䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷ᣢ⸳ਅ᳓㆏▤ᷯ䈱ᦝ↢⸳⸘↪䉸䊐䊃䉡䉢䉝䈱㐿⊒䌾䇸▤ᦝ↢䈱ᚻᒁ䈐䋨᩺䋩䇹䈮ၮ䈨䈒᭴ㅧ⸘▚䌾
SUPPORTING SYSTEM FOR RENOVATION DESIGN OF AGING REINFORCED CONCRETE
SEWAGE STRUCTURES

Ꮉἑ⾆ⴕ*䊶ਛ㊁㓷┨**䊶Ꮷ㩷 ⥄ᶏ**䊶᧖ጊੳታ***಴ญᢅⴕ****Takayuki KAWASE, Masaaki NAKANO, Zihai SHI, Hitomi SUGIYAMA and Toshiyuki DEGUCHIThe renovation design of aging RC sewers using the sewage pipe renewal (SPR) method
takes into account both the maximum load-carrying capacities of the existing and therenovated sewers. To facilitate the design practice, a user-friendly, high-performancecomputing system has been developed, aiming at reducing the computational time and cost.
The computational concept, which is based on a separate evaluation method for analyzing RCstructures, and verification with experimental studies are reported.

 Key Words㧦 aging RC sewage structures, renovation, ultimate load-carrying capacity,separate evaluation method, SPR method䈱⛽ᜬ▤ℂ䈏䈘䉏䈩䈇䈭䈇 4) 䇯䇸੍㒐଻ోဳ䇹⛽ᜬ▤ℂ䈱ታ㪈㪅㩷㩷䈲䈛䉄䈮㩷ㄭ ᐕ 䇮⠴ ↪ ᐕ ᢙ 䉕⿥ ㆊ 䈚䈢⠧ ᧎ ਅ ᳓ ㆏ ▤ ᷯ 䈱Ⴧ ട 䈮઻⃻ 䈮䈲⃻ ⁁ 䈱ஜ ో ᐲ 䉕ቯ ㊂ ⊛ 䈮⹏ ଔ 䈜䉎䈖䈫䈏㊀ ⷐ 䈪䈅䉎䈇䇮ᢙ ᄙ 䈒䈱ᦝ↢ ᛛ ⴚ 䈱㐿 ⊒ 䊶ታ ↪ ൻ 䈏ㅴ 䉄䉌䉏䈩䈇䉎ਛ 䇮䈏䇮⃻࿷䈲䈵䈶ഀ䉏䊶㋕╭㍕䈱᦭ή䈭䈬䈮䉋䉎ቯᕈ⊛䈭್ᢿᦝ ↢ ▤ 䈱⸳ ⸘ ᴺ 䉇⠴ ⩄ ⢻ ജ 䈱⹏ ଔ 䈮䈧䈇䈩⛔ ৻ ⊛ 䈭⷗ ⸃䈮䉋䉍䈭䈘䉏䈩䈇䉎䇯䈠䈱䈢䉄䇮㐳〒㔌䈮䈍䉋䈹ਅ᳓㆏▤ᷯ䉕䈏␜䈘䉏䈧䈧䈅䉎䇯䇸▤ᦝ↢䈱ᚻᒁ䈐䋨᩺䋩䇹 1) 䈱ਛ䈪䈲䇮㵰ⶄวല₸䉋䈒䇮ቯ㊂⊛䈮ஜోᐲ䉕⹏ଔ䈪䈐䉎䉿䊷䊦䈏᳞䉄䉌䉏䉎䇯▤䈱᭴ㅧ⸘▚䈲䇮ᣢ⸳▤䈱ഠൻ⁁ᘒ╬䉕෻ᤋ䈚䇮ⶄว▤䈱䈠䈖䈪䇮╩⠪䉌䈲᧲੩ㇺਅ᳓㆏䉰䊷䊎䉴䊺䇮Ⓧ᳓ൻቇᎿᬺ⚳ዪ⠴⩄ജ䉕⹏ଔ䈪䈐䉎㒢⇇⁁ᘒ⸳⸘ᴺ䈮䉋䉍ⴕ䈉䈖䈫䉕ේ䊺䇮⿷┙ᑪ⸳Ꮏᬺ䊺䈫౒ห䈪䇮৻⥸⸳⸘⠪䈮ะ䈔䈢 SPR Ꮏೣ䈫䈜䉎㵱䈫⸥ㅀ䈘䉏䈩䈇䉎䇯䈠䈱ታ⃻䈱䈢䉄䈮䈲䇮RC ᭴ㅧᴺ⸳⸘ᡰេ䉲䉴䊁䊛䋨SPRANA䋩䉕㐿⊒䈚䇮2002 ᐕ 4 ᦬䉋䉍‛䈱䈵䈶ഀ䉏䈱⊒↢䊶ㅴዷ䉕⠨ᘦ䈚䇮⚳ዪ⠴⩄ജ䉕⹏ଔ䈪䈐⽼ᄁ䉕㐿ᆎ䈚䈩䈇䉎䇯SPRANA 䈲ᠲ૞䈱◲ଢᕈ䉇ല₸ᕈ䉕䉎㕖✢ᒻ⸃ᨆᛛⴚ䈏ਇนᰳ䈪䈅䉎䇯㊀ⷞ䈚䇮䉮䉴䊃䊌䊐䉤䊷䊙䊮䉴䈮ఝ䉏䇮એਅ䈱․ᓽ䉕᦭䈜䉎䇯਄⸥ᛛⴚ䈲⋡ⷡ䈚䈇⊒ዷ䈮䉋䉍ታോ䊧䊔䊦䈪ㆡ↪䈘䉏䇮ᒰx▤ᦝ↢䈱ᚻᒁ䈐䋨᩺䋩䈮Ḱ䈛䈢᭴ㅧ⸘▚␠䈮䈍䈇䈩䈲䇮⥄␠㐿⊒䈚䈢㕖✢ᒻ䈵䈶ഀ䉏⸃ᨆ䉿䊷䊦 2)x

ቯ㊂⊛䈭ஜోᐲ⸻ᢿ䋨એ ਅ 䇮ᓥ ᧪ 䉿䊷䊦䋩䉕↪ 䈇䈩਄ ⸥ ේ ೣ 䈮Ḱ 䈛䈢䇮ⶄ ว ᦝ ↢x䉴䊏䊷䊂䉞䈮⸃ᨆ▤䋨଀䈋䈳䇮SPR Ꮏᴺ3) 䈮䉋䉎ᦝ↢▤䋩䈱⸳⸘䉕ⴕ䈦䈩䈇䉎䇯䈚䈎䈚䇮ᓥ᧪䉿䊷䊦䈲䇮xx

ᧄⓂ䈲 SPRANA 䈍䉋䈶⸃ᨆᚻᴺ䈱᭎ⷐ䉕␜䈜䉅䈱䈪䈅䉎䇯᳢↪ᕈ䈏㜞䈇෻㕙㜞ᐲ䈭ᛛⴚജ䈏ⷐ᳞䈘䉏䇮৻⥸⸳⸘⠪䈮䈲૶䈇䈖䈭䈜䈖䈫䈏࿎㔍䈪䈅䉎䈖䈫㪉㪅㩷㩷㪪㪧㪩 Ꮏᴺ⸳⸘ᡰេ䉲䉴䊁䊛䈱᭎ⷐ㩷౉ജ䊂䊷䉺૞ᚑ䊶⸃ᨆ䈱ᚲⷐᤨ㑆䈏㐳ᤨ㑆䈮䈭䉎䈖䈫䋨㪈䋩㩷 ᭎ⷐ䈭䈬䇮ታോ⸳⸘䈮ᦨㆡ䈫䈲⸒䈋䈭䈇㕙䈏䈅䉍䇮ᠲ૞ᕈ䈮ఝ䉏◲ଢ䈮⸘▚䈪䈐䉎䉿䊷䊦䈏ᦸ䉁䉏䈩䈇䉎䇯䉁䈢৻ᣇ䈪䇮⛽ᜬ▤ℂᬺോ䈱⃻⁁䈲⧰ᖱ䉇੐᡿䈏⊒↢䈚䇸ᄢญᓘ SPR Ꮏᴺ⸳⸘䊙䊆䊠䉝䊦䇹 5) 䈪䈲䇮㒢⇇⁁ᘒ⸳⸘ᴺ䈮ၮ䈨䈐䇮એਅ䈱ᾖᩏ䈪ᢿ㕙⸳⸘䉕ⴕ䈉䈫䈘䉏䈩䈇䉎䇯x䈩䈎䉌ಣ ℂ 䈜䉎䇸⊒ ↢ ኻ ᔕ ဳ 䇹䈏ਥ ૕ 䈪䈅䉍䇮䇸੍ 㒐 ଻ ో ဳ 䇹⚳ዪ㒢⇇⁁ᘒ䉕ᜰᮡ䈫䈚䈢ᬌ⸛㵺ᦝ↢▤䈱⚳ዪ⠴⩄ജ䈏䇮⸳⸘⩄㊀䈮ၮ䈨䈒⸳⸘⠴⩄ജ䈱 2.5 ୚એ਄䈱቟ో₸䉕᦭䈜䉎䈖䈫䉕⏕⹺䈜䉎䋨ઃ㍳ෳᾖ䋩**********␠ળⅣႺ䉣䊮䉳䊆䉝䊥䊮䉫੐ᬺㇱ㩷 䍵䍐䍪䍙䍐䍖䍷䍭䍦䍚䍼䍰䍻䍢ㇱ㩷ਛᄩ⎇ⓥᚲ ✚วᛛⴚ㐿⊒ㇱ㚂ㇺ࿤੐ᬺㇱ ㇺᏒၮ⋚ㇱ᧲੩ㇺਅ᳓㆏䉰䊷䊎䉴ᩣᑼળ␠x૶↪㒢⇇⁁ᘒ 䉕ᜰᮡ 䈫䈚䈢ᬌ ⸛㵺⸳⸘⩄㊀ 䉁䈪䈲ᣂ䈢䈭䈵䈶ഀ䉏䈏⊒↢䈚䈭䈇䈖䈫䉕⏕⹺䈜䉎㪈㪋㪌㩷

既設下水道管渠の更生設計用ソフトウェアの開発

SPRANA 䈲䇮೨⠪ 䈮㑐 䈚䈩ᦨᄢ⠴ ⩄ ജ䋨⚳ዪ⠴ ⩄ ജ䋩䇮ᓟ⠪䈮㑐䈚䈩䈵䈶ഀ䉏⠴⩄ജ䉕▚಴䈜䉎䉲䉴䊁䊛䈪䈅䉎䇯ᢿ 㕙䇮ᷫ⡺ ᢿ㕙 䇮ή ╭ᢿ 㕙䈎䉌ㆬ ᛯ䋩䉕ㆬᛯ 䈜䉎䈖䈫䈪ᣢ⸳▤䈱ഠൻ⁁ᘒ䉕⴫⃻䈪䈐䉎䇯䋨㪉䋩㩷 ᠲ૞ᣇᴺ࿑䋭㪈 䈮 SPRANA 䈱⸃ᨆᚻ㗅䉕␜䈜䇯ᣢ⸳▤䈮䈍䈇䈩䇮a.⸳⸘᧦ઙ䈱౉ജ䇮b.౉ജ᧦ઙ䈱⏕⹺䇮c.⸃ᨆ䇮d.⚿ᨐ಴ജ䈱㗅䈪ⴕ䈇䇮䈠䈱⚿ᨐⷐ᳞⠴⩄ജ䉕ḩ䈢䈘䈭䈇႐ว䈲䇮SPRᎿᴺ䈮䉋䉍ᦝ↢䈚䈢▤ᷯ䈮㑐䈚䈩ౣᐲ⸃ᨆ䉕ⴕ䈉䇯㩷㩷㪈㪀㩷 ⸳⸘᧦ઙ䈱౉ജ
5 䈧䈱䉺䊑䋨᭴ㅧᒻᑼ䇮‛ᕈ୯䇮⩄㊀䇮㋕╭䇮ᖱႎ䋩䈱ฦ㗄⋡䈮ᢙ୯䉕౉ജ䈜䉎䇯એਅ䈮ฦ䉺䊑䈗䈫䈱౉ജ㗄⋡䉕␜䈜䇯᭴ㅧᒻᑼ䉺䊑䋨࿑䋭㪉䋩x▤ ᷯ ᒻ ⁁ 䋨⍱ ᒻ 䇮⬄ ដ 䈔䇮౞ ᒻ 䇮㚍 か ᒻ 䈎䉌ㆬ ᛯ 䋩䇮ㇱ ᧚ኸᴺ䋨ේ▤ኸᴺ䇮ᦝ↢ㇱ᧚ኸᴺ䇮䊊䊮䉼ኸᴺ䋩䉕౉ജ䈜䉎䇯‛ᕈ୯䉺䊑䋨࿑䋭㪊䋩x

図－3 物性値タブᣢ⸳ㇱ᧚䈱䉮䊮䉪䊥䊷䊃䇮ᦝ↢ㇱ᧚䈱䊝䊦䉺䊦䈮㑐䈚䈩䇮⻉‛ᕈ୯䋨ᒢᕈଥᢙ䇮ᒝᐲ╬䋩䉕౉ജ䈜䉎䇯⩄㊀䉺䊑䋨࿑䋭㪋䋩x⸳⸘⩄㊀䋨ᱫ⩄㊀䇮ᵴ⩄㊀䋩䉕౉ജ䈜䉎䇯x㋕╭䉺䊑䋨࿑䋭㪌䋩㗂䈍䉋䈶ᐩ

䈱㈩ ╭ ⁁ᴫ 䉕⸳ ቯ 䈜䉎䇯ᢿ 㕙 ⁁ᴫ 䋨ᮡḰSTARTᣢ⸳▤a. ⸳⸘᧦ઙߩ౉ജb. ౉ജ᧦ઙߩ⏕⹺c. ⸃ᨆd.⚿ᨐ಴ജᦝ↢▤a. ⸳⸘᧦ઙߩ౉ജb. ౉ജ᧦ઙߩ⏕⹺c. ⸃ᨆd.⚿ᨐ಴ജ࿑䋭㪋㩷 ⩄㊀䉺䊑㩷ⷐ᳞⠴⩄ജⷐ᳞⠴⩄ജਇḩ⿷ਇḩ⿷ḩ⿷ḩ⿷END࿑䋭㪈㩷 ⸃ᨆᚻ㗅㩷࿑䋭㪉㩷 ᭴ㅧᒻᑼ䉺䊑㩷146END࿑䋭㪌㩷 ㋕╭䉺䊑㩷こうえいフォーラム第 11 号 / 2003.1

࿑䋭㪍㩷 ᖱႎ䉺䊑㩷࿑䋭㪏㩷 ⸃ᨆ⚿ᨐ㩷⸳⸘ᤨ㧗⃻⁁㧗ᦝ↢ᤨ 2 ࡄ࠲࡯ࡦ㧩4 ࡄ࠲࡯ࡦ䊂䊷䉺૞ᚑ䈍䉋䈶⏕⹺⸃ᨆ⚿ᨐ಴ജ

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ᓥ᧪࠷࡯࡞
524#0#17 ᣣᢙ࿑䋭㪐㩷 㩷 ⸃ᨆᬺോᎿ⒟䈱⍴❗ൻ䈱଀㩷䋨㪊䋩㩷 ⸃ᨆᤨ㑆⸃ ᨆ 䈱 ᚲ ⷐ ᤨ 㑆 䈲 䇮 ଀ 䈋 䈳 䇮 CPU:Pentium 㸉
500MHz䇮䊜䊝䊥:128MB 䈱േ૞ⅣႺਅ䈪䈅䉏䈳䇮ᢿ㕙ኸᴺ࿑䋭㪎㩷 ౉ജ᧦ઙ䈱⏕⹺↹㕙㩷

1500mm㬍1500mm 䈱⍱ᒻᷯ䈱႐ว䇮10 ಽ⒟ᐲ䈪䈅䉎䇯䈖䉏䈲䇮৻ ㅪ 䈱ᚻ 㗅 䉕⠨ 䈋䉎䈫䇮ᓥ ᧪ 䉿䊷䊦䉇Ꮢ ⽼ 䈱䈵䈶ഀxᖱႎ䉺䊑䋨࿑䋭㪍䋩⸃ᨆ䉺䉟䊃䊦䇮ᣣᤨ䇮⸃ᨆ䊜䊝䇮⸃ᨆ᧦ઙ䋨⩄㊀᧦ઙ䈍䉋䈶䉏㕖✢ᒻ⸃ᨆ䉮䊷䊄䈫Ყセ䈚䈩ᩰ೎䈮⍴ᤨ㑆䈪䈅䉎䇯࿑䋭㪐 䈮䇮৻ᢿ㕙䉕⸃ᨆ䈜䉎႐ว䋨⸳⸘ᤨ䋫⃻⁁䋫ᦝ↢ⷐ᳞⠴⩄ജ䋩䉕౉ജ䈜䉎䇯ᤨ 2 䊌䉺䊷䊮䋽4 䊌䉺䊷䊮䋩䈮䈍䈇䈩䇮䊂䊷䉺૞ᚑ䈎䉌⚿ᨐ಴㩷㩷㪉㪀㩷 ౉ജ᧦ઙ䈱⏕⹺ജ䉁䈪䈱ᣣᢙ䈮㑐䈚䈩 SPRANA 䈫ᓥ᧪䉿䊷䊦䈱Ყセ⚿ᨐ䉕1)⸳⸘᧦ઙ䈱౉ജ䈮䈍䈇䈩ฦ䉺䊑䈱㗄⋡䈮⸳⸘᧦ઙ䉕౉␜䈜䇯⋡቟䈫䈚䈩䇮ᓥ᧪䉿䊷䊦䈲 7 ᣣ⒟ᐲ䇮SPRANA 䈲 1 ᣣജᓟ䇮䇸ቢੌ䇹䊗䉺䊮䉕䉪䊥䉾䉪䈜䉎䈫䇮࿑䋭㪎 䈱䉋䈉䈮ឬ↹಴ജ⒟ᐲ䈪䈅䉎䇯䈖䈱ᣣᢙᏅ䈲䇮⥄േ䊜䉾䉲䊠૞ᚑᯏ⢻䈮䉋䉍㕙ୟ䈘䉏䉎䇯䈖䈖䈪䇮౉ജ䈚䈢⸳⸘᧦ઙ䉕⏕⹺䈜䉎䇯䈭⻉᧦ઙ䈱⸳ቯ䈏◲⇛ൻ䈘䉏䈩䈇䉎䈖䈫䉇䇮⸃ᨆᤨ㑆䈏⍴❗

㩷㩷㪊㪀㩷 ⸃ᨆ䈱ታⴕൻ䈘䉏䈩䈇䉎䈖䈫䈭䈬䈮䉋䉎䉅䈱䈪䈅䉎䇯౉ജ᧦ઙ䉕⏕⹺ᓟ䇮⸃ᨆ䉕ታⴕ䈜䉎䇯㩷㩷㪋㪀㩷 ⸃ᨆ⚿ᨐ䈱⴫␜䉁䈢䇮᧦ઙᄌᦝ䈏◲න䈭ᠲ૞䈪น⢻䈪䈅䉎䈢䉄䇮ᦝ↢ㇱ᧚ෘ䉇᧚ᢱ‛ᕈ䇮㋕╭䈱ᧄᢙ䈭䈬䉕⚦䈎䈒ᄌൻ䈘䈞䈩ⴕ䈉⹜ⴕ⸃ᨆ䈏⚳ੌ䈜䉎䈫䇮࿑䋭㪏 䈱䉋䈉䈮⸃ᨆ⚿ᨐ䈏⴫␜䈘䉏䉎䇯⸃ ᨆ 䈏⍴ ᤨ 㑆 䈪ታ ⴕ น ⢻ 䈪䈅䉎䇯ታ ോ ⸳ ⸘ 䈮䈍䈇䈩䈲䇮ว⸃ᨆ⚿ ᨐ 䈮䈲䇮್ቯ⚿ ᨐ 䈫䈚䈩ฦ 㒢⇇⁁ ᘒ 䋨૶↪䇮⚳ዪ 䋩䈪ℂ ⊛ 䈭⸳ ⸘ 䉕䈜䉎䈢䉄䈮೨ ㅀ 䈱䉋䈉䈭⹜ ⴕ ⸃ ᨆ 䉕ⴕ 䈉䈖䈫䈏䈱ᾖ ᩏ ⚿ ᨐ 䈏␜ 䈘䉏䉎䇯ⷐ ᳞ ⠴ ⩄ ജ 䉕ḩ ⿷ 䈚䈩䈇䉏䈳䇸ḩᗐቯ䈘䉏䉎䈢䉄䇮⥄േൻ䊶⍴ᤨ㑆ൻ䈱․ᓽ䉕᦭䈜䉎⿷䋣䋣䇹䇮䈠䈉䈪䈭䈔䉏䈳䇸ⷐᬌ⸛㵺䇹䈫಴ജ䈘䉏䉎䇯SPRANA 䈲㕖Ᏹ䈮᦭ല䈫⠨䈋䉎䇯147ᣢ⸳ਅ᳓㆏▤ᷯߩᦝ↢⸳⸘↪࠰ࡈ࠻࠙ࠚࠕߩ㐿⊒㪊㪅㩷㩷♖ᐲᬌ⸽⚿ᨐ㩷
SPRANA 䈱♖ᐲ䉕⏕⹺䈜䉎䈢䉄䇮▤ᷯ䈱⎕უታ㛎䉕ౣ⃻䈚䈢䇯ታ㛎䉬䊷䉴䈲䇮⍱ᒻ䋨ౝⓨኸᴺ䋺1,500㬍1,500䇮2,500㬍
2,500 䇮 2,500 㬍 3,500mm 䋩 䈍 䉋 䈶 ౞ ᒻ 䋨 ౝ ⓨ ኸ ᴺ 䋺 㱢
1,000mm䋩䈱ᣢ⸳▤䈫䈠䉏䉌䉕ᦝ↢䈚䈢▤ᷯ䈪䈅䉎䋨࿑䋭㪈㪇䋩䇯ᣢ⸳▤䈱⁁ᘒ䈫䈚䈩ஜో䈭䉅䈱䉇㋕╭䈏ᰳ⪭䈚䈢䉅䈱䇮ᦝ↢▤䈱⁁ᘒ䈫䈚䈩ᣢ⸳ㇱ᧚䈫ᦝ↢ㇱ᧚䈫䈱Ⴚ⇇㕙䈮䈍䈇䈩ઃ⌕䈏⹺䉄䉌䉏䉎䉅䈱䈫䈠䈉䈪䈭䈇䉅䈱䉇䇮㗂ㇱ䈫ᐩㇱ䈪ᦝ↢ㇱ᧚ෘ
1000䈏⇣䈭䉎䉅䈱╬䇮ో 18 䉬䊷䉴䈮䈧䈇䈩ⴕ䈦䈢 6)䇯
࿑䋭㪈㪈 䈮䇮SPRANA 䈫ᓥ᧪䉿䊷䊦䈮䉋䉎ታ㛎୯䋨ᦨᄢ⠴⩄ജ䋩䈱ౣ⃻⚿ᨐ䉕␜䈜䇯ᮮゲ䈮ታ㛎୯䇮❑ゲ䈮 SPRANA 䈫ᓥ(mm)᧪䉿䊷䊦䈮䉋䉎ౣ⃻⚿ᨐ䉕⴫䈚䈩䈇䉎䇯45 ᐲ✢䈮䊒䊨䉾䊃䈘䉏䉏䈳♖ᐲ⦟䈒ታ㛎୯䉕ౣ⃻䈚䈩䈇䉎䈖䈫䈮䈭䉎䇯࿑䈮䉋䉎䈫䇮
SPRANA 䈲ታ㛎୯䈮ኻ䈜䉎䈾䈿㫧20%䈱㗔ၞౝ䈮૏⟎䈜䉎࿑䋭㪈㪇㩷 㩷 ᄖ࿶⹜㛎᭎ⷐ㩷⚿ᨐ䈫䈭䈦䈢䇯ᓥ᧪䉿䊷䊦䉋䉍䊋䊤䉿䉨䈲ᄢ䈐䈇䈏䇮ታോ⸳⸘਄䈮䈲චಽ⠴䈋䉌䉏䉎♖ᐲ䈫⠨䈋䉌䉏䉎䇯㪪㪧㪩㪘㪥㪘୯ᓥ᧪䉿䊷䊦㧗20%㪎㪇㪇㪪㪧㪩㪘㪥㪘෸䈶ᓥ᧪䉿䊷䊦䋨㫂㪥㪆㫄䋩㪋㪅㩷㩷㪪㪧㪩㪘㪥㪘 䈮ㆡ↪䈚䈢ಽ㔌ᑼ㕖✢ᒻ⸃ᨆᚻᴺ㩷ታ⸳⸘䈮䈍䈔䉎⸃ᨆᤨ㑆䈱⍴❗ൻ䉕࿑䉎䈢䉄䇮SPRANA䈪䈲ಽ㔌ᑼ㕖✢ᒻ⸃ᨆᚻᴺ 7)8) 䉕ㆡ↪䈚䈩䈇䉎䇯ᧄ⸃ᨆᚻᴺ䈲䇮ㅢᏱ RC ৻૕᭴ㅧ䈮ኻ䈚䈩⸃䈒໧㗴䉕㋕╭䊝䊂䊦䈫ή╭᭴ㅧ䊝䊂䊦䈮ಽ㔌䈚䈩⸃䈒䈢䉄䇮FEM ⸃ᨆ䉕ㇱಽ⊛䈮ⴕ䈇⸃ᨆᤨ㑆䉕ᄢ᏷䈮⍴❗䈚䈩䈇䉎䇯એਅ䈮᭎ⷐ䉕␜䈜䇯䋨㪈䋩㩷 ⸃ᨆ᭎ᔨਅ᳓㆏▤ᷯ䈱㋕╭Ყ䈲ዊ䈘䈒䋨1%⒟ᐲ䋩䇮⎕უ䊝䊷䊄䈲ᦛ䈕ᒁ ᒛ ⎕ უ 䈏৻ ⥸ ⊛ 䈪䈅䉎䇯ᓥ 䈦䈩䇮ᦨ ᄢ⩄ ㊀ ᤨ 䈱ᔕ ജ ಽ㪍㪇㪇㪌㪇㪇

㧙20%㪋㪇㪇㪊㪇㪇㪉㪇㪇㪈㪇㪇㪇Ꮣ 䈲࿑ 䋭㪈㪉(a)䈱䉋䈉䈮䈭䉍䇮ᓥ ᧪ 䉿䊷䊦䉕૶ ↪ 䈚䈢႐ว䇮㕖㪇✢ᒻ FEM ⸃ᨆ䈮䉋䉍䈖䈱ᔕജಽᏓ⁁ᘒ䈱⩄㊀䉕⋥ធ᳞䉄䉎㪈㪇㪇㪉㪇㪇㪊㪇㪇㪋㪇㪇㪌㪇㪇㪍㪇㪇㪎㪇㪇ታ㛎୯䋨㫂㪥㪆㫄䋩䈖䈫䈮䈭䉎䇯䈖䉏䈮ኻ䈚䈩ᧄ⸃ᨆᚻᴺ䈪䈲䇮(a)䈱ᔕജಽᏓ䋨ᦨᄢ⠴⩄ജ䋩䉕(b)䈱㋕╭䊝䊂䊦䈫(c)䈱䉮䊮䉪䊥䊷䊃䈱ᒁᒛᔕജ࿑䋭㪈㪈㩷 㩷 ታ㛎୯䋨ᦨᄢ⠴⩄ജ䋩䈮ኻ䈜䉎 㪪㪧㪩㪘㪥㪘㩷䊝䊂䊦䈫䈮ಽ㔌䈚䇮䈠䉏䈡䉏䈱䊝䊂䊦䈎䉌೎୘䈮⠴⩄ജ䉕▚㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 䈍䉋䈶ᓥ᧪䉿䊷䊦䈮䉋䉎ౣ⃻⚿ᨐ㩷಴䈚䇮䈠䈱ว⸘୯䉕ᦨᄢ⠴⩄ജ䈫䈜䉎䉅䈱䈪䈅䉎䇯䈭䈍䇮ᦛ䈕ᒁ ᒛ ⎕ უ 䈱ᦨ ᄢ ⠴ ⩄ ജ 䈮෸ 䈿䈜࿶ ❗ ㋕ ╭ 䈱ᓇ 㗀 䈲ዊ 䈘䈇ᒁᒛ

࿶❗

0.85 f ’c

0.85 f ’cMu

ǍMc

Mus㧩

ft
As fy(a)RC ㇱ᧚ᢿ㕙ߩ  ᦨᄢᛶ᛫ࡕ࡯ࡔࡦ࠻ Mu

㧗

As fy(b)ᒁᒛ㋕╭ߩ㒠ફᔕജߦࠃࠆ  ᛶ᛫ࡕ࡯ࡔࡦ࠻ Mus࿑䋭㪈㪉㩷 㪩㪚 ᦛ䈕ㇱ᧚䈱ᔕജಽᏓ㩷㪈㪋㪏㩷ft(c)ࠦࡦࠢ࡝࡯࠻ߩᒁᒛᔕജߦࠃࠆ  ᛶ᛫ࡕ࡯ࡔࡦ࠻⽸₂ಽ 'Mc䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷CPu Puc 'Pc ⩄㊀Pus BPcrack D

Pus  'P 'P A߭߮ഀࠇ⊒↢ᒁᒛ㋕╭㒠ફᄌᒻ࿑䋭㪈㪊㩷 ᦛ䈕ㇱ᧚䈱⩄㊀ᄌ૏㑐ଥ㩷䈢䉄ᧄ⸃ᨆᚻᴺ䈪䈲࿶❗㋕╭䉕ήⷞ䈚䈩䈇䉎䇯㩷㩷㪈㪀㩷 ㋕╭䊝䊂䊦࿑䋭㪈㪉 䈱ᔕജಽᏓ䉕⩄㊀ᄌ૏㑐ଥ䈮⟎䈐឵䈋䉎䈫ᰴ䈱䉋䈉䈮䈭䉎䇯࿑䋭㪈㪊 䈮 RC 䈍䉋䈶ή╭䉮䊮䉪䊥䊷䊃᪞䈱⩄㊀ᄌ૏㑐ଥ䉕␜䈜䇯࿑ਛ䈱ታ✢䈲 RC ᪞䇮⎕✢䈲ή╭䉮䊮䉪䊥䊷䊃᪞䈱᜼േ䈪䈅䉎䇯A 䈪䈵䈶ഀ䉏䈏⊒↢䈚䇮B 䈪㋕╭䈱⽶ᜂಽ䈏ห৻タ⩄᧦ઙਅ䈪䈲䇮⩄㊀䈫ᦛ䈕䊝䊷䊜䊮䊃䈲Ყ଀㑐ଥ䉕᦭䈚䈩䈇䉎䈖䈫䈎䉌䇮ᰴ䈱䉋䈉䈭㑐ଥ䈏ᚑ┙䈜䉎䇯Pus
PcrackMusMcrack䋨5䋩ᄢ䈐䈒䈭䉍䇮C ઃㄭ䈪㋕╭䈏㒠ફ䈚ᆎ䉄䈩ᦨᄢ⩄㊀䉕ㄫ䈋䈢䈖䈖䈪䇮 Mus 䋺RC ⚳ዪᤨ䈱ᦛ䈕䊝䊷䊜䊮䊃䇮 Mcrack 䋺䈵䈶ᓟ⠴ജ䈏ૐਅ䈚䇮D 䈪⎕უ䈜䉎䇯࿑ਛ䈱 Pus 䈲࿑䋭㪈㪉(b)䈱

ഀ 䉏䈏⊒ ↢ 䈜䉎䈫䈐䈱ᦛ 䈕䊝䊷䊜䊮䊃䉕⴫ 䈜䇯⩄ ㊀ ଥ ᢙ O 䉕ᒁᒛ㋕╭䈱㒠ફᔕജ䈮䉋䉎ᛶ᛫䊝䊷䊜䊮䊃䈮⋧ᒰ䈚䇮↪䈇䈩䋨5䋩ᑼ䉕ᦠ䈐឵䈋䉎䈫એਅ䈱᭽䈮䈭䉎䇯'PcPu  Pus 䈲࿑䋭㪈㪉(c)䈱䉮䊮䉪䊥䊷䊃䈱ᒁᒛᔕജ䈮䉋䉎ᛶ᛫䊝䊷䊜䊮䊃⽸₂ಽ䈮⋧ᒰ䈜䉎䇯OusMus
 Ocrack 'Mcrack

䋨6䋩ᧄ ⸃ ᨆ ᚻᴺ䈪䈲䇮 'Pc 䉕ή ╭ 䉮䊮䉪䊥䊷䊃᪞ 䈮䈍䈔䉎ᦨ ᄢ䈖䈖䈪䇮 Ocrack' 䈲ᵴ⩄㊀䈱䉂䈱タ ⩄⁁ᘒ䈮䈍䈔䉎䈵䈶ഀ

Puc  Pcrack 䈪ㄭ ૃ 䈚䈩䉏⊒↢⩄㊀ଥᢙ䉕ᗧ๧䈚䈩䈍䉍䇮䋨4䋩ᑼ䈱 Ocrack 䈫䈲඙೎䈘ᦨᄢ⩄㊀䉕᳞䉄䈩䈇䉎䇯䈜䈭䉒䈤䇮ᦨᄢ⩄㊀ Pu 䈲ᰴᑼ䈱᭽䉏䉎䋨 Ocrack 䈱タ⩄⁁ᘒ䈲ᵴ⩄㊀䋫ᱫ⩄㊀䈪䈅䉎䋩䇯 Ocrack'䈮䈭䉎䇯Pu䉕↪䈇䈢ℂ↱ 䈲䇮⩄㊀䈫ᦛ 䈕䊝䊷䊜䊮䊃䈱Ყ଀㑐ଥ䉕଻ 䈧䈢⩄ ㊀ 䈫䈵䈶ഀ 䉏⩄ ㊀ 䈫䈱Ꮕ 'PPus  'PPus  Puc  Pcrack

䋨3䋩䉄䈮䈲ᱫ⩄㊀䉕㒰ᄖ䈜䉎ᔅⷐ䈏䈅䈦䈢䈢䉄䈪䈅䉎䇯䈖䈖䈪䇮 Pu䋺RCㇱ᧚䈱ᦨᄢ⩄㊀䇮 Pus䋺㋕╭䊝䊂䊦䈮䉋䉎⠴Mus 䈲䇮䉮䊮䉪䊥䊷䊃䈱࿶❗ജ䈫ᒁᒛ㋕╭䈱㒠ફᔕജ䈱㊒⩄ ജ 䈮⋧ ᒰ 䈜䉎⩄ ㊀ 䇮 Puc 䋺ή ╭ 䉮䊮䉪䊥䊷䊃ㇱ ᧚ 䈱ᦨ ᄢ ⩄ว䈇䈎䉌䇮 Mcrack 䈲䉮䊮䉪䊥䊷䊃䈱ᒁ ᒛᒝᐲ䈫ᢿ㕙ଥᢙ䈱Ⓧ㊀䇮 Pcrack 䋺䈵䈶ഀ䉏⩄㊀䉕⴫䈜䇯䈮䉋䈦䈩▚಴䈜䉎䇯䋨㪉䋩㩷 ਅ᳓㆏▤ᷯ䈻䈱ㆡ↪

MusSPR Ꮏᴺ䈱⸳⸘⸃ᨆ䈪䈲䇮⸳⸘⩄㊀䈮ኻ䈜䉎⩄㊀ଥᢙ

O 䈪⴫䈘䉏䈩䈍䉍䇮એ㒠 O 䉕↪䈇䉎䇯 O 䉕↪䈇䈩ᦠ䈐឵䈋䉎䈫
䋨3䋩ᑼ䈲એਅ䈱᭽䈮䈭䉎䇯Ou Ous  'O Ous  Ouc  Ocrack䋨4䋩ਅ᳓㆏▤ᷯ䈮䈍䈇䈩䈲䇮ㅢᏱ RC ᭴ㅧ䉕৻૕ൻ䈚䈩⸃䈒ో·§As  fys¸¸As  fys¨¨ d 2
0.
85fccb¹©

Mcrackftc bh2
6

䋨7䋩䋨8䋩

䉁䈢䇮 Ocrack' 䈲ή╭᭴ㅧ䊝䊂䊦䈎䉌▚಴䈜䉎䇯㩷㩷㪉㪀㩷 ή╭᭴ㅧ䊝䊂䊦૕ ♽ 䉕㋕ ╭ 䊝䊂䊦䈫ή ╭ ᭴ ㅧ 䊝䊂䊦䈮ಽ 㔌 䈚䇮㋕ ╭ 䊝䊂䊦ή ╭ ᭴ ㅧ 䊝䊂䊦䈱⸃ ᨆ 䈲䇮㋕ ╭ 䊝䊂䊦䈱䉋䈉䈭◲ න 䈭ᢙ䈎䉌 Ous 䉕▚ ಴ 䈚䇮ή ╭ ᭴ ㅧ 䊝䊂䊦䈎䉌 Ouc 䇮 Ocrack 䉕▚ ಴ᑼ䊧䊔䊦䈪᳞䉄䉌䉏䉎䉅䈱䈪䈲䈭䈒䇮䉮䊮䉪䊥䊷䊃䈱䈵䈶ഀ䉏䈱䈜䉎䈖䈫䉕ၮᧄ䈫䈚䈩䈇䉎䇯䈠䉏䈡䉏䈱䊝䊂䊦䈮䈧䈇䈩એਅ䈮⊒↢䊶ㅴዷ䉕⠨ᘦ䈚䈢⸃ᨆᚻᴺ䈏ᔅⷐ䈫䈭䉎䇯ᧄ⸃ᨆᚻᴺ䈪⺑᣿䈜䉎䇯䈲䇮Ꮷ䉌䈮䉋䈦䈩ឭ᩺䊶㐿⊒䈘䉏䈢䇮ಽᏓ䈵䈶ഀ䉏䊝䊂䊦䉕ㆡ↪䈚䈢ᓥ᧪䉿䊷䊦䋨FEM 䈮ၮ䈨䈒㕖✢ᒻ䈵䈶ഀ䉏⸃ᨆ䋩䉕↪
䈇䈩䈇䉎䇯㪈㪋㪐㩷ᣢ⸳ਅ᳓㆏▤ᷯߩᦝ↢⸳⸘↪࠰ࡈ࠻࠙ࠚࠕߩ㐿⊒ᓥ᧪䉿䊷䊦䉇Ꮢ⽼䈱 RC 㕖✢ᒻ⸃ᨆ䉮䊷䊄䉕↪䈇䈢႐ว䉕ታ ⃻ 䈚䈩䈇䉎䇯ᓥ ᧪ 䈱㕖 ✢ ᒻ 䈵䈶ഀ 䉏⸃ ᨆ 䉿䊷䊦䈮Ყ 䈼FEM 䈮ၮ䈨䈒⸃ᨆ䈱ኻ⽎䈲 RC ᭴ㅧ‛ో૕䈫䈭䉍䇮䈵䈶ഀ䈩䇮ᚻシ䈘䇮ᤨ㑆䇮⚻ᷣᕈ╬䈱ⷰὐ䈎䉌ታ⸳⸘䈮ㆡ↪䈚ᤃ䈒䉏⊒↢ᓟ䈱㋕╭䈱⽸₂䈮䉋䉍⸃ᨆᤨ㑆䈏㐳䈒䈭䉎䇯䈠䉏䈮ኻ䈭䈦䈩䈇䉎䇯䈚䈩䇮ᧄ⸃ᨆᚻᴺ䈪䈲䇮FEM 䈮ၮ䈨䈒ⶄ㔀䈭⸃ᨆ䈲ή╭᭴੹ ࿁ 䇮ਅ ᳓ ㆏ ▤ ᷯ 䈱৻ ᦝ ↢ Ꮏ ᴺ 䉕ኻ ⽎ 䈮㐿 ⊒ 䉕ⴕ 䈦䈢ㅧ䊝䊂䊦䈱䉂䈫䈭䉍䇮䈵䈶ഀ䉏⊒↢ᓟ䈎䉌ᦨᄢ⩄㊀ᤨ䉁䈪䈱䈏䇮䈠䈱ઁ䈱ᦝ↢Ꮏᴺ䉇ਅ᳓㆏▤ᷯએᄖ䈱 RC ᭴ㅧ‛䉕ኻᤨ㑆䈲೨ ⠪䉋䉍⍴䈒䈭䉎䇯㋕ ╭䊝䊂䊦䈱⸃ ᨆ䈲⍍ᤨ 䈪䈅䉎䈎⽎ 䈫䈚䈢ஜ ో ᐲ ⸻ ᢿ 䈍䉋䈶ኻ ╷ Ꮏ ⸳ ⸘ ᡰ េ 䉲䉴䊁䊛䈱㐿 ⊒䉌䇮ో૕䉕ㅢ䈚䈩⸃ᨆᤨ㑆䈏⍴❗䈘䉏䉎䇯䈭䈬⛽ᜬ▤ℂಽ㊁䈻᏷ᐢ䈒ᔕ↪䈪䈐䉎䈢䉄䇮⒳䇱䈱㐿⊒䉕ⴕ䈦䈩䈇䈒䈧䉅䉍䈪䈅䉎䇯䋨㪊䋩㩷 ฦ▤⒳䈮䈍䈔䉎䊌䊤䊜䊷䉺䈱▚಴ᣇᴺ▤ᷯ䈱⒳㘃䋨ᣢ⸳▤䇮ᦝ↢▤䋩䉇䈎䈹䉍䈱᦭ή╬䈱㆑䈇䈮ઃ㍳䋺⚳ዪ㒢⇇⁁ᘒ䈱ᬌ⸛䈮䈍䈔䉎቟ో₸ 㪉㪅㪌 䈱⠨䈋ᣇ 4)䉋䉍䇮ฦ䊌䊤䊜䊷䉺䋨 Mus 䇮 Mcrack 䇮 Ouc 䇮 Ocrack 䇮 Ocrack' 䋩䈱⃻ ⴕ 䈱㒢 ⇇ ⁁ ᘒ ⸳ ⸘ ᴺ 䈲䇮ㅢ Ᏹ 䈱✢ ᒻ ⸘ ▚ ▸ ࿐ ౝ 䈪䈱▚಴ᣇᴺ䈲⇣䈭䉎䇯એਅ䈮䇮㋕╭䈎䈹䉍䈏ᰳ⪭䈚䈢ᣢ⸳▤䇮⸘▚䈮ኻ䈚䈩ฦ⒳䈱ㇱಽ቟ోଥᢙ䉕ዉ౉䈚䈢䇮䈇䉒䉉䉎䇸ㇱ䈍䉋䈶䈠䈱ᣢ⸳▤䉕ᦝ↢䈚䈢▤ᷯ䉕଀䈮䈫䈦䈩▚಴ᣇᴺ䉕␜ಽ቟ోଥᢙ⸳⸘ᴺ䇹䈫䈭䈦䈩䈇䉎䇯䈚䈎䈚䇮㕖✢ᒻ⸃ᨆᚻᴺ䉕䈜䇯↪䈇䈩⚳ዪ㒢⇇⁁ᘒ䉕ౣ⃻䈜䉎᭴ㅧ⸘▚䈪䈲䇮⚳ዪ⠴⩄ജ㩷㩷㪈㪀㩷 ᣢ⸳▤䋨࿑䋭㪈㪋㩿㪸㪀䋩䉕⋥ធ⸘▚䈪䈐䉎䇯䈠䈱䈢䉄䇮᳞䉄䈢⚳ዪ⠴⩄ജ䈏଻᦭䈚䈩䊒䊧䉴䊃䊧䉴䉮䊮䉪䊥䊷䊃ᮡḰ␜ᣇᦠ䈮䈍䈇䈩 PC ㍑᧚䈫䉮䊮䉪䊥䊷䊃䈮ઃ⌕䈏ή䈇႐ว䈲䇮ઃ⌕䈏᦭䉎႐ว䉋䉍䉅ᦛ䈕⠴⩄ജ䉕 30%ૐᷫ䈜䉎䈫䈘䉏䈩䈍䉍 9) 䇮䈖䉏䈮ၮ䈨䈐ᧄ⸃ᨆᚻᴺ䈇䉎⸳⸘ᢿ㕙ജ䈮ኻ䈜䉎૛⵨ᐲ䋨቟ో₸ Fsu 䋩䈏䇮⃻ⴕ䈱ㇱಽ቟ోଥᢙ⸳⸘ᴺ䈪䈱ᾖᩏᤨ䈱቟ోଥᢙ䈫╬ଔ䈭㑐ଥ䈮䈭䉎䇯䈢䈣䈚䇮ㇱಽ ቟ ోଥ ᢙ⸳⸘ ᴺ 䈪䈲䇮⸳⸘ ᒝ ᐲ䈎䉌⸳⸘ ᢿ䈪䈲 Mus 䉕 30%ᷫ䈛䈩䈇䉎䇯㕙 ⠴ ജ䉕⹏ ଔ䈜䉎ㆊ⒟ 䈫䇮⸳⸘ ⩄ ㊀䈎䉌⸳⸘ ᢿ 㕙ജ 䉕▚ቯ㩷㩷㪉㪀㩷 ᦝ↢▤䋨ⶄว▤䋩䋨࿑䋭㪈㪋㩿㪹㪀䋩ᦝ↢▤䈱 Mus 䉕▚಴䈜䉎႐ว䇮䉴䉼䊷䊦⵬ᒝ᧚䉕㋕╭䈫ห᭽䈱᧚ᢱ䈫䈚䈩䊝䊂䊦ൻ䈚䈩䈇䉎䇯ᣢ⸳ㇱ᧚䈫ᦝ↢ㇱ᧚䈱Ⴚ⇇㕙䈮䈍䈇䈩ઃ⌕䈏䈅䉎႐ว䇮㋕╭ 䈫䉴䉼䊷䊦⵬ᒝ ᧚䉕╬ ଔ㋕╭ 䈮⟎ 䈐឵䈋න㋕ ╭ㇱ ᧚䈫䈜䉎ㆊ⒟䈮䈍䈇䈩቟ోଥᢙ䈏⚵ㄟ䉁䉏䈩䈇䉎䇯䈠䉏䉉䈋䇮⃻ⴕ 䈱ㇱ ಽ ቟ ోଥ ᢙ ⸳ ⸘ ᴺ 䈪䈱ᾖ ᩏ ᤨ 䈮↪䈇䉎቟ ో ଥᢙ J i䈪䈲䈭䈒䇮ฦ⒳቟ోଥᢙ䉕䈎䈔ว䉒䈞䈢 J i  J a  J b  J f  J m 䉕↪
䈇䉎䇯䈚䈢䈏䈦䈩䇮቟ో₸ Fsu 䈲ᰴᑼ䈱䉋䈉䈮䈭䉎䇯
Fsu J i J a J b J f J m

䈚䈩 Mus 䉕▚಴䈜䉎䇯ᣢ⸳ࠦࡦࠢ࡝࡯࠻bb䈖䈖䈪䇮 g i 䋺᭴ㅧ‛ଥᢙ䇮 g a 䋺᭴ㅧ⸃ᨆଥᢙ䇮 g b 䋺ㇱ᧚ଥᢙ䇮g m 䋺᧚ᢱଥᢙ䇮 g f 䋺⩄㊀ଥᢙ䈪䈅䉎䇯䇸ᄢญᓘ SPR Ꮏᴺ⸳⸘䊙䊆䊠䉝䊦䇹䈪䈲䇮ฦ቟ోଥᢙ䈮㑐!䈚䈩䇮 Jh1 h1 ᦝ↢ࡕ࡞࠲࡞Ⴚ⇇㕙㧔ઃ⌕᦭㧕h2 ╬ଔ㋕╭ࡊࡠࡈࠔࠗ࡞㧔ౝㇱߦࠬ࠴࡯࡞⵬ᒝ᧚㧕(a)ᣢ⸳▤(b)ᦝ↢▤࿑䋭㪈㪋㩷 ᣢ⸳▤䈍䉋䈶ᦝ↢▤䈱ᢿ㕙᭎ⷐ㩷㪌㪅㩷㩷䈍䉒䉍䈮㩷㜞ᐲ䈭⸃ᨆᛛⴚ䈱ታ↪ൻ䈫䈚䈩䇮ਅ᳓㆏▤ᷯ䈱ᦝ↢Ꮏᴺ䋨 SPR Ꮏ ᴺ 䋩 䉕 ኻ ⽎ 䈮 SPR Ꮏ ᴺ ⸳ ⸘ ᡰ េ 䉲 䉴 䊁 䊛 䋭SPRANA䋭䈱㐿⊒䉕ⴕ䈦䈢䇯
SPRANA 䈲䇮㽲䇸▤ᦝ↢䈱ᚻᒁ䈐䋨᩺䋩䇹䈮Ḱ䈛䈢᭴ㅧ⸘▚䇮㽳ቯ㊂⊛䈭⃻⁁▤䈱ஜోᐲ⸻ᢿ䇮㽴⸃ᨆᤨ㑆䈱ല₸ൻ

㪈㪌㪇㩷

i

1.1 䇮 J a

1.1 䇮 J b

1.3 䇮 J m

1.3 䇮 J f䈩䈍䉍䇮䈠䈱႐ว Fsu 䈲એਅ䈱䉋䈉䈮䈭䉎䇯Fsu 2.45 o 2.5

1.2 䈫⸳ቯ䈚䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷ෳ⠨ᢥ₂1)䋨␠䋩ᣣᧄਅ᳓㆏දળ䋺▤ᦝ↢䈱ᚻᒁ䈐䋨᩺䋩ෳ⠨⾗ᢱ䇮pp.ෳ 14-ෳ20䇮2001.

2)

Z.Shi et al : Three-dimensional finite element analysis on
crack behaviors of RC cantilever decks, Construction andBuilding Materials, Vol.13, pp.33-47, 1999.
3)ᄢㄼஜ৻ઁ䋺⥄↱ᢿ㕙 SPR Ꮏᴺ䈱㐿⊒䈫⃻႐ᣉᎿ䇮䊃䊮䊈䊦䈫࿾ਅ䇮╙ 30 Ꮞ 1 ภ䇮pp.53-61䇮1999.

4)䈢䈫䈋䈳㜞ἑⴕᑝ䋺ਅ᳓㆏䈱㐳ኼ๮ൻ䇮࿯ᧁቇળ⹹․㓸䇸䈖䉏䈎䉌䈱ㇺᏒ䈱࿾ਅ೑↪䇹䇮Vol.87䇮pp.23-25䇮2002.85)

᧲੩ㇺਅ᳓㆏䉰䊷䊎䉴䊺䇮Ⓧ᳓ൻቇᎿᬺ䊺䇮⿷┙ᑪ⸳Ꮏᬺ䊺䋺ᄢ
ญᓘ SPR Ꮏᴺ⸳⸘䊙䊆䊠䉝䊦䇮2000.

6)᧲੩ㇺਅ᳓㆏ዪ䇮᧲੩ㇺਅ᳓㆏䉰䊷䊎䉴䊺䇮Ⓧ᳓ൻቇᎿᬺ䊺䇮⿷┙ᑪ⸳Ꮏᬺ䊺䋺ᣢ⸳⍱ᒻᷯ╬䈱ᦝ↢Ꮏᴺ䈱㐿⊒౒ห⎇ⓥႎ๔
ᦠ䇮1998.

7)

Z.Shi et al : A separate method for evaluating the ultimate
load-carrying capacity of aging and renovated sewage
structures, Construction and Building Materials, Vol.15/5-6,pp.271-282, 2001.

8)

ਛ㊁㓷┨ઁ䋺⠧᧎ਅ᳓㆏▤ᷯ䈱⵬ᒝ⸳⸘䈮䈍䈔䉎ಽ㔌ᑼ㕖✢ᒻ⸃ᨆᴺ䈱ዉ౉䈍䉋䈶⸳⸘ᡰេ䉲䉴䊁䊛䈱㐿⊒䇮䉮䊮䉪䊥䊷䊃Ꮏቇᐕᰴ⺰ᢥ㓸䇮Vol.24䇮No.2䇮pp.1561-1566䇮2002.

9)࿯ᧁቇળ䋺䊒䊧䉴䊃䊧䉴䊃䉮䊮䉪䊥䊷䊃ᮡḰ␜ᣇᦠ䇮1979.

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