Key Words: CFRP plate, corroded steel plate, bonding, repair design ࠠࡢ࠼㧦CFRP ᧼㧘⣣㘩㍑᧼㧘ធ⌕㧘
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(2) VU VUF. 2. 2 lF lF. lP. l. VE J. lP. J. JF. VU. x. 0. VE. VUF. %(42᧼. VE. ធ⌕ ㍑᧼. DE DU. l. DE DU. (a) 㕙࿑ (b) ᢿ㕙ᰳ៊ㇱᢿ㕙࿑ (c) ৻⥸ㇱᢿ㕙࿑ ࿑㧙2 ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼. . ㍑᧼. 0U Z F0U Z. 0U Z. 0E Z F0E Z. ធ⌕. ǼZ D E FZ ㍑᧼. . . FZ. ǼZ D E FZ J. ធ⌕. ǼZ D E FZ. VUF . 0U Z. 0E Z. V U. JF. ǼZ D E FZ. 0E Z F0E Z. VE. %(42᧼. VE. %(42᧼. 0E Z. 0U Z F0U Z . FZ. (a) ᢿ㕙ᰳ៊ㇱ (b) ৻⥸ㇱ ࿑㧙3 ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ߩᓸዊ㑆ߩ᳓ᐔജߩߟࠅว ߔࠆ 2 㓏ߩᓸಽᣇ⒟ᑼ߇ߘࠇߙࠇዉߐࠇࠆ 2)㧚 2. d N s ( x) 2 cd N s ( x) dx 2. c d [ d P (0 d x d l d ). (1). d 2 N s ( x) c 2 N s ( x) dx 2. c 2[P (ld d x d l ). (2). 2. h 㧦 ৻⥸ㇱߩធ⌕ߩෘߐ㧘 l d 㧦 ᢿ㕙ᰳ៊ߩඨ㐳ߐ㧘 l n 㧦 ৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐ㧘 x 㧦 ᢿ㕙ᰳ៊ਛᄩ߆ࠄߩ〒㔌㧚 ᑼ(1)㧘(2)߆ࠄ㧘㍑᧼ߦ↢ߓࠆゲജ N s ( x) ߩ৻⥸⸃߇ᰴ ᑼߢਈ߃ࠄࠇࠆ㧚. ߎߎߦ㧘. cd. bc Ge bs hd. 2 1 [d. E s t sd. c. bc Ge bs h. 2 1[. Es t s. 1. (3). (4). [d. 1 1 2 Ec bc tc ( Es bs t sd ). (5). [. 1 1 2 Ec bc tc ( E s bs t s ). (6). l d ln. (7). l N s (x ) P Es Ec t sd ts tc bs bc Ge hd. 1. 㧦 ㍑᧼ߦ↢ߓࠆゲജ㧘 㧦 ↪ᄖജ㧘 㧦 ㍑᧼ߩࡗࡦࠣ₸㧘 㧦 CFRP ᧼ߩࡗࡦࠣ₸㧘 㧦 ᢿ㕙ᰳ៊ㇱߩ㍑᧼ߩ᧼ෘ㧘 㧦 ৻⥸ㇱߩ㍑᧼ߩ᧼ෘ㧘 㧦 CFRP ᧼ߩ᧼ෘ㧘 㧦 ㍑᧼ߩ㧘 㧦 CFRP ᧼ߩ( bc d bs )㧘 㧦 ធ⌕ߩߖࠎᢿᒢᕈଥᢙ㧘 㧦 ᢿ㕙ᰳ៊ㇱߩធ⌕ߩෘߐ㧘. N s ( x). ^A1 cosh(c d x) A2 sinh(c d x) [ d `P ° °( ޓ ޓޓޓޓޓޓޓޓޓޓ0 d x d l d ) (8) ®>B cosh^c( x l )` d ° 1 °¯ B2 sinh^c( x l d )` [ @P (l d d x d l ). ߎߎߦ㧘 A1 㧘 A2 㧘 B1 㧘 B2 㧦ߘࠇߙࠇ㧘ᧂቯଥᢙ㧚 ㍑᧼ߩゲജ N s (x) 㧘CFRP ᧼ߩゲജ N c (x) ߅ࠃ߮↪ᄖ ജ P ߦߪએਅߩ㑐ଥ߇ࠆ㧚 N s ( x) 2 N c ( x). P. (9). ᢿ㕙ᰳ៊ㇱ߅ࠃ߮৻⥸ㇱߩធ⌕ߦ↢ߓࠆߖࠎᢿᔕജ. W ( x) ߣ㍑᧼ߩゲജ N s ( x) ߩ㑐ଥߪᰴᑼߢਈ߃ࠄࠇࠆ㧚 W ( x). 1 dN s ( x) dx 2bc. (10). ࿑㧙2(a)ࠍෳᾖߒߡ㧘 x 0 ߢ㧘㍑᧼ߩゲജ߇ኻ⒓ߦߥ ࠆ᧦ઙ㧘 x ld ߢ CFRP ᧼ߩゲജ߇ㅪ⛯ߔࠆ᧦ઙ㧘 x ld ߢធ⌕ߩߖࠎᢿᄌ߇ㅪ⛯ߔࠆ᧦ઙ㧘߅ࠃ߮ x l ߢ㍑ ᧼ߩゲജ߇↪ᄖജߣ৻⥌ߔࠆ᧦ઙࠍႺ⇇᧦ઙߣߒߡਈ ߃ࠆߣ㧘ᑼ(8)ߩᧂቯଥᢙ A1 㧘 A2 㧘 B1 㧘 B2 ߇ߘࠇߙࠇᰴ ᑼߩࠃ߁ߦᓧࠄࠇࠆ㧚 A1. - 912 -. Z cosh(c d l d ). (11).
(3) 0. (12). [d [ Z. (13). c d hd Z tanh(c d l d ) ch. (14). 1[ [d [ cosh(cl n ) c h 1 d d tanh(cl n ) tanh(c d l d ) ch. (15). A2 B1 B2. ߎߎߦ㧘. Z. ߹ߚ㧘ᢿ㕙ᰳ៊ㇱߩធ⌕ߩෘߐߪᰴᑼߢਈ߃ࠄࠇࠆ㧚 hd. h. t s t sd 2. (16). ߣߒߡ㧘㧙1 ߩ᧦ઙ߅ࠃ߮ CFRP ᧼ߩඨ㐳ߐ l 125 mm ߦኻߒߡ㧘⇣ߥࠆᢿ㕙ᰳ៊ㇱߩ᧼ෘ t sd ߅ࠃ߮ ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ ld ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ߦ↢ߓ ࠆᔕജV s (x) 㧘CFRP ᧼ߦ↢ߓࠆᔕജV c (x) ߅ࠃ߮ធ⌕ ߦ↢ߓࠆߖࠎᢿᔕജW (x) ࠍ㧘ߘࠇߙࠇ࿑㧙4㨪6 ߦታ✢ߢ ␜ߔ㧚ߎࠇࠄߩ࿑ߢߪ㧘❑ゲߩV s (x) 㧘V c (x) ߅ࠃ߮W (x) ߇V sn ߢߘࠇߙࠇ㒰ߐࠇߚ୯߇␜ߐࠇߡࠆ㧚࿑㧙4㧘5 ߢ ߪ㧘CFRP ᧼ߣ㍑᧼ߩቢోวᚑᢿ㕙ࠍቯߒߚ႐วߩ㍑᧼ ߅ࠃ߮ CFRP ᧼ߦ↢ߓࠆᔕജV s 㧘V c ߽⎕✢ߢ␜ߐࠇߡ ࠆ㧚 ⸘▚ߢ↪ߒߚ CFRP ᧼ߩ᧼ෘ t c ߦߪ㧘ᑼ(22)ߢਈ߃ ࠄࠇࠆ㧘ቢోวᚑᢿ㕙ࠍቯߒߚ႐วߦ㧘ᢿ㕙ᰳ៊ㇱߩ ᕈࠍ㧘৻⥸ㇱߩ㍑᧼ߩᕈ E s bs t s ߹ߢ࿁ᓳߐߖࠆߩߦᔅⷐ ߥ CFRP ᧼ߩ᧼ෘ t c 0 ߇↪ࠄࠇߡࠆ㧚 tc0. 3㧚ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ߦ↢ߓࠆᔕജ. (1 O ) E s bs t s 2bc E c. (22). ࿑㧙4 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ 3.1 ᢿ㕙ᰳ៊ࠍߔࠆCFRP ᧼ធ⌕㍑᧼߅ࠃ߮CFRP ᧼ ⌕㍑᧼ߢߪ㧘CFRP ᧼ߩઃ⌕┵߆ࠄ㍑᧼ᔕജ߇ᓢߦޘૐਅ ߦ↢ߓࠆᔕജߥࠄ߮ߦធ⌕ߦ↢ߓࠆߖࠎᢿᔕജ ߒ㧘CFRP ᧼ߣ㍑᧼ߩቢోวᚑᢿ㕙ࠍቯߒߚV s ߩ୯ߦ ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ߦ↢ߓࠆᔕജV s (x) ᧤ߒߚᓟ㧘ᢿ㕙ᰳ៊ㇱߦㄭߠߊߦߟࠇߡ⧯ᐓૐਅߔࠆ߇㧘 ߪ㧘ᑼ(8)ߢਈ߃ࠄࠇࠆ N s (x) ࠍ㧘ᢿ㕙ᰳ៊ㇱߦኻߒߡ bs t sd 㧘 㧙1 ߣߒߡ↪ࠆ㍑᧼㧘CFRP ᧼ ৻⥸ㇱߦኻߒߡ bs t s ߢߘࠇߙࠇ㒰ߒߡᰴᑼߢਈ߃ࠄࠇࠆ㧚 ߅ࠃ߮ធ⌕ߩ᧚ᢱቯᢙ 1 (a) ㍑᧼ ° O ^A1 cosh(cd x) [ d `V sn ( ޓ0 d x d ld ) ° ᧼ෘ t s [mm] 9 (17) V s ( x) ®ޓޓޓޓޓޓޓޓ °>B1 cosh^c( x ld )` ࡗࡦࠣ₸ Es [ GPa] 200 ° ¯ B2 sinh^c( x ld )` [ @V sn (ld d x d l ) bs [mm] 50 ߎߎߦ㧘. O V sn. (b) CFRP ᧼. t sd ts. (18). P bs t s. (19). CFRP ᧼ߦ↢ߓࠆᔕജV c (x) ߪ㧘ᑼ(8)ߩ N s (x ) ࠍᑼ(9) ߳ઍߒߡ▚ߒߚ N c (x) ࠍ bc t c ߢ㒰ߒߡᰴᑼߢਈ߃ࠄ ࠇࠆ㧚. V c ( x). bsts ° 2b t ^1 [ d A1 cosh(cd x)`V sn ° cc °ޓޓޓޓޓޓޓޓޓޓޓ ( 0 d x d ld ) ° bt s s ® >1 [ B1 cosh^c( x ld )` ° 2bctc ° B2 sinh^c( x ld )`@V sn °ޓޓޓޓޓޓ °ޓޓޓޓޓޓޓޓޓޓޓ (ld d x d l ) ¯. ࡗࡦࠣ₸ Ec [GPa]. 150. bc [mm]. 50 (c) ធ⌕. ෘߐ h [mm]. 0.2. ߖࠎᢿᒢᕈଥᢙ Ge [GPa]. ǻ s (x)/ǻ s n. 0.735. 㧘 ޓޓ㧦FEM ⸃ᨆ୯. 1.2. t s d =6mm, t c = 2.0mm, l d =40mm. (20). 1.0 0.8. ធ⌕ߦ↢ߓࠆߖࠎᢿᔕജW (x) ߪ㧘ᑼ(8)ߩ N s (x) ࠍ㧘 ᑼ(10)ߦઍߒߡᰴᑼߢਈ߃ࠄࠇࠆ㧚. 0.6. cd bs t s (0 d x d l d ) ° 2b A1 sinh(cd x)V sn ޓޓ c °° (21) W ( x) ® cbs t s >B sinh^c( x l )` B cosh^c( x l )`@V 2 d d sn ° 2bc 1 ° ޓޓޓ (ld d x d l ) ¯°ޓޓޓޓޓޓޓ. 0.4. - 913 -. ቢోวᚑߩǻsǻ / sn t s d =4.5mm, t c =3.0mm, l d =20mm 0. 25. 50. 75. 100. 125. x[mm] ࿑㧙4 ㍑᧼ߦ↢ߓࠆᔕജߩಽᏓ.
(4) ǻ c (x)/ǻ s n 1.0. Ǽ (x)/ ǻ s n. 㧘 ޓޓ㧦FEM ⸃ᨆ୯. 㧘 ޓޓ㧦FEM ⸃ᨆ୯. 0.20. t s d =6mm, t c = 2.0mm, l d =40mm. 0.8. t s d =4.5mm, t c =3.0mm, l d =20mm. 0.15. ቢోวᚑߩǻcǻ / sn 0.6. t s d =6mm, t c = 2.0mm, l d =40mm. 0.10 0.4 t s d =4.5mm, t c =3.0mm, l d =20mm. 0.05. 0.2 0.0. 0. 25. 50. 75. 100. 0.00. 125. 0. 25. 50. 75. 100. 125. x[mm]. x[mm] ࿑㧙5 CFRP ᧼ߦ↢ߓࠆᔕജߩಽᏓ. ࿑㧙6 ធ⌕ߦ↢ߓࠆߖࠎᢿᔕജߩಽᏓ. CFRP᧼. CFRP᧼ ធ⌕. ធ⌕. ㍑᧼ ㍑᧼. V sn. ࿑㧙7 FEM ⸃ᨆࡕ࠺࡞ ৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߣߩႺ⇇㧘ߔߥࠊߜ x ld ߩ⟎ߢᲑ Ꮕ߇↢ߓ㧘ᢿ㕙ᰳ៊ㇱߢ㍑᧼ᔕജ߇ౣ߮ᄢ߈ߊߥࠆ㧚৻⥸ ㇱߦ߅ߡ㧘x ld ߩ⟎ߢᦨ߽㍑᧼ᔕജ߇ૐᷫߐࠇࠆ߇㧘 ᢿ㕙ᰳ៊ㇱߢߪ㧘ߘߩ⟎ߩ㍑᧼ᔕജ߇ᦨᄢߦߥࠅ㧘CFRP ᧼߇ធ⌕ߐࠇߡߥஜోㇱߩ㍑᧼ߦ↢ߓࠆ V sn ࠃࠅ߽ ᄢ߈ߊߥࠆ㧚ߎࠇߪ㧘㍑᧼ߣ CFRP ᧼ߩ߭ߕߺ߇หߓߦߥ ࠆ(ቢోวᚑᢿ㕙ߦߥࠆ)ࠃ߁ߦ↪⩄㊀߇㍑᧼ߣ CFRP ᧼ ߦಽᜂߐࠇࠆ㓙㧘৻⥸ㇱߢ㍑᧼߇ಽᜂߔࠆ⩄㊀ߣ㧘ᢿ㕙ᰳ ៊ㇱߢ㍑᧼߇ಽᜂߔࠆ⩄㊀߇⇣ߥࠆߚ㧘ߔߴߡߩᢿ㕙ߢ ቢోวᚑᢿ㕙ࠍቯߒߚ႐ว㧘㍑᧼ߩゲജߪ x ld ߢਇㅪ ⛯ߣߥࠆ㧚ߒ߆ߒ㧘ታ㓙ߦߪ x ld ߩ⟎ߢ৻⥸ㇱߣᢿ㕙 ᰳ៊ㇱߢ㍑᧼ߩゲജ߇ㅪ⛯ߔࠆࠃ߁ߦ⩄㊀߇ౣಽ㈩ߐࠇ㧘 ߘߩ⚿ᨐ㧘x ld ߩ⟎ߩᢿ㕙ᰳ៊ߩ㍑᧼ߦ↢ߓࠆᔕജ ߪV sn ࠃࠅ߽ᄢ߈ߊߥߞߡࠆ㧚 ߐࠄߦ㧘ᢿ㕙ᰳ៊ㇱߢߪ㧘ᰳ៊ㇱਛᄩ( x 0 )ߦㄭߠߊ ߦᓥߞߡ㧘㍑᧼ᔕജ߇ᓢߦޘૐਅߒߡࠆ㧚 ࿑㧙5 ߆ࠄ㧘CFRP ᧼ߦ↢ߓࠆᔕജߪ㧘CFRP ᧼ߩઃ⌕ ਛᄩ( x 0 )ߢᦨᄢߦߥࠅ㧘 x ߇Ⴧടߔࠆߦᓥߞߡ㧘ᢿ㕙 ᰳ៊ㇱߢߪ✭߿߆ߦᷫዋߔࠆ߇㧘৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߣߩ Ⴚ⇇( x ld )ߢᄢ߈ߊᷫዋߒ㧘CFRP ᧼ߣ㍑᧼ߩቢోวᚑ. ᢿ㕙ࠍቯߒߚV c ߩ୯ߦㄭߠߊ㧚ߐࠄߦ㧘CFRP ᧼ઃ⌕ ┵ߦㄭߠߊߦߟࠇߡౣ߮ᕆỗߦᷫዋߒ㧘CFRP ᧼ߩઃ⌕┵ ( x l )ߢ 0 ߦߥࠆ㧚 ធ⌕ߦ↢ߓࠆߖࠎᢿᔕജߪ㧘࿑㧙6 ߦ␜ߔࠃ߁ߦ㧘 CFRP ᧼ߩઃ⌕┵ߢᦨᄢߦߥࠅ㧘 x ߩ୯߇ዊߐߊߥࠆߦᓥ ߞߡ㧘0 ߦㄭߠߊ߇㧘৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߣߩႺ⇇( x ld ) ߦㄭߠߊߦᓥߞߡ㧘ౣ߮ᄢ߈ߊߥࠆ㧚 x ld ߩ৻⥸ㇱߣᢿ 㕙ᰳ៊ㇱߢᲑᏅ߇↢ߓ㧘ᢿ㕙ᰳ៊ㇱߢߪធ⌕ߦ↢ߓࠆߖ ࠎᢿᔕജߩ୯߇ዊߐߊ㧘 x 0 ߦㄭߠߊߦᓥߞߡ㧘ߐࠄߦ ዊߐߊߥߞߡࠆ㧚ᢿ㕙ᰳ៊ㇱߢߪ㧘ᑼ(16)߆ࠄಽ߆ࠆࠃ ߁ߦធ⌕߇ෘߊߥࠆߩߢ㧘ធ⌕ߦ↢ߓࠆߖࠎᢿᔕജߪ ዊߐߊߥࠆ㧚 3.2 FEM ⸃ᨆ ᧄ▵ߢߪ㧘ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ߩ FEM ߦࠃࠆ✢ᒻᒢᕈ⸃ᨆࠍⴕ㧘೨▵ߩℂ⺰୯ߣᲧセߔࠆ㧚 FEM ⸃ᨆࡕ࠺࡞ࠍ࿑㧙7 ߦ␜ߔ㧚ኻ⒓᧦ઙࠍㆡ↪ߒߡ 2 ᰴరߢ 1/4 ࡕ࠺࡞ߩ⸃ᨆࠍⴕߞߚ㧚⸃ᨆߦߪ᳢↪ߩ㒢ⷐ ⚛⸃ᨆࡊࡠࠣࡓ MARC14)ࠍ↪ߚ㧚㍑᧼߅ࠃ߮ធ⌕ߦ ߪ㧘4 ▵ὐߩᐔ㕙ᔕജⷐ⚛(Marc ⷐ⚛⇟ภ 3)ࠍ↪㧘CFRP. - 914 -.
(5) ᧼ߦߪ 2 ▵ὐߩ࠻ࠬⷐ⚛(Marc ⷐ⚛⇟ภ 9)ࠍ↪ߚ㧚ធ ⌕ߩⷐ⚛ߩࠨࠗ࠭ߪ 0.05×0.05mm ߢࠆ㧚3.1 ▵ߢ⸘▚ ߐࠇߚ᧦ઙߦኻߒߡ㧘ᢿ㕙ᰳ៊ࠍߔࠆ CFRP ᧼ធ⌕㍑᧼ ߩ FEM ⸃ᨆ⚿ᨐࠍ࿑㧙4㨪6 ߦ␜ߒߡࠆ㧚࿑ਛߩ FEM ⸃ᨆߩ⚿ᨐߦኻߔࠆ㍑᧼ߦ↢ߓࠆᔕജ߅ࠃ߮ធ⌕ߦ↢ ߓࠆߖࠎᢿᔕജߪ㧘ߘࠇߙࠇ㍑᧼ߩ᧼ෘߦኻߔࠆᐔဋᔕജ㧘 ធ⌕ߩෘߐߦኻߔࠆᐔဋߖࠎᢿᔕജ߇␜ߐࠇߡࠆ㧚 CFRP ᧼ߦ↢ߓࠆᔕജߪ㧘CFRP ᧼ߣߒߡ↪ߚ࠻ࠬⷐ ⚛ߦ↢ߓࠆゲജࠍᢿ㕙Ⓧ bc t c ߢ㒰ߒߚ୯߇␜ߐࠇߡࠆ㧚 ࿑㧙4㨪6 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘 FEM ⸃ᨆߩ⚿ᨐߣᑼ(17)㧘 (20)߅ࠃ߮ᑼ(21)߆ࠄ▚ߐࠇߚ V s ( x) 㧘 V c ( x) ߅ࠃ߮ W ( x) ߪ㧘ห᭽ߥะࠍ␜ߒߡࠆ㧚ߒ߆ߒ㧘 x ld ߩ ⟎ߩ৻⥸ㇱߩធ⌕ߦ↢ߓࠆߖࠎᢿᔕജߪ㧘FEM ୯߇ᑼ (21)ࠃࠅ߽㜞୯ߦߥߞߡ߅ࠅ㧘ߎߩᓇ㗀ߢ㧘FEM ⸃ᨆ⚿ ᨐߩᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജߪ㧘ᑼ(17)߆ࠄ▚ߐࠇࠆᔕജ ࠃࠅ߽ૐߊߥߞߡࠆ㧚 ߎࠇߪ㧘 ᑼ(21)ߩዉߦ߅ߡߪ㧘 ᰳ៊ㇱߩធ⌕ߩߖࠎᢿᔕജ߇৻⥸ㇱߣߩႺ⇇ߦ߅ߡ ߽᧼ෘᣇะߦ৻᭽ߢࠆߣቯߒߡࠆ߇㧘ታ㓙ߦߪ᧼ෘ ᣇะߦᄌൻ߇ࠅ㧘Ⴚ⇇ㇱߢߪ CFRP ᧼ㄭறߩߺ㜞ߊߥߞ ߡࠆߎߣ߇ේ࿃ߢࠆ㧚ߎߩߎߣ߆ࠄ㧘ᢿ㕙ᰳ៊ߩࠃࠅ ᄢ߈ t s 4.5 mm ߩ႐วߦߪ㧘 t s 6 mm ߩ႐วߣᲧߴ ߡ㧘FEM ⸃ᨆ⚿ᨐߣᑼ(17)߆ࠄ▚ߐࠇࠆᢿ㕙ᰳ៊ㇱ㍑᧼ ᔕജߣߩᏅ߇ᄢ߈ߊߥߞߡࠆ㧚. ǻs (0)/ǻs n 1.5 1.4. c d l d =0.2 1.2. 1 ®. Z. O ¯ cosh(cd ld ). ½ [ d ¾V sn ¿. (23). cd ld ߇ 0㧘0.2 ߅ࠃ߮ 2.0 ߩ႐วߦኻߒߡ㧘ᑼ(23)߆ࠄ▚ ߐࠇࠆV s (0) V sn ߣ cln ߩ㑐ଥࠍ࿑㧙8 ߦ␜ߔ㧚࿑㧙8 ߢ ߪ㧘㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)㧘߹ߚᑼ(22) ࠃࠅ▚ߐࠇߚ t c t c 0 2 mm ߇↪ࠄࠇߡࠆ㧚 cd ld 0 ߩ⁁ᘒߪ㧘ᢿ㕙ᰳ៊ߩ㐳ߐ߇ 0 ߢࠆ߇㧘x 0 ߩ ⟎ߢෘߐ t sd ߩㇱಽߢ㍑᧼ߩゲജࠍᜂߞߡࠆ⁁ᘒߢ ࠆ㧚ߎߩ࿑߆ࠄ㧘cd ld ߩ୯߇ᄢ߈ߊߥࠆ㧘ߟ߹ࠅᢿ㕙ᰳ៊ ߩඨ㐳ߐ ld ߇㐳ߊߥࠆߦᓥߞߡ㧘V s (0) ߇ૐᷫߐࠇࠆߎߣ ߇ಽ߆ࠆ㧚ߐࠄߦ㧘 cln ߩ୯߇ᄢ߈ߊߥࠆ㧘ߟ߹ࠅ৻⥸ㇱ ߳ CFRP ᧼ࠍ㐳ߊធ⌕ߔࠆߣ㧘V s (0) ߇৻ቯߩ୯ߦ᧤ߔ ࠆߎߣ߇ಽ߆ࠆ㧚 cln ߩ୯߇ᄢ߈ߊߥࠆߣ㧘V s (0) ߪᰴᑼ ߦ᧤ߔࠆ㧚. V s (0). ½ ° [d [ 1° [ d ¾V sn ® c h O ° cosh(c l ) d d sinh(c l ) ° d d d d ch ¿ ¯. (24). 㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)㧘t c 2 mm ߦ ኻߒߡ㧘ᑼ(24)߆ࠄ⸘▚ߐࠇࠆV s (0) V sn ߣ cd ld ߩ㑐ଥࠍ ࿑㧙9 ߦ␜ߔ㧚ߎߩ࿑߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ߩඨ㐳. c d l d =2.0. 1.1 1.0. 0. 2. 4. 6. 8. 10. 12. cl n ࿑㧙8 V s (0) V sn ߣ cln ߩ㑐ଥ. ǻs (0)/ǻs n 1.2 1.1 1.0 0.9 0.8 0.7. 3.3 ᢿ㕙ᰳ៊ਛᄩߦ↢ߓࠆ㍑᧼ᔕജ ࿑㧙4 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ㇱߦ߅ߡ㧘㍑᧼ᔕ ജߪᢿ㕙ᰳ៊ਛᄩߢᦨ߽ዊߐߊߥࠆ㧚ᢿ㕙ᰳ៊ਛᄩߦ↢ߓ ᑼ(17)߳ x 0 ࠍઍߒߡᰴᑼߢਈ߃ࠄࠇ ࠆᔕജV s (0) ߪ㧘 ࠆ㧚. V s (0). c d l d =0. 1.3. 0.6. 0. 1. 2. 3. 4. 5. 6. c d ld ࿑㧙9 V s (0) V sn ߣ cd ld ߩ㑐ଥ ߐ ld ߇⍴႐ว㧘ᢿ㕙ᰳ៊ਛᄩߦ↢ߓࠆᔕജV s (0) ߪᄢ߈ ߊߥࠅ㧘ld 0 ߩߣ߈ᦨᄢߣߥࠆ㧚߹ߚ㧘l d ߇㐳ߊߥࠆߦ ᓥߞߡV s (0) V sn 1 ߦ᧤ߒߡࠆ㧚 3.4 ᢿ㕙ᰳ៊ㇱߣ৻⥸ㇱߩႺ⇇ߦ↢ߓࠆ㍑᧼ᔕജ ࿑㧙4 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ㇱߣ৻⥸ㇱߩႺ⇇㧘 ߔߥࠊߜ x ld ߩ⟎ߦ߅ߡ㧘ᢿ㕙ᰳ៊ㇱߢߪ㍑᧼ᔕ ജ߇ᦨᄢߦߥࠅ㧘৻⥸ㇱߢߪ㍑᧼ᔕജ߇ᦨዊߦߥࠆ㧚 ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജߩᦨᄢ୯ V sD (l d ) ߅ࠃ߮৻⥸ㇱ ᑼ(17)߳ x ld ࠍઍߒߡ ߩ㍑᧼ᔕജߩᦨዊ୯V sN (ld ) ߪ㧘 ߘࠇߙࠇᰴᑼߢਈ߃ࠄࠇ㧘ᦨᄢ୯ V sD (l d ) ߪᦨዊ୯ V sN (ld ) ߩ1 O ߦߥߞߡࠆ㧚. V sD (ld ). 1. O. ([ d Z )V sn. V sN (ld ) O. V sN (ld ) ([ d Z )V sn. (25) (26). cd ld ߇ 0㧘0.2 ߅ࠃ߮ 2.0 ߩ႐วߦኻߒߡ㧘ᑼ(25)㧘(26) ߆ࠄ▚ߐࠇࠆ V sD (ld ) V sn ߅ࠃ߮ V sN (ld ) V sn ߣ cln ߩ 㑐ଥࠍ࿑㧙10 ߦ␜ߔ㧚ߎߩ࿑ߢߪ㧘㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)㧘 t c 2 mm ߇↪ࠄࠇߡࠆ㧚ߎ ߩ࿑߆ࠄ㧘ᢿ㕙ᰳ៊ߩඨ㐳ߐ l d ߇㐳ߊߥࠆߦᓥߞߡ㧘 V sD (l d ) ߅ࠃ߮V sN (ld ) ߩ୯ߪߦૐਅߔࠆߎߣ߇ಽ߆ࠆ㧚. - 915 -.
(6) ߐࠄߦ㧘৻⥸ㇱ߳ CFRP ᧼ࠍ㐳ߊធ⌕ߔࠆ( cln ߩ୯ࠍᄢ߈ ߊߔࠆ)ߎߣߦࠃࠅ㧘V sD (ld ) ߅ࠃ߮V sN (ld ) ߩ୯߇৻ቯߩ ୯ߦ᧤ߔࠆߎߣ߇ಽ߆ࠆ㧚৻⥸ㇱ߳ CFRP ᧼ࠍ㐳ߊធ⌕ ߔࠆߣ㧘ᢿ㕙ᰳ៊ㇱ߅ࠃ߮৻⥸ㇱߩ㍑᧼ᔕജߪߘࠇߙࠇᰴ ᑼߦ᧤ߔࠆ㧚. V sD (ld ). V sN (ld ) O. ½ [d [ °° °° ®[ d ¾V sn c h ° 1 d d tanh(cd l d ) ° °¯ °¿ ch. V sN (l d ). ǻs D (ld )/ǻs n , ǻs N (l d )/ǻs n 1.6. ǻ s D (l d ) ǻ s N (l d ). 1.4 1.2. (27). 1.0 c d l d =0.2. c d l d =0. c d l d =2.0. 0.8. (28). 0.6. 㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)㧘t c 2 mm ߦ ኻߒߡ㧘ᑼ(27)㧘(28)߆ࠄ⸘▚ߐࠇࠆV sD (ld ) V sn ߣ cd ld ߩ 㑐ଥ߅ࠃ߮V sN (ld ) V sn ߣ cd ld ߩ㑐ଥࠍ࿑㧙11 ߦ␜ߔ㧚ߎ ߩ࿑߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߇⍴ߊߥࠆ ߣ㧘V sD (l d ) ߣV sN (ld ) ߩ୯߇ᄢ߈ߊߥࠅ㧘ld 0 ߩ႐ว㧘 ਔ⠪ߪᦨᄢߦߥࠆ㧚 l d ߇㐳ߊߥࠆߣV sD (l d ) ߣV sN (ld ) ߩ ୯ߪ㧘ߘࠇߙࠇ৻ቯߩ୯ߦ᧤ߔࠆ㧚. 0. 2. 4. 6. 8. 10. 12. cl n ࿑㧙10 V sD (ld ) V sn ߣ cln ߩ㑐ଥ߅ࠃ߮ V sN (ld ) V sn ߣ cln ߩ㑐ଥ. ǻs D (l d )/ǻs n , ǻs N (l d )/ǻs n 1.2 1.1. 4㧚CFRP ᧼ߩᔅⷐធ⌕㐳ߐߣ᧼ෘ. 1.0. 4.1 CFRP ᧼ߩᔅⷐធ⌕㐳ߐ ᑼ(25)ߢਈ߃ࠄࠇࠆ৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߩႺ⇇㕙ߩᢿ㕙 ᰳ៊ߦ↢ߓࠆᔕജV sD (l d ) ߇ᑼ(27)ߩV sD (l d ) ߦ᧤ߔ ࠆ⒟ᐲࠍK d ( ! 1 )ߣߔࠆ㧚ห᭽ߦ㧘ᑼ(23)ߢਈ߃ࠄࠇࠆᢿ 㕙ᰳ៊ਛᄩߩ㍑᧼ߦ↢ߓࠆᔕജV s (0) ߇ᑼ(24)ߩV s (0) ߦ ᧤ߔࠆ⒟ᐲࠍK dc ( ! 1 )ߣߔࠆ㧚 cd ld ߇ 0㧘0.2 ߅ࠃ߮ 2.0 ߩ႐วߦኻߒߡ㧘K d ߣ cln ߩ㑐 ଥ߅ࠃ߮K dc ߣ cln ߩ㑐ଥࠍ࿑㧙12 ߦ␜ߔ㧚ߎߩ࿑ߢߪ㧘 㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)㧘 t c 2 mm ߇ ↪ࠄࠇߡࠆ㧚cd ld ߇ 0 ߅ࠃ߮ 0.2 ߩ႐ว㧘K d ߣ cln ߩ 㑐ଥߣK dc ߣ cln ߩ㑐ଥߪ߶߷㊀ߥߞߡࠆ㧚߹ߚ㧘cd ld ߇ 0 ߩ႐ว㧘K d ߣK dc ߇ 1 ߦㄭߠߊ cln ߩ୯߇ᄢ߈ߊߥࠆߎ ߣ߇ಽ߆ࠆ㧚ߔߥࠊߜ㧘ᢿ㕙ᰳ៊ߩ㐳ߐ߇㕖Ᏹߦ⍴ߊಾᰳ ߈ߩࠃ߁ߥᰳ៊ߩ႐ว㧘ᢿ㕙ᰳ៊ㇱߦ↢ߓࠆᔕജV sD (l d ) ߅ࠃ߮V s (0) ࠍ㧘ߘࠇߙࠇV sD (l d ) ߅ࠃ߮V s (0) ߦ᧤ߐ ߖࠆ৻⥸ㇱߩ CFRP ᧼ߩធ⌕ඨ㐳ߐ߇㐳ߊߥࠆ㧚 cd ld ߇ 0 ߩ႐ว㧘K d ߣK dc ߪߦᰴᑼߩK ߢਈ߃ࠄࠇ㧘 K ߪ᧼ෘᱷሽᲧ O ߦߪ㑐ଥߖߕ㧘৻⥸ㇱߩ㍑᧼߅ࠃ߮ CFRP ᧼ߩ⻉రߩߺߩ㑐ᢙߣߥࠆ㧚. K 1. 1[ [ cosh(cln ). 0.8. 1 [ ½ 1 cosh 1 ® ¾ c ¯ [ (K 1) ¿. 0.6. 0. 1. 2. 3. 4. 5. 6. c d ld ࿑㧙11 V sD (ld ) V sn ߣ cd ld ߩ㑐ଥ߅ࠃ߮ V sN (ld ) V sn ߣ cd ld ߩ㑐ଥ. ǯd㧘 ǯdc 1.5. ǯd ǯdc. 1.4 1.3. c d l d =0.0. 1.2. c d l d =0.2 c d l d =2.0. 1.1 1.0. (29). 0.9. 0. 1. 2. 3. 4. 5. 6. cl n ࿑㧙12 K d ߣ cln ߩ㑐ଥ߅ࠃ߮K dc ߣ cln ߩ㑐ଥ. (30). ᑼ(30)ߩK ߦ 1 ߦㄭ୯( K ! 1 )ࠍਈ߃ࠆߎߣߦࠃࠅ㧘 c d l d 0 ߩ႐วߦ߅ߡV sD (l d ) ߇V sD (l d ) ߦ᧤ߔࠆߩ ߦචಽߥ৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐ l n ࠍ⸳⸘ߔࠆߎߣ. ǻ s N (l d ). 0.7. ߎߩᑼࠍ㧘৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐߦኻߒߡ⸃ߊߣ ᰴᑼߦߥࠆ㧚. ln. ǻ s D (l d ). 0.9. ߇ߢ߈㧘ߎߩ l n ࠍ↪ࠇ߫㧘c d l d ! 0 ߩ႐วߦ߅ߡో ߩ⸳⸘ߣߥࠆ㧚ߐࠄߦ▚ߐࠇߚ l n ߦᢿ㕙ᰳ៊ㇱߩඨ㐳 CFRP ᧼ߩᔅⷐធ⌕ඨ㐳ߐ l ߇ቯߢ߈ࠆ㧚 ߐ l d ࠍ⿷ߒߡ㧘. - 916 -.
(7) t c /t c 0. 4.2 CFRP ᧼ߩᔅⷐ᧼ෘ ࿑㧙4 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᑼ(22)ࠍḩ⿷ߔࠆ᧼ෘߩ CFRP ᧼ࠍធ⌕ߒߡ߽㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജV s ߪV sn ࠃࠅ߽ ᄢ߈ߊߥࠅ㧘৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߩႺ⇇㕙ߩᢿ㕙ᰳ៊ߦ ߅ߡᦨᄢߦߥࠆ㧚 ᑼ(30)ߩK ߦ 1 ߦㄭ୯ࠍਈ߃ߡ CFRP ᧼ߩ 㐳ߐ l n ߇⸳⸘ߐࠇߚ႐ว㧘৻⥸ㇱߣᢿ㕙ᰳ៊ㇱߩ Ⴚ⇇㕙ߩᢿ㕙ᰳ៊ߦ↢ߓࠆᔕജ߇V sD (ld ) ߦ᧤ߔࠆߩ ߢ㧘V sD (ld ) ߇V sn એਅߦߥࠇ߫㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജ ߇V sn એਅߦߥࠆ㧚V sD (ld ) ߇V sn એਅߣߥࠆ᧦ઙߪᰴᑼ ߢਈ߃ࠄࠇࠆ㧚 ½ [d [ 1 °° °° ®[ d ¾ d1 c h O° 1 d d tanh(cd l d ) ° °¯ °¿ ch. (1 O ) E s bs t s 2Obc Ec. 1. O. tc0. [ d [ h 1[ O O d h 1 [d. d1. dz = 0.5. 0. 25. 50. 75. 100. 125. (31). 150. ld. ࿑㧙13 ᑼ(31)ࠍḩ⿷ߔࠆ t c t c 0 ߣ l d ߩ▸࿐. (32). ߎߩᑼ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ld 0 ߩ႐ว㧘ᢿ㕙ᰳ៊ㇱߩ ㍑᧼ᔕജࠍV sn એਅߦߢ߈ࠆ CFRP ᧼ߩ᧼ෘߪ㧘tc 0 ߩ1 O ߣߥࠆ㧚 ৻ᣇ㧘ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߇㐳႐ว㧘ᰴᑼࠍḩ⿷ߔ ࠆ CFRP ᧼ߩ᧼ෘ t c ࠍធ⌕ߔࠆߎߣߦࠃࠅ㧘ᢿ㕙ᰳ៊ㇱߩ ㍑᧼ᔕജࠍV sn એਅߦߢ߈ࠆ㧚. [d O. dz = 0.67 1.5. 1.0. 㧙1 ߩ᧦ઙࠍ↪ߡ㧘ᑼ(31)ࠍḩ⿷ߔࠆ CFRP ᧼ߩ᧼ ෘ t c ߣ l d ߩ㑐ଥࠍ࿑㧙13 ߦ␜ߔ㧚࿑ߩ❑ゲߩ t c ߪ㧘ᑼ(22) ߆ࠄ⸘▚ߐࠇࠆቢోวᚑᢿ㕙ࠍቯߒߚ႐วߦᔅⷐߥ CFRP ᧼ߩ᧼ෘ tc 0 ߢ㒰ߒߚ୯߇␜ߐࠇߡࠆ㧚 ࿑ߩታ✢ߩ ߇㧘ᑼ(31)ࠍḩ⿷ߔࠆ t c t c 0 ߣ l d ߩ▸࿐ߢࠆ㧚ߎߩ ࿑߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജࠍV sn એਅߦ ߔࠆߚߩ CFRP ᧼ߩᔅⷐ᧼ෘ t c ߪ㧘ᑼ(22)ߢਈ߃ࠄࠇࠆ ቢోวᚑᢿ㕙ࠍቯߒߚ႐วߦᔅⷐߥ CFRP ᧼ߩ᧼ෘ tc 0 ࠃࠅ߽Ᏹߦෘߊߥࠆ㧚߹ߚ㧘᧼ෘᱷሽᲧ O ߩ୯߇ዊߐߊߥ ࠅᢿ㕙ᰳ៊ߩഀว߇ᄢ߈ߊߥࠆߣ㧘ᑼ(31) ࠍḩ⿷ߔࠆ t c t c 0 ߩ୯߇ᄢ߈ߊߥࠆ㧚ߐࠄߦ㧘ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߇ ⍴ߊߥࠆߣ㧘หߓ᧼ෘᱷሽᲧ O ߢߞߡ߽ᑼ(31)ࠍḩ⿷ߔ ࠆ CFRP ᧼ߩ᧼ෘ t c ߪෘߊߥࠅ㧘ld 0 ߩ႐ว㧘ᦨᄢߦߥ ৻ቯߩ୯ߦ᧤ߒߡࠆ㧚 ࠆ㧚l d ߇㐳ߊߥࠆߣ㧘t c t c 0 ߪ㧘 ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߇⍴႐ว㧘ᑼ(31)߳ ld 0 ࠍઍ ߒߡᰴᑼߢਈ߃ࠄࠇࠆ᧼ෘߩ CFRP ᧼ࠍធ⌕ߔࠆߎߣߦ ࠃࠅ㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജࠍV sn એਅߦߢ߈ࠆ㧚 tc t. 2.0. (33). ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߩ㐳⍴ߪ㧘ᑼ(31)ਛߩ tanh(cd ld ) ߦ ࠃࠅ್ᢿߒ㧘 tanh(cd ld ) ߪ㧘 l d ߇⍴ߊߥࠆߣ 0 ߦㄭߠ߈㧘 ld ߇㐳ߊߥࠆߣ 1 ߦㄭߠߊ㧚 cd ld t 3 ߩ▸࿐ߢߪ㧘 tanh(cd ld ) t 0.995 ߣߥࠅ㧘ld ߪචಽߦ㐳ߣ್ᢿߢ߈ࠆ㧚 ᑼ(3)ߦࠃࠆ cd ߩ⸘▚ߦߪ tc ߇ᔅⷐߣߥࠆ߇㧘 tc ߇ቯߐ ࠇߡߥᲑ㓏ߢߪ㧘ᑼ(32)ߢ⸘▚ߐࠇࠆ tc ࠍ↪ߡ cd ࠍ ⸘▚ߒ㧘ᢿ㕙ᰳ៊ߩඨ㐳ߐ ld ߩ㐳⍴ࠍ್ߔࠆߣࠃ㧚 ᰴߦ㧘ᑼ(31)ࠍḩ⿷ߔࠆᦨዊߩ t c t c 0 ߣᢿ㕙ᰳ៊ㇱߩ᧼. t c /t c 0 3.0. l d =0mm l d =5mm. 2.5. l d =20mm l d =40mm. 2.0 1.5 l d =100mm 1.0 0.0 0.2. 0.4. 0.6. 0.8. 1.0. dz. ࿑㧙14 ᑼ(31)ࠍḩ⿷ߔࠆ t c t c 0 ߣ O ߩ㑐ଥ ෘᱷሽᲧ O ߣߩ㑐ଥࠍ࿑㧙14 ߦ␜ߔ㧚ߎߩ࿑ߢ߽㧘㧙1 ߩ᧦ઙࠍ↪ߡࠆ㧚࿑ਛߩ ld 0 ߩ႐วߪᑼ(32)ࠍߒ㧘 ld =100mm ߩ႐วߪ㧘ᑼ(33)ࠍḩ⿷ߔࠆ tc ߣ߶߷╬ߒߊߥ ࠆ㧚 ࿑㧙14 ߆ࠄ㧘หߓᢿ㕙ᰳ៊㊂ߢߞߡ߽㧘ᢿ㕙ᰳ៊ㇱ ߩ㍑᧼ᔕജࠍV sn એਅߦߢ߈ࠆ CFRP ᧼ߩ᧼ෘߪ㧘l d ߦࠃ ߞߡᄢ߈ߊ⇣ߥࠅ㧘ld 0 ߩߣ߈ᔅⷐ᧼ෘ tc ߪᦨᄢ(ᑼ(32) ࠍḩ⿷ߔࠆ tc )ߦߥࠅ㧘 ld ߇ᄢ߈ߊߥࠆߦᓥ৻ቯߩᦛ✢ (ᑼ(33)ࠍḩ⿷ߔࠆ tc )ߦ᧤ߔࠆߎߣ߇ࠄ߆ߢࠆ㧚߹ ߚ㧘O ߇ 0.5 એਅߢ ld ߇⍴႐ว㧘CFRP ᧼ߩᔅⷐ᧼ෘ tc ߪ㧘 tc 0 ߩ 2 એᔅⷐߦߥࠆ㧚 l d ߇ࠆ⒟ᐲ㐳႐วߢ ߽㧘 O ߇㕖Ᏹߦዊߐߊߥࠆߣ㧘CFRP ᧼ߩᔅⷐ᧼ෘ tc ߪ㧘 tc 0 ߩᢙᔅⷐߣߥࠆߚ㧘 O ߇ 0.5 એਅߦߥࠆࠃ߁ߥᢿ 㕙ᰳ៊߇ᄢ߈႐ว㧘CFRP ᧼ߦࠃࠆធ⌕ୃ⸳⸘ߦߪᵈ ᗧߔࠆᔅⷐ߇ࠆ㧚 ߐࠄߦ㧘ធ⌕ୃ⸳⸘ߢߪ㧘ᱫ⩄㊀ߦࠃߞߡᢿ㕙ᰳ៊ㇱ ߦ↢ߓࠆᔕജ߇Ⴧടߔࠆߎߣࠍ⠨ᘦߒߡ㧘V sn ࠍቯߒߥ ߌࠇ߫ߥࠄߥߦ߽ᵈᗧ߇ᔅⷐߢࠆ㧚 5㧚CFRP ᧼ߩߪߊ㔌߇↢ߓࠆ⟎ ⸳⸘⩄㊀ਅߢ CFRP ᧼߇ߪߊ㔌ߔࠆ߆ุ߆ߪ㧘ធ⌕ߦ ↢ߓࠆᦨᄢߖࠎᢿᔕജW max ࠍߪߊ㔌ߖࠎᢿᒝᐲߣᲧセߔ. - 917 -.
(8) Ǽ(l d )/ǻs n ,Ǽ(l)/ǻs n. ࿑㧙4 ߆ࠄࠄ߆ߥࠃ߁ߦ㧘 ࠆߎߣߦࠃࠅ್ᢿߢ߈ࠆ 2)㧘8)㧚 ធ⌕ߩߖࠎᢿᔕജߪ㧘ᢿ㕙ᰳ៊ㇱߣ৻⥸ㇱߣߩႺ⇇ߩ৻ ⥸ㇱ( x ld )߅ࠃ߮ CFRP ᧼ߩઃ⌕┵( x l )ߢᄢ߈ߊߥ ࠆ㧚ߘࠇࠄ 2 ὐߢߩߖࠎᢿᔕജW (l d ) 㧘W (l ) ߪ㧘ᑼ(21)߳ x ld ߅ࠃ߮ x l ࠍઍߒߡߘࠇߙࠇᰴᑼߢਈ߃ࠄࠇࠆ㧚 cbs t s W (ld ) B2V sn (34) 2bc cbs t s ^B1 sinh(cln ) B2 cosh(cln )`V sn (35) W (l ) 2bc 㧙1 ߩ᧦ઙߣ O. 0.67 ( t sd. 6 mm)㧘t c. 0.6. 0.4. c d l d =0.2. 0.2 0.1. ߦኻߒߡ㧘ᑼ(34)㧘(35)߆ࠄ⸘▚ߐࠇࠆW (ld ) V sn ߣ cln ߩ. 0.0. 㑐ଥ߅ࠃ߮W (l ) V sn ߣ cln ߩ㑐ଥࠍ࿑㧙15 ߦ␜ߔ㧚ߎߩ࿑. 0. 2. ߆ࠄ㧘 cln ߩ୯߇ᄢ߈ߊߥࠆߣW (l d ) ߅ࠃ߮W (l ) ߪ㧘ߘࠇ. 6. 8. 10. 12. ࿑㧙15 W (ld ) V sn ߣ cln ߩ㑐ଥ߅ࠃ߮ W (l ) V sn ߣ cln ߩ㑐ଥ. ߥࠆߣW (l d ) ߅ࠃ߮W (l ) ߪߘࠇߙࠇᰴᑼߦ᧤ߔࠆ㧚 cbs t s [ d [ (36) W (ld ) V sn 2bc ch {cd hd tanh(cd ld )} 1. Ǽ (l d )/ Ǽ (l) 0.7. (37). 0.6. ᑼ(31)ࠍḩ⿷ߔࠆ႐ว㧘ߔߥࠊߜᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജ ߇ V sn એਅߦߥࠆ᧦ઙࠍḩ⿷ߔࠆ႐วߦߟߡ㧘. 0.5. l d =100mm l d =40mm l d =20mm. 0.4. W (l d ) / W (l ) ߣ᧼ෘᱷሽᲧ O ߣߩ㑐ଥࠍߊߟ߆ߩ ld ߦߟ ߡࡊࡠ࠶࠻ߒߚ⚿ᨐࠍ࿑㧙16 ߦ␜ߔ㧚ߎߩ࿑߆ࠄࠄ ߆ߥࠃ߁ߦ㧘ᑼ(31)߆ࠄ tc ࠍቯߒߚ႐ว㧘 O ߦࠃߞߡ. l d =5mm. 0.3 0.2 0.1. W (l d ) / W (l ) ߩ୯ߪᄌൻߔࠆ߇㧘W (l d ) ߪᏱߦW (l ) ࠃࠅዊߐ ߊߥࠆ㧚߹ߚ㧘ᑼ(30)߆ࠄ ln ࠍቯߒߚ႐ว㧘CFRP ᧼ߩ ઃ⌕┵ߩធ⌕ߦ↢ߓࠆߖࠎᢿᔕജW (l ) ߪ㧘K ࠃࠅ߽ 1. l d =1mm. 0.0 0.0. 0.2. 0.4. 0.6. 0.8. 1.0. dz. ࿑㧙16 W (l d ) / W (l ) ߣ᧼ෘᱷሽᲧ O ߣߩ㑐ଥ. ߦㄭ♖ᐲߢᑼ(37)ߩW (l ) ߦ᧤ߔࠆߎߣ߆ࠄ㧘W (l ) ߇ߪ ߊ㔌ߖࠎᢿᒝᐲࠃࠅዊߐߊߥࠆࠃ߁㧘ߟ߹ࠅ㧘CFRP ᧼ߩ ઃ⌕┵߆ࠄߩߪߊ㔌ࠍ㒐ᱛߔࠆ⸳⸘ࠍⴕ߃߫ࠃ㧚. 㧙2 CFRP ᧼ߩᔅⷐ᧼ෘߣᔅⷐធ⌕ඨ㐳ߐ tc [mm] l n [mm] l req [mm]. 6㧚CFRP ᧼ធ⌕ߦࠃࠆᢿ㕙ᰳ៊ߩୃ⸳⸘. ld =5mm. ᧄ┨ߢߪ㧘㧙1 ߩ᧦ઙ߅ࠃ߮ O 0.67 ( t sd 6 mm)ߦ ኻߒߡ㧘ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ ld ߇ 5mm ߣ 100mm ߩ႐ว ߩ CFRP ᧼ធ⌕ୃߩ⸳⸘ࠍ␜ߔ㧚 6.1 CFRP ᧼ߩᔅⷐ᧼ෘߩ⸳⸘ O 0.67 ( t sd 6 mm)ߩ႐ว㧘ቢోวᚑᢿ㕙ࠍቯߒߚ ᑼ(22)ߢਈ߃ࠄࠇࠆ CFRP ᧼ߩ᧼ෘߪ 2.0mm ߦߥࠆ߇㧘ᢿ 㕙ᰳ៊ㇱߩඨ㐳ߐ ld ߇ 5mm ߣ 100mm ߦኻߒߡ㧘ᑼ(31) ࠍḩ⿷ߔࠆ CFRP ᧼ߩᔅⷐ᧼ෘߩᦨዊ୯ߪ㧘ߘࠇߙࠇ 2.54mm ߣ 2.20mm ߦߥࠆ㧚ߎߩ᭽ߦ㧘CFRP ᧼ធ⌕ୃߢ ߪ㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ෘ߇৻ቯߢߞߡ߽㧘ᢿ㕙ᰳ៊ㇱߩ 㐳ߐߦࠃߞߡធ⌕ߔࠆ CFRP ᧼ߩᔅⷐ᧼ෘ߇⇣ߥࠆ㧚 ᑼ(31)ࠍḩ⿷ߔࠆ t c ࠍ↪ߒߡ cd ld ࠍ⸘▚ߔࠆߣ㧘ld ߇ 5mm ߣ 100mm ߦኻߒߡ㧘cd ld ߪߘࠇߙࠇ 0.21 ߣ 4.1 ߣߥ ࠅ㧘5mm ߩ႐วߪᲧセ⊛⍴ ld ߢࠅ㧘100mm ߩ႐วߪ චಽߦ㐳 ld ߢࠆߣ್ߢ߈ࠆ㧚ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ߇. 4. cl n. ߙࠇ৻ቯߩ୯ߦ᧤ߒߡࠆߎߣ߇ಽ߆ࠆ㧚 cln ߇ᄢ߈ߊ. W (l ). c d l d =2.0. 0.3. 2 mm ߩ႐ว. cbs t s (1 [ )V sn 2bc. Ǽ (l d ) Ǽ (l). 0.5. ld =100mm. ᑼ(31) ᑼ(32) ᑼ(31) ᑼ(33). 2.54 3.00 2.20 2.20. 57.5 62.4 53.4 53.4. 62.5 67.4 153.4 153.4. 5mm ߣ⍴႐วߦኻߒߡ㧘ᑼ(32)ࠍ↪ߡ CFRP ᧼ߩᔅⷐ ᧼ෘߩᦨዊ୯ࠍ▚ߔࠆߣ 3mm ߦߥࠆߩߢ㧘ᑼ(32)ࠍ↪ ߡ CFRP ᧼ߩᔅⷐធ⌕ෘߐ߇ోߦ⸳⸘ߢ߈ࠆ㧚৻ᣇ㧘 ᑼ(33) ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ߇ 100mm ߣ㐳႐วߦኻߒߡ㧘 ࠍ↪ߡ CFRP ᧼ߩᔅⷐ᧼ෘߩᦨዊ୯ࠍ▚ߔࠆߣ 2.2mm ߦߥࠅ㧘ᑼ(31)߆ࠄ▚ߐࠇࠆ୯ߣ╬ߒ㧚 6.2 CFRP ᧼ߩᔅⷐធ⌕㐳ߐߩ⸳⸘ ㍑᧼㧘CFRP ᧼(6.1 ▵ߢ⸳⸘ߒߚ᧼ෘࠍ↪ࠆ)߅ࠃ߮ធ ⌕ߩኸᴺߣ᧚ᢱቯᢙࠍᑼ(30)߳ઍߒ㧘ߐࠄߦK =1.001 ߣߒߡ㧘৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐ ln ࠍ▚ߔࠆߣ㧙 2 ߩ୯ߦߥࠆ㧚ߐࠄߦ㧘CFRP ᧼ߩᔅⷐធ⌕ඨ㐳ߐ lreq ߪ㧘. - 918 -.
(9) ǻ s (x)/ǻ s n. ln ߦᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ ld ࠍട߃ߡਈ߃ࠄࠇ㧘㧙2 ߦ૬ ߖߡ␜ߔ㧚 㧙2 ߆ࠄಽ߆ࠆࠃ߁ߦ㧘ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐ ld =5mm ߦኻߒߡ㧘ᑼ(32)߆ࠄ▚ߒߚ CFRP ᧼ߩᔅⷐ᧼ෘߪ㧘ᑼ (31)߆ࠄ▚ߒߚ႐วࠃࠅ߽ෘߊߥࠆߩߢ㧘ᢿ㕙ᰳ៊ㇱߩ ㍑᧼ᔕജࠍ᧤ߐߖࠆߩߦᔅⷐߥ৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐ ln ߇㐳ߊߥࠆ㧚. 1.2 1.0 t c = 2.54mm. 0.8 0.6. 6.3 ㍑᧼ߦ↢ߓࠆᔕജ 6.1 ▵߅ࠃ߮ 6.2 ▵ߢ⸳⸘ߐࠇߚ㧘CFRP ᧼ࠍធ⌕ߔࠆߎ ߣߦࠃࠅୃߐࠇߚᢿ㕙ᰳ៊ࠍߔࠆ㍑᧼ߦ↢ߓࠆᔕജ (ᑼ(17))ߩಽᏓࠍ࿑㧙17 ߦ␜ߔ㧚࿑ߩ❑ゲߦߪ㧘㍑᧼ᔕജ V s (x) ߇V sn ߢ㒰ߐࠇߚ୯߇␜ߐࠇߡࠆ㧚ߎߩ࿑߆ࠄ㧘 6.1 ▵߅ࠃ߮ 6.2 ▵ߢ⸳⸘ߐࠇߚ CFRP ᧼ߩᔅⷐធ⌕㐳ߐߣ ᧼ෘࠍ↪ߒߚ႐ว㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജߪᏱߦV sn એ ਅߦߥߞߡ߅ࠅ㧘ㆡಾߦୃ⸳⸘߇ⴕ߃ߚߎߣ߇ಽ߆ࠆ㧚. 0.4. t c = 3.0mm. 0. 20. 40. 60. 80 x[mm]. 120. 160 x[mm]. (a) ld =5mm. ǻ s (x)/ǻ s n 1.2. 7㧚߹ߣ. 1.0. ᧄ⎇ⓥߢߪ㧘CFRP ᧼߇ធ⌕ߐࠇߚᢿ㕙ᰳ៊ࠍߔࠆ㍑ ᧼߇ゲജࠍฃߌࠆ႐วߦߟߡ㧘ℂ⺰⸃ᨆ߅ࠃ߮ FEM ⸃ ᨆࠍⴕ㧘ᢿ㕙ᰳ៊ㇱߦ⊒↢ߔࠆᔕജࠍஜోㇱߩᔕജએਅ ߦߔࠆߚߦᔅⷐߥ CFRP ᧼ߩធ⌕㐳ߐ߅ࠃ߮᧼ෘࠍᬌ ⸛ߒ㧘એਅࠍࠄ߆ߦߒߚ㧚 1) CFRP ᧼߇ធ⌕ߐࠇߚᢿ㕙ᰳ៊ࠍߔࠆ㍑᧼ߦ↢ߓࠆ ᔕജ㧘CFRP ᧼ߦ↢ߓࠆᔕജ߅ࠃ߮ធ⌕ߦ↢ߓࠆᔕ ജࠍዉߒߚ㧚 2) ℂ⺰⸃ᨆߣ FEM ⸃ᨆ⚿ᨐ߆ࠄ㧘ᓥ᧪ߩ⸳⸘ᣇᴺߣห ᭽ߦ CFRP ᧼ߣᢿ㕙ᰳ៊ㇱߩ㍑᧼߇ቢోวᚑߐࠇߚ ႐วߩᢿ㕙ߦ↢ߓࠆᔕജ߇㧘ஜోㇱߩ㍑᧼ᔕജߣ╬ߒ ߊߥࠆࠃ߁ߥ CFRP ᧼ߩ᧼ෘ(ᑼ(22))߇ធ⌕ߐࠇߚ႐ วߢ߽㧘ᢿ㕙ᰳ៊ㇱߩ㍑᧼ᔕജ߇ஜోㇱߩߘࠇࠃࠅ߽ 㜞ߊߥࠆߎߣࠍ␜ߒߚ㧚 3) ធ⌕ߒߚ CFRP ᧼ߦචಽߦᔕജࠍવ㆐ߔࠆߚߦᔅ ⷐߥធ⌕㐳ߐ(৻⥸ㇱߩ CFRP ᧼ 㐳ߐ)ࠍᑼ(30)ߦ ࠃࠅឭ᩺ߒߚ㧚 4) ᑼ(31)ࠍḩ⿷ߔࠆ᧼ෘߣ㧘ᑼ(30)ߩK ߦ 1 ߦㄭ୯ࠍ ઍߒߡ▚ߐࠇࠆ৻⥸ㇱߩ CFRP ᧼ߩ 㐳ߐߦ ᢿ㕙ᰳ៊ㇱߩඨ㐳ߐࠍ⿷ߒߚᔅⷐ㐳ߐࠍߔࠆ CFRP ᧼߇ធ⌕ߐࠇߚ႐ว㧘ᢿ㕙ᰳ៊ㇱߦ↢ߓࠆ㍑᧼ᔕജߪ㧘 ஜోㇱߩ㍑᧼ᔕജએਅߦߢ߈ࠆߎߣࠍ␜ߒߚ㧚 ෳ⠨ᢥ₂ 1) ㋈ᧁඳਯ㧘᳗ፒᄩ㓁㧘㆙⮮ാ৻㧘ᳰ↰৻㧦߈ⵚࠍ ߔࠆ᧚ߩ⚛❫⛽ᒝൻ᮸⢽᧼ߦࠃࠆᒝ㧘㍑᭴ㅧ ᐕᰴ⺰ᢥႎ๔㓸㧘╙ 8 Ꮞ㧘pp.683-688㧘2000㧚 2) ᄢୖ৻㇢㧘໑ᄦ㧘ਛ๋㧘᧻ᵏਃ㧦⚛❫ ⛽ࠪ࠻ߦࠃࠆ㍑᧼ᔕജߩૐਅߣߪߊ㔌ߖࠎᢿᔕജ㧘 ᧁቇળ⺰ᢥ㓸 No.689/I-57㧘pp.239-249㧘2001㧚 3) ㊁㒋స⟵㧘㊄ሶᄢᤓ㧘ฎᎹ༜ᦶ㧘㋈Ꮉ⎇ੑ㧘 㕏㧦 CFRP ᧼ធ⌕ᒝߦ߅ߡⵍ⌕ෘߐ߇ᒝലᨐߦ ਈ߃ࠆᓇ㗀ߦ㑐ߔࠆታ㛎⊛⎇ⓥ㧘㍑᭴ㅧ⺰ᢥ㓸㧘╙. 0.8 0.6 0.4. 0. 40. 80 (b) ld =100mm. ࿑㧙17 ᔅⷐធ⌕㐳ߐߣ᧼ෘ߇⸳⸘ߐࠇߚ CFRP ᧼߇ធ ⌕ߐࠇߚᢿ㕙ᰳ៊ࠍߔࠆ㍑᧼ߦ↢ߓࠆᔕജ. 10 Ꮞ ╙ 38 ภ㧘pp.61-68㧘2003㧚 4) ਛ৻ผ㧘⻉ᢘཅ㧘㋈ᧁඳਯ㧘೨↰⎇৻㧘ㇱቁ ᄦ㧦ṁធ⛮ᚻߦ⊒↢ߒߚ∋ഭ߈ⵚߩⓍጀ CFRP ᧼ߦ ࠃࠆୃലᨐ㧘㍑᭴ㅧᐕᰴ⺰ᢥႎ๔㓸㧘╙ 13 Ꮞ㧘 pp.89-96㧘2005㧚 5) ⍹Ꮉᢅਯ㧘ᄢୖ৻㇢㧘༑ᄙિ㧦❫⛽ࠪ࠻߇ᝌ ߐࠇߚ⚛❫⛽ࡊ࠻ធ⌕㍑᧼ߩߪߊ㔌ߖࠎᢿᔕ ജ㧘᭴ㅧᎿቇ⺰ᢥ㓸 Vol.52A㧘pp.1317-1326㧘2006㧚 6) ⑲ᾢ㧘ዊᨋ ᦶ㧘┙⍹᥏ᵗ㧘㐳ᱜ༹㧘ችਅ 㧦 CFRP ࠬ࠻ࡦ࠼ࠪ࠻ߦࠃࠆ㍑᧼ߩᒝലᨐߦ㑐 ߔࠆ⎇ⓥ㧘 ㍑᭴ㅧᐕᰴ⺰ᢥႎ๔㓸㧘Vol.17㧘pp.643-650㧘 2009㧚 7) ┙⍹᥏ᵗ㧘ዊᨋ ᦶ㧘ᮮ↰ ᒄ㧘ጤᵄశ㧘ട⮮⛗ ਁ㧦ᶏᵗⅣႺਅߦ߅ߌࠆ㍑᧼ߩ CFRP ࠬ࠻ࡦ࠼ࠪ ࠻ធ⌕ᒝലᨐߦ㑐ߔࠆᬌ⸛㧘╙ 3 ࿁ FRP ⶄว᭴ ㅧᯅߦ㑐ߔࠆࠪࡦࡐࠫ࠙ࡓ⺰ᢥ㓸㧘pp.85-90㧘2009㧚 8) Bocciarelli, M., Colombi, P., Fave, G. and Poggi, C.: Prediction of debonding strength of tensile steel/CFRP joints using fracture mechanics and stress based criteria, Engineering Fracture Mechanics, vol.76, pp.299-313, 2009.. - 919 -.
(10) 9) Miller, T. C., Chajes, M. J., Mertz, D. R. and Hastings, J. N.: Strengthening of a steel bridge girder using CFRP plates, Journal of Bridge Engineering, Vol.6, Issue 6, pp.514-522, 2001. 10) ᧼၂৻㧘ᷰㆺᙗᏒ㧘㋈ᧁඳਯ㧦⚛❫⛽ᒝൻ᮸⢽᧼ 㧔ࠞࡏࡦ᧼㧕ߦࠃࠆ㍑ᯅᒝߩ㧘╙ 8 ࿁㍑᭴ ㅧߩୃᒝᛛⴚႎ๔⺰ᢥ㓸㧘pp.49-54㧘2002㧚 11) Moy, S. S. J. and Bloodworth, A. G.: Strengthening a steel bridge with CFRP composites, Structures & Buildings, Vol.160, Issue SB2, pp.81-93, 2007. 12) ₹ብ┨㧘㜞᧻㓉ᄦ㧘ㇱ↢㧘Ἧ⼱ᓼᴦ㧘ᰞᐸ ⺈㧦. ⚛❫⛽ࡊ࠻ߦࠃࠆൻቇࡊࡦ࠻᨞᭴ዊ߫ࠅ ߩᣉᎿ㧘㍑᭴ㅧᐕᰴ⺰ᢥႎ๔㓸㧘╙ 13 Ꮞ㧘 pp.545-552㧘2005㧚 13) ᧖ᶆ ᳯ㧘ዊᨋ ᦶ㧘Ⓑ⪲ዏᢥ㧘ᧄ㑆ᷕผ㧘ᄢ၂⾐ᵤ 㓶㧘㐳ᱜ༹㧦㍑ㇱ᧚⣣㘩៊்ㇱߩ⚛❫⛽ࠪ࠻ ߦࠃࠆୃᛛⴚߦ㑐ߔࠆ⸳⸘ᣉᎿᴺߩឭ᩺㧘ᧁ ቇળ⺰ᢥ㓸 F㧘Vol.65㧘No.1㧘pp.106-118㧘2009㧚 14) ᣣᧄࠛࡓࠛࠬࠪ㧦MSC.MARC2005r3 ࠝࡦࠗࡦࡑ ࠾ࡘࠕ࡞㧘ᣣᧄࠛࡓࠛࠬࠪ㧘2005㧚 㧔2010 ᐕ 3 9 ᣣ ฃઃ㧕. - 920 -.
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