕߅ࠃ߮ᷫ⡺⹜㛎૕ߢ 10MPa㧘߈ⵚߟ߈⹜
㛎૕ߢ 8MPa ߦ⸳ቯߒߚ㧚ᐔᚑ 11 ᐕᐲߦታᣉߒߚ⹜㛎૕
㧔3D_A01㧘3D_C01㧘3D_D01㧕ߦߟ޿ߡߪ㧘⹜㛎૕߇⎕៊ߒౝㇱ᳓ߩṳᵨࠍ⋡ⷞ⏕⹺ߒߚᤨὐߢᝄേบߩ౉ജࠍ⚳ੌߐߖߚ߇㧘ᐔᚑ 12 ᐕᐲߦታᣉߒߚ⹜㛎૕㧔3D_C02㧘
3D_C03㧘3D_D02㧕ߢߪ㧘ṳᵨࠍ⏕⹺ߒߚᓟ߽㧘࿑ 
ߦ␜ߒߚടㅦᐲ౉ജ߇⚳ੌߔࠆ߹ߢടᝄࠍ⛮⛯ߒߚ㧚5(a) Time history of input acceleration.

M agnification of Response Acc.[Gal/Gal]࠻߇ᦨᄢߣߥࠆᣇะ㧔Zゲ㧗ᣇะ㧕ߦ৻⥌ߐߖߚ㧚
(6)‫⹜ޓ‬㛎૕ฬ㧦3D_D02
ഠൻ᧦ઙ㧦EDM ߈ⵚ
3D_D01 ߣหߓ૏⟎ߩࠛ࡞ࡏ 1 ㄭறߩ⋥▤ㇱಽߦ
ో๟ EDM ߈ⵚࠍዉ౉ߒߚ㧚߈ⵚᷓߐߪ⡺ෘߩ
50% ߣߒߚ㧚Acc.[Gal]࿑ ‫┙ޓ‬૕㈩▤♽⹜㛎૕ߩᝄേࡕ࡯࠼
Fig.2.2-6 The vibration mode of the 3-D piping model.

20h=0.00515

h=0.01h=0.0210h=0.05h=0.155h=0.10h=0.20h=0.25

0
0

1

2

3

4

5

Frequency [Hz](b) Response spectrum (h: damping ratio).
࿑  ┙૕㈩▤♽⹜㛎ߢ૶↪ߒߚ⁜Ꮺၞ࡜ࡦ࠳ࡓᵄ
Fig.2.2-7 Narrow band random wave used for the piping systemtest of the 3-D piping model.

(4)
(5)
(6)
(7)

ౝ࿶
⹜㛎૕ᄖ⴫㕙ߩゲᣇะ߅ࠃ߮๟ᣇะ߭ߕߺ
ࠛ࡞ࡏ 3 ߩ૏⟎ߦ߅ߌࠆਃᰴర⛘ኻᄌ૏߈ⵚ㐿ญᄌ૏㧔߈ⵚߟ߈⹜㛎૕ߩߺ㧕‫ޓ‬࿑ߦ⹜㛎૕ߩ⸘᷹ὐࠍ␜ߔ㧚ߎࠇࠄߪోߡ 500Hz
ߩࠨࡦࡊ࡝ࡦࠣ๟ᵄᢙߢ෼㍳ߒߚ㧚߹ߚ㧘ஜో⹜㛎૕߅ࠃ߮ᷫ⡺⹜㛎૕ߢߪ㧘ߎߩઁߦ⹜㛎ߩ೨ᓟߦ߅޿ߡࠛ࡞ࡏ
ㇱಽߩ㈩▤ᄖᓘࠍ᷹ቯߒߚ㧚⸘᷹
‫ޓ‬ታ㛎ߢߪએਅߩ㗄⋡ࠍ⸘᷹ߒߚ㧚(1) ᝄേบടㅦᐲ
(2) ⹜㛎૕߅ࠃ߮ࠕࡦࠞ࡯ߩᔕ╵ടㅦᐲ(3) ࠛ࡞ࡏ 1 ߣࠛ࡞ࡏ 2 ߩ㕙ౝ㐿㐽ᄌ૏− 1155 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

Y
S098

Z

X

S097

(Top)
S121

(Top)
S101

(Top)
S091

S092

S108

S093

Ԡ

S096

S102

S107

S094

S106

S095

#:

S124

#; A04

S103

ԡ

S122

S123

#<

S104

ԣ

S105

D00 &:

500

A00 #:

#:

50

100

#; A07

S014

S088
S012

Ԙ

510

(Top)
S081

(Top)
S011

S087

&

50

D02
(Top)
S111

S082
S083

ԟ

S086

S013

50

#<

S114

S112

Ԣ

S084
S085

#:

S113

(Top)
S071

#; A06

100

S074

50

#<

Ԟ

S072

S073

#:

#:
A01 #;#; A03



#:

#<

#<

#;

(Top)
S021

#<
#:

S024

S022

ԙ

: Accelerometer#:

A02 # ;

& : Displacement

#<

#<

S023

% : Crip gauge (for 3D_D01 & 3D_D02)# ; A05: Strain gauge (Axial)

&:
&;

D03
(from outside of the shaking table)&<

Z: Strain gauge (Hoop): Strain gauge (45deg between axial and hoop): Pressure

X

Anchor A-02

50
S064

ԝ

S062

S063

ᱡࠥ࡯ࠫߪࠕࡦࠞὐ #㨪# ߦะ߆ߞߡ
ᤨ⸘๟ࠅ‫ޕ‬┙ߜ਄߇ࠅ㈩▤ߪ㨆ᣇะߦะ߆ߞߡ‫ޔ‬㨅ࠍၮḰߦᤨ⸘๟ࠅߣߔࠆ‫ޕ‬

S051
C01

S052

S058

S053

%

S057
S056

For 3D_D01 & 3D_D02

D01

P01

Ԝ
S054
S055

50

&

Anchor A-01

510

Y

S061

50
(Top)
S031
S038
S037

500
S032

Ԛ

S036

S033
S034

S041
S048
S047

S042

ԛ

S046

S043
S044

S045

S035

࿑  ┙૕㈩▤♽⹜㛎૕‫⸘ޓ‬᷹ὐ
Fig.2.2-8 Measurement points of the 3-D piping model.

− 1166 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ታ㛎⚿ᨐⷐ⚛⹜㛎  ࿑  ೋᦼ SCC ߈ⵚ߆ࠄߩ⽾ㅢ㧔SC01㧕
Fig. 3.1.1-1 Crack penetration from initial SCC (SC01).
Test specimen
SCC induced area

8.6

13.5

Thicker wall pipe

Broken position ofBroken position of
SC02 & SC04 Broken position of
SC01, SC03,SC07 & SC08
SC05 & SC06
(Broken from initial SCC)࿑  ฦ SCC ⹜㛎૕ߩ߈ⵚ⽾ㅢ૏⟎
Fig. 3.1.1-2 Broken positions of SCC specimens.

࿑  ో๟⎕ᢿߩ⁁ᴫ        㧔EM02㧘ో๟ EDM ߈ⵚઃ߈⹜㛎૕㧕
Fig. 3.1.1-3 Full circumferential break(EM02, with full circumferential initial EDM notch).
50

Bending moment [kN-m]

߈ⵚઃ߈㈩▤⎕៊⁁ᴫⷐ⚛⹜㛎ߩ߁ߜ߈ⵚઃ߈㈩▤ߩ⹜㛎⚿ᨐࠍ⴫ߦ
ߣࠅ߹ߣ߼ߡ␜ߔ㧚⹜㛎૕ߩ߁ߜᱜᒏᵄߦࠃࠅタ⩄ߒߚ߽ߩߦߟ޿ߡߪ㧘߈ⵚ⽾ㅢ߹ߢߦⷐߒߚᱜᒏᵄቯᏱㇱಽߩᵄᢙࠍ⴫ਛߦ૬⸥ߒߚ㧚ഠൻᒻ⁁ߏߣߩ⎕៊⁁ᴫߪએਅߩࠃ߁ߦߥߞߚ㧚(1)‫ޓ‬SCC ⹜㛎૕8 ૕ታᣉߒߚ SCC ⹜㛎૕ߩ߁ߜ㧘4 ૕ߢ➅ࠅ㄰ߒタ⩄ߦ઻޿ዉ౉ߒߚೋᦼ SCC ߆ࠄ∋ഭ߈ⵚ߇ㅴ
ዷߒ㧘⽾ㅢߒߚ㧚߈ⵚ⽾ㅢㇱಽߦሽ࿷ߒߚೋᦼ
SCCᒻ⁁ߪ࿑ߦ␜ߒߚߣ߅ࠅߢ޽ࠆ㧚߈ⵚ⽾ㅢᓟߩᓟ⛯ࠨࠗࠢ࡞ߦࠃࠆ๟ᣇะ߳ߩᕆㅦવ
᠞ߪ↢ߓߥ߆ߞߚ㧚࿑  ߦ⹜㛎૕ SC01 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚ೋᦼ SCC ߆ࠄ߈ⵚ߇⽾ㅢߒߥ
߆ߞߚ4૕ߪ㧘⹜㛎㈩▤ࠍ⵬ᒝ▤ߣធวߔࠆߚ߼
ߦടᎿߒߚṁធㇱಽ߿࠹࡯ࡄ㐿ᆎㇱߢ߈ⵚ߇⽾ㅢߒߚ㧚࿑ߦSCC⹜㛎૕ߩ⎕៊૏⟎ࠍ␜ߔ㧚(2)‫ోޓ‬๟ 50% ᷓߐߩ EDM ߈ⵚઃ߈⹜㛎૕㧔EM01 㨪 EM04㧕
ోߡߩ⹜㛎૕ߦ߅޿ߡ㧘ᦨᄢᦛߍࡕ࡯ࡔࡦ࠻߇
૞↪ߔࠆᣇะߢ➅ࠅ㄰ߒタ⩄ߦ઻޿߈ⵚ߇⡺ෘᣇะߦㅴዷߒ㧘⽾ㅢߒߚ㧚⽾ㅢߒߚ߈ⵚߪᓟ⛯ߩᢙࠨࠗࠢ࡞ߦࠃࠅ๟ᣇะߦㅴዷߒ㧘ో๟⎕ᢿࠍ⿠ߎߒߚ㧚࿑ߦEM02ߩ⎕៊⁁ᴫࠍ␜ߔ㧚ታ㛎ߢߪᱜᒏᵄߣ࡜ࡦ࠳ࡓᝄ᏷ᵄࠍ↪޿ߡタ⩄ߒߚ߇㧘౉ജᵄᒻߦࠃࠆ⎕៊ᒻᘒߩ㆑޿ߪ⷗ࠄ
ࠇߥ߆ߞߚ㧚
(3)‫ޓ‬ౝⷺ 90q50% ᷓߐߩ EDM ߈ⵚઃ߈⹜㛎૕㧔EM05㧘EM09㧕
➅ࠅ㄰ߒタ⩄ߦ઻޿ೋᦼEDM߈ⵚㇱಽ߆ࠄ߈ⵚ
߇ㅴዷߒ㧘⽾ㅢߒߚ㧚߈ⵚߪ⽾ㅢߩߺߢᓟ⛯ࠨࠗࠢ࡞ߦࠃࠆ๟ᣇะ߳ߩᕆㅦવ᠞ߪ↢ߓߥ߆ߞߚ㧚(4)‫ޓ‬SCC ࠍᮨᡆߒߚ EDM ߈ⵚઃ߈⹜㛎૕㧔EM06 㨪 EM08㧕
ోߡߩ⹜㛎૕ߢዉ౉ߒߚEDM߈ⵚㇱಽ߆ࠄ߈ⵚ
߇ㅴዷߒ㧘⽾ㅢߒߚ㧚SCC ⹜㛎૕ߣห᭽㧘⎕៊ᒻᘒߪ߈ⵚߩ⽾ㅢ߅ࠃ߮ṳᵨߢ㧘ᓟ⛯ࠨࠗࠢ࡞ߦ
ࠃࠆ๟ᣇะ߳ߩ߈ⵚߩᕆㅦવ᠞ߪ↢ߓߥ߆ߞߚ㧚એ਄߆ࠄ㧘ᧄታ㛎ߢ⏕⹺ߐࠇߚ߈ⵚઃ߈㈩▤ߩ⎕៊ᒻᘒߪ㧘ㇱಽ߈ⵚઃ߈㈩▤ߢߪ߈ⵚߩ⽾ㅢ㧘ో๟߈ⵚઃ߈㈩▤ߢߪో๟⎕ᢿߣߥߞߚ㧚

40
30

EM 02
EM 03
EM 04
EM 05
EM 06
EM 07
EM 08
EM 09

20
10
0

߈ⵚઃ߈㈩▤ߩ⩄㊀ᄌᒻ․ᕈ
࿑ߦEDM⹜㛎૕ߩᦨᄢ౉ജᄌᒻⷺߣᦛߍࡕ࡯
ࡔࡦ࠻ߣߩ㑐ଥࠍ␜ߔ㧚ߚߛߒ㧘EM01 ߪ౉ജ࡟ࡌ࡞ࠍㅜ
ਛߢᄌᦝߒߡ޿ࠆߩߢ㧘એਅߩᬌ⸛ߢߪኻ⽎ᄖߣߒߚ㧚࿑ߢߪ㧘⹜㛎૕ߩᄌᒻߪోߡ߈ⵚㇱಽߢ⿠߈ߡ޿ࠆߣߒߡ౉
− 1177 −

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Rotation angle [rad]࿑  EDM ⹜㛎૕ߦ߅ߌࠆᦨᄢ౉ജᄌᒻⷺߣ
ᦨᄢᦛߍࡕ࡯ࡔࡦ࠻ߩ㑐ଥ
Fig. 3.1.1-4 Relation between max. input rotation angle andmax. bending moment of EDM specimen.

49

49

49

49

EM01

EM02

EM03

EM04

18
18 −

49

48

51

48

EM06

EM07

EM08

EM09

50

49

SC08

8

50

SC07

EDM

49

SC06

−

EM05

48

8

49

SC04

SCC

49

SC03

SC05

49

Hoop stressby P ( V H )
[MPa]

SC02

Internalpressure (P)
[MPa]

49

Type ofdefect

SC01

Name

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

0.16

V H /S y

Sinusoidal

Sinusoidal

Sinusoidal

Sinusoidal

RandomSinusoidal

RandomSinusoidal

RandomSinusoidal

35

50

50

50

35

21

25

25

15
30

50

0.09

0.13

0.13

0.13

0.09

0.05

0.06

0.06

0.04
0.08

0.13

Input condition
Max. amp. of input
Pattern of input
disp. wave
[mm]
[rad]

92

5
(127 cycles)
5(117 cycles)
35
2
1(16 cycles)94

2(32 cycles)3(55 cycles)
4(108 cycles)1(19 cycles)

77

90

108

79

66

1
(18 cycles)
4

69

10

67

71

93

114

104

4

6

92

95

5
(128 cycles)
6

83

96

5
(108 cycles)
21

Max. reaction
force [kN]

No. ofloading⴫  ⷐ⚛⹜㛎‫ⵚ߈ޓ‬ઃ߈㈩▤⹜㛎૕⹜㛎⚿ᨐ
Table 3.1.1-1 Test results of pipe element tests using cracked specimens

Crack penetration at
EDM notch
Crack penetration at
EDM notch
Crack penetration at
EDM notch
Crack penetration at
EDM notch
Crack penetration at
EDM notch

Full circumferential break

Full circumferential break

Full circumferential break

Full circumferential break

Crack penetration at SCC

Crack penetration at SCC

Crack penetration at the
tapering section
Crack penetrationnear the weld
Crack penetrationnear the weld

Crack penetration at SCC

Crack penetration at the
tapering section

Crack penetration at SCC

Test results㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ജᄌ૏ࠍ࿁ォⷺߦ㧘4ὐᦛߍ⹜㛎ⵝ⟎ߩᐞ૗ቇ⊛ᒻ⁁߆ࠄ෻ജࠍᦛߍࡕ࡯ࡔࡦ࠻ߦ឵▚ߒߡ␜ߒߚ㧚ߎߎߢ㧘౉ജᄌ૏ࠍ δ㧘4 ὐᦛߍ⹜㛎ⵝ⟎ߩᡰὐ㑆〒㔌ࠍ l㧘࿁ォⷺࠍ φ㧘ࡠ࡯࠼࠮࡞⸘᷹୯ࠍP㧘⹜㛎૕ߦ૞↪ߔࠆᦛߍࡕ࡯ࡔࡦ࠻
ࠍ M ߣߔࠆߣ㧘φ㧘M㧘ߪߘࠇߙࠇએਅߩᑼߢ⴫ߐࠇࠆ㧚2δl(3.1.1)

P⋅lM=
2(3.1.2)φ=ߚߩߦኻߒ㧘EM08 ߢߪ߶߷ห⒟ᐲߣߥߞߚ㧚⃻ᤨὐߢߪߎߩ㆑޿߇↢ߓߚℂ↱ߪ᣿⏕ߢߪߥ޿߇㧘࿶❗タ⩄ᤨߦ߅ߌࠆ߈ⵚ㕙ߩធ⸅ߦ઻߁࿶❗߭ߕߺߩ಴ᣇߩ㆑޿߿㧘ೋᦼ SCC ߩ┙૕⊛ᒻ⁁ߥߤ㧘߈ⵚᒻ⁁ࠍᮨᡆߔࠆ㓙ߦ⠨ᘦߒߚᛩᓇ߈ⵚ㕙Ⓧએᄖߩⷐ࿃߇߈ⵚㅴዷߦᓇ㗀ࠍਈ߃ߡ޿ࠆน⢻ᕈ߇⠨߃ࠄࠇࠆ㧚⎕㕙⸃ᨆ ⹜㛎૕ߩ෻ജ߆ࠄ⸘▚ߒߚᦛߍࡕ࡯ࡔࡦ࠻ߩᦨᄢ୯ߪ
౉ജߩᄢ߈ߐߦᔕߓߡ⚂ 25kN-m ߆ࠄ 40kN-m ߩ▸࿐ߦಽᏓߒߡ޿ࠆ㧚࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚEM03ߣEM05ߪ㧘ᱜᒏᵄߢタ⩄ߒߚEM02߅ࠃ߮EM09ߣ߶߷ห╬ߩ෻ജߣߥࠅ㧘౉ജᵄᒻߦࠃࠆ෻ജߩ㆑޿ߪ޽ࠄࠊࠇߥ߆ߞߚ㧚࿑ߦ㧘ᱜᒏᵄタ⩄ࠍⴕߞߚEM02㧘EM06㧘EM09
ߦߟ޿ߡ㧘ᱜᒏᵄߩẋჇㇱಽߢߩ࿁ォⷺߣ⹜㛎૕෻ജߣߩ㑐ଥࠍ␜ߔ㧚EM02 ߪో๟߈ⵚࠍ㧘EM06 ߪ SCC ࠍᮨᡆߒߚ EDM ߈ⵚࠍ㧘EM09 ߪౝⷺ 90qߩ⍱ᒻ߈ⵚࠍടᎿߒ
ߡ޽ࠆ߇㧘࿑  ߆ࠄ㧘ߎࠇࠄߩ߈ⵚߩᄢ߈ߐߪ⹜㛎૕ߩ෻ജߦ߶ߣࠎߤᓇ㗀ࠍਈ߃ߡ޿ߥ޿ߣ⸒߃ࠆ㧚5%% ߈ⵚߣ '&/ ߈ⵚߩ⎕៊ኼ๮Ყセ
EDM ⹜㛎૕ EM06㧘EM07㧘EM08 ߪ㧘ߘࠇߙࠇ SCC ⹜㛎૕SC01㧘SC03㧘SC07ߩೋᦼSCCᒻ⁁ࠍ╬ଔߥ߈ⵚᷓߐ
ߣ㕙Ⓧࠍᜬߟඨᬦ౞ᒻ⁁ߢᮨᡆߒߚEDM߈ⵚࠍઃਈߒߚ
⹜㛎૕ߢ޽ࠆ㧚ߎࠇࠄߩ⹜㛎૕ߢߪ㧘⥄ὼ߈ⵚߣੱᎿᰳ㒱ߩ⎕៊ኼ๮ߩᲧセࠍⴕ߁ߚ߼ߦ㧘ౝ࿶㧘⹜㛎૕ߩ᧚⾰㧘౉ജᄌ૏㧘౉ജᵄᒻߩ᧦ઙࠍห৻ߦߒߡタ⩄⹜㛎ࠍⴕߞߚ㧚ߘߩ⚿ᨐ㧘߈ⵚ⽾ㅢߦⷐߒߚᱜᒏᵄߩቯᏱㇱಽߩࠨࠗࠢ
࡞ᢙߪ㧘SC01 ߢ 108 ࠨࠗࠢ࡞㧘SC01 ߩ SCC ࠍᮨᡆߒߚ
EM06 ߢ 32 ࠨࠗࠢ࡞ߢ޽ߞߚ㧚ห᭽ߦ㧘SC03 ߢ 128 ࠨࠗࠢ࡞㧘EM07 ߢ 55 ࠨࠗࠢ࡞㧘SC07 ߢ 117 ࠨࠗࠢ࡞㧘EM08
ߢ108ࠨࠗࠢ࡞ߣߥߞߚ㧚EM06ߣEM07ߢߪᮨᡆߒߚSCC
ߦኻߒߡ߈ⵚ⽾ㅢ߹ߢߦ2㨪3୚ߩ➅ࠅ㄰ߒᢙ߇ᔅⷐߛߞ

EDM ⹜㛎૕ߩ߁ߜ㧘ో๟ EDM ߈ⵚઃ߈㈩▤ߢᱜᒏᵄࠍ↪޿ߡタ⩄ߒߚ E M 0 2 㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ
EM03㧘ౝⷺ 90qߩ⍱ᒻ EDM ߈ⵚࠍᜬߜ㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ EM05 ߩ 3 ૕ߦߟ޿ߡ㧘⿛ᩏဳ㔚ሶ㗼ᓸ㏜
㧔SEM㧕ࠍ૶↪ߒߚ⎕㕙ⷰኤࠍⴕߞߚ㧚⎕㕙ߩⷰኤ૏⟎ߪ࿑  ߦ␜ߒߚ૏⟎ߢ޽ࠆ㧚ࡑࠢࡠ⊛ߥ⎕㕙ߪ㧘࿑ߦ␜ߒߚࠃ߁ߦ㧘タ⩄ߦࠃࠅ߈ⵚ߇ㅴዷߒߚㇱಽ㧔એਅㇱಽ A ߣߔࠆ㧕ߣᕆㅦ⎕ᢿㇱಽ㧔એਅㇱಽ B ߣߔࠆ㧕ߦಽ߆ࠇߚ㧚ߎߩ߁ߜ㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ⹜㛎૕ߩㇱಽ A ࠍ SEM ߢⷰኤߔࠆ
ߣ㧘࿑ߦ␜ߔࠃ߁ߦ❋ᮨ᭽߇⹺߼ࠄࠇࠆ㗔ၞ㧔A1㧘ࠬ࠻࡜ࠗࠛ࡯࡚ࠪࡦ㗔ၞ㧕ߣ㧘߶ߣࠎߤ․ᓽߩ⃻ࠇߥ޿㗔ၞ㧔A-2㧘ࠬ࠻࡟࠶࠴࠱࡯ࡦ㗔ၞ㧕ߩ 2 ⒳㘃ߩ⎕㕙߇੤੕ߦ⃻ࠇࠆߎߣ߇⏕⹺ߐࠇߚ㧚࿑  D ߦ␜ߒߚ࡜
ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ႐วߦ߈ⵚㅴዷㇱಽߢ2⒳㘃ߩ⎕㕙߇⃻ࠇࠆߩߪ㧘ᦨᄢᝄ᏷એᄖߩㇱಽߢA-1ߩ⎕㕙߇㧘ᦨᄢᝄ᏷ㇱಽߢA-2ߩ⎕㕙߇ᒻᚑߐࠇࠆߚ߼ߣ⠨߃ࠄࠇࠆ㧚ᓥߞߡ㧘A-1 ߣ A-2 ߩ⎕㕙 1 ⚵߇࡜ࡦ࠳ࡓᝄ᏷ᵄ 1 ᵄߦࠃࠆ߈ⵚㅴዷ㊂ߦ⋧ᒰߔࠆ㧚৻ᣇ㧘ᱜᒏᵄߢタ⩄ߒߚ EM02
ߩ SEM ⷰኤ⚿ᨐߢߪ A-1 ߩࠃ߁ߥ⎕㕙ߪ⹺߼ࠄࠇߕ㧘ోߡㇱಽ A-2 ߣห᭽ߩ⎕㕙ߢ޽ࠅ㧘SEM ⷰኤ⚿ᨐ߆ࠄᔕജ
ࠨࠗࠢ࡞Ფߩ߈ⵚㅴዷ㊂ࠍ․ቯߔࠆߎߣߪߢ߈ߥ߆ߞߚ㧚
90q

Loading
direction

Bending moment [kN-m]

35
30

8.6

25

(a) EM02 & EM03.

114.3

Observation point

4.3(b) EM05.

࿑  ೋᦼ EDM ߈ⵚᒻ⁁ߣ SEM ⷰኤὐ
Fig. 3.1.1-6 Geometry of initial EDM notch and observation point
by SEM.

20
15
10

EM 02

Dimple area

EM 06

5

EM 09
0
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Rotation angle [rad]࿑  ᱜᒏᵄߩᝄ᏷ẋჇㇱߦ߅ߌࠆ౉ജᄌᒻⷺߣ
 ᦛߍࡕ࡯ࡔࡦ࠻ߩ㑐ଥ
Fig. 3.1.1-5 Relation between input rotation angle and bending
moment at amplitude increasing part of Sinusoidal
input wave.

Fatigue crack
propagation
Initial EDM notch࿑  ߈ⵚㅴዷ㕙ߩࡑࠢࡠ᭽⋧㧔EM03㧕
Fig. 3.1.1-7 View of crack surface (EM03).

− 1199 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬⴫ߦታ㛎⚿ᨐߣ㧘╙5┨ߢㅀߴࠆ೎ㅜታᣉߐࠇ
ߚFEMߦࠃࠆ߈ⵚㅴዷ⸃ᨆ⚿ᨐߦࠃࠅᓧࠄࠇߚ߈ⵚ⽾ㅢ߹ߢߩタ⩄࿁ᢙࠍ␜ߔ㧚⸃ᨆߢߪታ㛎⚿ᨐߣᲧセߒߡዋߥ޿➅ࠅ㄰ߒᢙߢ߈ⵚ߇⽾ㅢߔࠆ⚿ᨐ߇ᓧࠄࠇߡ޿ࠆ㧚৻ᣇ㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ 2 ૕ߦߟ޿ߡ㧘SEM ⷰኤߦࠃࠆ߈ⵚㅴዷㇱಽߢ⏕⹺ߐࠇߚ⎕㕙 A-1 ߣ A-2 ߩ⚵ߪ㧘EM03 ߢ 10 ⚵㧘EM05 ߢ 4 ⚵ߣߥߞߚ㧚਄ㅀߩࠃ߁ߦ㧘⎕㕙ߩ➅ࠅ㄰ߒᢙߪ߈ⵚ⽾ㅢߦⷐߒߚ࡜ࡦ࠳ࡓᝄ᏷ᵄߩタ⩄࿁ᢙߦ⋧ᒰߔࠆ㧚ᓥߞߡ㧘ታ㛎ߢ߈ⵚ⽾ㅢ߹ߢߦⷐߒ
ߚ➅ࠅ㄰ߒᢙߩ߁ߜ㧘߈ⵚ⊒↢ߦᶖ⾌ߐࠇߚ࿁ᢙߪήⷞ
ߢ߈ࠆ⒟ᐲߢ޽ࠅ㧘߶ߣࠎߤߪ߈ⵚߩવ᠞ߦ⾌߿ߐࠇߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚ᰴߦ㧘SEM ⷰኤߢ⺒ߺߣߞߚࠬ࠻࡜ࠗࠛ࡯࡚ࠪࡦ㑆㓒
㧔S㧕߅ࠃ߮ࠬ࠻࡟࠶࠴࠱࡯ࡦ᏷㧔SZW㧕ߣ㧘ታ㛎ߢᓧࠄࠇߚᔕജ᜛ᄢଥᢙ▸࿐ࠍኻᔕߐߖ㧘da/dN - ∆K 㑐ଥࠍ᳞߼ߚ㧚ߥ߅㧘EM02 ߦߟ޿ߡߪ SEM ⷰኤߦࠃࠆฦタ⩄ࠨࠗࠢ࡞Ფߩ߈ⵚㅴዷ㊂ߩ․ቯߪߢ߈ߥ߆ߞߚ߇㧘ታ૕㗼ᓸ
㏜౮⌀ࠃࠅ⎕ᢿ೨2ࠨࠗࠢ࡞ಽߩ߈ⵚㅴዷ㊂ࠍ․ቯߢ߈ߚߚ߼㧘ߎߩ2ࠨࠗࠢ࡞ߦߟ޿ߡᔕജᝄ᏷ߣ߈ⵚㅴዷ㊂ࠍኻᔕߐߖߚ㧚ߎߎߢ㧘ࠬ࠻࡜ࠗࠛ࡯࡚ࠪࡦ㗔ၞߢߪ㧘S ߇⪺ߒߊᄌൻߒߡ޿ߥ޿ᢙᵄߩᐔဋ୯ࠍda/dN ߦ૶↪ߒ㧘ࠬ࠻࡟࠶࠴㗔ၞߢߪ SZWࠍ࡜ࡦ࠳ࡓᝄ᏷ᵄߩᦨᄢᝄ᏷ᵄߦ
ࠃࠆ da/dN ߣߒߚ㧚߹ߚ㧘ᔕജ᜛ᄢଥᢙ▸࿐ ∆K ߪਅᑼߢ᳞߼ߚ㧚
(3.1.3)∆K = F (ξ ) ⋅ ∆σ π aߎߎߢ㧘F ξ 㧦K ୯ߩ⵬ᱜଥᢙ‫∆ޓ‬σ㧦૞↪ᔕജᝄ᏷‫ޓ‬‫ޓޓޓޓ‬a㧦߈ⵚ㐳ߐ૞↪ᔕജᝄ᏷∆σߪ㧘ᑼ 3.1.2 ߢᓧࠄࠇࠆ෻ജ߆ࠄ⸘▚ߒߚࡕ࡯ࡔࡦ࠻ࠍᢿ㕙ଥᢙZߢ㒰ߒߡ᳞߼ߚ㧚ߐࠄߦ㧘⎕㕙ⷰኤ૏⟎ߦ߅ߌࠆᔕജ⁁ᘒࠍ㧘ㄭૃ⊛ߦ ஥ߦ߈ⵚߩ
޽ࠆᏪ᧼ߩ৻᭽ᒁᒛ㧛࿶❗ߣߒߡ⠨߃㧘ᔕജᝄ᏷ߣ߈ⵚ
㐳ߐ߆ࠄᓧࠄࠇࠆ∆Kߦኻߒ㧘ᰴᑼߢਈ߃ࠄࠇࠆ⵬ᱜଥᢙ
ࠍਸ਼ߓߡ୯ࠍ⵬ᱜߒߚ㧚F (ξ ) = 1.12 − 0.231ξ + 10.55ξ 2 − 21.72ξ 3 + 30.39ξ 4ߎߎߢ㧘ξ = a/W a㧦߈ⵚ㐳ߐ㧘W㧦᧼ෘⷰኤ⚿ᨐߣ Sasaki ࠄߩ㜞ࠨࠗࠢ࡞∋ഭ⹜㛎⚿ᨐ 5 ࠍ࿑ ߦ␜ߔ㧚࿑ਛ㧘⊕ᛮ߈ߩ⪉ᒻ߇ Sasaki ࠄߦࠃࠆታ
㛎⚿ᨐ㧘Ⴃࠅߟ߱ߒߚὐ߇⎕㕙⸃ᨆ߆ࠄᓧࠄࠇߚ da/dN ∆K㑐ଥߢ޽ࠆ㧚ታ✢ߢ␜ߒߚ⋥✢ߪSasakiࠄߦࠃࠆታ㛎⚿ᨐߩ߈ⵚવ᠞ㅦᐲߩㄭૃᑼߢ޽ࠅ㧘ਅᑼߢ⴫ߐࠇࠆ㧚ߎߎߢ㧘da/dN ߪ mm/cycle㧘∆K ߪ MPa㨯m1/2 ߢ޽ࠆ㧚da= 1.76 ∗ 10 −9 ⋅ ∆K
dN

(3.1.5)࿑ߦ␜ߒߚࠃ߁ߦ㧘ᧄታ㛎ߢ⎕㕙⸃ᨆ߆ࠄᓧࠄ
ࠇߚ߈ⵚવ᠞ㅦᐲߪ㧘ᣢᓔߩ⎇ⓥߢᓧࠄࠇߡ޿ࠆ da/dN ∆K㑐ଥߣ⦟ߊ৻⥌ߒߚ㧚ᧄታ㛎ߢ૶↪ߒߚ࡜ࡦ࠳ࡓᝄ᏷
ᵄߩࠃ߁ߥᄌേᝄ᏷ߩ⩄㊀߇૞↪ߔࠆ႐ว㧘߈ⵚㅴዷߦ

Striation(A-1)

da/dN [m/cycle]

Stretched zone
(A-2)

Striation(A-1)

Stretched zone
(A-2)࿑  ⎕㕙ߩ SEM ⷰኤ⚿ᨐ㧔EM03㧘╙ 2 㨪╙ 3 ࡉࡠ࠶ࠢ㧕
Fig. 3.1.1-8 SEM image of fracture surface(EM03, block No.2-No.3).

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

10

-8

10

-9

Ref.5)
E M 02(S)E M 03(S)E M 05(S)

10

-10

10

-11

1

SZW by test
SUS304(R=-1)
10

100
10 00
1/2
∆ K [M Pa*m ]104࿑  ߈ⵚㅴዷ㊂㧙ᔕജ᜛ᄢଥᢙ▸࿐㑐ଥ
Fig. 3.1.1-9 Relation between crack propagation rate and stressintensity factor range.

⴫  ታ㛎㧘FEM ⸃ᨆ㧘߅ࠃ߮ SEM ⷰኤ߆ࠄᓧࠄࠇߚ߈ⵚ⽾ㅢߦⷐߒߚ౉ജ➅ࠅ㄰ߒᢙ
Table 3.1.1-2 Number of loading blocks obtained from tests, FEM analysis and SEM observation.

Name

Type

EM02
EM03
EM05

EDM

Condition of defectFull angle
Depth *
360q

0.5t

90q

** ‘t’
denotesthethenormal
thickness
normal part‘t’ denotes
pipeatthickness(3.1.4)

Type ofloadingMax. 'V[MPa]

Sinusoidal

707

RandomRandom700
820

Loading times
Test results
FEM **
1
1(16 cycles)(8cycles)102
4
2** Results from FEM analysis in Chapter 5− 2200 −

SEM
-10
4

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ㆃᑧ߿ടㅦ߇⿠߈ࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ߇㧘ᧄታ㛎ߢណ↪ߒߚᵄᒻߪṖࠄ߆ߦᄌൻߒߡ޿ࠆߩߢ㧘ߘߩࠃ߁ߥ㗼⪺ߥ⃻⽎ߪ⹺߼ࠄࠇߥ߆ߞߚ㧚ᷫ⡺㈩▤߅ࠃ߮ஜో㈩▤⎕៊⁁ᴫⷐ⚛⹜㛎ߩ߁ߜᷫ⡺㈩▤߅ࠃ߮ஜో㈩▤ߩ⹜㛎⚿ᨐࠍ⴫ߦߣࠅ߹ߣ߼ߡ␜ߔ㧚⹜㛎૕ߩ߁ߜᱜᒏᵄߦࠃࠅタ⩄ߒߚ߽ߩߦߟ޿ߡߪ㧘⎕៊߹ߢߦⷐߒߚᱜᒏᵄቯ
Ᏹㇱಽߩᵄᢙࠍ⴫ਛߦ૬⸥ߒߚ㧚ᷫ⡺㈩▤ߢߪ㧘ᷫ⡺㊂߅ࠃ߮ౝ࿶୯ߩ㑐ଥߦࠃࠅએਅߩ⎕៊ᒻᘒ߇⏕⹺ߐࠇߚ㧚(1)‫ޓ‬ᷫ⡺㊂ 25% 㨪 60%㧘ౝ࿶ 11MPa
㧔EC01 㨪 EC05㧘EC08㧘EC09㧕ౝ࿶ߦࠃࠅᷫ⡺ㇱಽߦ↢ߓࠆ⤑ᔕജߪ㧘㒠ફᔕജࠍ σy ߣߔࠆߣ 25% ᷫ⡺⹜㛎૕㧔EC08㧕ߢ 0.30

σy㧘50%ᷫ⡺⹜㛎૕㧔EC01㨪EC05㧕ߢ0.45σy㧘60%ᷫ⡺⹜㛎૕㧔EC09㧕ߢ 0.58 σy ߢ޽ߞߚ㧚ߎࠇࠄߩ⹜㛎૕ߪ㧘ోߡᷫ⡺ㇱಽߢ࡜࠴ࠚ࠶࠻ߦࠃࠅ
㈩▤ᄖᓘ߇⤘ࠄߺ㧘ߎߩ࡜࠴ࠚ࠶࠻ᄌᒻㇱಽߢૐࠨࠗࠢ࡞∋ഭ߈ⵚ߇⽾ㅢߒߚ㧚࿑  ߦ
EC05 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚࡜࠴ࠚ࠶࠻ߦࠃࠆ㈩▤ᄖᓘߩჇട₸ߪ 10% 㨪 20% ߣߥߞߚ㧚タ⩄ጁᱧߩ㆑޿ߦࠃࠆ⎕៊ᒻᘒߩ㆑޿ߪ⏕⹺ߐࠇߥ߆ߞ
ߚ㧚ߥ߅㧘EC03 ߪ㧘⹜㛎೨ߩᝄേบ࠙ࠜ࡯ࡒࡦ
ࠣࠕ࠶ࡊᤨߦタ⩄ⵝ⟎ߩਇౕวߩߚ߼ㆊᄢߥᒝ
೙ᄌ૏߇૞↪ߒ⎕៊ߒߚߚ߼࠺࡯࠲߇ᓧࠄࠇߥ
߆ߞߚ㧚
(2)‫ޓ‬ᷫ⡺㊂ 50%㧘ౝ࿶ߥߒ㧔EC06㧕ౝ࿶ߩߥ޿⹜㛎૕ߢߪ㧘タ⩄ߦ઻޿ᷫ⡺ㇱಽ߇㈩▤ౝ㕙ߦ᛬ࠇᦛ߇ࠆዪㇱᐳዮ߇⊒↢ߒߚ㧚ߎߩᐳዮᄌᒻߩ㗂ㇱߢ߈ⵚ߇⊒↢ߒ㧘ᓟ⛯ߩᢙࠨࠗࠢ࡞ߦࠃࠅో๟⎕ᢿߦ⥋ߞߚ㧚ߎߩ⚿ᨐ߆ࠄ㧘ౝ࿶ߩߥ޿ᷫ⡺㈩▤ߩ⎕៊ᒻᘒߪዪㇱᐳዮࠍ઻߁ૐࠨࠗࠢ࡞∋ഭ⎕უߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚࿑ ߦ EC06 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚タ⩄ᣇะߩᄖᓘߪ⚂ 20% ᷫዋߒߡ޿ߚ㧚(3)‫ޓ‬ᷫ⡺㊂ 75%㧘ౝ࿶ 11MPa㧔EC07㧕ౝ࿶ߦࠃࠅᷫ⡺ㇱಽߦ↢ߓࠆ⤑ᔕജߪ㧘0.9 σy ߣߥߞߚ㧚ߎߩ⹜㛎૕ߢߪ㧘➅ࠅ㄰ߒタ⩄ߦ઻޿ᷫ⡺ㇱಽߢ࡜࠴ࠚ࠶࠻ᄌᒻ߇㗼⪺ߦ↢ߓߚ㧚ᦨ⚳⊛ߦᷫ⡺ㇱಽߢ๟ᣇะߦ߈ⵚ߇⽾ㅢߔࠆߣߣ߽ߦ㧘㈩▤๟ᣇะߩ 3ࡩᚲߢゲᣇะ߈ⵚ߇⊒↢ߒߚ㧚࿑  ߦ EC07 ߩ⎕៊ᒻᘒࠍ㧘࿑ ߦゲᣇะ߈ⵚߩ⊒↢૏⟎ࠍ␜ߔ㧚࡜࠴ࠚ࠶࠻ᄌ
ᒻߩߚ߼ߦᄖᓘߪ 30% એ਄Ⴧടߒߚ㧚߹ߚゲᣇะ߈ⵚߩ⊒↢ߒߚㇱಽߩ⡺ෘߪ 1.1mm 㨪 1.6mm
ߦᷫዋߒߡ޿ߚ㧚৻ᣇ100A ߩ㈩▤ߢ 11MPaߩౝ࿶ࠍ଻ᜬߔࠆߩߦᔅⷐߥ⡺ෘߪ 1.46mm ߣߥࠆ㧚ߒߚ߇ߞߡ㧘๟ᣇะ߅ࠃ߮ゲᣇะߦ⊒↢ߒߚ߈ⵚߣゲᣇะ߈ⵚ⊒↢૏⟎ߦ߅ߌࠆ⡺ෘߩᷫዋ߆
ࠄ㧘EC07 ߢߪౝ࿶ߦࠃࠆ⎕ⵚߣૐࠨࠗࠢ࡞∋ഭ

Ratchet deformation

Circumferential crack࿑  ࡜࠴ࠚ࠶࠻ߦࠃࠆᷫ⡺ㇱಽߩᄌᒻ        㧔EC05㧘ౝ࿶޽ࠅ 50% ᷫ⡺⹜㛎૕㧕
Fig. 3.1.2-1 Deformation at thinned wall part caused by ratchet(EC05, 50% thinned wall with internal pressure).

Buckling deformation

Circumferential crack࿑  ᷫ⡺ㇱಽߢߩዪㇱᐳዮᄌᒻ        㧔EC06㧘ౝ࿶ߥߒ 50% ᷫ⡺⹜㛎૕㧕
Fig. 3.1.2-2 Buckling deformation at thinned wall part(EC06, 50% thinned wall without internal pressure).

Circumferential crack

Longitudinal crack࿑  ๟ᣇะ෸߮ゲᣇะ߈ⵚߣ࡜࠴ࠚ࠶࠻ᄌᒻ        㧔EC07㧘ౝ࿶޽ࠅ 75% ᷫ⡺⹜㛎૕㧕
Fig. 3.1.2-3 Circumferential and longitudinal cracks and ratchet
deformation(EC07, 75% thinned wall with internal pressure).
Top

Loading direction

Longitudinal cracks
Bottom࿑  EC07 ߢ⏕⹺ߐࠇߚゲᣇะ߈ⵚߩᢿ㕙਄ߩ⊒↢૏⟎
Fig. 3.1.2-4 Position of the longitudinal cracks that appeared in
EC07.

− 2211 −

−

22
22 −

No defect

EA02

69

68

EA01

11

180

EC09

93

11

EC08

0

286

0

145

EC07

EC06

EC05

140

Wall
thinning

EC04

137

137

Hoop stressby P ( V H )
[MPa]

--

11

Internalpressure(P) [MPa]

EC03

EC02

EC01

Name

Type ofdefect

0.22

0.22

0.58

0.30

0.92

0.00

0.46

0.45

--

0.44

0.44

V H /S y

Sin 5 cycles

Monotonic

Sinusoidal

Sinusoidal

Sinusoidal

Sinusoidal

Sinusoidal

Random--Sinusoidal

0.006 –
0.24

0.35

Up to
140
2.5 - 95

0.06

0.09

0.06

0.09

0.09

0.09

--

0.06

25

35

25

35

35

35

--

25

Input condition
Max. amp. of input
[mm]
[rad]
15
0.04
25
0.06
30
0.08
Random
35
0.09
45
0.11

Pattern of input
disp. wave

1 for each
input

--

86

1
(11 cycles)1(9 cycles)1(9 cycles)
7(164 cycles)1(22 cycles)

135

186

51

80

38

69

64

--

67

78

Max. reaction
force [kN]

5

15
15
5
5
3
3
(73 cycles)--

No. ofloading⴫ 
ⷐ⚛⹜㛎‫ޓ‬ᷫ⡺⹜㛎૕෸߮ஜో⹜㛎૕⹜㛎⚿ᨐ
Table 3.1.2-1 Test results of pipe element tests using thinned wall specimens and nominal wall thickness specimens.

Crack penetration at weld line

Low-cycle fatigue failure withswelling by ratchet
Broken by accident
Low-cycle fatigue failure withswelling by ratchet
Low-cycle fatigue failure withswelling by ratchet
Buckling and low-cycle fatigue
at thinned wall
Mixture of low-cycle fatigue
with ratchet and burst
Low-cycle fatigue failure withswelling by ratchet
Low-cycle fatigue failure withswelling by ratchet
No failure (No crack was foundafter the test)

Low-cycle fatigue failure withswelling by ratchet

Test results㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ᷫ⡺㊂ߣ࡜࠴ࠚ࠶࠻ᄌᒻ㊂ߩ㑐ଥౝ࿶ࠍ⽶⩄ߒߡタ⩄ታ㛎ࠍⴕߞߚ⹜㛎૕ߢߪ㧘➅ࠅ㄰ߒタ⩄ߦ઻޿࡜࠴ࠚ࠶࠻ᄌᒻࠍ↢ߓߚ㧚࡜࠴ࠚ࠶࠻ߦࠃ
ࠆᄖᓘᄌൻ㊂ࠍᛠីߔࠆߚ߼ߦ㧘⹜㛎ߩ೨ᓟߢࡁࠡࠬࠍ
૶↪ߒߡᷫ⡺ㇱಽߩᄖᓘࠍ⸘᷹ߒߚ㧚ߎߎߢ㧘⹜㛎ᓟߩᄖ࿑  140mm ౉ജᤨߩ EA01 ߩᄌᒻ
Fig. 3.1.2-5 Deformation of EA01 at 140 mm input displacement.

Crack࿑  ṁធ✢⣁ߢߩ߈ⵚ⽾ㅢ㧔EA02㧘ஜో⹜㛎૕㧕
Fig. 3.1.2-6 Crack penetration at welding line (EA02, no defect).

ᓘ߆ࠄ⹜㛎೨ߩᄖᓘߩᏅࠍߣࠅ㧘⹜㛎೨ߩᄖᓘߢ㒰ߒߚ୯ࠍᄖᓘᄌൻ₸ߣߔࠆ㧚ᷫ⡺㊂ߣᄖᓘᄌൻ₸ߩ㑐ଥߪ࿑ ߩࠃ߁ߦߥࠆ㧚࿑ਛ㧘Ⴃࠅߟ߱ߒߚࡑ࡯ࠢߪタ⩄ᣇะߩᄖᓘᄌൻ₸ࠍ㧘⊕ᛮ߈ߩࡑ࡯ࠢߪタ⩄ᣇะߣ⋥੤ߔࠆᣇะ㧔એਅ⋥੤ᣇะߣߔࠆ㧕ߩᄖᓘᄌൻ₸ࠍ␜ߔ㧚ߚ
ߛߒ㧘EC01 ߦߟ޿ߡߪ⎕៊೨ߦタ⩄࡟ࡌ࡞ࠍᢙ࿁ᄌᦝߒ
ߡ޿ࠆߚ߼㧘એਅߩᬌ⸛ߢߪኻ⽎ᄖߣߒߚ㧚ߎߩ࿑߆ࠄ㧘➅ࠅ㄰ߒタ⩄ߦ઻޿タ⩄ᣇะ࡮⋥੤ᣇะߣ߽ߦ࡜࠴ࠚ࠶࠻ᄌᒻߩߚ߼ᄖᓘ߇Ⴧടߔࠆ߇㧘ᄖᓘᄌൻ₸ߪ⋥੤ᣇะߦセߴߡタ⩄ᣇะߩᣇ߇ᄢ߈޿ߎߣ߇ࠊ
߆ࠆ㧚࿑ਛߦᦛ✢ߢ␜ߒߚࠃ߁ߦ㧘EC04㧘EC05㧘EC08 ߪ౉ജᄌ૏ 35mm ߢ㧘EC02㧘EC07㧘EC09 ߪ౉ജᄌ૏ 25mm
ߢタ⩄ࠍⴕߞߚ㧚ߎࠇࠄߩ⹜㛎૕ߩᲧセ߆ࠄ㧘ᦨ⚳⊛ߥ࡜࠴ࠚ࠶࠻ᄌᒻ㊂ߪ㧘౉ജ࡟ࡌ࡞߇หߓߢ޽ࠇ߫ᷫ⡺㊂߇ᄙ޿߶ߤᄢ߈ߊߥࠆ௑ะ߇޽ࠆߎߣ߇ࠊ߆ࠆ㧚߹ߚ㧘ᷫ⡺㊂50%ߩ⹜㛎૕ߢ޽ࠆEC02ߣEC05ߩᄖᓘᄌൻ₸߆ࠄ㧘ᷫ
⡺㊂߇หߓ႐ว㧘౉ജ࡟ࡌ࡞߇ᄢ߈޿ߣ࡜࠴ࠚ࠶࠻ᄌᒻ
㊂ߪᄢ߈ߊߥࠆ௑ะ߇޽ࠆߣ޿߃ࠆ㧚৻ᣇ㧘EC04ߣEC05ߪ౉ജᄌ૏㊂߇╬ߒߊ౉ജᵄߩ⒳㘃ߛߌ߇⇣ߥߞߡ޿ࠆ
߇㧘ߎߩ 2 ߟߩ⹜㛎૕߆ࠄ㧘౉ജᵄߩ⒳㘃ߪᦨ⚳⊛ߥ࡜࠴ࠚ࠶࠻ᄌᒻ㊂ߦߪᓇ㗀ߒߥ޿ߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߢタ⩄ߒߚ EC04 ߦߟ޿ߡ㧘౉ജᄌ૏㧘ౝ࿶㧘タ⩄ᣇะߩ๟ᣇะ߭ߕߺߩᤨೞᱧᵄᒻࠍ࿑       ߦ␜ߔ㧚๟ᣇะ߭ߕߺߩᤨೞᱧᵄᒻ߆ࠄ㧘࡜࠴ࠚ࠶࠻ᄌᒻߦ㑐ଥߔࠆ๟ᣇะ߭ߕߺߩ᳗ਭჇടߪ㧘ਥߦ౉ജᄌ૏ᵄᒻߩᦨᄢᝄ᏷ㄭறߢ⊒↢ߒ㧘ߘߩઁߩ౉ജ
ࠨࠗࠢ࡞ߦࠃࠆ߭ߕߺߪ㧘߭ߕߺᝄ᏷ߣߒߡᓇ㗀ߔࠆ߇࡜࠴ࠚ࠶࠻߭ߕߺߩჇടߣߒߡߪ߶ߣࠎߤነਈߒߡ޿ߥ
޿ߎߣ߇ࠊ߆ࠆ㧚߹ߚ㧘࡜࠴ࠚ࠶࠻ᄌᒻ߇⊒↢ߔࠆߣᄖᓘ
߇Ⴧടߔࠆᓇ㗀ߢ㧘ᄌᒻߩ⊒↢ߒߚᤨὐ߆ࠄ⧯ᐓߩౝ࿶
ૐਅ߇⿠߈ࠆߎߣ߇ࠊ߆ࠆ㧚

Input disp. [mm]⎕უ߇ᷙ࿷ߔࠆ⎕៊ᒻᘒߣߥߞߚߣ⠨߃ࠄࠇࠆ㧚એ਄߆ࠄ㧘ᧄታ㛎ߢ⏕⹺ߐࠇߚᷫ⡺㈩▤ߩ⎕៊ᒻᘒߪ㧘࡜࠴ࠚ࠶࠻ࠍ઻߁ૐࠨࠗࠢ࡞∋ഭ⎕უ㧘ᐳዮ㧘ૐࠨࠗࠢ࡞
∋ഭ⎕უߣ⎕ⵚߣߩᷙ࿷ߩ 3 ⒳㘃ߣߥߞߚ㧚ஜో㈩▤ߦߟ޿ߡߪ㧘න⺞タ⩄ߩ߽ߩߪⵝ⟎ߩᦨᄢ⸵ኈ౉ജᄌ૏ߢ޽ࠆ140mm߹ߢᄌ૏ࠍჇടߐߖߚ߇⎕៊ߪ↢ߓߥ߆ߞߚߚ߼㧘⎕៊ߐߖߕߦ⹜㛎ࠍ⚳ੌߒߚ㧚➅ࠅ㄰ߒタ⩄ߩ߽ߩߪ౉ജᄌ૏r95mmߢ⹜㛎㈩▤ߣ⵬ᒝ㈩▤ࠍធวߒߚṁធㇱಽߢ߈ⵚ߇⽾ㅢߒߚ㧚࿑ߦන⺞タ⩄ࠍⴕߞߚEA01ߩ140mm౉ജᤨߩᄌᒻ⁁ᘒࠍ㧘࿑ ߦ➅ࠅ㄰ߒタ⩄ࠍⴕߞߚ EA02 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚

40
20
0
-20
-40

0

Time[s] 30

45

60

45

60

45

60

(a) Input displacement.
Pressure [M Pa]

40
EC 02
EC 04

35

Input 25mm

EC 05
EC 07

30
25

11
10.8
10.6
10.4

0

15

EC 08
EC 09
EA02

20
15

T ime[s] 30(b) Internal pressure.

Input 35mm
Strain [micro]

Deformation of diameter [%]

15

10
5

80 00
60 00
40 00
20 00
0

0

15

T ime[s] 30(c) Hoop strain at S043H.

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

W all thinning ratio࿑  ᷫ⡺㊂ߣᄖᓘᄌൻ₸ߩ㑐ଥ
Fig. 3.1.2-7 Relation between wall thinning ratio and deformationof diameter.

࿑  ๟߭ߕߺߩ࡜࠴ࠚ࠶࠻᜼േ
㧔EC04㧘2 ࿁⋡ߩタ⩄㧕
Fig. 3.1.2-8 Ratcheting behavior of hoop strain(EC04, 2nd time loading)− 2233 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᷫ⡺㊂ߣ⹜㛎૕෻ജߩ㑐ଥ㈩▤ߦᷫ⡺߇ሽ࿷ߔࠆߣ㧘⹜㛎૕ߩ෻ജ߇ૐਅߔࠆߎ
ߣ߇⠨߃ࠄࠇࠆ㧚޽ࠆᷫ⡺㈩▤ߩタ⩄⹜㛎ߢᓧࠄࠇߚ෻
ജߦኻߒ㧘หߓ౉ജᄌ૏ߩタ⩄ߢᓧࠄࠇߚஜో⹜㛎૕
㧔EA02㧕ߩ෻ജ୯ࠍ෻ജߩၮḰ୯ߣߔࠆ㧚ᷫ⡺⹜㛎૕߆ࠄᓧࠄࠇߚ෻ജ୯ߩၮḰ୯ߦኻߔࠆഀวߣᷫ⡺㊂ߩ㑐ଥߪ࿑  ߩࠃ߁ߦߥࠆ㧚EC05 ߪ଀ᄖߣߥࠆ߇㧘ߘߩઁߩ⹜㛎૕ߢߪ߶߷ᷫ⡺㊂ߦᔕߓߡ෻ജ߇ૐਅߔࠆ௑ะ߇
⃻ࠇߡ޿ࠆ㧚ߎߎߢ㧘࿑ਛߦ␜ߒߚᦛ✢ߪ㧘⹜㛎㈩▤ㇱಽ㧔sch80 ߩ㈩▤ࠍ૶↪ߒߡ޿ࠆㇱಽ㧕߇ోߡᷫ⡺ߒߡ޿ࠆߣߒߡᒢᕈ⸘▚ࠍⴕߞߚ႐วߩ㧘ᷫ⡺㊂ߦᔕߓߡૐਅߔ
ࠆ෻ജ࡟ࡌ࡞ࠍ␜ߒߡ޿ࠆ㧚ߎߩᦛ✢ߪᷫ⡺▸࿐ࠍᐢߊขߞߡ޿ࠆߩߢෳ⠨Ყセߣߥࠆ߇㧘ᷫ⡺㊂߇ᄙߊߥࠆߣ
ᒢᕈ⸘▚߆ࠄ੍ᗐߐࠇࠆ෻ജ࡟ࡌ࡞ࠃࠅ߽ૐਅߩᐲว޿
߇⪺ߒߊߥࠆ㧚ߎࠇߪ㧘タ⩄⹜㛎ߢߪోߡߩ⹜㛎૕ߢᷫ⡺ㇱಽ߇႟ᕈၞߦ౉ࠆᔕജ࡟ࡌ࡞ߢ޽ࠅ㧘႟ᕈൻߦ઻޿ዪ

Ratio of reaction force decreasing

1.2
1
0.8
E C02
E C04
E C05
E C06
E C07
E C08
E C09

0.6
0.4
0.2

ᚲ⊛ߥᷫ⡺ㇱಽߦᄌᒻ߇㓸ਛߒ㧘ᦼᓙߐࠇࠆ෻ജ߇ᓧࠄ
ࠇߥ޿ߚ߼ߣ⠨߃ࠄࠇࠆ㧚ஜో⹜㛎૕ߩ⩄㊀ᄌᒻ․ᕈ
ஜో⹜㛎૕ߢߪ㧘න⺞ߦ౉ജࠍჇടߐߖࠆන⺞タ⩄ߣ㧘౉ജᄌ૏ࠍᲑ㓏⊛ߦჇടߐߖߥ߇ࠄᱜᒏ5ᵄࠍ૶↪ߒߡタ⩄ߔࠆ➅ࠅ㄰ߒタ⩄ࠍⴕߞߚ㧚න⺞タ⩄ࠍⴕߞߚ⹜㛎૕
㧔EA01㧕ߦߟ޿ߡ㧘ᄌᒻⷺߣᦛߍࡕ࡯ࡔࡦ࠻ߩ㑐ଥࠍ࿑ ߦ␜ߔ㧚⹜㛎ߢߪ 5mm ߕߟ㗅ᰴ౉ജᄌ૏ࠍჇട
ߐߖߚ߇㧘࿑  ߢߪᦨᄢ౉ജᄌ૏߹ߢߩᄌᒻⷺߣ
ᦛߍࡕ࡯ࡔࡦ࠻ࠍ⚥Ⓧߒߡ␜ߒߚ㧚߹ߚ㧘࿑  ߦන⺞タ⩄ߩᄌᒻⷺ㧙ᦛߍࡕ࡯ࡔࡦ࠻㑐ଥߣ➅ࠅ㄰ߒタ⩄ࠍⴕߞߚ⹜㛎૕㧔EA02㧕ߩᄌᒻⷺ㧙ᦛߍࡕ࡯ࡔࡦ࠻㑐ଥ
ࠍ㊀ߨߚ߽ߩࠍ␜ߔ㧚࿑  ߆ࠄ㧘ஜో㈩▤ߪᄌᒻⷺ⚂ 0.0375[rad]㧔౉ജᄌ૏ 15mm㧕⒟ᐲߢ႟ᕈၞߦ౉ࠆߎ
ߣ߇ࠊ߆ࠆ㧚႟ᕈၞߦ౉ࠆߣ㧘න⺞タ⩄ߩ⩄㊀ᄌᒻᦛ✢ߢߪ౉ജᄌ૏㊂߇Ⴧടߒߡ߽෻ജ߇߶ߣࠎߤჇടߒߥ޿㧘㒠ફ᫜ߩࠃ߁ߥ⁁ᘒࠍ⚻ߡ߆ࠄౣ߮౉ജᄌ૏㊂ߩჇടߦ઻޿෻ജ߇Ⴧടߔࠆࠃ߁ߦߥࠆ߇㧘➅ࠅ㄰ߒタ⩄ߢᓧࠄࠇߚ⩄㊀ᄌᒻᦛ✢ߢߪ㧘㒠ફ᫜ߩࠃ߁ߥ⁁ᘒߪ⃻ࠇߕ㧘ᦨᄢ෻ജߪ౉ജᄌ૏㊂ߩჇടߦ઻޿Ⴧടߒߡ޿ࠆ㧚ߎߩࠃ߁ߥ⃻⽎ߩߚ߼㧘ᒢᕈၞߢߪ➅ࠅ㄰ߒタ⩄ߩጁᱧᦛ✢ߪන⺞タ⩄ߢᓧࠄࠇߚ⩄㊀ᄌᒻᦛ✢ߣ߶߷৻⥌ߔࠆ߇㧘႟ᕈၞߦ౉ࠆߣ➅ࠅ㄰ߒタ⩄ߩ෻ജߪห৻౉ജᄌ૏ߩන⺞タ⩄ߢᓧࠄࠇߚ෻ജߦኻߒ 10% 㨪 20% 㜞޿୯ࠍ␜ߒߚ㧚

0
0

0.2

0.4

0.6

0.8

1

W all thinning ratio࿑  ᷫ⡺㊂ߣ෻ജૐਅ₸ߩ㑐ଥ
Fig. 3.1.2-9 Relation between wall thinning ratio and decreased
reaction force ratio.
80

80
60

Elastic

60
50

Bending moment [kN-m]

Bending moment [kN-m]

70

25mm
35mm

40
30
20

40

15mm
25mm
35mm
45mm
55mm

20
0

65mm

-20

75mm
85mm

-40

95mm
-60

10
0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-80
-0.4

0.4

࿑  ࿁ォⷺ㧙ᦛߍࡕ࡯ࡔࡦ࠻㑐ଥ㧔EA01㧕
Fig. 3.1.2-10 Relation between rotation angle and bending
moment of EA01.

-0.2

0

0.2

0.4

Rotation A ngle [rad]Rotation Angle [rad]࿑  EA01 ߣ EA02 ߩ࿁ォⷺ㧙ᦛߍࡕ࡯ࡔࡦ࠻㑐ଥ
Fig. 3.1.2-11 Relation between rotation angle and bending moment
of EA01 & EA02.

− 2244 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆

㈩▤♽⹜㛎ᐔ㕙㈩▤♽⹜㛎⎕៊⁁ᴫᐔ㕙㈩▤♽⹜㛎ߩ⹜㛎⚿ᨐࠍ⴫ߦ␜ߔ㧚ฦ⹜㛎૕ߩ⎕៊⁁ᴫߪએਅߩࠃ߁ߦߥߞߚ㧚(1)‫ޓ‬ஜో⹜㛎૕‫ ޓ‬2D_A01
ࠬࠗ࡯ࡊടᝄߢᓧࠄࠇߚ࿕᦭ᝄേᢙߪ3.35 Hzߢ޽ߞߚ㧚߹ߚ㧘ࠬࠗ࡯ࡊടᝄߢᓧࠄࠇߚવ㆐㑐ᢙࠃࠅ᳞߼ߚᷫ⴮Ყߪ0.44%ߢ޽ߞߚ㧚ᒢᕈၞ࡟ࡌ
࡞ߢߩ⹜㛎૕ߩᔕ╵․ᕈࠍᓧߚᓟ㧘႟ᕈၞ࡟ࡌ
࡞ߩടᝄߣߒߡ౉ജ࡟ࡌ࡞400㧘700㧘1300 Galߩടᝄࠍߘࠇߙࠇ5࿁ታᣉߒߚ㧚ߎࠇࠄߩടᝄ⹜㛎ߦ߅޿ߡ㧘⎕៊ߪⷰኤߐࠇߥ߆ߞߚ㧚߹ߚ㧘ടᝄ⹜㛎ᓟ㧘⹜㛎૕ߦ߅ߌࠆ3▎ᚲߩࠛ࡞ࡏࠍಾࠅ಴
ߒ㧘ߘߩౝ㕙ߩᶐㅘត்ᬌᩏࠍታᣉߒߚ⚿ᨐ㧘߈ⵚߩ⊒↢ߪ⹺߼ࠄࠇߥ߆ߞߚ㧚(2)‫▤⋥ޓ‬ㇱᷫ⡺⹜㛎૕‫ ޓ‬2D_B01
ࠬࠗ࡯ࡊടᝄߢᓧࠄࠇߚ࿕᦭ᝄേᢙ෸߮ᷫ⴮Ყ
ߪ㧘ߘࠇߙࠇ 3.28 Hz㧘0.42% ߢ޽ߞߚ㧚ᒢᕈၞ࡟ࡌ࡞ߢߩ⹜㛎૕ߩᔕ╵․ᕈࠍᓧߚᓟ㧘႟ᕈၞ࡟ࡌ࡞ߩടᝄࠍታᣉߒߚ㧚౉ജ࡟ࡌ࡞ 400㧘1200
Gal ߩടᝄࠍߘࠇߙࠇ 5 ࿁ታᣉߒߚᓟ㧘1600 Gal
ߢߩടᝄࠍ⎕៊߹ߢ➅ࠅ㄰ߒߚ㧚౉ജ࡟ࡌ࡞
1600 Gal ߩ 22 ࿁⋡ߩടᝄߦ߅޿ߡ㧘⹜㛎૕ࠕࡦࠞㇱ㧔100A㧘Sch120 ㈩▤஥ߩࠕࡦࠞㇱ㧕ㄭறߦ߅޿ߡ㧘๟ᣇะ߈ⵚ߇⊒↢ߒ㧘⎕ᢿኸ೨ߩ⁁ᘒߣߥߞߡ޿ࠆߎߣ߇⏕⹺ߐࠇߚ㧚ߎߩ⎕៊ߪ㧘ࠕࡦࠞㇱㄭறߩ㈩▤஥ㇱ㧔⹜㛎૕ᝄേᔕ╵ߢߩᦛߍࡕ࡯ࡔࡦ࠻ߦࠃࠅᔕജ߇ᄢ߈ߊߥࠆ᳓ᐔᣇะߩ
஥ㇱ㧕ߩ࿶ജ࠮ࡦࠨ⸳⟎↪บᐳߩ㓈⡺ṁធㇱࠃࠅ߈ⵚ߇⊒↢ߒ㧘๟ᣇะߦ߈ⵚ߇ㅴዷߒߚ߽ߩ
ߣ್ᢿߐࠇࠆ㧚࿑  ߦ⎕៊⁁ᴫࠍ␜ߔ㧚⎕៊ㇱㄭறߩ߭ߕߺ⸘᷹࠺࡯࠲ࠍ⏕⹺ߒߚߣߎࠈ㧘౉ജ࡟ࡌ࡞1600 Galߢߩടᝄ3࿁⋡ࠃࠅ಴ജߦ⇣Ᏹࠍ↢ߓߡ޿ߚ㧚ᓥߞߡ㧘ߎߩ⎕៊ߪ౉ജ࡟ࡌ࡞
1600 Gal ߩടᝄ3 ࿁⋡ࠃࠅ⊒↢ߒߡ߅ࠅ㧘ടᝄߩ➅㄰ߒߦࠃࠅ߈ⵚ߇ㅴዷߒ㧘22 ࿁⋡ߩടᝄߢ⎕ᢿߦㄭ޿⁁ᘒߦ⥋ߞߚߣផቯߐࠇࠆ㧚‫ޓ‬਄⸥ߩࠕࡦࠞㇱㄭறߢߩ⎕៊ߩᓟ㧘⎕៊ㇱࠍಾࠅ಴ߒ㧘ߘߩㇱಽ߳⍴▤ࠍṁធߔࠆߎߣߢ⵬
ୃࠍⴕߞߚ㧚⵬ୃᓟ㧘1600 Galߢߩടᝄࠍౣ㐿ߒߚ⚿ᨐ㧘28 ࿁⋡ߩടᝄߦ߅޿ߡࠛ࡞ࡏ 2 ߩ஥ㇱ㧔ਅ㕙㧕ߢᓸዊߥ߈ⵚߩ⽾ㅢߦࠃࠆ㧘ౝㇱ᳓ߩዋ㊂ߩṳᵨ߇⏕⹺ߐࠇߚ㧚ߐࠄߦടᝄࠍ⛮⛯ߒ㧘29࿁⋡ߩടᝄߦ߅޿ߡห▎ᚲߦ߅޿ߡ᣿ࠄ߆ߥゲᣇะ߈ⵚ߇⊒↢ߒ㧘ౝㇱ᳓ߩྃ಴߇⏕⹺ߐࠇߚ㧚ߎߩ㓙ߩ⎕៊⁁ᴫࠍ࿑  ߦ␜ߔ㧚‫ߦ▤⋥ޓ‬ዉ౉ߒߚ50%ో๟ᷫ⡺ㇱಽߦߟ޿ߡߪ㧘࡜࠴ࠚ࠶࠻ᄌᒻߣߒߡߩ㗼⪺ߥ߰ߊࠄߺ߇⏕⹺ߐࠇߚ߇㧘߈ⵚߩ⊒↢ߪ⏕⹺ߐࠇߥ߆ߞߚ㧚ߥ߅㧘ߎߩ߰ߊࠄߺߪ㧘⹜㛎૕ᝄേᔕ╵ߦࠃࠅ↢ߓ

Crack initiation part࿑  2D_B01 ߦ߅ߌࠆࠕࡦࠞㄭறߢߩ⎕៊
Fig. 3.2.1-1 Unexpected break of pipe near an anchor on the testof 2D_B01.

Elbow 2࿑  ࠛ࡞ࡏ 2 ߢߩ߈ⵚ⽾ㅢ㧔2D_B01㧕
Fig. 3.2.1-2 Penetration of the crack on Elbow 2 of 2D_B01.

− 2255 −

−

26
26 −

0.3t

Wall thinningof Elbow1

2D_C01* ‘t’ denotes the normal pipe thickness

0.5t

0

Depth *

Wall thinningat straight pipe

No defectType

2D_B01

2D_A01

Name

Condition of defect

11

11

11

Internalpressure(P) [MPa]f = 3.22 [Hz]h = 0.0045

f = 3.28 [Hz]h = 0.0042

f = 3.35 [Hz]h = 0.0044

Natural frequency (f)and damping ratio (h)at 1st mode

5
29

1200
1600
30 – 120(Elastic level)
400
1200
1600

10
5
27

5

5

400

Contents of the excitation test
by narrow band random wave
Max. input acc.
Number of times[Gal]
30 – 120
10(Elastic level)
400
5
700
5
1300
5
30 – 120
7(Elastic level)⴫   ᐔ㕙㈩▤♽⹜㛎‫⹜ޓ‬㛎⚿ᨐTable 3.2.1-1 Test results of 2-D piping system test.

* A fatigue crack penetrated at Elbow 1(the thinned wall elbow).
* Small cracks were observed on the
inner surface of the elbows.

* A fatigue crack penetrated at Elbow 2.
* Thinned wall part swelled because ofratchet but no crack appeared on the
inner surface.
* Small cracks were observed on the
inner surface of the elbows.

* No failure occurred after 5 excitation
tests with an input level of 1300Gal.
* Small cracks were observed on the
inner surface of the elbows.

Test results㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ࠆᦛߍᔕജ߇ᄢ߈ߊߥࠆᣇะ㧔᳓ᐔᣇะ㧕ߦ߅޿ߡ㗼⪺ߦ⴫ࠇߡ޿ࠆ㧚࿑ ߦ㧘ᷫ⡺ㇱߢߩ߰ߊࠄߺߩ⁁ᴫࠍ␜ߔ㧚‫⹜ޓ‬㛎ᓟ㧘ోߡߩࠛ࡞ࡏ෸߮⋥▤ᷫ⡺ㇱಽࠍಾࠅ಴ߒ㧘ߘߩౝ㕙ߩᶐㅘត்ᬌᩏࠍታᣉߒߚ㧚ౝ㕙ߩ᭽ሶࠍ࿑ߦ␜ߔ㧚ߎߩ౮⌀ߦ␜ߔࠃ߁ߦ㧘߈ⵚ⽾ㅢㇱߢ޽ࠆࠛ࡞ࡏ2ߩౝ㕙ߦ߅޿ߡߪ㧘ᄖ㕙ࠃࠅ߽ᐢ޿▸࿐ߦࠊߚࠅゲᣇะ߈ⵚߩ
⊒↢߇⏕⹺ߐࠇߚ㧚߹ߚ㧘߈ⵚ߇⽾ㅢߒߚ஥ㇱߩ෻ኻ஥ߩ஥ㇱౝ㕙ߦ߅޿ߡ߽㗼⪺ߥゲᣇะ߈ⵚߩ⊒↢߇⏕⹺ߐࠇߚ㧚ߎߩߎߣ߆ࠄࠛ࡞ࡏ2ߦ߅ߌࠆ߈ⵚߪ㧘ౝ㕙ߦ߅޿ߡೋ↢ߒ㧘ᄖ㕙ߦะߌߡㅴዷ㧘⽾ㅢߦ⥋ߞߚ߽ߩߣ್ᢿߐࠇࠆ㧚ᦝߦ㧘ࠛ
࡞ࡏ2એᄖߩࠛ࡞ࡏౝ㕙஥ㇱߦ߅޿ߡ߽ゲᣇะ߈ⵚߩ⊒↢߇⏕⹺ߐࠇߚ㧚‫ޓ‬ᷫ⡺ㇱߢ޽ࠆ⋥▤ㇱಽߦߟ޿ߡߪ㧘ᄖᓘߩ߰ߊࠄߺߪ㗼⪺ߢߪ޽ߞߚ߇㧘ߘߩౝ㕙ߦߪోߊ߈ⵚߩ⊒↢ߪ⏕⹺ߐࠇߥ߆ߞߚ㧚ᷫ⡺ㇱߢ޽ࠆ⋥▤ㇱߩ߰ߊࠄߺߪ㧘ߎߩ▎ᚲߩᦛߍ೰ᕈࠍᄢ
߈ߊߔࠆലᨐ㧘߅ࠃ߮ᢿ㕙ଥᢙࠍᄢ߈ߊߔࠆല

Thinned wall
straight pipe part

Elbow 1࿑  2D_B01 ߦ߅ߌࠆᷫ⡺ㇱಽߩ⤘ࠄߺ
Fig. 3.2.1-3 Bulge of the thinned wall part of 2D_B01.

࿑  ࠛ࡞ࡏ 1㧔ᷫ⡺ࠛ࡞ࡏ㧕ߦ߅ߌࠆ߈ⵚ⽾ㅢ㧔2D_C01㧕
Fig. 3.2.1-5 Penetration of crack on Elbow 1 (thinned wall elbow)
of 2D_C01.

(a) Crack on side inner surface of Elbow 1.

Penetration part

Penetration part(b) Crack on side inner surface of Elbow 2.

(a) Crack on side inner surface of Elbow 1.

(c) No crack on thinned wall straight pipe part.

(b) Small crack on side inner surface of Elbow 2.

࿑  2D_B01 ߩᶐㅘត்⹜㛎⚿ᨐ
Fig. 3.2.1-4 Penetration test results of 2D_B01.

࿑  2D_C01 ߩᶐㅘត்⹜㛎⚿ᨐ
Fig. 3.2.1-6 Penetration test results of 2D_C01.

− 2277 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

100
0.06
0.13
0.44
0.38
0.38
0.64
0.70 Input
0.77 Level
1.28
(G)
1.28
1.27

50

0
2.5

2.7

2.9

3.1

3.3

Frequency (Hz)(a) 2D_A01.

3.5

A012X/A000X

A012X/A000X

ᝄേᢙߩᄌൻ
‫ޓ‬ᐔ㕙㈩▤♽⹜㛎૕ߩᒢᕈၞߦ߅ߌࠆ࿕᦭ᝄേᢙߪ㧘ஜ
ో2D_A01㧘⋥▤ㇱᷫ⡺2D_B01㧘ࠛ࡞ࡏ1ᷫ⡺2D_C01ߢ㧘ߘࠇߙࠇ 3.35 Hz㧘3.28 Hz㧘3.22 Hz ߢ޽ࠆ㧚ᦨ߽࿕᦭ᝄ
േᢙߩૐ޿ࠛ࡞ࡏ1 ᷫ⡺㧔ో๟30%ᷫ⡺㧕⹜㛎૕ߩ࿕᦭ᝄ
േᢙߪ㧘ஜో⹜㛎૕ߩ࿕᦭ᝄേᢙࠃࠅ߽4%ૐߊߥߞߡ޿
ࠆ㧚߹ߚ㧘ࠛ࡞ࡏ 1 ᷫ⡺⹜㛎૕ࠃࠅ߽⋥▤ㇱᷫ⡺⹜㛎૕
㧔50% ో๟ᷫ⡺㧕ߩ࿕᦭ᝄേᢙ߇㜞ߊߥߞߡ޿ࠆ㧚ᷫ⡺ࠍઃਈߒߚ૏⟎ߪ㧘ਔ⹜㛎૕౒ߦࠕࡦࠞㇱㄭறߩ૏⟎ߢ޽ࠅ㧘ᝄേᔕ╵ߦࠃࠆࡕ࡯ࡔࡦ࠻࡟ࡌ࡞ߪ㧘߶߷ห╬ߩ૏⟎ߣ⠨߃ࠄࠇࠆ㧚ࠛ࡞ࡏ 1ᷫ⡺⹜㛎૕ߩ࿕᦭ᝄേᢙ߇㧘ᷫ⡺㊂ߩࠃࠅᄢ߈޿⋥▤ㇱᷫ⡺⹜㛎૕ࠃࠅ߽ૐߊߥߞߡ޿ࠆ
ߩߪ㧘ࠛ࡞ࡏߦ߅ߌࠆ㕙ౝᦛߍ೰ᕈ߇㧘ᷫ⡺ࠍઃਈߒߚ⋥▤ㇱߩᦛߍ೰ᕈࠃࠅ߽⹜㛎૕ో૕ߩࡕ࡯࠼೰ᕈ߳ߩᓇ㗀߇ᄢ߈޿ߎߣࠍ␜ߒߡ޿ࠆ㧚ߎߩߎߣ߆ࠄ㧘ࠛ࡞ࡏߢߩᷫ
⡺ߪ㧘⋥▤ㇱߦᷫ⡺߇޽ࠆ႐วࠃࠅ߽࿕᦭ᝄേᢙૐਅ߳
ߩᓇ㗀߇ᄢ߈ߊߥࠆߣ⠨߃ࠄࠇࠆ㧚‫⹜ޓ‬㛎૕ߩ႟ᕈᄌᒻࠍ઻߁ᔕ╵߇↢ߓࠆ႐วߩᝄേᢙߩ
ᄌൻࠍᛠីߔࠆߚ߼ߦ㧘ฦടᝄ࡟ࡌ࡞ߢߩવ㆐㑐ᢙࠍ⺞

100
0.06
0.44
0.47
0.47
1.19
1.30
1.30 Input
Level
1.56
(G)
1.55
1.52

50

0
2.5

2.7

2.9

3.1

3.3

Frequency (Hz)3.5(b) 2D_B01.
࿑  વ㆐㑐ᢙߩᄌൻ
Fig. 3.2.1-7 Change of transfer function.

− 2288 −A012X/A000X

ߴߚ㧚3 ⒳㘃ߩ⹜㛎૕ߩടᝄ⹜㛎ߢᓧࠄࠇߚવ㆐㑐ᢙ㧔ᔕ╵ടㅦᐲ㧛౉ജടㅦᐲ㧕ࠍ࿑ ߦ␜ߔ㧚ߎߩ࿑ߦ␜
ߔࠃ߁ߦ㧘౉ജ࡟ࡌ࡞ߩᄢ߈޿႟ᕈၞߩᝄേᔕ╵ߦ߅޿ߡߪ㧘ᝄേᢙ߇ૐਅߔࠆߣ⸒߁ࠃࠅ߽㧘ථ⿧ࡇ࡯ࠢ߇ഀ
ࠇ㧘ᔕ╵୚₸߇ૐਅߒߡߊࠆߣ޿߁⃻⽎߇⃻ࠇߡ޿ࠆ㧚ߎࠇߪ㧘ᒢ႟ᕈᔕ╵ߢߪ㧘ᒢᕈၞߢߩᝄേᔕ╵ߣ㧘႟ᕈၞߢߩᝄേᔕ╵߇ᷙ࿷ߒߡ޿ࠆߚ߼ߣ⠨߃ࠄࠇࠆ㧚ౕ૕⊛ߦㅀߴࠆߣ㧘ᒢ႟ᕈᔕ╵ߩᤨೞᱧᄌൻߢߪ㧘ᔕ╵߇ᄢ߈ߊߥ
ࠆᤨ㑆Ꮺߣᒢᕈၞ࡟ࡌ࡞ߩᔕ╵ߩዊߐߥᤨ㑆Ꮺ߇ሽ࿷ߒ㧘ᔕ╵࡟ࡌ࡞ߩᄢ߈޿ᤨ㑆Ꮺߢߪ႟ᕈᄌᒻߦࠃࠆ๟ᦼߩિ
߮෸߮ࠛࡀ࡞ࠡᶖᢔ߇↢ߓ㧘ᔕ╵࡟ࡌ࡞ߩዊߐ޿ᤨ㑆Ꮺߢߪ✢ᒻ♽ߣߒߡߩ࿕᦭ᝄേᢙߣᷫ⴮Ყߢߩᔕ╵߇↢ߓߡ޿ࠆߣ޿߁ߎߣߢ޽ࠆ㧚࿑  ߩવ㆐㑐ᢙߪ㧘ోᤨ㑆Ꮺߩ౉ജടㅦᐲᤨೞᱧ࠺࡯࠲෸߮ᔕ╵ടㅦᐲᤨೞᱧ
࠺࡯࠲ߦኻߒߡ FFT㧔㜞ㅦࡈ࡯࡝ࠛᄌ឵㧕ߩಣℂࠍᣉߒ㧘ᔕ╵୚₸ߩ๟ᵄᢙ․ᕈࠍ᳞߼ߡ޿ࠆ㧔ࠕࡌ࡟࡯ࠫࡦࠣή
ߒ㧕㧚ߘߩߚ߼㧘વ㆐㑐ᢙߢ⴫⃻ߐࠇࠆ๟ᵄᢙવ㆐․ᕈߪ
✢ᒻ♽ߩᝄേ․ᕈߣ႟ᕈᄌᒻࠍ઻߁㕖✢ᒻߩᝄേ․ᕈ߇
ᷙ࿷ߒߡ߅ࠅ㧘ᒢᕈၞߩ࿕᦭ᝄേᢙઃㄭ㧔ᔕ╵࡟ࡌ࡞ߩᄢ
߈ߊߥࠆᝄേᢙ㗔ၞ㧕ߢߪ㧘႟ᕈᄌᒻߦࠃࠅᝄേᢙߩૐਅ
ߒߚᔕ╵ᚑಽߣᒢᕈၞߢᝄേᢙߩૐਅߒߥ޿ᔕ╵ᚑಽ߇ᷙߑࠅ㧘⷗߆ߌ਄ࠬࡍࠢ࠻࡞ࡇ࡯ࠢߩഀࠇ߇⃻ࠇߡ޿ࠆߣផኤߐࠇࠆ㧚‫ޓ‬਄⸥ߩࠃ߁ߥᔕ╵࡟ࡌ࡞߇ᄢ߈ߊ႟ᕈᄌᒻࠍ઻߁႐ว
ߩᝄേᢙߩૐਅࠍⵣઃߌࠆߚ߼ߦ㧘ᦨᄢᔕ╵⊒↢ᤨὐ1ࠨࠗࠢ࡞ߦ߅ߌࠆ๟ᦼࠍ⺞ߴߚ㧚ஜో⹜㛎૕ߢߩᦨᄢᔕ╵⊒↢ᤨὐ 1 ࠨࠗࠢ࡞ߩᔕ╵ᄌ૏㧔ᝄേบߣߩ⋧ኻᄌ૏㧕ᤨೞᱧᵄᒻࠍ࿑ ߦ␜ߔ㧚ߎߩ࿑ߢߪ㧘ฦ౉ജ࡟ࡌ࡞
ߦ߅ߌࠆ1ࠨࠗࠢ࡞ߩᵄᒻࠍᲧセߔࠆߚ߼ߦ㧘ᦨᄢᔕ╵㊂ߢᱜⷙൻߒߚᵄᒻ߽␜ߒߡ޿ࠆ㧚ߎߩ࿑ߦ␜ߔࠃ߁ߦ㧘౉ജ࡟ࡌ࡞ߩჇᄢߣ౒ߦ㧘1ࠨࠗࠢ࡞ߩ๟ᦼ߇㐳ߊߥߞߡ޿
ࠆߎߣ߇ࠊ߆ࠆ㧚ߎߩ 1ࠨࠗࠢ࡞ߩ๟ᦼߩㅒᢙߣߒߡ㧘ᦨᄢᔕ╵⊒↢ᤨὐߦ߅ߌࠆᝄേᢙࠍ᳞߼ߚ㧚౉ജ࡟ࡌ࡞ߣ
ᦨᄢᔕ╵⊒↢ᤨὐ1ࠨࠗࠢ࡞ߩᝄേᢙૐਅ₸㧔ᦨᄢᔕ╵⊒↢ᤨὐߩ1ࠨࠗࠢ࡞ߩᝄേᢙࠍᒢᕈၞടᝄߢߩᐔဋᝄേᢙ
ߢ㒰ߒߚᲧ₸㧕ߩ㑐ଥࠍ࿑ ߦ␜ߔ㧚ߎߩ࿑ߦ␜ߔ
ࠃ߁ߦ੹࿁ߩ⹜㛎ߦ߅ߌࠆථ⿧ᝄേᢙߩૐਅߪ㧘⚂ 10 %ᨐ߇޽ࠅ㧘⤘ࠄ߻ߎߣߢᦛߍᄌᒻߣߎࠇߦࠃࠅ
↢ߓࠆᔕജߪዊߐߊߥߞߡ޿ߞߚߣផኤߐࠇࠆ㧚(3)‫ ࡏ࡞ࠛޓ‬1 ᷫ⡺⹜㛎૕‫ ޓ‬2D_C01
ࠬࠗ࡯ࡊടᝄߢᓧࠄࠇߚ࿕᦭ᝄേᢙ෸߮ᷫ⴮Ყ
ߪ㧘ߘࠇߙࠇ 3.22 Hz㧘0.45% ߢ޽ߞߚ㧚ᒢᕈၞ࡟ࡌ࡞ߢߩ⹜㛎૕ߩᔕ╵․ᕈࠍᓧߚᓟ㧘႟ᕈၞ࡟ࡌ࡞ߩടᝄࠍታᣉߒߚ㧚౉ജ࡟ࡌ࡞ 400Gal ߩടᝄࠍ 10 ࿁㧘1200 Gal ߩടᝄࠍ 5 ࿁ታᣉߒߚᓟ㧘
1600 Galߢߩടᝄࠍ⎕៊߹ߢ➅ࠅ㄰ߒߚ㧚౉ജ࡟
ࡌ࡞1600 Galߩ27࿁⋡ߩടᝄߦ߅޿ߡ㧘ో๟30%ᷫ⡺ㇱߢ޽ࠆࠛ࡞ࡏ 1 ߦ߅޿ߡ㧘߈ⵚ߇⽾ㅢߒߚ㧚߈ⵚ⽾ㅢ⁁ᴫࠍ࿑  ߦ␜ߔ㧚‫⹜ޓ‬㛎ᓟ㧘ోߡߩࠛ࡞ࡏࠍಾࠅ಴ߒ㧘ౝ㕙ߩᶐㅘត்ᬌᩏࠍⴕߞߚ⚿ᨐ㧘߈ⵚ߇⽾ㅢߒߚࠛ࡞ࡏ1ߪ߽ߣࠃࠅ㧘ࠛ࡞ࡏ2ߩౝ㕙஥ㇱߦ߅޿ߡゲᣇะ߈ⵚߩ⊒↢߇⏕⹺ߐࠇߚ㧚ౝ㕙ᶐㅘត்ᬌᩏ⚿ᨐࠍ࿑  ߦ␜ߔ㧚

100
0.06
0.44
0.56
0.55
0.94
1.13
Input
1.14
1.56 Level
(G)
1.55
1.54

50

0
2.5

2.7

2.9

3.1

Frequency (Hz)3.3(c) 2D_C01.

3.5

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ߢ޽ࠆߎߣ߇ࠊ߆ߞߚ㧚࿑ߦ␜ߒߚવ㆐㑐ᢙߩࠬࡍࠢ࠻࡞ߦ߅޿ߡ㧘౉ജ࡟ࡌ࡞߇ᄢ߈޿ࠤ࡯ࠬߢߪ㧘2.8
㨪 2.9Hz ㄭறߩࡇ࡯ࠢ߇ሽ࿷ߔࠆ߇㧘ᦨᄢᔕ╵⊒↢ᤨὐ 1ࠨࠗࠢ࡞ߢߩᝄേᢙૐਅ߇ 10 㨪 12% ߣߒߚ႐ว㧘ߎߩࡇ࡯ࠢߩᝄേᢙߣ৻⥌ߔࠆߎߣߣߥࠆ㧚‫ޓ‬਄⸥ߩᝄേᢙૐਅߪ㧘ᒢᕈၞߩᔕ╵߇ᄢ߈ߊߥࠅ႟ᕈ
ၞߦ౉ߞߚ⚿ᨐߣߒߡ↢ߓߚ߽ߩߢ޽ࠅ㧘1ࠨࠗࠢ࡞ߩ๟
ᦼߩિ߮ߣߒߡ⃻ࠇߚ߽ߩߢ޽ࠆ㧚෩ኒߦߪ㧘ߎߩ1ࠨࠗࠢ࡞ߩਛߢ߽ᒢᕈၞߩᤨ㑆Ꮺߣ႟ᕈၞߩᤨ㑆Ꮺ߇ᷙ࿷ߒ
ߡ޿ࠆ㧚ᒢᕈၞߢߩ✢ᒻᝄേᔕ╵ߩᑧ㐳ߣߒߡ႟ᕈၞߩ
ᔕ╵߇ሽ࿷ߔࠆߎߣߣߥࠆ㧚ߘߩߚ߼㧘ᝄേᢙ߇ૐਅߒߡ

D011X (mm)200޿ࠆߣߪ޿߃㧘ૐਅߒߚᝄേᢙߣ৻⥌ߒߚᝄേᚑಽ߇౉
ജߐࠇߚߣߒߡ߽㧘ૐਅߒߚᝄേᢙߢߩ౒ᝄ߇↢ߓࠆ߆ߤ߁߆ߪਇ᣿ߢ޽ࠆ㧚ഠൻ᧦ઙߣᔕ╵୯ߩ㑐ଥ‫౉ޓ‬ജടㅦᐲߣฦ⹜㛎ߢߩᦨᄢᔕ╵ടㅦᐲ㧔⛘ኻടㅦᐲ㧕ߩ㑐ଥ෸߮౉ജടㅦᐲߣᦨᄢᔕ╵ᄌ૏㧔ᝄേบߣߩ⋧ኻᄌ૏㧕ߩ㑐ଥࠍ㧘࿑  ෸߮࿑  ߦ␜ߔ㧚ߥ߅㧘࿑  ߦߪ㧘ஜో⹜㛎૕ߩᒢᕈၞടᝄ⹜㛎ߢߩᔕ╵ᄌ૏෸߮ࠛ࡞ࡏ┵ㇱ߭ߕߺࠍၮߦᑼ (3.5.1) ߢ⸘▚ߒߚᔕജ࡟ࡌ࡞ࠍ␜ߔ㧚ߎߎߢߩ Sm ୯ߪ㧘⹜㛎૕ߦ↪޿ࠄࠇߚࠛ࡞ࡏߩ㒠ફᔕജ෸߮ᒁᒛࠅᒝߐ㧔ࡒ࡞ࠪ࡯࠻୯㧕ࠃࠅ⸘▚ߒߚታജ୯ߢ޽ࠆ㧚0

15
2D_A01-200
0.00

2D_B01
0.10

0.20

2D_C010.30

Time (s)10
A012X (G)(a) Original response displacement.
Input Level 0.04G
Input Level 0.25G
Input Level 0.59G

5Input Level 0.92G
D011X/D011Xmax

1.0

0.0

0
0.0

0.5

1.0

-1.0
0.00

0.10

0.20

0.30

2.0

࿑  ౉ജടㅦᐲ㧙ᔕ╵ടㅦᐲ㑐ଥ
Fig. 3.2.1-10 Relation between input acc. and response acc..

Time (s)(b) Normalized response displacement.
࿑  ᦨᄢᔕ╵ὐߦ߅ߌࠆᵄᒻ
Fig. 3.2.1-8 Waveform at the maximum response.

300
2D_A01
2D_B01

1.2

2D_C01

2D_A01
2D_B01
2D_C01

1.1

200
D011X (mm)Dominant Frequency (Hz)1.5

Input Level (G)(M ax. Acc. of A000X)

1.0

5.5 Sm
4.5 Sm100

3.0 Sm

0.9
0.8
0

500

1000

1500

2000

Input Acc. (Gal)

0
0.0

0.5

1.0

1.5

2.0

Input Level (G)(M ax. Acc. of A000X)

࿑  ᦨᄢᔕ╵ὐߦ߅ߌࠆᝄേᢙߩᄌൻ
Fig. 3.2.1-9 Change of dominant frequency of the maximum
response.

࿑  ౉ജടㅦᐲ㧙ᔕ╵ᄌ૏㑐ଥ
Fig. 3.2.1-11 Relation between input acc. and response disp..

− 2299 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬Stress Level =

1 
pD

⋅  B1 ⋅+ B2 ⋅ E ⋅ S107 A 
Sm 
2t


(3.5.1)1 pD=⋅  B1 ⋅+ B2 ⋅ E ⋅ α ⋅ D 011X 
Sm 
2t

࿑3.2.1ෳᾖ
α = 12.42 × 10−6 (࿑− 12ෳᾖ
) )B1 = 0.5, B2 = 2.15, E = 203000߃㧘ᔕ╵ᄌ૏߇╬ଔߣߥࠆࠃ߁ߥᷫ⴮Ყࠍ㧘✢ᒻᔕ╵⸃ᨆ㧔ᔕ╵ࠬࡍࠢ࠻࡞⸃ᨆ㧕ࠍ੺ߒߡ᳞߼ߡ޿ࠆ㧚࿑ 
ߦߪ㧘ஜో⹜㛎૕2D_A01ߢߩᷫ⴮Ყࠍࡄ࡜ࡔ࡯࠲ߣߒߚ
✢ᒻᔕ╵⸃ᨆ⚿ᨐߣߩᲧセࠍ␜ߔ㧚ߎߩ࿑ߦ␜ߔࠃ߁ߦ㧘ஜో⹜㛎૕ߢߩᦨᄢ౉ജ࡟ࡌ࡞⚂1300 Galߩടᝄߢߪ㧘ᦨᄢᔕ╵ᄌ૏ߩᲧセߦࠃࠅ6%⒟ᐲߩ╬ଔᷫ⴮Ყߢ޽ࠆߎߣ
߇ࠊ߆ߞߚ㧚

S m㧦⸳⸘ᔕജᒝߐ (ታജ୯ 155N/mm 2 )p㧦ౝ࿶ (MPa),(mm)
D㧦㈩▤ᄖᓘ (mm), 㧦㈩▤⡺ෘtS107A㧦ࠛ࡞ࡏ┵ㇱ߭ߕߺ
D011X㧦⹜㛎૕ᦨᄢᔕ╵ᄌ૏ (mm)‫ޓ‬࿑෸߮࿑ߦ␜ߔࠃ߁ߦ౉ജ࡟ࡌ࡞ߩ
ᄢ߈޿ടᝄߢߪ㧘ᦨᄢᔕ╵ടㅦᐲ෸߮ᦨᄢᔕ╵ᄌ૏౒ߦ㧘౉ജ࡟ࡌ࡞ߦኻߔࠆჇട₸߇ዊߐߊߥߞߡ޿ߊ௑ะߦ޽
ࠆ㧚ߎࠇߪ㧘⹜㛎૕ߩ႟ᕈᄌᒻߦ઻޿ᝄേࠛࡀ࡞ࠡ߇ᶖᢔ
ߐࠇߚߚ߼ߢ޽ࠆ㧚߹ߚ㧘ᧄ⹜㛎⚿ᨐߢߪ㧘౉ജ࡟ࡌ࡞ߣ
ᦨᄢᔕ╵ߩ㑐ଥߦ߅޿ߡ㧘ᷫ⡺ߩ᦭ή㧘⋥▤ߣࠛ࡞ࡏߢߩ
ᷫ⡺ߩ㆑޿ߦࠃࠆ㗼⪺ߥ௑ะߩ㆑޿ߪ⏕⹺ߐࠇߥ߆ߞߚ㧚‫ޓ‬႟ᕈᄌᒻߦࠃࠆࠛࡀ࡞ࠡᶖᢔߢߩᷫ⴮ലᨐ㧘╬ଔᷫ⴮Ყߦߟ޿ߡᬌ⸛ࠍⴕߞߚ㧚೨㗄ߦ␜ߒߚવ㆐㑐ᢙࠍ⷗ࠆ㒢ࠅવ㆐㑐ᢙ߆ࠄߩ╬ଔᷫ⴮Ყߩ▚ቯߪ࿎㔍ߢ޽ࠆߣ⠨㪏㪇㪇㫐㩷㪔㩷㪈㪉㪅㪋㪉㫏㪩㪉㩷㪔㩷㪇㪅㪐㪐㪌㪏

S107A

㪪㪈㪇㪎㪘㩿㱘㪀

㪍㪇㪇
D011X

㪋㪇㪇
㪉㪇㪇
㪇
㪇

㪉㪇
㪋㪇
㪛㪇㪈㪈㪯㩿㫄㫄㪀㪍㪇࿑  ᦨᄢᔕ╵ᄌ૏ߣࠛ࡞ࡏ┵ㇱߦ߅ߌࠆ߭ߕߺߩ㑐ଥ
Fig. 3.2.1-12 Relation between maximum response disp. and thestrain at an end of an elbow.
300⹜㛎૕ߩᄖᓘᄌൻ
‫ޓ‬ஜో⹜㛎૕ 2D_A01㧘⋥▤ᷫ⡺⹜㛎૕ 2D_B01 ෸߮ࠛ࡞ࡏᷫ⡺⹜㛎૕ 2D_C01 ߢߩਥⷐㇱಽߩᄖᓘᄌൻ₸ࠍ࿑ ߦ␜ߔ㧚ߎߩᄖᓘᄌൻ₸ߪ㧘ടᝄ⹜㛎ᓟߩᄖᓘᄌൻ㊂ࠍടᝄ⹜㛎೨ߩᄖᓘߢ㒰ߒߚᲧ₸ߣߒߡ␜ߒߚ߽
ߩߢ޽ࠆ㧚ߎߩ࿑ߦ␜ߔࠃ߁ߦ㧘ஜో⹜㛎૕ߢߩᄖᓘᄌൻ
ߪ߶ߣࠎߤήߊ㧘⋥▤ㇱᷫ⡺⹜㛎૕෸߮ࠛ࡞ࡏㇱᷫ⡺⹜㛎૕ฦ‫ߩߢޘ‬ᷫ⡺ㇱಽߩᄖᓘᄌൻ߇ᄢ߈޿ߎߣ߇ࠊ߆ࠆ㧚․╩ߔߴ߈ߪ㧘⋥▤ㇱᷫ⡺⹜㛎૕ߦ߅ߌࠆᷫ⡺ㇱಽߢߪ
11%એ਄ߩᄖᓘᄌൻ㧔߰ߊࠄߺ㧕߇⏕⹺ߐࠇߚߦ߽㑐ࠊࠄߕ㧘೨㗄ߢㅀߴߚߣ߅ࠅ∋ഭ߈ⵚߩ⊒↢ߪ⏕⹺ߐࠇߡ޿
ߥ޿ߎߣߢ޽ࠆ㧚⋥▤ᷫ⡺ㇱߩ߰ߊࠄߺߪ㧘೨ㅀߩࠃ߁ߦ
㈩▤ߩ߰ߊࠄߺ߇㈩▤ߩᦛߍߦኻߔࠆ೰ᕈࠍ㜞߼㧘ᦛߍߦࠃࠅ↢ߓࠆ㈩▤ゲᣇะ߭ߕߺߩᝄ᏷߇ടᝄࠍ➅ࠅ㄰ߔߣ౒ߦዊߐߊߥߞߡ޿ߞߚߣផኤߐࠇࠆ㧚৻ᣇ㧘ࠛ࡞ࡏᷫ⡺⹜㛎૕ߢߪ㧘ᷫ⡺ࠛ࡞ࡏߩ㕙ᄖᣇะߦ⚂ 2% ߩᄖᓘᄌൻ߇⃻ࠇߡ޿ࠆ㧚ᄌൻ₸ߣߒߡߪ㧘਄⸥ߩ⋥▤ᷫ⡺ㇱࠃࠅ߽ዊߐ޿㧚ࠛ࡞ࡏߢߪ㧘㕙ౝᦛߍ߇⽶⩄ߐࠇߚ႐ว㧘ߘߩᢿ㕙߇➅㄰ߒᬦ౞ൻߔࠆߎߣߢ㧘੤⇟⊛ߥ๟ᣇะ߭ߕߺ߇⊒↢ߔࠆ㧚ߎߩ⚿ᨐ㧘ౝ㕙ߦゲᣇะ߈ⵚ߇↢ߓ∋ഭ⎕៊ߦ⥋ࠆߣ⠨߃ࠄࠇࠆ㧚ߎߩ⃻⽎ߦኻߔࠆᢿ㕙ߩ߰ߊࠄߺߩലᨐࠍ⠨߃ࠆߣ㧘߰ߊࠄ߻ߎߣߪᬦ౞
ൻߦኻߔࠆ೰ᕈࠍૐਅߐߖࠆߎߣߦߥࠆߣ⠨߃ࠄࠇࠆ㧚ߥ߅㧘ߎߩലᨐߦߟ޿ߡߪ㧘⃻⁁㧘චಽߥᬌ⸛߇ߥߐࠇߡ
޿ߥ޿㧚ᷫ⡺㈩▤ߩᒝᐲࠍᬌ⸛ߔࠆ਄ߢߩ੹ᓟߩ⺖㗴ߩ৻ߟߦߥࠆߣ⠨߃ࠄࠇࠆ㧚

Elastic Analysis of 2D_A01
with Damping Ratio

Elbow 1 In plane

Elbow 1 Out of plane

0.005

Elbow 2 In plane

Elbow 2 Out of plane

Straight pipe In plane

Straight pipe Out of plane

0.010
0.020

D011X (mm)200

Ratio of ratchet deformation (%)

0.050
0.100
0.200

100

0
0.0

0.5

1.0

1.5

2.0

20
10
0
-10
-20
2D_A01

Input Level (G)(M ax. Acc. of A000X)

2D_B01

2D_C01Name of specimen࿑  ታ㛎⚿ᨐߣ✢ୱᔕ╵⸃ᨆߣߩᲧセ㧔2D_A01㧕
Fig. 3.2.1-13 Comparison to linear response analysis of 2D_A01.

࿑  ᐔ㕙㈩▤♽⹜㛎૕ߦ߅ߌࠆ࡜࠴ࠚ࠶࠻ᄌᒻ㊂
Fig. 3.2.1-14 Ratio of ratchet deformation of 2D piping models.

− 3300 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆┙૕㈩▤♽⹜㛎㧟⎕៊⁁ᴫ┙૕㈩▤♽⹜㛎ߩ⹜㛎⚿ᨐࠍ⴫ߦ␜ߔ㧚ฦ⹜㛎૕ߩ⎕៊⁁ᴫߪએਅߩࠃ߁ߦߥߞߚ㧚(1)‫ޓ‬ஜో⹜㛎૕㧔3D_A01㧕
ࠬࠗ࡯ࡊടᝄ߆ࠄᓧࠄࠇߚ 1 ᰴ࿕᦭ᝄേᢙߪ
2.78Hz ߢ޽ߞߚ㧚ᒢᕈၞ࡟ࡌ࡞ߢ⹜㛎૕ߩᔕ╵․ᕈࠍᓧߚ޽ߣᒢ႟ᕈ࡟ࡌ࡞ߩടᝄࠍታᣉߒߚ㧚౉ജടㅦᐲ 1850Gal ߩᒢ႟ᕈ࡟ࡌ࡞ടᝄ 13 ࿁⋡߇⚳ੌߒߚᓟ㧘ࠛ࡞ࡏ  ⣁⣻ 㕙㧔࿑  ߦ߅
ߌࠆS047-S048ߩ૏⟎㧘એਅS047஥ߣ޿߁㧕ߢ㈩▤ᄖ⴫㕙ߦߊ߷ߺߩ⊒↢߇⏕⹺ߐࠇ㧘14 ࿁⋡ߢߘߩㇱಽ߆ࠄ㈩▤ゲᣇะߦ∋ഭ߈ⵚ߇⽾ㅢߒߚ㧚࿑  ߦࠛ࡞ࡏ 1 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚(2)‫ ࡏ࡞ࠛޓ‬2ࡩᚲᷫ⡺⹜㛎૕㧔3D_C01㧕
ࠬࠗ࡯ࡊടᝄ߆ࠄᓧࠄࠇߚ 1 ᰴ࿕᦭ᝄേᢙߪ
2.42Hzߢ޽ߞߚ㧚౉ജടㅦᐲ1850Galߩᒢ႟ᕈ࡟
ࡌ࡞ടᝄ1࿁⋡ߢ㧘ࠛ࡞ࡏ1⣁⣻S047஥ߢ㈩▤ᄖ⴫㕙ߩߊ߷ߺ⊒↢߇⏕⹺ߐࠇߚ㧚ߘߩᓟ㧘౉ജട
ㅦᐲ1850Galߩടᝄ3࿁⋡ߢゲᣇะߦ∋ഭ߈ⵚ߇⽾ㅢߒߚ㧚࿑  ߦ 3D_C01 ߩ៊்⁁ᴫࠍ␜ߔ㧚(3)‫ ࡏ࡞ࠛޓ‬1 ᷫ⡺⹜㛎૕㧔3D_C02㧕
ࠬࠗ࡯ࡊടᝄ߆ࠄᓧࠄࠇߚ 1 ᰴ࿕᦭ᝄേᢙߪ
2.55Hzߢ޽ߞߚ㧚౉ജടㅦᐲ1400Galߩᒢ႟ᕈ࡟
ࡌ࡞ടᝄ1࿁⋡ߩᓟߦࠛ࡞ࡏ1⣁⣻S047஥ߢ㈩▤ᄖ⴫㕙ߩᄌൻ߇⹺߼ࠄࠇߚ㧚߹ߚ㧘౉ജടㅦᐲ
1850Gal ߩടᝄ 1 ࿁⋡ߩᓟߦࠛ࡞ࡏ 1 ߩ෻ኻ஥ߩ
⣁⣻㧔࿑  ߦ߅ߌࠆ S042-S043 ߩ૏⟎㧘એਅ
S043஥ߣ޿߁㧕ߢ߽ߊ߷ߺߩ⊒↢߇⏕⹺ߐࠇߚ㧚ߎߩ⹜㛎૕ߪ౉ജടㅦᐲ 1850Gal ߩടᝄ 3 ࿁⋡
ߢ㧘S047 ஥ߩࠛ࡞ࡏ⣁⣻ߢゲᣇะߩ∋ഭ߈ⵚ߇⽾ㅢߒߚ㧚߈ⵚ⽾ㅢᓟ߽ടᝄࠍ⛮⛯ߒߚߚ߼㧘
S043 ஥ߩࠛ࡞ࡏ⣁⣻߆ࠄ߽߈ⵚ߇⽾ㅢߒߚ㧚࿑ߦ߈ⵚ⽾ㅢ೨ߦ⋡ⷞ⏕⹺ߐࠇߚ㈩▤ᄖ⴫㕙ߩߊ߷ߺࠍ㧘࿑  ߦࠛ࡞ࡏ 1 ߩ៊்⁁ᴫࠍ␜ߔ㧚(4)‫ ࡏ࡞ࠛޓ‬2 ᷫ⡺⹜㛎૕㧔3D_C03㧕
ࠬࠗ࡯ࡊടᝄ߆ࠄᓧࠄࠇߚ 1 ᰴ࿕᦭ᝄേᢙߪ
2.62Hzߢ޽ߞߚ㧚౉ജടㅦᐲ1400Galߩᒢ႟ᕈ࡟
ࡌ࡞ടᝄ 2 ࿁⋡ߩᓟߦࠛ࡞ࡏ 2 ⣁⣻ 㕙㧔࿑ ߦ߅ߌࠆS094-S095ߩ૏⟎㧘એਅS095஥ߣ޿߁㧕ߢ㈩▤ᄖ⴫㕙ߦߊ߷ߺ߇⊒↢ߒߚ㧚ߘߩᓟ㧘౉ജ
ടㅦᐲ1850Galߩടᝄ1࿁⋡ߦߎߩㇱಽߢゲᣇะ∋ഭ߈ⵚ߇⽾ㅢߒߚ㧚࿑  ߦ 3D_C03 ߩ⎕៊⁁ᴫࠍ␜ߔ㧚(5)‫ޓ‬ㇱಽ EDM ߈ⵚߟ߈⹜㛎૕㧔3D_D01㧕
ࠬࠗ࡯ࡊടᝄ߆ࠄᓧࠄࠇߚ 1 ᰴ࿕᦭ᝄേᢙߪ
2.79Hz ߢ޽ߞߚ㧚ߎߩ⹜㛎૕ߢߪታ㛎ߩㅜਛ߆ࠄࠢ࡝࠶ࡊࠥ࡯ࠫࠍ૶↪ߒߡ⸘᷹ߒߡ޿ߚEDM
߈ⵚߩ㐿ญᄌ૏߇Ⴧടߒߥߊߥߞߚߚ߼㧘⎕៊࿑  ࠛ࡞ࡏ 1 ߦ߅ߌࠆ∋ഭ߈ⵚ㧔3D_A01㧕
Fig. 3.2.2-1 Fatigue crack at Elbow 1, 3D_A01.

(a) Crack penetration occurred at
Elbow 1 during 1850Gal_#03
excitation.

(b) Fatigue crack at Elbow 1.

࿑  3D_C01 ߩ⎕៊ᒻᘒ
Fig. 3.2.2-2 Failure mode of 3D_C01.

(a) S047 side.

(b) S043 side.

࿑  3D_C02 ࠛ࡞ࡏ 1 ߢ⏕⹺ߐࠇߚ߈ⵚ⽾ㅢ೨ߩ㈩▤⴫㕙ߩᄌൻ㧔1850Gal㧘1 ࿁⋡ߩടᝄᓟ㧕
Fig. 3.2.2-3 Pipe surface deformation before crack penetration at
Elbow 1, 3D_C02 (after 1850Gal_#01 excitation test).

(a) S047 side.

(b) S043 side.

࿑  ࠛ࡞ࡏ 1 ߦ߅ߌࠆ∋ഭ߈ⵚ㧔3D_C02㧕
Fig. 3.2.2-4 Fatigue crack at Elbow 1, 3D_C02.

(a) Crack penetration occurred at
Elbow 2 during 1850Gal_#01
excitation.

− 3311 −(b) Leak of water at Elbow 2.

࿑  3D_C03 ߩ⎕៊ᒻᘒ
Fig. 3.2.2-5 Failure mode of 3D_C03.

− 3322 −

0.48t

0.49t

0.5t

Wall thinning
at Elbow2

Partial EDM
notch atstraight pipe

Full circle
EDM notch atstraight pipe

3D_C03

3D_D01

3D_D0281010Internalpressure(P) [MPa]f = 2.75 [Hz] *2
h = 0.00938

f = 2.79[Hz]h = 0.0100

f = 2.62 [Hz]h = 0.0109

f = 2.55 [Hz]h = 0.0131

f = 2.42 [Hz]h = 0.0121

f = 2.78 [Hz]h = 0.0106

Natural frequency (f)and damping ratio (h)at 1st mode

*2 Obtained from a wide band random wave excitation test

*1 ‘t’ denotes the normal pipe thickness

0.48t

Wall thinning
at Elbow1

0.48t

Wall thinning
at Elbow1& 2

3D_C01

3D_C020Depth * 1

No defectType

3D_A01

Name

Condition of defectContents of the excitation test
by narrow band random wave
Max. input acc.
Number of times[Gal]
20 – 100
10(Elastic level)
400 – 700
4
1400
2
1850
14
20 – 80
4(Elastic level)
700
1
1400
2
1850
3
20 – 80
4(Elastic level)
700
1
1400
2
1850
3
20 – 80
4(Elastic level)
700
1
1400
2
1850
1
20 – 80
4(Elastic level)
800
1
1200
13
20 – 80
4(Elastic level)1850
2⴫ 
┙૕㈩▤♽⹜㛎‫⹜ޓ‬㛎⚿ᨐTable 3.2.2-1 Test results of 3-D piping system test.

* Full circumferential break occurred atsecond excitation with elastic-plastic
level.

* Excitation test was ended before thefailure occurred. Initial EDM notch did
not penetrate after 13 excitation tests.

* Penetration of a fatigue crack in alongitudinal direction at Elbow 2.
* No crack was observed at Elbow 1.

* Penetration of fatigue cracks in alongitudinal direction at Elbow 1.
* No crack was observed at Elbow 2.

* Penetration of a fatigue crack in alongitudinal direction at Elbow 1.
* No crack was observed at Elbow 2.
* The residual deformation was clearlyobserved after the test.

* Penetration of fatigue cracks in alongitudinal direction at Elbow 1.
* A number of small cracks were observedon the inner surface of Elbow 2.

Test results㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆࿑  1850Gal 2 ࿁⋡ߩടᝄਛߦ߅ߌࠆ߈ⵚ⽾ㅢߩ⁁ᴫ
Fig. 3.2.2-7 Crack penetration occurred at EDM notch during
1850Gal_#02 excitation test.

Broken point(a) View from the front.

(b) View from the excitation
direction.

࿑  3D_D02 ߩ⎕៊⁁ᴫ
Fig. 3.2.2-8 Failure mode of 3D_D02.
Full circumferential break
Crack penetration
Acc. [Gal]⹜㛎⚳ੌᓟ㧘3D_A01 ߅ࠃ߮ 3D_C01 㨪 3D_C03 ߦߟ޿ߡߪࠛ࡞ࡏ 1㧘2 ࠍಾࠅ಴ߒߡᶐㅘត்ᬌᩏࠍⴕߞߚ㧚ߘߩ⚿ᨐ㧘3D_A01 ߢߪ⎕៊ߒߥ߆ߞߚࠛ࡞ࡏ 2 ߩౝ㕙ߦ⧯ᐓߩᓸዊߥ߈ⵚߩ⊒↢߇⹺߼ࠄࠇߚ߇㧘ߘߩઁߩ⹜㛎૕ߢߪ⎕៊ߒߚࠛ࡞ࡏએᄖߩౝ㕙ߦ߈ⵚߩ⊒↢ߪ⹺߼ࠄࠇ
ߥ߆ߞߚ㧚߹ߚ㧘⎕៊ߒߚࠛ࡞ࡏߩౝ㕙ߦߪ㧘⽾ㅢ߈ⵚએᄖߦᄙᢙߩᓸዊߥᧂ⽾ㅢ߈ⵚߩ⊒↢߇⹺߼ࠄࠇߚ㧚߈ⵚ⽾ㅢ߹ߢߦⷐߒߚᒢ႟ᕈ࡟ࡌ࡞ߩടᝄ࿁ᢙߪ㧘ஜో⹜㛎૕ߢ 20 ࿁㧘ᷫ⡺⹜㛎૕ߢ 4 ࿁㨪 6 ࿁ߣߥߞߚ㧚㈩▤♽ߩᒢ႟ᕈᔕ╵ᵄᒻߪ⹜㛎૕ߏߣߦ⇣ߥࠆߚ߼㧘ടᝄ࿁ᢙߩߺߢૐࠨࠗࠢ࡞∋ഭ៊்ߦⷐߒߚࠨࠗࠢ࡞ᢙࠍ▚ቯߔࠆߎߣߪߢ߈ߥ޿߇㧘ߎࠇࠄߩ⚿ᨐ߆ࠄ㧘ࠛ࡞ࡏㇱಽߦ
50% ⒟ᐲߩᷫ⡺߇ሽ࿷ߔࠆߎߣߦࠃߞߡ㈩▤♽ߩ⎕៊ኼ๮ߪ⚂ 1/3 એਅߦૐਅߒߚߣ⸒߃ࠆ㧚┙૕㈩▤♽⹜㛎૕ߢߪ3D_C01ߦ߅޿ߡ㧘⹜㛎⚳ੌᓟࠛ
࡞ࡏ 1 ߇㐿ߊᣇะߦ⚂ 2.6qߩᱷ⇐ᄌᒻ߇⊒↢ߒߚ߇㧘ߎߩᄌᒻ߇ਇ቟ቯߦㅴⴕߔࠆࠃ߁ߥ⃻⽎ߪ↢ߓߥ߆ߞߚ㧚ᧄታ㛎ߦ߅޿ߡߪ㧘ᷓߐ 50% ߩో๟߈ⵚࠍᣉߒߚ⹜㛎૕એᄖߢߪ៊்ߦ઻޿ᄌᒻ߇ਇ቟ቯߦㅴዷߔࠆࠃ߁ߥ⃻⽎ߪ⷗ࠄࠇߕ㧘ታ㛎ߢ⏕⹺ߐࠇߚ㈩▤♽ߩ⎕៊ᒻᘒߪ⩄㊀ಽᜂߩᄢ߈޿ࠛ࡞ࡏㇱಽߦ߅ߌࠆ∋ഭ៊்ߢ޽ߞߚ㧚࿑  3D_D02 ߦ߅޿ߡ EDM ߈ⵚ߆ࠄߩ߈ⵚ⽾ㅢ೨ߦ㈩▤⴫㕙ߢ⏕⹺ߐࠇߚ╭㧔1850Gal㧘1 ࿁⋡ߩടᝄᓟ㧕
Fig. 3.2.2-6 A line on the pipe surface before crack penetration at
EDM notch, 3D_D02 (after 1850Gal_#01 excitationtest).

6000
4000
2000
0
-2000
-4000
-6000

0

10

Time[s] 20

30

40

30

40

(a) Response acc. at Elbow3.
Pressure [kPa]ߐߖߕߦታ㛎ࠍ⚳ੌߒߚ㧚ߎߩ⹜㛎૕ߦኻߒߡ
ߪᒢ႟ᕈ࡟ࡌ࡞ߩടᝄࠍ㧘౉ജടㅦᐲ 800Gal ߩ߽ߩࠍ 1 ࿁㧘1200Gal ߩ߽ߩࠍ 13 ࿁ታᣉߒߚ߇㧘⹜㛎૕ߪ⎕៊ߒߥ߆ߞߚ㧚⹜㛎⚳ੌᓟ㧘߈ⵚዉ౉㕙ࠍಾࠅ಴ߒߡⷰኤߒߚߣߎࠈ㧘ೋᦼ EDM ߈ⵚ߆ࠄߩ߈ⵚㅴዷ㊂ߪ⚂ 0.5mm ߣߥߞߡ޿ߚ㧚(6)‫ోޓ‬๟ EDM ߈ⵚߟ߈⹜㛎૕㧔3D_D02㧕
ߎߩ⹜㛎૕ߢߪ㧘ࠬࠗ࡯ࡊടᝄࠍⴕ߁ߣ౒ᝄ⁁ᘒߦߥߞߚߣ߈ߦ߈ⵚ߇ㅴዷߔࠆ߅ߘࠇ߇޽ߞ
ߚߚ߼㧘ᐢᏪၞ࡜ࡦ࠳ࡓᵄࠍ૶↪ߒߡ࿕᦭ᝄേ
ᢙࠍ᳞߼ߚ㧚ᐢᏪၞ࡜ࡦ࠳ࡓᵄടᝄ߆ࠄᓧࠄࠇ
ߚ 1 ᰴ࿕᦭ᝄേᢙߪ 2.75Hz ߢ޽ߞߚ㧚౉ജടㅦ
ᐲ1850Galߩടᝄ1࿁⋡߇⚳ੌߒߚᓟ㧘EDM߈ⵚ
ࠍઃਈߒߚ૏⟎ߦኻᔕߔࠆ㈩▤ᄖ⴫㕙ߩ৻ㇱߦߊ߷ߺ߇⊒↢ߒߚ㧔࿑ 㧕㧚EDM ߈ⵚߪ౉ജടㅦᐲ 1850Gal ߩടᝄ 2 ࿁⋡ߢ࿑  ߦ߅ߌࠆ S032 ᣇะߦ⽾ㅢߒߚ㧚⽾ㅢᓟ߽ടᝄࠍ⛮⛯ߒߚߚ߼㧘ᓟ⛯ߩᔕ╵ߦࠃࠅ๟ᣇะߦ߈ⵚ߇વ᠞
ߒ㧘ో๟⎕ᢿߦ⥋ߞߚ㧚߈ⵚ⽾ㅢᣇะ߇ S031 ᣇะ߆ࠄߕࠇߡ޿ࠆߩߪ㧘⹜㛎૕ߩࠛ࡞ࡏ1ㄭறߩᄌᒻߪࠛ࡞ࡏߩ⚐☴ߥ㕙ౝᦛߍߢߪߥߊ⧯ᐓߩ
㕙ᄖᄌᒻ߇ᷙ࿷ߒߡ޿ࠆߚ߼ߣ⠨߃ࠄࠇࠆ㧚࿑       ߦ߈ⵚ߇⽾ㅢߒߚߣ߈ߩ⁁ᴫࠍ㧘࿑ߦో๟⎕ᢿᓟߩ⹜㛎૕ߩ⁁ᴫࠍ␜ߔ㧚߹ߚ㧘࿑ߦ߈ⵚ߇⽾ㅢߒߚടᝄߦ߅ߌࠆࠛ
࡞ࡏ3ߩᔕ╵ടㅦᐲߣౝ࿶ᄌൻߩᤨೞᱧᵄᒻࠍ␜
ߔ㧚࿑  ߆ࠄ㧘߈ⵚ⽾ㅢᓟ㧘5 㨪 6 ࠨࠗࠢ࡞ߢో๟⎕ᢿߦ⥋ߞߚߎߣ߇ࠊ߆ࠆ㧚

4

1 10
8000
6000
4000
2000
0
-2000

− 3333 −010Time[s] 20(b) Internal pressure.
࿑  ࠛ࡞ࡏ 3 ߦ߅ߌࠆᔕ╵ടㅦᐲߣ㈩▤ౝ࿶㧔3D_D02㧘1850Gal 2 ࿁⋡㧕Fig. 3.2.2-9 Response acc. at Elbow 3 and internal pressure(3D_D02, 1850Gal_#02).

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

Response Acc. [Gal]

5000
4000
3000
2000
1000
0

Elastic response
0500

3D _A 01
3D _C01
3D _C02

1000
Input A cc. [G al]

3D _C03
3D _D 01
3D _D 02
1500

10
3D _A 01 Elbow1
3D _A 01 Elbow2
3D_ C01 Elbow1
3D_ C01 Elbow2
3D_ C02 Elbow1
3D_ C02 Elbow2
3D_ C03 Elbow1
3D_ C03 Elbow2

8

6

4

2

0
0

50

100

150

200

250

300

࿑  ᦨᄢᔕ╵ᄌ૏㧙ࠛ࡞ࡏᄌᒻⷺ▸࿐㑐ଥ
Fig. 3.2.2-11 Relation between max. response disp. and range ofelbow deformation angle.
4
3D _A 01
3D _C01

3.5

3D _C02
3D _C03

3
2.5
2
1.5
1
0.5
0
10

2000

100

1000

Input accerelation [G al]࿑  ౉ജടㅦᐲߣࠛ࡞ࡏ 3 ߦ߅ߌࠆᔕ╵ടㅦᐲ㑐ଥ
Fig. 3.2.2-10 Relation between input acc. and response acc. at
Elbow 3.

350

Response displacement[mm]R atio of elbow deformation (D 01/D 02)

6000

ኻᄌᒻ㊂ߢ޽ࠅ㧘એᓟ⹜㛎૕ߩᔕ╵ᄌ૏ߣ⴫⸥ߔࠆ㧚ஜో⹜㛎૕߅ࠃ߮ᷫ⡺⹜㛎૕ߦߟ޿ߡ㧘⹜㛎૕ߩᦨᄢᔕ╵ᄌ૏ߣࠛ࡞ࡏ 1 㧘2 ߩᦨᄢ㐿㐽ᄌᒻⷺ▸࿐ߣߩ㑐ଥߪ࿑ ߩࠃ߁ߦߥࠆ㧚ߎߎߢ㧘ࠛ࡞ࡏߩᦨᄢ㐿㐽ᄌᒻⷺ▸࿐ߪᦨᄢ㐿߈ᄌᒻⷺ߆ࠄᦨᄢ㐽ߓᄌᒻⷺߩᏅࠍߣߞ
ߚ߽ߩߣቯ⟵ߒߚ㧚࿑ਛ㧘Ⴃࠅߟ߱ߒߚශߪஜోࠛ࡞ࡏ
ࠍ㧘⊕ᛮ߈ߩශߪᷫ⡺ࠛ࡞ࡏࠍᗧ๧ߒߡ޿ࠆ㧚࿑  ࠃࠅ㧘หߓ⹜㛎૕ᔕ╵ᄌ૏ߦኻߒߡ㧘ᷫ⡺ࠛ࡞ࡏߩᄌ
ᒻ㊂ߪஜోࠛ࡞ࡏߩᄌᒻ㊂ߩ2㨪3୚ߣߥߞߡ޿ࠆߎߣ߇
ࠊ߆ࠆ㧚ᓥߞߡ㧘㈩▤♽ౝߦᷫ⡺ߒߚࠛ࡞ࡏ߇޽ࠆ႐ว㧘㈩▤♽ߩᄌᒻߪᷫ⡺ߒߚࠛ࡞ࡏㇱಽߦ㓸ਛߔࠆ௑ะߣߥ
ࠆߣ⠨߃ࠄࠇࠆ㧚࿑  ߦ㧘ஜో⹜㛎૕ߣᷫ⡺⹜㛎૕ߦߟ޿ߡ㧘ࠛ
࡞ࡏ 1 ߣࠛ࡞ࡏ 2 ߩᄌᒻⷺᲧߣ౉ജടㅦᐲߣߩ㑐ଥࠍ␜ߔ㧚ߎߎߢ㧘ࠛ࡞ࡏ 1 ߣࠛ࡞ࡏ 2 ߩᄌᒻⷺᲧߣߪ㧘ࠛ࡞ࡏߩᦨᄢ㐿㐽ᄌᒻⷺ▸࿐ࠍࠛ࡞ࡏ2ߩᦨᄢ㐿㐽ᄌᒻⷺ▸࿐ߢ㒰ߒߚ߽ߩߢ޽ࠆ㧚ᒢᕈၞ࡟ࡌ࡞ߩടᝄߦ߅޿ߡߪ޿
ߕࠇߩ⹜㛎૕ߦߟ޿ߡ߽ࠛ࡞ࡏߩᄌᒻⷺᲧߪ߶߷৻ቯߢ
ផ⒖ߔࠆ㧚ᒢ႟ᕈ࡟ࡌ࡞ߢߪߎߩᄌᒻⷺᲧ߇⧯ᐓᄌൻߒ㧘ஜో⹜㛎૕㧔3D_A01㧕ߢߪᒢᕈၞ࡟ࡌ࡞ߩᔕ╵ߢ૞↪ᦛߍࡕ࡯ࡔࡦ࠻߇ᄢ߈޿ࠛ࡞ࡏ 1 ߩ㧘߹ߚ㧘ࠛ࡞ࡏ 1 ᷫ⡺⹜㛎૕㧔3D_C02㧕߅ࠃ߮ࠛ࡞ࡏ 2 ᷫ⡺⹜㛎૕㧔3D_C03㧕ߢ

Elbow deformation angle [deg]ഠൻ᧦ઙߣᔕ╵୯ߩ㑐ଥታ㛎߆ࠄᓧࠄࠇߚஜో㈩▤⹜㛎૕ߩ 1 ᰴ࿕᦭ᝄേᢙߪ
2.78Hz ߢ޽ߞߚ㧚ߎࠇߦኻߒ㧘߈ⵚઃ߈⹜㛎૕ߩ࿕᦭ᝄ
േᢙߪ㧘3D_D01 ߢ 2.79Hz㧘3D_D02 ߢ 2.75Hz ߣ߶߷ஜో
⹜㛎૕ߣห╬ߣߥߞߚ㧚৻ᣇ㧘ࠛ࡞ࡏ 1 ᷫ⡺⹜㛎૕ߩ࿕᦭ᝄേᢙߪ 2.55Hz㧘ࠛ࡞ࡏ 2 ᷫ⡺⹜㛎૕ߪ 2.62Hz㧘ࠛ࡞ࡏ2ࡩᚲᷫ⡺⹜㛎૕ߩ࿕᦭ᝄേᢙߪ2.42Hzߣߥࠅ㧘ஜో⹜㛎૕ߩ࿕᦭ᝄേᢙߦᲧߴ㧘ߘࠇߙࠇ⚂ 8%㧘6%㧘13% ૐਅߒߚ㧚ߎࠇࠄߩ⚿ᨐ߆ࠄ㧘߈ⵚ߇ሽ࿷ߒߡ߽㈩▤♽ߩ࿕᦭ᝄേᢙߦߪ߶ߣࠎߤᓇ㗀߇⃻ࠇߥ޿߇㧘ᷫ⡺߇ሽ࿷ߔࠆߣ
♽ߩ࿕᦭ᝄേᢙ߇ૐਅߔࠆߎߣ߇ࠊ߆ߞߚ㧚߹ߚ㧘ߎߩ࿕᦭ᝄേᢙߩૐਅഀวߪᷫ⡺ߩ⒟ᐲ㧔ᧄታ㛎ߩ႐วߪᷫ⡺ߩ୘ᢙ㧕ߦଐሽߒߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚ᧄታ㛎ߢߪࠛ࡞ࡏ
1㧘2 ࠍߘࠇߙࠇᷫ⡺ߐߖߚ⹜㛎૕ࠍ૶↪ߒߡᝄേታ㛎ࠍታᣉߒߚ߇㧘ᷫ⡺ࠛ࡞ࡏߩሽ࿷૏⟎ߣ࿕᦭ᝄേᢙߩૐਅ
₸ߦ㗼⪺ߥ㆑޿ߪ⃻ࠇߥ߆ߞߚ㧚ߎࠇߪ㧘੹࿁૶↪ߒߚ⹜㛎૕ߩࠛ࡞ࡏ 1 ߣࠛ࡞ࡏ 2 ߢߪ㧘ߘࠇߙࠇߩ㕙ౝᦛߍ೰ᕈ
߇⹜㛎૕ߩࡕ࡯࠼೰ᕈߦਈ߃ࠆᓇ㗀ߦᄢ߈ߥᏅ߇ߥ޿ߚ
߼ߣ⠨߃ࠄࠇࠆ㧚࿑ߦ┙૕㈩▤♽⹜㛎૕ߩ౉ജടㅦᐲߣࠛ࡞ࡏ
3 ߩ૏⟎ߦ߅ߌࠆᔕ╵ടㅦᐲߩ㑐ଥࠍ␜ߔ㧚౉ജടㅦᐲ
400Gal એ਄ߩᒢ႟ᕈ࡟ࡌ࡞ടᝄߢߪ㧘౉ജടㅦᐲߩჇട
₸ߦኻߒᔕ╵ടㅦᐲߩჇട₸߇ૐߊߥࠆ௑ะ߇⹺߼ࠄࠇ
ߚ㧚ߎࠇߪ㧘⹜㛎૕ߩ৻ㇱߦ႟ᕈᄌᒻ߇⊒↢ߒ㧘ߘࠇߦ઻޿ᝄേࠛࡀ࡞ࠡ࡯߇ᶖ⾌ߐࠇߚߚ߼ߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘ห৻ߩ౉ജടㅦᐲߦኻߔࠆᔕ╵ടㅦᐲߩ࡟ࡌ࡞ࠍ⹜㛎૕㑆ߢᲧセߔࠆߣ㧘߈ⵚઃ߈⹜㛎૕ߢߪஜో⹜㛎૕ߣ߶߷
ห⒟ᐲߢ޽ࠆ߇㧘ࠛ࡞ࡏࠍᷫ⡺ߐߖߚ⹜㛎૕ߢߪஜో⹜
㛎૕ߩᔕ╵ടㅦᐲߦᲧߴૐ޿୯ߣߥߞߚ㧚ᷫ⡺⹜㛎૕ߦ߅ߌࠆᔕ╵ടㅦᐲߩஜో⹜㛎૕ߦኻߔࠆૐਅഀวߪ㧘࿕᦭ᝄേᢙߩૐਅߣห᭽ᷫ⡺ߩ⒟ᐲߦଐሽߒ㧘ᷫ⡺ߩሽ࿷૏⟎ߦࠃࠆ㆑޿ߪ⃻ࠇߥ߆ߞߚ㧚ታ㛎ߢߪ㧘శቇᑼਃᰴరᄌ૏⸘ࠍ૶↪ߒߡᝄേบᄖㇱ߆ࠄࠛ࡞ࡏ3ߩ૏⟎ߦ߅ߌࠆ⛘ኻᄌ૏ࠍ᳞߼ߚ㧚ߎߩ⸘᷹⚿ᨐߦࠃࠆടᝄᣇะᄌ૏ࠃࠅᝄേบ౉ജᄌ૏ߩᏅࠍߣߞ
ߚ߽ߩ߇ࠛ࡞ࡏ3૏⟎ߦ߅ߌࠆᝄേบߦኻߔࠆ⹜㛎૕ߩ⋧࿑  ౉ജടㅦᐲ㧙ࠛ࡞ࡏᄌᒻⷺᲧ㑐ଥ
Fig. 3.2.2-12 Relation between input acc. and ratio of elbow
deformation.

− 3344 −10

4ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ߪ㧘ߘࠇߙࠇᷫ⡺ࠛ࡞ࡏߩᄌᒻ߇ᄢ߈ߊߥߞߡ޿ߊ㧚৻ᣇ㧘2ࡩᚲߩࠛ࡞ࡏࠍᷫ⡺ߐߖߚ⹜㛎૕㧔3D_C01㧕ߢߪ㧘౉ജടㅦᐲ 700Gal ߩടᝄߢᄌᒻⷺᲧ߇ࠊߕ߆ߦჇടߒߚ
޽ߣ㧘1400Gal ߅ࠃ߮ 1850Gal ߩടᝄߢߪ㧘ᒢ႟ᕈ࡟ࡌ࡞
ߩടᝄߦ઻޿ᄌᒻⷺᲧ߇ᷫዋߔࠆ௑ะ㧘ߔߥࠊߜࠛ࡞ࡏ1ߦኻߔࠆࠛ࡞ࡏ 2 ߩᄌᒻ㊂߇⋧ኻ⊛ߦᄢ߈ߊߥࠆ௑ะߣ
ߥߞߚ㧚ߎࠇࠄߩᄌᒻⷺᲧߩᄌൻߪ㧘ᒢ႟ᕈᔕ╵ᤨߦߪ⹜㛎૕ߩᝄേᔕ╵ᒻ⁁߇ᒢᕈၞߦ߅ߌࠆᔕ╵ᒻ⁁߆ࠄᄌൻߒ㧘㈩▤♽ౝߢᦨ߽႟ᕈൻߒ߿ߔ޿ㇱಽߦᄌᒻ߇㓸ਛߒߡ޿ߊߎߣࠍ␜ߒߡ޿ࠆ㧚3D_C01 ߢߪࠛ࡞ࡏ 2 ߩᄌᒻ㊂߇Ⴧടߔࠆ௑ะ߇⃻ࠇߚ߇㧘ߎࠇߪ㧘ᧄታ㛎ߢታᣉߒߚᒢ
႟ᕈ࡟ࡌ࡞ߩടᝄߦࠃࠆᝄേᔕ╵ߢ㧘⹜㛎૕ߩࠛ࡞ࡏ1߇
⩄㊀ߩ㒢⇇ὐߦ㆐ߒ㧘⹜㛎૕ౝߢ⩄㊀ಽᜂߩᄌൻ߇⿠ߎ
ࠅ㧘ࠛ࡞ࡏ2ㇱಽߩ⽶ᜂߔࠆ⩄㊀߇Ⴧടߒߚߚ߼ߢߪߥ޿
߆ߣ⠨߃ࠄࠇࠆ㧚࿑  ߦ␜ߒߚࠃ߁ߦ㧘3D_C02 ߅
ࠃ߮3D_C03ߩᷫ⡺ࠛ࡞ࡏߦߟ޿ߡ㧘ᒢ႟ᕈ࡟ࡌ࡞ߩ㐿㐽ᄌᒻⷺ▸࿐ߪ3D_C01ߩࠛ࡞ࡏߣห⒟ᐲߢ޽ࠅ㧘ߎࠇࠄߩࠛ࡞ࡏ߽⩄㊀ߩ㒢⇇ὐߦ㆐ߒߚน⢻ᕈ߇޽ࠆ㧚ߒ߆ߒ㧘ߎࠇࠄߩ⹜㛎૕ߢߪ৻ᣇ߇೰ᕈߩ㜞޿ஜోࠛ࡞ࡏߢ޽ࠆߚ
߼㧘ᄌᒻⷺᲧߦᓇ㗀߇⃻ࠇࠆ߶ߤߩᄢ߈ߥ⩄㊀ಽᜂߩᄌൻ߇↢ߓߥ߆ߞߚߣ⠨߃ࠄࠇࠆ㧚ࠛ࡞ࡏߩᄖᓘᄌൻ
ஜో⹜㛎૕߅ࠃ߮ᷫ⡺⹜㛎૕ߢߪ㧘⹜㛎ߩ೨ᓟߦ߅޿
ߡࠛ࡞ࡏ 1 ߅ࠃ߮ࠛ࡞ࡏ 2 ߩᄖᓘࠍ⸘᷹ߒߚ㧚⸘᷹૏⟎ߪࠛ࡞ࡏߩਛᄩᢿ㕙㧔ࠛ࡞ࡏߩᆎὐ߆ࠄ 45qߩ૏⟎㧕ߢ޽ࠆ㧚ฦ⹜㛎૕ߩᄖᓘᄌൻ₸ࠍ࿑ߦ␜ߔ㧚࿑ ߢ㧘٤ߪࠛ࡞ࡏ 1 㕙ౝᣇะ㧘‫ ࡏ࡞ࠛߪغ‬1 㕙ᄖᣇะ㧘ٌߪࠛ࡞ࡏ 2 㕙ౝᣇะ㧘٠ߪࠛ࡞ࡏ 2 㕙ᄖᣇะߩᄖᓘᄌൻ₸ߢ޽ࠆ㧚߹ߚ㧘Ⴃࠅߟ߱ߒߚශߪஜోࠛ࡞ࡏࠍ㧘⊕ᛮ߈ߩශߪᷫ⡺ࠛ࡞ࡏࠍᗧ๧ߒߡ޿ࠆ㧚ߎߩ࿑߆ࠄ㧘ࠛ࡞ࡏߪタ⩄ߦ઻޿㕙ౝᣇะߩᄖᓘ߇ᷫ
ዋߒ㧘㕙ᄖᣇะߩᄖᓘ߇Ⴧടߔࠆ௑ะ߇޽ࠆߎߣ߇ࠊ߆
ࠆ㧚ߎࠇߪࠛ࡞ࡏਛᄩㇱ߇㕙ᄖᣇะࠍ㐳ゲߣߒߚᬦ౞ᒻ
ߦ஍ᐔൻߒߡ޿ࠆߎߣࠍ␜ໂߒߡ޿ࠆ㧚ᷫ⡺ࠛ࡞ࡏߢߪ㧘
3D_C01 ߩࠛ࡞ࡏ 1 ߩࠃ߁ߦ㕙ౝᣇะ࡮㕙ᄖᣇะߣ߽ߦᄖ
ᓘ߇Ⴧടߔࠆ߽ߩ߽޽ࠆ߇㧘ߎࠇߪᢿ㕙ߩ஍ᐔൻߦ࡜
࠴ࠚ࠶࠻ᄌᒻ߇㊀⇥ߔࠆߚ߼ߣ⠨߃ࠄࠇࠆ㧚៊்ߒߚࠛ
࡞ࡏߣ៊்ߒߥ߆ߞߚࠛ࡞ࡏߣߢߪ៊்ߒߚࠛ࡞ࡏߩᣇ
߇ᄖᓘᄌൻ₸߇ᄢ߈ߊߥࠆ௑ะ߇޽ࠆ߇㧘․ߦ ᣇߩࠛ࡞ࡏߩߺᷫ⡺ߒߚ 3D_C02 ߅ࠃ߮ 3D_C03 ߢߪ㧘ஜోࠛ࡞ࡏߦߪ߶ߣࠎߤᄖᓘᄌൻ߇ߥߊ㧘ᷫ⡺ࠛ࡞ࡏ߇⪺ߒߊᄌᒻߔࠆ௑ะ߇޽ࠆ㧚៊்ߒߚࠛ࡞ࡏߩᦨ⚳⊛ߥ㕙ᄖᣇะߩᄖᓘჇട₸ߪ㧘ஜోࠛ࡞ࡏߢ⚂ 3%㧘ᷫ⡺ࠛ࡞ࡏߢߪ⚂10 㨪 12% ߣߥߞߚ㧚࿑  ߦ⹜㛎૕ 3D_C01 ߩᒢ႟ᕈ࡟ࡌ࡞ടᝄ 1 ࿁⋡㧔౉ജടㅦᐲ 700Gal㧕ߦ߅ߌࠆ౉ജടㅦᐲ㧘ࠛ࡞ࡏ 1 ߩࠛ࡞ࡏ㐿㐽ᄌᒻⷺ㧘ࠛ࡞ࡏ  ⣁஥஥㕙㧔S047 ஥㧕ߦ߅ߌࠆ๟ᣇะ߭ߕߺߩᤨೞᱧᵄᒻࠍ␜ߔ㧚࿑߆ࠄ㧘ࠛ࡞ࡏㇱಽߢ߭ߕߺ߇⪺ߒ޿࡜࠴ࠚ࠶࠻⃻⽎ࠍ␜ߒߡ޿ࠆߎߣ߇ࠊ߆
ࠆ㧚߹ߚ㧘࡜࠴ࠚ࠶࠻߭ߕߺߩჇടߪ㧘ⷐ⚛⹜㛎ߩ࡜ࡦ࠳ࡓᝄ᏷ᵄߦࠃࠆタ⩄ߣห᭽㧘ᝄേᔕ╵ਛᓢ‫⚥ߦޘ‬Ⓧߒߡ
޿ߊߩߢߪߥߊ㧘ࠛ࡞ࡏ㐿㐽ᄌᒻⷺߩᄢᝄ᏷ㄭறߢᢙ࿁
ߦࠊߚߞߡ⊒↢ߒ㧘ߘߩઁߩㇱಽߢߪ߭ߕߺᝄേᚑಽߩ
ߺ߇↢ߓߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚A cc. [G al]

10 00

10

0

20

T ime[s] 40

60

80

60

80

D01 [rad]

0.04

-5

-15

0
-500

(a) Input acceleration.

0

-10

500

-10 005

Elbow 1 In plane
Elbow1 O ut of plane
Elbow 2 In plane
Elbow2 O ut of plane
3D _A01

3D_C01

0.02
0
-0.02
-0.04

0

20

T ime[s] 40(b) Elbow deformation angle of Elbow 1.
3D_C02

3D_C03

N ame of specimen࿑  ┙૕㈩▤♽⹜㛎૕ߩ࡜࠴ࠚ࠶࠻ᄌᒻ㊂
Fig. 3.2.2-13 Ratio of ratchet deformation of 3D piping systemmodels.

1.5 104

1 10

4Strain [micro]

Ratio of ratchet deformation [%]

15

5000
0
-5000

0

20

Time[s] 406080(c) Hoop strain at S047 (Elbow 1, side surface).
࿑  ᷫ⡺ࠛ࡞ࡏ஥㕙ߩ๟߭ߕߺߦ߅ߌࠆ࡜࠴ࠚ࠶࠻
᜼േ
Fig. 3.2.2-14 Ratcheting behavior of hoop strain at side surface ofthinned wall elbow.

− 3355 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬ ㈩▤ⷐ⚛ߦኻߔࠆ⹦⚦⸃ᨆ

EC04 ߦߪr35mm ߩ࡜ࡦ࠳ࡓᝄ᏷ᵄࠍ㧘EC05㧘EC06㧘 ᧄ┨ߩ⋡⊛෸߮᭴ᚑ

EC08 ߦ߅޿ߡߪr35mm ߩᱜᒏᵄࠍਈ߃ߡ޿ࠆ㧚ߎߎߢᧄ┨ߢߪ㧘㈩▤ⷐ⚛ߦኻߒߡታᣉߒߚ⹦⚦⸃ᨆߦߟ޿

ᱜᒏᵄߣ࡜ࡦ࠳ࡓᝄ᏷ᵄߩᒻ⁁ࠍ࿑  ߦ␜ߔ㧚߹ߚᷫ⡺ᷓߐߦ㑐ߒߡ߽⇣ߥࠅ EC02 ෸߮ EC04㨪EC06 ߦ߅ߡㅀߴࠆ㧚⸃ᨆߩ⋡⊛ߪ㧘ᰳ㒱㧔ᷫ⡺࡮߈ⵚ㧕ࠍ᦭ߔࠆ㈩▤ߦኻ޿ߡߪ㧘ᦨᄢᷫ⡺ᷓߐ߇⡺ෘߩඨಽߢ޽ࠅ㧘EC07 ߦ߅ߒߡ᦭㒢ⷐ⚛ᴺߦࠃࠆᒢ႟ᕈ⸃ᨆࠍ↪޿㧘ታ㛎ߢᓧࠄࠇ޿ߡߪᦨᄢᷫ⡺ᷓߐ߇⡺ෘߩ 75㧑㧘EC08 ߪᦨᄢᷫ⡺ᷓߚ⚿ᨐߣᲧセߔࠆߎߣߦࠃࠅ㧘ታ㛎ࠍ޽ࠆ⒟ᐲ߹ߢౣ⃻ߐ߇⡺ෘߩ 25㧑㧘EC09 ߪᦨᄢᷫ⡺ᷓߐ߇⡺ෘߩ 60㧑ߣߢ߈ࠆࠪࡒࡘ࡟࡯࡚ࠪࡦࡕ࠺࡞ࠍ᭴▽ߔࠆߎߣߢ޽ࠆ㧚ߒߡ޿ࠆ㧚ᷫ⡺ᒻ⁁ࠍ࿑  ߦ␜ߔ㧚ᧄ┨ߢߪታ㛎ࠍᮨᡆߒߚ⸃ᨆࡕ࠺࡞ࠍឭ᩺ߒ㧘⸃ᨆࠍߐࠄߦ᭴▽ߒߚࡕ࠺࡞ߦၮߠ޿ߚࡄ࡜ࡔ࠻࡝࠶ࠢߥ⸃ᨆ
ࠍㅢߓߡ㧘ᢿ㕙ౝߩ⹦ߒ޿ᔕജ⁁ᘒ߿߭ߕߺಽᏓ߇㈩▤ㅢߓߡ⚿ᨐߩ⠨ኤࠍⴕߥߞߚ㧚ߩᄌᒻ᜼േߦ޿߆ߦ㑐ࠊࠅ㧘ኼ๮߇ߤߩࠃ߁ߦᄌൻߔࠆ
 ⸃ᨆࡕ࠺࡞ߣ᧦ઙ

߆⠨ኤߔࠆߎߣߢ޽ࠆ㧚਄ㅀߒߚታ㛎ߦኻߒ᦭㒢ⷐ⚛ᴺࠍ↪޿⸃ᨆࠍⴕߞߚ㧚᦭㒢ⷐ⚛⸃ᨆߩ઀᭽ߣߘߩ᧦ઙߦߟ޿ߡ⸥ㅀߔࠆ㧚ᧄ┨ߩ᭴ᚑࠍએਅߦ␜ߔ㧚⸃ᨆߦ㑐ߒߡߪࡕ࠺࡞ߩ૞ᚑ෸߮ⷐ⚛ಽഀࠍⴕߥ߁ ߢߪ㧘ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ⋥▤ߦߟ޿ߡߩ⠨ኤࡊ࡝ࡊࡠ࠮࠶ࠪࡦࠣߦߪ J-VISION ࠍ㧘ታ㓙ߦ⸘▚ࠍⴕߥ߁࠰࡞ࡃ࡯ߦߪ ABAQUS ࠍ㧘⸃ᨆ⚿ᨐߩ಴ജࠍⴕߥ

ࠍ⸥ߔ㧚
╙ 2 ┨ߢㅀߴߚታ㛎ߢⴕࠊࠇߚዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ⋥▤ⷐ⚛⹜㛎ߦߟ޿ߡ㧘FEM ࠍ↪޿ߡ⸃ᨆࠍⴕ޿㧘ታ㛎߁ࡐࠬ࠻ࡊࡠ࠮࠶ࠪࡦࠣߦߪ ABAQUS POST ࠍߘࠇߙࠇ↪޿ߚ㧚⚿ᨐߣߩᲧセࠍⴕߞߚ㧚ߐࠄߦ∋ഭߣᑧᕈᶖ⠻ߩᓇ㗀ࠍᧄ⎇ⓥߢߪ㧘ߘࠇߙࠇߩ⹜㛎૕ߦߟ޿ߡ౉ജᵄᒻࠍᮨ

⠨ᘦߒߚ⎕უ⹏ଔᚻᴺࠍ↪޿ࠆ੐ߢ㧘ᷫ⡺ᒻ⁁෸߮౉ജᡆߒߚ㕒⊛ߥ 3 ᰴరᒢ႟ᕈ⸃ᨆࠍ㧝ࡉࡠ࠶ࠢߕߟⴕߞߚ㧚㕒⊛ߥ 3 ᰴరᒢ႟ᕈ⸃ᨆߢ޽ࠆߩߢᤨ㑆ゲࠍήⷞߒߡ߅

ᵄߩᄌൻߦኻߔࠆ⎕უ᜼േߦߟ޿ߡ⠨ኤࠍⴕߞߚ㧚ࠅ࿑  ߦ߅޿ߡᤨ㑆ߪ㑐ଥߥߊߎߩ㗅ᐨߢᒝ೙ᄌ૏ ߢߪ㧘ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆࠛ࡞ࡏ㈩▤ߦߟ޿ߡߩߺࠍ౉ജߒߚ㧚ࡕ࠺࡞ൻߒߚ㈩▤ߪࠕࠗ࠰ࡄ࡜ࡔ࠻࡝
࠶ࠢ 20 ▵ὐⷐ⚛ࠍ↪޿㧘ᒻ⁁ߣߒߡߪኻ⒓ᕈࠍ⠨ᘦߒߡߩ⠨ኤࠍ⸥ߔ㧚ታ㛎ߢⴕࠊࠇߚ㈩▤♽ߩേ⊛ടᝄ⹜㛎ߦߟ޿ߡ㧘ߘߩ

1㧛4 ࡕ࠺࡞ࠍ૶↪ߒᄌ૏೙ᓮߢ⸃ᨆߒߚ㧚߹ߚౝ࿶ߦߟ

㈩▤♽ߩࠛ࡞ࡏㇱߩߺࠍⷐ⚛⊛ߦขࠅߛߒ㧘FEM ࠍ↪޿޿ߡߪታ㛎ߦḰߓߚ߽ߩࠍ⽶⩄ߒ㧘ౝ࿶ߩᓇ㗀ߦࠃࠅ㈩ߡ⸃ᨆࠍⴕߞߚ㧚ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆࠛ࡞ࡏ㈩▤߇㧘▤߇⤘ࠄࠎߢ߆ࠄᒝ೙ᄌ૏ࠍਈ߃ࠆࠃ߁ߦߒߚ㧚ⷐ⚛ᢙᦛߍ⩄㊀ߦࠃߞߡߤߩࠃ߁ߦ⎕უߦ⥋ࠆ߆ࠍ⠨ኤߒߚ㧚

ߪ 1104㧘▵ὐᢙߪ 6041 ߢ޽ࠅ㧘࿑  ߦ␜ߔㅢࠅ㈩▤ᢿ㕙ߦㄭߠߊߦߟࠇಽഀⷐ⚛߇⚦߆ߊߥࠆࠃ߁ߦߒߚ㧚 ߢߪ㧘⴫㕙߈ⵚࠍ᦭ߔࠆ㈩▤ߦߟ޿ߡ㧘࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ࠍ↪޿ߚ FEM ⸃ᨆࠍⴕ߁੐ߢ㧘߈ⵚㅴዷ࡮

ߎߎߢߪ࿑  ߦ߅޿ߡᏀ࿑ߩฝ஥ࠍ࿕ቯߒ㧘Ꮐ஥ߩ⍫ශߦᄌ૏ࠍਈ߃ࠆᒻߣߥࠆ㧚ᒢ႟ᕈ⸃ᨆߦ૶↪ߒߚᑼߪ Mises ߩ㒠ફ᧦ઙߦၮߠߊ

⽾ㅢ߹ߢࠍ⸃ᨆߒߚ㧚߈ⵚᒻ⁁ߩᄌൻ߇㧘߈ⵚㅴዷߦߤ

Prandtle-Reuss ߩᑼߢ޽ࠆ㧚߹ߚ౉ജߒߚ᧚ᢱ࠺࡯࠲ߪ⒖ߩࠃ߁ߥᓇ㗀ࠍਈ߃ࠆ߆ࠍ⠨ኤߒߚ㧚േ⎬ൻೣࠍ઒ቯߒ㧘ታ㛎ߢ૶↪ߒߚ὇⚛㍑▤㧔STS410㧕
ߩනゲᒁᒛ⹜㛎ࠍ߽ߣߦ㧞⋥✢ㄭૃߒߚ߽ߩࠍ౉ജߒߚ㧚 ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⸃ᨆ⊛∋ഭ⹏ଔ 

2 ⋥✢ㄭૃࠍߔࠆ㓙㧘➅㄰ߒ⎬ൻߦࠃࠆ 2 ᰴ⋥✢ߩ௑߈㧔⋥▤㧕 ታ㛎᭎ⷐ߇㧘නゲᒁᒛ⹜㛎ࠃࠅ㜞ߊߥࠆ੐߇ ᔨߐࠇࠆὑ㧘ታ㛎ᧄ▵ߢᛒ߁⸃ᨆࡕ࠺࡞ߪ㧘 ߢㅀߴߚⷐ⚛⹜㛎ߢ૶↪

⚿ᨐߣᾖળߒߥ߇ࠄ 2 ᰴ൨㈩ࠍ᳿ቯߒߚ㧚ߘߩࠣ࡜ࡈࠍ

ߒߚᷫ⡺⹜㛎૕ߢ޽ࠆ㧚ᧄ┨ߢߪ⎇ⓥߩ╙৻ᱠߣߒߡ⚻࿑  ߦ␜ߔ㧚ߎߩ᧚ᢱࡕ࠺࡞ߪᭂૐࠨࠗࠢ࡞ߩታ㛎ᐕഠൻࠍᐞ૗ቇ⊛ߥዪᚲᷫ⡺ߢࡕ࠺࡞ൻߒߡ⸃ᨆࠍⴕߞ

㧔100 ࠨࠗࠢ࡞એਅ㧕ߦߪ㕖Ᏹߦ৻⥌ߒߚ௑ะ߇⷗ࠄࠇ㧘ߚ㧚ଏ⹜᧚ߪᄖᓘ 114.3mm㧘⡺ෘ 8.6mm ߩ὇⚛㍑㈩▤ㅒߦߘࠇએ਄ߩ㜞ࠨࠗࠢ࡞ߦߪ৻⥌߇㔍ߒ޿㧚ਔᣇߩᔕ(STS410)ߢ㧘ౝ஥ో๟ߦࠊߚߞߡᯏ᪾ടᎿߦࠃࠅᷫ⡺߇ജ࡟ࡌ࡞ߦኻߒ৻⥌ߐߖࠆߦߪ㧘2 ⋥✢ㄭૃߢߪ࿎㔍ߢᣉߐࠇߡ޿ࠆ㧚ߎߩ὇⚛㍑▤ߦ EC02 ෸߮ EC04㨪EC09޽ࠆߩߢ੹ᓟᄙ⋥✢ㄭૃࠍ↪޿ࠆ੐߇ᔅⷐߢ޽ࠆ㧚߹ߢߩ⹜㛎૕⇟ภࠍઃߌ౉ജᵄ㧘ౝ࿶㧘ᷫ⡺㊂ߩ᧦ઙࠍ ߹ߚ‫⚻ޔ‬ᐕഠൻߦ઻߁᧚⾰ᄌൻߩᓇ㗀ߦߟ޿ߡߪ㧘੹ߘࠇߙࠇᄌ߃ߡታ㛎ࠍⴕߞߡ޿ࠆ㧚࿑  ߦ੹࿁ⴕࠊ

࿁ߩ⸃ᨆߢߪ⠨ᘦߒߡ޿ߥ޿㧚ࠇߚ⹜㛎ⵝ⟎ߩᒻ⁁෸߮ኸᴺࠍ␜ߔ㧚߹ߚ⴫  ߦฦ⹜㛎૕ߩ⹜㛎᧦ઙ෸߮⚿ᨐࠍ␜ߔ㧚⴫ߦ߽޽ࠆࠃ߁ߦ
EC02㧘EC07㧘EC09 ߪ⩄㊀ὐᄌ૏r25mm ߩᱜᒏᵄࠍ㧘

− 36

−

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

1200
True Stress (MPa)

1000
800
600
400
200
0
0

࿑  FEM ⸃ᨆߦ↪޿ߚࡔ࠶ࠪࡘ࿑
Fig.4.2-1 Finite element mesh subdivision.

0.1

0.2
0.3
Natural strain

0.4

0.5

࿑ ⸃ᨆߦ↪޿ߚ᧚ᢱቯᢙ
Fig.4.2-2 Material property for the analysis.

 ታ㛎⚿ᨐߣ⸃ᨆ⚿ᨐߩᲧセᧄ⎇ⓥߢߪ߹ߕታ㛎ߣ⸃ᨆࠍᲧセߔࠆߎߣߢ⸃ᨆߩା

ߒ߆ߒਛ┙㕙਄ߩ 0q෸߮ 180qߢߪᄖᓘߩჇട෸߮

㗬ᕈߦߟ޿ߡ⹏ଔࠍⴕ߁㧚㧣ߟ޽ࠆ⹜㛎૕ߩ߁ߜ㧘EC05⡺ෘߩᷫዋߪߘࠇ⒟㗼⪺ߢߪߥߊ㧘ߎࠇߪਛ┙㕙ߦ߅޿ࠍ଀ߦ᜼ߍ㧘ᄌᒻߩᲧセ࿑ࠍ࿑ 㧔Ꮐ࿑߇⸃ᨆ㧘ฝߡߪゲᣇะߩ➅ࠅ㄰ߒᄌᒻ߇ή޿ὑߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚࿑߇ታ㛎㧕ߦ␜ߔ㧚࿑ਛߩǰ=90q㧙270qߪ 90qߣ 270q

৻ᣇ㧘ታ㛎⚿ᨐߪ౞๟ᣇะߩ 90q෸߮ 270q㧘0q෸߮ߩᢿ㕙ࠍឬ౮ߒߡ޿ࠆ੐ࠍ␜ߔ㧚ቯ㊂⊛ߥᢙ୯ߩᲧセߪ

180qߣ߽৻᭽ߦᄖᓘߩჇടࠍ␜ߒߡ߅ࠅ㧘࡜࠴ࠚ࠶࠻⃻࿑  ߦ߅޿ߡ␜ߔ߇㧘ਔ࿑ߦ߅޿ߡ࡜࠴ࠚ࠶࠻ᄌᒻ

⽎ߪ᣿⏕ߦ␜ߐࠇߡ޿ࠆ߽ߩߩቯ㊂⊛ߦߪ⸃ᨆ⚿ᨐߣ⧯߇㗼⪺ߦ⴫ࠇߡ޿ࠆ੐߇ⷰኤߐࠇࠆ㧚߹ߚ㧼-Ǭࠞ࡯ࡉࠍᐓ⇣ߥߞߡ޿ࠆ㧚ታ㛎ߩ⸘᷹߇㧝ࡉࡠ࠶ࠢߩ➅ࠅ㄰ߒߩ࿑  ߦ␜ߔ㧚ߐࠄߦ࿑  ߦߪ⩄㊀ὐ෻ജ㧙ࠨࠗ⚳ੌᓟߦⴕࠊࠇߚߎߣ㧘߹ߚߘߩᤨὐߢߪ߈ⵚߩ⊒↢߇ࠢ࡞ᢙߩࠣ࡜ࡈࠍ␜ߔ㧚ታ㛎ߢߪ 20 ࠨࠗࠢ࡞૏ߢ෻ജ୯

⹺߼ࠄࠇߚߎߣߥߤ߆ࠄታ㛎ߣ⸃ᨆߣߢቢోߦኻᔕߔࠆ

߇ᕆỗߦૐਅߒߡ޿ࠆߩߢ㧘⸃ᨆߪ 20 ࠨࠗࠢ࡞߹ߢߩ⸘Ყセߦߥߞߡ޿ߥ޿੐߇ߘߩℂ↱ߣߒߡ᜼ߍࠄࠇࠆ㧚▚ࠍⴕߞߚ߇㧘ታ㛎ߣ⸃ᨆࠍᲧセߔࠆߣ➅㄰ߒߩࡅࠬ࠹

߹ߚౝ࿶ߩߥ޿ࡕ࠺࡞㧔EC06㧕ߦߟ޿ߡ߽ߘߩା㗬ᕈ࡝ࠪࠬࠞ࡯ࡉ෸߮⩄㊀ὐ෻ജߦߟ޿ߡ޿ߕࠇ߽ቯᕈ⊛ߥࠍ⠨ኤߔࠆ㧚⸃ᨆߩା㗬ᕈࠍ⹏ଔߔࠆὑ㧘ታ㛎ߣ⸃ᨆߩ৻⥌ࠍ␜ߒߡ޿ࠆߎߣ߇ಽ߆ࠆ㧚ߎߎߢߪ⋭⇛ߔࠆ߇ઁᄌᒻ᜼േᲧセࠍ࿑  ߦ㧘ᄖᓘᄌൻߩᲧセ෸߮⸃ᨆߩ

ߩ⹜㛎૕߽⧯ᐓߩᏅߪ޽ࠆ߽ߩߩห᭽ߩ⚿ᨐ߇ᓧࠄࠇߡ

⡺ෘᄌൻࠍ࿑  ߦ␜ߔ㧚ߎߩ㧞ߟߩ࿑߆ࠄ್ࠆࠃ߁޿ࠆ㧚ߦ㧘ታ㛎ߣ⸃ᨆ߇߆ߥࠅㄭ޿᜼േ෸߮୯ࠍ␜ߒߡ޿ࠆ㧚߹ߚታ㛎ߩ߈ⵚ⽾ㅢᤨߦ߅ߌࠆᄖᓘ⸘᷹⚿ᨐߣ⸃ᨆ⚿ᨐߩᲧセࠍ࿑  ߦ␜ߔ㧚࿑  ߦ߅޿ߡ㧘Y1 ゲߪߟ߹ࠅౝ࿶ߩ᦭ήߦ߆߆ࠊࠄߕ⸃ᨆߩା㗬ᕈߦߟ޿ߡߪ
⏕଻ߐࠇߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚ᄖᓘࠍ␜ߒ㧘Y2 ゲߪ⡺ෘࠍ␜ߒߡ޿ࠆ㧚߹ߕ⸃ᨆ⚿ᨐߦᵈ⋡ߔࠆߣ㧘➅ࠅ㄰ߒᦛߍᔕജࠍฃߌࠆㇱ૏ߢ޽ࠆ 90q
෸߮ 270qߦ߅޿ߡ⚂ 7 ࠨࠗࠢ࡞⋡޽ߚࠅ߆ࠄ㗼⪺ߥᄖᓘߩჇട෸߮⡺ෘߩᷫዋ߇␜ߐࠇߡ߅ࠅ㧘ゲᣇะߩ➅ࠅ㄰ߒᄌᒻࠍฃߌࠆ૏⟎ߢߩౝ࿶ߦࠃࠆ࡜࠴ࠚ࠶࠻⃻⽎߇↢ߓߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚

0
90
270 q
180

q

Loading
Direction(b) Experiment.

(a) Analysis(ǰ㧩90q㧙270q).
࿑ EC05 ߩᄌᒻ࿑Ყセ
Fig.4.2-3 Deformation comparison of EC05.

−

37 −

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬

100
Reaction Force (kN)

Reaction Force (kN)

100
50
0
-50

-100

50
0
-50

-100
-50 -40 -30 -20 -10 0 10 20 30 40 50
Disp. 䋨mm䋩-50 -40 -30 -20 -10 0 10 20 30 40 50
Disp. 䋨mm䋩(a) Analysis.

(b) Experiment.
࿑  EC05 ߩ P-Ǭࠞ࡯ࡉFig.4.2-4 P-Ǭof EC05100
Reaction Force (kN)

Reaction Force (kN)

100
50
0
-50

-100

50
0
-50

-100
10
15
20
Number of cycles

25

30

0

5

(a) Analysis.

10
15
20
Number of cycles(b) Experiment.

࿑  EC05 ߦ߅ߌࠆ⩄㊀ὐ෻ജጁᱧ࿑
Fig.4.2-5 Load point reaction of EC05 for Number of cycles.

5150

Wall䇭thickness (mm)5Outer diameter (mm)

0

140

4.5

130

4

120

3.5
3

110
0

5
10 15 20
Number of cycle

Outer diameter
Analysis:90°&270°
Outer diameter
Analysis:0°&180°
Outer diameter
Experiment:90°&270°
Outer diameter
Experiment:0°&180°
Wall Thickness
Analysis:90°&270°
Wall Thickness
Analysis:0°&180°

࿑  EC05 ߩࠨࠗࠢ࡞ᢙߦኻߔࠆᄖᓘ෸߮⡺ෘᄌൻFig.4.2-6 Outer diameter and wall thickness change of EC05  

Number of cycles.

−

38 −

25

30

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

0
90q
270 q
180

Loading
Direction(a) Analysis(ǰ㧩90º㧙270º).

(b) Experiment.

࿑ EC06 ߩᄌᒻ࿑Ყセ
Fig.4.2-7 Deformation comparison of EC06.

5Wall䇭thickness (mm)Outer diameter (mm)

125
115

4.5

105

4

95

3.5

85

3
0

5
10 15 20
Number of cycle

Outer diameter
Analysis:90°&270°
Outer diameter
Analysis:0°&180°
Outer diameter
Experiment:90°&270°
Outer diameter
Experiment:0°&180°
Wall Thickness
Analysis:90°&270°
Wall Thickness
Analysis:0°&180°

࿑  EC06 ߩࠨࠗࠢ࡞ᢙߦኻߔࠆᄖᓘ෸߮⡺ෘᄌൻFig.4.2-8

Outer diameter and wall thickness change of EC06
for Number of cycles.

ߔ㧚ߎࠇࠄߩ࿑߆ࠄએਅߩߎߣ߇⸒߃ࠆ㧚 ᷫ⡺㈩▤ߩ߈ⵚ⊒↢ࡔࠞ࠾࠭ࡓߣ⎕უ᜼േ೨▵ߢ⸃ᨆߩା㗬ᕈࠍ⹏ଔߒߚ EC05 ࠍ߹ߕ଀ߦߣߞ

(1) ➅ࠅ㄰ߒߩㅴⴕߣ౒ߦ౞๟ᣇะߩᐔဋ߭ߕߺߪჇᄢ
ߒ㧘ඨᓘᣇะߩᐔဋ߭ߕߺߪᷫዋߔࠆ㧚ߎࠇߪ࿑ߡ㧘ߘߩ⎕უࡔࠞ࠾࠭ࡓࠍ⠨ኤߔࠆ㧚
EC05 ߩ ㈩ ▤ ᢿ 㕙 ߢ ߩ ⋧ ᒰ ႟ ᕈ ߭ ߕ ߺ ಽ Ꮣ ࿑ ࠍ ࿑ ߦ߅޿ߡ␜ߐࠇߚ 90qߩㇱ૏ߦ߅ߌࠆ㗼⪺ߥ ߦ␜ߔ㧚࿑ߦ߅޿ߡ⦡߇Ớߊߥࠆߦߟࠇߡ⋧ᒰ႟ᄖᓘߩჇട෸߮⡺ෘߩᷫዋߦኻᔕߒߡ߅ࠅ㧘ߎߩㇱᕈ߭ߕߺ߇ᄢ߈ߊߥࠆ㧚࿑ਛߩᢙ୯ߪ㧘➅ࠅ㄰ߒ⩄㊀ࠍಽߢ࡜࠴ࠚ࠶࠻ᄌᒻ߇↢ߓߡ޿ࠆ੐ࠍ␜ߒߡ޿ࠆ㧚ฃߌࠆߔߴߡߩጁᱧߦኻߔࠆ⋧ᒰ႟ᕈ߭ߕߺჇಽߩ✚๺ߒߚ߇ߞߡᧄ⸃ᨆߢߪ࡜࠴ࠚ࠶࠻ᄌᒻߦኻߔࠆ․೎

ߢ޽ࠆὑ㧘㕖Ᏹߦᄢ߈ߥ୯ߣߥߞߡ޿ࠆ㧚ߎߩࠃ߁ߦቯ

ߥ઒ቯࠍⴕߞߡ޿ߥ޿ߦ߽߆߆ࠊࠄߕ৻⥸⊛ߥᒢ႟⟵ߐࠇߚ⋧ᒰ႟ᕈ߭ߕߺߪ㧘∋ഭߦࠃࠆ࠳ࡔ࡯ࠫࠍ੍᷹

ᕈߦ㑐ߔࠆ᭴ᚑᑼࠍ↪޿ߡ࡜࠴ࠚ࠶࠻ᄌᒻ߇⴫⃻ߢߔࠆ৻ߟߩ⋡቟ߣߥࠆ੐߇⠨߃ࠄࠇࠆ㧚ߎߩ࿑߆ࠄ⠨ኤ߈ࠆ੐ࠍ␜ߒߡ޿ࠆ㧚ߢ߈ࠆߎߣߪ㧘㈩▤ਛᄩᢿ㕙ߩౝოㇱὐ B ߦ߭ߕߺ߇㓸(2) 㧟ᣇะߩ߭ߕߺᝄ᏷ߩਛߢゲᣇะߩ߭ߕߺᝄ᏷߇ᦨ

ਛߒߡ޿ࠆߎߣߢ޽ࠆ㧚ታ㛎ߢ߽ߎߩㇱಽ߆ࠄ߈ⵚ߇⊒߽ᄢ߈޿㧚ታ㛎ߦ߅޿ߡ㧘㧮ὐㄭற߆ࠄ౞๟ᣇะߦ

↢ߒߡ߅ࠅߘߩ㧟ᣇะߩ߭ߕߺࠍᵈᗧᷓߊⷰࠆᔅⷐ߇޽

߈ⵚ߇⊒↢ߒߡ޿ࠆߩߪߎߩゲᣇะߩ߭ߕߺᝄ᏷ߦ
ࠃࠆ߽ߩߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚ࠆ㧚࿑  ߪ B ὐߦ߅ߌࠆ㧟ᣇะߔߥࠊߜゲᣇะ㧘౞(3) ඨᓘᣇะ෸߮౞๟ᣇะߩ߭ߕߺᝄ᏷ߩ૏⋧ߪゲᣇะ๟ᣇะ෸߮ඨᓘᣇะߩ➅ࠅ㄰ߒ߭ߕߺߩ᜼േࠍ␜ߔ㧚߹ߩ߭ߕߺᝄ᏷ߩ૏⋧ߣቢోߦㅒォߒߡ޿ࠆ㧚ߎࠇߪߚ࿑  ߪหߓὐߩኻᔕߔࠆ➅ࠅ㄰ߒᔕജ᜼േࠍ␜

➅ࠅ㄰ߒᦛߍߦࠃࠅ߹ߕゲᣇะߦᄢ߈ߥ߭ߕߺ߇↢

−

39 −

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬ߓ㧘ඨᓘᣇะ෸߮౞๟ᣇะߩ߭ߕߺߪゲᣇะ߭ߕߺ ߐࠄߦߎߩዪᚲ⊛ߦੑߟߩᦛߍ߇⿠ߎࠆ⃻⽎ߪᷫ⡺ᒻߦኻߒߡࡐࠕ࠰ࡦലᨐߦࠃࠅ↢ߓߡ޿ࠆߚ߼ߢ޽ࠆ

⁁߇หߓߢr25mm ߩᱜᒏᵄࠍਈ߃ߡ޿ࠆ EC02 ߦ߽ᒰߣ⠨߃ࠄࠇࠆ㧚ߡߪ߹ࠆ㧚ߟ߹ࠅߎࠇࠄߩࡕ࠺࡞ߢߪὐ B ߦ߅޿ߡゲᣇߐࠄߦ㈩▤ߩਛᔃㄭறߦߟ޿ߡ㧘ὐ B ࠍ฽߼ߡ⠨ኤࠍะߩ߭ߕߺᝄ᏷߇ᦨᄢߣߥࠅ㧘਄ㅀߒߚࠃ߁ߥ▤ో૕ߣⴕ߁㧚࿑  ߦ߅ߌࠆὐ A㨪ὐ D ߦ߅޿ߡゲᣇะߩ߭ዪᚲ⊛ߥᦛߍߩࡔࠞ࠾࠭ࡓߦࠃߞߡὐ B ߦ๟ᣇะߦ߈ⵚߕߺࠍᲧセߒߚ߽ߩࠍ࿑  ߦ␜ߔ㧚ὐ B ߇⧯ᐓߩ߇౉ࠆ߽ߩߣ⠨߃ࠄࠇࠆ.EC06 ࠍ㒰ߊోߡߩࡕ࠺࡞ߦ߅

࿶❗ߩᐔဋ߭ߕߺߢᄢ߈ߥᝄ᏷ࠍ଻ߟߩߦኻߒ㧘หߓ㈩޿ߡߩ⎕უࡔࠞ࠾࠭ࡓߪ㧘EC05 ߩᒻᘒߦㅊ㓐ߔࠆ㧚▤ਛᄩᢿ㕙ߢ޽ࠅᄖო஥ߩὐ A ߦ߅޿ߡߪ 10 ࠨࠗࠢ࡞ߣߎࠈ߇ౝ࿶ߩߥ޿ EC06 ߦ㑐ߒߡߪ߹ߞߚߊ⇣ߥࠆ㧔⩄㊀ὐᄌ૏߇r35mm ߩቯᏱߦߥࠆࠨࠗࠢ࡞ᢙ㧕૏ߢ⎕უᒻᘒߣߥࠆ㧚EC06 ⹜㛎૕߇ 20 ࠨࠗࠢ࡞ߩടᝄࠍ⚳ᒁᒛࠅߦォߓ㧘߭ߕߺᝄ᏷߽ᓢ‫ߦޘ‬ᷫዋߒߡ޿ߊ㧚ߎࠇ߃ߚᤨὐߩ⋧ᒰ႟ᕈ߭ߕߺߩಽᏓ࿑ࠍ࿑  ߦ␜ߔ㧚ߪ㈩▤߇⤘ࠄ߻ߦߟࠇᒻ⁁ᄌൻߩ૞↪ߢ㧘࿑  ߦ␜ߎߩ࿑߽Ớߊߥࠆߦߟࠇߡ⋧ᒰ႟ᕈ߭ߕߺߩ୯߇ᄢ߈ߊߔ ࠃ ߁ ߦ ᢿ 㕙 㧭 㧙 㧮 ㇱ ಽ ߦ ㈩ ▤ ో ૕ ߩ ᦛ ߍ 㧔 Globalߥࠆ㧚࿑ߦ߅޿ߡ㧘ਛᄩߩ਄ਅᢿ㕙ߦ߅޿ߡዪᚲ⊛ߥᐳ

bending 㧕 ߣ ㅒ ะ ߈ ߦ ૞ ↪ ߔ ࠆ ዪ ᚲ ⊛ ߥ ᦛ ߍ 㧔 Localዮ߇⊒↢ߒߡ޿ࠆߩ߇ⷰኤߐࠇࠆ㧚ߎࠇߪࠨࠗࠢ࡞ࠍ㊀

bending㧕߇↢ߓࠆߚ߼ߢ޽ࠆߎߣ߇⠨߃ࠄࠇࠆ㧚ߎߩ㧞ߨࠆߏߣߦᢿ㕙߇஍ᐔൻߒ㧘ᦛߍ೰ᕈ߇ૐਅߒߡ㧘ᦨᓟߟߩᦛߍ૞↪߇㊀ߥࠆߎߣߦࠃࠅὐ B ߢ㕖Ᏹߦᄢ߈ߥゲߦ AB ᢿ㕙ㄭற㧔90q෸߮ 270qㄭற㧕ߢዪᚲ⊛ᐳዮࠍᣇะߩ߭ߕߺᝄ᏷߇↢ߓࠆ㧚⊒↢ߐߖࠆߦ೔ߞߚ߽ߩߣផቯߐࠇࠆ㧚߹ߚ࿑  ߦߪὐ A㨪D ߢߩゲᣇะߩ߭ߕߺጁᱧࠍ

߹ߚὐ C ෸߮ὐ D ߦ߅޿ߡߪ࠹࡯ࡄߩ㐿ᆎㇱߣ޿߁ߎߣ߽޽ࠅ㧘૗ࠄ߆ߩ⃻⽎߇޽ࠆߩߢߪߥ޿߆ߣ⠨߃ߚ߇㧘␜ߔ㧚ߎߩࠣ࡜ࡈߢ߽ὐ B ߩ૏⋧߇ 13 ࠨࠗࠢ࡞૏߆ࠄ

ὐ C ߦ߅޿ߡߪὐ A ߇ᒁᒛࠄࠇࠆᓇ㗀ߢ࿶❗஥ߦ㧘߹ߚㅒォߒߡ޿ࠆ੐߇ࠊ߆ࠆ㧚ߟ߹ࠅ 13 ࠨࠗࠢ࡞޽ߚࠅ߆ࠄ

ὐ D ߪὐ B ߇࿶❗ߦߥࠆᓇ㗀ߢᒁᒛࠅߦߥࠆ㧚ߟ߹ࠅ▤ᐳዮߦ߅ߌࠆᢿ㕙਄ਅㇱߩ᛬ࠇߎߺ߇ỗߒߊߥߞߚߣ⸒

ో૕ߩᦛߍߦኻߒߡὐ A㨪D ߦ߅޿ߡዪᚲ⊛ߦੑߟߩᦛ

߃ࠃ߁㧚ߘߒߡᒻ⁁ߩ૞↪߆ࠄ੹ᐲߪὐ㧭ߩゲᣇะ߭ߕߍ߇⿠ߎߞߡ޿ࠆߣ⠨߃ࠄࠇ㧘ߎߩੑߟߩᦛߍ߇㈩▤ߩߺᝄ᏷߇ᦨᄢߣߥࠅᄖ஥߆ࠄ๟ᣇะߦ߈ⵚ߇⊒↢ߒߚߎ⎕უߦኻߒᓇ㗀ࠍਈ߃ߡ޿ࠆ߽ߩߣ⠨߃ࠄࠇࠆ㧚࿑ߣ߇੍ᗐߐࠇࠆ㧚 ߪ㈩▤ਛᄩᢿ㕙਄ㇱ߇࿶❗ߐࠇߡ޿ࠆᤨߩ㧘ゲᣇะߩᔕജಽᏓࠍ␜ߔ㧚ߎߩ࿑ߦ߅޿ߡ⦡߇Ớߊߥࠆߦߟ
ࠇߡᒁᒛᔕജ߇ᄢ߈ߊߥࠆߎߣࠍ␜ߒ㧘਄ㅀߒߚࠃ߁ߦ
ੑߟߩᦛߍ߇⿠ߎߞߡ޿ࠆ㧚

B
D

Axial

Strain

C

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

A

Radial
Hoop

0

5

10
15
Number of cycle20࿑ ⋧ᒰ႟ᕈ߭ߕߺಽᏓ࿑㧔EC05㧕࿑ B ὐߦ߅ߌࠆ 3 ᣇะߩ߭ߕߺ

Fig.4.2-9 Equivalent plastic strain distribution of EC05.

Fig.4.2-10 Strain of 3directions at B point.

−

40 −

25

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

600
200

Axial

0

Radial

-200

Hoop

-400
-600
-800
0

5

10
15
Number of cycle

20

B
A
C
D

StrainStress䋨MPa䋩

400

25

0

5

10
15
Number of cycle

2025࿑  B ὐߦ߅ߌࠆ 3 ᣇะߩᔕജ࿑  ฦὐߦ߅ߌࠆゲᣇะ߭ߕߺ㧔EC05㧕

Fig.4.2-11 Stress of 3directions at B point.

Fig.4.2-12 Axial strain at each point㧔EC05㧕.

Global bending

C

B

D

Local bending
C

B

D

A

࿑  ో૕ߩᦛߍߦࠃࠆ࿶❗ᤨߩᔕജಽᏓ࿑  ⋧ᒰ႟ᕈ߭ߕߺಽᏓ࿑㧔EC06㧕

Fig.4.2-13 Axial stress in compression.

Fig.4.2-14 Equivalent plastic strain distribution of EC06.

0.3
0.2
Strain

0.1

A
B
C
D

0

-0.1
-0.2
-0.3
0

5

10
15
Number of cycle20࿑  ฦὐߦ߅ߌࠆゲᣇะ߭ߕߺ㧔EC06㧕
Fig.4.2-15 Axial strain at each point㧔EC06㧕.

−

41 −

25

A

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬ ⚥Ⓧ∋ഭ៊்ೣࠍ↪޿ߚኼ๮⹏ଔ ߪᰴᑼࠍឭ᩺ߒߡ޿ࠆ㧚Dfߕߺᝄ᏷ߦട߃㧘ᑧᕈᶖ⠻ࠍ⠨ᘦߒߚ⚥Ⓧ߭ߕߺ߇㊀K

㧔4.2.6㧕

1

Dd  D f

࡜࠴ࠚ࠶࠻ᄌᒻࠍ઻߁∋ഭ⹏ଔኼ๮ߩ੍᷹ߦߪ㧘߭n㧔4.2.7㧕

ⷐߥࡄ࡜ࡔ࡯࠲ߣ⠨߃ࠄࠇࠆ㧚ߎࠇߪ Coffin ࠄ߇ឭ໒਄ᑼߦ߅޿ߡ n ߪቯᢙࠍ␜ߔ㧚㡻ᚭญ 3)ߩ⷗⸃෸߮ᦺ

ߔࠆ⚥Ⓧ߭ߕߺߩሽ࿷ߦ઻߁ᑧᕈᶖ⠻ߩᓇ㗀ߦࠃࠅ㧘↰ 4)ࠄߩ⹜㛎⚿ᨐߦၮߠߌ߫㧘৻⥸⊛ߥ㋕㍑᧚ᢱߩ Df ߪ㧘ૐࠨࠗࠢ࡞∋ഭᒝᐲ߇ૐਅߔࠆߣ޿߁⠨߃ᣇߦၮߠ޿

Kࠍ 0.6 ਸ਼ߒߚ୯ߣߐࠇߡ޿ࠆ㧚ᦺ↰ߪ⭯⡺ㇱࠍ⸳ߌߚ㈩▤ࠍ↪޿ߚౝ࿶࡜࠴ࠚ࠶࠻∋ഭ⹜㛎ߩ⚿ᨐ߆ࠄ㧘ታ㛎⊛ߦౝ࿶ߦࠃࠆᄙゲᔕജ႐ߦ߅޿ߡߪ㧘(4.2.7)ᑼߢ᳞߼ࠄ
ࠇࠆ୯ࠃࠅૐࠨࠗࠢ࡞ኼ๮߇⍴ߊߥࠆߣߒߡ㧘ᄙゲᔕജ႐ߦ߅ߌࠆૐࠨࠗࠢ࡞࡜࠴ࠚ࠶࠻∋ഭኼ๮⹏ଔᑼߣߒߡ㧘એਅߩ 2 ߟߩታ㛎ᑼࠍឭ᩺ߒߚ㧚ߡ޿ࠆ㧚ၮᧄ⊛ߥ⠨߃ᣇߣߒߡߪ߭ߕߺᝄ᏷߆ࠄ᳞߼
ࠄࠇࠆ∋ഭ៊்ߩࡄ࡜ࡔ࡯࠲ Df ߦኻߒ㧘⚥Ⓧ߭ߕߺߩሽ࿷ߦ઻߁ᑧᕈᶖ⠻ࠍ⠨ᘦߒߚ Dd ࠍ᳞߼㧘⚥Ⓧ߭ߕߺߩሽ࿷ߦ઻߁ૐࠨࠗࠢ࡞∋ഭᒝᐲߩૐਅࠍቯ㊂⊛ߦ⹏ଔߔࠆ੐ࠍ⋡⊛ߣߒߡ޿ࠆ㧚∋ഭ៊்ߩࡄ࡜ࡔ࡯࠲ Df ߪࡑࠗ࠽࡯ೣߦᓥ߁߽ߩߣ
⠨߃ࠄࠇ㧘ߘߩ㓙㧘὇⚛㍑ STS410 ᧚ߩૐࠨࠗࠢ࡞∋ഭᦺ↰ߩታ㛎ᑼΣᦛ✢ߪ Manson-Coffin ೣ㧘෸߮ Basquin ೣ߆ࠄᰴᑼߩࠃ

3Dd  D f

߁ߦ⴫ߐࠇࠆ㧚ߎߩᑼߦᓥ߃߫ో߭ߕߺ▸࿐ǍHt ߣ⎕ᢿDd  3D f

ኼ๮ Nf ߩ㑐ଥ߇ᓧࠄࠇࠆ㧚'H t

Ce N f ke

 Cp N f

kp1

D f d 0.25

1

D f ! 0.25

㧔4.2.8㧕ᦺ↰ߩታ㛎ᑼΤ

㧔4.2.1㧕

D f  2 D f Dd  Dd

਄ᑼߦ߅޿ߡ Ce ߪᒢᕈ∋ഭᒝᐲଥᢙ㧘-ke ߪᒢᕈ∋ഭ1

㧔4.2.9㧕ᒝᐲᜰᢙ㧘Cp ߪ႟ᕈ∋ഭᒝᐲଥᢙ㧘-kp ߪ႟ᕈ∋ഭᒝᐲߥ߅㧘਄ᑼߦ߅޿ߡHf ߪ⤘ᒛߒߚ㈩▤ߩᦨ⚳⊛ߥ๟ᣇᜰᢙߢ޽ࠆ㧚ᧄ⎇ⓥߢߪᰴᑼߢ⴫ߐࠇࠆේሶജ⊒㔚ᛛะ߭ߕߺߣߒߡ޿ࠆ㧚߹ߚ㧘ࠢࡠࠬࡋ࠶࠼ߦࠃࠆ⽶⩄ᄌⴚᯏ᭴ 2)ߢ᳞߼ࠄࠇߚ὇⚛㍑ STS410 ߩቶ᷷⹜㛎ߩ⚿ᨐ૏ࠍ⭯⡺ㇱᐔⴕ㐳ߐߢ㒰ߒߚ୯ࠍో߭ߕߺᝄ᏷ߣߒߡ
Df ࠍ▚಴ߒߡ޿ࠆ㧚ߔߥࠊߜᑼ㧔4.2.7㧕෸߮(4.2.8)ߢߪ

ࠍ↪޿ࠆ੐ߣߒߚ㧚'H t

0.6158 N f

0.0746

 89.08 N f

0.5414

㧔4.2.2㧕߈ⵚ⊒↢ㇱߦ߅ߌࠆ⹜㛎૕ߩዪㇱ⊛ߥ߭ߕߺࠍ↪޿ߥ޿ࡑࠢࡠ⊛ߥᄌᒻ߆ࠄ㘃ផߒߚታ㛎ᑼߢ޽ࠆ㧚ߒߚ߇ߞߡ

਄ᑼࠍ↪޿ߚ⚿ᨐ㧘ࡑࠗ࠽࡯ೣࠃࠅ㧘ⶄᢙߩో߭ߕ

ዪᚲ⊛ߥ⌀߭ߕߺ▸࿐ࠍ⠨ኤߢ߈ࠆ FEM ⸃ᨆߦㆡ↪ߔߺᝄ᏷ǍHti ߇ߘࠇߙࠇ Ni ࿁➅ࠅ㄰ߐࠇߚ႐วߩ៊்₸ࠆߣㆊᐲߦ቟ో஥ߩ⚿ᨐߣߥࠆ੐ߪุ߼ߥ޿㧚ߒ߆ߒߥǯߪᰴᑼߦࠃߞߡ⴫ߐࠇࠆ㧚߇ࠄ࡜࠴ࠚ࠶࠻ᄌᒻߩ⠨ኤࠍⴕ߁਄ߢ㧘ᑧᕈᶖ⠻ࠍ⠨ᘦ

n

Ni

¦N

K

i 1

ߔࠆ੐߇ᄢᄌ㊀ⷐߥⷐ࿃ߢ޽ࠅ㧘Df ߦኻߔࠆ Dd ߩ୯ࠍ
㧔4.2.3㧕fi᛽಴ߔࠆ੐ߪᷫ⡺㈩▤ߩ቟ోᕈ⹏ଔߦ㕖Ᏹߦ᦭ലߢ޽ࠆ
ߣ⠨߃ࠄࠇࠆ㧚ߘߎߢ࿑  ߦౝ࿶߇⽶⩄ߐࠇߡ޿ߥ޿ EC06 ࠍ㒰਄ᑼߦ߅޿ߡ㧘⚥Ⓧ߭ߕߺ߇ή޿႐วK=1 ߦߥߞߚ޿ߚో⹜㛎૕ߦኻߒ㧘ᦨ߽ゲᣇะ߭ߕߺᝄ᏷߇㜞޿ὐ Bᤨ⎕ᢿߔࠆ㧚
߹ߚ Coffin ࠄߦࠃࠆߣᑧᕈᶖ⠻ߩࡄ࡜ࡔ࡯࠲ Dd ߪએᕈᶖ⠻ߩࡄ࡜ࡔ࡯࠲ Dd ࠍ❑ゲߦࡊࡠ࠶࠻ߒߚ Dd - Df ✢ਅߩࠃ߁ߦ⴫ߐࠇࠆ㧚
Dd

Hf
Hf0

࿑ࠍ␜ߔ㧚ߥ߅✢࿑ߦ૶↪ߒߚHf ߪ㧘ฦࠨࠗࠢ࡞ߦ߅ߌ
㧔4.2.4㧕਄ᑼߦ߅޿ߡHf ߪ⚥Ⓧ߭ߕߺ㊂㧘H f0 ߪଏ⾗᧚ߩ⌀⎕ᢿᑧᕈࠍ⴫ߔ㧚H f0 ߦߟ޿ߡߪᰴᑼߢ␜ߐࠇࠆන⺞ᒁᒛ⹜㛎ߢᓧࠄࠇࠆ⎕ᢿ⛉ࠅ M (%)ߦࠃߞߡቯ⟵ߐࠇࠆ㧚

Hf0ߦߟ޿ߡ㧘∋ഭ៊்ߩࡄ࡜ࡔ࡯࠲ Df (n=0.6)ࠍᮮゲߦ㧘ᑧln

100
100  M

㧔4.2.5㧕ߥ߅ᧄ⸃ᨆߢ↪޿ߚ⌀⎕ᢿᑧᕈ Hf0 ߩ୯ߪේሶജ⊒㔚ᛛⴚᯏ᭴ 2)ߢ᳞߼ࠄࠇߚ὇⚛㍑ STS410 ߩ᧚ᢱ⹜㛎⚿ᨐ
ࠃࠅ 112.4㧑ߣߒߚ㧚ૐࠨࠗࠢ࡞࡜࠴ࠚ࠶࠻∋ഭᒝᐲߩ⹏ଔᴺߣߒߡ Coffin−ࠆ๟ᣇะ߭ߕߺHh ߩᐔဋ୯ࠍߣߞߡ߅ࠅ㧘ฦࠨࠗࠢ࡞ߩ

Hhmax ߣHhmin ࠍ⿷ߒߡ㧘2 ߢഀߞߚ୯ߢ޽ࠆ㧚࿑ਛߦ߅޿ߡ EC05 ߅ࠃ߮ EC07 ߪ 20 ࠨࠗࠢ࡞߹ߢߩ㧘ߘߩઁߩࡕ࠺࡞ߪ 50 ࠨࠗࠢ࡞߹ߢߩടᝄߦࠃࠆ Dd-Df✢࿑ߩጁᱧߢ޽ࠆ㧚ߎߩࠨࠗࠢ࡞ᢙߪᱜᒏᵄߩẋჇ࡮ẋᷫㇱࠍ฽߻ߚ߼㧘50 ࠨࠗࠢ࡞ߢᱜᒏᵄ 1 ࡉࡠ࠶ࠢߦ⋧ᒰ
ߔࠆ㧚EC05 ߅ࠃ߮ EC07 ߦߟ޿ߡߪታ㛎ߢ⎕უߔࠆ߹ߢ
ߩࠨࠗࠢ࡞ᢙߣߒ㧘20 ࠨࠗࠢ࡞߹ߢ૶↪ߒߚ㧚࿑ਛ㧘ฦࡕ࠺࡞ߩጁᱧߪടᝄ೨ߦ Dd 㧘Df ߣ߽ 0 ࠍߣࠅ㧘ടᝄߦ઻޿ᓢ‫ߩߘߦޘ‬୯ࠍߩ߫ߒߡ޿ࠆ㧚੹࿁ߩ⸃ᨆ⚿ᨐߢ Coffin ᑼࠍḩߚߒߚ߽ߩߪ EC09 ߩߺ㧘߹ߚᦺ↰ߩታ㛎ᑼΣࠍḩߚߒߚ߽ߩߪ EC09 ෸߮
42 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

EC05 ߣߥߞߚ㧚߹ߚᦺ↰ߩታ㛎ᑼΤࠍḩߚߔ߽ߩߪ⴫  ߦታ㛎⚿ᨐߣ⸃ᨆ⚿ᨐߩᲧセᬌ⸛ࠍⴕߞߡ޿

EC05㧘EC09 ߦട߃ߡ EC07 ߣ EC02 ߇ḩߚߒߡ޿ࠆ.࿑

ࠆ㧚⴫ਛ߆ࠄࠊ߆ࠆߣ߅ࠅ Df > 0.25 ߢᑧᕈᶖ⠻ߩᓇ㗀ࠍ߆ࠄᵈ⋡ߢ߈ࠆ੐ߣߒߡ EC07㧔75㧑ᷫ⡺㧕෸߮ EC09ᦨ߽⠨ᘦߔࠆᦺ↰ߩታ㛎ᑼΤߩ⚿ᨐ߇㧘ㆊᐲߩ቟ో஥ߥ

㧔60㧑ᷫ⡺㧕⹜㛎૕ߩ Dd ୯߇ઁߩ⹜㛎૕ߦᲧߴ㜞ߊߥ߇ࠄታ㛎⚿ᨐߩ௑ะߦ⸃ᨆ⚿ᨐ߇ᦨ߽ㄭߊߥߞߡ޿ࠆߣ

ߞߡ޿ࠆ੐ߢ޽ࠆ㧚ߟ߹ࠅ⡺ෘ߇⭯޿ࡕ࠺࡞ߪ㧘࡜࠴ࠚ⠨߃ࠄࠇࠆ㧚ታ㛎ߢߪ EC07 ߇ᦨ߽ᣧߊ⎕უߦ⥋ߞߡ߅࠶࠻ߦࠃࠅᐔဋ๟ᣇะ߭ߕߺ߇㜞ߊߥࠅ㧘ߘߩಽᑧᕈᶖ

ࠅ㧘ᑧᕈᶖ⠻ߩᓇ㗀߇⦡Ớߊ಴ߡ޿ࠆ㧚⎕უࠨࠗࠢ࡞ᢙ

⠻୯߇㜞ߊߥߞߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚ታ㓙ߩታ㛎ߢ߽㧘ߩᣧ޿㗅ߦ EC07ψEC05ψEC09ψEC02 ߩ௑ะࠍᧄ⸃ᨆ

⡺ෘߩ⭯޿ࡕ࠺࡞ߪᭂ┵ߦᣧ޿࿁ᢙߢ߈ⵚ߇⽾ㅢߒߡ޿ߦ߅ߌࠆᦺ↰ߩታ㛎ᑼΤߪ㕖Ᏹߦ⦟ߊᝒ߃ߡ߅ࠅ㧘⎕უࠆ㧚ߔߥࠊߜᷫ⡺ㇱߩᷓߐߪ㈩▤ߩ⎕უ࿁ᢙߦᦨ߽ᓇ㗀ߦኻߔࠆ৻ߟߩ‛Ꮕߒߣߒߡ㧘ߎߩ Dd - Df ✢࿑߇᦭ലߢ

ࠍਈ߃ࠆࡄ࡜ࡔ࡯࠲ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚޽ࠆ੐ࠍ␜ߒߡ޿ࠆ㧚1
Coffin equation
Asada Σ0.8
Dd (=ǭ㨔/ǭf)Asada Τ

0.6

EC02

0.4

EC05

EC04
EC07
EC08

0.2

EC09

0
0

Dd ( = İ䌨 / İf )

0.2

0.2

0.4

0.6

0.8

1

0.1

0
0

0.2

0.4

0.6

0.8

1

Df ( =Ș0.6 )࿑ ฦ⹜㛎૕ߩ Dd – Df ✢࿑
Fig.4.2-16 Relation between Dd and Df.
⴫  ฦ⹜㛎૕ߩ⸃ᨆ⚿ᨐ
Table 4.2-1 Analytical result of each test specimen.

Test specimen nameThinned depth(㨙㨙)Frequency input into
the analysis
Pattern of input disp.wave
Damage rate Ș (In the last cycle)
Df㩷 (In the last cycle)
Dd㩷 (Maximum value)
Destruction number of cycles
using the Coffin equation
Destruction number of cycles
using AsadaΣ
Destruction number of cycles
using AsadaΤ
Destruction number of cycles
by Experiment

EC02

EC04

EC05

EC07

EC08

EC09

4.3

4.3

4.3

6.45

2.15

5.16

1 block

1 block

20 cycles 20 cycles
1 block(0.4 block) (0.4 block)1 block

Sine wave

Random amplitude
wave

0.545

0.088

0.784

0.305

0.096

0.869

0.695
0.093

0.233
0.073

0.863
0.106

0.491
0.146

0.245
0.072

0.919
0.114

-

-

-

-

-

36

-

-

16

-

-

25

12

-

9

8

-

11

3 × 505 × 50

20

19

7×50

33

Sine wave Sine wave Sine wave Sine wave

did not reach destruction during 20 or 50 cycles in analysis.
−

43 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬޿৻⥌ࠍ␜ߒߡ޿ࠆ㧚߭ߕߺߦ㑐ߒߡߪ Shell ࡕ࠺࡞ߢ 5JGNN ࡕ࠺࡞ߦࠃࠆ◲ᤃ⸃ᨆᚻᴺ
೨▵߹ߢߦ߅޿ߡ㧘ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⎕უ޽ࠆὑ㧘ዪᚲ⊛ߥ᧼ෘᣇะߩ߭ߕߺߪ಴ജߔࠆ੐߇಴᧪

ࡔࠞ࠾࠭ࡓࠍ⠨ኤߔࠆ੐߇ߢ߈㧘߈ⵚ⊒↢ㇱߩ․ቯߣߘ

ߥ޿߇㧘ઁߩ 2 ᣇะߩ߭ߕߺߦ㑐ߒߡߪ⦟޿৻⥌ࠍ␜ߒߩ⎕უኼ๮੍᷹ࠍⴕ߁੐߇಴᧪ߚ㧚ߎߎߢߪߐࠄߦ㧘ߡ޿ࠆ㧚Shell ࡕ࠺࡞ࠍ↪޿ࠆ੐ߢ㧘೨▵߹ߢߦⴕߞߚ⸃ᨆࠍࠃࠅ

߹ߚౝ࿶ߩή޿ EC06 ߦ㑐ߒߡ߽ห᭽ߦ㧘ࠨࠗࠢ࡞ᢙ

◲නߦ⹏ଔߒ㧘࡜ࡦ࠳ࡓᝄ᏷ᵄߩࡄ࡜ࡔ࠻࡝࠶ࠢ⹏ଔ⸃

ߦኻߔࠆ⩄㊀ὐ෻ജ୯ߦߟ޿ߡ㧘Solid ࡕ࠺࡞ߣ Shell ࡕᨆࠍ⹜ߺߚ㧚

࠺࡞ߩ୯ࠍᲧセߒߚ࿑ࠍ࿑  ߦ㧘ࠨࠗࠢ࡞ᢙߦኻߔ

⸃ᨆߦ㑐ߒߡߪࡕ࠺࡞ߩ૞ᚑ෸߮ⷐ⚛ಽഀࠍⴕߥ߁

ࠆ A ὐߩ߭ߕߺߦߟ޿ߡ㧘ߘࠇߙࠇᲧセߒߚ࿑ࠍ࿑

ࡊ࡝ࡊࡠ࠮࠶ࠪࡦࠣߦ Microsoft ߩ⴫⸘▚࠰ࡈ࠻ EXCEL

 ߦߘࠇߙࠇ␜ߔ㧚⩄㊀ὐ෻ജߩጁᱧߦߟ޿ߡ߽⦟

ࠍ㧘ታ㓙ߦ⸘▚ࠍⴕߥ߁࠰࡞ࡃ࡯ߦߪ ABAQUS ࠍ㧘⸃޿৻⥌ࠍ␜ߒߡ߅ࠅ㧘ߎࠇࠄߩ࿑߆ࠄ⎕უࡔࠞ࠾࠭ࡓߩ

ᨆ⚿ᨐߩ಴ജࠍⴕߥ߁ࡐࠬ࠻ࡊࡠ࠮࠶ࠪࡦࠣߦߪ

⇣ߥࠆ EC06 ߦ㑐ߒߡ߽㧘㕖Ᏹߦ♖ᐲߩ㜞޿⸘▚⚿ᨐ߇

ABAQUS POST ࠍߘࠇߙࠇ↪޿ߚ.ᧄ⸃ᨆߩ․ᓽߩ৻ߟ

␜ߐࠇߡ޿ࠆ੐߇ࠊ߆ࠆ㧚એ਄ࠃࠅ Shell ࡕ࠺࡞ߪ Solid ࡕ࠺࡞ߣోߊห᭽ߩ⸃ᨆ

ߣߒߡࡊ࡝ࡊࡠ࠮࠶ࠪࡦࠣߦ EXCEL ࠍ↪޿ߚ੐߇᜼ߍ
ࠄࠇࠆ㧚EXCEL ࠍ૶↪ߔࠆߣ㧘ૃߚࠃ߁ߥࡕ࠺࡞ࠍ޿ߊ

⚿ᨐࠍ␜ߔߎߣ߇ࠊ߆ߞߚ㧚ᧄ⸃ᨆߦ↪޿ߚ Shell ࡕ࠺ߟ߽૞ᚑߔࠆ႐ว㧘৻ߟߩࡕ࠺࡞ࠍ૞ᚑߔࠇ߫ᓟߪᄌᢙ

࡞ߪෘ⡺ 4 ▵ὐࡕ࠺࡞ߢ޽ࠆὑ㧘᧼ෘߩᄌൻߥߤࠍ಴ജ

ࠍᄌ߃ࠆߛߌߢ㧘ࡕ࠺࡞߇૞ᚑ಴᧪ࠆὑ㧘ࡄ࡜ࡔ࡯࠲⸘

ߔࠆ੐߇಴᧪ࠆ߇㧘Shell ߢ޽ࠆὑዪᚲ⊛ߥ᧼ෘᣇะߩᔕ

▚ࠍߔࠆ㓙ߩࡕ࠺࡞૞ᚑߦᄢᄌ᦭೑ߢ޽ࠆ㧚․ߦ Shellജ߿߭ߕߺߪ೨ㅀߒߚㅢࠅ಴ജߔࠆ੐߇಴᧪ߥ޿㧚ߒ߆ࡕ࠺࡞ߩ૞ᚑߦߪ᭴ᚑߔࠆ࠻ࡐࡠࠫࠞ࡞ࠝ࡯࠳࡯߇㕖Ᏹߒ Solid ࡕ࠺࡞ߢ⹦⚦ߥᔕജ⁁ᘒࠍᛠីߒ㧘㊀ⷐߥㇱಽߦන⚐ߢ޽ࠆὑ㧘ᄢᄌ᦭ലߢ޽ࠆ㧚߇᳿ቯߐࠇߚ႐ว㧔ᧄ⸃ᨆߢߪ B ὐ෸߮ A ὐ㧕㧘㕖Ᏹߦ

Shell ࡕ࠺࡞ߩࡕ࠺࡞࿑ࠍ࿑  ߦ␜ߔ㧚ࡕ࠺࡞ൻ◲ᤃ⊛ߢ᦭ലߥᚻᲑߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚ߒߚ㈩▤ߪᄌᒻߦ઻߁᧼ෘᄌൻ߇⠨ᘦߢ߈ࠆ 4 ▵ὐෘ⡺
Shell ⷐ⚛ࠍ↪޿㧘ኻ⒓ᕈ߿ౝ࿶㧘ᒢ႟ᕈ⸃ᨆߦ૶↪ߒߚᑼߥߤߪߔߴߡ 4.2.2 ߦኻᔕߔࠆ㧚▵ὐᢙߪ 582㧘ⷐ⚛ᢙߪ 530 ߢ㧘EC05 ߩࡕ࠺࡞ࠍ⸘▚ߔࠆߩߦ೨ㅀߒߚ Solidࡕ࠺࡞߇ CPU-time ߢ 8hours㧔HP ⵾ J5000 ૶↪㧕ߢ޽ࠆߩߦኻߒ㧘Shell ࡕ࠺࡞ߪ 35min ߣ Solid ࡕ࠺࡞ߩ⚂ 7.3%
ߩ⸘▚ᤨ㑆ߢ⸘▚߇಴᧪ࠆ㧚ߎߩ⸘▚ᤨ㑆ߩ⍴❗ߪ૗ㅢࠅ߽ߩ⸃ᨆࠍⴕ߁ࡄ࡜ࡔ࡯࠲⸃ᨆߦኻߒ㕖Ᏹߦ᦭↪ߢ޽ࠅ㧘߹ߚࠬࡍ࠶ࠢߩૐ޿ EWS ࡑࠪࡦߢ߽⸘▚߇಴᧪ࠆ㧚
Shell ࡕ࠺࡞ߩା㗬ᕈࠍ⹏ଔߔࠆߚ߼ߦ㧘EC05 ߩ P-Ǭ
ࠞ࡯ࡉࠍ Solid ࡕ࠺࡞ߣ Shell ࡕ࠺࡞ߩਔᣇߦߟ޿ߡ࿑
 ߦ␜ߔ㧚߹ߚࠨࠗࠢ࡞ᢙߦኻߔࠆ B ὐߩ߭ߕߺߦ
ߟ޿ߡ㧘ߘࠇߙࠇᲧセߒߚ߽ߩࠍ࿑  ߦ␜ߔ㧚⩄㊀࿑  Shell ࡕ࠺࡞ߦ߅ߌࠆࡔ࠶ࠪࡘ࿑

ὐ෻ജߩ୯ߣߒߡߪ㧘߶ߣࠎߤ৻⥌ߒߡ߅ࠅ㧘ߘߩᦨᄢFig.4.2-17

Finite element mesh subdivision.

୯߽ Solid ࡕ࠺࡞ߢ 55.4kN㧘Shell ࡕ࠺࡞ߢ 55.5kN ߣ⦟
100
Reaction Force (kN)

Reaction Force (kN)

100
50
0
-50

-100

50
0
-50

-100
-50 -40 -30 -20 -10 0 10 20 30 40 50
Disp. 䋨mm䋩-50 -40 -30 -20 -10 0 10 20 30 40 50
Disp. 䋨mm䋩(a) Solid model. (b) Shell model.  ࿑  EC05 ߦ߅ߌࠆ Solid ߣ Shell ࡕ࠺࡞ߩ P-Ǭࠞ࡯ࡉFig.4.2-18

P-Ǭcurves of EC05 Solid and Shell model.

−

44 −

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

Radial
Hoop

0

5

10
15
Number of cycle

20

Axial

StrainStrain

Axial

Hoop

0

25

5

10
15
Number of cycle

2025(b) Shell model.  (a) Solid model.  ࿑  EC05 ߦ߅ߌࠆ B ὐߩ߭ߕߺጁᱧ
Fig.4.2-19

Strain history of EC05 at B point.

100
Reaction Force (kN)

Reaction Force (kN)

100
50
0
-50

50
0
-50

-100

-100
0

5

10
15
20
Number of cycles

25

0

30

5

10
15
20
Number of cycles

2530(b) Shell model.  (a) Solid model.  ࿑  EC06 ߦ߅ߌࠆ⩄㊀ὐ෻ജጁᱧ࿑
Fig.4.2-20

0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4

Load point reaction hysteresis of EC06.

0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4

Radial
Hoop

0

5

10
15
Number of cycle

20

Axial

StrainStrainAxial

25

Radial051015Number of cycle(b) Shell model.  (a) Solid model.  ࿑  EC06 ߦ߅ߌࠆ A ὐߩ߭ߕߺጁᱧ
Fig.4.2-21

Strain history of EC06 at A point.

−

45 −

20

25

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬ ࡜ࡦ࠳ࡓᝄ᏷ᵄߩ⩄㊀ጁᱧߦኻߔࠆ∋ഭኼ๮⹏ଔ

⸃ᨆ⚿ᨐߣߒߡ࿑  ߦ EC04㧘EC041 ෸߮ EC042

EC04 ⹜㛎૕ߦ↪޿ࠄࠇߚ࿑  D ߦ␜ߔ࡜ࡦ࠳ࡓ

ߩᄖᓘ෸߮⡺ෘߩᄌൻࠍߘࠇߙࠇ␜ߔ㧚࿑ߦ߅޿ߡᄖᓘ

ᝄ᏷ᵄߩᒝ೙ᄌ૏㗅ᐨࠍ౉ࠇᦧ߃㧘4.2.6 ߢቯ⟵ߒߚ Shell

ߪ Y1 ゲߦ㧘⡺ෘߪ Y2 ゲߦߘࠇߙࠇኻᔕߔࠆ㧚ߎߩ࿑߆ࡕ࠺࡞ࠍ↪޿ߡ⸃ᨆࠍⴕ߁ߎߣߢᄌ૏㗅ᐨߩᓇ㗀ࠍ⠨ኤࠄ㧘޽ࠆ৻ቯએ਄ߩᝄ᏷ߢᄖᓘ෸߮⡺ෘߩᄌൻ߇⿠߈㧘ߒߚ㧚ߘࠇએਅߢߪᄌൻ߇⿠ߎߞߡ޿ߥ޿ߎߣ߇ࠊ߆ࠆ㧚࿑  D ߣหߓᄌ૏ࠍਈ߃㧘ߘߩ㗅ᐨࠍᄢ߆ࠄዊ߳߹ߚ࿑  ߦ㧟ߟߩࡕ࠺࡞ߩὐ B ߦ߅ߌࠆ㧞ᣇะ

⒖ⴕߐߖࠆࡕ࠺࡞ࠍ EC041㧘ዊ߆ࠄᄢ߳⒖ⴕߐߖߚࡕ࠺

ߩ߭ߕߺࠍ␜ߔ߇㧘߿ߪࠅ㧞ᣇะߣ߽৻ቯ୯એਅߩᄌ૏

࡞ࠍ EC042 ߣߒߚ㧚࿑  ߦߘߩ౉ജᵄᒻࠍ␜ߔ㧚ߢߪ෻ᔕࠍ␜ߐߕ㧘࡜࠴ࠚ࠶࠻ߪᒝ೙ᄌ૏߇ᄢ߈ߊ㧘޽ࠆ৻ቯ୯ࠍ⿥߃ߚᤨߦߩߺ⿠ߎߞߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚
40

20

Disp䋨mm䋩

Disp䋨mm䋩

40

0

-20

20
0

-20

-40

-40

20
30
Number of cycle
㧔a㧕EC041.

40

50

0

࿑  ౉ജᵄᒻFig.4.2-22

10

20
30
Number of cycle
㧔b㧕EC042.

Input waveform.

4.5
Wall䇭thickness (mm)150
Outer diameter (mm)Outer diameter
Analysis:90°&270°

140

4

130

3.5

Outer diameter
Analysis:0°&180°

120

3Wall Thickness
Analysis:90°&270°

110

2.5
0

10 20 30 40
Number of cycle

50

Wall Thickness
Analysis:0°&180°

㧔a㧕EC04.

150

4.5Wall䇭thickness (mm)10Outer diameter (mm)0Outer diameter
Analysis:90°&270°

140

4

130

3.5

Outer diameter
Analysis:0°&180°

120

3Wall Thickness
Analysis:90°&270°

110

2.5
0

10 20 30 40
Number of cycle

50

Wall Thickness
Analysis:0°&180°

㧔b㧕EC041.
࿑  ฦ⹜㛎૕ߩᄖᓘ෸߮⡺ෘᄌൻ
Fig.4.2-23

Outer diameter and wall thickness change of each analysis specimen.

−

46 −

40

50

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

StrainStrain

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

Axial
Hoop

0

10

20
30
Number of cycle

50

Hoop

0

10

20
30
Number of cycle

4050㧔b㧕EC041.

0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2

Strain㧔a㧕EC04.

40

Axial

Axial
Hoop

0

10

20
30
Number of cycle

4050㧔c㧕EC042.
࿑  ฦ⹜㛎૕ߩ B ὐߩ߭ߕߺጁᱧ
Fig.4.2-24

Strain history at B point for each analysis model.

 ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⸃ᨆ 㧔ᦛ▤㧕
55sec ઃㄭ㧘3D-C01 ߢߪ 9㨪60sec ઃㄭߩࠛ࡞ࡏ㐿㐽ᝄ᏷㧝 ⸃ᨆࡕ࠺࡞ߣ᧦ઙ
ᧄ▵ߢߪ㧘2.2.2 ߢㅀߴߚ 3 ᰴర㈩▤♽⹜㛎૕߆ࠄࠛ࡞
ࡏㇱಽࠍⷐ⚛⊛ߦขࠅ಴ߒ㧘ߘߩജቇ⊛⁁ᘒࠍ⹦⚦ߦᛠ

ᄌ૏㊂ࠍ᛽಴ߒ౉ജᵄߣߒߚ㧚⸃ᨆߢ૶↪ߒߚࠨࠗࠢ࡞
ᢙߦኻߔࠆࠛ࡞ࡏ㐿㐽ᄌ૏㊂ࠍ࿑  ߦ␜ߔ㧚ីߔࠆߎߣࠍ⋡⊛ߦ⸃ᨆࠍⴕߞߚ㧚⸃ᨆߩኻ⽎ߦߒߚߩࡕ࠺࡞ൻߒߚ㈩▤ߪࠕࠗ࠰ࡄ࡜ࡔ࠻࡝࠶ࠢ 20 ▵ὐⷐߪ὇⚛㍑▤ߩࠛ࡞ࡏㇱಽߢ޽ࠅ㧘ஜోߥ߽ߩߣౝ஥ో๟

⚛ࠍ↪޿㧘ᒻ⁁ߣߒߡߪኻ⒓ᕈࠍ⠨ᘦߒߡ 1㧛2 ࡕ࠺࡞ࠍᷫ⡺ࠍਈ߃ߚ߽ߩߩ 2 ⒳㘃ߢ޽ࠆ㧚ߎࠇࠄߪߘࠇߙࠇ┙૶↪ߒᄌ૏೙ᓮߢ⸃ᨆߒߚ㧚߹ߚౝ࿶ߦߟ޿ߡߪታ㛎ߦ૕㈩▤♽⹜㛎૕ 3D-A01㧘3D-C01 ߩࠛ࡞ࡏ㧝ߦኻᔕߔࠆ㧚Ḱߓߚ߽ߩࠍ⽶⩄ߒ㧘ౝ࿶ߩᓇ㗀ߦࠃࠅ㈩▤߇⤘ࠄࠎߢ߹ߚ㧘㈩▤♽ߦߪ 9.8MPa ߩౝ࿶߇৻᭽ߦਈ߃ࠄࠇߡ޿

߆ࠄᒝ೙ᄌ૏ࠍਈ߃ࠆࠃ߁ߦߒߚ㧚ⷐ⚛ᢙߪ 3D-A01 ߢࠆ㧚࿑ 1 ߦታ㛎ߦ߅ߌࠆࠛ࡞ࡏᄌᒻ㊂ߩ⸘᷹૏⟎ࠍ

1944㧘3D-C01 ߢ 2160㧘▵ὐᢙߪ 3D-A01 ߢ 10545㧘3D-C01

␜ߔ㧚߹ߚ㧘࿑  ߦታ㛎ߢ㈩▤♽ߦ౉ജߒߚടㅦᐲ

ߢ 11669 ߢ޽ࠆ㧚ߘࠇߙࠇߩࡔ࠶ࠪࡘ࿑ࠍ࿑  ߦ␜ࠍ㧘࿑  ߦฦ⹜㛎૕ߩࠛ࡞ࡏ㐿㐽ᄌ૏ࠍ␜ߔ㧚ߔ㧚೙ᓮᴺߣߒߡߪฦ࿑ਛ਄ㇱߩ⍫ශߦᒝ೙ᄌ૏ࠍਈ߃㧘⸃ᨆߦ㑐ߒߡߪࡕ࠺࡞ߩ૞ᚑ෸߮ⷐ⚛ಽഀࠍⴕߥ߁

ਅㇱߩਃⷺὐࠍᡰᜬߒߡ޿ࠆ㧚ࡊ࡝ࡊࡠ࠮࠶ࠪࡦࠣߦߪ J-VISION ࠍ㧘ታ㓙ߦ⸘▚ࠍⴕታ㛎ࠍᮨᡆߔࠆ㓙㧘ࠛ࡞ࡏㇱߦߪ㐿㐽ᄌ૏㊂એᄖߦߨߥ߁࠰࡞ࡃ࡯ߦߪ ABAQUS ࠍ㧘⸃ᨆ⚿ᨐߩ಴ജࠍⴕߥ

ߓࠅࠍ⠨ᘦߔࠆᔅⷐ߇޽ࠆ߇㧘ᧄታ㛎ߦ߅޿ߡ⸘᷹߇࿎

߁ࡐࠬ࠻ࡊࡠ࠮࠶ࠪࡦࠣߦߪ ABAQUS POST ࠍߘࠇߙ㔍ߢ޽ࠆ੐ߣ㧘ߨߓࠅ㊂߇ᓸ㊂ߣ੍ᗐߐࠇࠆߎߣ߆ࠄᧄ

ࠇ↪޿ߚ㧚⸃ᨆߢߪߨߓࠅࡕ࡯ࡔࡦ࠻ࠍ⠨ᘦߖߕߦ⸃ᨆࠍⴕߞߚ㧚ᧄ⎇ⓥߢߪ㧘4.2 ห᭽㧘2 ߟߩ⹜㛎૕ߦߟ޿ߡ౉ജᵄᒻ

ᒢ႟ᕈ⸃ᨆߦ૶↪ߒߚᑼߪ 4.2 ห᭽ Mises ߩ㒠ફ᧦ઙࠍᮨᡆߒߚ㕒⊛ߥ 3 ᰴరᒢ႟ᕈ⸃ᨆࠍⴕߞߚ㧚㕒⊛ߥ 3ߦၮߠߊ Prandtle-Reuss ߩᑼߢ޽ࠆ㧚߹ߚ౉ജߒߚ᧚ᢱ

ᰴరᒢ႟ᕈ⸃ᨆߢ޽ࠆߩߢᤨ㑆ゲࠍήⷞߒ㧘ߐࠄߦ౉ജ

࠺࡯࠲߽ 4.2 ߢ૶↪ߒߚ߽ߩߣห᭽㧞⋥✢ㄭૃߒߚ⒖േ

ᝄ᏷߽ࠛ࡞ࡏㇱߦᓇ㗀ࠍਈ߃ࠆㇱಽߩߺਈ߃⸃ᨆࠍⴕߞ

⎬ൻࡕ࠺࡞ߢ⸃ᨆࠍⴕߞߚ㧚ߚ㧚 ౕ૕⊛ߦߪ㧘࿑  ߩᤨ㑆ߦߒߡ 3D-A01 ߢߪ 8㨪
−

47 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬

Elbow displacement
measurement position

510

500

࿑  ࠛ࡞ࡏᄌ૏⸘᷹୘ᚲ
Fig.4.3-1

Elbow displacement measurement position.

The
input
acceleration
(Gal)
Input
acceleration(Gal)౉ജടㅦᐲ䋨Gal䋩

2000

1500
1000
500
0
-500
-1000
-1500
-2000
0

20

40

60

1500
1000
500
0
-500
-1000
-1500
-2000
0

80

20

40

Time ᤨ㑆䋨sec䋩
(sec)

Time ᤨ㑆䋨sec䋩(sec)(a) 3D-A01.

(b) 3D-C01.

60

80

60

80

࿑  ᝄേบߩ౉ജടㅦᐲ
Input acceleration in the shaking table test.
Elbow 䉣䊦䊗㐿㐽ᄌ૏㊂䋨䌭䌭䋩
opening-closing displacement

Fig.4.3-2
30
20
10

)

䉣䊦䊗㐿㐽ᄌ૏㊂䋨䌭䌭䋩Elbow opening-closing displacement

0

-10

(

Input
acceleration (Gal)౉ജടㅦᐲ䋨Gal䋩

2000

-20
-30
0

20

40

60

80

30
20
10
0
-10
-20
-30

ᤨ㑆䋨sec䋩
Time
(sec)

0

40
Time
(sec)
ᤨ㑆䋨sec䋩(a) 3D-A01.

(b) 3D-C01.

࿑  ࠛ࡞ࡏㇱߩ㐿㐽ᄌ૏㊂
Fig.4.3-3 Elbow opening-closing displacement.

−

48 −

20

30

displacement

30

䉣 20

20
10

opening-closing

䊦 10

0

0

䊗

-10

㐿 -10

-20

㐽

-30
0

20

40

60

80

100

120

140

Elbow

Elbow
opening-closing displacement䉣䊦䊗㐿㐽ᄌ૏㊂䋨䌭䌭䋩ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

-20
-30
0

20

40

60

䉰䉟䉪䊦ᢙ
Number ofcycle

Numberof cycle䉰䉟䉪䊦ᢙ(a) 3D-A01.

(b) 3D-C01.

80

100

120

࿑  ⸃ᨆߦ౉ജߒߚࠛ࡞ࡏㇱߩ㐿㐽ᄌ૏㊂
Fig.4.3-4 Elbow opening-closing displacement input into analysis.

(b) 3D-C01.

(a) 3D-A01.
࿑  ⸃ᨆߦ૶↪ߒߚࠛ࡞ࡏㇱ᧚ߩࡔ࠶ࠪࡘ࿑
Fig.4.3-5

Finite element mesh subdivision.

ਔ⹜㛎૕ߩടᝄᓟߩ⋧ᒰ႟ᕈ߭ߕߺಽᏓ࿑ࠍ࿑ 

 ࠛ࡞ࡏ㈩▤ߩ߈ⵚ⊒↢ࡔࠞ࠾࠭ࡓߣ⎕უ᜼േߎߎߢߪ߹ߕታ㛎ߣหߓࠛ࡞ࡏㇱ㐿㐽ᄌ૏ᝄ᏷ࠍ⸃ᨆ

ߦ␜ߔ㧚ਔ⹜㛎૕ߣ߽ࠛ࡞ࡏㇱߩ㈩▤ౝ㕙ߦ⣁⣻ߩㇱಽߦ౉ജߔࠆ੐ߢ㧘ࠛ࡞ࡏㇱߩജቇ⊛᜼േࠍᛠីߔࠆ੐ߣ㧘㧔࿑ਛ A ὐ㧕ߢゲᣇะߦ߭ߕߺ㓸ਛㇱ߇⏕⹺ߢ߈ࠆ㧚ᷫታ㛎ߢ⏕⹺ߐࠇߚ߈ⵚ⊒↢ㇱ߇㧘4.2 ߢㅀߴߚࠃ߁ߥ߭ߕ

⡺ࠍ᦭ߔࠆ 3D-C01 ߩᣇ߇߭ߕߺ㊂ߣߘߩ▸࿐߇ 3D-A01

ߺ㓸ਛㇱߦߥࠆ߆ߤ߁߆ࠍ⏕⹺ߒߡ߅߈ߚ޿㧚ߦᲧߴ㗼⪺ߦߥߞߡ޿ࠆ੐߽ࠊ߆ࠆ㧚ஜోߥࠛ࡞ࡏ▤ 3D-A01 ߣ㧘ᷫ⡺ㇱࠍ᦭ߔࠆࠛ࡞ࡏ▤ࠛ࡞ࡏㇱߩ⣁⣻ߦߎߩࠃ߁ߦ㗼⪺ߥ߭ߕߺ㓸ਛㇱ߇಴

3D-C01 ߦߟ޿ߡߘࠇߙࠇߩ⩄㊀ὐᄌ૏㧙⩄㊀ὐ෻ജᦛ᧪ࠆℂ↱ߣߒߡߪ࿑  ߦ߅޿ߡ⺑᣿߇ߟߊ㧚ߎߩ࿑✢ࠍ࿑  ߦ␜ߔ㧚3D-A01 ߣ 3D-C01 ߦ߅޿ߡ⽶⩄ߐߪ 3D-C01 ߦ߅ߌࠆടᝄᤨߩࠛ࡞ࡏㇱਛᄩᢿ㕙ߦ߅ߌࠆࠇߚᄌ૏߇⇣ߥࠆߩߢ৻᭎ߦᲧセߪ಴᧪ߥ޿߇㧘ᵈ⋡ߢᄖᓘᄌൻㆊ⒟ࠍ␜ߒߚ߽ߩߢ޽ࠆ㧚ߎߎߢ㧘a-a’㕙߇ࠛ߈ࠆߩߪ⩄㊀ὐ෻ജߩ୯߇ᷫ⡺ㇱࠍ᦭ߔࠆ੐ߢ⪺ߒߊૐ࡞ࡏߩ⢛-⣻ᣇะ㧘b-b’㕙߇⣁⣻ᣇะߢ޽ࠆ㧚࿑ਛߩ a-a’ਅߔࠆ੐ߢ޽ࠆ㧚ߎߩ⼏⺰ߦߟ޿ߡߪ㈩▤♽ߔߴߡࠍㅢ

㕙ߩᄖᓘᄌൻ㊂ߦᲧߴ b-b’㕙ߩᄖᒻᄌൻ㊂෸߮㧘ߘߩᝄߒߡ⺰ߓߥߌࠇ߫ߥࠄߥ޿੐ߢߪ޽ࠆ߇㧘ᷫ⡺ㇱࠍ᦭ߔ᏷߇౒ߦᄢ߈ߊߥߞߡ޿ࠆ㧚ߟ߹ࠅࠛ࡞ࡏࠍ㐿㐽ߔࠆ੐ࠆ㈩▤♽ߪߘࠇߛߌࠛ࡞ࡏㇱߢߩ႟ᕈ፣უ⩄㊀߇ૐਅߔߢࠛ࡞ࡏㇱਛᄩᢿ㕙ో૕߇ᄢ߈ߊ஍ᐔൻߒߡ޿ࠆߎߣ߇

ࠆߚ߼ో૕ߣߒߡᄢ߈ߥᔕ╵ߣߥࠅ㧘߹ߚࠛ࡞ࡏㇱන૕ࠊ߆ࠆ㧚ߘߒߡ b-b’㕙߇ߘߩᬦ౞ߦ߅ߌࠆ㐳ゲㇱࠍᜂ޿㧘ߢߺࠆߣᒝᐲ෸߮೰ᕈ߇⪺ߒߊૐਅߔࠆὑߦ㧘෻ജ୯߇࿑ਛ b ෸߮ b’ㇱ㧘ߟ߹ࠅࠛ࡞ࡏㇱߩ⣁⣻ㇱಽ߇๟ᣇะߦ

ૐߊߥࠆ੐߇ࠊ߆ࠆ㧚ᦛߍߣߥࠅ㧘㈩▤ౝ㕙ߦᄢ߈ߥ๟ᣇะ߭ߕߺᝄ᏷߇ടࠊ
−49 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬߹ߚ 3D-C01 ߦߟ޿ߡ߽߿ߪࠅᐔဋ๟ᣇะ߭ߕߺ߇ᒁ

ࠆ੐߇ᗐ௝಴᧪ࠆ㧚ߘߎߢਔ⹜㛎૕ߩࠨࠗࠢ࡞ᢙߦኻߔࠆ࿑  ਛ A ὐᒛࠅߣߥࠅ㧘ᐔဋゲᣇะ߭ߕߺ߽ᵄᒻࠍ߶ߣࠎߤ⷗ߖߥ

ߩ 3 ᣇะߩ߭ߕߺࠍ࿑  ߦ␜ߔ㧚߹ߕ 3D-A01 ߦߟ޿ᒻߢᒁᒛࠅߣߥߞߡ޿ࠆ㧚ߘߒߡߎࠇࠄ 2 ゲߩ߭ߕߺ޿ߡߪૐ޿࡟ࡌ࡞ߢߪ޽ࠆ߽ߩߩᐔဋߩ๟ᣇะ߭ߕߺ߇

ߩᓇ㗀ࠍฃߌᐔဋඨᓘᣇะ߭ߕߺߪ๟ᣇะߩ߭ߕߺߦㅒ

ᒁᒛࠅ㧘ᐔဋߩඨᓘᣇะ߭ߕߺ߇ㅒ૏⋧ߢ࿶❗ߣߥࠅ㧘૏⋧ߩᒻߢ࿶❗ߣߥߞߡ޿ࠆ㧚ߎࠇߪᄢ߈ߥ⡺ෘᷫዋࠍゲᣇะߩ߭ߕߺߪࠛ࡞ࡏㇱో૕ᦛߍߩਛ┙ゲߦ૏⟎ߔࠆᗧ๧ߒ㧘߹ߚ߭ߕߺᝄ᏷ߣߒߡߪ๟ᣇะ߇ᦨᄢࠍ␜ߒߡ

ߩߢ߶ߣࠎߤᄌൻ߇ߥ޿㧚ߟ߹ࠅ๟ᣇะ߭ߕߺߩ᜼േ߇

߅ࠅ㧘೨ㅀߒߚㇱಽߢߩ߈ⵚ⊒↢ߦᦨ߽ነਈߒߡ޿ࠆߩ

ߎߩㇱಽߩജቇ⁁ᘒࠍᡰ㈩ߒߡ߅ࠅ㧘߹ߚᝄ᏷ߣߒߡ߽

ߪ๟ᣇะߩ߭ߕߺᝄ᏷ߢ޽ࠆߣᢿቯߢ߈ࠆ㧚๟ᣇะ߭ߕߺ߇߽ߞߣ߽ᄢ߈ߊߥߞߡ޿ࠆ㧚

120
90
60
30
0
-30
-60
-90
-120

Reaction Force (kN)

Reaction Force (kN)

120
90
60
30
0
-30
-60
-90
-120

-30

-20

-10
0
10
Disp. 䋨mm䋩

20

30

-30

-20

-10
0
10
Disp. 䋨mm䋩2030(b) 3D-C01.

(a) 3D-A01.
࿑  ฦࡕ࠺࡞ߩ⩄㊀ὐᄌ૏෻ജᦛ✢Fig.4.3-6

Load point displacement-reaction force curve of each model.

Elbow division

Elbow division

Elbow division

Elbow division

outside surface

inner surface

outside surface

inner surfaceAA(a) 3D-A01.

(b) 3D-C01.

࿑  ฦࡕ࠺࡞ߩ⋧ᒰ႟ᕈ߭ߕߺಽᏓ࿑
Fig.4.3-7

Equivalent plastic strain distribution.

−

50 −

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

㪈㪉㪏

a
b

㪈㪉㪋

a’

㪦㫌㫋㪼㫉㩷㪻㫀㪸㫄㪼㫋㪼㫉䋨㫄㫄㪀

b’

a

㪈㪉㪇

㪈㪈㪍

㪈㪈㪉

a’

㪸㪄㪸㩾
㪹㪄㪹㩾

㪈㪇㪏
㪇

㪉㪇

㪋㪇
㪍㪇
㪥㫌㫄㪹㪼㫉㩷㫆㪽㩷㪺㫐㪺㫃㪼

㪏㪇

㪈㪇㪇

࿑  3D-C01 ߩࠛ࡞ࡏਛᄩᢿ㕙ߩᄖᒻᄌൻ㊂
Outer diameter deformation history at center of Elbow (3D-C01).

0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08

Hoop
Axial

StrainRadial

0

25

50
75
100
Number of cycle

0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08

Hoop

StrainFig.4.3-8

Axial
Radial

0

125

25

50
75
Number of cycle

100

125

(b) 3D-C01.

(a) 3D-A01.
࿑  A ὐߦ߅ߌࠆฦᣇะߩ߭ߕߺ
Fig.4.3-9

Strain history of each direction at A point.

ߩࡕ࠺࡞૞ᚑߦᄢᄌ᦭೑ߥ੐ߣ㧘Shell ࡕ࠺࡞ߩߚ߼ࡔ࠶

 5JGNN ࡕ࠺࡞ߦࠃࠆ◲ᤃ⸃ᨆᚻᴺ
਄ㅀߒߚ⸃ᨆߩ⚿ᨐ㧘ታ㛎ਛߩࠛ࡞ࡏㇱߩജቇ⁁ᘒࠍ
޽ࠆ⒟ᐲ੍᷹ߔࠆ੐߇ߢ߈㧘߈ⵚ⊒↢ㇱߩ․ቯࠍⴕ߁੐

ࠪࡘࠍಾࠆ㓙ߩ⸘▚ᑼ߇㕖Ᏹߦන⚐ߢ޽ࠆ੐߇᜼ߍࠄࠇ
ࠆ㧚߇಴᧪ߚ㧚ߎߎߢߪߐࠄߦ㧘੹ᓟࡄ࡜ࡔ࠻࡝࠶ࠢ⸃ᨆࠍ

ߎߎߢ Shell ࡕ࠺࡞ߩ 3D-A01 ⹜㛎૕ߩࡕ࠺࡞࿑ࠍ࿑

ⴕ߁㓙ߦᔅⷐߣߥࠆ◲ᤃ⸃ᨆᚻᴺࠍ⹜ߺߚ㧚ታ㛎ߢⴕࠊ ߦ␜ߔ㧚ࡕ࠺࡞ൻߒߚ㈩▤ߪ 4 ▵ὐෘ⡺ Shell ⷐࠇߡ޿ߥ޿߇㧘ࠛ࡞ࡏㇱන૕ࠍࡄ࡜ࡔ࠻࡝࠶ࠢߦ⸃ᨆࠍ

⚛ࠍ↪޿㧘ኻ⒓ᕈ߿ౝ࿶㧘ᒢ႟ᕈ⸃ᨆߦ૶↪ߒߚᑼߥߤ

ⴕ߁੐ߢᷫ⡺ߣᒝᐲߩ㑐ଥ߇ᶋ߆߮਄߇ߞߡߊࠆ߽ߩߣ

ߪߔߴߡ 4.3.2 ߦኻᔕߔࠆ㧚▵ὐᢙߪ 1071㧘ⷐ⚛ᢙߪ 1000ᕁࠊࠇࠆ㧚

ߢ㧘3D-A01 ߩࡕ࠺࡞ࠍ⸘▚ߔࠆߩߦ೨ㅀߒߚ Solid ࡕ࠺ࡄ࡜ࡔ࠻࡝࠶ࠢߦ⸘▚ࠍⴕ߁㓙㧘4.2 ห᭽⸘▚ᤨ㑆ߩ࡞߇ CPU-time ߢ 27.2hours㧔HP ⵾ J5000 ૶↪㧕ߢ޽ࠆߩ⍴❗߇᳞߼ࠄࠇࠆ㧚♖ᐲ⦟ߊല₸⊛ߦ⸘▚ࠍⴕ߁ߚ߼ᧄ

ߦኻߒ㧘Shell ࡕ࠺࡞ߪ 70min ߣ Solid ࡕ࠺࡞ߩ⚂ 4.3%ߩ

▵ߢ߽ Shell ࡕ࠺࡞ࠍዉ౉ߔࠆ੐ߣߒߚ㧚⸘▚ᤨ㑆ߢ⸘▚߇಴᧪ࠆ㧚
Shell ࡕ࠺࡞ߩା㗬ᕈࠍ⹏ଔߔࠆߚ߼ߦ㧘Shell ࡕ࠺࡞⸃ᨆߦ㑐ߒߡߪࡕ࠺࡞ߩ૞ᚑ෸߮ⷐ⚛ಽഀࠍⴕߥ߁
ࡊ࡝ࡊࡠ࠮࠶ࠪࡦࠣߦ 4.2 ห᭽ Microsoft ߩ⴫⸘▚࠰ࡈ࠻

ߩ 3D-A01㧘3D-C01 ਔࡕ࠺࡞ߩ⩄㊀ὐᄌ૏㧙⩄㊀ὐ෻ജ

EXCEL ࠍ㧘ታ㓙ߦ⸘▚ࠍⴕߥ߁࠰࡞ࡃ࡯ߦߪ ABAQUSᦛ✢ࠍ࿑  ߦ␜ߔ㧚ߎߩ࿑ߪ Solid ࡕ࠺࡞ߩ࿑ 

ࠍ㧘⸃ᨆ⚿ᨐߩ಴ജࠍⴕߥ߁ࡐࠬ࠻ࡊࡠ࠮࠶ࠪࡦࠣߦߪ

ߦኻᔕߔࠆ߇㧘ਔࡕ࠺࡞ߦߟ޿ߡᲧセߔࠆߣ Solid ߣ

ABAQUS POST ࠍߘࠇߙࠇ↪޿ߚ㧚

Shell ߩਔᣇߦߟ޿ߡ߶ߣࠎߤᄌࠊࠄߥ޿୯߇಴ߡ޿ࠆ㧚

EXCEL ዉ౉ߩℂ↱ߣߒߡߪ೨ㅀߒߚߣ߅ࠅᄌᢙࠍᄌ߃߹ߚ࿑  ਛ A ὐߩ 2 ᣇะߩ߭ߕߺߦߟ޿ߡ࿑ 

ࠆ႐วߩಣℂ߇ᩰᲑߦㅦ޿ὑ㧘ࡄ࡜ࡔ࡯࠲⸘▚ࠍߔࠆ㓙

ߦ␜ߔ㧚Shell ࡕ࠺࡞ߢ޽ࠆߩߢ Radial ᣇะߩ߭ߕߺߪ಴

−

51 −

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬ജߢ߈ߥ޿߇㧘ਔ Shell ࡕ࠺࡞ߣ߽๟ᣇะߩᐔဋ߭ߕߺ

ߎࠇߪ∋ഭኼ๮⹏ଔߩ㓙㧘Solid ࡕ࠺࡞ߦᲧߴᣧ޿߈ⵚ

߇ Solid ࡕ࠺࡞ࠃࠅ⧯ᐓ㧔߭ߕߺ㊂ߢ 0.07 ⒟ᐲ㧘3D-C01

ㅴዷ࡮⽾ㅢࠍ੍᷹ߒ㧘⚿ᨐߣߒߡ቟ో஥ߩ⹏ଔߣߥࠆ㧚ߢߪ Solid ߣ Shell ߢ 20㧑⒟ᐲߩ⺋Ꮕ㧕㜞߼ߦߥߞߡ߅ࠅ㧘ㆊ⵨ᐲߦߥࠄߥ޿ࠃ߁Ᏹߦᵈᗧߔࠆᔅⷐ߇޽ࠆ߇㧘Solidᝄ᏷ߣߒߡ߽ᄢ߈ߊߥߞߡ޿ࠆ㧚߹ߚゲᣇะߩᐔဋ߭ߕ

ࡕ࠺࡞ߣ௑ะ߇㊀ߥࠅ㧘ߐࠄߦ቟ో஥ߩ⹏ଔ߇น⢻ߢ޽ߺߪૐ߼ߦߥߞߡ߅ࠅ㧘ᝄ᏷ߪ߿ߪࠅᄢ߈ߊߥߞߡ޿ࠆ㧚ࠆ Shell ࡕ࠺࡞ߪ߆ߥࠅ᦭↪ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚ߎߎߢ㊀ⷐߥߩߪ߈ⵚ⊒↢ߦᦨ߽ᓇ㗀ߔࠆ๟ᣇะߩ߭ߕ
ߺᝄ᏷߇ Solid ࡕ࠺࡞ࠃࠅᄢ߈޿੐ߢ޽ࠆ㧚࿑  4 ▵ὐෘ⡺ Shell ߦࠃࠆࠛ࡞ࡏ㈩▤⸃ᨆࡕ࠺࡞
Fig.4.3-10

Elbow piping analysis model according to4 nodes thick shell model.

120
90
60
30
0
-30
-60
-90
-120

Reaction Force (kN)

Reaction Force (kN)

120
90
60
30
0
-30
-60
-90
-120
-30

-20

-10
0
10
Disp. 䋨mm䋩

20

30

-30

-20

(a) 3D-A01.

-10
0
10
Disp. 䋨mm䋩2030(a) 3D-C01.
࿑  ⩄㊀ὐᄌ૏෻ജᦛ✢Fig.4.3-11

Load point displacement-reaction force curve.

0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08

StrainStrain

0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08

Hoop
Axial

0

25

50
75
Number of cycle

100

Hoop
Axial

0

125

(a) 3D-A01.

25

50
75
Number of cycle(b) 3D-C01.

࿑  A ὐߦ߅ߌࠆ 2 ᣇะߩ߭ߕߺ
Fig.4.3-12

Strain of 2directions at A point.

−

52 −

100

125

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

⴫㕙߈ⵚઃ߈㈩▤ߩૐࠨࠗࠢ࡞∋ഭ߈ⵚㅴዷ⹏ଔ

dadN ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ࠍ↪޿ߚ߈ⵚㅴዷ⸃ᨆ
 ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛

C 'J

m

㧔4.4.3㧕 ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ߪ㧘ᧂ⽾ㅢ߈ⵚߩ⚻ᷣ⊛ߥ⹏ଔߎߩ da/dN㧙ǍJ ․ᕈߪ㧘ዊⷙᮨ㒠ફਅߩ da/dN㧙ǍK2/E

ᣇᴺߢ޽ࠆ㧚ߘߩၮᧄ⊛ߥ⠨߃ߪ㧘߈ⵚߩߥ޿ᒻ⁁ߩߣ߽৻⥌ߒ㧘⹜㛎

Shell ࡕ࠺࡞ߩਛߦ㧘߈ⵚవ┵ߩ․⇣ᕈࠍ᦭ߔࠆዪᚲ⊛ߥߣ߇ታ⸽ߐࠇߡ޿ࠆ㧚m ߪ 1 ೨ᓟߩ୯ߣߥࠅ㧘ߒ߆߽ߎ⸃ࠍዉ౉ߔࠆߣ޿߁߽ߩߢ޽ࠆ㧚ߘߩߚ߼㧘ᣂߚߥ⥄↱ߩ C㧘m ୯ߪ᧚ᢱ㧘ᔕജᲧ㧘᷷ᐲߦኻߒߡ㊰ᗵߣߥࠆ㧚ᐲࠍਈ߃ࠆ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ࠍ߈ⵚߦᴪ߁ࠃ߁ߦࡕ

߹ߚ਄ᑼ߇ᚑ┙ߔࠆߎߣߪ㧘߈ⵚవ┵ߩ႟ᕈᄌᒻ߇߈ⵚ

࠺࡞ౝߦዉ౉ߔࠆ㧚ㅊട⥄↱ᐲߦ㑐ߔࠆ࡜ࠗࡦࠬࡊ࡝ࡦ

ᚑ㐳ࠍᡰ㈩ߔࠆߎߣࠍᗧ๧ߔࠆ߽ߩߣ⠨߃ࠄࠇࠆ㧚਄ᑼࠣߩࠦࡦࡊ࡜ࠗࠕࡦࠬߪ㧘ో૕ᔕ╵ߩਛߦዪᚲ⸃ࠍዉ౉

ਛߩቯᢙ C㧘m ߦߟ޿ߡߪ㧘ߔࠆ㧚ABAQUS ߪ㧘ࠦࡦࡊ࡜ࠗࠕࡦࠬߦ౒ᓎߥ⋧ኻᄌ૏

SUS304 ㍑Უ᧚ߦ߅޿ߡ㧘ߣ࿁ォ߆ࠄ߈ⵚߦᴪ߁૏⟎ߩ㑐ᢙߣߒߡ J Ⓧಽࠍ⸘▚ߔᒻ⁁࡮ኸᴺ㧘⽶⩄ᣇᴺߦࠃࠄߥ޿ߎ

C 1.4615 u 103
m 1.3742ࠆ㧚ߎߩⷐ⚛ߪ◲නߥߚ߼㧘߈ⵚߩߥ޿ Shell ߩ⸃ᨆߦᲧߴߡ⸃ᨆ⾌↪ࠍᄢ߈ߊჇ߿ߔߎߣߪߥ޿㧚ᄙߊߩ৻⥸⊛ߥ໧㗴ߦኻߒߡචಽߥ♖ᐲߩ⚿ᨐࠍਈ߃ࠆ㧚ߣߔࠆ 8).

 ➅ࠅ㄰ߒ , Ⓧಽ▸࿐Ǎ, ߩ⹏ଔ ߈ⵚㅴዷߩ⹏ଔᚻ㗅ᄢⷙᮨ㒠ફࠍ઻߁➅ࠅ㄰ߒ⽶⩄ࠍฃߌࠆ߈ⵚࠍ᦭ߔ ᄢⷙᮨ㒠ફࠍ઻߁➅ࠅ㄰ߒ⩄㊀ਅߦ߅޿ߡߪ㧘ࠨࠗࠢ࡞Ფߦㆊᄢߥ㒰⩄㧘ౣ⽶⩄ߣ޿ߞߚㆊ⒟ࠍ⚻ߥ߇ࠄ߈ⵚ

ࠆ㈩▤ߦኻߔࠆ⎕უ⹏ଔᚻ㗅ߪ㧘ᰴߩㅢࠅߢ޽ࠆ㧚߇ㅴዷߔࠆߎߣ߆ࠄ㧘છᗧߩ᧦ઙߦ߅޿ߡᡰ㈩ࡄ࡜ࡔ࡯

࡮߹ߕ㧘ೋᦼ߈ⵚࠍᗐቯߒ㧘╙ 1 ࠨࠗࠢ࡞ߦ߅ߌࠆ࠲ǍJ ࠍ૗ࠄ߆ߩ㕖ᒢᕈ᭴ᚑೣߦၮߠ߈⋥ធ⊛ߦ⹏ଔߔ

Jmax ࠍ᦭㒢ⷐ⚛⸃ᨆࠦ࡯࠼ ABAQUS ࠍ↪޿ߡ⸘▚ࠆߎߣߪ߈ࠊ߼ߡ࿎㔍ߢ޽ࠆ㧚ߎߎߢߪ㧘⸃ᨆߢᓧࠄࠇ

ߔࠆ㧚ߚ Jmax ߆ࠄǍJ ࠍዉ಴ߔࠆߎߣࠍ⠨߃ࠆ㧚
CT ⹜㛎

࡮㧔4.4.2㧕ᑼߦᓥ޿㧘╙ 1 ࠨࠗࠢ࡞ߦ߅ߌࠆǍ㧶ࠍ⸘ࠍ↪޿ߚૐࠨࠗࠢ࡞∋ഭ⹜㛎ߦࠃࠇ߫㧘ቢ▚ߔࠆ㧚ోਔᝄࠅ㧔R= -1㧕ߢ߈ⵚߩ㐽ญ߇ήⷞߢ߈ࠆ႐วߦߪ㧘'J

4 J max࡮㧔4.4.3㧕ᑼߦᓥ޿㧘╙ 1 ࠨࠗࠢ࡞ߦ߅ߌࠆ߈ⵚㅴዷ
㊂ࠍ da/dN ߩⓍಽߦࠃࠅ⸘▚ߔࠆ㧚

㧔4.4.1㧕࡮ೋᦼ߈ⵚ㐳ߐ a0 ߦ ߈ⵚㅴዷ㊂ࠍട߃㧘߈ⵚ㐳ߐ aߣߒߡᎿቇ⊛ߦᅷᒰߥ⹏ଔ߇น⢻ߢ޽ࠆߣߐࠇߡ޿ࠆ 5)㧚

ࠍᦝᣂߔࠆ㧚

ߒ߆ߒ㧘หᑼߪࠨࠗࠢ࡞ᒰߚࠅߩ߈ⵚㅴዷ߇ᓸዊߢ޽ࠆ

࡮⎕៊ߩ್ቯࠍⴕ߁㧚ߎߣࠍ೨ឭߣߒߡ޿ࠆ㧚࿑  ߪቶ᷷ਅߩ৻ቯᝄ᏷ਔ

⎕៊ߦ⥋ࠄߥ޿႐วߦߪᰴࠨࠗࠢ࡞ߦߟ޿ߡ਄⸥ߩᚻ㗅ᝄࠅ➅ࠅ㄰ߒ⩄㊀ࠍ߁ߌࠆ๟ᣇะ⽾ㅢ߈ⵚ౉ࠅ㈩▤ߦ߅ࠍ➅ࠅ㄰ߔ㧚

޿ߡታ㛎⊛ߦᓧࠄࠇߚǍJ/ Jmax ߩ߈ⵚㅴዷߦ઻߁ផ⒖ࠍ

࿑  ߦ⎕უ⹏ଔᴺߩ⹏ଔࡈࡠ࡯ࠍ␜ߔ㧚␜ߒߚ߽ߩߢ޽ࠆ 6)㧚߈ⵚㅴዷߩዊߐ޿㗔ၞߢߪǍJ/ Jmaxߩ୯߇㧘᭎ߨ 4 ߣߥߞߡ޿ࠆ߇㧘߈ⵚߩㅴዷߦߟࠇߡߘ
ߩ୯߇ૐਅߒߡ޿ࠆ㧚ߔߥࠊߜ㧘
㧔4.4.1㧕ᑼࠍᄢⷙᮨ㒠ફࠍ઻߁➅ࠅ㄰ߒ⩄㊀⹜㛎ߦߘߩ߹߹ㆡ↪ߔࠆߎߣߪㆊᄢ
ߥ߈ⵚㅴዷࠍ⹏ଔߔࠆᕟࠇ߇޽ࠆߣ⠨߃ࠄࠇࠆ㧚ߎࠇߦኻߒ㧘GE/EPRI Estimation Scheme ߩో㕙႟ᕈ⸃߆ࠄᓧࠄࠇࠆ㧘Jmax ࠃࠅǍJ ࠍ⹏ଔߔࠆ◲ᤃᑼ 7)㧘
'J |2a / a0
J max
a / a0  1/ 2

㧔4.4.2㧕ߪ㧘߈ⵚㅴዷ߇ߥ޿ߣ߈ߦ㧔4.4.1㧕ᑼߦ৻⥌ߒ㧘߈ⵚㅴዷߦ઻޿ǍJ/ Jmax ߇ 2 ߦẋㄭߒߡ޿ߊ㧚 ߈ⵚㅴዷೣ
ᄢⷙᮨ㒠ફࠍ઻߁➅ࠅ㄰ߒ⩄㊀ࠍฃߌࠆ㈩▤ߦ߅ߌࠆ߈ⵚㅴዷೣߦߟ޿ߡߪ㧘߈ⵚㅴዷㅦᐲ da/dN ߇ǍJ ߦኻߒએਅߩߴ߈ਸ਼ೣߢ⸥ㅀߐࠇࠆ߽ߩߣߔࠆ㧚−53 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬

Start
Assume Initial Crack 㧘 a0Estimate J max(ABAQUS)Translate J max into ӠJ

Estimate Crack Growth da/dN

Update Crack Length㧘 aNo࿑  ߈ⵚㅴዷߦ઻߁ӠJ/Jmax ߩផ⒖ߩ଀
Fig.4.4-1

Leak?

Example of the transition ofǍJ/ Jmax withYes

Crack Extension6).
End࿑  ⎕უ⹏ଔᴺߩ⹏ଔࡈࡠ࡯
Fig.4.4-2

Flow of the simulation for
low cycle fatigue crack propagations.

ABAQUS ߩᒢ႟ᕈ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ߪ㧘⤑ᄌᒻߣ ⸃ᨆࡕ࠺࡞ߣ᧦ઙ
ᧄ⸃ᨆߩ⋡⊛ߪ㧘ᦨᄢᄌ૏ᤨߩ Jmax ࠍ᳞߼ࠆߎߣߢ޽

ᦛߍᄌᒻߦࠃߞߡࡕ࡯࠼Σ߇ථ⿧ߔࠆ Shell ߩ⴫㕙߈ⵚࠆ㧚㈩▤ߪ㧘ࠕࠗ࠰ࡄ࡜ࡔ࠻࡝࠶ࠢ 8 ▵ὐෘ⡺ Shell ⷐߩ໧㗴ߦ㕖ᒢᕈᄌᒻߩലᨐࠍ⚻ᷣ⊛ߥᣇᴺߢ฽߼ࠆߎߣ

⚛ࠍ↪޿ߡಽഀߒ㧘⴫㕙߈ⵚߦᴪߞߡߪኻ⒓࡜ࠗࡦࠬࡊ

߇ߢ߈ࠆ㧚੹࿁ߩ⸃ᨆߢߪ߈ⵚ㐽ญߩᓇ㗀ߪήⷞߒ㧘߈࡝ࡦࠣⷐ⚛ࠍ↪޿ߚ㧚ⷐ⚛ᢙ 350㧘▵ὐᢙ 980 ߢ޽ࠅ㧘ⵚ㐿ญߩߺߩᓇ㗀ࠍ⠨ኤߒߚ㧚ߘߩὑ߈ⵚ߇㐿ญߔࠆᣇᔕജ㧙߭ߕߺᦛ✢ߪ㧘Ramberg - Osgood ߩᑼߦᓥ߁߽ߩ

ะߩߺߦᒝ೙ᄌ૏ࠍਈ߃ࠆ㧘ߣߒ㧘ᄙ⋥✢ㄭૃߒߡ↪޿ߚ㧚࿑  ߦᔕജ߭ߕߺᦛ

ߞߚ㧚ߎߩߎߣࠃࠅ㧘࡜ࠗࡦࠬࡊ࡝ࡦࠣࡕ࠺࡞ߪ⩄㊀ጁ

✢ 9㧕ࠍ㧘㧔4.4.4㧕ᑼߦㄭૃᑼࠍ␜ߔ㧚ᱧߦኻߔࠆലᨐߪ⠨ᘦߢ߈ߥ޿߇㧘ૐࠨࠗࠢ࡞∋ഭᒝᐲᝄࠅᄌ૏೙ᓮߩ⸃ᨆࠍⴕ

ߦኻߒ㧘ฦࠨࠗࠢ࡞ߩ߈ⵚㅴዷࠍ⚻ᷣ⊛ߦ⴫⃻ߢ߈ࠆࡕ࠺࡞ߣ⠨߃ࠄࠇࠆ㧚

H

§V ·
V
 H 0D ¨ ¸
E
©V0 ¹

n

ታ㛎ߢߪᱜᒏᵄߩ⽶ᣇะߩ౉ജ߇߈ⵚ㐿ญᣇะߦᒰߚ
ࠆߚ߼࿑  C ߦ␜ߒߡ޽ࠆ⽶ߩᄌ૏ߩߺࠍ౉ജߒ
ߚ㧚߹ߚ ታ㓙ߩ⹜㛎ߢߪ౉ജᄌ૏߇৻ቯᝄ᏷ߦ㆐ߔࠆ߹
ߢߦචᢙࠨࠗࠢ࡞ⷐߒߡ޿ࠆ߇㧘⸃ᨆߢߪ৻ቯᝄ᏷ߦ㆐

E

193 G Pa
0 .1 0 1 5 2 %H0
V 0
196 M PaD
1 .9 7n
5 .4 4ߔࠆએ೨ߩᝄ᏷ߪήⷞߒߚ㧚࡜ࡦ࠳ࡓᝄ᏷ᵄߦ㑐ߒߡ߽࿑  D ߦ␜ߔ㧘⽶ߩᄌ૏ߩߺ౉ജߒߚ㧚ࡕ࠺࡞ߪኻ⒓ᕈࠍ⠨ᘦߒߡ㧘⹜㛎૕ߩ 2 ಽߩ 1 ࠍࡕ࠺(4㨯4㨯4)࡞ൻߒ㧘ో๟߈ⵚߩ⹜㛎૕ߪᢿ㕙ߩඨ๟ߦ߈ⵚࠍዉ౉ߒ㧘ߘߩઁߩࡕ࠺࡞ߪታ㛎ߣห᭽ߩᒻ⁁ࠍ౉ജߒ⸃ᨆࠍⴕߞ
ߚ㧚㈩▤┵㕙ߦߪ೰૕ⷐ⚛ࠍ↪޿ߚ㧚ⷐ⚛ಽഀ࿑ࠍ࿑
 ߦ␜ߔ㧚࿑ਛߩᄥ✢ߢ␜ߒߚߪࠅⷐ⚛߇ో๟ EDM
ࡕ࠺࡞ߩ࡜ࠗࡦࠬࡊ࡝ࡦࠣⷐ⚛ߢ޽ࠆ㧚߹ߚ㧘ౝ࿶㧘㐽ญ┵᧦ઙߩゲᔕജߦ⋧ᒰߔࠆ✼⩄㊀ߩ޿ߕࠇ߽ਈ߃ߡ޿
ߥ޿㧚
−

54 −

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆



Stress(MPa)


















Strain(%)࿑  ᧚ᢱቯᢙ࿑  ㈩▤ⷐ⚛ಽഀ࿑

Fig.4.4-3

Fig.4.4-4

Stress-Strain curve.

Finite element mesh subdivision.

 ⸃ᨆ⚿ᨐߣ⠨ኤታ㛎ߣ⸃ᨆߦ߅ߌࠆ߈ⵚ⽾ㅢࠨࠗࠢ࡞ᢙࠍᲧセߒߚⵚ߇⽾ㅢߒߡ޿ࠆ㧚ታ㛎ߢߪ 3 ᰴర⊛ߥⷐ࿃㧔EDM ߪ㈩ࠣ࡜ࡈ෸߮⴫ࠍ࿑ 㧘⴫ ߦ␜ߔ㧚߹ߚ㧘౉ജ▤๟ᣇะߦ⋥✢⊛ߥಾᰳ߈ߛ߇㧘SCC ߪ๟ᣇะߦ⋥✢⊛ᵄ߇࡜ࡦ࠳ࡓᝄ᏷ᵄએᄖߩฦࡕ࠺࡞ߦ߅ߌࠆ㧘߈ⵚㅴዷߥ߈ⵚᒻ⁁ߢߪߥ޿㧕߽㊀ߥߞߡ޿ࠆߩߦኻߒ㧘⸃ᨆߢ

ߩㆊ⒟ࠍ࿑  ߦ␜ߔ㧚࿑  ෸߮⴫  ࠃࠅታߪ 2 ᰴరᒻ⁁ߩߺࠍ⠨ᘦߔࠆὑ㧘ታ㛎ߣ⸃ᨆ߇ቢోߥኻ

㛎ߦ߅ߌࠆฦ⹜㛎૕ߩ߈ⵚㅴዷ㧛⽾ㅢ௑ะࠍ⸃ᨆ߇ᝒ߃

ᔕ㑐ଥߣߥߞߡ޿ߥ޿㧚ߡ޿ࠆ੐߇ࠊ߆ࠆ㧚߹ߚో๟߈ⵚ෸߮㧘90q߈ⵚࠍᮨᡆ

੹࿁ߩ⸃ᨆߢߪ⺋Ꮕⷐ࿃ࠍᄙಽߦ฽ࠎߢ޿ࠆᭂૐࠨ

ߒߚ߽ߩߦߟ޿ߡߪ⸃ᨆ⚿ᨐߩᣇ߇ᣧߊ⽾ㅢߒߡ޿ࠆ߇㧘ࠗࠢ࡞ߩ∋ഭ߈ⵚㅴዷ㧛⽾ㅢ᜼േߦኻߒ㧘޿ߕࠇߩ⹜㛎ઁߩඨᬦ౞߈ⵚ෸߮ⶄ㔀ߥᒻ⁁ࠍߒߚᓸዊ߈ⵚߦ㑐ߒߡ૕߽࿑  ߦ␜ߔ⸃ᨆߣታ㛎⚿ᨐ߇৻⥌ߔࠆ⋥✢ઃㄭߪ㧘ታ㛎⚿ᨐࠃࠅ㐳ኼ๮஥ߩ⚿ᨐߣߥࠆ߽ߩ߇ᄙ޿㧚ᓸߦὐ࿷ߔࠆ੐߆ࠄ㧘ല₸⊛߆ߟ♖ᐲ⦟ߊ⸃ᨆࠍⴕ߁੐߇

ዊ߈ⵚ߶ߤ⸃ᨆߢߪㅴዷ߇ㆃߊߥࠆ௑ะߣߥߞߡ޿ࠆ㧚಴᧪ߚߣ⸒߃ࠆ㧚ታ㛎⚿ᨐߢߪ㧘EDM ࡁ࠶࠴ߩᣇ߇ SCC ߈ⵚࠃࠅᣧ޿ࠨ

੹ᓟߩ⺖㗴ߣߒߡߪ㧘਄⸥ߩ⹏ଔᚻᴺࠍ〯߹߃ߚ਄ߢ㧘ࠗࠢ࡞ᢙߢ߈ⵚ߇⽾ㅢߔࠆ௑ะߦ޽ࠆ߇㧘⸃ᨆߢߪ SC07⩄㊀ጁᱧߩ⠨ᘦߥߤ࡜ࠗࡦࠬࡊ࡝ࡦࠣࡕ࠺࡞ߢ⴫⃻ߢ߈

ߣ EM08 ࠍᲧセߔࠆߣ SC07 ߩᣇ߇ᣧ޿ࠨࠗࠢ࡞ᢙߢ߈

ߥ޿໧㗴ߦߟ޿ߡ㧘ᣂߚߦ⹏ଔᚻᴺࠍឭ᩺ߔࠆ੐ߢ޽ࠆ㧚㪫㪿㪼㩷㫅㫌㫄㪹㪼㫉㩷㫆㪽㩷㪺㫉㪸㪺㫂㩷㫇㪼㫅㪼㫋㫉㪸㫋㫀㫆㫅㪺㫐㪺㫃㪼㫊㩷㫀㫅㩷㪼㫏㫇㪼㫉㫀㫄㪼㫅㫋

㪈㪇㪇㪇

㪜㪤㪇㪉
㪜㪤㪇㪋
㪜㪤㪇㪍
㪜㪤㪇㪏
㪜㪤㪇㪐
㪪㪚㪇㪈
㪪㪚㪇㪎
㪜㪤㪇㪊
㪜㪤㪇㪌

㪈㪇㪇

㪈㪇

㪈
㪈

㪈㪇

㪈㪇㪇

㪈㪇㪇㪇

㪫㪿㪼㩷㫅㫌㫄㪹㪼㫉㩷㫆㪽㩷㪺㫉㪸㪺㫂㩷㫇㪼㫅㪼㫋㫉㪸㫋㫀㫆㫅㩷㪺㫐㪺㫃㪼㫊㫀㫅㩷㪸㫅㪸㫃㫐㫊㫀㫊࿑  ታ㛎ߣ⸃ᨆߦ߅ߌࠆ߈ⵚ⽾ㅢ߹ߢߩ➅ࠅ㄰ߒᢙߩᲧセ
Fig.4.4-5

Comparison of the number of crack penetration cycles in the experiment and analysis.

−

55 −

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬⴫  ታ㛎⚿ᨐߣ⸃ᨆ⚿ᨐ
Table 4.4-1

Test specimen.

Comparison of analytical results and experimental results.

Flaw shape and type

Name Material Crack Type

SC01 SUS304

SCC

SC07 SUS304

SCC

EM02 SUS304

EDM

EM03 SUS304

EDM

EM04 SUS304

EDM

EM05 SUS304

EDM

EM06 SUS304

EDM

EM08 SUS304

EDM

EM09 SUS304

EDM

Loading condition Experimental result Analytical result

Input displacement(mm)×Penetration cycle
test frequency.
71± 50 mm ×
Sinusoidal(3 blocks
5blocks
correspond. )173± 50 mm ×
䋨7 blocks
Sinusoidal
5 blocks
correspond.䋩
± 25 mm ×
1block0.5t
360
Sinusoidal
8(Constant region 16
waves)
69
Random amplitude± 25 mm ×䋨2 blocks
0.5t
360
wave
10 blocks
correspond.䋩
± 21 mm ×
1 block
0.5t
360
Sinusoidal
10(Constant region18
waves)
61
Random amplitude± 35 mm ×䋨2 blocks
0.5t
90
wave
4 blocks
correspond.䋩
44
SCC Crack and equivalent cross section± 50 mm ×
Sinusoidal(2 blocks(SC01 simulation)
2 blocks
correspond.)214
SCC Crack and equivalent cross section± 50 mm ×
Sinusoidal(9 blocks(SC07 simulation)
4 blocks
correspond.)± 35 mm ×
1 block
0.5t
90
Sinusoidal
10(Constant region 19
waves)
Depth
t㧦Thickness


deg

−

Pattern of Disp

56 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

㪎㪇㪠㫅㫎㪸㫃㫃

㪍㪇㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪌㪇㪋㪺㫐㪺㫃㪼㫊

㪋㪇㪎㪺㫐㪺㫃㪼㫊

㪊㪇㪏㪺㫐㪺㫃㪼㫊

㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㪏㪇

㧔a㧕EM02.

㪠㫅㫎㪸㫃㫃
㪎㪇㪜㫏㫋㪼㫉㫅㪸㫃
㫎㪸㫃㫃㪠㫅㫀㫋㫀㪸㫃
㪚㫉㪸㪺㫂㪍㪺㫐㪺㫃㪼㫊㪍㪇㪌㪇㪋㪇㪐㪺㫐㪺㫃㪼㫊

㪊㪇㪈㪇㪺㫐㪺㫃㪼㫊

㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㪏㪇

㧔b㧕EM04.

㪠㫅㫎㪸㫃㫃
㪎㪇㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪍㪇㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪌㪇㪉㪇㪺㫐㪺㫃㪼㫊

㪋㪇㪋㪇㪺㫐㪺㫃㪼㫊
㪋㪋㪺㫐㪺㫃㪼㫊

㪊㪇
㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㧔c㧕EM06.

࿑  ߈ⵚㅴዷᒻ⁁(2/2)
Fig.4.4-6 Surface crack extension with increasing load cycles (1/2).

−

57 −

㪏㪇

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ ╙ 220 ภ 2001 ᐕ 10 ᦬㪠㫅㫎㪸㫃㫃
㪎㪇㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪍㪇㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪌㪇㪈㪇㪇㪺㫐㪺㫃㪼㫊㪋㪇㪈㪌㪇㪺㫐㪺㫃㪼㫊㪊㪇㪉㪇㪇㪺㫐㪺㫃㪼㫊㪉㪈㪋㪺㫐㪺㫃㪼㫊

㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㪏㪇

㧔d㧕EM08.
㪎㪇㫀㫅㫎㪸㫃㫃
㪍㪇㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪌㪇㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪋㪇㪍㪺㫐㪺㫃㪼㫊

㪊㪇㪐㪺㫐㪺㫃㪼㫊

㪉㪇㪈㪇㪺㫐㪺㫃㪼㫊

㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㪏㪇

㧔e㧕EM09.
㪠㫅㫎㪸㫃㫃
㪎㪇㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪍㪇㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪌㪇㪉㪇㪺㫐㪺㫃㪼㫊
㪋㪇㪺㫐㪺㫃㪼㫊

㪋㪇㪍㪇㪺㫐㪺㫃㪼㫊

㪊㪇㪎㪈㪺㫐㪺㫃㪼㫊
㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㪏㪇

㧔f㧕SC01.
㪠㫅㫎㪸㫃㫃
㪜㫏㫋㪼㫉㫅㪸㫃㩷㫎㪸㫃㫃㪎㪇㪠㫅㫀㫋㫀㪸㫃㩷㪚㫉㪸㪺㫂㪍㪇㪍㪇㪺㫐㪺㫃㪼㫊

㪌㪇㪈㪉㪇㪺㫐㪺㫃㪼㫊㪋㪇㪈㪌㪇㪺㫐㪺㫃㪼㫊㪊㪇㪈㪎㪋㪺㫐㪺㫃㪼㫊
㪉㪇
㪈㪇
㪇
㪄㪏㪇

㪄㪍㪇

㪄㪋㪇

㪄㪉㪇

㪇

㪉㪇

㪋㪇

㪍㪇

㧔g㧕SC07.

࿑  ߈ⵚㅴዷᒻ⁁(2/2)
Fig.4.4-6 Surface crack extension with increasing load cycles (2/2).

−

58 −

㪏㪇

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ ႎ๔ᦠ̆ਛ᧛߶߆

࡜࠴ࠚ࠶࠻ᄌᒻ೨ࠃࠅ࡜࠴ࠚ࠶࠻ᄌᒻᓟߦടࠊࠆ⩄㊀ ᧄ┨ߩ߹ߣ߼
ᧄ┨ߢߪ㧘ᰳ㒱ࠍ᦭ߔࠆ㈩▤ߦߟ޿ߡ㧘᦭㒢ⷐ⚛ᴺ߇ᷫ⡺ㇱߩ⎕უᒝᐲߦᓇ㗀ࠍਈ߃ࠆ੐߇ࠊ߆ߞߚ㧚ࠍ↪޿ߡ⸃ᨆࠍⴕ޿㧘ߘࠇߙࠇߩᰳ㒱ㇱߩ⎕უߦኻߔ
4.3 ߢߪዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆࠛ࡞ࡏ▤ߦߟ޿ߡ㧘ࠆ⹏ଔࠍⴕߞߚ㧚એਅߦᧄ┨ߢᓧࠄࠇߚᚑᨐߦߟ޿ߡ␜ߔ㧚

Solid ⷐ⚛෸߮ Shell ⷐ⚛ࠍ↪޿ߚᒢ႟ᕈ⸃ᨆࠍⴕߞߚ㧚

4.2 ߢߪዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ⋥▤ߦኻߒ㧘⸃ᨆࠦ࡯ 4.4 ߢߪ⴫㕙߈ⵚࠍ᦭ߔࠆ㈩▤ߩૐࠨࠗࠢ࡞∋ഭ߈࠼ ABAQUS ࠍ↪޿ߡᒢ႟ᕈ⸃ᨆࠍⴕߞߚ㧚Solid ⷐ⚛

ⵚㅴዷ⸃ᨆࠍⴕߞߚ㧚⸃ᨆࠦ࡯࠼ ABAQUS ߦ߅ߌࠆ࡜

ࠍ↪޿ߡ㧘ታ㛎ߢⴕࠊࠇߚ➅㄰ߒ⋥▤ 4 ὐᦛߍ⹜㛎ࠍࠗࡦࠬࡊ࡝ࡦࠣࡕ࠺࡞ࠍ↪޿㧘⎕უജቇࡄ࡜ࡔ࡯࠲ Jmax⸃ᨆߔࠆ੐ߢ㧘࡜࠴ࠚ࠶࠻⃻⽎ߦ઻߁㈩▤ߩᒻ⁁ᄌൻࠍ▚಴ߔࠆߎߣߢ㧘߈ⵚㅴዷ㊂ࠍ᳿ቯߒ㧘ߘߩ⹏ଔᚻ

ࠍࠪࡒࡘ࡟࡯࠻ߒ㧘߭ߕߺ㓸ਛㇱߩᢿቯߣߘߩේ࿃ࠍ

㗅ࠍ➅ࠅ㄰ߔߎߣߢ㧘⴫㕙߈ⵚ߇ㅴዷߒ⽾ㅢߔࠆ߹ߢ

⠨ኤߢ߈ߚ㧚ߐࠄߦ Shell ⷐ⚛ࠍ↪޿◲ᤃൻߒ㧘⸃ᨆߩߩࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕ߁੐߇಴᧪ߚ.ᧄ⎇ⓥߢឭ᩺ߒା㗬ᕈࠍ៊ߥࠊߕᄙ⒳ߩ⸃ᨆࠍⴕ߁੐߇ߢ߈ߚ㧚ߚࡕ࠺࡞ࠍ↪޿ࠆ੐ߢ㧘ⶄ㔀ߥ㧞ᰴరᒻ⁁ߩ߈ⵚߦኻ

Coffin㧘㡻ᚭญ㧘ᦺ↰ࠄߦࠃߞߡቯ⟵ߐࠇߚ࡜࠴ࠚ࠶

ߒ㧘߈ⵚㅴዷߩ⹏ଔࠍⴕ߁੐߇ߢ߈㧘ታ㛎ߦ߅ߌࠆ⎕࠻ߦࠃࠆᑧᕈᶖ⠻ߩᓇ㗀ࠍ⠨ᘦߒߚᚻᴺࠍ↪޿㧘∋ഭუࠨࠗࠢ࡞ᢙߣᲧߴ㧘᭎ߨ⦟ᅢߥ⚿ᨐ߇ᓧࠆߎߣ߇಴

⎕უኼ๮ߩ੍᷹ࠍⴕ߁੐ߢ㧘⩄㊀㗅ᐨߩᄌൻߦኻߒ㧘

᧪ߚ㧚

−

59 −

㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬㈩▤♽ߩേ⊛ᔕ╵ߦኻߔࠆ⹏ଔ
᭎ⷐ
ㆊᄢߥ࿾㔡േ߇㈩▤♽ߦ౉ജߐࠇߚ႐ว㧘㈩▤♽ߦㆊᄢߥᝄേᔕ╵߇↢ߓ㧘ࠛ࡞ࡏ╬ߩᄌᒻߩ㓸ਛㇱߦ߅޿ߡዪᚲ⊛ߥ႟ᕈᄌᒻ߇↢ߓࠆน⢻ᕈ߇޽ࠆ㧚㈩▤♽ߦዪᚲ⊛ߥ႟ᕈᄌᒻ߇⊒↢ߔࠆ႐ว㧘ᝄേࠛࡀ࡞ࠡ߇ᶖᢔߐࠇ㧘㈩▤♽ߩᝄേᔕ╵ߪૐᷫߔࠆߎߣ߇৻⥸⊛ߦ⍮ࠄࠇߡ޿ࠆ㧚⃻࿷㧘ᣣᧄߩේሶജ⊒㔚ࡊ࡜ࡦ࠻㈩▤♽ߩ⠴㔡⸳⸘ߢߪ㧘࿾㔡⩄㊀ߦࠃࠅ㈩▤ߦ↢ߓࠆᔕജࠍ▚ቯߒ㧘፣უߦኻߔࠆ⹏ଔߢ޽ࠆ1ᰴᔕജ⹏ଔ෸߮∋ഭ⹏ଔ߇ⴕࠊࠇࠆ㧚ߎࠇࠄߩ⹏ଔߩኻ⽎ߣߥࠆᔕജߪ㒠ફᔕജએ਄ߩ୯ߦߥࠆ
ߎߣ߇⸵ኈߐࠇߡ߅ࠅ㧘႟ᕈᄌᒻߪ⸵ኈߐࠇߡ޿ࠆߎߣ
ߣߥࠆ㧚ߒ߆ߒ㧘㈩▤♽ߩ࿾㔡ᔕ╵⸘▚ߦ↪޿ࠆᷫ⴮Ყߣ
ߒߡߪ㧘႟ᕈᄌᒻ߇⠨ᘦߐࠇߡ޿ߥ޿ᷫ⴮Ყ㧔⠴㔡⸳⸘↪
ᷫ⴮ቯᢙ㧕߇↪޿ࠄࠇߡ޿ࠆ㧚ߥ߅㧘ߎߩᷫ⴮Ყߪ㧘㈩▤ᡰᜬౕߦ߅޿ߡᶖᢔߐࠇࠆࠛࡀ࡞ࠡࠍ⠨ᘦߒ⸳ቯߐࠇߚ
߽ߩߢ޽ࠆ 1)㧚ߎߩࠃ߁ߦ㧘႟ᕈᄌᒻߦࠃࠆᝄേࠛࡀ࡞ࠡ
ߩᶖᢔ߇ᦼᓙߢ߈ࠆߦ߽㑐ࠊࠄߕ㧘ᒢᕈᄌᒻ㗔ၞߩᷫ⴮Ყߣห᭽ߩᷫ⴮Ყ߇↪޿ࠄࠇࠆߎߣߪ㧘㈩▤♽ߩᝄേᔕ╵ࠍㆊᐲߦᄢ߈ߊ⷗Ⓧ߽ࠆⷐ࿃ߣߥࠆ㧚೨㗄߹ߢߦ␜ߒߚࠃ߁ߦ㧘ᐔ㕙㈩▤♽෸߮┙૕㈩▤♽⹜㛎૕ߦኻߔࠆടᝄታ㛎ࠍⴕ޿㧘ߎࠇࠄߩታ㛎ߦ߅޿ߡ㧘㈩▤♽⹜㛎૕ߢߩᒢ႟ᕈᔕ╵․ᕈߦ㑐ߔࠆ࠺࡯࠲ࠍขᓧ
ߔࠆߎߣ߇ߢ߈ߚ㧚ߎߎߢߪ㧘ᒢ႟ᕈᔕ╵ߦ߅ߌࠆᦨᄢᔕ
╵㊂ࠍ੍᷹ߔࠆᚻᴺࠍ┙᩺ߒ㧘਄⸥ታ㛎࠺࡯࠲ߣߩᲧセߦࠃࠅߘߩㆡ↪ᕈߩᬌ⸛ࠍታᣉߒߡ޿ࠆ㧚ߎߩᒢ႟ᕈᔕ╵੍᷹ᚻᴺߢߪ㧘ᔕ╵ᄌ૏ߦኻߔࠆࠛ࡞
ࡏߢߩᶖᢔࠛࡀ࡞ࠡߩᄌൻࠍ㧘FEM ࠍ↪޿ߚ㕒⊛ᒢ႟ᕈ⸃ᨆߦࠃࠅ⸘▚ߒ㧘㈩▤♽ో૕ߩᝄേࠛࡀ࡞ࠡߣߩᲧ₸ߣߒߡ╬ଔᷫ⴮Ყࠍផቯߒߡ޿ࠆ㧚ߎߩ╬ଔᷫ⴮Ყߪ㧘ᔕ╵ᄌ૏ߦଐሽߔࠆ㕖✢ᒻߩᷫ⴮ߣߥࠆ㧚৻ᣇ㧘ᔕ╵ᄌ૏ߪᷫ⴮Ყߦଐሽߔࠆ㊂ߢ޽ࠆߚ߼㧘ᄌ૏ଐሽဳߩᷫ⴮ߩၮ
ߢᝄേᔕ╵ࠍ੍᷹ߔࠆߦߪ෼᧤⸘▚߇ᔅⷐߣߥࠆ㧚ߎߎߢㅀߴࠆᒢ႟ᕈᔕ╵੍᷹ᚻᴺߢߪ㧘ᝄേᔕ╵㊂߇ᷫ⴮Ყࠍࡄ࡜ࡔ࡯࠲ߣߒߚᄙ㗄ᑼߢㄭૃߢ߈ࠆߣ઒ቯߒ㧘਄⸥෼᧤⸘▚ߩ◲⇛ൻࠍ࿑ߞߡ޿ࠆ㧚ߎߩᒢ႟ᕈᔕ╵੍᷹ᚻ
ᴺߢ▚ቯߐࠇߚᔕ╵㊂ࠍታ㛎⚿ᨐߣᲧセߒߚ⚿ᨐ㧘႟ᕈᄌᒻߦࠃࠆᔕ╵ૐᷫലᨐߩ௑ะ߇ౣ⃻ߐࠇ㧘ታ㛎⚿ᨐࠃࠅ߽଻቞⊛ߥᔕ╵㊂ࠍ▚ቯߢ߈ࠆߎߣ߇ࠊ߆ߞߚ㧚ᒢ႟ᕈᔕ╵੍᷹ᚻᴺߩ᭎ᔨ
ߎߎߢߩᒢ႟ᕈᔕ╵੍᷹ᚻᴺߪ㧘႟ᕈᄌᒻࠍ઻߁ㆊᄢ
ߥ࿾㔡ᔕ╵߇⊒↢ߔࠆ႐วߩᦨᄢᔕ╵㊂ࠍ੍᷹ߔࠆᚻᴺ
ߢ޽ࠆ㧚⃻࿷ߩ㈩▤♽ߩ⠴㔡⸳⸘ߦ߅޿ߡߪ㧘ਥߦ㧘ᔕ╵ࠬࡍࠢ࠻࡞⸃ᨆ㧔✢ᒻᝄേᔕ╵⸃ᨆ㧕ࠍ↪޿ߡ㧘㈩▤♽ߩᦨᄢᔕ╵㊂㧔㈩▤♽ฦㇱߦ↢ߓࠆࡕ࡯ࡔࡦ࠻㧕ࠍ᳞߼ߡ޿
ࠆ㧚ߎߩᦨᄢᔕ╵㊂ࠍၮߦ㈩▤♽ฦㇱߩᔕജࠍ▚಴ߒ㧘1ᰴᔕജߣߒߡߩ⹏ଔࠍታᣉߒߡ޿ࠆ㧚߹ߚ㧘∋ഭ⹏ଔߦ߅
޿ߡߪ㧘㈩▤♽ߩ࿾㔡ᔕ╵ࠍ⹦⚦ߥᤨೞᱧ࠺࡯࠲ߣߒߡ
᳞߼ߡ⹏ଔߒߡ޿ࠆߩߢߪߥߊ㧘⹏ଔ਄቟ో஥ߦ⸳ቯߐ

ࠇߚ╬ଔ➅㄰ߒ࿁ᢙߛߌ࿾㔡ᔕ╵ߢߩᦨᄢᔕജ߇➅㄰ߒ↢ߓࠆߣߒߡ⹏ଔࠍታᣉߒߡ޿ࠆ㧚ߎߩࠃ߁ߦ㧘⃻ⴕߩ⠴㔡⸳⸘ߢߪ㧘࿾㔡ᔕ╵ߩᦨᄢ୯ߩߺࠍ▚ቯߒ㧘ߎߩᦨᄢᔕ
╵ࠃࠅ▚಴ߐࠇߚᔕജߦኻߒߡᒝᐲ⹏ଔ߇ⴕࠊࠇߡ޿ࠆ㧚ߎߎߢㅀߴࠆᒢ႟ᕈᔕ╵੍᷹ᚻᴺ߽㧘࿾㔡ᔕ╵ߩᦨᄢ୯ߩߺࠍ᳞߼ࠆ߽ߩߢ޽ࠅ㧘㈩▤♽߇႟ᕈᄌᒻࠍ↢ߓࠆࠃ߁ߥㆊᄢߥ࿾㔡ᔕ╵߇↢ߓࠆ႐วߩᦨᄢᔕ╵㊂ࠍ⸘▚
ߔࠆᚻᴺߩ߭ߣߟߢ޽ࠆ㧚ߥ߅㧘⹦⚦ߦᒢ႟ᕈᔕ╵ߩጁᱧࠍ᳞߼ࠆߚ߼ߩᚻᴺߣߒߡߪ㧘FEM ߦࠃࠆ㕖✢ᒻ㧔᧚ᢱ෸߮ᐞ૗ቇ⊛㕖✢ᒻ㧕ߩᤨೞᱧᔕ╵⸃ᨆ߇᜼ߍࠄࠇࠆ㧚ߎߩ⹦⚦ᒢ႟ᕈᔕ╵⸃ᨆߢߪ㧘㈩▤♽ߩో૕ߣߒߡߩᒢ႟
ᕈᔕ╵᜼േ㧔႟ᕈᄌᒻߦࠃࠆ೰ᕈߩૐਅ෸߮ࠛࡀ࡞ࠡᶖ
ᢔߦ઻߁ᝄേᔕ╵᜼േߩᄌൻ㧕෸߮ዪᚲ⊛ߥ႟ᕈ߭ߕߺ
ߩጁᱧࠍᛠីߔࠆߚ߼ߦ㧘㕖✢ᒻߪࠅⷐ⚛㧔ߪࠅⷐ⚛ߩ๟ᣇะ෸߮ゲᣇะߦⓍಽὐࠍ᦭ߔࠆᡆૃࠪࠚ࡞ⷐ⚛㧕㧘ࠪࠚ࡞ⷐ⚛߽ߒߊߪ࠰࡝࠶࠼ⷐ⚛ߦࠃࠆ FEM ࡕ࠺࡞ࠍ᭴▽ߒ㧘േ⊛ߥ⸃ᨆߢ޽ࠆ⋥ធⓍಽᴺߦࠃࠆᤨೞᱧ⸃ᨆ߇ⴕ
ࠊࠇࠆߎߣߣߥࠆ㧚਄⸥ߩ FEM ࡕ࠺࡞ࠍ᭴▽ߔࠆߦߪ㜞ᐲߥᛛⴚߣᤨ㑆ࠍⷐߔࠆ㧚߹ߚ㧘ࡕ࠺࡞ߩⓍಽὐᢙ߇㕖Ᏹߦᄙߊߥࠅ㧘ߘߩࡕ࠺࡞ߦኻߒߡേ⊛ߥ㕖✢ᒻ㧔᧚ᢱ㧘ᐞ૗ቇ⊛㕖✢ᒻ㧕⸃ᨆࠍታᣉߔࠆߚ߼㧘ᄙᄢߥᤨ㑆ࠍⷐߔࠆ㧚ߎߩࠃ߁ߥ⹦⚦⸃ᨆࠍ㧘ᄙ᭽ߥᒻ⁁ߩ㈩▤♽ߩోߡߩ⸳⸘ߦ↪޿ࠆߎߣߪਇน⢻ߣ⠨߃ࠄࠇࠆ㧚એ਄ߩߎߣࠍ
〯߹߃ߡ㧘ታ㓙ߩ㈩▤♽ߩ⠴㔡⸳⸘ߦㆡ↪ߒᓧࠆ◲ᤃ⸘
▚ᚻᴺߣߒߡ㧘ᧄᒢ႟ᕈᔕ╵ᚻᴺࠍ┙᩺ߒߚ㧚ᒢ႟ᕈᔕ╵੍᷹ᚻᴺߩᚻ㗅ࠍ࿑ߦ␜ߔ㧚ߎߩᒢ႟ᕈᔕ╵੍᷹ᚻᴺߪ㧘ᄢ߈ߊಽߌߡ3⒳㘃ߩ⸘▚ࠃࠅ᭴ᚑߐ
ࠇࠆ㧚ߎࠇࠄ⸘▚ߩ᭎ⷐࠍએਅߦ␜ߔ㧚Ԙ㈩▤♽ߩਛߩᔕജ㓸ਛㇱߢ޽ࠆ㈩▤⛮ᚻ㧔ᧄᬌ⸛ߢߪ
ࠛ࡞ࡏ㧕ߦ߅ߌࠆᶖᢔࠛࡀ࡞ࠡࠍ᳞߼ࠆ㧚ࠛ࡞ࡏ╬ߩElasto-plastic analysis

Modal analysis

Elastic response
analysis

Dissipation energy

Natural frequency
Effective mass

Max. response disp.
Bending angle
Ratio of these values

Relationship between
bending angle anddissipation energy

Vibration energy and dissipationenergy of piping system
Equivalent damping ratio
Relationship between the max.
response displacement and theequivalent damping ratio

Prediction ofelastic-plastic responseof piping system
Relationship between the damping ratio andthe max response displacement࿑  ᧄ┨ߢឭ᩺ߒߚᒢ႟ᕈᔕ╵੍᷹ᴺߩᚻ㗅
Fig. 5.2-1 Procedure of elastic-plastic prediction method proposedin this section.

− 6600 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆➅㄰ߒᦛߍ⹜㛎߽ߒߊߪFEM⸃ᨆߦࠃࠅ⩄㊀ᄌ૏ᦛ✢ࠍ᳞߼㧘ߘߩౝㇱ㕙Ⓧࠃࠅᶖᢔࠛࡀ࡞ࠡࠍ᳞߼ࠆ㧚ԙ ㈩▤♽ߩࡕ࡯࠼⸃ᨆ෸߮✢ᒻߩᝄേᔕ╵⸃ᨆ㧔ᧄᬌ⸛ߢߪᔕ╵ࠬࡍࠢ࠻࡞⸃ᨆ㧕ࠍⴕ޿㧘㈩▤♽ߩ᦭ല⾰㊂㧘࿕᦭ᝄേᢙ㧘ᷫ⴮Ყߣ࿾㔡ᔕ╵ߩ㑐ଥࠍ᳞߼ࠆ㧚Ԛ ╙ 3 ߦᶖᢔࠛࡀ࡞ࠡߣ㈩▤♽ో૕ߩᝄേࠛࡀ࡞ࠡߩᲧ
₸߆ࠄ╬ଔᷫ⴮Ყߣᔕ╵ᄌ૏ߩ㑐ଥࠍ᳞߼㧘╙ 2 ߩࡄ࡯࠻ߦ߅޿ߡ᳞߼ࠄࠇߚ࿾㔡ᔕ╵ߣᷫ⴮Ყߩ㑐ଥࠍ⚵ߺวࠊߖࠆߎߣߦࠃࠅᒢ႟ᕈᔕ╵㊂ࠍ▚಴ߔࠆ㧚ᧄ⎇ⓥߢታᣉߒߚߎࠇࠄ3⒳㘃ߩ⸘▚ߩ⹦⚦ࠍએ㒠ߦ␜ߔ㧚 ᒢ႟ᕈᔕ╵੍᷹ᚻᴺߩ⸘▚ߩ⹦⚦ᶖᢔࠛࡀ࡞ࠡࠍ᳞߼ࠆߚ߼ߩ ('/ ⸃ᨆ㈩▤♽ߩ࿾㔡ᔕ╵ߦ߅޿ߡ႟ᕈᄌᒻ߇↢ߓࠆߩߪ㧘㈩▤♽ߩਛߢᔕജ߇㓸ਛߔࠆࠛ࡞ࡏ㧘࠹ࠖ㧘࡟࠺ࡘ࡯ࠨ㧘ࡁ࠭࡞ߩㇱಽߣ⠨߃ࠄࠇࠆ㧚৻⥸⊛ߦ㧘㈩▤♽ߢᦨᄢᔕജ⊒↢▎ᚲߣߥࠆߩߪ㧘ߎࠇࠄߩ㈩▤⛮ᚻㇱߢ޽ࠅ㧘ㅢᏱߩ⋥▤ㇱߦ߅޿ߡ႟ᕈᄌᒻ߇↢ߓࠆߎߣߪ߹ࠇߥߎߣߣ⠨߃ࠄࠇࠆ㧚㈩▤⛮ᚻߦ߅ߌࠆ႟ᕈᄌᒻߩᶖᢔࠛࡀ࡞ࠡࠍ᳞⴫ 
ࠛ࡞ࡏߩ઀᭽
Table 5.3-1 Specification of elbows.

Outer
Diameter
(mm)

Elbow
Name
100A
SCH80

Thickness(mm)߼ࠆߎߣߦࠃࠅ㧘ᝄേᔕ╵ࠍૐᷫߔࠆലᨐ㧘ߔߥࠊߜᷫ⴮
ࠍઃਈߔࠆലᨐࠍ᳞߼ࠆ㧚઒ߦ㧘ታ㓙ߩ㈩▤♽ߦ↪޿ࠄࠇࠆోߡߩ㈩▤⛮ᚻߩᶖᢔࠛࡀ࡞ࠡࠍ㧘⹜㛎߽ߒߊߪ FEM
⸃ᨆߦࠃࠅ⸘▚ߢ߈ࠇ߫㧘છᗧߩ㈩▤♽ో૕ߦ߅ߌࠆ႟
ᕈᄌᒻߦ઻߁ᶖᢔࠛࡀ࡞ࠡࠍ▚ቯߢ߈ࠆߣ⠨߃ࠄࠇࠆ㧚ߎߎߢߪ㧘ࠛ࡞ࡏߩ㕙ౝᦛߍߦࠃࠆ႟ᕈᄌᒻߢߩᶖᢔ
ࠛࡀ࡞ࠡࠍ FEM ⸃ᨆߦࠃࠅ▚ቯߒߚ㧚FEM ⸃ᨆࠍታᣉߒ
ߚࠛ࡞ࡏߩ઀᭽ࠍ⴫ߦ␜ߔ㧚⸃ᨆߩኻ⽎ߣߥߞߚࠛ
࡞ࡏߪ㧘ᧄ⎇ⓥߢടᝄታ㛎߇ⴕࠊࠇߚᐔ㕙㈩▤♽⹜㛎૕෸߮┙૕㈩▤♽⹜㛎૕ߦ૶↪ߐࠇߡ޿ࠆࠛ࡞ࡏߢ޽ࠆ㧚㈩▤♽ߩᝄേࡕ࡯࠼ࠍ⠨ᘦߔࠆߣ㧘ߎࠇࠄߩࠛ࡞ࡏߢߩ
ᄌᒻߪ㕙ౝᦛߍᄌᒻ߇ᡰ㈩⊛ߢ޽ࠆߎߣ߆ࠄ㧘㕙ౝᦛߍ⽶⩄ߔࠆᒢ႟ᕈ⸃ᨆࠍታᣉߒߡ޿ࠆ㧚‫⸃ޓ‬ᨆߩࡕ࠺࡞ࠍ࿑ ߦ␜ߔ㧚ߎߩࡕ࠺࡞ߪ㧘ࠛ࡞ࡏߩ๟ᣇะࠍ 48 ಽഀ㧘ゲᣇะࠍ 12 ಽഀߒ㧘ࠪࠚ࡞ⷐ⚛ߦࠃࠅ᭴ᚑߐࠇߚࡕ࠺࡞ߢ޽ࠆ㧚ࠛ࡞ࡏߩ┵ㇱߦߪ㈩▤ᄖᓘߩ 3.5 ୚ߩ㐳ߐߩ⋥▤ࠍធ⛯ߒߚࡕ࠺࡞ߣߥߞߡ޿ࠆ㧚㕙ౝᦛߍߩߺࠍ⠨ᘦߔࠆߎߣ߆ࠄࠛ࡞ࡏߩඨಽࠍࡕ࠺࡞ൻ
ߒߡ޿ࠆ㧚ߎߩ⸃ᨆࡕ࠺࡞ߦኻߒߡ㧘⴫ ߦ␜ߔౝ࿶
෸߮㕙ౝᦛߍߩᒝ೙ᄌ૏ࠍ⽶⩄ߒߚ㧚ߥ߅㧘ߎߩౝ࿶ߪታ
㛎ߢ⽶⩄ߒߚౝ࿶ࠍ↪޿ߡ޿ࠆ㧚‫ޓ‬FEM ⸃ᨆߦࠃࠅᓧࠄࠇߚࠛ࡞ࡏߩ㕙ౝᦛߍߦࠃࠆ⩄㊀ᄌ૏ᦛ✢ࠍ࿑ߦ␜ߔ㧚႟ᕈᄌᒻߦࠃࠅᶖᢔߐࠇࠆࠛ

Bending
Radius(mm)

8.0E+04100A
SCH120Moment (Nm)

8.6
114.3

152.4
11.1

0.0E+00-8.0E+04
-0.15

0.00

0.15

Bending angle (rad)(a) 100A SCH80.
8.0E+04(+)࿑  ࠛ࡞ࡏ⸃ᨆࡕ࠺࡞
Fig. 5.3-1 Analysis model of an elbow.
⴫ 
ࠛ࡞ࡏᒢ႟ᕈ⸃ᨆߩ౉ജ᧦ઙ
Table 5.3-2 Input condition of elasto-plastic analysis of elbows.

Elbow Name
100A SCH80

Pressure(MPa)
11

Amplitude of Input Disp.
(mm)

Moment (Nm)(-)

Input displacement

0.0E+00-8.0E+04
-0.15

0.00

0.15

Bending angle (rad)5, 10, 15, 20, 25,30,35,40(b) 100A SCH120.

100A SCH120

05, 10, 15, 20, 25,30

࿑  ࠛ࡞ࡏߩ⩄㊀ᄌ૏․ᕈ
Fig. 5.3-2 Load-displacement curves of an elbow.

− 6611 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬ࡀ࡞ࠡߪ㧘ߎߩ⩄㊀ᄌ૏ᦛ✢ߩౝㇱߩ㕙Ⓧߣߒߡ᳞߼ࠆ
ߎߣ߇ߢ߈ࠆ㧚౉ജ᧦ઙߢ޽ࠆᒝ೙ᄌ૏߆ࠄ᳞߼ࠄࠇࠆ
ᦛߍⷺᐲߣᶖᢔࠛࡀ࡞ࠡߩ㑐ଥࠍ࿑ߦ␜ߔ㧚ߎߩ࿑ߦ␜ߔࠃ߁ߦ㧘ߎߩᒢ႟ᕈᔕ╵੍᷹ᚻᴺߢߪߎߩᦛߍⷺ
ᐲߣᶖᢔࠛࡀ࡞ࠡߩ㑐ଥࠍᰴᑼߢㄭૃߔࠆߎߣߣߔࠆ㧚∆e = A1 ⋅ (θ − A2 )(5.3.1)A1 , A2 㧦ㄭૃᑼߩଥᢙ∆e 㧦ࠛ࡞ࡏߢߩᶖᢔࠛࡀ࡞ࠡθ 㧦ࠛ࡞ࡏߩ㕙ౝᦛߍߩⷺᐲᄌ૏

ᝄേࡕ࡯࠼⸃ᨆ
‫ޓ‬ᝄേࡕ࡯࠼⸃ᨆߢߪᝄേࡕ࡯࠼ߩ᦭ല⾰㊂ߣ࿕᦭ᝄേ
ᢙࠍ᳞߼㧘(5.3.2)ᑼߦࠃࠅ㈩▤♽ో૕ߩᝄേࠛࡀ࡞ࠡࠍ᳞
߼ࠆ㧚⸃ᨆࡕ࠺࡞ࠍ࿑  ෸߮࿑  ߦ␜ߔ㧚

2.0E+04
AnalysisǻE(Nm)

1.5E+04‫⸃ޓ‬ᨆߢ᳞߼ࠄࠇߚᶖᢔࠛࡀ࡞ࠡࠍ਄ᑼߢᦨዊ2ਸ਼ᴺߦࠃࠅㄭૃߒߚ⚿ᨐ㧘⴫  ߦ␜ߔଥᢙ߇ᓧࠄࠇߚ㧚‫ޓ‬એ਄ߩࠃ߁ߦ㧘ᧄ㗄ߢߪ⸃ᨆߢ⽶⩄ߐࠇߚᦛߍⷺᐲߣ㧘ߘߩ⚿ᨐߣߒߡᓧࠄࠇࠆᡰᜬ෻ജ߆ࠄ᳞߼ࠄࠇࠆࡕ࡯ࡔ
ࡦ࠻ࠍၮߦ⩄㊀ᄌ૏ᦛ✢ࠍ᳞߼㧘ߘߩ⩄㊀ᄌ૏ᦛ✢ߩౝㇱߩ㕙Ⓧߣߒߡᶖᢔࠛࡀ࡞ࠡ߇▚಴ߐࠇߚ㧚ߘߩ⚿ᨐ㧘㕙ౝᦛߍⷺᐲߣᶖᢔࠛࡀ࡞ࠡߩ㑐ଥ߇᳞߼ࠄࠇߚߎߣߣߥ
ࠆ㧚ߎߩ㑐ଥߪ㧘㈩▤♽ߢᒢ႟ᕈᄌᒻ߇↢ߓࠆ႐วߩᷫ⴮
ലᨐࠍᛠីߔࠆߚ߼ߩၮ␆࠺࡯࠲ߣߥࠆ㧚

Approximation

1.0E+04

5.0E+03

0.0E+00
0.00

0.05

0.10

0.15

Bending Angle (rad)(a) 100A SCH80.
2.0E+04
AnalysisǻE(Nm)

1.5E+04

Approximation

1.0E+04

5.0E+03

0.0E+00
0.00

0.05

0.10

0.15

Bending Angle (rad)࿑  ⸃ᨆࡕ࠺࡞㧔ᐔ㕙㈩▤♽⹜㛎૕㧕
Fig. 5.3-4 Analysis model (2D piping model).

(b) 100A SCH120.
࿑  ࠛ࡞ࡏߩᶖᢔࠛࡀ࡞ࠡ
Fig. 5.3-3 Dissipation energy of an elbow.
⴫ 

ᶖᢔࠛࡀ࡞ࠡߣࠛ࡞ࡏᦛߍ೰ᕈߩ㑐ଥࠍ⴫ߔㄭૃ
ᑼߩଥᢙ
Table 5.3-3 Coefficients of approximation of dissipation energy
and bending elasticity of an elbow.
Elbow Name

A1

A2

100A SCH80

1.242E5

2.964E-2

100A SCH120

1.989E5

2.511E-2* The coefficients are calculated by using Nm as the unit࿑  ⸃ᨆࡕ࠺࡞㧔┙૕㈩▤♽⹜㛎૕㧕
Fig. 5.3-5 Analysis model (3D piping model).

of dissipation.

− 6622 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆E=

1
2⋅ meq ⋅ ω 2 ⋅ X max
2(5.3.2)ω 㧦࿕᦭ⷺᝄേᢙ
E 㧦ᝄേࠛࡀ࡞ࠡ
X max 㧦ᦨᄢᔕ╵ᄌ૏meq 㧦᦭ല⾰㊂
2⒳㘃ߩ⹜㛎૕ߩ⌕⋡ߔࠆᝄേࡕ࡯࠼㧔1ᰴᝄേࡕ࡯࠼㧕ߦ߅ߌࠆ࿕᦭ᝄേᢙ㧘ࡕ࡯࠼⾰㊂෸߮ೝỗଥᢙࠍ⴫
ߦ␜ߔ㧚ߎߩࡕ࡯࠼⾰㊂ߣടᝄᣇะߦኻߔࠆೝỗଥᢙࠃࠅ㧘ߘߩ᦭ല⾰㊂ࠍ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚એ਄ߩ⸘▚ࠃࠅ㧘ᔕ╵ᄌ૏ߦଐሽߔࠆ㈩▤♽ో૕ߩᝄേࠛࡀ࡞ࠡ㧔⌕⋡ߔࠆᝄേࡕ࡯࠼ߩᝄേࠛࡀ࡞ࠡ㧕ࠍ▚಴ߔࠆߎߣ߇ߢ߈
ࠆ㧚ᝄേᔕ╵⸃ᨆ⌕⋡ߔࠆᝄേࡕ࡯࠼ߩᦨᄢᄌ૏ߣฦࠛ࡞ࡏ㕙ౝᦛߍߦ߅ߌࠆᦛ߇ࠅⷺᐲߩ㑐ଥࠍ᳞߼ࠆߚ߼ߦ㧘⌕⋡ߔࠆᝄേࡕ࡯࠼ߩߺࠍബᝄߔࠆᔕ╵⸃ᨆ㧔ᔕ╵ࠬࡍࠢ࠻࡞⸃ᨆ㧕ࠍታᣉߔࠆ㧚ߥ߅㧘⸃ᨆࡕ࠺࡞ߪ㧘೨㗄ߩᝄേࡕ࡯࠼⸃ᨆߣ
ห৻ߩࡕ࠺࡞ࠍ↪޿ߡ޿ࠆ㧚⴫ ෸߮⴫  ߦ2⒳㘃ߩ⹜㛎૕ߩᦨᄢᔕ╵ᄌ૏㊂ߣࠛ࡞ࡏߩᦛ߇ࠅⷺᐲ෸߮ߎࠇࠄߩ୯ߩᲧ₸ࠍ␜ߔ㧚ࠛ࡞ࡏߦ߅ߌࠆᦛ߇ࠅⷺᐲߪ㧘ࠛ࡞ࡏਔ┵ߦធ⛯ߐࠇߡ޿ࠆ⋥▤ㇱߩ▵ὐߩ࿁ォⷺᐲ㧔࿁ォᄌ૏㧕ࠃࠅ▚಴ߒߚ㧚ᦨᄢᔕ╵㊂ߣࠛ࡞ࡏߩᦛ߇ࠅⷺᐲߩᲧ₸ߪ㧘ᦨᄢᔕ╵߇⊒↢ߔࠆ1ࠨࠗࠢ࡞ߦ߅޿ߡ႟ᕈᄌᒻߦࠃࠅ↢ߓࠆᶖᢔࠛ
ࡀ࡞ࠡࠍ᳞߼ࠆߚ߼ߩ୯ߣߥࠆ㧚႟ᕈᄌᒻ߇⊒↢ߔࠆߣ㈩▤♽ߩᄌᒻ⁁ᴫ߇ᄌൻߔࠆߚ
߼ߦ㧘✢ᒻ⸃ᨆߦࠃࠆ਄⸥ߩᲧ₸ߪ෩ኒߦߪ⇣ߥࠆ㧚ᧄᒢ႟ᕈᔕ╵੍᷹ᚻᴺߢߪ㧘႟ᕈᄌᒻߩ⊒↢߇㈩▤♽ߦ߅ߌࠆ৻ㇱߩ⛮ᚻߩዪᚲ⊛㗔ၞߢ↢ߓࠆߣߒ㧘㈩▤♽ో૕ߩᄌᒻ⁁ᴫߪᒢᕈᄌᒻߣ߶ߣࠎߤห৻ߢ޽ࠆߣ޿߁઒ቯߩ
ၮߦ㧘✢ᒻߩᝄേᔕ╵ߣߒߡขࠅᛒߞߡ޿ࠆ㧚ᧄᚻᴺߪ㧘ᒢ႟ᕈᄌᒻߦࠃࠆ㕖✢ᒻߩᶖᢔࠛࡀ࡞ࠡࠍ╬ଔ✢ᒻᷫ⴮ߣߒߡ⠨ᘦߒ㧘✢ᒻᔕ╵⸃ᨆߢᒢ႟ᕈᔕ╵ࠍ੍᷹ߔࠆ߽
ߩߢ޽ࠆ㧚ᝄേᔕ╵⸃ᨆߢߪ㧘਄⸥ࠛ࡞ࡏᦛ߇ࠅⷺᐲߩᲧ₸ߩઁߦ㧘ᷫ⴮Ყߣᔕ╵ᄌ૏ߩ㑐ଥࠍ᳞߼ࠆ㧚ߎࠇߪ㧘࡜ࡦ࠳ࡓᵄ౉ജߢߩᦨᄢᔕ╵㊂ࠍᷫ⴮Ყߩ㑐ᢙߣߒߡ⴫ߔ߽ߩߢ
޽ࠆ㧚✢ᒻߩ࡜ࡦ࠳ࡓᔕ╵ߪ㧘ㆊᷰᔕ╵㧔⥄↱ᝄേ㧕㧘⺞๺ᝄേ෸߮ᒝ೙ᝄേ㧔ᄖജ㧕ߩᚑಽߩ㊀ߨวࠊߖߣߒߡ⴫
ߔߎߣ߇ߢ߈ࠆߣ⠨߃㧘࡜ࡦ࠳ࡓᵄ౉ജߦࠃࠆᝄേᔕ╵㧔ᦨᄢᔕ╵㊂㧕ࠍᰴߩᑼߢㄭૃߔࠆ㧚B

X max = α input ⋅  1 + B2 ⋅ exp ( − B3 ⋅ ζ ) + B4 ζ


(5.3.3)

α input 㧦౉ജᵄߩᦨᄢടㅦᐲ㧔౉ജ࡟ࡌ࡞㧕ζ 㧦ᷫ⴮Ყ㧔⥃⇇ᷫ⴮Ყ㧕
B1 , B2 , B3 , B4 㧦ㄭૃᑼߩଥᢙ
X max 㧦ᦨᄢᔕ╵ᄌ૏‫ޓ‬ᐔ㕙㈩▤♽⹜㛎෸߮┙૕㈩▤♽⹜㛎ߦ↪޿ߚ౉ജᵄ
㧔⁜Ꮺၞ࡜ࡦ࠳ࡓᵄ㧕ࠍ࿑  ෸߮࿑  ߦ␜ߔ㧚ߎࠇࠄߩ࡜ࡦ࠳ࡓᵄࠍ౉ജߒߚ႐วߩᔕ╵ࠬࡍࠢ࠻࡞⸃ᨆ
⚿ᨐࠍၮߦ਄⸥ㄭૃᑼߢߩଥᢙࠍቯ߼ߚ㧚⹜㛎૕ᦨᄢᔕ╵ᄌ૏ࠍㄭૃߒߚ⚿ᨐ෸߮ߎߩㄭૃߢ᳞߼ࠄࠇߚଥᢙࠍ
࿑෸߮⴫ߦ␜ߔ㧚ߥ߅㧘਄ᑼߦ߅ߌࠆଥᢙߪ㧘
౉ജᵄߣ㈩▤♽ߩᝄേ․ᕈߦଐሽߔࠆ୯ߢ޽ࠅ㧘㈩▤♽ߩᝄേᔕ╵ߦ߅ߌࠆㆊᷰᔕ╵㧘⺞๺ᝄേ㧘ᒝ೙ᝄേᚑಽߩ
Ყ₸ࠍ⴫ߔ୯ߣߥࠆ㧚⴫   ᝄേ․ᕈ
Table 5.3-4 Vibration characteristic.

Piping Model

Fundamental NaturalFrequency (Hz)Modal Mass
M (kg)

Participation Factor in the
Excitation Direction

Effective Massmeq (kg)

2D-A01

3.16

623

0.841

524

3D-A01

2.58

391

0.772

302

⴫   ࠛ࡞ࡏᦛߍⷺᐲߣᦨᄢᔕ╵ᄌ૏ߩᲧ₸㧔2D_A01㧕
Table 5.3-5 Ratio of bending angle and max. response displacement(2D-A01).

Elbow No.

ǫ(=ǰ/ Xmax)⴫   ࠛ࡞ࡏᦛߍⷺᐲߣᦨᄢᔕ╵ᄌ૏ߩᲧ₸㧔3D_A01㧕
Table 5.3-6 Ratio of bending angle and max. response displacement(3D-A01).

Elbow No.

(rad/m)ǫ(=ǰ/ Xmax)

EL 1

0.1848EL 1

0.1082EL 20.1833EL 20.0888EL 30.1722− 6633 −(rad/m)㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬

0.10
Max response displacement (m)Acc. (G)

0.15

0.00

-0.15
0

20

Time (s)

40

2.0

1.0

2.0

3.0

4.0

5.0

0.02

0.05

0.10

0.15

0.20

(a) 2D piping model.
0.10

0.0
0.0

0.04

Critical Damping ratio ζȗMax response displacement (m)

0.5

0.06

0.00

0.005
0.010
0.015
0.020
0.050
0.100
0.200
0.500

1.0

Approximation

0.00

Damping Ratio

1.5

Response Acc. (G)60

Response analysis
0.08

6.0

Frequency (Hz)࿑  ᐔ㕙㈩▤♽⹜㛎ߦ߅ߌࠆടᝄᵄᒻߣᔕ╵ࠬࡍࠢ࠻࡞
㧔౉ജ࡟ࡌ࡞㧦0.1G㧕
Fig. 5.3-6 Excitation wave and response spectrum for 2D piping
model ( Input level 0.1 G ).

Response analysis
0.08

Approximation

0.06
0.04
0.02
0.00
0.00

0.05

0.10

0.15

0.20

Critical Damping ratio ζȗ(b) 3D piping model.

Acc. (G)0.15

࿑  ㈩▤♽⹜㛎૕ߩᔕ╵୯ߩㄭૃ㧔౉ജ࡟ࡌ࡞㧦1m/s 2㧕
Fig. 5.3-8 Approximation of responses for piping models( Input level 1 m/s2 ).

0.00

-0.15
0

20

40

Time (s)602.0Response Acc. (G)Damping Ratio⴫  ᒢᕈᔕ╵ㄭૃᑼߩଥᢙ
Table 5.3-7 Coefficients of approximation of elastic response.

0.005
0.010
0.020
0.050
0.100

1.5

1.0

0.5

Piping
model

B1

B2

B3

B4

2D-A012.145E-5

2.365E-2

1.592E1

3.802E-3

3D-A011.685E-4

2.387E-2

1.471E1

6.643E-3

0.0
0.0

1.0

2.0

3.0

4.0

5.0

6.0

Frequency (Hz)࿑  ┙૕㈩▤♽⹜㛎ߦ߅ߌࠆടᝄᵄᒻߣᔕ╵ࠬࡍࠢ࠻࡞
㧔౉ജ࡟ࡌ࡞㧦0.1G㧕
Fig. 5.3-7 Excitation wave and response spectrum for 3D piping
model ( Input level 0.1 G ).

* The coefficients are calculated by using m as the unit of− 6644 −maximum response displacement and m/s2 as the unit of
the input level.

ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆╬ଔᷫ⴮Ყ෸߮ᦨᄢᔕ╵㊂ߩ⸘▚‫ޓ‬೨㗄߹ߢߦ␜ߒߚࠛ࡞ࡏ㕙ౝᦛߍߢߩ႟ᕈᄌᒻߦࠃࠆ
ᶖᢔࠛࡀ࡞ࠡ෸߮㈩▤♽ో૕ߩᝄേࠛࡀ࡞ࠡࠍၮߦ㧘⌕⋡ߔࠆᝄേࡕ࡯࠼ߩ╬ଔᷫ⴮Ყࠍ᳞߼ࠆ㧚ߎߎߢ↪޿ࠆᶖᢔࠛࡀ࡞ࠡߣߪ㧘㈩▤♽ߩోࠛ࡞ࡏߦ߅ߌࠆᶖᢔࠛࡀ
࡞ࠡߩว⸘୯ߢ޽ࠆ㧚∆E
4 ⋅π ⋅ E∆E = ∑ ∆eiζ =(5.3.4)i∆E 㧦㈩▤♽ߩࠛ࡞ࡏ㕙ౝᦛߍߢߩోᶖᢔࠛࡀ࡞ࠡ
.1 ߢ⸘▚ߐࠇࠆ႟ᕈᄌᒻ߇↢ߓࠆ∆ei 㧦ᑼ(5.3-1)
ࠛ࡞ࡏߩᶖᢔࠛࡀ࡞ࠡ
.2 ߢ⸘▚ߐࠇࠆᝄേࠛࡀ࡞ࠡ
E 㧦ᑼ(5.3-2)‫ޓ‬਄ᑼߦ㧘ᑼ (5.3.1) ෸߮ (5.3.2) ࠍ਄ᑼߦઍ౉ߔࠆߎߣߦ
ࠃߞߡ㧘ਅᑼߩߣ߅ࠅ㈩▤♽ߩᷫ⴮Ყࠍᔕ╵ᄌ૏ߩ㑐ᢙߣߒߡ⴫ߔߎߣ߇ߢ߈ࠆ㧚ߎߎߢߩᷝ߃ሼ i ߪ㧘႟ᕈᄌᒻ߇↢ߓᶖᢔࠛࡀ࡞ࠡ⸘▚ߩኻ⽎ߣߥࠆฦࠛ࡞ࡏߩ⇟ภࠍ␜ߒߡ޿ࠆ㧚ζ =∑ A ⋅ (γ ⋅ X
1i

i

max

i

− A2 i )2 ⋅ π ⋅ meq ⋅ ω 2 ⋅ X max

Q
∵


2

∑C ⋅ X
1=

C1 = ∑ A1i ⋅ γ i ,
i

max

− C2

i

2 ⋅ π ⋅ meq ⋅ ω 2 ⋅ X max

2
C2 = ∑ A1i ⋅ A2i 
i



 B1

 X max = α input ⋅  + B2 ⋅ exp ( − B3 ⋅ ζ ) + B4 
ζ




∑i C1 ⋅ X max − C2ζ =22 ⋅ π ⋅ meq ⋅ ω 2 ⋅ X max
(5.3.6)

ߎߩ෼᧤⸘▚ߪ㧘ᒢ႟ᕈᔕ╵ߦ߅ߌࠆ╬ଔᷫ⴮Ყߣᦨ
ᄢᔕ╵㊂ߩ㑐ଥࠍḩ⿷ߔࠆ୯ࠍᢙ୯⸘▚ߢ᳞߼ࠆ߽ߩߢ
޽ࠆ㧚ᔕ╵߇ᄢ߈ߊߥࠆߣ႟ᕈᄌᒻߦࠃࠆ╬ଔᷫ⴮Ყߪ
Ⴧᄢߔࠆ㧚ㅒߦ㧘ᷫ⴮Ყ߇ᄢ߈ߊߥࠆߣᔕ╵㊂ߪዊߐߊߥ
ࠆ㧚ߘߩߚ߼㧘ߎࠇࠄ 2 ⒳㘃ߩ㑐ଥߪᔅߕ 1 ὐߢ੤Ꮕߔࠆ
෼᧤୯߇޽ࠅ㧘Ყセ⊛቟ቯߒߚ෼᧤⸘▚ߣߥࠆ㧚ߜߥߺߦ⪺⠪ߪ㧘Microsoft Excelߩ࠰࡞ࡃ࡯ᯏ⢻ࠍ೑↪ߒߡߎߩ෼
᧤⸘▚ࠍታᣉߒ㧘ኈᤃߦ෼᧤୯ࠍ᳞߼ࠆߎߣ߇ߢ߈ߚ㧚ᒢ႟ᕈᔕ╵੍᷹⚿ᨐ‫ޓ‬೨㗄ߦ␜ߒߚᒢ႟ᕈᔕ╵੍᷹ᚻᴺࠍ↪޿ߡᐔ㕙㈩▤♽⹜㛎૕෸߮┙૕㈩▤♽⹜㛎૕ߦ߅ߌࠆᔕ╵㊂ߩ੍᷹ࠍታ
ᣉߒߚ㧚ฦ⹜㛎૕ߦ߅ߌࠆᦨᄢᔕ╵ᄌ૏㊂੍᷹⚿ᨐࠍ࿑ ߦ⹜㛎⚿ᨐߣวࠊߖߡ␜ߔ㧚߹ߚ㧘ᦨᄢᔕ╵㊂੍᷹
ߩ㓙ߦᓧࠄࠇߚฦ⹜㛎૕ߩ╬ଔᷫ⴮Ყࠍ࿑ ߦ␜ߔ㧚ߎࠇࠄߩ࿑ߦ␜ߔࠃ߁ߦ㧘ᧄᒢ႟ᕈᔕ╵੍᷹ᚻᴺߢ᳞߼
ࠄࠇߚᦨᄢᔕ╵ᄌ૏㊂ߩ౉ജ࡟ࡌ࡞ߦኻߔࠆᄌൻߩ௑ะ
ࠍ⦟ߊౣ⃻ߢ߈ߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚߹ߚ㧘ᦨᄢᔕ╵ᄌ૏㊂ߩ੍᷹⚿ᨐߪ㧘ታ㛎⚿ᨐࠃࠅ߽ᄢ߈ߥ୯ߣߥߞߡ޿ࠆ㧚ߎߩේ࿃ߣߒߡߪએਅߩߎߣ߇᜼ߍࠄࠇࠆ㧚(5.3.5)γ i 㧦ฦࠛ࡞ࡏߢߩᦛ߇ࠅⷺᐲߣ㈩▤♽ߩᦨᄢᔕ╵ᄌ૏ߩᲧ₸ω 㧦࿕᦭ⷺᝄേᢙ
X max 㧦㈩▤♽ߩᦨᄢᔕ╵ᄌ૏㊂
A1 , A2 㧦ࠛ࡞ࡏᶖᢔࠛࡀ࡞ࠡㄭૃᑼߩଥᢙ
C1 , C2 㧦ࠛ࡞ࡏᶖᢔࠛࡀ࡞ࠡㄭૃᑼߩଥᢙ
meq 㧦᦭ല⾰㊂‫ޓ‬એ਄ߩᶖᢔࠛࡀ࡞ࠡ෸߮ᦨᄢᔕ╵㊂ߦ㑐ࠊࠆቯᑼൻ߆
ࠄ㧘ᒢ႟ᕈᔕ╵ࠍ੍᷹ߔࠆߚ߼ߩએਅߩㅪ┙ᣇ⒟ᑼ߇ᓧ
ࠄࠇߚ㧚ߎߩXmax ෸߮Ǯߦ㑐ߔࠆㅪ┙ᣇ⒟ᑼߪ㧘㕖✢ᒻߩ
ᣇ⒟ᑼߢ޽ࠅ㧘⋥ធ⸃ࠍዉ಴ߔࠆߎߣߪ࿎㔍ߢ޽ࠆߎߣ
߆ࠄ㧘ᢙ୯⸘▚ߦࠃࠅߎߩㅪ┙ᣇ⒟ᑼࠍḩ⿷ߔࠆ⸃ࠍ᳞
߼ࠆߎߣߣߥࠆ㧚ౕ૕⊛ߦߪ㧘ᷫ⴮ᲧǮࠍࡄ࡜ࡔ࡯࠲ߣߒ
ߚ෼᧤⸘▚ࠍታᣉߒ㧘ㅪ┙ᣇ⒟ᑼࠍḩ⿷ߔࠆXmax෸߮Ǯࠍ᳞߼ߡ޿ࠆ㧚Ԙ ࠛ࡞ࡏ㕙ౝᦛߍ⩄㊀ᄌ૏․ᕈ߆ࠄ᳞߼ߚࠛ࡞ࡏߢߩᶖ
ᢔࠛࡀ࡞ࠡ߇㧘ታ㓙ߩ߽ߩࠃࠅ߽ዊߐߊߥߞߡ޿ࠆ㧚ߎࠇߪ㧘⩄㊀ᄌ૏․ᕈߦ߅ߌࠆ႟ᕈ㗔ၞߩ೰ᕈ߇ዊߐ
޿ߎߣߦࠃࠅ↢ߓࠆ⸘▚⺋Ꮕߢ㧘ࠛ࡞ࡏߢߩ㕒⊛ᒢ႟ᕈ⸃ᨆߦ߅޿ߡ↪޿ࠆᔕജ̆߭ߕߺ㑐ଥ㧔ࡃࠗ࡝࠾ࠕ
ߢߩㄭૃ㧕ߢߩ 2 ᰴ൨㈩ߦଐሽߔࠆ㧚2 ᰴ൨㈩ࠍᄢ߈ߊ
ߣࠆߎߣߦࠃࠅ㧘ࠛ࡞ࡏ㕙ౝᦛߍߩⷺᐲߣᶖᢔࠛࡀ࡞
ࠡߩ㑐ଥߦ߅ߌࠆᶖᢔࠛࡀ࡞ࠡߩჇടഀว߇ᄢ߈ߊߥ
ࠅ㧘ࠃࠅታ㛎⚿ᨐߦㄭ޿੍᷹୯߇ᓧࠄࠇࠆߣ⠨߃ࠄࠇࠆ㧚ԙ ㈩▤♽ߦ߅޿ߡ႟ᕈᄌᒻߔࠆࠃ߁ߥᔕ╵⁁ᘒߢߪ㧘㈩▤♽ో૕ߩᄌᒻᒻ⁁߇ᒢᕈၞߢߩᄌᒻᒻ⁁߆ࠄᄌൻߒ
ߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚ౕ૕⊛ߦߪ㧘ࠛ࡞ࡏߢߩ႟ᕈᄌ
ᒻ߇↢ߓߚ႐ว㧘ߎߎߢߩ⷗߆ߌߩ೰ᕈ߇ૐਅߔࠆߎ
ߣ߆ࠄ㧘㈩▤♽ో૕ߣߒߡߩᄌᒻߩࡃ࡜ࡦࠬ߇ᄌൻߒ㧘ᒢᕈၞߩᄌᒻߩࡃ࡜ࡦࠬߣߪᄌࠊߞߡߊࠆ㧚ߔߥࠊߜ㧘႟ᕈᄌᒻ߇↢ߓߡ޿ࠆࠛ࡞ࡏㇱಽߦᦝߦᄌᒻ߇㓸ਛߔࠆࠃ߁ߥ⃻⽎ߢ޽ࠆ㧚ߎࠇߦࠃߞߡ㧘㈩▤♽ߩᦨᄢᔕ╵ᄌ૏㊂ߦኻߔࠆฦࠛ࡞ࡏߢߩᦛ߇ࠅⷺᐲߩᲧ₸߇ᄌࠊߞߡߊࠆ㧚ࠛ࡞ࡏ߳ߩᄌᒻߩ㓸ਛߪ㧘ᶖᢔࠛࡀ࡞ࠡ
ߩჇᄢߐߖࠆߎߣ߆ࠄ㧘ᧄ੍᷹ᚻᴺߦ߅޿ߡߎߩലᨐ
ࠍട๧ߢ߈ࠇ߫ࠃࠅታ㛎୯ߦㄭ޿ᔕ╵㊂ࠍ੍᷹ߢ߈ࠆ
ߣ⠨߃ࠄࠇࠆ㧚− 6655 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬‫ޓ‬ᔕ╵੍᷹⚿ᨐߣታ㛎⚿ᨐߩਵ㔌ߩⷐ࿃ߣߒߡߪએ਄ߩ
ߎߣ߇⠨߃ࠄࠇࠆ߇㧘ㅒߦ⸒߃߫㧘⃻࿷ߩ੍᷹ᚻᴺࠍ਄⸥
ߩ㗄⋡ߦ㑐ߒߡୃᱜࠍട߃ࠆߎߣߦࠃߞߡ㧘ࠃࠅᱜ⏕ߥᒢ႟ᕈᔕ╵੍᷹߇น⢻ߦߥࠆߣ⠨߃ࠄࠇࠆ㧚ᦝߦ㧘਄⸥ԙߩⷐ࿃ࠍ⸃᳿ߔࠆߎߣ߇ߢ߈ࠇ߫㧘㈩▤♽ో૕ߩਛߢߩ
ᄌᒻߩࡃ࡜ࡦࠬᄌൻ߇⠨ᘦߐࠇߚᔕ╵㊂ߩ੍᷹߇ߢ߈ࠆ
ߣหᤨߦ㧘ࠛ࡞ࡏ╬ߩ㈩▤ⷐ⚛ߦኻߔࠆ⹦⚦ᒝᐲ⹏ଔ߳

ߩ౉ജ᧦ઙࠍ㧘਄⸥ᄌᒻߩ㓸ਛࠍ⠨ᘦߒߚ᧦ઙߣߒߡ▚ቯߢ߈ࠆ㧚ߔߥࠊߜ㧘ᧄ੍᷹ᚻᴺߦࠃࠅ㈩▤♽ో૕ߣߒߡ
ߩᒢ႟ᕈᔕ╵ࠍ੍᷹ߒߚᓟ㧘㈩▤♽ฦㇱಽߢߩ⹦⚦ᒝᐲ⹏ଔ߇น⢻ߦߥࠆߣ⠨߃ࠄࠇࠆ㧚ߎࠇࠄߩߎߣߦߟ޿ߡ
ߪ㧘㈩▤♽ߩᒢ႟ᕈᔕ╵⹏ଔ߆ࠄ⹦⚦ᒝᐲ⹏ଔࠍⴕ߁ᚻ
ᴺߣߒߡ㧘੹ᓟ㧘ᬌ⸛ߒߡ޿ߊᔅⷐ߇޽ࠆ㧚

0.08
Excitation test

Prediction

Prediction

0.4

Equivalent damping ratio

Max response displacement (m)

0.5

0.3

0.2

0.1

0.0

Elastic damping

0.06

0.04

0.02

0.00
0

5

10

15

20

0

5

Input Level (m/s 2)(a) 2D piping model.

15

20

15

20

(a) 2D piping model.

0.5

0.08
Excitation test

Prediction

Prediction

0.4

Equivalent damping ratio

Max response displacement (m)10
Input Level (m/s 2)

0.3

0.2

0.1

0.0

Elastic damping

0.06

0.04

0.02

0.00
0

5

10

15

20

0

2

5

10
2

Input Level (m/s )Input Level (m/s )(b) 3D piping model.

(b) 3D piping model.

࿑  ᒢ႟ᕈᔕ╵੍᷹⚿ᨐ
Fig. 5.4-1 Elastic-plastic response prediction.

࿑  ╬ଔᷫ⴮Ყ੍᷹⚿ᨐ
Fig. 5.4-2 Equivalent damping ratio by prediction.

− 6666 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆߹ߣ߼
㜞⚻ᐕൻߦ઻߁᭴ㅧഠൻ߇⊒↢ߒߚ㈩▤♽ࠍኻ⽎ߣߒߚേ⊛⎕უታ㛎ࠍⴕߞߚ㧚߹ߚ㧘ታ㛎ߢᓧࠄࠇߚ࠺࡯࠲ࠍ
૶↪ߒߡ⒳‫⸃ߩޘ‬ᨆࠍታᣉߒߚ㧚ᓧࠄࠇߚਥߥ⍮⷗ࠍએਅߦ␜ߔ㧚(1)‫ޓ‬㈩▤ⷐ⚛ߩ⎕៊᜼േ1) ฦഠൻᒻ⁁߅ࠃ߮ౝ࿶㧘౉ജᄌ૏᧦ઙߦኻߒߡ
⎕៊ᒻᘒ߅ࠃ߮⎕៊ኼ๮ࠍታ㛎⊛ߦᛠីߒߚ㧚ߘߩ⚿ᨐ㧘ᷫ⡺㈩▤ߢߪᷫ⡺㊂ߣౝ࿶ߩ᧦ઙߦ
ࠃߞߡ⇣ߥࠆ⎕៊ᒻᘒࠍ␜ߔߎߣ߇ࠊ߆ߞߚ㧚߹ߚ㧘⥄ὼ߈ⵚߢ޽ࠆ SCC ߦኻߒߡタ⩄ታ㛎ࠍⴕ޿㧘ੱᎿ߈ⵚߢ޽ࠆ EDM ߈ⵚߣߩ⽾ㅢኼ๮ߩ㆑޿ࠍᓧߚ㧚
2) EDM ߈ⵚઃ߈㈩▤ߩ SEM ߦࠃࠆ⎕㕙ⷰኤ⚿ᨐ߆ࠄ㧘߈ⵚ⽾ㅢ߹ߢߦⷐߒߚ➅ࠅ㄰ߒᢙߩ߶ߣ
ࠎߤߪ߈ⵚߩવ᠞ߦ⾌߿ߐࠇߡ޿ࠆߎߣ߇ࠊ
߆ߞߚ㧚߹ߚ㧘⎕㕙⸃ᨆ߆ࠄᓧࠄࠇߚ߈ⵚવ᠞ㅦ
ᐲߪ㧘ᣢᓔߩ⎇ⓥߢᓧࠄࠇߡ޿ࠆ da/dN - ∆K㑐ଥߣ⦟ߊ৻⥌ߒߚ㧚3) ⋥▤ᷫ⡺㈩▤ࠍ࠰࡝࠶࠼ⷐ⚛ࠍ↪޿ߡࡕ࠺࡞ൻ
ߒ㧘⸃ᨆࠦ࡯࠼ ABAQUS ࠍ૶↪ߒߡ⸃ᨆࠍታᣉ
ߒߚ㧚ߎߩ⸃ᨆߦࠃࠅ㧘ታ㛎ߢᓧࠄࠇߚᄖᓘᄌൻ
߿⩄㊀ᄌᒻ․ᕈࠍ♖ᐲ⦟ߊౣ⃻ߢ߈ߚ㧚߹ߚ㧘⸃ᨆ⚿ᨐ߆ࠄ㧘࡜࠴ࠚ࠶࠻ߥߤߦࠃࠆᷫ⡺ㇱಽߩዪᚲᄌᒻߣᦛߍߦࠃࠆో૕ᄌᒻ߇㊀⇥ߒߡ߭ߕߺ㓸ਛㇱ߇⊒↢ߔࠆߣ⎕៊ࡔࠞ࠾࠭ࡓ߇᣿ࠄ߆ߦߥߞߚ㧚4) ㈩▤♽⹜㛎ߢ૶↪ߒߚࠛ࡞ࡏㇱಽࠍ࠰࡝࠶࠼ⷐ
⚛ࠍ૶↪ߒߡࡕ࠺࡞ൻߒ㧘ABAQUS ࠍ૶↪ߒߡ⸃ᨆࠍታᣉߒߚ㧚⸃ᨆ⚿ᨐࠃࠅ㧘ࠛ࡞ࡏㇱߦߟ޿ߡ߽࡜࠴ࠚ࠶࠻⃻⽎ߣዪᚲᦛߍ߇㊀⇥ߒ㧘ᱡߺ㓸ਛㇱߩ⊒↢ߔࠆ⃻⽎߇⿠߈ࠆߎߣ߇ࠊ߆ߞߚ㧚5) ⋥▤ᷫ⡺߅ࠃ߮ࠛ࡞ࡏᷫ⡺㈩▤ߣ߽ߦ㧘ࠪࠚ࡞ⷐ⚛ࠍ૶↪ߒߡ⸃ᨆߩ◲⚛ൻࠍⴕ޿㧘࠰࡝࠶࠼ⷐ⚛ࡕ࠺࡞ߦࠃࠆ⚿ᨐߣᲧセߒߡචಽߥ⸃ᨆ♖ᐲࠍ᦭ߒߡ޿ࠆߎߣࠍ⏕⹺ߒߚ㧚ߎࠇࠄߩࡕ࠺
࡞ߪ੹ᓟ㧘ᷫ⡺ᒻ⁁ߣ⎕៊ኼ๮ߩቯ㊂⹏ଔߦᔅⷐߥᄙ⒳ߩࡄ࡜ࡔ࡯࠲⸃ᨆࠍታᣉߔࠆ㓙ߦ᦭↪
ߢ޽ࠆ㧚6) ABAQUS ߦ߅ߌࠆ࡜ࠗࡦࠬࡊ࡝ࡦࠣࡕ࠺࡞ࠍ૶
↪ߒߡ⎕უജቇࡄ࡜ࡔ࡯࠲Jmax ࠍ▚಴ߒ㧘➅ࠅ㄰ߒ⸘▚ࠍⴕߞߡ߈ⵚㅴዷ㊂ࠍ⹏ଔߒߚ㧚ߎߩࡕ࠺࡞ࠍ૶↪ߔࠆߎߣߢ㧘ⶄ㔀ߥ2ᰴరᒻ⁁ߩ߈ⵚߦኻߒല₸⊛߆ߟ♖ᐲ⦟޿⎕៊⹏ଔ߇ߢ߈ࠆ㧚(2)‫ޓ‬㈩▤♽ߩ⎕៊᜼േ߅ࠃ߮ᝄേ․ᕈ
1) ᷫ⡺߹ߚߪ߈ⵚࠍ᦭ߔࠆၮᧄ⊛ߥᒻ⁁ߩ㈩▤♽ߦኻߒߡᝄേบࠍ↪޿ߚᝄേታ㛎ࠍⴕ޿㧘ഠൻ߇޽ࠆ㈩▤♽ߩᒢ႟ᕈᔕ╵ᕈ⁁㧘៊்૏⟎෸߮៊்ᒻᘒ㧘⎕៊ኼ๮ࠍታ㛎⊛ߦᛠីߒߚ㧚ߘߩ⚿ᨐ㧘ᷫ⡺߇޽ࠆ㈩▤♽ߩ⎕៊ᒻᘒߪ㧘⽶⩄⩄㊀ߩ

2)3)ᄢ߈޿ࠛ࡞ࡏㇱಽߦ߅ߌࠆゲᣇะ∋ഭ߈ⵚߩ⊒↢㧘⽾ㅢߢ޽ߞߚ㧚ో๟߈ⵚߩ޽ࠆ㈩▤♽ߢߪ⡺ෘᣇะ߳ߩ߈ⵚ⽾ㅢᓟ㧘ᓟ⛯ߩ࿾㔡ᔕ╵ᢙࠨࠗࠢ࡞ߦࠃࠅో๟⎕ᢿߦ⥋ߞߚ߇㧘SCC ࠍᮨᡆߒ
ߚ EDM ߈ⵚࠍᜬߟ㈩▤♽ߢߪ㧘10࿁ࠍ⿥߃ࠆᒢ
႟ᕈ࡟ࡌ࡞ߩടᝄߢ߽߈ⵚߪ⽾ㅢߒߥ߆ߞߚ㧚ᷫ⡺ߩሽ࿷ߦࠃࠅ㈩▤♽ߩ೰ᕈ߇ૐਅߒ㧘࿕᦭ᝄേᢙߩૐਅ߿ᔕ╵ᄌ૏㊂ߩჇടߣ޿ߞߚᓇ㗀߇⃻ࠇߚ㧚ߎߩᓇ㗀ߩ⒟ᐲߪᷫ⡺ߩ⒟ᐲߦ㑐ଥߒߡ޿ߚ㧚৻ᣇ㧘߈ⵚߩሽ࿷ߪ㈩▤♽ߩᝄേ․ᕈ
ߦ߶ߣࠎߤᓇ㗀ࠍਈ߃ߥ߆ߞߚ㧚႟ᕈᄌᒻߦࠃࠆᝄേࠛࡀ࡞ࠡߩᶖᢔࠍ⠨ᘦߦ౉ࠇߚᒢ႟ᕈᔕ╵ᄌ૏ߩ◲ᤃ੍᷹ᚻᴺࠍឭ᩺ߒߚ㧚ߎߩ੍᷹ᚻᴺߦࠃࠅ㧘႟ᕈᄌᒻߦࠃࠆᔕ╵ૐᷫലᨐࠍ⠨ᘦߦ౉ࠇ㧘ታ㛎⚿ᨐࠃࠅ߽଻቞⊛ߥᔕ╵㊂ࠍ੍᷹ߢ߈ࠆ㧚޽ߣ߇߈
ᧄႎ๔ᦠߢᛒߞߚේሶജ቟ో⎇ⓥ‫ޟ‬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ߪޠ‬㧘ᐔᚑ8ᐕᐲ߆ࠄᐔᚑ 12 ᐕᐲ߹ߢߩ 5ࡩᐕ⸘↹ߢታᣉߒߚ㧚ᐔᚑ 13ᐕᐲએ㒠ߪ㧘ᐔᚑ17ᐕᐲ߹ߢߩ5ࡩᐕ⸘↹ߢ㧘ኻ⽎ߣߔࠆഠൻ᧦ઙࠍᷫ⡺ߦ㒢ቯߒ㧘‫ޟ‬࿾㔡⩄㊀ࠍฃߌࠆᷫ⡺㈩▤ߩ⎕უㆊ⒟⸃᣿ߦ㑐ߔࠆ⎇ⓥ‫ࠍޠ‬ታᣉߔࠆߎߣ߇᳿ቯߒߚ㧚ߎߩ⎇ⓥ⺖㗴ߩਛߢߪ㧘ࠛ࡞ࡏᷫ⡺ߩⷐ⚛⹜㛎߿ㇱಽᷫ⡺ߩዉ౉ߥߤ㧘ߎࠇ߹ߢߦขࠅᛒߞߡ޿ߥ޿᧦ઙߢ⹜㛎ࠍታᣉߒ㧘⎕៊᜼േ߿㒢⇇ᒝᐲߦߟ޿ߡታ㛎⊛ߦ⚿ᨐࠍ
⫾Ⓧߔࠆߣߣ߽ߦ㧘ᧄႎ๔ᦠߢㅀߴߚ⸃ᨆࡕ࠺࡞╬ࠍ೑↪ߒߡᷫ⡺㈩▤ߩ⎕៊᜼േߦᓇ㗀ࠍਈ߃ࠆⷐ࿃ߩቯ㊂⊛⹏ଔࠍⴕ߁㧚ߐࠄߦߘࠇࠄߩ⚿ᨐࠍ㈩▤♽ߩ࿾㔡ᔕ╵ਅߦ߅ߌࠆ⎕៊⹏ଔߦ෻ᤋߒ㧘⠴㔡቟ోᕈ⹏ଔߦ߅ߌࠆ⚻ᐕഠൻㇱಽߩขࠅᛒ޿ߦߟ޿ߡ⹏ଔᚻᴺࠍ␜ߔߎߣࠍ⋡ᮡߣߒߡ޿ࠆ㧚㧨⻢ㄉ㧪ᧄ⎇ⓥߩታᣉߦ޽ߚࠅ㧘APᆔຬળᆔຬฦ૏߆ࠄ⾆㊀ߥߏഥ⸒ࠍ޿ߚߛ߈߹ߒߚ㧚߹ߚ㧘ᩊ↰⏉᧲੩ᄢቇฬ⹷ᢎ᝼
ߦߪ㧘⎇ⓥో૕ߩ⸘↹߆ࠄታ㛎ታᣉ㧘ߣࠅ߹ߣ߼ߦ⥋ࠆ߹ߢᢙ‫ߏߩޘ‬ᜰዉࠍ޿ߚߛ߈߹ߒߚ㧚ታ㛎ߩታᣉߦ޽ߚߞ
ߡߪ㧘㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲߩ㘵↰᥍↵᳁㧘⍹Ꮉፉ᠞⏴㊀Ꮏ
ᬺߩ⋧↰㊀৻᳁㧘⍹Ꮉፉᬌᩏ⸘᷹ߩౝ↰ᒄ᳁ߩߏදജࠍ
޿ߚߛ߈߹ߒߚ㧚⎕㕙⸃ᨆߦ㓙ߒߡߪ‛⾰࡮᧚ᢱ⎇ⓥᯏ᭴ߩ᧻ጟਃ㇢ඳ
჻㧘┻ౝᖝ↵ඳ჻ߦᄙᄢߥߏᜰዉߣߏഥ⸒ࠍ޿ߚߛ߈߹
ߒߚ㧚߹ߚ㧘╙ 4 ┨ߢㅀߴߚ⸃ᨆߩታᣉߦߪ㧘ᮮᵿ࿖┙ᄢቇ⊕㠽⎇ⓥቶߩ໊ỈᏁ᳁㧔⃻ᣣᧄ⊒᧦ࢃ㧕㧘⍫ୖᱞ⬿᳁㧔⃻࠳ࠗࡂ࠷Ꮏᬺࢃ㧕㧘⿧ᥓᵗᰴ᳁ߦᄙߊߩߏදജࠍ޿ߚ
ߛ߈߹ߒߚ㧚ߎߎߦ⸥ߒߡᗵ⻢ߩᗧࠍ⴫ߒ߹ߔ㧚− 6677 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬㧨ෳ⠨ᢥ₂㧪
╙1┨1) ㅢ໡↥ᬺ⋭⾗Ḯࠛࡀ࡞ࠡ࡯ᐡ㧔1999㧕
㧦㔚᳇੐ᬺ⠪ߩේሶജ⊒㔚ᚲ㜞⚻ᐕൻߩ⹏ଔ෸߮੹ᓟߩ㜞⚻ᐕൻߦ㑐ߔࠆౕ૕⊛ขࠅ⚵ߺߦߟ޿ߡ㧚2) ᣣᧄේሶജ⎇ⓥᚲ㧔1993㧕
㧦㈩▤ା㗬ᕈታ⸽⹜㛎ᛛⴚႎ๔ᦠ㧚JAERI-M 93-076
93-076㧚
3)ች࿦ᤘ౎㇢㧘ᬀ↰⣑ਃ㧘ᩊ↰ൎਯ㧘⏷ፒᢅ㇌㧘㝩ᴛ㇌㓶㧘ਛၔᙗⴕ㧘ᩙේ⦟৻㧘ᯅญ৻↢㧘ട⮮ẖ㧔1987㧕
㧦ࠨ࡝࡯ේሶജ⊒㔚ᚲߩ㈩▤⎕ᢿ੐᡿㧚ᣣᧄේሶജቇળ
⹹㧘29
29  11㧘952-969㧚
4) Schmidt, R.A., Wilkowski, G.M., Mayfield, M.E. (1991):
The International Piping Integrity Research Group (IPIRG)
Program: An Overview. SMiRT 11, G, 177-188.
5) Miura, N., Fujioka, T., Kashima, K., Kanno, S., Hayashi,
M., Ishiwata, M., and Gotoh, N. (1994) : Low cycle fatigue
and ductile fracture for Japanese carbon steel piping underdynamic loadings. Nuclear Engineering and Design, 153
153,

6)

7)

57-69.
㐳⼱Ꮉ㇌ᄦ㧘⩲㊁ᥓ㧘ᐔ㊁᣿ᒾ㧘⍹ᷰ㓷ᐘ㧘ᓟ⮮િⓄ㧔1991㧕㧦ゲജࠍฃߌࠆ὇⚛㍑㈩▤ߩࠛࡠ࡯࡚ࠫࡦ
ߦࠃࠆዪㇱᷫ⡺ߩ⸵ኈၮḰ㧚ᣣᧄᯏ᪾ቇળ⺰ᢥ㓸㧔A✬㧕㧘57
57539㧘6-10㧚
57

Miyazaki, K., Kanno, S., Ishiwata, M., Hasegawa, K., Ahn,
S.H., and Ando, K. (1999) : Fracture behavior of carbon
steel pipe with local wall thinning subjected to bending
load. Nuclear Engineering and Design, 191, 195-204.
8) ቟⏋ᾔ㧘቟⮮ᩇ㧘⍹ᷰ㓷ᐘ㧘㐳⼱Ꮉ㇌ᄦ㧔1998㧕㧦ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤߇ᦛߍ⩄㊀ࠍฃߌߚߣ߈ߩ႟ᕈ፣უ
᜼േߣᷫ⡺ߩ⸵ኈ㒢⇇㧔╙ 1 ႎ㧘ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩᦛߍᒝᐲߣ⎕უ᜼േ㧕㧚࿶ജᛛⴚ㧘36
364㧘 33-41㧚369) 㧔⽷㧕ේሶജ⊒㔚ᛛⴚᯏ᭴㧔2001㧕㧦ᐔᚑ 12 ᐕᐲ‫ޓ‬ේሶജ⊒㔚ᣉ⸳⠴㔡ା㗬ᕈታ⸽⹜㛎ߦ㑐ߔࠆႎ๔ᦠ‫ߘޓ‬ߩ 3‫ޓ‬ᷫ⡺㈩▤⠴㔡ታ⸽⹜㛎㧚10)ᣣᧄ㔚᳇දળ㧔1973,1974,1975㧕
㧦࿾㔡ᤨߦ߅ߌࠆේሶ
ജᣉ⸳ߩ㒢⇇⸳⸘ߦ㑐ߔࠆ⹜㛎⎇ⓥ‫ޓ‬ᚑᨐႎ๔ᦠ
㧔ᤘ
๺ 46 ᐕᐲ㧘ᤘ๺ 47 ᐕᐲ㧘ᤘ๺ 48 ᐕᐲ㧕㧚11) ㆙⮮౐㇢㧘ᮮ↰ඳ㧘ዊ㊁ᖗ㧘ฎᎹ⌀৻㧘⮮⧯┙਽
㧔1999㧕
㧦ේሶജ⊒㔚ᚲߩ㈩▤⠴㔡⸳⸘ၮḰߩวℂൻ⎇ⓥ㧔ߘߩ㧝㧕
㧔ߘߩ㧞㧕㧚ᣣᧄᯏ᪾ቇળ 1999 ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘ΥΥ㧘407-410㧚
12) ㋈ᧁ⻞৻㧘㒙ㇱᶈ㧘૒‫ᧁޘ‬㓁৻㧘⍹ᷰ㓷ᐘ㧘㋈ᧁᶈᐔ
㧔1999㧕㧦㈩▤♽⚳ዪᒝᐲ⠴㔡ታ⸽⹜㛎㧔ో૕⸘↹㧕㧚‫ޓޓ‬ᣣᧄᯏ᪾ቇળ 1999 ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘ΥΥ㧘‫ޓޓ‬411-412㧚

13) Jaquay, K. (1998) : Seismic Analysis of Piping Final Program
5361.
Report. NUREG/CR-5361
536114) Gerry C. Slagis (2000) : Assessment of Piping Seismic
Response. ASME PVP-402-1, 49-55.
15) Touboul, F., Blay, N., and Lacire, M.H. (1999) : Experimental,
Analytical, and Regulatory Evaluation of Seismic Behavior
of Piping Systems. Transactions of the ASME, 121
121, 388392.
16)ේሶജ቟ోᆔຬળ㧔1996㧕
㧦ේሶജᣉ⸳╬቟ో⎇ⓥᐕᰴ⸘↹㧔ᐔᚑ 8 ᐕᐲ㨪ᐔᚑ 12 ᐕᐲ㧕㧚╙2┨1) Otani, A., Kobayashi, H., Ogawa, N., Nakamura, I. andShiratori, M. (1999) : Strength of Locally Thinned Piping
Subjected to Cyclic Loading. ASME PVP-387
387, 55-62.
3872) Nakamura, I., Ogawa, N., Otani, A., Kobayashi, H., andShiratori, M. (1999) : Dynamic Collapse Test of Cracked
Pipes. 15th SMiRT, IX, 69-76
3) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᄢ⼱┨ੳ㧘ዊᨋඳᩕ㧘⊕㠽ᱜ᮸㧔1999㧕㧦᭴ㅧ⊛ഠൻㇱࠍ᦭ߔࠆ㈩▤♽ߩേ⊛⎕უታ㛎㧚ᣣᧄᯏ᪾ቇળ1999ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘Υ 㧘413-414㧚
4) Nakamura, I., Ogawa, N., Otani, A. and Shiratori, M. (2000): An Experimental Study on Dynamic Behavior of Piping
Systems with Local Degradation. ASME PVP-403-1
403-1,
403-1
15-22.
╙3┨1) Otani, A., Kobayashi, H., Ogawa, N., Nakamura, I. andShiratori, M. (1999) : Strength of Locally Thinned Piping
Subjected to Cyclic Loading. ASME PVP-387
387, 55-62.
3872) Nakamura, I., Ogawa, N., Otani, A., Kobayashi, H., andShiratori, M. (1999) : Dynamic Collapse Test of Cracked
Pipes. 15th SMiRT, IX
IX, 69-76.
3) Nakamura, I., Ogawa, N., Otani, A. and Shiratori, M. (2000): An Experimental Study on Dynamic Behavior of Piping
Systems with Local Degradation. ASME PVP- 403-1
403-1,
15-22.
4) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᄢ⼱┨ੳ㧘⊕㠽ᱜ᮸㧔2001㧕
㧦࿾㔡⩄㊀ࠍฃߌࠆ߈ⵚઃ߈㈩▤ߩ⎕㕙⸃ᨆ㧚ᣣᧄᯏ᪾ቇળ 2001 ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘ΣΣ㧘427-428㧚
5) Sasaki, E., Ohta, A., and Kosuge, M. (1977) : Fatigue Crack
Propagation Rate and Stress Intensity Threshold Level ofSeveral Structural Materials at Varying stress Ratios (-1㨪
0.8). Transactions of National Research Institute for Metals,
19 - 4, 183-199.

− 6688 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆╙4┨1) Otani, A., Nakamura, I., Ogawa, N. and Shiratori, M. (2000): The Damping Characteristics of Piping with Plastic
Deformation. ASME PVP- 402-1
402-1, 23-28.
2) 㧔⽷㧕ේሶജ⊒㔚ᛛⴚᯏ᭴㧔2000㧕
㧦ᐔᚑ 11 ᐕᐲ‫ޓ‬ේሶജ⊒㔚ᣉ⸳⠴㔡ା㗬ᕈታ⸽⹜㛎ߦ㑐ߔࠆႎ๔ᦠ‫ߘޓ‬ߩ 3‫ޓ‬㈩▤♽⚳ዪᒝᐲ⠴㔡ታ⸽⹜㛎㧚3) ᣣᧄᯏ᪾ቇળ㧔1983㧕㧦㊄ዻ᧚ᢱ∋ഭᒝᐲߩ⸳⸘⾗ᢱΦ‫ޓ‬ૐࠨࠗࠢ࡞∋ഭᒝᐲ㧚4) Namaizawa, J., Ueno, K, Ishikawa, A., and Asada, Y. (1993): Life Prediction Technique for Ratcheting Fatigue. ASME
PVP-266
266, 3-11.
2665) Iwasaki, K., Shimakawa, T., Nakamura, K., Takahashi, H.,
Uno, T., and Watashi, K. (1991) : Application of Simplified
J-Estimation Methods to Surface Cracked Structures under
Creep-Fatigue Loadings. 11th SMiRT, IX
IX, 217-222.
6) ਃᶆ⋥᮸㧘⮮ጟᾖ㜞㧘㣮ፉశ৻㧘ችፒస㓷㧘⩲㊁ᥓ㧘⍹ᷰ㓷ᐘ㧔1997㧕㧦߈ⵚࠍ᦭ߔࠆ㈩▤ߩേ⊛⎕უ⹏ଔᴺߩ㐿⊒㧚㔚ജਛᄩ⎇ⓥᦠႎ๔㧘T47
T47㧚
T47

7) 㧔⽷㧕㔚ജਛᄩ⎇ⓥᚲ㧔1994㧕㧦㜞ㅦἹᯏེ߳ߩ㕖ᒢᕈ⎕უജቇߩㆡ↪ߦ㑐ߔࠆᜰ㊎㧔᩺㧕㧚⊒㔚↪ᣂဳἹ
ᛛⴚ⏕⸽⹜㛎⺞ᩏႎ๔ᦠ㧚8) CRIEPI (1997) : Drafts for Standard about Application of
Nonlinear Fracture Mechanics to Fast Breeder Nuclear
Reactor Components. Report of the Research Committee
on Technology Assurance Testing of New Type Electricity
Generating Reactor, CRIEPI.
9) Shibata, K. : Private communication. Japan Atomic Energy
Research Institute (JAERI).
╙5┨1) Shibata, H., Makiguchi, M., Ito, A., Ichihashi, I., Hirose, J.,
Kajimura, Y., Niino, Y., Hayashi, T., Chiba, T. (1983) :A DAMPING CHARACTERISTICS OF PIPINGSYSTEMS IN NUCLEAR POWER PLANTS. ASME PVP73, 151-178.
73
㧔ේⓂฃℂ‫ޓ‬㧦‫ޓ‬2001 ᐕ 9 ᦬ 6 ᣣ㧕

− 6699 −㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ⎇ⓥ⾗ᢱ‫ ╙ޓ‬220 ภ‫ޓ‬2001 ᐕ 10 ᦬㧨㑐ㅪ⊒⴫⺰ᢥ㧪1) ዊᎹାⴕ㧘ᓮሶᩊᱜ㧔1998㧕
㧦ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻࠍ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ㧚ᐔᚑ8ᐕᐲ࿖┙ᯏ㑐ේሶജ⹜㛎⎇ⓥᚑᨐႎ๔ᦠ㧔╙ 37 㓸㧕㧘
9-19-4㧚
2) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᓮሶᩊᱜ㧔1999㧕㧦ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻࠍ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ㧚
ᐔᚑ9ᐕᐲ࿖┙ᯏ㑐ේሶജ⹜㛎⎇ⓥᚑᨐႎ๔ᦠ㧔╙38
㓸㧕㧘9-19-4㧚
3) Otani, A., Hiroe, K., Ogawa, N., Nakamura, I. and Shiratori,
M. (1999) : Strength of Locally Thinned Piping Subjected
to Cyclic Loading. ASME PVP- 387
387, 55-62.
4) Otani, A., Hiroe, K., Ogawa, N., Nakamura, I. and Shiratori,
M. (1999) : A Study on the Strength of Locally Thinned
Wall Pipes Subjected to Cyclic Loading. 15th SMiRT, IX
IX,
137-144.
Nakamura, I., Ogawa, N., Otani, A., Hiroe, K., and Shiratori,
M. (1999) : Dynamic Collapse Test of Cracked Pipes. 15th
SMiRT, IX
IX, 69-76.
6) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᄢ⼱┨ੳ㧘ዊᨋඳᩕ㧘⊕㠽ᱜ᮸㧔1999㧕㧦᭴ㅧ⊛ഠൻㇱࠍ᦭ߔࠆ㈩▤♽ߩേ⊛⎕უታ㛎㧚ᣣᧄᯏ᪾ቇળ1999ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘Υ㧘413-414㧚
7) ᄢ⼱┨ੳ㧘ዊᎹାⴕ㧘ਛ᧛޿ߕߺ㧘⊕㠽ᱜ᮸㧔1999㧕
㧦➅ࠅ㄰ߒᦛߍࠍฃߌࠆᷫ⡺㈩▤ߩᒝᐲߦ㑐ߔࠆ⎇ⓥ㧚
ᣣᧄᯏ᪾ቇળ1999ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘Σ㧘145146㧚
8) ⊕㠽ᱜ᮸㧘੓ᒝ㧘໊ỈᏁ㧘⍫ୖᱞ⬿㧔1999㧕㧦⴫㕙߈ⵚࠍ᦭ߔࠆ㈩▤ߩૐࠨࠗࠢ࡞∋ഭ߈ⵚㅴዷ⸃ᨆ㧚ᣣᧄᯏ᪾ቇળ1999ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘Σ㧘139-140㧚
9) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᓮሶᩊᱜ㧔2000㧕㧦ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻࠍ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ㧚
ᐔᚑ 10 ᐕᐲ࿖┙ᯏ㑐ේሶജ⹜㛎⎇ⓥᚑᨐႎ๔ᦠ㧔╙
39 㓸㧕㧘9-19-4㧚10) ᄢ⼱┨ੳ㧘ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘⊕㠽ᱜ᮸㧔2000㧕
㧦ᷫ⡺㈩▤ 4 ὐᦛߍ⹜㛎ߢߩౝᄖ㕙߭ߕߺߦ㑐ߔࠆ⠨ኤ㧚ᣣᧄᯏ᪾ቇળ᧚ᢱജቇㇱ㐷ಽ⑼ળ࡮⎇ⓥળวหࠪࡦࡐࠫ࠙ࡓ⻠Ṷ⺰ᢥ㓸㧘209-214㧚
11) Nakamura, I., Ogawa, N., Otani, A. and Shiratori, M. (2000): An Experimental Study on Dynamic Behavior of Piping
Systems with Local Degradation. ASME PVP- 403-1
403-1, 15– 22.
5)12) Otani, A., Nakamura, I., Ogawa, N. and Shiratori, M. (2000): The Damping Characteristics of Piping with Plastic
Deformation. ASME PVP- 402-1
402-1, 23 – 28.
13) Shiratori, M., Yakura, M., Karasawa, T., Nakamura, I. andOtani, A. (2000) : Failure Analysis of Degraded Piping
Against Seismic Loading. ASME PVP- 402-1
402-1, 37 – 48.
14) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᄢ⼱┨ੳ㧘቟⮮ᩇ㧔2000㧕㧦࡜ࡦ࠳ࡓ౉ജߦኻߔࠆ߈ⵚઃ߈㈩▤ߩ∋ഭኼ๮⹏ଔ㧚ᣣᧄᯏ᪾ቇળ᧚ᢱജቇㇱ㐷⻠Ṷળ⻠Ṷ⺰ᢥ㓸㧘391392㧚
15) ⍫ୖᱞ⬿㧘⊕㠽ᱜ᮸㧘ዊ═ේ᳗ਭ㧘ਛ᧛޿ߕߺ㧘ᄢ⼱┨ੳ㧔2000㧕㧦ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩૐࠨࠗࠢ
࡞∋ഭ⹏ଔ㧘
ᣣᧄᯏ᪾ቇળ᧚ᢱജቇㇱ㐷⻠Ṷળ⻠Ṷ⺰ᢥ㓸㧘393-394㧚
16) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᓮሶᩊᱜ㧔2001㧕㧦ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻࠍ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ㧚
ᐔᚑ 11 ᐕᐲ࿖┙ᯏ㑐ේሶജ⹜㛎⎇ⓥᚑᨐႎ๔ᦠ㧔╙40㓸㧕㧘9-19-4㧚17) ⊕㠽ᱜ᮸㧘⍫ୖᱞ⬿㧘ዊ═ේ᳗ਭ㧘ਛ᧛޿ߕߺ㧘ᄢ⼱┨ੳ㧔2001㧕㧦ዪᚲ⊛ᷫ⡺ㇱࠍ᦭ߔࠆ㈩▤ߩ⠴㔡⵨ᐲ⹏ଔߦ㑐ߔࠆ⸃ᨆ⊛⎇ⓥ㧚ᣣᧄᯏ᪾ቇળ⺰ᢥ㓸㧔A✬㧕㧘67
67654㧘209-215㧚
6718) Otani, A., Nakamura, I., Ogawa, N. and Shiratori, M. (2001): The Damping Characteristics of Piping with Plastic
Deformation, Part2. ASME PVP- 428-1
428-1, 21 – 29.
19) ⊕㠽ᱜ᮸㧘⿧ᥓᵗᰴ㧘໊ỈᏁ㧘ᄢ⼱┨ੳ㧘ਛ᧛޿ߕߺ
㧔2001㧕
㧦⴫㕙߈ⵚࠍ᦭ߔࠆ㈩▤ߩૐࠨࠗࠢ࡞∋ഭ߈ⵚㅴዷ⸃ᨆ㧚ᣣᧄᯏ᪾ቇળ᧚ᢱജቇㇱ㐷⻠Ṷળ⻠Ṷ⺰ᢥ㓸㧘297-298㧚20) ਛ᧛޿ߕߺ㧘ዊᎹାⴕ㧘ᄢ⼱┨ੳ㧘⊕㠽ᱜ᮸㧔2001㧕
㧦࿾㔡⩄㊀ࠍฃߌࠆ߈ⵚઃ߈㈩▤ߩ⎕㕙⸃ᨆ㧚ᣣᧄᯏ᪾Σ㧘427-428㧚
ቇળ 2001 ᐕᐲᐕᰴᄢળ⻠Ṷ⺰ᢥ㓸㧘Σ21) Shiratori, M., Ochi, Y., Karasawa, T., Nakamura, I. andOtani, A. (2001) : Low Cycle Crack Growth Analysis for
the Piping with a Surface Crack. Proc. of APCFS & ATEM
’01, Sendai (to be published).

− 7700 −ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޓ‬ႎ๔ᦠ㧙ਛ᧛߶߆ⷐ‫ޓ‬ᣦ‫ޓ‬㜞⚻ᐕൻߦ઻޿᭴ㅧഠൻ߇⊒↢ߒߚ㈩▤♽ߩ࿾㔡ᤨߦ߅ߌࠆ᜼േࠍ᣿ࠄ߆ߦߔࠆߚ߼ߦ㧘⋥▤ࠍ૶↪ߒߚ➅ࠅ㄰ߒ 4 ὐᦛߍ⹜㛎ߣ㈩▤♽⹜㛎૕ࠍ૶↪ߒߚᝄേบታ㛎ࠍታᣉߒߚ㧚ᧄ⎇ⓥߢߪഠൻᒻ⁁ߣߒߡᷫ⡺߹ߚߪ߈ⵚࠍ૶↪ߒߚ㧚ߎࠇࠄߩታ㛎ࠍㅢߓߡ㧘޿ߊߟ߆ߩ⩄㊀᧦ઙ෸߮ഠൻ᧦ઙਅߦ߅ߌࠆ⚻ᐕഠൻ㈩▤ߩ៊்᜼േ߇ᛠីߢ߈ߚ㧚‫ߩࠄࠇߎޓ‬ታ㛎⚿ᨐߦኻߒ㧘⸃ᨆࠦ࡯࠼ ABAQUS ࠍ૶↪ߒߡᷫ⡺߹ߚߪ߈ⵚࠍ᦭ߔࠆ㈩▤ⷐ⚛ߩᒢ႟ᕈ⸃ᨆࠍታᣉߒߚ㧚⸃ᨆߢߪታ
㛎ߢᓧࠄࠇߚ៊்᜼േࠍౣ⃻ߒ㧘⎕უߦ⥋ࠆේ࿃ࠍ⠨ኤߔࠆߎߣ߇ߢ߈ߚ㧚߹ߚ㧘႟ᕈᄌᒻߦࠃࠆᝄേࠛࡀ࡞ࠡߩᶖᢔࠍ⠨ᘦߦ౉ࠇߚᒢ႟ᕈᔕ╵ᄌ૏ߩ◲ᤃ੍᷹ᚻᴺࠍ⠨᩺ߒ㧘ታ㛎⚿ᨐࠃࠅ߽଻቞⊛ߥᔕ╵㊂ߩ੍᷹ࠍน⢻ߣߒߚ㧚ࠠ࡯ࡢ࡯࠼㧦⚻ᐕഠൻ㧘㈩▤㧘߈ⵚ㧘ᷫ⡺㧘ᝄേบታ㛎㧘⎕៊ᒻᘒ㧘᦭㒢ⷐ⚛ᴺ⸃ᨆ㧘◲ᤃᒢ႟ᕈᔕ╵੍᷹ᴺ− 7711 −㧨ᷝઃ 㧪‫ޟޓ‬ᯏེ࡮㈩▤♽ߩ⚻ᐕᄌൻߦ઻߁⠴㔡቟ో⵨ᐲ⹏ଔᚻᴺߩ⎇ⓥ‫ޠ‬ታ㛎ታᣉᆔຬળ‫ޓ‬ฬ★

ᆔຬ㐳‫⊕ޓ‬㠽‫ޓ‬ᱜ᮸‫ޓ‬቟⮮‫ޓ‬ᩇᮮᵿ࿖┙ᄢቇᎿቇㇱ↢↥Ꮏቇ⑼‫ޓ‬ᢎ᝼ᮮᵿ࿖┙ᄢቇᎿቇㇱ‛⾰Ꮏቇ⑼‫ޓ‬ᢎ᝼‫ޓޓޓޓ‬㜞↰‫৻ޓ‬ᮮᵿ࿖┙ᄢቇᄢቇ㒮Ꮏቇ⎇ⓥ⑼ᯏ᪾ࠪࠬ࠹ࡓ▤ℂᎿቇ‫ޓ‬ᢎ᝼‫ޓޓޓޓ‬ᅏ↰‫ޓ‬ᵗมᮮᵿ࿖┙ᄢቇᎿቇㇱ↢↥Ꮏቇ⑼‫ޓ‬ഥᢎ᝼‫ޓޓޓޓ‬੓‫ޓޓ‬ᒝᮮᵿ࿖┙ᄢቇᎿቇㇱ↢↥Ꮏቇ⑼‫ޓ‬ഥᢎ᝼㧔ᐔᚑ 22 ᐕ 7 ᦬߹ߢ㧕‫ޓ‬ዊ═ේ‫ޓ‬᳗ਭ㒐ⴡᄢቇᩞࠪࠬ࠹ࡓᎿቇ⟲ᯏ᪾Ꮏቇ⑼ᒝᐲ⸳⸘⻠ᐳ‫ޓ‬ഥᚻ㧔ᐔᚑ 10 ᐕ 7 ᦬߆ࠄ㧕‫ޓ‬ዊᎹ‫ޓ‬ାⴕ㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ✚ว㒐ἴ⎇ⓥㇱ㐷‫✚ޓ‬᜝ਥછ⎇ⓥຬ‫ޓ‬ਛ᧛‫ߺߕ޿ޓ‬㒐ἴ⑼ቇᛛⴚ⎇ⓥᚲ✚ว㒐ἴ⎇ⓥㇱ㐷‫⎇ޓ‬ⓥຬ‫ޓ‬ᩊ↰‫ޓ‬ൎਯᣣᧄේሶജ⎇ⓥᚲ᧲ᶏ⎇ⓥᚲ࿾㔡ᖱႎવ㆐⎇ⓥ․೎࠴࡯ࡓ࡝࡯࠳࡯࡮ᰴ㐳‫ޓ‬㣮ፉ‫ޓ‬శ৻㔚ജਛᄩ⎇ⓥᚲ㊄ዻ᧚ᢱㇱ‫ޓ‬ㇱ㐳‫ޓ‬ਃᶆ‫⋥ޓ‬᮸㔚ജਛᄩ⎇ⓥᚲ㊄ዻ᧚ᢱㇱ‫ޓ‬ਥછ⎇ⓥຬ㧔ᐔᚑ 11 ᐕ 10 ᦬߆ࠄ㧕‫ޓ‬㜞ᯅ‫␭ޓ‬ᴦ᧲੩㔚ജ㧔ᩣ㧕ේሶജᛛⴚㇱ‫⺖ޓ‬㐳㧔ᐔᚑ 11 ᐕ 1 ᦬߹ߢ㧕‫ޓ↰⑔ޓ‬ବᒾ᧲੩㔚ജ㧔ᩣ㧕ේሶജᛛⴚㇱ‫⺖ޓ‬㐳㧔ᐔᚑ 11 ᐕ 10 ᦬߆ࠄ㧕‫ޓ‬૒⮮‫ޓ‬㓉᧲੩㔚ജ㧔ᩣ㧕ේሶജᛛⴚㇱ‫ޓ‬೽㐳㧔ᐔᚑ 12 ᐕ 7 ᦬߆ࠄ㧕‫ޓ‬㐳Ỉ‫ޓ‬๺ᐘ᧲੩㔚ജ㧔ᩣ㧕ේሶജᛛⴚㇱ‫ޓ‬ਥછ‫ޓ‬㧔ᐔᚑ 11 ᐕ 7 ᦬߆ࠄᐔᚑ 11 ᐕ 10 ᦬߹ߢ㧕‫⊕ޓ‬੗‫⧷ޓ‬჻㑐⷏㔚ജ㧔ᩣ㧕ේሶജἫജᧄㇱේሶജ቟ోᛛⴚ⺖‫⺖ޓ‬㐳‫ޓ‬⍹ᷰ‫ޓ‬㓷ᐘᩣ ᣣ┙⵾૞ᚲᣣ┙Ꮏ႐ේሶജ㩖㩩㩡㩧㩎ᑪ⸳ㇱ‫ޓ‬ਥછᛛᏧ‫ޓ‬ዊፉ‫ޓ‬ାਯਃ⪉㊀Ꮏ ᩣ ේሶജ੐ᬺᧄㇱシ᳓Ἱࡊ࡜ࡦ࠻ᛛⴚㇱ‫ޓ‬ਛፉ‫ޓ‬᡽㓉ᩣ ᧲⦼ේሶജᯏེ⸳⸘ㇱ‫ޓ‬ਥᩏ‫ޓ‬ጟᧄ‫ޓ‬ᣤᄦ⍹Ꮉፉ᠞⏴㊀Ꮏ㧔ᩣ㧕ේሶജ✚ว⸳⸘ㇱ‫ޓ‬ㇱ㐳‫ޓ‬ዊᨋ‫ޓ‬ඳᩕ⍹Ꮉፉ᠞⏴㊀Ꮏ㧔ᩣ㧕ේሶജ✚ว⸳⸘ㇱ‫⺖ޓ‬㐳‫ޓ‬ਃᨑ‫ޓ‬ദ⍹Ꮉፉ᠞⏴㊀Ꮏ㧔ᩣ㧕ේሶജኈེ⸳⸘ㇱ‫⺖ޓ‬㐳‫ޓ‬ᄢ⼱‫┨ޓ‬ੳ⍹Ꮉፉ᠞⏴㊀Ꮏ㧔ᩣ㧕ේሶജ╙  ࡊ࡜ࡦ࠻⸳⸘ㇱ㧔ᐔᚑ 11 ᐕ 1 ᦬߆ࠄ㧕㧔ᓎ⡯ߪᆔຬዞછᒰᤨ‫ޔ‬ᢘ⒓⇛㧕

− 7722 −＜添付 2 ＞ 実験結果等カラー図版＜要素試験＞ （本文 P17 〜 P24）(a) Initial SCC in SC01.

(b) Initial SCC in SC03.

(c) Initial SCC in SC07.

(d) Initial SCC in SC08.

図 A-1 SCC 試験体の初期 SCC き裂
Fig. A-1 Initial shape of SCC in SCC specimens.

図 A-3
全周破断の状況 （EM02, 全周 EDM き裂付き試験体）
Fig. A-3 Full circumferential break(EM02, with full circumferential EDM notch).

図 A-2 初期 SCC き裂からの貫通（SC01）
Fig. A-2 Crack penetration from initial SCC (SC01).

Ratchet deformation

Circumferential crack

図 A-4
ラチェットによる減肉部分の変形（EC05, 内圧あり 50％減肉試験体）
Fig. A-4 Deformation at thinned wall part caused by ratchet (EC05, 50% thinned wall with internal pressure).

Buckling deformation

Circumferential crack

図 A-5
減肉部分での局部座屈変形（EC06, 内圧なし 50％減肉試験体）
Fig. A-5 Buckling deformation at thinned wall part (EC06, 50% thinned wall without internal pressure).

73

Circumferential crack

Longitudinal crack

図 A-6
周方向及び軸方向き裂とラチェット変形（EC07, 内圧あり 75％減肉試験体）
Fig. A-6 Circumferential and longitudinal cracks and ratchet deformation (EC07, 75% thinned wall with internal pressure).

Crack
図 A-7
140mm 入力時の EA01 の変形
Fig. A-7 Deformation of EA01 at 140mm input displacement.

＜平面配管系試験＞

図 A-8
溶接線脇でのき裂貫通（EA02, 健全試験体）
Fig. A-8 Crack penetration at welding line (EA02, no defect).

（本文 P25 〜 P30）

Elbow2

Crack initiation part

図 A-10 エルボ 2 でのき裂貫通（2D̲B01）
Fig. A-10 Penetration of crack on Elbow2 of 2D_B01.

図 A-9
2D̲B01 におけるアンカ近傍での破損
Fig. A-9 Unexpected break of pipe near an anchor on the test of
2D_B01.

74

Thinned wall
straight pipe part(a) Crack on side inner surface of Elbow1.

Penetration part(b) Crack on side inner surface of Elbow2.

(c) No crack on thinned wall straight pipe part.
図 A-12 2D̲B01 の浸透探傷試験結果
Fig. A-12 Penetration test results of 2D_B01.

図 A-11 2D̲B01 における減肉部分の膨らみ
Fig. A-11 Bulge of thinned wall part of 2D_B01.

Elbow1(a) Crack on side inner surface of Elbow1.

(b) Small crack on side inner surface of Elbow2.
図 A-14 2D̲C01 の浸透探傷試験結果
Fig. A-14 Penetration test results of 2D_C01.

図 A-13
エルボ 1（減肉エルボ）におけるき裂貫通（2D̲C01）
Fig. A-13 Penetration of crack on Elbow1 (thinned wall elbow) of
2D_C01.

75

＜立体配管系試験＞（本文 P31 〜 P35）

図 A-15
エルボ 1 における疲労き裂（3D̲A01）
Fig. A-15 Fatigue crack at Elbow1, 3D_A01.

(a) Crack penetration occurred at Elbow1. during 1850Gal_#03
excitation.

(b) Fatigue crack at Elbow1.

図 A-16
3D̲C01 の破損形態
Fig. A-16 Failure mode of 3D_C01.

(a) S047 side.

(b) S043 side.

図 A-17
3D̲C02 エルボ 1 で確認されたき裂貫通前の配管表面の変化（1850Gal, 1 回目の加振後）Fig. A-17 Pipe surface deformation before crack penetration at Elbow1, 3D_C02 (after 1850Gal_#01 excitation test).

(a) S047 side.

(b) S043 side.
図 A-18
エルボ 1 における疲労き裂（3D̲C02）
Fig. A-18 Fatigue crack at Elbow1, 3D_C02.

76

(a) Crack penetration occurred at Elbow2. during 1850Gal_#01
excitation.

(b) Leak of water at Elbow2.

図 A-193D̲C03 の破損形態
Fig. A-19 Failure mode of 3D_C03.

図 A-20

3D̲D02 において EDM き裂からのき裂貫通前に配管表面で確認された筋（1850Gal, 1 回目の加振後）Fig. A-20

A line on the pipe surface before crack penetration at EDM notch, 3D_D02 (after 1850Gal_#02 excitation test).

図 A-21
1850Gal 2 回目の加振中におけるき裂貫通の状況
Fig. A-21 Crack penetration occurred at EDM notch during 1850Gal_#02 excitation test.

Broken point(a) View from the front.

(b) View from the excitation direction.
図 A-22
3D̲D02 の破損状況
Fig. A-22 Failure mode of 3D_D02.

77

＜詳細解析結果＞（本文 P36 〜 P59）
1
Coffin equation
Asada I

0.8

Dd (= εh / ε f )Asada II
EC02

0.6

EC04
EC05

0.4

EC07
EC08

0.2

EC09
0
0

0.2

0.4

0.6

0.8

1

Dd (= εh / ε f )

0.2

0.1

0
0

0.2

0.4

0.6

0.8

1

0.6

Df (= η )図 A-23
各試験体の Dd-Df 線図
Fig. A-23 Relation between Dd and Df.

Elbow division

Elbow division

Elbow division

Elbow division

outside surface

inner surface

outside surface

inner surfaceAA(a) 3D_A01.

(b) 3D_C01.

図 A-24各モデルの相当塑性ひずみ分布図
Fig. A-24 Equivalent plastic atrain distribution.

78