Received May 28, 2013/ revised June 17, 2013/ accepted July 16, 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵ǤͷǤͳͷ Ǥ ǤǤ
FRP ⯾ⴲ⭲#⊲ᇓ#㔖㘪Ὢ㡶#ኳ⢚㉲ⴖ#⬓㍓ሮᦗ
ࢽ০ ȵଲஂ ȵౖଠ
Cho, Baiksoon*, Lee, Jong-Han**, Choi, Eunsoo***
Axial Behavior of Concrete Cylinders Confined with FRP Wires
ABSTRACT
The application of FRP wire as a mean of improving strength and ductility capacity of concrete cylinders under axial compressive load through confinement is investigated experimentally in this study. An experimental investigation involves axial compressive test of three confining amounts of FRP wire and three concrete compressive strengths. The effectiveness of FRP wire confinement on the concrete microstructure were examined by evaluating the internal concrete damage using axial, circumferential, and volumetric strains. The axial stress strain relations of FRP wire confined concrete showed bilinear behavior with transition region. It showed strain-hardening behavior in the post-cracking region. The load carrying capacity was linearly increased with increasing of the amount of FRP wire. The ultimate strength of the 35 MPa specimen confined with 3 layer of FRP wire was increased by 286% compared to control one. When the concrete were effectively confined with FRP wire, horizontal cracks were formed by shearing. It was developed from sudden expansion of the concrete due to confinement ruptures at one side while the FRP wire was still working in hindering expansion of concrete at the other side of the crack. The FRP wire failure strains obtained from FRP wire confined concrete tests were 55 90%, average 69.5%, of the FRP wire ultimate uniaxial tensile strain. It was as high as any other FRP confined method. The magnitude of FRP wire failure strain was related to the FRP wire effectiveness.
Key words : FRP wire, Concrete confinement, Effective FRP wire failure strain, Effectiveness of confinement, Zero volumetric strain, Stress-hardening behavior
Ⅹಾ
⎹Ⓧญ✙Ŗℕ᮹ᦶ⇶vࠥ᪡ᩑᖒᖒ܆ᮥ⨆ᔢ┅ʑ᭥⦹ᩍFRP ᪡ᯕᨕ᮹ᱢᬊᮥᝅ⨹ᱢᮝಽᩑǍ⦹ᩡ݅. ᪡ᯕᨕᅕvĚᙹ᪡⎹Ⓧญ✙ᦶ
⇶vࠥ᮹ᄡ⪵aŁಅࡽ᪡ᯕᨕᅕvŖℕ᮹ᦶ⇶ᝅ⨹ᮥᝅ⦹ᩡ݅. FRP ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶࡽ⇶ႊ⨆ᄡ⩶ශ, ᬱᵝႊ⨆
ᄡ⩶ශ, ℕᱢᄡ⩶ශᨱ᮹⦽᪡ᯕᨕԕᇡ⎹Ⓧญ✙᮹ᗱᔢᔢ┽ෝᇥᕾ⦹ᩍ᪡ᯕᨕᅕv⬉ŝෝ⠪a⦹ᩡ݅. FRP ᪡ᯕᨕᅕvŖℕ᮹᮲ಆᄡ
⩶ශᖁࠥ۵ࢱ}᮹ḢᖁǍeŝᄡ⪹ǍeᮝಽǍᖒࡽäᮝಽ⊂ᱶࡹᨩᮝ໑, Ɂᩕᯕ⬥Ǎeᨱᕽ᮲ಆᔢÑ࠺⦹ᩡ݅. ᪡ᯕᨕᅕvŖℕ᮹Ɂ
ᩕvࠥ᪡↽ݡvࠥ۵᪡ᯕᨕᅕvĚᙹᨱእಡ⦹ᩍ᷾a⦹۵äᮝಽ⠪aࡹᨩ݅. ᪡ᯕᨕa3Ěᅕvࡽ35 MPa Ŗℕ᮹↽ݡvࠥ۵ྕᅕvŖ
ℕ᮹ᦶ⇶vࠥᅕ݅286% ׳í⊂ᱶࡹᨩ݅. FRP ᪡ᯕᨕᅕvŖℕ᮹ԕᇡ⎹Ⓧญ✙❭ƕ⩶┽۵i) ᙹḢɁᩕੱ۵ĞᔍɁᩕ❭ƕ; ii) ᙹ⠪Ɂ
ᩕ❭ƕಽǍᇥࡹᨩ݅. ✚⯩, ᙹ⠪Ɂᩕ❭ƕ۵᪡ᯕᨕᨱ᮹⦽Ǎᗮ᧞⪵ಽᯙ⦹ᩍrᯱʑԕᇡ⎹Ⓧญ✙a➞⦹۵ᇡᇥŝ᪡ᯕᨕaᦥḢԕᇡ⎹
Ⓧญ✙ෝ⬉ŝᱢᮝಽǍᗮ⦹۵ᇡᇥ᮹ᱥ݉⬉ŝಽၽᔾ⦹ᩡᮝ໑, ᙹ⠪ɁᩕᮡŖℕ᮹ᵲᦺᇡෝʑᵡᮝಽᩍ్໕ᮝಽၽᔾ⦹ᩡᮝ໑, ᪡ᯕᨕ ᨱ᮹⦽Ǎᗮ⬉ŝaᬑᙹ⦽Ŗℕᨱၽᔾ⦹ᩡ݅. FRP ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ᪡ᯕᨕ↽ݡ❭݉ᄡ⩶ශᨱݡ⦽ᯙᰆ❭݉ᄡ⩶ශ᮹እ a55-90%ಽ⊂ᱶࡹᨩᮝ໑, ⠪Ɂ69.5%ಽӹ┡ԍ݅. ᯕ۵ᯝၹFRP ✙ᅕvŖℕᝅ⨹ᨱᕽ⊂ᱶࡽ✙❭݉ᄡ⩶ශᅕ݅݅ᗭ׳ᮡsᮝ ಽFRP ᪡ᯕᨕᅕvŖჶ᮹ᬑᙹᖒᮥ᯦᷾⦽݅.
áᔪᨕ FRP ᪡ᯕᨕ, ᅕv⎹Ⓧญ✙Ŗℕ, FRP ᪡ᯕᨕ❭݉ᄡ⩶ශ, FRP ᪡ᯕᨕᅕv⬉ŝ, ᱽಽℕᱢᄡ⩶ශ, ᮲ಆᔢÑ࠺
ĵܓėॡ
(a) FRP Wire on a Frame (b) FRP Wire Around a Concrete Cylinder
(c) FRP Wire with Uniform Tensile Force
(d) Equipment to Maintain Uniform Tension Fig. 1. A Process of Introducing Uniform Tensile Force to FRP wire
1. ᕽು
↽ɝᨱᖍᮁv⪵ᅖ⧊ᰍഭ(fiber reinforced polymers, FRP)۵
ʑ᳕Õᖅᰍഭෝݡℕ⧁ᙹᯩ۵ᔩಽᬕᰍഭಽᯙࡹŁᯩᮝ໑,
⎹Ⓧญ✙Ǎ᳑ྜྷ᮹ᅕᙹੱ۵ᅕvᨱᦥᵝ⬉ŝᱢᯙᰍഭಽbŲၼ Łᯩ݅. ℁ɝ⎹Ⓧญ✙⮉ᇡᰍ᮹ᯙᰆ⊂ᨱFRPෝᇡ₊┉FRP ᮹⧕Ƚࡹᨩ݅(Bencardino et al., 2002; El-Refaie et al., 2003;
Brena et al., 2003). ə్ӹFRP᮹᳑ʑ┩ᨱ᮹⦽FRP ᅕv
⮉ᇡᰍ᮹ᩑᖒqᗭ۵FRP ᅕvႊჶ᮹ᱢᬊᮥᱽ⦽┉݅. ᳑႒ᙽ
॒(2010)ᮡ⎹Ⓧญ✙ᦶ⇶ᄡ⩶ශᯕ0.003ᨱࠥݍ⦹ʑᱥᨱFRPa
᳑ʑ┩⦹໕, FRP ᅕv⮉ᇡᰍ᮹Ŗ⋎⮉༉ູ✙ᔑᱶᨱvࠥᖅĥ ჶᮥᱢᬊ⦹۵äᮡྕญaᯩᮥᙹᯩ݅ŁᅕŁ⦹ᩡ݅. FRP ᅕv
⮉ᇡᰍ᪡۵ݍญ, ⎹Ⓧญ✙ᦶ⇶ᇡᰍ᮹ᇡᨱFRPෝᇡ₊┉
FRP ᅕvᦶ⇶ᇡᰍ۵vࠥ, ᩑᖒ, ᄡ⩶ශᱡ⧎ᖒ܆ᯕ༉ࢱⓍí
⨆ᔢࡹ۵äᮝಽᅕŁࡹᨩ݅(Demers and Naela 1999; Chaallal et al. 2003; Bisby et al. 2005; Matthys et al. 2005).
⎹Ⓧญ✙ᦶ⇶ᇡᰍෝࢹ్FRP۵ԕᇡ⎹Ⓧญ✙᮹➞ᮥ
Ǎᗮ⦹ᩍᦶ⇶ᇡᰍ᮹ᖒ܆ᮥ⨆ᔢ┉݅. ԏᮡᦶ⇶ᬦಆᯕ᯲ᬊࡹ
ᨕԕᇡ⎹Ⓧญ✙᮹⇶ႊ⨆ᄡ⩶ශᯕԏᮡ݉ĥᨱᕽ۵ᬱᵝႊ⨆
ᄡ⩶ශ(FRPᨱ۵ᯙᰆᄡ⩶ශ)ᮡๅᬑԏᮡᔢ┽ᯕ݅. ᯕ݉ĥᨱᕽ ۵FRPᨱ᮹⦽ԕᇡ⎹Ⓧญ✙᮹ǍᗮಆᯕๅᬑԏᦥFRP ᅕv
ᦶ⇶ᇡᰍ᮹ᖒ܆ᮡÑ᮹⨆ᔢࡹḡᦫ۵݅. ԕᇡ⎹Ⓧญ✙᮹᮲ಆᯕ
⎹Ⓧญ✙᮹ᦶ⇶vࠥᨱɝᱲ⦹໕, ԕᇡ⎹Ⓧญ✙ᨱɁᩕᯕၽᔾࡹ
໑➞⦽݅. FRP۵ԕᇡ⎹Ⓧญ✙᮹➞ᮥᱽᨕ⦹۵ᙹ࠺ᱢᯙ
ᩎ⧁(passive action)ᮥ⦹໑, FRP ᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍ᮹᮲ಆ
ᄡ⩶ශÑ࠺ᮡFRPᨱ᮹⦽⬂ႊ⨆Ǎᗮಆᨱⓑᩢ⨆ᮥၼ۵݅.
FRPᨱ ᮹⦽ Ǎᗮ⬉ŝ۵ FRP ᳦ඹ, FRP ᧲, ⎹Ⓧญ✙᪡ FRP ᔍᯕ᮹ᱲ₊ಆ, FRP ℕđႊჶ॒FRP ᅕvᜅ▽ᨱ᮹⧕đᱶࡽ݅.
FRP Ǎᗮ⬉ŝ۵FRP ᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍᝅ⨹ᨱᕽ⊂ᱶࡽ
FRP ❭݉ᄡ⩶ශ᮹ Ⓧʑ᪡ ʕၡ⦽ šĥa ᯩ݅.
FRPᨱ᮹⦽ԕᇡ⎹Ⓧญ✙᮹➞ᱽᨕ᯲ᬊᮡ⎹Ⓧญ✙᪡FRP ᮹᪥ᄞ⦽ᇡ₊ᨱᕽ᯲ࡽ݅. Harries and Carey(2003)۵⎹Ⓧญ
✙ᦶ⇶ᇡᰍ᪡FRP ᔍᯕ᮹᪥ᄞ⦹ḡ༜⦽ᇡ₊ᮡFRPᨱ᮹⦽
Ǎᗮ⬉ŝෝḡᩑ⍽FRP ᅕvᦶ⇶ᇡᰍ᮹ᖒ܆ᨱᩢ⨆ᮥၙ⊹۵
äᮥᝅ⨹ᮝಽȽ⦹ᩡ݅. ⎹Ⓧญ✙᪡ᅕvᰍ᮹᪥ᄞ⦽ᇡ₊ᮥ
᭥⦹ᩍ⥥ญᜅ✙౩ᜅෝ᯦ࠥ⦹۵ႊჶᯕᱽᦩࡹᨩ݅. Xiao and Ma(1997)ᮡFRP ᇡᨱᄉ✙ෝᯕᬊ⦹ᩍFRP ᅕvᦶ⇶ᇡᰍᨱ
⥥ญᜅ✙౩ᜅෝ᯦ࠥ⦹۵ႊჶᮥᱽᦩ⦹ᩡŁ, ↽ɝᨱ۵Choi et al.(2009, 2010)ᮡvᰍᇡᨱᦶಆᮥa⦹ᩍvᰍᅕvᦶ⇶ᇡᰍ ᨱ ⥥ญᜅ✙౩ᜅෝ ᯦ࠥ⦹۵ ႊჶᮥ ᱽᦩ⦹ᩡ݅. Harries and Kharel(2002)ŝHarries and Carey(2003)ᮡ⎹Ⓧญ✙᪡ᅕvᰍ
ᯙvᰍੱ۵FRP ᔍᯕ᮹✩᮹᪥ᄞ⦽⧕đ᮹ᨕಅᬡᮥᇡb⎑݅.
ᯕᩑǍ۵⥥ญᜅ✙౩ᜅෝ᯦ࠥ⦽᪡ᯕᨕ⩶┽(wire type)᮹
FRPෝ⎹Ⓧญ✙ᦶ⇶ᇡᰍᨱᇡ₊⍽ԕᇡ⎹Ⓧญ✙᮹Ǎᗮ⬉ŝ
ෝɚݡ⪵⦹۵FRP ᪡ᯕᨕᅕvᦶ⇶ᇡᰍ᮹ᩎ⦺ᱢ✚ᖒᮥŁₑ⦹
ᩡ݅. ᯕෝ᭥⦹ᩍFRP ᪡ᯕᨕᅕvĚᙹ, FRP ᪡ᯕᨕᅕvႊჶ, FRP᪡ᯕᨕᱲ₊ႊჶ, əญŁ⎹Ⓧญ✙ᦶ⇶vࠥaŁಅࡽℕĥᱢ ᯙFRP ᪡ᯕᨕᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍ᮹ᦶ⇶ᝅ⨹ᮥᝅ⦹ᩡ݅.
FRP ᪡ᯕᨕᅕvᦶ⇶ᇡᰍ᮹ᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶ⦽᮲ಆ⇶ႊ⨆
ᄡ⩶ශᖁࠥ, ᮲ಆ⾈ᬱᵝႊ⨆ᄡ⩶ශᖁࠥ, ℕᱢᄡ⩶ශ, ℕᱢᄡ⩶
ශ⇶ႊ⨆ᄡ⩶ශᖁࠥ, Ɂᩕvࠥ, ↽ݡvࠥ, ↽ݡvࠥࠥݍᄡ⩶
ශ, ᱽಽℕᱢᄡ⩶ශ, FRP ᪡ᯕᨕ❭݉ᄡ⩶ශ॒ᮥᇥᕾ⦹ᩍ⎹Ⓧ
ญ✙ ᦶ⇶ᇡᰍᨱ ݡ⦽ FRP ᪡ᯕᨕ ᅕvႊჶ᮹ ᱢᬊ ┡ݚᖒᮥ
ᔕ⠕ᅕᦹ݅. ᯕםྙᨱᕽᩑǍࡽFRP ᪡ᯕᨕಽᅕvࡽᦶ⇶ᇡᰍ᮹
ᦶ⇶ᝅ⨹đŝ۵ʑ᳕⎹Ⓧญ✙ᦶ⇶ᇡᰍᨱݡ⦽ᅕvႊჶᮝಽ
FRP ᪡ᯕᨕᅕvႊჶᮥᱢᬊ⧁ᙹᯩ۵ʑᚁᱢ႑ĞᮥᱽŖ⧁
äᮝಽ ❱݉ࡽ݅.
2. FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕᱽ᯲ŝᦶ⇶ᝅ⨹
2.1 FRP ଲઘ࣪Գࠤൈվਏ఼୪ୁ
FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍ᮹ᦶ⇶ᖒ܆ᮥŁₑ⦹ʑ
᭥⦹ᩍḡ150 mm, ׳ᯕ300 mmᯙ⎹Ⓧญ✙ᬱᵝ⩶Ŗℕ᮹
ᇡᨱFRP ᪡ᯕᨕaqʕFRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕෝ
ᱽ᯲⦹ᩡ݅. ᯕᩑǍᨱᔍᬊࡽ᪡ᯕᨕ۵ḡ1.0 mmᯙᮁญᖍᮁ
FRPᯕ݅. FRP ᪡ᯕᨕ᮹ᯙᰆvࠥ۵1230.6 MPa, ❭݉ᄡ⩶ශᮡ
0.0294, ┥ᖒĥᙹ۵41.84 GPaᯕ݅. Fig. 1(a)۵✡ᨱqĉᯩ۵
(a) Start of Coiling FRP Wire (b) Middle of Coiling FRP Wire
(c) End of Coiling FRP Wire (d) Concrete Specimen Confined with FRP Wire Fig. 2. A View of Coiling FRP Wire Around a Concrete Cylinder
(a) 1-Layer Confinement (b) 2-Layer Confinement (c) 3-Layer Confinement Fig. 3. Concrete Cylinders Confined with FRP Wire
Table 1. Summary of Experimental Specimens
Layers of FRP wire Compressive strength of concrete (MPa)
35 45 55
0 3 3 3
1 2 2 2
2 2 2 2
3 2 2 2
FRP ᪡ᯕᨕᔍḥᯕ݅. Fig. 1(b)۵✚ᄥ⯩ᱽ᯲ࡽ᪡ᯕᨕq۵
ʑǍෝᯕᬊ⦹ᩍᯝᱶ⦽eĊᮥᮁḡ⦹໑FRP ᪡ᯕᨕෝ⎹Ⓧญ✙
Ŗℕᨱ q۵ ŲĞᯕ݅. ᯕ ݉ĥᨱᕽ ᱲ₊ᱽ۵ ᦥḢ ࠥ⡍ࡹḡ
ᦫᦹ݅. Ŗℕᨱ ᪡ᯕᨕෝ qᮥ ভ ᜅ⥥ยᮝಽ Ǎᖒࡽ ʑǍෝ
ᯕᬊ⦹໕᪡ᯕᨕᨱᯝᱶ⦽ᯙᰆಆᮥᮁḡ⎑݅(Fig. 1(c) ₙ᳑).
Fig. 1(d)۵᪡ᯕᨕᨱᯝᱶ⦽ᯙᰆಆᮥᮁḡ┅۵ʑǍ᮹ᔍḥᯕ
݅. ᯕᩑǍᨱᕽ۵᪡ᯕᨕᨱᯙᰆಆ25 Nᮥ᯲ᬊ⎑ᮝ໑, ᪡ᯕᨕᨱ
᯲ᬊࡽᯙᰆ᮲ಆᮡ31.83 MPaᯕ໑, ᄡ⩶ශᮡ0.000773ᯕ݅. ᯙᰆ ᮲ಆ31.83 MPaᮡŖℕᨱǍᗮಆᮡ᯲ᬊ┅ʑḡᦫᮝ໑, Ŗ
ℕ᪡ ᪡ᯕᨕෝ ✩ᯕ ᨧᯕ qʑí ⦹۵ ∊ᇥ⦽ ᦶಆᯕ݅. ੱ⦽, FRP᪡ᯕᨕෝqᮥভ᪡ᯕᨕᵲᝍeÑญෝ1 mmಽ⦹ᩍ᪡ᯕᨕ
᪡᪡ᯕᨕᔍᯕ✩ᯕᨧí᪡ᯕᨕෝŖℕᨱᇡ₊⦹ᩡ݅. ᪡ᯕᨕෝ
q۵࠺ᦩ᪡ᯕᨕ᮹⣡ฝᮥႊḡ⦹ʑ᭥⦹ᩍ᪡ᯕᨕ᮹Ҿᇡᇥᨱ
✚ᙹᱲ₊ᱽෝၽŖℕᨱᇡ₊⎑݅. Ŗℕᨱ᪡ᯕᨕෝq۵
mmෝᱽ⦽ᱥǍe280 mmᨱᇡ₊⦹ᩍ᪡ᯕᨕᅕv⨹ℕ᮹
Ҿᇡᇥ⬉ŝ(end effect)ෝᱽÑ⦹ᩡ݅. ᪡ᯕᨕq۵᯲ᨦᯕҾӹ໕
᪡ᯕᨕ᧲Ҿᇡᇥᨱᱲ₊ᱽෝࠥ⡍⦹ᩍ᪡ᯕᨕෝŖℕᨱᱶ₊
⎑݅. ᱽᦩࡽ ᪡ᯕᨕ ᅕv᯲ᨦᮡ Ě⊖ᮝಽ Ŗ a܆⦹໑, Fig.
3ᮡ Ŗℕᨱ ᪡ᯕᨕa 1ⴇ3Ě ᇡ₊ࡽ ᔍḥᯕ݅.
⎹Ⓧญ✙Ŗℕᨱݡ⦽FRP ᪡ᯕᨕ᮹ᅕv⬉ŝෝŁₑ⦹ʑ
᭥⦹ᩍᖙ᳦ඹ᮹⎹Ⓧญ✙ᦶ⇶vࠥ(35, 45, 55 MPa) əญŁ
ᖙ᳦ඹ᮹᪡ᯕᨕᅕvĚᙹ(1, 2, 3Ě)ᮥᖁ┾⦹ᩡ݅. ྕᅕvʑᵡ
Ŗℕ۵bb3}ᦊ, ᅕvŖℕ۵bb2}ᦊ, ⧊ĥ27}FRP
᪡ᯕᨕᅕvŖℕᨱݡ⦽ᦶ⇶ᝅ⨹ᮥᝅ⦹ᩡ݅. FRP ᪡ᯕᨕ
ᅕv Ŗℕ ᝅ⨹ᯝ௭⢽ෝ Table 1ᨱ ӹ┡ԕᨩ݅.
2.2 ਓࢺ࣑
2,000 kN ᬊప᮹ ᰍഭ⨹ʑෝ ᔍᬊ⦹ᩍ FRP ᪡ᯕᨕ ᅕv
Fig. 4. An Axial Compressive Test of a Concrete Cylinder Confined with FRP Wire
(a) 35 MPa
(b) 45 MPa
(c) 55 MPa
Fig. 5. Circumferential and Axial Stress-Strain Curves of Concrete Confined with FRP Wire
ᔍᯕᨱḡ150 mm, ׳ᯕ300 mmᯙŖℕෝᖅ⊹⦹ᩍᦶ⇶ಆᮥ
᯲ᬊ⎑݅. ⦹ᵲaಆᮡᰍഭ⨹ʑ᮹ᄡ᭥ĥෝ2.0 mm/min.᮹
ᗮࠥಽŖℕa❭ƕࢁভʭḡaಆ⦹ᩡ݅. aᦶ❱ŝaᦶ❱ᔍᯕ ᨱ 3}᮹ ᄡ᭥ĥ(LVDT)ෝ 120o eĊᮝಽ ᖅ⊹⦹ᩍ Ŗℕ᮹
⇶ႊ⨆ᄡ᭥ෝ⊂ᱶ⦹ᩡ݅. 3}᮹ᄡ᭥ĥᨱᕽ⊂ᱶࡽᄡ᭥᮹⠪Ɂ sᮥŖℕ᮹⇶ႊ⨆ᄡ᭥ಽᔍᬊ⦹ᩡ݅. ੱ⦽, ⊂ᱶʙᯕa200 mmᯙᯖᜅ▱ᗭၙ░(extensometer)ෝŖℕ᮹ᵲᦺᨱᖅ⊹⦹ᩍ
⇶ႊ⨆ᄡ᭥ෝ⊂ᱶ⦹ᩡ݅. FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹
ᬱᵝႊ⨆ᄡ⩶ශŝŖℕ᮹⬂ႊ⨆ᮝಽᇡ₊ࡽ᪡ᯕᨕ᮹ᯙᰆᄡ⩶
ශᮥ⊂ᱶ⦹ʑ᭥⦹ᩍℕᯙ⩶┽ಽ✚ᙹᱽ᯲ࡽᬱᵝႊ⨆ᄡ᭥⊂ᱶ ʑෝᔍᬊ⦹ᩡ݅. Fig. 4۵Ŗℕ᮹⇶ႊ⨆ᄡ᭥ĥ᪡ᬱᵝႊ⨆
ᄡ᭥⊂ᱶʑaᖅ⊹ࡽFRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹ᦶ⇶ᝅ
⨹ŲĞ ᔍḥᯕ݅.
3. FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕᦶ⇶ᝅ⨹đŝၰם᮹
3.1 ଦߚƇ࣡෴ࠔটܑ
FRP᪡ᯕᨕᅕvŖℕ᪡ྕᅕvŖℕ᮹ᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶ
⦽ ᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශ
Þ Ƅ
Ɓà Ļ
ſß
ᖁࠥ᪡ ᮲ಆ⾈ᬱᵝႊ⨆ᄡ⩶ශÞ Ƅ
Ɓà Ļ
Ɓß
ᖁࠥෝFig. 5ᨱࠥ⦹ᩡ݅. ⇶ႊ⨆ᄡ⩶ශĻ
ſ۵ᦶ⇶ᮥӹ┡ԕ໑, ᬱᵝႊ⨆ᄡ⩶ශ
Ļ
Ɓᮡᯙᰆᮥӹ┡ԙ݅. ⇶ႊ⨆ᄡ⩶ශᮡɁᩕvࠥࠥݍᯕᱥǍeᨱ۵ᯖᜅ▱ᗭၙ░(extensometer)ᨱᕽ⊂
ᱶࡽ ᄡ᭥ෝ ᔍᬊ⦹ᩡᮝ໑, Ɂᩕvࠥ ᯕ⬥Ǎeᨱᕽ۵ ᄡ᭥í (LVDT)ᨱᕽ⊂ᱶࡽᄡ᭥ෝᔍᬊ⦹ᩡ݅. ᬱᵝႊ⨆ᄡ⩶ශᮡℕᯙ
⩶┽ಽ✚ᙹᱽ᯲ࡽᬱᵝႊ⨆ᄡ᭥⊂ᱶʑᨱᕽ⊂ᱶࡽᄡ᭥ෝᔍᬊ
⦹ᩡ݅. əฝ᮹(a), (b), (c)۵bb⎹Ⓧญ✙ᦶ⇶vࠥa35, 45,
55 MPaᯙ ᪡ᯕᨕ ᅕv Ŗℕ᮹ ᝅ⨹đŝᯕ݅.
ྕᅕvŖℕ᮹᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ۵ᯝၹ⎹Ⓧญ✙᪡
zᯕᦶ⇶vࠥࠥݍ⬥᮲ಆᯕqᗭ⦹۵᮲ಆqᗭÑ࠺(stress-softening behavior)ᮥ⦹ᩡ݅. ᯕ᪡۵ݍญ᪡ᯕᨕᅕvŖℕ᮹᮲ಆ⾈⇶
ႊ⨆ᄡ⩶ශᖁࠥ۵Ɂᩕvࠥ
Ƅ
ƍ ࠥݍ⬥, ❭ƕᨱࠥݍ⧁ভʭḡTable 2. Results of Axial Compressive Tests on the Specimens
Compressive
Strength (MPa) Layers Ƅ
ƍ*
(MPa) Ļ
ƍ** Ƅ
ƁƁ(MPa) Ļ
ƓſĻ
ſƔƍĻ
ƓƁĻ
Ɠ Ɣć Ƅ
ƁƍƄ
ƁƁ35
0 36.09 0.002322 0.004465 0.002570 -0.009340 -0.015130 1 48.84 0.003002 73.53 0.029286 0.003002 -0.025727 -0.022169 2.037 2 57.12 0.004112 113.15 0.044152 0.004112 -0.022912 -0.001671 3.135 3 64.20 0.005458 139.37 0.052957 0.005458 -0.021549 0.009859 3.861
45
0 47.16 0.002514 0.003713 0.002427 -0.015158 -0.026602 1 56.32 0.002716 74.82 0.026811 0.002716 -0.021636 -0.016461 1.586 2 64.28 0.003411 107.85 0.031822 0.003411 -0.019341 -0.006861 2.287 3 74.78 0.005333 144.69 0.047519 0.005333 -0.021024 0.005470 3.068
55
0 57.10 0.002288 0.003106 0.002421 -0.011926 -0.020746 1 67.69 0.002634 78.81 0.024524 0.002634 -0.022978 -0.021431 1.380 2 79.34 0.003630 109.98 0.024167 0.003630 -0.017625 -0.011083 1.926 3 88.63 0.004019 144.52 0.027732 0.004019 -0.017544 -0.007355 2.531 * Average of three test results for the non-confined specimen and that of two test results for the confined specimen
** Positive(+) value indicates compression and negative(-) value tension
᮲ಆᮡḡᗮᱢᮝಽ᷾a⦹ᩍ᮲ಆᔢÑ࠺(stress-hardening behavior)ᮥ ⦹ᩡ݅. ᪡ᯕᨕᅕvŖℕ᮹᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ۵Ɂᩕ
vࠥෝʑᵡᮝಽࢱ}᮹ḢᖁǍeᮝಽǍᖒࡽäᮝಽᅝᙹᯩ݅.
Ɂᩕvࠥࠥݍ⬥᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ᮹ʑᬙʑqᗭ۵᪡ᯕ ᨕಽࢹ్ᯙԕᇡ⎹Ⓧญ✙Ɂᩕಽ⇶vᖒᯕqᗭ⦹ᩡʑভྙᯕ
݅. ℌṙḢᖁǍeᯙɁᩕᯕᱥǍeᨱᕽྕᅕvŖℕ᪡᪡ᯕᨕ
ᅕvŖℕ᮹ʑᬙʑ۵Ñ᮹zᮡäᮝಽӹ┡ӹ᪡ᯕᨕ۵Ŗℕ ᮹⇶vᖒᨱⓑᩢ⨆ᮥၙ⊹ḡᦫ۵äᮝಽ⠪aࡽ݅. ə్ӹ᪡ᯕᨕ
ᅕvĚᙹa᷾a⧁ᙹಾ᪡ᯕᨕᅕvŖℕ᮹Ɂᩕvࠥ۵᷾aࡹ
ᨕ᪡ᯕᨕ۵Ŗℕ᮹Ɂᩕvࠥᨱᩢ⨆ᮥၙ⊹۵äᮝಽ⠪aࡽ݅.
ࢱჩṙḢᖁǍeᯙɁᩕᯕ⬥Ǎeᨱᕽ᪡ᯕᨕᅕvŖℕ۵᪡ᯕ ᨕᨱ᮹⦽ԕᇡ⎹Ⓧญ✙Ǎᗮᮝಽ❭ƕᨱࠥݍ⧁ভʭḡᄡ⩶ශ
᷾aᨱݡ⧕᮲ಆᮡḡᗮᱢᮝಽ᷾a⦹ᩡᮝ໑, ᅕvĚᙹa᷾a⧁
ᙹಾ⇶vᖒࠥ᷾a⦹ᩡ݅. ᪡ᯕᨕᅕvŖℕ᮹❭ƕ⇶ႊ⨆ᄡ⩶
ශᮡ᪡ᯕᨕᅕvĚᙹaฯᮥᙹಾəญŁ/ੱ۵⎹Ⓧญ✙ᦶ⇶vࠥ
aԏᮥᙹಾ׳í⊂ᱶࡹᨩ݅. ᪡ᯕᨕ3Ěᯕᅕvࡽ35 MPa Ŗℕ ᨱᕽ⊂ᱶࡽ❭ƕ⇶ႊ⨆ᄡ⩶ශᮡ0.055ಽ⊂ᱶࡹᨕྕᅕvŖℕ ᮹❭ƕ⇶ႊ⨆ᄡ⩶ශᅕ݅10႑ᯕᔢⓑäᮝಽ⠪aࡹᨩ݅. FRP
᪡ᯕᨕ۵⎹Ⓧญ✙ෝǍᗮ⍽Ŗℕ᮹⦹ᵲᱡ⧎ᖒ܆ŝᄡ⩶ᱡ⧎
ᖒ܆ᯕⓍí⨆ᔢ⎑ᮝ໑, ✚⯩ᨱթḡ⯂ᙹᖒ܆ᮥๅᬑⓍí
⨆ᔢ⎑݅. ᯕǍeᨱᕽ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹ᖒ܆ᮡ
Ñ᮹᪡ᯕᨕᨱ᮹⧕đᱶࡹ໑, ᪡ᯕᨕᨱ᮹⦽ᅕv⬉ŝa┢ᬵ⦹í
Ǎ⩥ࡹᨩ݅.
᮲ಆ⾈ᬱᵝႊ⨆ᄡ⩶ශᖁࠥ۵᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ᪡ษ
₍aḡಽɁᩕvࠥෝʑᵡᮝಽ2}᮹ḢᖁǍeᮝಽǍᖒࡽäᮝಽ
⠪a⧁ᙹᯩ݅. ɁᩕᯕᱥǍeᨱᕽ۵࠺ᯝ⦽᮲ಆᙹᵡᨱᕽᬱᵝႊ
⨆ᄡ⩶ශᮡ ⇶ႊ⨆ᄡ⩶ශᅕ݅ ᯲í ⊂ᱶࡹᨩ݅. ᯕ۵ ᪡ᯕᨕಽ
ࢹ్ᯙԕᇡ⎹Ⓧญ✙۵Ñ᮹➞⦹ḡᦫᮡᔢ┽ᯕ໑, ⇶ႊ⨆ᄡ
⩶ශŝᬱᵝႊ⨆ᄡ⩶ශᮡ⡍ᦥᘂእ᪡šĥaᯩʑভྙᯕ݅. Ɂᩕ
ᯕ⬥Ǎeᨱᕽ۵ԕᇡ⎹Ⓧญ✙ᨱɁᩕᯕၽᔾࡹŁ➞ࡹᨕᬱᵝ
ႊ⨆ᄡ⩶ශ᮹᷾aᗮࠥ۵᷾a⦹ᩡ݅. ⎹Ⓧญ✙ᦶ⇶vࠥa᯲ᮡ
᪡ᯕᨕᅕvŖℕ᮹ᬱᵝႊ⨆ᄡ⩶ශᮡ⇶ႊ⨆ᄡ⩶ශᅕ݅᷾aᗮ
ࠥa ᯲ᮡ äᮝಽ ⊂ᱶࡹᨩ݅. ə్ӹ ⎹Ⓧญ✙ ᦶ⇶vࠥa ⓑ
55 MPa ᪡ᯕᨕᅕvŖℕ᮹ᬱᵝႊ⨆ᄡ⩶ශŝ⇶ႊ⨆ᄡ⩶ශ᮹
᷾aᗮࠥ۵ Ñ᮹ እ⦽ äᮝಽ ⊂ᱶࡹᨩ݅. FRP ᪡ᯕᨕ ᅕv
Ŗℕ᮹ᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶࡽ↽ݡᬱᵝႊ⨆ᄡ⩶ශ
Ļ
ƓƁ۵ᅕvĚ ᙹəญŁŖℕ⎹Ⓧญ✙ᦶ⇶vࠥᨱšĥᨧᯕ᧞0.02 ᱶࠥಽ⊂ᱶࡹᨩ݅. Mirmiran and Shahawy(1997), Spoelstra and Monti(1999), Moran and Pantelides(2002)۵FRP ᅕv⎹Ⓧญ✙
ᦶ⇶ᇡᰍ᮹᮲ಆ⾈ᄡ⩶ශᖁࠥᨱᕽᬱᵝႊ⨆ᄡ⩶ශ᮹ᵲᖒᮥ
ḡᱢ⦹ᩡ݅.
Table 2ᨱFRP ᪡ᯕᨕᅕvŖℕᝅ⨹ᨱᕽ⊂ᱶ⦽Ɂᩕvࠥ
, Ɂᩕvࠥ ࠥݍ ⇶ႊ⨆ᄡ⩶ශĻ
,↽ݡvࠥ
᪡ ↽ݡvࠥࠥݍ⇶ႊ⨆ᄡ⩶ශ
Ļ
ෝᱶญ⦹ᩡ݅. Ɂᩕvࠥ۵ԕᇡ⎹Ⓧญ✙᮹Ɂᩕၽᔾᮝಽ᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ᮹ʑᬙʑaɪᄡ⧁ভ᮹
᮲ಆᯕ໑, ↽ݡvࠥ۵ᝅ⨹ᨱᕽ ⊂ᱶࡽ↽ݡ᮲ಆᯕ݅. Fig. 6ᨱ
᪡ᯕᨕᅕvŖℕ᮹Ɂᩕvࠥ᪡᪡ᯕᨕᅕvĚᙹ᮹šĥෝࠥ
⦹ᩡ݅. bᖁॅᮡᕽಽ݅ෙ⎹Ⓧญ✙ᦶ⇶vࠥᨱݡ⦽Ɂᩕ⦹ᵲᮥ
Ḣᖁ⫭ȡᇥᕾ⦽đŝᯕ݅. ᦶ⇶vࠥ55 MPaᯙŖℕ᮹ʑᬙʑa
ᱽᯝⓍŁ, ݅ᮭᮝಽᦶ⇶vࠥ35 MPaᯙŖℕ, ษḡสᮝಽᦶ⇶
Fig. 6. Peak Strength of Concrete with an Increase in the Layer of FRP Wire
Fig. 7. Ultimate Strength of Concrete with an Increase in the Layer of FRP Wire
vࠥ45 MPaᯙŖℕᩡᮝӹ, ə₉ᯕ۵Ⓧḡᦫᮡäᮝಽӹ┡ԍ
݅. ᕽ᪡ᯕᨕᅕvŖℕ᮹Ɂᩕ⦹ᵲᮡŖℕ᮹⎹Ⓧญ✙
ᦶ⇶vࠥ᪡šĥᨧᯕ᪡ᯕᨕᅕvĚᙹᨱእಡ⦹ᩍ᷾a⦹۵äᮝ ಽ⠪aࡽ݅. ᪡ᯕᨕa3Ěᅕvࡽ35 MPa Ŗℕ᮹Ɂᩕvࠥ۵
ྕᅕvŖℕ᮹Ɂᩕvࠥᅕ݅78% ׳í⊂ᱶࡹᨩ݅. ࠺ᯝ⦽ᅕv Ěᙹᨱ ݡ⦽ 45 MPa Ŗℕ᮹ Ɂᩕvࠥ ᷾ḥ⬉ŝ۵ ᧞ 59%, 55 MPa Ŗℕ᮹Ɂᩕvࠥ᷾ḥ⬉ŝ۵᧞55%ಽ⊂ᱶࡹᨩ݅.
ᕽ᪡ᯕᨕᅕvŖℕ᮹Ɂᩕvࠥ۵ᅕvᰍᯙ᪡ᯕᨕᅕvĚ ᙹᨱእಡ⦹ᩍ᷾a⦹۵äᮝಽ⊂ᱶࡹᨩᮝ໑, ᪡ᯕᨕ᮹ᅕv⬉ŝ ۵ᦶ⇶vࠥaԏᮡŖℕᨱݡ⧕ᬒᬑᙹ⦽äᮝಽӹ┡ԍ݅.
ᯕ۵Ǎᗮಆᯕ࠺ᯝ⦹í᯲ᬊࡹᨩᮝӹᦶ⇶vࠥaԏᮡŖℕᨱ
᯲ᬊࡽǍᗮಆᯕᔢݡᱢᮝಽⓍí᯲ᬊࡹᨩʑভྙᯙäᮝಽ❱݉
ࡽ݅.
Fig. 7ᨱ᪡ᯕᨕᅕvŖℕ᮹↽ݡvࠥ᪡ᅕvĚᙹ᮹šĥෝ
ࠥ⦹ᩡᮝ໑, Ḣᖁ⫭ȡᇥᕾ⦽đŝࠥ⧉̹ࠥ⦹ᩡ݅. 3 ᖁᯕ
Ñ᮹࠺ᯝᖁᔢᨱᯩ۵äᮝಽӹ┡ӹ᪡ᯕᨕᅕvŖℕ᮹↽ݡv
ࠥ۵⎹Ⓧญ✙ᦶ⇶vࠥ᪡šĥᨧᯕÑ᮹࠺ᯝ⦹໑, ᅕvĚᙹᨱ
እಡ⦹۵äᮝಽ⠪aࡽ݅. ᪡ᯕᨕa3Ěᅕvࡽ35 MPa Ŗℕ᮹
↽ݡvࠥ۵ྕᅕvŖℕ᮹ᦶ⇶vࠥᅕ݅286% ׳í⊂ᱶࡹᨩ݅.
࠺ᯝ⦽ᅕvĚᙹᨱݡ⦽45 MPa Ŗℕ᮹↽ݡvࠥ᷾ḥ⬉ŝ۵
᧞207%, 55 MPa Ŗℕ᮹↽ݡvࠥ᷾ḥ⬉ŝ۵᧞153%ಽ
⊂ᱶࡹᨩ݅. ࠺ᯝ⦽᪡ᯕᨕᅕvĚᙹᨱݡ⦽45 MPa Ŗℕ᮹
↽ݡvࠥ᷾ḥ⬉ŝ۵᧞207%, 55 MPa Ŗℕ᮹↽ݡvࠥ᷾ḥ⬉
ŝ۵ ᧞ 153%ಽ ӹ┡ԍ݅.
3.2 ఼ୡ࣡෴ࠔ Ļ Ɣ
ℕᱢᄡ⩶ශ
Ļ
Ɣ۵FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕᝅ⨹ᨱᕽ⊂ᱶࡽ⇶ႊ⨆ᄡ⩶ශ
Ļ
ſ᪡ᬱᵝႊ⨆ᄡ⩶ශĻ
Ɓ᮹2႑᮹⧊ᮝಽᱶ᮹ࡽ݅(Pantelides and Yan 2007; Saen and Pantelides 2007).
ℕᱢᄡ⩶ශ
Ļ
Ɣෝ⇶ႊ⨆ᄡ⩶ශĻ
ſ᪡ᬱᵝႊ⨆ᄡ⩶ශĻ
Ɓ᮹šĥᮝ ಽ ӹ┡ԕ໕, ݅ᮭŝ z݅.Ļ
Ɣá Ļ
ſâÏĻ
Ɓ (1)ᩍʑᕽ
Ļ
ſ᪡Ļ
Ɓᮡᦶ⇶ᯕ໕᧲ᯕŁ, ᯙᰆᯕ໕ᮭᯕ݅. (1)᮹Ļ
Ɣa᧲ᯕ໕FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹ℕᱢᮡᙹ⇶ᮥ᮹ၙ⦹໑, ᮭᯕ໕ ➞ᮥ ᮹ၙ⦽݅. ྕᅕv ⎹Ⓧญ✙ Ŗℕ᪡
᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹ᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶ⦽ℕᱢᄡ⩶ශ
Ļ
Ɣ᪡ ⇶ႊ⨆ᄡ⩶ශĻ
ſෝ Fig. 8ᨱ እƱ⦹ᩡ݅. əฝ᮹ (a), (b), (c)۵bb⎹Ⓧญ✙ᦶ⇶vࠥa35, 45, 55 MPaᯙ᪡ᯕᨕᅕvŖℕ᮹ ᝅ⨹đŝᯕ݅.
ℕᱢᄡ⩶ශ⾈⇶ႊ⨆ᄡ⩶ශ
Þ Ļ
Ɣà Ļ
ſß
ᖁࠥ᮹ⅩʑǍeᨱᕽྕᅕ vŖℕ᪡FRP ᪡ᯕᨕᅕvŖℕ۵ᦶ⇶ಆᮥၼᦥᙹ⇶⦹໑, ℕᱢᄡ⩶ශᮡ᧲ᮝಽӹ┡ԍ݅. ᯕǍeᨱᕽℕᱢᄡ⩶ශŝ⇶ႊ⨆ᄡ⩶ශ᮹šĥ۵⡍ᦥᘂእ᪡ၡᱲ⦽šĥaᯩ݅. ℕᱢᄡ⩶ශᯕ
↽ݡᨱ ࠥݍ⧁ ভʭḡ ྕᅕv Ŗℕ᪡ ᪡ᯕᨕ ᅕv Ŗℕ᮹
ℕᱢᄡ⩶ශ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ۵Ñ᮹ᯝ⊹⦹໑, ᪡ᯕᨕᨱ᮹⦽
ᅕv ⬉ŝa Ñ᮹ ᨧ۵ äᮝಽ ⠪aࡽ݅. ℕᱢᄡ⩶ශᯕ ↽ݡᨱ
ࠥݍ⦽⬥, FRP ᪡ᯕᨕᅕvĚᙹaฯᯕᔍᬊࡹᨩᮥᙹಾℕᱢᄡ⩶
ශ᮹qᗭᗮࠥ۵ࢵ⪵ࡹᨕ᪡ᯕᨕᨱ᮹⦽ᅕv⬉ŝaӹ┡ӹʑ
᯲⦽݅.
ℕᱢᄡ⩶ශᯕ“0”ᨱࠥݍ⦹໕, ྕᅕvŖℕ᪡᪡ᯕᨕᅕv
Ŗℕ۵➞⦹ʑ᯲⦹໑, ᯕভ᮹ℕᱢᄡ⩶ශᮥᱽಽℕᱢᄡ⩶
ශ
Ļ
Ɣƍᱶ᮹⦹ᩡ݅. Fig. 8ᨱࠥࡽၵ᪡zᯕ, ྕᅕvŖℕ᮹⬂ႊ⨆Ǎᗮᮡᛞḡᦫᦹᮝӹ, ᪡ᯕᨕ۵ԕᇡ⎹Ⓧญ✙᮹➞ᮥ
Ǎᗮ⍽᪡ᯕᨕᅕvŖℕ᮹ᱽಽℕᱢᄡ⩶ශࠥݍ⇶ႊ⨆ᄡ⩶
ශ
Ļ
ƍ᪡ᱽಽℕᱢᄡ⩶ශࠥݍvࠥƄ
ƍ۵᷾a⎑݅. ₙŁಽᱽಽℕ ᱢᄡ⩶ශࠥݍ⇶ႊ⨆ᄡ⩶ශᮡ3.1ᱩᨱᕽᨙɪ⦽Ɂᩕvࠥࠥݍ(a) 35 MPa
(b) 45 MPa
(c) 55 MPa
Fig. 8. Volumetic and Axial Strains of Concrete Confined with FRP Wire
(a) 1 Layer of FRP Wire (b) 2-3 Layers of FRP Wire Fig. 9. Failure Modes of Concrete Cylinders Confined with FRP Wire
⇶ႊ⨆ᄡ⩶ශᯕ໑, ᱽಽℕᱢᄡ⩶ශࠥݍvࠥ۵Ɂᩕvࠥ᪡࠺ᯝ
⦹݅. ℕᱢᄡ⩶ශᯕ᧲ᯙǍe(ᙹ⇶ᔢ┽)᮹ℕᱢᄡ⩶ශ⾈⇶ႊ⨆ᄡ
⩶ශᖁࠥෝ⪶ݡ⦹ᩍFig. 8᮹ԕᇡᨱࠥ⦹ᩡ݅. ᪡ᯕᨕᨱ᮹⧕
ԕᇡ⎹Ⓧญ✙᮹➞ᯕǍᗮࡹᨕ᪡ᯕᨕᅕvĚᙹa᷾a⧁ᙹಾ
ᱽಽℕᱢᄡ⩶ශ ࠥݍᯕ ḡᩑࡹ۵ ᔢ⫊ᮥ Fig. 8᮹ ԕᇡ əฝᮡ
ཹᔍ⦹Łᯩ݅. ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽᱽಽℕᱢᄡ⩶
ශࠥݍ⇶ႊ⨆ᄡ⩶ශ
Ļ
ſƔƍ۵ 0.00253ⴇ0.00579ᮝಽ⊂ᱶࡹᨩ݅.ᯕ۵FSP ᅕv⎹Ⓧญ✙Ŗℕᝅ⨹(᳑႒ᙽ॒; 2011)ᨱᕽ⊂ᱶࡽ
0.00149ⴇ0.00252ŝSaenz and Pantelides(2007)᮹ᩑǍđŝᯙ
0.00206ᅕ݅ⓑäᮝಽӹ┡ӹFRP ᪡ᯕᨕ᮹⎹Ⓧญ✙Ŗℕᨱ
ݡ⦽ ᅕv⬉ŝa ᬑᙹ⦽ äᮝಽ ⠪aࡽ݅.
ᱽಽℕᱢᄡ⩶ශ ࠥݍ ⬥ ⇶ႊ⨆ᄡ⩶ශᯕ ᷾a⧁ᙹಾ ➞ᯕ
ᱽᨕࡹḡᦫᮡྕᅕvŖℕ᮹ℕᱢᄡ⩶ශᮡḡᗮᱢᮝಽqᗭ⦹
ᩡ݅. ₙŁಽℕᱢᄡ⩶ශᯕᮭᯕ໕Ŗℕ᮹ℕᱢᮡ᷾a⦹ᩡᮭᮥ
᮹ၙ⦽݅. FRP ᪡ᯕᨕ1Ěᯕᅕvࡽ35 MPa Ŗℕ۵ྕᅕv
Ŗℕ᮹ᦶ⇶vࠥᅕ݅׳ᮡ᮲ಆᨱᕽᙹ⇶ᨱᕽ➞ᮝಽᄡ⪹⦹
ᩡ݅. ❭ƕᨱࠥݍ⧁ভʭḡ➞ᮡḡᗮᱢᮝಽ᷾a⦹ᩡᮝӹ᪡ᯕ ᨕᨱ᮹⧕➞᷾aᗮࠥ۵qᗭ⦹ᩡ݅. ᪡ᯕᨕ2ĚᅕvࡽŖℕ ۵➞᷾aᗮࠥaqᗭ⦹ᩡᮥᐱᦥܩ➞ᯕ᷾aᨱᕽqᗭಽ
ᄡ⪹ࡹᨩᮝӹ, Ŗℕ۵➞ᔢ┽ᨱᕽ❭ƕࡹᨩ݅. ᪡ᯕᨕa3Ě
ᅕvࡽŖℕ۵➞ᯕᙹ⇶ᮝಽᄡ⪹⦹ᩡᮝ໑, Ŗℕ۵ᙹ⇶ᔢ
┽ᨱᕽ❭ƕࡹᨩ݅. ᪡ᯕᨕ1Ěŝ2Ěᯕᅕvࡽ45 MPa Ŗℕ۵
❭ƕᨱ ࠥݍ⧁ ভʭḡ ➞ᔢ┽ෝ ᮁḡ⦹ᩡᮝӹ, 3Ěᯕ ᅕvࡽ
Ŗℕ۵ ➞ᯕ ᙹ⇶ᮝಽ ᄡ⪹ࡹᨕ ᙹ⇶ᔢ┽ᨱᕽ ❭ƕࡹᨩ݅.
ə్ӹ 55 MPaᯙ Ŗℕ۵ ❭ƕᨱ ࠥݍ⧁ ভʭḡ ➞ᔢ┽ෝ
ᮁḡ⦹ᩡ݅. ➞ᯕ ᙹ⇶ᮝಽ ᄡ⪹⦽ ᪡ᯕᨕ 3Ěᯕ ᅕvࡽ 35 MPaŝ45MPa Ŗℕ᮹↽ݡvࠥ۵ྕᅕvŖℕ᮹ᦶ⇶vࠥᅕ
݅3.86ŝ3.07႑ⓑäᮝಽ⊂ᱶࡹᨩ݅. ᯕđŝ۵➞ᯕᙹ⇶ᮝಽ
ᄡ⪹ࡹ۵ྕᅕvŖℕ᮹ᦶ⇶vࠥݡእᅕvŖℕ᮹↽ݡvࠥ
እෝ2.1ಽᱽ⦽Mirmiran and Shahawy(1997)ᅕ݅݅Ł׳ᮡ
äᮝಽ ⠪aࡹᨩ݅.
3.3 FRP ଲઘ࣪Գվਏ఼ଭ൞֏
FRP ᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ۵᪡ᯕᨕᅕvĚᙹᨱ
ݍญ❭ƕࡹᨩ݅. ᪡ᯕᨕa1ĚᅕvࡽŖℕ۵⠙׳ᯕᵲᦺᇡ ᮹➞ᮝಽᵲᦺᇡᨱ᭥⊹⦽᪡ᯕᨕa⦽Ŕᨱᕽᱩ݉ࡹᨕ⎹Ⓧญ
✙༉ᰍᨱᇡ₊ࡹḡᦫᮡ᪡ᯕᨕa┩ࡹ໕ᕽɪ᯲ᜅí❭ƕࡹ
ᨩ݅(Fig. 9(a) ₙ᳑). ᪡ᯕᨕa 2Ě ੱ۵ 3Ě ᅕvࡽ Ŗℕ۵
⠙׳ᯕᵲᦺᇡᨱ᭥⊹⦽᪡ᯕᨕaᩍ్Ŕᨱᕽᱩ݉ࡹᨕ᪡ᯕᨕ a ┩ࡹ໕ᕽ ɪ᯲ᜅí ❭ƕࡹᨩ݅(Fig. 9(b) ₙ᳑).
No. of Layers
No layer 1 layer 2 layers 3 layers
35MPa
45MPa
55MPa
Fig. 10. Failure Modes of the Concrete Confined with FRP Wire
FRP ᪡ᯕᨕᅕvŖℕ᮹ԕᇡ⎹Ⓧญ✙❭ƕ⩶┽۵i) ᙹḢɁ
ᩕੱ۵ĞᔍɁᩕ❭ƕ; ii) ᙹ⠪Ɂᩕ❭ƕಽǍᇥࡹᨩ݅. ᙹḢɁᩕ
ੱ۵ĞᔍɁᩕ❭ƕ۵ྕᅕvŖℕੱ۵᪡ᯕᨕᨱ᮹⦽Ǎᗮಆᯕ
᧞⦽Ŗℕ(᪡ᯕᨕ1Ěᯕᅕvࡽ55 MPa Ŗℕ)ᨱᕽၽᔾࡹ۵
❭ƕ⩶┽ᯕ݅(Fig. 10 ₙ᳑). ᙹ⠪Ɂᩕ❭ƕ۵᪡ᯕᨕᨱ᮹⦽Ǎᗮ
᧞⪵ಽᯙ⦹ᩍrᯱʑԕᇡ⎹Ⓧญ✙a➞⦹۵ᇡᇥŝ᪡ᯕᨕa
ᦥḢԕᇡ⎹Ⓧญ✙ෝ ⬉ŝᱢᮝಽǍᗮ⦹۵ᇡᇥ᮹ᱥ݉⬉ŝಽ
ၽᔾ⦽݅. ᙹ⠪ɁᩕᮡŖℕ᮹ᵲᦺᇡෝʑᵡᮝಽᩍ్໕ᮝಽ
ၽᔾa܆⦹໑, ᪡ᯕᨕᨱ᮹⦽Ǎᗮ⬉ŝaᬑᙹ⦽Ŗℕ(᪡ᯕᨕa
3Ě ᅕvࡽ Ŗℕ)ᨱ ၽᔾ⦽݅.
4. FRP ᪡ᯕᨕ᮹Ǎᗮ
4.1 ֜ুตր
⬂ႊ⨆ᮝಽǍᗮࡽ⎹Ⓧญ✙ᦶ⇶ᇡᰍ᮹↽ݡvࠥෝ⠪a⦹۵
ᯝၹᱢᯙ ᱽᦩᮡ ݅ᮭŝ z݅.
ć Ƅ
ƁƍƄ
ƁƁá Î âƉ
Îć Ƅ
ƁƍƄ
Ɗ(2)
ᩍʑᕽ
Ƅ
Ɓƍ۵ྕᅕvŖℕ᮹ᦶ⇶vࠥᯕ໑,Ɖ
Îᮡᅕvᰍᨱć Ƅ
ƁƍƄ
Ɗć Ƅ
ƁƍƄ
ƁƁFig. 11. Effective Confinement Constant ( Ɖ
Î) for the Concrete Confined with FRP Wire
ć Ƨ
ƄƓƧ
ƐƓć Ƅ
ƁƍƄ
ƊFig. 12. Ratio of the Fracture Strain to the Maximum Tensile Strain of FRP Wire
᮹⦽ᮁ⬉Ǎᗮᔢᙹᯕ໑,
Ƅ
Ɗᮡᅕvᰍᨱ᮹⦽⬂ႊ⨆Ǎᗮಆᯕ݅.(2)۵Richart et al.ᨱ᮹⧕1928֥ᗭ}ࡹᨩ݅. Fardis and Khalili(1982)۵ᯕᱽᦩᮥFRP ✙ᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍᨱ
ᱢᬊ⧁ᙹᯩ݅Łᱽᦩ⦹ᩡ݅. Richart et al.(1928)ᮡ܆࠺ᱢᮝಽ
⬂ᅕvࡽ(actively confined) ᦶ⇶ᇡᰍᨱݡ⦽
Ɖ
Îᮥ4.1ಽᱽᦩ⦹ᩡ݅. Miyauchi et al.(1999)ᮡFRP ✙ᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍ ᨱݡ⦽
Ɖ
Îᮥ2.98ಽᱽᦩ⦹ᩡ݅. ੱ݅ෙᱽᦩᨱᕽƉ
Îᮡć Ƅ
Ɓƍ
Ƅ
Ɗ ᮹⧉ᙹ(Karbhari and Gao, 1997; Saafi et al., 1999; Tautanji, 1999) ੱ۵
Ƅ
Ɗ᮹ ⧉ᙹ(Samaan et al., 1998)ಽ ᱽᦩ⦹ᩡ݅.FRP ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ⊂ᱶࡽǍᗮእ
Þ ć Ƅ ƄƁƍƁƁß
ෝ
Table 2ᨱӹ┡ԕᨩᮝ໑, ⫭ȡᇥᕾđŝෝFig. 11ᨱࠥ⦹ᩡ݅.
35 MPa Ŗℕ᮹ FRP ᪡ᯕᨕ ᮁ⬉Ǎᗮᔢᙹ
Ɖ
Îᮡ 2.557, 45 MPa Ŗℕ᮹Ɖ
Îᮡ2.714, 55 MPa Ŗℕ᮹Ɖ
Îᮡ2.552ಽ⠪aࡹᨩ݅. ᷪ, ᪡ᯕᨕᨱ᮹⦽Ǎᗮ⬉ŝ۵Ŗℕ᮹ᦶ⇶vࠥ᪡šĥa
ᨧ۵äᮝಽ⠪aࡹᨩ݅. ᯕᩑǍᨱᕽᝅ⦽༉ुFRP ᪡ᯕᨕ
ᅕv Ŗℕ ᝅ⨹ᨱᕽ ⊂ᱶࡽ ⠪Ɂ
Ɖ
Îᮡ 2.608ಽ ⠪aࡹᨩ݅.Lam and Teng(2002)ᮡ FRP ᅕv ᦶ⇶ᇡᰍ᮹ ᝅ⨹ᨱᕽ
Ɖ
Îᮥ2.0ᮝಽᦩᱥ⊂ᮝಽᱽᦩ⦹ᩡᮝӹ, ⠪Ɂᮡ2.62ಽᅕŁ⦹ᩡ݅. ə
్အಽ, ᯕᩑǍᨱᕽᔍᬊࡽFRP ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ
⊂ᱶࡽ
Ɖ
ÎᮡᅕŁࡽFRP ✙ᅕvŖℕ᮹ᝅ⨹đŝ᪡฿۵äᮝಽ ⠪a⧁ ᙹ ᯩ݅.
4.2 କตFRP ଲઘ൞ۚ࣡෴ࠔ
Xiao and Wu(2000), Moran and Pantelides(2002), Lam and Teng(2003), Matthys et al.(2005), Caret and Foster(2010) ॒᮹
ᩑǍđŝFRP ❭݉ᄡ⩶ශᮡFRP ↽ݡᯙᰆᄡ⩶ශ᮹50ⴇ60%ᮝ
ಽᅕŁ⦹ᩡ݅. ᳑႒ᙽ॒(2011)᮹CFSP ᅕv⎹Ⓧญ✙Ŗℕᨱ ᕽ⊂ᱶࡽCFSP᮹❭݉ᄡ⩶ශᮡ⠪Ɂ0.01269, GFSP ᅕv⎹Ⓧญ
✙ Ŗℕᨱᕽ ⊂ᱶࡽ GFSP᮹ ❱݉ᄡ⩶ශᮡ ⠪Ɂ 0.01148ಽ
ᅕŁ⦹ᩡ݅. FRP ᅕv⎹Ⓧญ✙ᦶ⇶ᇡᰍᝅ⨹ᨱᕽ⊂ᱶ⦽FRP
❭݉ᄡ⩶ශᮡFRP ᯙᰆᰍഭ⨹ᨱᕽ⊂ᱶࡽ↽ݡᯙᰆᄡ⩶ශᅕ݅
᯲ᮡäᮡᯝၹ⪵ࡽᔍᝅᯕ݅. əᯕᮁ۵݅ᮭŝz݅(Teng and Lam 2004; Carey and Harries 2005; Matthys et al. 2005;
Pantelides and Yan 2007; Saenz and Pantelides 2007). i) ⎹Ⓧญ
✙ ༉ᰍ᮹ Ɂᩕᮡ FRPᨱ ᮲ಆᮥ Ḳᵲ⍽ FRP᮹ ᳑ʑ┩ᮥ
ᮁၽ┉݅; ii) ⎹Ⓧญ✙༉ᰍᨱᇡ₊ࡽFRP᮹łශ⬉ŝෝᮁၽ
┉݅. FRP۵⎹Ⓧญ✙༉ᰍ᪡ᇡ₊ࡽᔢ┽ಽᯕᩑǍᨱᕽᔍᬊ⦽
FRP ᪡ᯕᨕ۵⎹Ⓧญ✙᪡᪡ᯕᨕᔍᯕᨱᱲ₊ᱽෝᔍᬊ⦹ḡᦫᦥ
ᇡ₊ᯕᯕᨕḡḡᦫᦹ݅. ݉ḡษₑอ᳕ᰍ⧁ᐱᯕ݅. Ɂᩕࡽ
⎹Ⓧญ✙᮹᮲ಆŝ݅ෙᇡᇥ᮹᮲ಆ₉ᯕaษₑಆᅕ݅Ⓧ݅໕,
᪡ᯕᨕᨱ۵᮲ಆᯕᰍᇥ႑ࢁäᯕ໑, ᪡ᯕᨕᨱ᯲ᬊࡽ↽ݡ᮲ಆᮡ
qᗭࢁäᯕ݅. ᪡ᯕᨕᨱᯙᰆಆᯕ᯲ᬊ⧁ᙹಾษₑಆᮡ᷾a⦹ʑ
ভྙᨱ, ᨕਅ⦽ĥᨱࠥݍ⦹໕, ษₑಆᮡᯕᔢ᪡ᯕᨕᨱᕽ᮲ಆ
ᰍᇥ႑ෝ ⧁ ᙹ ᨧ݅. ᮲ಆḲᵲ⩥ᔢᮝಽ đǎ ᪡ᯕᨕ۵ ❭݉ࢁ
äᯕ݅. ᕽ᪡ᯕᨕᨱi)ᮡᇡᇥᱢᮝಽᱢᬊ⧁ᙹᯩḡอ, ii)᮹
ᱢᬊᮡᛞḡᦫ݅. ᪡ᯕᨕ↽ݡᯙᰆᄡ⩶ශᨱݡ⦽❭݉ᄡ⩶ශ᮹
እෝ Fig. 12ᨱ ӹ┡ԕᨩ݅. ᪡ᯕᨕ ᅕvĚᙹ əญŁ ⎹Ⓧญ✙
ᦶ⇶vࠥa ᷾a⧁ᙹಾ FRP ᪡ᯕᨕ ❭݉ᄡ⩶ශᮡ qᗭ⦹ᩡ݅.
FRP ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ᪡ᯕᨕ↽ݡ❭݉ᄡ⩶ශᨱ
ݡ⦽ᯙᰆ❭݉ᄡ⩶ශ᮹እa55-90%ಽ⊂ᱶࡹᨩᮝ໑, ⠪Ɂ69.5%
ಽӹ┡ԍ݅. ᯕ۵ᯝၹFRP ✙ᅕvŖℕᝅ⨹ᨱᕽ⊂ᱶࡽ
✙❭݉ᄡ⩶ශᅕ݅݅ᗭ׳ᮡsᮝಽFRP ᪡ᯕᨕᅕvŖჶ᮹
ᬑᙹᖒᮥ ᯦᷾⦽݅.
5. đು
FRP᪡ᯕᨕᅕv⎹Ⓧญ✙Ŗℕ᮹ᦶ⇶ᝅ⨹ᨱᕽ݅ᮭŝzᮡ
đುᮥ ࠥ⇽⦹ᩡ݅.
(1) FRP ᪡ᯕᨕᅕvŖℕ᮹᮲ಆ⾈⇶ႊ⨆ᄡ⩶ශᖁࠥ᪡᮲ಆ
⾈ᬱᵝႊ⨆ᄡ⩶ශᖁࠥ۵Ɂᩕvࠥ
Ƅ
ƍ ࠥݍ⬥, ❭ƕᨱࠥݍ⧁ভʭḡ ᮲ಆᮡ ḡᗮᱢᮝಽ ᷾a⦹ᩍ ᮲ಆᔢÑ࠺(stress- hardening behavior)⦹ᩡᮝ໑, ᖁࠥ۵Ɂᩕvࠥෝʑᵡᮝಽ
ࢱ }᮹ ḢᖁǍeᮝಽ Ǎᖒࡽ äᮝಽ ᅝ ᙹ ᯩ݅.
(2) FRP ᪡ᯕᨕ۵⎹Ⓧญ✙ෝǍᗮ⍽Ŗℕ᮹⦹ᵲᱡ⧎ᖒ܆ŝ
ᄡ⩶ᱡ⧎ᖒ܆ᯕⓍí⨆ᔢ⎑ᮝ໑, ✚⯩ᨱթḡ⯂ᙹᖒ܆ᮥ
ๅᬑⓍí⨆ᔢ⎑݅. Ɂᩕᯕ⬥Ǎeᨱᕽ᪡ᯕᨕᅕvŖℕ ᮹ᖒ܆ᮡÑ᮹᪡ᯕᨕᨱ᮹⧕đᱶࡹ໑, ᪡ᯕᨕᨱ᮹⦽ᅕv⬉
ŝa ┢ᬵ⦹í Ǎ⩥ࡹᨩ݅.
(3) FRP ᪡ᯕᨕᅕvŖℕ᮹Ɂᩕ⦹ᵲᮡŖℕ᮹⎹Ⓧญ✙
ᦶ⇶vࠥ᪡šĥᨧᯕ᪡ᯕᨕᅕvĚᙹᨱእಡ⦹ᩍ᷾a⦹໑,
᪡ᯕᨕᅕvŖℕ᮹↽ݡvࠥ۵⎹Ⓧญ✙ᦶ⇶vࠥ᪡šĥᨧ ᯕ Ñ᮹ ࠺ᯝ⦹Ł ᅕvĚᙹᨱ እಡ⦹۵ äᮝಽ ⠪aࡽ݅.
(4) FRP ᪡ᯕᨕ3Ěᯕᅕvࡽ35᪡45 MPa Ŗℕ᮹ℕᱢÑ࠺ᮡ
➞ᨱᕽ ᙹ⇶ᮝಽ ᄡ⪹⦹ᩍ ᙹ⇶ᔢ┽ᨱᕽ ❭ƕࡹᨩ݅.
(5) FRP ᪡ᯕᨕa1ĚᅕvࡽŖℕ۵⠙׳ᯕᵲᦺᇡ᮹➞ᮝ ಽᵲᦺᇡᨱ᭥⊹⦽᪡ᯕᨕa⦽Ŕᨱᕽᱩ݉ࡹᨕ⎹Ⓧญ✙
༉ᰍᨱᇡ₊ࡹḡᦫᮡ᪡ᯕᨕa┩ࡹ໕ᕽɪ᯲ᜅí❭ƕࡹ
ᨩ݅. ᪡ᯕᨕa2Ěੱ۵3ĚᅕvࡽŖℕ۵⠙׳ᯕᵲᦺᇡ ᨱ᭥⊹⦽᪡ᯕᨕaᩍ్Ŕᨱᕽᱩ݉ࡹᨕ᪡ᯕᨕa┩ࡹ໕ᕽ
ɪ᯲ᜅí❭ƕࡹᨩ݅. ྕᅕvੱ۵᪡ᯕᨕᨱ᮹⦽Ǎᗮಆᯕ
᧞⦽ Ŗℕ᮹ ԕᇡ ⎹Ⓧญ✙۵ ᙹḢɁᩕ ੱ۵ ĞᔍɁᩕಽ
❭ƕࡹᨩ݅. ᙹ⠪Ɂᩕ❭ƕ۵᪡ᯕᨕᨱ᮹⦽Ǎᗮ᧞⪵ಽᯙ⦹ᩍ
rᯱʑԕᇡ⎹Ⓧญ✙a➞⦹۵ᇡᇥŝ᪡ᯕᨕaᦥḢԕᇡ
⎹Ⓧญ✙ෝ⬉ŝᱢᮝಽǍᗮ⦹۵ᇡᇥ᮹ᱥ݉⬉ŝಽၽᔾ⦹ᩡ
ᮝ໑, ᙹ⠪ɁᩕᮡŖℕ᮹ᵲᦺᇡෝʑᵡᮝಽᩍ్໕ᮝಽၽ ᔾ⦹ᩡᮝ໑, ᪡ᯕᨕᨱ᮹⦽Ǎᗮ⬉ŝaᬑᙹ⦽Ŗℕᨱၽᔾ
⦹ᩡ݅.
(6) 35 MPa Ŗℕ᮹ FRP ᪡ᯕᨕ ᮁ⬉Ǎᗮᔢᙹ
Ɖ
Îᮡ 2.777, 45 MPa Ŗℕ᮹Ɖ
Îᮡ2.460, 55 MPa Ŗℕ᮹Ɖ
Îᮡ2.096ᮝ ಽ⠪aࡹᨩ݅. ᷪ, Ŗℕ᮹ᦶ⇶vࠥaԏᮥᙹಾǍᗮ⬉ŝaᬑᙹ⦽äᮝಽ⠪aࡹᨩ݅. FRP ᪡ᯕᨕᅕvĚᙹəญŁ⎹Ⓧ
ญ✙ᦶ⇶vࠥa᷾a⧁ᙹಾFRP ᪡ᯕᨕ❭݉ᄡ⩶ශᮡqᗭ
⦹ᩡ݅. ᪡ᯕᨕᅕvŖℕᦶ⇶ᝅ⨹ᨱᕽ᪡ᯕᨕ↽ݡ❭݉ᄡ
⩶ශᨱݡ⦽ᯙᰆ❭݉ᄡ⩶ශ᮹እa55-90%ಽ⊂ᱶࡹᨩᮝ໑,
⠪Ɂ69.5%ಽӹ┡ԍ݅. ᯕ۵ᯝၹFRP ✙ᅕvŖℕ
ᝅ⨹ᨱᕽ⊂ᱶࡽ✙❭݉ᄡ⩶ශᅕ݅݅ᗭ׳ᮡsᮝಽFRP
᪡ᯕᨕ ᅕv Ŗჶ᮹ ᬑᙹᖒᮥ ᯦᷾⦽݅.
qᔍ᮹ɡ
ᯕםྙᮡ2011֥ᱶᇡ(Ʊᮂŝ⦺ʑᚁᇡ)᮹ᰍᬱᮝಽ⦽ǎᩑǍ ᰍ݉᮹ḡᬱᮥၼᦥᙹ⧪ࡽʑⅩᩑǍᔍᨦᯕ໑, ḡᬱᨱݡ⧕qᔍෝ
⢽⦹۵ ၵ᯦ܩ݅(No. 2011-0023281).
