Received October 10 2012, Revised January 27 2013, Accepted March 7 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͵͵Ǥ͵ǤͻͲͳ Ǥ ǤǤ
ⴲ⇧㭣#㳦ⴏᷣ♿㚚ⴖ#㔖㘪Ὢ㡶#ᇓᦂ#㡷⛯/#㘪Ꮾ㱦ኺ#⇍#㫺Ḛሮᦗ⮎#ኾ㬚#
⢢㮖#⮮ጪ
ֈ ȵฅ
Zi, Goangseup*, Kim, Jihwan**
An Experimental Study on Strength Properties, Size Effect, and Fatigue Behaviour of Concrete under Biaxial Flexural Stress State
ABSTRACT
In this study, flexural strength properties of concrete under biaxial stress state were experimentally investigated. Tests for size effect and fatigue behaviour of concrete under biaxial stress were carried out by the ASTM C 1550 and the biaxial flexure test(BFT). The results given by the biaxial tests were compared to those by the third-point bending test. Test results showed that biaxial flexural strengths obtained from the ASTM C 1550 and the biaxial flexure test are greater than the strength by the third-point bending test. As the size increases, the uniaxial and biaxial flexural strength decreases. However, the slope of the size effect of the biaxial strength was greater than that of the uniaxial strength. Finally, the fatigue response of concrete under the biaxial stress state was similar with that for uniaxial stress state.
Key words : Biaxial flexural stress, Biaxial flexural strength, Biaxial flexure test, Size effect, Fatigue
Ⅹಾ
ᅙםྙᨱᕽ۵ᯕႊ⨆᮲ಆᔢ┽ᨱᕽ᮹⎹Ⓧญ✙vࠥ✚ᖒŝⓍʑ⬉ŝəญŁ⦝ಽÑ࠺ᨱš⦽ᩑǍෝᙹ⧪⦹ᩡ݅. ᯕෝ᭥⧕ASTM C 1550
⨹ჶŝᯕႊ⨆⮉vࠥ⨹(biaxial flexure test; BFT)ᮥᱢᬊ⦹ᩍⓍʑ⬉ŝၰ⦝ಽ⨹ᮥᝅ⦹ᩡᮝ໑, ݉ᙽᅕ᮹3॒ᇥᱱ⦹ᵲᨱ᮹⦽
⎹Ⓧญ✙⮉vࠥ⨹(third-point bending test) đŝ᪡እƱ⦹ᩡ݅. ᝅ⨹đŝ3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᨱ᮹⦽ᯝႊ⨆᮲ಆᔢ┽᮹vࠥᅕ
݅۵ASTM C 1550 ⨹ჶŝᯕႊ⨆⮉vࠥ⨹ჶᨱ᮹⦽ᯕႊ⨆᮲ಆᔢ┽᮹vࠥaⓑäᮝಽ⊂ᱶࡹᨩ݅. 3॒ᇥᱱᰍ⦹⮉vࠥ⨹, ASTM C 1550, ᯕႊ⨆⮉vࠥ⨹ჶ༉ࢱ⠙᮹Ⓧʑa᷾a⧉ᨱvࠥ۵qᗭ⦹۵äᮝಽšₑࡹᨩᮝ໑, ᯕႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ
⬉ŝaᯝႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ⬉ŝᅕ݅ⓑäᮝಽ⪶ᯙࡹᨩ݅.S-N łᖁᨱ᮹⦽ᯝႊ⨆ŝᯕႊ⨆⮉vࠥ᮹⦝ಽᙹᮡᮁᔍ⦽äᮝಽ
ᇥᕾࡹᨩ݅.
áᔪᨕ ᯕႊ⨆⮉᮲ಆ, ᯕႊ⨆⮉vࠥ, ᯕႊ⨆⮉vࠥ⨹, Ⓧʑ⬉ŝ, ⦝ಽ
1. ᕽು
⎹Ⓧญ✙Ʊపᜍ௹ቭ, Ŗ⧎ᯕӹŁᗮࠥಽ⡍ᰆℕ᪡zᮡǍ᳑ྜྷॅᨱ᯲ᬊ⦹۵᮲ಆᮡ⇶ႊ⨆ᯙᰆᅕ݅۵⮉ᯙᰆᮥᵝಽၼʑভྙᨱ
ࡓࡾν࣡ėॡ
(a) (b) Fig. 1. (a) biaxial flexure test, (b) ASTM C 1550 methods.
⮉⨹ᮥ☖⧕ᕽᮡᯙᰆvࠥaᝅᱽ⎹Ⓧญ✙᮹ᰍഭᱢᖒḩᮥ
ӹ┡ԕŁᯩᨕ, ᖅĥʑᵡvࠥ᪡⎹Ⓧญ✙⣩ḩđᱶၰšญ
॒ᨱ⎹Ⓧญ✙ᦶ⇶vࠥ᪡ ᇩᨕ⮉ᯙᰆvࠥaᵝಽᔍᬊࡹŁ
ᯩ݅. ḡɩʭḡ⎹Ⓧญ✙᮹⮉ᯙᰆvࠥ۵⠙ᱽ᯲ŝ⨹᮹ᬊᯕ ᖒᮝಽĞᱽᱢᯕ໕ᕽࠥ, ⮉ᯙᰆ᮲ಆᔢ┽ᨱݡ⦽ᱡ⧎ᖒᮥၹᩢ
⧁ᙹᯩ۵3॒ᇥᱱᰍ⦹⮉vࠥ⨹(third-point bending test)ᨱ
᮹⧕ đᱶࡹᨕ ᪵݅.
3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᮡᰆႊ⩶᮹ྕɝ⎹Ⓧญ✙ᅕ⨹ℕ
ෝᔍᬊ⦹ʑভྙᨱ⨹⨹ℕaᯝႊ⨆⮉ᯙᰆ᮲ಆᔢ┽ᨱᕽ
əvࠥađᱶࡽ݅. ə్ӹᦿᨱᕽᨙɪ⦽ᜍ௹ቭ, ⡍ᰆℕ॒ŝ
zᯕᇡᰍ᮹ʙᯕᨱእ⧕ࢱ̹a᧨ᮡ❱ੱ۵ᚹ⩶┽᮹⎹Ⓧญ✙
Ǎ᳑ྜྷॅᮡ ᇡ ⦹ᵲ ၰ Õ᳑ᙹ⇶ŝ zᮡ ԕᇡᱢᯙ ᯙᮝಽ
ᯙ⧕ᯝႊ⨆ᯙᰆ᮲ಆᔢ┽ᯕʑᅕ݅۵ᯕႊ⨆ᯙᰆ᮲ಆᔢ┽ᨱ
״ᯕíࡽ݅. ə్အಽ⎹Ⓧญ✙ᇡᰍॅ᮹ᝅᱽ᮲ಆᔢ┽ෝŁಅ⦽
Ǎ᳑ᱢᖒ܆⠪aෝ᭥⧕ᕽ۵ ᯕႊ⨆ᯙᰆ᮲ಆᔢ┽ᨱᕽđᱶࡽ
vࠥᨱ ݡ⦽ ᝅ⨹ŝ ə đŝ᮹ Łₑᯕ Ǎࡽ݅.
↽ɝ Õᖅᇥᨱᕽ ᖍᮁᅕv ⎹Ⓧญ✙᮹ ⮉ᯙᖒᮥ ⠪a⯩ʑ
᭥⦽centrally loaded round panel test(ASTM C 1550)᪡ྕɝ
⎹Ⓧญ✙᮹ᯕႊ⨆⮉ᯙᰆvࠥ⊂ᱶᮥ᭥⦽ᯕႊ⨆⮉vࠥ⨹
(biaxial flexure test; BFT)ᯕ}ၽࡹᨩ݅(Zi ॒, 2008). ࢱ⨹ჶ
ᮡ ༉ࢱ Fig. 1ŝ zᯕ ➉ձ ⩶┽᮹ ⨹ℕෝ ᯕᬊ⦹ᩍ ⨹ᮥ
ᙹ⧪⦹໑, 3॒ᇥᱱᰍ⦹⮉vࠥ⨹ౝəᱩ₉ae⠙⦹ŁĞ ᱽᱢᯕᨕᕽ⩥ᰆᨱᕽᙹ⧪ᯕa܆⦹݅. ੱ⦽, ❱Ǎ᳑ྜྷ᮹᮲ಆᔢ┽
ෝᯕᔢᱢᮝಽ༉ᔍ⧁ᙹᯩŁ, ❭ƕ༉ऽaᝅᱽ❱Ǎ᳑ྜྷŝᮁᔍ⦽
ᯕᱱᮥ aḡŁ ᯩ݅.
⎹Ⓧญ✙᪡zᮡ≉ᖒᰍഭ᮹vࠥ۵⨹ℕ᮹ᰍഭᱢ✚ᖒᨱ
ࠥə❭ƕ✚ᖒᮝಽᯙ⧕⨹ℕӹǍ᳑ྜྷ᮹Ⓧʑᨱᩢ⨆ᮥၼ۵
äᮝಽӹ┡ԍ݅. Bažantᮡ⎹Ⓧญ✙ᰍഭᨱ❭ƕᩎ⦺ᮥ᯦ࠥ⦹
ᩍ⎹Ⓧญ✙vࠥ᮹Ⓧʑ⬉ŝ(size effect)ෝᖅ⦹ᩡᮝ໑, ⩥ᰍ
deterministic size effect, energetic size effect, statistical energy size effect ḡ႑ᱢᯕ݅(Bažant, 1984; Bažant᪡Planas, 1998).
ə్ӹᯕ్⦽ Ⓧʑ⬉ŝ ჶ⊺ॅᮡ༉ࢱ ⎹Ⓧญ✙ ᦶ⇶vࠥ ၰ
ᅕ⨹ℕෝᯕᬊ⦽ᯝႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ⬉ŝᨱš⦽ᩑǍಽ
ᦥḢʭḡᯕႊ⨆⮉ᯙᰆ᮲ಆᔢ┽ᨱᕽ᮹⎹Ⓧญ✙Ⓧʑ⬉ŝᨱš
⦽ᩑǍ۵ᯕᨕḥၵᨧ݅. ੱ⦽, Ŗ⧎ၰࠥಽ⡍ᰆℕ᪡zᮡ
⎹Ⓧญ✙Ǎ᳑ྜྷॅᮡᰆʑeᨱÙℱ⦝ಽ⦹ᵲᯕ᯲ᬊࡹအಽᯕႊ
⨆᮲ಆᔢ┽ᨱᕽ᮹⦝ಽᙹᨱš⦽ᩑǍa⦥⦹݅. ↽ɝʭḡ
݅⇶᮲ಆ(ᯕႊ⨆ ᦶ⇶ŝ ᯕႊ⨆ ᯙᰆ) ᔢ┽᮹ ⎹Ⓧญ✙ ✚ᖒᮥ
⠪a⦹ʑ᭥⦽ᩑǍॅᯕḥ⧪ࡹᨕ᪵݅. ə్ӹᯕႊ⨆᮲ಆ ᔢ┽᮹Ǎ⩥ᮥ᭥⦽ᝅ⨹᮹ᅖᰂᖒŝእĞᱽᖒᮝಽᯙ⦹ᩍᩑǍ
đŝ۵ᱽ⦽ᱢᯝᐱอᦥܩ(Nelson ॒, 1988; Su᪡Hsu, 1988;
Subramaniam ॒, 1999), ᯕႊ⨆⮉ᯙᰆᔢ┽ᨱᕽ᮹⎹Ⓧญ✙⦝ಽ Ñ࠺ᨱ š⦽ ᩑǍ۵ ᙹ⧪ࡽ ၵ ᨧ݅.
ᕽ, ᅙᩑǍᨱᕽ۵⎹Ⓧญ✙᮹ᯕႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ
⬉ŝȽŝᯕႊ⨆᮲ಆᔢ┽ᨱᕽ᮹⦝ಽÑ࠺ᇥᕾᮥ᭥⦽ᝅ⨹
ᱢᩑǍෝᙹ⧪⦹ᩡ݅. ᯕෝ᭥⦹ᩍASTM C 1550ŝᯕႊ⨆⮉
vࠥ⨹ᮥᯕᬊ⦽Ⓧʑ⬉ŝၰ⦝ಽᝅ⨹ᮥᝅ⦹ᩡᮝ໑, ᯝႊ⨆
ᯙᰆ᮲ಆᔢ┽᮹3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᨱ᮹⦽đŝ᪡እƱ⦹ᩡ
݅. ᝅ⨹đŝᨱݡ⦽Łₑŝᇥᕾᮥ☖⦹ᩍᯝႊ⨆ᯙᰆ᮲ಆᔢ┽᮹
vࠥ✚ᖒ, Ⓧʑ⬉ŝəญŁ⦝ಽÑ࠺ŝ᮹ᔢššĥෝᮁ⇵⦹ᩍ
ᯕႊ⨆᮲ಆᔢ┽᮹Ǎ᳑ྜྷÑ࠺⠪aᨱݡ⦽ʑⅩᯱഭಽᱽŖ⦹Ł
ᯱ ⦽݅.
Table 1. Mixture proportion of concrete
W/C (%) S/a (%) Unit weight (kg/m3)
W C S G
42 49 170 405 866 934
Table 2. Dimensions of third-point bending test
sizes third-point bending test
h [mm] w [mm] l [mm] L [mm]
S 30 30 90 190
M 48 48 144 244
L 75 75 225 325
Table 3. Dimensions of the biaxial flexure test and ASTM C 1550 specimens
sizes biaxial flexure test / ASTM C 1550
h [mm] R [mm] a [mm] b0 [mm] b [mm] be [mm]
S 30 131 125 5.5 31.5 10.55
M 48 210 200 11 50 17.58
L 75 328.5 312.5 14 78 26.44
2. ᝅ⨹}ၰႊჶ
ᯝႊ⨆ŝᯕႊ⨆ᯙᰆ᮲ಆᔢ┽ᨱᕽ⨹ℕ᮹Ⓧʑᨱෙvࠥ
ᄡ⪵᪡, ၹᅖ⦹ᵲᨱ᮹⦽⦝ಽᙹ₉ᯕෝȽ⦹ʑ᭥⦹ᩍᝅ⨹
ᮥᙹ⧪⦹ᩡ݅. ᯕෝ᭥⧕ᅕ⨹ℕෝᯕᬊ⦽ᯝႊ⨆⮉ᯙᰆ᮲ಆᔢ
┽᮹Ⓧʑ⬉ŝ᪡⦝ಽ⨹ᮡASTM C 78ᨱȽᱶࡽ3॒ᇥᱱᰍ⦹
⮉vࠥ⨹ᮥ ᱢᬊ⦹ᩡ݅. ᬱ⩶ ➉ձᮥ ᯕᬊ⦽ ᯕႊ⨆ ⮉ᯙᰆ
᮲ಆᔢ┽᮹Ⓧʑ⬉ŝ᪡⦝ಽ⨹ᮡASTM C 1550 ʑᵡŝᯕႊ⨆
⮉vࠥ⨹ႊჶ(Kim ॒, 2013)ᨱᵡ⦹ᩍ⨹ᮥᙹ⧪⦹ᩡ݅.
༉ु⨹ℕ۵28ᯝ༊⢽vࠥෝ30 MPaಽᖅĥ⦹ᩡŁ, ǖᮡʼnᰍ
↽ݡ⋌ᙹ۵Ⓧʑ⬉ŝᨱᔍᬊࡹ۵aᰆ᯲ᮡ⨹ℕ(Ɔ=30 mm)ෝ
Łಅ⦹ᩍ6.5 mmᯙᇡᙽǖᮡʼnᰍෝᔍᬊ⦹ᩡ݅. ᱢᬊࡽ⎹Ⓧญ✙
႑⧊ᖅĥ۵ Table 1ᨱ ᱶญ⦹ᩡ݅.
b⨹ჶᨱෙᰍഭvࠥ۵⊂ᱶࡽ⦹ᵲ᮹↽ݴsᮝಽᇡ░
ᔑᱶ⦹ᩡ݅. 3॒ᇥᱱ ᰍ⦹ ⮉vࠥ ⨹᮹ vࠥ۵ ┥ᖒᅕᯕುᨱ
ʑⅩ⦽ (1)ᨱ ᮹⧕ ĥᔑ⦹ᩡ݅.
ňƓá ćƕ ƆÏ
©Ɗ (1)
ᩍʑᕽ, ňƓ۵⎹Ⓧญ✙ᯝႊ⨆⮉ᯙᰆvࠥ(MPa), ©۵↽ݡ⦹
ᵲ(N), Ɗᮡ⨹ℕ᮹ḡe(mm), Ɔ۵⨹ℕ׳ᯕ(mm)ᯕ໑, ƕ۵
⨹ℕ᮹ ⡎(mm)ᯕ݅.
ᯕႊ⨆⮉vࠥ⨹᮹vࠥ۵┥ᖒ❱ᯕುᨱɝÑ⦽(2)ෝ
ᔍᬊ⦹ᩍ ĥᔑ⦹ᩡ݅.
ňƀá ×íÏÐÕÔćƆÏ
© ƙ
ƜƚÏÞÎ âŊß ćƀſ âÞÎàŊßć«Ï ÞſÏà ƀÏßƛ
Ɲƞ (2) ᩍʑᕽ, ňƀᮡ⎹Ⓧญ✙ᯕႊ⨆⮉ᯙᰆvࠥ(MPa), ©۵↽ݡ⦹
ᵲ(N), Ɔ۵⨹ℕ׳ᯕ(mm)ᯕ໑, ſ,ƀ,«ᮡbbᬱ❱⨹ℕ᮹
ᵲᦺᱱᇡ░ḡḡᱱၰaಆᱱʭḡ᮹Ñญ(mm), ⨹ℕ᮹ၹḡ
(mm)ᯕ݅. Ŋ۵⎹Ⓧญ✙⡍᪡ᘂእᯕ݅. vࠥĥᔑ⦥⦽Ŋ۵
ᝅ⨹ᨱ ᮹⧕ ⊂ᱶࡽ 0.184ෝ ᔍᬊ⦹ᩡ݅.
ASTM C 1550 ʑᵡᨱ۵⮉ᯙᰆvࠥᔑᱶᮥ᭥⦽ᯕುᯕ
ᱽࡹᨕ ᯩḡ ᦫᦥ ᖙၚ ᇥ᮹ ball-on three-balls ⨹᮹
vࠥ ᔑᱶᮥ ᔍᬊ⦹ᩡ݅(Kim ॒, 2013).
ňƄá ×íÏÐÕÔćƆÏ
© ƙ
Ɯ
ƚ
ÞÎ âŊßÞ
Î âÏ ćƀſƃß
â ćÞÎ à ŊßÏ«ÞÏſÏÏà ƀƃÏßƛƝƞ
ƀƃáöćÎíÓƀ×ÏâƆÏà ×íÓÔÒƆì Þƀ×ï ×íÒƆß (3)
ᩍʑᕽ, ňƄᮡ⎹Ⓧญ✙ᯕႊ⨆⮉ᯙᰆvࠥ(MPa), ©۵↽ݡ⦹
ᵲ(N), Ɔ۵⨹ℕ׳ᯕ(mm)ᯕ໑,«ᮡ⨹ℕ᮹ၹḡ(mm)ᯕ
݅.ſ۵ᬱ❱⨹ℕ᮹ᵲᦺᱱᇡ░ḡḡᱱʭḡ᮹Ñญ, ƀƍ᪡ƀƃ۵
aಆᰆ⊹᪡⨹ℕaษᵝݠᮡ໕ᱢ᮹ၹḡ(mm)ŝᮁ⬉ၹḡ
(mm)ᯕ݅.
2.1 ׆ตրਓ
3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᮥ ᯕᬊ⦽ᅕ⨹ℕ᮹ᯝႊ⨆⮉ᯙᰆ
vࠥ᮹Ⓧʑ⬉ŝ᪡ASTM C 1550ŝᯕႊ⨆⮉vࠥ⨹ᮥ ᯕᬊ⦽
ᬱ⩶➉ձ᮹ᯕႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ⬉ŝෝᦥᅕʑ᭥⦹ᩍ
3aḡ Ⓧʑ(Ɔ= 30, 48, 75 mm)ಽᅕ⨹ℕ᪡➉ձ⨹ℕෝ
ᱽ᯲⦹ᩡ݅. b⨹ჶᨱෙᵝ⨹ᄡᙹ۵Table 2᪡3ᨱ
ӹ┡ԕᨩᮝ໑, Ⓧʑ⬉ŝ⨹ᨱᔍᬊࡽᅕ⨹ℕ᪡➉ձ⨹ℕ᮹
ࢱ̹۵࠺ᯝ⦹݅. ⨹ℕ۵vࠥ᮹☖ĥᱢᇥᔑᮥŁಅ⦹ʑ᭥⧕
bb᮹Ⓧʑᨱ13}ᦊⅾ39}᮹ᅕ⨹ℕ᪡ASTM C 1550 ŝᯕႊ⨆⮉vࠥ⨹ᮥ ᭥⦽78}᮹➉ձ⨹ℕෝᱽ᯲⦹ᩡ݅.
(a) (b) Fig. 2. (a) steel molds for round specimens, and (b) concrete specimens
(a) (b)
Fig. 3. Test set-ups for (a) biaxial flexure test, and (b) ASTM C 1550
➉ձ⨹ℕ⦹໕᮹⠪┥ᖒ⪶ᅕෝ᭥⦹ᩍÑ⣙ḲᮡFig. 2(a)᪡
zᯕᬱ⩶℁❱ᮝಽᱽ᯲⦹ᩡ݅. ੱ⦽, Ɂᯝ⦽⨹ℕᱽ᯲ᮥ᭥⦹ᩍ
౩ၙ⎹ᮝಽ┡ᖅ⦽⬥24eᯕĞŝ⦹ᩍÑ⣙ḲᮥᱽÑ⦹ᩡᮝ໑,
⨹ᙹ⧪ʭḡ᧲ᔾ᳑ᨱᕽᙹᵲ᧲ᔾᮥᝅ⦹ᩡ݅. Fig. 2(b)۵
┡ᖅᱥĞᯕ݅. ⎹Ⓧญ✙᮹ᦶ⇶vࠥ۵5}᮹100200 mm ᝅŖℕෝᱽ᯲⦹ᩍASTM C 39 ʑᵡᨱ᮹⧕⊂ᱶ⦹ᩡᮝ໑,
⠪Ɂ33 MPaಽᨕᲭ݅. Ⓧʑ⬉ŝෝ᭥⦽⦹ᵲᰍ⦹۵100 kN ᬊప᮹ᮁᦶᨲ≥ᨱᯕ░(hydraulic actuator)ෝᔍᬊ⦹ᩍ, 1 mm/min ᄡ᭥ᱽᨕ(displacement control) ႊᮝಽ⦹ᵲᮥᰍ⦹⦹ᩡ݅. ༉
ु ⨹ℕ۵ ⨹⠙ᯕ ❭ƕࢁ ভʭḡ᮹ ↽ݡ ⦹ᵲᮥ ⊂ᱶ⦹ᩍ
vࠥෝ ĥᔑ⦹ᩡ݅.
2.2 ߦਓ
3॒ᇥᱱᰍ⦹⮉vࠥ⨹, ASTM C 1550 əญŁᯕႊ⨆⮉
vࠥ⨹ᮥᯕᬊ⦹ᩍ⎹Ⓧญ✙ᅕ⨹ℕ᪡➉ձ⨹ℕᨱᯝᱶ
᮲ಆᙹᵡᮝಽၹᅖᱢᮝಽa⧕ḡ۵⦝ಽ⨹ᮥᙹ⧪⦹ᩡ݅. ⦝ಽ
⨹ŝ⦝ಽ᮲ಆᙹᵡđᱶᮥ᭥⦽ᱶᱢ⨹ᮥ᭥⧕ⅾ14}᮹
ᅕ ⨹ℕ᪡ 28}᮹ ➉ձ ⨹ℕෝ ᱽ᯲⦹ᩡ݅. ⨹ℕ ᱽᬱᮡ
Table 2᪡3᮹M Ⓧʑ(Ɔ= 48 mm)᮹ᱽᬱᮥᱢᬊ⦹ᩡᮝ໑, Ⓧʑ⬉
ŝᝅ⨹ŝ࠺ᯝ⦽႑⧊(Table 1)ᮥᯕᬊ⦹ᩍ⨹ℕෝ⇵aᱽ᯲⦹
ᩡ݅. ⨹ᙹ⧪ʭḡ⦝ಽ⨹ᵲvࠥ᷾ḥᨱෙ⠙₉ෝ↽ᗭ⪵
⦹ʑ᭥⧕⨹ℕෝ90ᯝe᧲ᔾ᳑ᨱᕽᙹᵲ᧲ᔾᮥᝅ⦹ᩡŁ, ᯕ⬥ᝅ⨹ࠥᵲᨱᙹᇥᮝಽᯙ⦽⨹ℕvࠥᄡ⪵᮹ᩢ⨆ᮥᵥᯕʑ
᭥⦹ᩍ᧞2ݍ࠺ᦩʑÕ᧲ᔾ⦽⬥ᝅ⨹ᮥᙹ⧪⦹ᩡ݅. ⎹Ⓧญ✙᮹
90ᯝ ᦶ⇶vࠥ۵ ⠪Ɂ 70 MPaಽ ᨕᲭ݅.
ᱶᱢ⨹ᨱᕽb⨹ჶᨱ5}᮹⨹ℕෝᯕᬊ⦹ᩍ⨹
ᮥᙹ⧪⦹ᩡ݅. ᱶᱢ⨹ᮡ1 mm/min᮹ᄡ᭥ᱽᨕႊᮝಽ⦹ᵲ
ᮥa⦹ᩍ⨹ℕ᮹❭ƕvࠥෝ⊂ᱶ⦹ᩡŁ, ⊂ᱶࡽᱶᱢ⨹᮹
↽ݡ⦹ᵲᮥၵ┶ᮝಽ⦝ಽ⨹ᮥ᭥⦽᮲ಆᙹᵡᮥđᱶ⦹ᩡ݅.
⦝ಽ᮲ಆᙹᵡ(Smax)ᮡᱶᱢ⮉vࠥ᮹90%, 80%, 70%ಽ⦹ᩡ݅.
b↽ݡ᮲ಆᙹᵡᨱݡ⦹ᩍ3}᮹⠙ᮥᔍᬊ⦹ᩍ⦝ಽvࠥෝ⊂
ᱶ⦹ᩡᮝ໑, ⦝ಽ⦹ᵲᯕಆᮡsine❭ෝᔍᬊ⦹ᩡ݅. ⦹ᵲᗮࠥ۵10 HzಽŁᱶ⦹ᩡŁ, ⦹ᵲᯕᵲesᨱࠥݍ⦹۵ߑɪĊ⦽⦹ᵲᄡ⪵ෝ
Łಅ⦹ᩍ1~20 cycles ࠺ᦩ5݉ĥಽӹ٥ᨕ⦹ᵲᮥᕽᕽ⯩᷾a
⎑݅. ੱ⦽, ᯕႊ⨆⮉vࠥ⨹ŝASTM C 1550 ⨹ᮥᯕᬊ⦽
⦝ಽ⨹⦝ಽ٥ᱢᨱෙ➉ձ᮹ᄡ⩶ᱶࠥෝᦥᅕʑ᭥⦹ᩍ
⨹ℕᵲᦺ᮹ᦥఌ໕ᨱ2}᮹ᄡ⩶ශíᯕḡෝƱ₉⦹ࠥಾᇡ₊⦹
ᩍ, ၹᅖ⦹ᵲᨱෙ⦹ᵲ-ᄡ⩶ශᯕಆᮥ⊂ᱶ⦹ᩡ݅. Fig. 3ᮡ
ᯕႊ⨆⮉vࠥ⨹ŝASTM C 1550᮹ᝅ⨹ᱥĞᮥᅕᩍᵡ݅.
Table 4. Test results of size effect in concrete strengths under different stress states
test methods third-point bending test ASTM C 1550 biaxial flexure test
h [mm] 30 48 75 30 48 75 30 48 75
mean strength [MPa] 5.43 4.41 4.24 11.31 10.19 8.71 8.28 6.88 5.59
S.D [MPa] 0.39 0.49 0.20 1.21 0.96 0.72 0.48 0.65 0.31
c.o.v [%] 7 11 5 11 9 8 6 10 6
Fig. 4. Size effect in flexural strengths of concrete
3. ᝅ⨹đŝၰŁₑ
3.1 ׆ตր
Table 4۵⨹ℕ᮹Ⓧʑᨱෙᯝႊ⨆⮉ᯙᰆvࠥ᪡ᯕႊ⨆
⮉ᯙᰆvࠥ᮹⨹đŝෝ᧞⦽äᯕ݅. ⨹đŝಽᇡ░3॒ᇥ ᱱᰍ⦹⮉vࠥ⨹ᨱ᮹⦽ᯝႊ⨆⮉vࠥᅕ݅۵ASTM C 1550 ŝ ᯕႊ⨆ ⮉vࠥ ⨹ᨱ ᮹⦽ ᯕႊ⨆ ⮉vࠥa ⓑ äᮝಽ
ӹ┡ԍ݅. ə్ӹࢱ̹30 mm ⨹ℕᨱᕽ᮹ASTM C 1550ŝ
ᯕႊ⨆⮉vࠥ⨹ᨱ᮹⦽ᯕႊ⨆⮉ᯙᰆvࠥ᪡3॒ᇥᱱᰍ⦹
⮉vࠥ⨹᮹ᯝႊ⨆⮉ᯙᰆvࠥ᪡᮹Ⓧʑእ۵2.08ŝ1.52ಽ
⊂ᱶࡹᨩŁ, ࢱ̹75 mm ⨹ℕᨱᕽ۵bb2.05᪡1.32a⊂ᱶ
ࡹᨕ, ᯝႊ⨆ŝᯕႊ⨆⮉ᯙᰆvࠥ₉ᯕ۵⨹ℕ᮹Ⓧʑᨱ
ᔢᯕ⦽äᮝಽӹ┡ԍ݅. ᄡ࠺ĥᙹ(coefficient of variation; c.o.v) ۵ ᯝႊ⨆ŝ ᯕႊ⨆ ⮉ᯙᰆvࠥ ༉ࢱ 11% ᯕ⦹ಽ, ᝁ⧁ ᙹ
ᯩ۵ ᝅ⨹đŝa šₑࡹᨩ݅.
Fig. 4ᨱ۵⨹ℕ᮹Ⓧʑᨱෙᯝႊ⨆ŝᯕႊ⨆⮉vࠥᇥ⡍
ෝࠥ⦹ᩡ݅. ᯝၹᱢᮝಽ⎹Ⓧญ✙᪡zᮡ≉ᖒᰍഭ۵⨹ℕ᮹
Ⓧʑa᷾a⧉ᨱvࠥ۵qᗭ⦹۵Ğ⨆ᮥӹ┡ԕ۵äᮝಽ
ಅᲙ ᯩ݅. ᅙ ᩑǍᨱᕽࠥ ASTM C 1550ŝ ᯕႊ⨆ ⮉vࠥ
⨹ᨱ ᮹⧕ ⊂ᱶࡽ ⮉vࠥ۵ ⨹ℕ᮹ Ⓧʑa ᷾a⧉ᨱ
qᗭ⦹۵äᮝಽ⊂ᱶࡹᨩ݅. ə్ӹ3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᨱ
᮹⦽ ᯝႊ⨆ ⮉vࠥ۵ ⨹ℕ᮹ ࢱ̹a 30 mmᨱᕽ 48 mmಽ
᷾a⧉ᨱ vࠥ Ⓧʑa qᗭ⦽ ၹ໕, 48 mmᨱᕽ 75 mm
⨹ℕᨱᕽ۵ᯝᱶ⦽vࠥsᮥaḡ۵äᮝಽӹ┡ӹ, Fig. 4ᨱᕽ
ᩩᔢ⧁ᙹᯩ۵äŝzᯕ⨹ℕ᮹Ⓧʑa᷾a⧉ᨱᯕႊ⨆ŝ
ᯝႊ⨆ vࠥ᮹ ₉ᯕ۵ qᗭ⧁ äᮝಽ ❱݉ࡽ݅. ᯕ్⦽ đŝ۵
ᯕႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ⬉ŝaᯝႊ⨆⮉ᯙᰆvࠥ᮹Ⓧʑ⬉ŝᅕ
݅ⓑäᮥ᮹ၙ⦹໑, ࢱ᮲ಆᔢ┽ᨱᕽ᮹⎹Ⓧญ✙Ⓧʑ⬉ŝᨱ
š⦽ᅕ݅ᯱᖙ⦽ԕᬊᮡ⬥ᗮםྙᨱᕽ݅Łᯩ݅(Zi ॒, 2013).
3.2 ߦਏ
⦝ಽ⨹ᨱᦿᕽᙹ⧪⦽ᯝႊ⨆(3॒ᇥᱱᰍ⦹⮉vࠥ⨹) ŝᯕႊ⨆(ASTM C 1550, ᯕႊ⨆⮉vࠥ⨹) ᱶᱢ⨹ᨱᕽ
⊂ᱶࡽvࠥđŝ᪡⦝ಽᝅ⨹đŝෝTable 5᪡6ᨱbbᱶญ⦹ᩡ
݅. ᅙᝅ⨹ᨱᕽࠥⓍʑ⬉ŝᝅ⨹đŝ᪡zᯕᯕႊ⨆⮉ᯙᰆvࠥa
ᯝႊ⨆⮉ᯙᰆvࠥᅕ݅ⓑäᮝಽӹ┡ԍᮝ໑, ᄡ࠺ĥᙹ۵༉ࢱ
5% ᯕ⦹ಽ⊂ᱶࡹᨩ݅. ⦝ಽᝅ⨹ᨱᕽ۵༉ु⨹ჶᨱᕽ᮲ಆᵡᯕ
ԏᦥḱᨱ⦝ಽᙹᯕ᷾a⦹ᩡᮝ໑, ᝅ⨹đŝ᮹⠙₉aⓑ
äᮝಽ ӹ┡ԍ݅.
Fig. 5۵ᯕႊ⨆⮉vࠥ⨹ᮥ ᯕᬊ⦽↽ݡ᮲ಆᙹᵡ80%᮹
⦝ಽᝅ⨹ᨱᕽ➉ձ⨹ℕᯙᰆ໕ᵲᦺᨱᕽ⊂ᱶࡽ⦹ᵲၹᅖ⬀ᙹ ᨱෙࢱᄡ⩶ශsᮥእƱ⦽äᯕ݅. ᬱ⩶➉ձᨱၹᅖ⦹ᵲᯕ
᯲ᬊ⦹۵Ⅹʑᨱ۵ࢱᄡ⩶ශsᯕÑ᮹ᯝ⊹⦹۵äᮝಽӹ┡ԍᮝ ӹ, ⦹ᵲၹᅖ⬀ᙹa᷾a⧉ᨱࢱᄡ⩶ශᯕ᷾a⦹໕ᕽə
₉ᯕੱ⦽᷾a⦹۵äᮝಽӹ┡ԍ݅. ⨹ℕ❭ƕᨱ۵⦹ӹ᮹
ᄡ⩶ශᯕɪĊ⯩᷾a⦹ᩍ❭ƕࡹ۵äᮝಽšₑࡹᨩᮝ໑, ᯕ۵
ၹᅖ⦹ᵲⅩʑᨱอᬱ⩶➉ձᯕ॒ႊᖒ᮲ಆᔢ┽ᨱ״ᯕŁ, ⦹ᵲၹ ᅖ⬀ᙹa᷾a⧉ᨱእ॒ႊᖒ᮲ಆᔢ┽ᨱ״ᯕíࡹᨕ❭ƕᨱ
ᯕ۵äᮥ᮹ၙ⦽݅. ə్ӹᯕ్⦽ǎᗭ⪵(localization) ⩥ᔢᮡ
ᗱᔢᯕӹ Ɂᩕၽ⩥ ྙᱽᨱᕽ ಅᲙ ᯩ۵ ྙᱽᯕ໑ ᰍഭ᮹
ᄡ⩶Ğ⪵(strain-hardening) ✚ᖒᯕᨧ۵Ğᬑᯝၹᱢᯙ⩥ᔢᯕ݅
(Bažant᪡Planas, 1998). ᷪ, ॒ႊ⨆᮹᮲ಆᔢ┽ᯕࠥᰍഭ᮹
❭ƕ۵⦽ႊ⨆ᨱᕽၽᔾ⦽݅. ASTM C 1550ŝᯕႊ⨆⮉vࠥ
⨹ᮥᯕᬊ⦽⎹Ⓧญ✙➉ձ᮹॒ႊᖒ᮲ಆᔢ┽᮹Ǎ⩥ᩍᇡෝ
᷾⦹ʑ᭥⦽ᱶᱢᝅ⨹(Kim ॒, 2012)ᨱᕽ۵⦹ᵲᰍ⦹᪡࠺ᨱ
⊂ᱶࡽࢱ}᮹⦹ᵲ-ᄡ⩶ශłᖁᯕ❭ƕḢᱥʭḡÑ᮹ᯝ⊹⦹۵
äᮝಽ ᅕŁࡽ ၵ ᯩ݅.
Table 5. Test results of static tests
test methods third-point bending test
biaxial flexure
test ASTM C 1550
mean strength [MPa] 7.43 9.68 12.73
S.D [MPa] 0.13 0.39 0.57
c.o.v [%] 2 4 5
Table 6. Test results of fatigue tests
test methods no.
number of cycles to failure, Nf
Smax= 90% Smax= 80% Smax= 70%
third-point bending test
1 71 32,741 1,016,199
2 2,797 67,972 2,000,000*
3 7,641 439,985 2,000,000*
ASTM C 1550
1 445 38,760 935,597
2 11,759 45,593 2,000,000*
3 16,749 504,178 2,000,000*
biaxial flexure test
1 147 3,635 423,344
2 832 87,391 786,570
3 1,967 154,931 2,000,000*
* : number of cycles to failure over 2×106 cycles
Fig. 5. The strain values of a round panel for biaxial flexure test according to the number of cycles
Fig. 6. The maximum strain values of a round panel for ASTM C 1550 according to the number of cycles
Fig. 7. S-N curves
Fig. 6ᮡASTM C 1550ᮥᯕᬊ⦽↽ݡ᮲ಆᙹᵡ80%᮹⦝ಽ ᝅ⨹ᨱᕽ⨹ℕᯙᰆ໕ᵲᦺᨱᕽ⊂ᱶࡽ⦹ᵲၹᅖ⬀ᙹᨱෙ
ࢱᄡ⩶ශsᮥእƱ⦽äᯕ݅. ⦹ᵲၹᅖ⬀ᙹᨱ↽ݡᄡ⩶ශᯕ
Ⓧí3݉ĥಽӹ٥ᨕḡ۵äᮥᙹᯩ݅. Ⅹʑ݉ĥ۵ᄡ⩶ශᯕ
í ᷾a⦹۵ ၹ໕, ə ᷾aᮉᮡ ᱱᱱ qᗭ⦹۵ äᮥ ᙹ
ᯩŁ, ᵲe ݉ĥᨱᕽ۵ ᄡ⩶ශᯕ ᯝᱶ⦹í ᷾a⦹݅a, ษḡส
❭ƕḢᱥ᮹݉ĥᨱ݅ᄡ⩶ශᯕɪĊ⦹í᷾a⦹ᩡ݅. ᯕ్⦽
đŝ۵ ⎹Ⓧญ✙ ԕᇡ᮹ ၙᖙɁᩕ᮹ ᖒᰆᨱ ᮹⦽ vᖒ ᄡ⪵ᨱ
ʑᯙ⦹໑, ᯝႊ⨆ᦶ⇶ၹᅖ⦹ᵲᨱᕽ᮹⎹Ⓧญ✙Ñ࠺ŝࠥᮁᔍ⦹
݅(Holmen, 1982; Neville, 1995).
Fig. 7ᨱ۵᮲ಆᙹᵡᨱෙ❭ƕၹᅖ⬀ᙹ᮹šĥෝ⫭ȡᇥ ᕾ⦹ᩍǍ⦽S-N šĥಽӹ┡ԕᨩ݅. ᯕႊ⨆᮲ಆᔢ┽᮹⦝ಽᙹ
ᮡ ASTM C 1550ᨱ ᮹⦽ ⦝ಽ ᙹᯕ ᯕႊ⨆ ⮉vࠥ ⨹ᨱ
᮹⦽⦝ಽᙹᅕ݅ⓑäᮝಽӹ┡ԍᮝ໑, 3॒ᇥᱱᰍ⦹⮉v
ࠥ⨹ᨱ᮹⦽ᯝႊ⨆⮉ᯙᰆvࠥ᮹⦝ಽᙹᮡASTM C 1550 ŝᯕႊ⨆⮉vࠥ⨹ᨱ᮹⦽đŝᔍᯕᨱ᮹ᔍᯕᨱᯩ۵äᮥ
ᙹ ᯩ݅.
Table 7ᮡᝅ⨹ᨱ᮹⧕⊂ᱶࡽ3॒ᇥᱱᰍ⦹⮉vࠥ⨹, ᯕ
ႊ⨆⮉vࠥ⨹ŝASTM C 1550 ⨹ჶ᮹S-N šĥŝ⦹ᵲ
ၹᅖ⬀ᙹ200อᨱᕽ᮹⦝ಽvࠥෝእƱ⦹ᩡ݅. ᝅ⨹đŝಽᇡ░
3॒ᇥᱱᰍ⦹⮉vࠥ⨹, ᯕႊ⨆⮉vࠥ⨹ŝASTM C 1550
⨹ℕ᮹ၹᅖ⬀ᙹ200อᨱᕽ᮹⦝ಽvࠥ۵bbᱶᱢ⦹ᵲ᮹
74%, 70%, 73%ᯙäᮝಽӹ┡ԍ݅. ʑ᳕ᩑǍᨱᕽᯕႊ⨆ᦶ⇶᮲ ಆᔢ┽ᨱᕽ᮹⦝ಽvࠥ۵ᯝႊ⨆ᦶ⇶᮲ಆᔢ┽ᨱᕽ᮹⦝ಽvࠥᅕ
݅ⓑäᮝಽᅕŁࡽၵᯩ݅(Su᪡ Hsu, 1988). ə్ӹᅙᩑǍᨱ ᕽ۵⎹Ⓧญ✙⦝ಽᝅ⨹᮹ⓑᇥᔑᖒᮥŁಅ⦽݅໕ᯝႊ⨆ŝᯕႊ
⨆ ⮉ᯙᰆ᮲ಆᔢ┽᮹ ⦝ಽᙹᮡ ᮁᔍ⦽ äᮝಽ ❱݉ࡽ݅.
Table 7. S-N relation
test methods S-N relation fatigue strengths to 2×106 cycles
third-point bending test Smax=102.52-4.56 log(N) 74% of the static strength biaxial flexure test Smax=104.18-5.46 log(N) 70% of the static strength
ASTM C 1550 Smax=108.58-5.64 log(N) 73% of the static strength
4. đು
ᅙᩑǍᨱᕽ۵ᯕႊ⨆᮲ಆᔢ┽ᨱᕽ᮹⎹Ⓧญ✙vࠥ✚ᖒŝ
Ⓧʑ⬉ŝəญŁ⦝ಽÑ࠺ᮥ⠪a⦹ʑ᭥⧕ᬱ⩶➉ձ⨹ℕෝ
ᱽ᯲⦹ᩍⓍʑ⬉ŝ᪡⦝ಽ⨹ᮥᙹ⧪⦹ᩡᮝ໑, ᯝႊ⨆ᯙᰆ᮲ಆ ᔢ┽᮹3॒ᇥᱱᰍ⦹⮉vࠥ⨹đŝ᪡እƱ⦹ᩡ݅. ᩑǍđŝಽ ᇡ░ ݅ᮭŝ zᮡ đುᮥ ᨩ݅.
(1) ᅙᝅ⨹ᮥ☖⧕↽ݡ⮉ᯙᰆvࠥ۵ASTM C 1550ŝᯕႊ⨆
⮉vࠥ⨹ᨱ᮹⦽ᯕႊ⨆⮉ᯙᰆvࠥa3॒ᇥᱱᰍ⦹⮉vࠥ
⨹ᨱ᮹⦽ᯝႊ⨆⮉ᯙᰆvࠥᅕ݅ⓑäᮝಽšₑࡹᨩ݅.
(2) 3॒ᇥᱱᰍ⦹⮉vࠥ⨹, ASTM C 1550, ᯕႊ⨆⮉vࠥ
⨹༉ࢱ⠙᮹Ⓧʑa᷾a⧉ᨱvࠥ۵qᗭ⦹۵äᮝ ಽšₑࡹᨩᮝ໑, ᯕႊ⨆⮉ᯙᰆvࠥ(ASTM C 1550, ᯕႊ⨆
⮉vࠥ⨹)᮹Ⓧʑ⬉ŝaᯝႊ⨆⮉ᯙᰆvࠥ(3॒ᇥᱱᰍ⦹
⮉vࠥ ⨹)᮹ Ⓧʑ⬉ŝᅕ݅ ⓑ äᮝಽ ⪶ᯙࡹᨩ݅.
(3)ᯕႊ⨆⮉vࠥ⨹ŝASTM C 1550ᨱ᮹⦽ᯕႊ⨆ᯙᰆvࠥ
᮹⦝ಽÑ࠺ŝ3॒ᇥᱱᰍ⦹⮉vࠥ⨹ᨱ᮹⦽ᯝႊ⨆ᯙᰆv
ࠥ᮹⦝ಽÑ࠺ෝ⫭ȡᇥᕾ⦹ᩍǍ⦽S-N šĥᨱ᮹⦹໕ᯝႊ⨆
ŝ ᯕႊ⨆ ᯙᰆᔢ┽᮹ ⦝ಽᙹᮡ ᮁᔍ⦽ äᮝಽ ӹ┡ԍ݅.
qᔍ᮹ɡ
ᯕםྙᮡ2012֥ࠥᱶᇡ(Ʊᮂŝ⦺ʑᚁᇡ)᮹ᰍᬱᮝಽ⦽ǎᩑ Ǎᰍ݉ʑⅩᩑǍᔍᨦ᮹ḡᬱ(2012R1A1B3004227)ŝ, ǎ☁⧕᧲
ᇡᔑ⦹⦽ǎ⧕᧲ŝ⦺ʑᚁḥ⯆ᬱ᮹℉݉⧎อÕᖅʑᚁ}ၽᔍᨦᩑ Ǎእ ḡᬱ(20120093)ᮥ ၼᦥ ᙹ⧪ࡹᨩܩ݅.
References
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ASTM (2008). ASTM C 1550-08: Standard test method for flexural toughness of fiber-reinforced concrete (Using centrally-loaded round panel), ASTM International, West Conshohocken, PA, USA.
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