Received September 28, 2012/ revised November 16, 2012/ accepted August 9, 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͵͵ǤǤʹͳͻͷ Ǥ ǤǤ
㉞Ꮊ㔖㘪Ὢ㡶#ᐈ⳾#⊲#⡢㡶ᶽ-㙾ⴲ#ᤶⴖ#㔖㘪Ὢ㡶#⡢㡶ᶽⴖ#Ⳟ㱦ᇓᦂ
త෮ ȵଗઽࢀ
Chae, Hyun Soo*, Yun, Young Mook**
Effective Strengths of Concrete Struts in Strut-Tie Models of Reinforced Concrete Deep Beams
ABSTRACT
The effective strength of concrete struts must be determined accurately for the reliable strut-tie model analysis and design of structural concrete. In this study, the equations of the effective strength, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete deep beams employed in current design codes, are proposed. The effects of shear span-to-effective depth ratio, compressive strength of concrete, and flexural and shear reinforcement ratios are reflected in the development of the proposed equations. To examine the appropriateness of the proposed equations, the strengths of 241 reinforced concrete deep beams, all tested to shear failure, are evaluated by using the three types of strut-tie models with the existing and proposed equations.
Key words : Reinforced concrete, Deep beam, Strut-tie model, Effective strength of strut, Ultimate strength
Ⅹಾ
ᜅ✙ౠ-┡ᯕ༉ߙႊჶᮥᯕᬊ⦹ᩍ℁ɝ⎹Ⓧญ✙ʫᮡᅕෝᱶ⪶⦹í⧕ᕾ⦹Łᦩᱥ⦹íᖅĥ⦹ʑ᭥⧕ᕽ۵⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥෝᱶ
⪶⦹íđᱶ⦹ᩍ⦽݅. ᯕᩑǍᨱᕽ۵ᩍ్ᖅĥʑᵡᕽၰᩑǍྙ⨭ᨱᕽᱽᦩࡽᖙ᳦ඹ᮹ݡ⢽ᱢᯙ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᜅ✙ౠ-┡ᯕ༉
ߙᮥ᭥⦹ᩍ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᱥ݉Ğeእ, ⎹Ⓧญ✙᮹ᦶ⇶vࠥ, əญŁ⮉℁ɝၰᱥ݉℁ɝእ॒᮹ᵝᖅĥᄡᙹॅ᮹ᩢ⨆ᮥᱶ⪶⦹
íၹᩢ⧁ᙹᯩ۵⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥᮥ}ၽ, ᱽᦩ⦹ᩡ݅. ⩥⧪ᖅĥʑᵡᕽၰᩍ్ᩑǍྙ⨭᮹⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥŝ
ᯕᩑǍᨱᕽᱽᦩ⦽ᮁ⬉vࠥᮥᯕᬊ⦹ᩍ❭ƕᝅ⨹ᯕᙹ⧪ࡽ241}℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ɚ⦽vࠥෝ⠪a⦹ᩡᮝ໑, əđŝ᮹እƱᇥᕾ
ᮥ☖⧕ᯕᩑǍᨱᕽᱽᦩ⦽ᜅ✙ౠᮁ⬉vࠥ᮹ᱢ⧊ᖒᮥ⠪a⦹ᩡ݅.
áᔪᨕ ℁ɝ⎹Ⓧญ✙, ʫᮡᅕ, ᜅ✙ౠ-┡ᯕ༉ߙ, ᜅ✙ౠᮁ⬉vࠥ, ɚ⦽vࠥ
1. ᕽು
ᜅ✙ౠ-┡ᯕ༉ߙႊჶᮡ⎹Ⓧญ✙ ᇡᰍ ၰ Ǎ᳑ྜྷ᮹ ᱥ ᩢᩎᨱ Ù⊽ ᖅĥෝ ⨆ᔢ┅ʑ ᭥⦽ äᮝಽᕽ, ᅖᰂ⦽ ⦹ᵲ᳑Õ ၰ ʑ⦹⦺ᱢ
⩶ᔢᮥ w۵ ⎹Ⓧญ✙ ᇡᰍ ၰ Ǎ᳑ྜྷ᮹ ᖅĥᨱ ⬉ŝᱢᯕŁ ಅᲙ ᯩ݅. ə్ӹᜅ✙ౠ-┡ᯕ༉ߙႊჶᮥ⎹Ⓧญ✙Ǎ᳑ᇡᰍ᮹ɚ⦽vࠥ
⧕ᕾၰᖅĥᨱᱢᬊ⦹ʑ᭥⧕ᕽ۵ᖁᱶ⦽ᜅ✙ౠ-┡ᯕ༉ߙ᮹ᱢ⧊ᖒ❱݉ᨱ⦥⦽⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥෝᱶ⪶⦹íđᱶ⦹ᩍ⦽݅.
⩥ᰍʭḡ ⎹Ⓧญ✙ ᜅ✙ౠ᮹ ᮁ⬉vࠥෝ đᱶ⦹ʑ ᭥⦽ ᝅ⨹ᩑǍa ฯᮡ ᩑǍᯱॅᨱ ᮹⧕ ḥ⧪ࡹᨕ ᪵ᮝ໑, ᩍ్ ᳦ඹ᮹ ᮁ⬉vࠥ
ᯕ ᱽᦩࡹᨩ݅(Thulimann, 1976; Nielsen et al., 1978; Marti, 1985; Schlaich et al., 1987; Bergmeister et al., 1993; MacGregor, 1997;
ࡓࡾν࣡ėॡ
(a) Strut-Tie Model of Arch Load Transfer Mechanism
(b) Strut-Tie Model of Truss Load Transfer Mechanism
(c) Strut-Tie Model of Combined Load Transfer Mechanism Fig. 1. Strut-Tie Models for Reinforced Concrete Deep Beams
FIB, 2010; AASHTO, 2010; ACI 318M-11, 2011). ə్ӹ ᱽᦩࡽ
ᜅ✙ౠ᮹ᮁ⬉vࠥᮡݡᇡᇥ✚ᱶ⦽⦹ᵲၰ⩶ᔢ᳑Õᮥ
w۵⎹Ⓧญ✙ᇡᰍ᮹ᝅ⨹ၰᙹ⊹⧕ᕾđŝᨱၵ┶ᮥࢵäᮝಽ, ᱥ݉Ğeእ, ⎹Ⓧญ✙ᦶ⇶vࠥ, ⮉℁ɝపၰᱥ݉℁ɝప॒ᮥ
⡍⧉⦽ᵝᖅĥᄡᙹᨱᅖᰂ⦽❭ƕÑ࠺ᮥᅕᯕ۵℁ɝ⎹Ⓧ
ญ✙ʫᮡᅕ᮹ᜅ✙ౠ-┡ᯕ༉ߙ⧕ᕾၰᖅĥᨱəݡಽᔍᬊ⦹۵
äᮡ ᱢᱩ⦹ḡ ᦫ݅.
ᯕᩑǍᨱᕽ۵⩥ᰍʭḡᱽᦩࡽᜅ✙ౠ᮹ᮁ⬉vࠥᮥᖙĥᵝ
ᖅĥʑᵡᕽ(FIB, 2010; AASHTO, 2010; ACI 318M-11, 2011) ၰ
ᩑǍྙ⨭(Foster and Gilbert, 1998; Kim and Yun, 2011)ᨱᕽᱽᦩ
ࡽᖙ᳦ඹ᮹ݡ⢽ᱢᯙ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᜅ✙ౠ-┡ᯕ༉ߙ, ᷪ
⦹ᵲᱱŝḡḡᱱᮥ⦹ӹ᮹ᜅ✙ౠᮝಽḢᱲᩑđ⦽ᦥ⊹⦹ᵲᱥݍ
ີ⍅ܩ᷹᮹ ᜅ✙ౠ-┡ᯕ ༉ߙ, ⦹ᵲᱱŝ ḡḡᱱᮥ Ğᔍ ᜅ✙ౠ, ᙹ⠪ᜅ✙ౠ, əญŁᙹḢ℁ɝ┡ᯕಽᩑđ⦽ᙹḢ✙్ᜅ⦹ᵲᱥݍ
ີ⍅ܩ᷹᮹ᜅ✙ౠ-┡ᯕ༉ߙ, əญŁᯕॅࢱ}᮹⦹ᵲᱥݍີ⍅
ܩ᷹ᮥ᳑⧊⦽ᅖ⧊⦹ᵲᱥݍີ⍅ܩ᷹᮹ᜅ✙ౠ-┡ᯕ༉ߙ॒ᨱ
ᱢᬊ⦹ᩍ❭ƕᝅ⨹ᯕᙹ⧪ࡽ241}℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹❭ƕv
ࠥෝ⠪a⦹ᩡᮝ໑, bᜅ✙ౠᮁ⬉vࠥ᮹ᱢ⧊ᖒᮥᇥᕾ⦹ᩡ݅.
ੱ⦽ 2₉ᬱ᮲ಆᮥၼ۵ྕɝ⎹Ⓧญ✙᮹ᵝ᮲ಆᔢ┽ၰ℁ɝᨱ᮹⦽
⎹Ⓧญ✙᮹Ǎᗮ⬉ŝෝŁಅ⦹۵ᮅᩢྖ(2005)᮹ᮁ⬉vࠥđᱶႊ
ჶᨱ⎹Ⓧญ✙ᦶ⇶vࠥ᮹ᩢ⨆ᮥ⇵a⦹ᩍ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹
ᱥ݉Ğeእ, ⎹Ⓧญ✙᮹ᦶ⇶vࠥ, əญŁ⮉℁ɝၰᱥ݉℁ɝእ॒
᮹ᵝᖅĥᄡᙹॅ᮹ᩢ⨆ᮥᱶ⪶⯩ၹᩢ⧁ᙹᯩ۵ᜅ✙ౠᮁ⬉vࠥ
ᮥ}ၽ, ᱽᦩ⦹ᩡᮝ໑, ᱽᦩ⦽᮹ᱢ⧊ᖒᮥá᷾⦹ᩡ݅.
2. ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᜅ✙ౠ-┡ᯕ༉ߙ
CSA(2004)᪡AASHTO(2010)ᨱᕽ۵ᖅĥᩢᩎ᮹⦹ᵲĞಽӹ
᮲ಆ⮱ᮥ ᱢᱩ⯩ ⢽⩥⧁ ᙹ ᯩ۵ ༉ߙᮥ ᖁᱶ⦹ᩍ ⦽݅۵
ʑᅙᱢ}ֱᮥᱽ⦹ᩡᮝ໑, Fig. 1(a)᪡zᮡᜅ✙ౠ-┡ᯕ༉ߙᮥ
ᯕᬊ⦹ᩍ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᖅĥෝᙹ⧪⧁ᙹᯩࠥಾ⦹Ł
ᯩ݅. ᯕ్⦽}ֱᮡACI 318M-11(2011)ᨱᕽ᯦ࠥࠥࡹᨕFig.
1(a)᪡zᮡ⦹ᵲᱱŝḡḡᱱᮥḢᱲᩑđ⦽ᦥ⊹⦹ᵲᱥݍີ⍅ܩ
᷹᮹ᱶᱶ✙్ᜅǍ᳑᮹ᜅ✙ౠ-┡ᯕ༉ߙ(ᯕ⦹ᱶᱶᜅ✙ౠ-┡ᯕ
༉ߙ)ᮥᯕᬊ⦹ᩍ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ᖅĥෝᙹ⧪⧁ᙹᯩࠥಾ
⦹Łᯩ݅. ə్ӹACI 318M-11ᨱᕽ۵ᦶ⇶ŝᯙᰆ᮹ႊ⨆ᯕ
ᮁᔍ⧁ᙹᨧ݅۵ᬱ⊺ᨱ᯦b⦹ᩍᜅ✙ౠŝ┡ᯕ᮹ᯕ۵bᯕ
25oᅕ݅⍅⦽݅۵ʑᵡᮥᱽ⧉ᨱFig. 1(a)᪡zᮡ༉ߙᮡ
ᝅᱽᱢᮝಽſîƂ á ÎíÕ(ſîƘ á Ïí×,Ƙ á ×íÖƂ,Ƃ á ×íÖƆ)ᯕ⦹᮹ᇡ ᰍᨱᕽอᱢᬊᯕa܆⦹݅. ᕽſîƂ > ÎíÕ᮹ʫᮡᅕᨱݡ⧕ᕽ ۵ ACI 445(2002)᮹ ᜅ✙ౠ-┡ᯕ ༉ߙ ᖅĥᩩᱽ᪡ zᯕ Fig.
1(b)᪡zᮡᙹḢ✙్ᜅ⦹ᵲᱥݍີ⍅ܩ᷹᮹ᱶᱶᜅ✙ౠ-┡ᯕ
༉ߙᮥᯕᬊ⦹ࠥಾȽᱶ⦹Łᯩ݅. CSA, AASHTO, əญŁACI 318M-11ᨱᕽ۵ᖅĥෝ᭥⦽ᇡᱶᱶ✙్ᜅǍ᳑᮹ᜅ✙ౠ-┡ᯕ
༉ߙ(ᯕ⦹ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙ)ᨱš⦽ᄥࠥ᮹ʑᵡᮥᱽ⦹
Ł ᯩḡ ᦫ݅.
FIB(2010)۵℁ɝၰ⥥ญᜅ✙౩ᜅ✙⎹Ⓧญ✙ʫᮡᅕ᮹ᖅĥ
ෝ᭥⧕ᱥ݉ḡeݡ༉ູ✙❵ʙᯕ᮹እſîƘa0.5 ᯕ⦹ᯙĞᬑ۵
Fig. 1(a)᮹ᦥ⊹ີ⍅ܩ᷹᮹ᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥ, əእa
2.0ᯕᔢᯙĞᬑ۵Fig. 1(b)᮹ᙹḢ✙్ᜅີ⍅ܩ᷹᮹ᱶᱶᜅ✙ౠ -┡ᯕ༉ߙᮥ, əญŁəእa0.5᪡2.0 ᔍᯕᯙĞᬑ۵Fig. 1(c)᮹
ᦥ⊹ີ⍅ܩ᷹ŝᙹḢ✙్ᜅີ⍅ܩ᷹ᮥ᳑⧊⦽ᅖ⧊ີ⍅ܩ᷹᮹
ᇡᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙᮥ ᱽᦩ⦹ᩡ݅. ᦥ⊹ ີ⍅ܩ᷹ŝ ᙹḢ
✙్ᜅີ⍅ܩ᷹ᮥ᳑⧊⦽Fig. 1(c)᮹ᜅ✙ౠ-┡ᯕ༉ߙᮡ1₉
ᇡᱶᱶ✙్ᜅǍ᳑ᯕအಽ, FIBᨱᕽ۵ᦥ⊹ີ⍅ܩ᷹ŝᙹḢ✙్
ᜅີ⍅ܩ᷹ᯕbbᇡݕ⦹۵ᱥ݉ಆ᮹Ⓧʑෝ⦹ᵲᇥ႑ᮉಽȽᱶ
⦹ᩍᱽ⦹ᩡ݅. ⦹ᵲᇥ႑ᮉᮡ1₉ᇡᱶᱶ✙్ᜅǍ᳑᮹ᜅ✙ౠ-
┡ᯕ༉ߙᮥᱶᱶ᮹✙్ᜅǍ᳑ಽᄡ⪹┅အಽ, ᇡᱶᱶᜅ✙ౠ-┡
ᯕ ༉ߙᮥ ᯕᬊ⦽ ⎹Ⓧญ✙ ʫᮡ ᅕ᮹ ᜅ✙ౠ-┡ᯕ ༉ߙ ⧕ᕾ
ၰ ᖅĥ ᇡᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙ᮹ b ᱩᱱᨱᕽ ⯹ᨱ š⦽
Table 1. Shear Span-to-Effective Depth Ratios for Deep Beam Strut-Tie Models
Strut-Tie Model Foster and Gilbert (1998) FIB(2010) AASHTO(2010), ACI 318(2011) Kim and Yun(2011), Chae(2012)
Type I, Fig. 1(a) ſîƘ = Îí× ſîƘ = ×íÒ ſîƂ = ÎíÕ -
Type II, Fig. 1(b) ſîƘ >öćÐ ſîƘ > Ïí× ſîƂ ðÎíÕ -
Type III, Fig. 1(c) Îí× ïſîƘ ïöćÐ ×íÒ ïſîƘ ïÏí× - ſîƂ = Ðí×
Except for FIB(2010), §ƑƂ= 0 in Fig. 1(c); In general, Ƙ á ×íÖƂ
⠪⩶᳑Õᮥ ᱢᬊ⦹ᩍ ༉ु ᜅ✙ౠŝ ┡ᯕ᮹ ݉໕ಆᮥ Ǎ⧁ ᙹ
ᯩí ⦽݅. FIBᨱᕽ ᱽ⦽ ⦹ᵲᇥ႑ᮉķ۵ ݅ᮭŝ z݅.
ķ á ć©
©ƕ
á ćÐ à §ÏſîƘ à ÎƑƂî© (1)
ᩍʑᕽ,©ƕ۵ᙹḢ┡ᯕ᮹݉໕ಆ,©۵᯲ᬊ⦹ᵲ, əญŁ§ƑƂ۵
ᇡᰍᨱ ᯲ᬊ⦹۵ ⇶ಆᮥ ӹ┡ԙ݅.
Foster and Gilbert(1998)ᮡFIB(2010)᪡zᯕ℁ɝ⎹Ⓧญ✙
ᅕ᮹ᖅĥෝ᭥⧕ᖙaḡ⩶┽᮹༉ߙ, ᷪ§ƑƂ=0ᯕŁᱢᬊჵ᭥a
ſîƘ = ÎᯙFig. 1(a)᮹ᦥ⊹ີ⍅ܩ᷹᮹ᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥ,
§ƑƂ=0ᯕŁᱢᬊჵ᭥aſîƘ >öćÐᯙFig. 1(b)᮹ᙹḢ✙్ᜅ
ີ⍅ܩ᷹᮹ᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥ, əญŁ§ƑƂ=0ᯕŁᱢᬊჵ᭥
aÎ ï ſîƘ ïöćÐᯙFig. 1(c)᮹ᦥ⊹ၰᙹḢ✙్ᜅີ⍅ܩ᷹᮹
᳑⧊⦽ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙ॒ᮥᱽᦩ⦹ᩡ݅. ੱ⦽əॅᯕ
ᱽ⦽ Fig. 1(c) ༉ߙ᮹ ⦹ᵲᇥ႑ᮉķ۵ ݅ᮭŝ z݅.
ķÞÜß á ć©
©ƕ
á ćöſîƘ à ÎćÐ à Î (2)
Kim and Yun(2011)ŝ₥⩥ᙹ(2012)۵℁ɝ⎹Ⓧญ✙ᱥ݉Ğ eእa3.0 ᯕ⦹ᯙ℁ɝ⎹Ⓧญ✙ʫᮡᅕᨱᱢᬊ⧁ᙹᯩ۵§ƑƂ= 0ᯙ Fig. 1(c)᮹ ᇡᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙᮥ ᱽᦩ⦹ᩡ݅. ੱ⦽
₥⩥ᙹ(2012)۵ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙ᮹⦹ᵲᇥ႑ᮉᮥ݅ᮭŝ
zᯕ ᱽᦩ⦹ᩡ݅.
ķÞÜß á ÞſîƂà ÎíÒß âĸ ſîƂ = ÎíÒ ķÞÜß á ÞſîƂà ÎíÒß âĸ ÎíÒ ï ſîƂ = Ľ
ſÞÜß á ÞſîƂà Ľß âĹ ſîƂ ð Ľ
(3)
Eq. (3)ᨱᕽ,,,,Ľ,ĸ,Ĺ۵ᵝᖅĥᄡᙹᨱෙ⦹ᵲᇥ႑ ᮉ᮹ ᄡ⪵ෝ Łಅ⦹۵ ᄡᙹಽᕽ ݅ᮭŝ zᯕ ᱶ᮹⦹ᩡ݅.
á ÔÕ à ×íÎƄƁƉâÞÎÕ à ×íÑƄƁƉßŇîŇƀ
á ÓÔ à ×íÎƄƁƉâÞÎ à ×íÐƄƁƉßŇîŇƀ
á ÎÔÞÎ à ŇîŇƀß â×íÏÞƄƁƉà Ï×ßŇîŇƀ
(4a)
Ľ á ÏíÐ à ŇîÞÐŇƀß
ĸ á ÐÓíÒ â×í×ÒƄƁƉâÐÏŇîŇƀ Ĺ á ĸ â ÞĽ à ÎíÒß
(4b)
ᩍʑᕽ, Ňƀ۵⮉⠪⩶℁ɝእෝӹ┡ԙ݅. Table 1ᮡ℁ɝ⎹Ⓧญ
✙ʫᮡᅕᜅ✙ౠ-┡ᯕ༉ߙ᮹ᱢᬊჵ᭥ෝ᧞⧕ᕽᱶญ⦽äᯕ݅.
3. ⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥ
3.1 ׆֜ࢫডծ׆ஜছଭକตԳܑਐ
⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥƄƁƑ۵ᯝၹᱢᮝಽ⎹Ⓧญ✙᮹ᦶ⇶
vࠥᯙƄƁƉ᮹⧉ᙹಽӹ┡ԙ݅. ᩍ్ᩑǍᯱၰᖅĥʑᵡᕽ۵⧕ᕾᱢ
ၰᝅ⨹ᱢᩑǍෝ☖⦹ᩍ݅᧲⦽⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥၰ
sᮥᱽᦩ⦹ᩡ݅. Thulimann(1976), Nielsen et al.(1978), Marti (1985), Schlaich et al.(1987), MacGregor(1997), AASHTO (2007, 2010), ACI 318(2008, 2011) ॒ᯕᱽᦩ⦽ᮁ⬉vࠥၰ
sᮡJeun and Yun(2010)᮹ᩑǍםྙᨱᔢᖙ⯩ᗭ}ࡹᨕᯩ݅.
Bergmeister et al.(1993)ᮡᯝၹᱢᯙ➍, ᄲ༉᧲, ੱ۵⥥ญ᷹ᜅ
✙ౠᨱݡ⦽ᮁ⬉vࠥĥᙹŃƑÞá ƄƁƑîƄƁƉßෝᝅ⨹đŝᨱɝÑ⦹ᩍ
Eq. (5)᪡zᯕᱽᦩ⦹ᩡᮝ໑, ੱ⦽ᦶ⇶᮹ݡbᜅ✙ౠ᮹ᮁ⬉vࠥĥ ᙹෝ×íÓŃƑಽᱽᦩ⦹ᩡ݅. ӹᖁ℁ɝᯕӹு℁ɝᮝಽǍᗮࡽ3₉ᬱ
⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥᮥ℁ɝ᮹Ǎᗮಆ, ⥥᪡ᘂእ, ḡᦶ❱
ၰᜅ✙ౠ᮹݉໕ᱢ, ᜅ✙ౠ᮹ᦶ⇶ಆ॒ᮥ⡍⧉⦽ᩍ్ᄡᙹॅ᮹⧉
ᙹಽᱽᦩ⦹ᩡ݅.
ŃƑá ×íÕ× ƄƁƉ= ÏÕ¦©ſ
ŃƑá ×íÖ à ×íÏÒƄƁƉîÔ× ÏÕ ï ƄƁƉï Ôצ©ſ ŃƑá ×íÓÒ ƄƁƉ> Ôצ©ſ
(5)
(a) Biaxial Compression - Compression
(b) Biaxial Tension - Compression
Fig. 2. Relationship Between Principal Stress and Effective Strength of Finite Element
Fig. 3. Algorithm for Considering Effect of Reinforcing Bars in Determination of Effective Strength of Concrete Struts FIB (2010)۵⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥĥᙹෝEq. (6)ŝzᯕ
ᱽᦩ⦹ᩡ݅.
ŃƑá ķÞÐ×îƄƁƉßÎîÐÞćĹƁ
ķƁƁ
ß (6)
ᩍʑᕽ,ƄƁƉ᮹݉᭥۵MPaᯕ໑,ķƁƁ۵⎹Ⓧญ✙᮹ᦶ⇶vࠥᨱၙ
⊹۵e᮹᳕ᱢĥᙹᯕ໑, əญŁĹƁ۵ᇡᇥᦩᱥĥᙹ(ᯝၹᱢᯙĞ ᬑ1.5ᯥ)ᯕ݅. ੱ⦽ķ۵vࠥqᗭĥᙹಽᕽ, ᮲ಆᯕƱࡹḡᦫᮡ
ᯝ⇶ᦶ⇶᮲ಆᔢ┽ᨱ״ᯙᜅ✙ౠੱ۵᧲ႊ⨆ᦶ⇶᮲ಆᔢ┽ᨱ״ᯙ
ᜅ✙ౠ᮹Ğᬑ۵1.0, ᜅ✙ౠ᮹⇶ႊ⨆ᮝಽɁᩕᯕၽᔾ⦹Łᜅ✙ౠ
⇶᮹Ḣbႊ⨆ᮝಽᯙᰆᮥၼ۵℁ɝᯕ႑⊹ࡽᜅ✙ౠ᮹Ğᬑ۵0.75, əญŁᜅ✙ౠ᮹⇶ႊ⨆ᮝಽɁᩕᯕၽᔾ⦹Łᜅ✙ౠ⇶᮹Ḣbႊ⨆
ᮝಽᯙᰆᮥၼ۵℁ɝᯕ႑⊹ࡹḡᦫᮡᜅ✙ౠ᮹Ğᬑ۵0.55ᯕ݅.
Eq. (6)ᨱᕽ,ķÞÐ×îƄƁƉßÎîÐ᮹sᮥbᜅ✙ౠ᮹Ğᬑᨱݡ⦹ᩍbb
1.0, 0.8, 0.55ಽᱽ⦽⦹ᩡ݅.
3.2 ෮֜ଭକตԳܑਐ
ᮅᩢྖ(2005)ᮡ2₉ᬱ᮲ಆᮥၼ۵ྕɝ⎹Ⓧญ✙᮹ᵝ᮲ಆᔢ┽
(Fig. 2), 2₉ᬱᦶ⇶ᵝ᮲ಆ⮱ŝᜅ✙ౠ᮹⇶ႊ⨆ŝ᮹₉ᯕb, ə
ญŁ℁ɝᨱ᮹⦽⎹Ⓧญ✙᮹Ǎᗮ⬉ŝ(Fig. 3) ॒ᮥᯕᬊ⦹ᩍᜅ✙ౠ ᮹ᮁ⬉vࠥෝđᱶ⦹۵ႊჶᮥᱽᦩ⦹ᩡ݅. Fig. 2۵2₉ᬱᮁ⦽
ᗭ᮹ᵝ᮲ಆŝᮁ⬉vࠥ᪡᮹šĥෝᅕᯙäᮝಽ, ⠪໕᮲ಆ⪚ᮡ⠪
໕ᄡ⩶ශᮁ⦽ᗭ⧕ᕾᮝಽᇡ░⎹Ⓧญ✙ᜅ✙ౠᯕ᭥⊹⦽Ŕ᮹⦽
ᮁ⦽ᗭ᮹ᵝ᮲ಆňÎƎၰňÏƎෝŁ, ྕɝ⎹Ⓧญ✙᮹❭ƕ⡍ᖁ ᮝಽᇡ░ᯕᗭ᮹ᵝ᮲ಆᨱ⧕ݚࡹ۵ňÎƄᷪ⎹Ⓧญ✙ᜅ✙ౠ᭥⊹
ᨱ״ᯙᮁ⦽ᗭ᮹ᮁ⬉vࠥƄƁƑƃෝ۵݅. ᩍʑᕽ, ᵝ᮲ಆňÎƎၰ
ňÎƄ۵bbňÏƎၰňÏƄᅕ᯲݅Ñӹz݅.ᯝၹᱢᮝಽ⎹Ⓧญ✙ᜅ✙ౠ
ᮡᩍ్}᮹⠪໕Łℕᮁ⦽ᗭᨱÙℱᯩᮝအಽ, ࠺ᯝ⦽ႊჶᮝಽ
ᯕᮁ⦽ᗭॅ᮹ƄƁƑƃෝđᱶ⦽݅. đᱶ⦽ᩍ్ᮁ⦽ᗭॅ᮹ƄƁƑƃs
ᵲᨱᕽᯕॅs᮹⢽ᵡ⠙₉ჵ᭥ԕᨱॅᨕ᪅۵sॅᮥᔑᚁ⠪Ɂ⦽
sᮥ⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥƄƁƑಽ≉⦽݅. อ᧞⎹Ⓧญ✙ᜅ✙
ౠᯕ᭥⊹⦽ᮁ⦽ᗭ᮹ᵝᦶ⇶᮲ಆbᯕ⎹Ⓧญ✙ᜅ✙ౠ᮹ႊ⨆ŝ
ľ᮹bࠥಽ₉ᯕaӽ݅໕ᯕᮁ⦽ᗭ᮹ᮁ⬉vࠥ۵ᵝ᮲ಆ᮹⇶ᄡ
⪹ᮥᯕᬊ⦹ᩍqᗭ┉݅.
ƙ
Ɯƚ ƛ
Ɲƞ
ƄƁƑƃ ƄÎÏ
ƄÏÎƄÎÎ á ƙƜƚ ƛ
Ɲƞ
ľ ľ à ľ ľ ƙ
Ɯƚ ƛ
Ɲƞ
ňÎƄ ×
× ňÏƄ
ƙƜ
ƚ ƛ
Ɲƞ
ľ ľ à ľ ľ
(7)
ƄƁƑƃ ၰƄƁƑෝđᱶ⦹ʑ᭥⦽᭥ŝᱶᨱᕽ۵℁ɝ᮹ᩢ⨆ᮥŁಅ⦹ḡ
ᦫᮡᔢ┽ᨱᕽྕɝ⎹Ⓧญ✙᮹ᮁ⦽ᗭ⧕ᕾᮥ☖⧕đᱶ⦽ᵝ᮲ಆ
ᮥᯕᬊ⦹ᩡ݅. ᕽ℁ɝᨱ᮹⦽⎹Ⓧญ✙Ǎᗮ᮹ᩢ⨆ᮥŁಅ⦹
ʑ᭥⦹ᩍFig. 3ᨱᵝᨕḥᱩ₉ᨱᵝ᮲ಆňÎƎၰňÏƎ᮹đᱶ
℁ɝ┡ᯕ᮹݉໕ಆᮥᇡ᮹⦹ᵲᮝಽ᯲ᬊ⍽ྕɝ⎹Ⓧญ✙᮹ᮁ
⦽ᗭ⧕ᕾᮥ݅ᙹ⧪⦽݅. ᯕ᪡zᮡŝᱶᮥᜅ✙ౠŝ┡ᯕ᮹݉
Fig. 4. Specification and Strut-Tie Model for Determining Effective Strength of Concrete Struts
Fig. 5. Coefficient of Effective Strength of Concrete Strut E Associated with Design Variables
໕ಆᯕEq. (8)᮹᳑Õᮥอ᳒⧁ভʭḡ2~3₉ಡၹᅖ⦹ᩍᜅ✙ౠ᮹
ᮁ⬉vࠥෝ↽᳦ᱢᮝಽđᱶ⦽݅. Eq. (8)ᨱᕽ,ƌᮡᜅ✙ౠŝ┡ᯕ᮹
ᙹෝ, ƇƑƒƃƎ à ÎၰƇƑƒƃƎ۵ᱥၹᅖ݉ĥၰ⩥ၹᅖ݉ĥෝ, əญŁ
۵݉໕ಆ᮹norm sᯕ݅.
ćƌ
ƇƑƒƃƎà ƇƑƒƃƎàÎ
= ×í×Î (8)
ᔢʑŝᱶᮡၹᅖᱢᯙᙹ⊹⧕ᕾŝฯᮡ᧲᮹᯲ᨦᯕ⦥⦹အಽ, ᯕෝ᭥⦽ᱥྙᱢᯙ⥥ಽəఉᮥ}ၽ⦹ᩍᔍᬊ⦹ḡᦫ۵݅໕ᝅྕ
ᱢᬊᨱⓑ⦽ĥaᯩ݅. ᯕᩑǍᨱᕽ۵ᮅᩢྖ(2005)᮹ႊჶᮥ3.0 4᮹℁ɝ⎹Ⓧญ✙ʫᮡᅕᨱᱢᬊ⦹ᩍᖙ᳦ඹᜅ✙ౠ-┡ᯕ༉ߙ᮹
۵ᜅ✙ౠ-┡ᯕ༉ߙᨱ᯲ᬊ⦹۵⦹ᵲ©ᨱݡ⧕⦥⦽⮉ၰᱥ݉
℁ɝపᯕ݅. ᯕᩑǍ᮹ᵝᖅĥᄡᙹ᮹ჵ᭥ᨱᕽᙹฯᮡᖅĥᄡᙹ᮹
᳑⧊ᮥw۵ʫᮡᅕෝݡᔢᮝಽᔢʑᱡᯱ᮹ႊჶᮝಽFig. 4᮹༉ु
⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉vࠥƄƁƑෝǍ⦹ᩡ݅. ⦽ᩩಽ, Fig. 5۵Fig.
4᮹Ğᔍᜅ✙ౠE᮹ᮁ⬉vࠥĥᙹŃÎ (=ƄƁƑîƄƁƉ,ƄƁƑ=ᮅᩢྖ(2005) ᮹ႊჶᮝಽǍ⦽ᜅ✙ౠ᮹ᮁ⬉vࠥ)ᮥ⮉℁ɝእa0.6ᯙĞᬑᨱ
ݡ⦹ᩍǍ⦽äᯕ݅. ༉ुᖅĥᄡᙹ᮹᳑⧊⦹ᨱᕽłᖁ᳑ᱶᮥ☖⧕
đᱶ⦽ᙹ⠪ᜅ✙ౠA ၰĞᔍᜅ✙ౠC, E, F᮹ᮁ⬉vࠥĥᙹŃÎ۵
Eq. (9)᪡zᯕ, əญŁᙹ⠪ᜅ✙ౠB᮹ᮁ⬉vࠥĥᙹ۵1.0ᮝಽđ ᱶ⦹ᩡ݅.
ŃÎì ƑƒƐƓƒ áĒ ēĔ
ĕ
ĕ
×íÕ â×íÎſîƂ ſîƂ = Ïí×
Îí× Ïí× ï ſîƂ= Ðí× (9a)
ŃÎì ƑƒƐƓƒ ì ì á ĸÞſîƂà Ïí×ß âĹ (9b)
Eq. (9b)ᨱᕽ, Ğᔍᜅ✙ౠC, E, F᮹ᮁ⬉vࠥĥᙹෝ᭥⦽ĥᙹ
-┡ᯕ༉ߙ᮹Ğᬑ0) ॒᮹ᩢ⨆ᮥၹᩢ⦹۵äᮝಽ, ݅ᮭ᮹ŝz݅.
ĸáĒ ē Ĕ
ĕ ĕ
×í×Ò â×íÏƉƄâÞ×í×Ò à ×íÎÒƉƄßƉƔ ſîƂ = Ïí×
×íÑ× à ×íÐƉƄà ×íÏÒÞÎ àƉƄßƉƔ Ïí× ï ſîƂ = Ðí×
Ĺá ×íÐÒ â×íÑƉƄâÞ×íÐ× à×íÏÒƉƄßƉƔ
(10a)
ĸáĒ ēĔ
ĕ ĕ
×íÎÞÎ à ƉƔßƉƄâ×í×ÒƉƔ ſîƂ = Ïí×
×íÔ à ×íÓÒÞÎ à ƉƔßƉƄà ×íÓÒƉƔ Ïí× ï ſîƂ = Ðí×
Ĺá ×íÎ â×íÔÒƉƄâÞ×íÔÒ à ×íÓÒƉƄßƉƔ
(10b)
ĸáĒ ē Ĕ
ĕ ĕ
à ×íÎ â×í×ÒƉƄà ×íÐÒÞÎ àƉƄßƉƔ ſîƂ = Ïí×
à ×íÐ â×íÒƉƄâÞ×íÎÒ à ×íÐÒƉƄßƉƔ Ïí× ï ſîƂ = Ðí×
Ĺá ×íÏ â×íÑƉƄâ×íÏÒƉƄƉƔ
(10c)
ᯕᩑǍᨱᕽ۵⎹Ⓧญ✙᮹ᦶ⇶vࠥa⎹Ⓧญ✙ᜅ✙ౠ᮹ᮁ⬉v
ࠥᨱၙ⊹۵ᩢ⨆ᮥŁಅ⦹ʑ᭥⦽Eq. (11)᮹ᮁ⬉vࠥĥᙹŃÏෝEq.
(9)᮹ᮁ⬉vࠥĥᙹŃÎᨱŒ⦹ᩍ↽᳦ᱢᯙᜅ✙ౠ᮹ᮁ⬉vࠥƄƁƑ(=
ŃÎŃÏƄƁƉ)ෝđᱶ⦹ᩡ݅.
Table 2. Specification of Reinforced Concrete Deep Beams Tested to Failure
Investigators No. of Beams ƀ(mm) Ƃ(mm) Ɔ(mm) ƄƁƉ(MPa) ƄƗ(MPa) ſîƂ Ň(%) ŇîŇƀ Smith and Vantsiotis(1982) 52 102 305 356 16.1-22.7 431-437 1.00-2.08 1.93 0.87-1.23
Tan et al. (1995) 17 110 463 500 41.1-58.8 375-504 0.27-2.70 1.23 0.36-0.43 Teng et al. (1996) 13 150-160 525-550 600 37.0-40.0 350-600 1.09-1.71 0.92-1.93 0.42-0.94 Tan et al. (1997a) 21 110 398-448 500 54.7-74.1 353-538 0.28-2.98 2.31-5.75 0.69-1.10 Tan et al. (1997b) 19 110 443 500 56.3-86.3 353-499 0.85-1.69 2.58 0.71-0.76 Tan and Lu(1999) 12 140 444-1559 500-1750 30.8-49.1 437-520 0.56-1.14 1.84-2.60 0.74-1.16
Shin et al. (1999) 30 125 215 250 52.0-73.0 414 1.50-2.50 3.77 0.80-0.88
Oh and Shin(2001) 53 120-130 500 560 23.7-73.6 414 0.50-2.00 1.29-1.56 0.27-0.64 Kim and Park(2005) 24 150 403 450 28.9-37.7 375-482 0.88-1.63 1.97 0.68-0.83 Total 241 102-160 215-1559 250-1750 16.1-86.3 350-600 0.27-2.98 0.92-5.75 0.27-1.23
Fig. 6. Reinforcement Details of Beam 2B4-52 (Smith & Vantsiotis, 1982) ŃÏá
Ē ē Ĕ
ĕĕ
Îí×
ÎíÎ à ×íÏÒƄƁƉîÔ×
ƄƁƉ= ÏÕ¦©ſ
ÏÕ ï ƄƁƉï Ôצ©ſ
×íÕÒ ƄƁƉ> ÔצƎſ
(11)
4. ℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹⧕ᕾ
⩥⧪ᩍ్ᖅĥʑᵡᕽၰʑ᳕ᩑǍྙ⨭᮹ᜅ✙ౠᮁ⬉vࠥŝᯕ
ᩑǍᨱᕽᱽᦩ⦽ᮁ⬉vࠥ᮹ᱢ⧊ᖒᮥá☁⦹ʑ᭥⦹ᩍSmith and Vantsiotis(1982), Tan et al.(1995, 1997a, 1997b), Teng et al.(1996), Tan and Lu(1999), Shin et al.(1999), Oh and Shin(2001), əญŁ
Kim and Park(2005) ॒ᨱ ᮹⧕ ❭ƕᝅ⨹ᯕ ᙹ⧪ࡽ ᱥ݉Ğe
እa0.25~3.0᮹ჵ᭥ᨱᯩ۵℁ɝ⎹Ⓧญ✙ʫᮡᅕ241}᮹ɚ⦽
vࠥෝFig. 1᮹ᖙ᳦ඹ᮹ᜅ✙ౠ-┡ᯕ༉ߙᮥᯕᬊ⦹ᩍ⠪a⦹ᩡ
݅. ℁ɝ⎹Ⓧญ✙ʫᮡᅕ⨹ℕ᮹eఖ⦽ᱽᬱၰᵝᖅĥᄡᙹ᮹
ჵ᭥۵Table 2᪡zᮝ໑, b⨹ℕ᮹ᝅ⨹ᰆ⊹, ℁ɝ႑⊹⩶┽,
❭ƕ᧲ᔢ, əญŁʑ┡ᔢᖙ⦽ᱶᅕ۵bₙŁྙ⨭ᨱᙹಾࡹᨕᯩ݅.
℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹ɚ⦽vࠥ⠪aᱩᱱᩢᩎ᮹ᮁ⬉vࠥ
aᜅ✙ౠ-┡ᯕ༉ߙ⧕ᕾđŝᨱၙ⊹۵ᩢ⨆ᮥ↽ᗭ⪵⦹ʑ᭥⧕
ǍᗮࡹḡᦫᮡəญŁḡᦶ❱ᨱ᮹⧕⩶ᖒࡹ۵ᱩᱱᩢᩎᨱᕽᯝၹ ᱢᮝಽaᰆⓑsᮥw۵Bergmeister et al.(1993)᮹sᮥᔍᬊ⦹
ᩡ݅. əॅᯕᱽᦩ⦽ᱩᱱᩢᩎ᮹ᮁ⬉vࠥƄƁƌᮡ݅ᮭ᮹ŝz݅.
ƄƁƌá ŃƑƄƁƉÞîƀß×íÒ = ÏíÒƄƁƉ (12)
ᩍʑᕽ, ŃƑ۵ Eq. (5)ᨱᕽ ᱶ᮹⦽ ᜅ✙ౠ᮹ ᮁ⬉vࠥĥᙹෝ,
ƀ۵ḡᦶ❱᮹໕ᱢᮥ, əญŁ۵ḡᦶ❱ŝࠥᝍᯕzᮝ໑ḡᦶ❱
ŝ࠺ᯝ⦽ ⩶ᔢᮝಽ ᱩᱱᯕ᭥⊹⦽ ݉໕ʭḡ aಽᖙಽእ2:1᮹
እᮉಽ ⪶ᰆ⦽ ໕ᱢᮥ ӹ┡ԕ໑, îƀ᮹ sᮡ 4ෝ Ⅹŝ⧁ ᙹ
ᨧ݅. əḡᦶ❱ᨱ᮹⧕⩶ᖒࡹḡᦫ۵ᱩᱱᩢᩎ᮹ᮁ⬉vࠥಽ۵
əॅ᮹ᱽᦩᨱEq. (5)᮹ŃƑᨱ⎹Ⓧญ✙᮹ᦶ⇶vࠥƄƁƉෝ
Œ⦽ sᮥ ᔍᬊ⦹ᩡ݅.
4.1 ୨୨ਆൈߍ-ଲࡦ܄ଡଲැজ
Figs. 1(a) and 1(b)᮹ᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥᯕᬊ⦽℁ɝ⎹Ⓧ
ญ✙ʫᮡᅕ᮹ɚ⦽vࠥ⠪aŝᱶᮥᱥ݉ĞeእſîƂa1.21ᯙ
Fig. 6᮹ʑ⦹⦺ᱢ⩶ᔢၰ႑ɝᔢᖙෝw۵Smith and Vantsiotis (1982)᮹ ⨹ℕ 2B4-52ෝ ݡᔢᮝಽ ᗭ}⦹ᩡ݅. ᯕ ⨹ℕ᮹
(a) Determinate Strut-Tie Model of Arch Load Transfer Mechanism (b) Provided Cross-Sectional Widths of Concrete Struts
(c) Provided Widths of Nodal Zone Boundaries
Fig. 7. Provided Cross-sectional Widths of Struts and Nodal Zone Boundaries in Statically Determinate Strut-Tie Model of Beam 2B4-52
⎹Ⓧญ✙᮹ᦶ⇶vࠥƄƁƉ۵21.8MPaᯕ໑, ⮉ၰᱥ݉℁ɝ᮹⧎ᅖ vࠥƄƗ۵bb431 ၰ437MPaᯕ݅. ੱ⦽ᯕ⨹ℕ᮹⦹ᵲ❱
ၰḡḡ❱᮹⡎ᮡ102mmᯕ໑, ᵝᯙᰆ℁ɝእŇ۵⠪⩶℁ɝእ᮹
0.91႑ᯕ݅.
ACI 318M-11᮹ᜅ✙ౠ-┡ᯕ༉ߙ ᖁᱶʑᵡᮥ ⨹ℕ
2B4-52᮹ᱥ݉Ğeእa1.8ᅕ᯲݅ᮝအಽFig. 7(a)᪡zᮡᦥ⊹
ີ⍅ܩ᷹᮹ ᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙᮥ ᖁᱶ⦹ᩡ݅. ᯕ ༉ߙᨱᕽ,
℁ɝ┡ᯕT1ᮡ⮉℁ɝ᮹ࠥᝍᨱ᭥⊹⎑ᮝ໑, ॒a᮲ಆት᮹
ʫᯕ(=ƑƄƗîÞ×íÕÒƄƁƉƀß, ƀ=102mm)᮹݉໕⡎ᮥw۵⎹Ⓧญ✙
ᜅ✙ౠ S1ᮡ ᯕ ᜅ✙ౠ᮹ ݉໕ ᔢ݉Ğĥᖁᯕ ⨹ℕ᮹ ᔢ݉ŝ
ᯝ⊹⦹ࠥಾ ᭥⊹⎑݅.
ᜅ✙ౠ-┡ᯕ༉ߙᮥᯕᬊ⦽⨹ℕ2B4-52᮹ɚ⦽vࠥ۵ᜅ✙
ౠ, ┡ᯕ, əญŁᱩᱱᩢᩎĞĥ໕॒᮹↽ݡ݉໕ᱢŝ⦥݉໕ᱢ᮹
ⓍʑෝእƱ⦹ᩍbᗭ᮹vࠥෝá☁⦹۵⩥⧪ᵝᜅ✙ౠ-┡ᯕ
༉ߙᖅĥʑᵡᕽ᮹ႊჶᮝಽǍ⦹ᩡ݅. ᜅ✙ౠၰᱩᱱᩢᩎĞĥ໕ ᮹↽ݡ݉໕ᱢᮡ ḡᦶ❱᮹ Ⓧʑၰ ᜅ✙ౠŝ ┡ᯕ᮹᭥⊹ ॒ᮥ
Łಅ⦹۵ACI 445(2002)᮹ႊჶᮝಽǍ⦹ᩡᮝ໑, ┡ᯕ᮹↽ݡ݉
໕ᱢᮡ┡ᯕ᮹᭥⊹ᨱ႑⊹ࡽ℁ɝ᮹݉໕ᱢᮝಽ≉⦹ᩡ݅. Fig.
7(b)۵ᜅ✙ౠ᮹↽ݡ݉໕⡎ၰ┡ᯕ᮹↽ݡ݉໕ᱢᮥ, əญŁFig.
7(c)۵ࢱᱩᱱᩢᩎĞĥ໕᮹↽ݡ݉໕⡎ᮥᅕᯙäᯕ݅. ⨹ℕ᮹
Table 3. Effective Strengths of Concrete Struts in Statically Determinate Strut-Tie Model of Beam 2B4-52
ŃƑ(=ƄƁƑîƄƁƉ) Effective Strength
Bergmeister et al.(1993) MacGregor (1997) FIB(2010) AASHTO(2010) ACI 318 (2011) Present Study Strut Number
S1 0.80 0.82 0.85 0.85 0.85 1.00
S2 0.48 0.65 0.47 0.44 0.64 0.77
ƄƁƑ: effective strength of concrete strut; Refer to Fig. 7(a) for strut number.
Table 4. Strength Evaluation of Beam 2B4-52 by using Statically Determinate Strut-Tie Model of Arch Load Transfer Mechanism (a) Strength Verification of Struts and Tie
S1 1.00 21.8 21.8 233.2 104.9 136.8 1.305
S2 0.77 21.8 16.8 277.2 161.8 141.0 0.871 ×
T1 1.00 431.0 431.0 233.2 541 600 1.109
ŃƑ and Ńƒ: coefficients of eff. strengths of strut and tie; eff. strength of concrete strut: ƄƁƑá ŃƑƄƁƉ; eff. strength of steel tie: ƄƁƒá ŃƒƄƗ;Ɠ: cross-sectional
(b) Strength Verification of Nodal Zones Node
No.
Node Type Ńƃ
,ƀ (mm2) Ńƌ
ƄƁƉ (MPa)
ƄƁƌ (MPa)
Ɠ (kN)
(mm)
Safety
1 CCT 0.80 306×102,
102×102 1.39 21.8 30.2
R 130.6 42.4 102.0 2.406
S2 241.6 76.6 144.2 1.883
T1 203.2 65.9 102.0 1.547
2 CCC 0.80 376×102,
102×102 1.54 21.8 33.5
V 130.6 38.3 102.0 2.666
S1 203.2 59.5 136.8 2.299
S2 241.6 70.6 170.7 2.418
Ńƌ(=Ńƃöćîƀ): coefficient of eff. strength of nodal zone; eff. strength of nodal zone: ƄƁƌá ŃƌƄƁƉ;Ɠ: cross-sectional force at nodal zone boundary at at nodal zone boundary (refer to Fig. 7(c))
ࢱ̹ƀaᯝᱶ⦹အಽ⎹Ⓧญ✙ᜅ✙ౠੱ۵ᱩᱱᩢᩎĞĥ໕᮹
Œ⦹ᩍ۵݅. ᜅ✙ౠၰ┡ᯕᗭ᮹⦥݉໕ᱢᮡᯕ⨹ℕ᮹
ᝅ⨹❭ƕ⦹ᵲ149.9kNᯕ᯲ᬊ⧁ভ᮹Fig. 7(b)ᨱ⢽ʑ⦽bᗭ ᮹݉໕ಆᮥ⧕ݚᮁ⬉vࠥಽӹ٥ᨕǍ⦹ᩡ݅. ᱩᱱᩢᩎĞĥ໕᮹
⦥݉໕ᱢᮡFig. 7(c)᪡zᯕᱩᱱᩢᩎᨱᩑđࡽᜅ✙ౠ(ੱ۵
┡ᯕ)᮹݉໕ಆᮥᱩᱱᩢᩎĞĥ໕ᙹḢႊ⨆᮹݉໕ಆᮝಽ⊹⪹⦽
⬥ə݉໕ಆᮥᱩᱱᩢᩎ᮹ᮁ⬉vࠥಽӹ٥ᨕǍ⦹ᩡ݅. ᜅ✙ౠ᮹
ᮁ⬉vࠥ۵3ᰆᨱᗭ}⦽ႊჶᮝಽǍ⦹ᩡᮝ໑, ℁ɝ┡ᯕ᮹ᮁ⬉
vࠥ۵℁ɝ᮹⧎ᅖvࠥಽ≉⦹ᩡ݅. ᱩᱱᩢᩎ᮹ᮁ⬉vࠥ۵Eq.
(12)ಽᇡ░Ǎ⦹ᩡ݅. ᯕםྙ3ᰆ᮹ₙŁྙ⨭᮹ႊჶᮝಽǍ⦽
ᜅ✙ౠS1 ၰS2᮹ᮁ⬉vࠥĥᙹŃƑ(=ƄƁƑîƄƁƉ)۵Table 3ŝz݅.
ᜅ✙ౠS1ᮡɁᩕᯕၽᔾ⦹ḡᦫ۵Ŕᨱ᭥⊹⦹အಽᱡᯱ᮹ႊჶᨱ
᮹⦽ᯕᜅ✙ౠ᮹ᮁ⬉vࠥĥᙹŃƑ۵1.0ᯕ݅. ᱡᯱ᮹ႊჶᨱ᮹⦽
ᜅ✙ౠS2᮹ᮁ⬉vࠥĥᙹŃƑ۵Eq. (10b)ಽᇡ░Ǎ⦽ĸ(=0.1) ၰĹ(=0.85)ෝ Eq. (9)ᨱ ݡ᯦⦹ᩍ ᮁ⬉vࠥĥᙹŃÎ(=0.77)ᮥ
Ǎ⦽⬥ᯕෝEq. (11)᮹ŃÏ(=1.0)᪡Œ⦽äᯕ݅. ⨹ℕ2B4-52ᨱ
႑⊹ࡽ⮉℁ɝᮡᝅ⨹❭ƕ⦹ᵲᔢ┽ᨱᕽ⦥⦽℁ɝపᅕ݅
ฯᮝအಽ⮉℁ɝእƉƄෝ1.0ᮝಽ≉⦹ᩡᮝ໑, ᱥ݉℁ɝᮡ႑⊹ࡹ
ᨩᮝӹᙹḢ✙్ᜅີ⍅ܩ᷹ᯕ᳕ᰍ⦹ḡᦫᦥᱥ݉℁ɝᨱ᮹⦽
Ǎᗮ⬉ŝෝŁಅ⧁ᙹᨧᮝအಽᱥ݉℁ɝእƉƔෝ0ᮝಽ≉⦹ᩡ݅.
b ႊჶᨱ ᮹⦽ ᜅ✙ౠ S1 ၰ S2᮹ ᮁ⬉vࠥ đᱶŝᱶᨱ ݡ⦽
ᖅᮡ ᔾఖ⦽݅.
Table 4۵⎹Ⓧญ✙ᜅ✙ౠ᮹ᩍ్ᮁ⬉vࠥsᵲ⩥ᩑǍ᮹
ᜅ✙ౠᮁ⬉vࠥsᮥᯕᬊ⦹ᩍ⨹ℕ2B4-52᮹ɚ⦽vࠥ⠪aŝ ᱶᮥᗭ}⦽äᮝಽ, ᯕ⨹ℕ᮹ɚ⦽vࠥ۵bǍᖒᗭ᮹❭ƕ⦹
Table 5. Ultimate Strengths of Deep Beams Evaluated by Statically Determinate Strut-Tie Models
©ƒƃƑƒî©ƁſƊ Eff. Strut Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO
(2010) ACI 318 (2011) Present Study Inv estigators
Smith and Vantsiotis(1982) 2.04 1.50 2.10 2.46 1.58 1.28
Tan et al.(1995) 1.87 1.59 2.07 1.49 1.45 1.37
Teng et al.(1996) 1.62 1.30 1.72 2.42 1.33 1.07
Tan et al.(1997a) 1.58 1.36 1.77 1.27 1.18 1.13
Tan et al.(1997b) 1.72 1.27 1.93 1.52 1.17 1.23
Tan and Lu(1999) 1.68 1.37 1.77 1.33 1.51 1.08
Shin et al.(1999) 1.50 1.37 1.91 1.85 1.29 1.21
Oh and Shin(2001) 1.44 1.29 1.53 1.31 1.27 1.24
Kim and Park(2005) 1.92 1.51 2.01 2.22 1.45 1.21
Total Mean 1.71 1.40 1.87 1.81 1.37 1.22
STDEV 0.42 0.28 0.43 0.74 0.28 0.29
STDEV: standard deviation; The strut-tie models of Figs. 1(a) and 1(b) were used for the beams with ſîƂ = ÎíÕ and, ſîƂ ðÎíÕ respectively.
ƕ⦹ᵲ᮹87.1%ᯙ130.6kNᯕ᯲ᬊ⧁ভᜅ✙ౠS2a❭ƕࡹᨩᮝ ໑, 130.6kN᮹⦹ᵲᯕ᯲ᬊ⧁ভᱩᱱᩢᩎᮡ❭ƕࡹḡᦫᦹ݅.
ᕽᯕ⨹ℕ᮹ɚ⦽vࠥ۵ᝅ⨹❭ƕᵲ᮹87.1%ಽđᱶࡹᨩ
݅. อ᧞ᨱ130.6kN᮹90%ᨱᕽᱩᱱᩢᩎᯕ❭ƕࡽ݅໕ᯕ⨹ℕ ᮹ɚ⦽vࠥ۵78.4%(=.871x.90)ᮝಽđᱶࡽ݅. ᯕ᪡࠺ᯝ⦽ႊჶ ᮝಽӹນḡ⨹ℕ᮹vࠥෝ⠪a⦹ᩡᮝ໑, əđŝ۵Table 5᪡
z݅.ſîƂ ï ÎíÕᯙᅕᨱݡ⦽ᦥ⊹ີ⍅ܩ᷹᮹ᜅ✙ౠ-┡ᯕ༉ߙ
ၰſîƂ > ÎíÕᯙᅕᨱݡ⦽✙్ᜅີ⍅ܩ᷹᮹ᜅ✙ౠ-┡ᯕ༉ߙᮥ
ᱢᬊ⦽đŝ, Table 5᪡zᯕBergmeister et al.(1993), FIB(2010), əญŁAASHTO(2010) ॒ᨱ᮹⦽ᜅ✙ౠ᮹ᮁ⬉vࠥᮡ℁ɝ
⎹Ⓧญ✙ʫᮡᅕ᮹vࠥෝๅᬑᅕᙹᱢᮝಽ⠪a⦹ᩡᮝ໑, ✚⯩
AASHTO(2010)ᨱ᮹⦽äᮡaᰆⓑ⢽ᵡ⠙₉ෝӹ┡ԕᨩ݅.
ၹ໕ᨱᯕᩑǍᨱᕽᱽᦩ⦽ᜅ✙ౠ᮹ᮁ⬉vࠥᮡ℁ɝ⎹Ⓧญ✙
ʫᮡ ᅕ᮹ vࠥෝ ⠪Ɂᱢᮝಽ aᰆ ᧲⪙⦹í ⠪a⦹ᩡ݅.
4.2 ऀ୨୨ਆൈߍ-ଲࡦ܄ଡଲැজ
⩥ᩑǍ᮹ᮥ⡍⧉⦽ḡɩʭḡᱽᦩࡽᩍ్ᜅ✙ౠᮁ⬉vࠥ
᮹ᱢ⧊ᖒᮥá☁⦹ʑ᭥⦹ᩍ241}℁ɝ⎹Ⓧญ✙ ʫᮡ ᅕ᮹ ɚ⦽v
ࠥෝ Fig. 1(c)᮹ ᅖ⧊ ີ⍅ܩ᷹᮹ ᇡᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙᮥ
ᯕᬊ⦹ᩍ⠪a⦹ᩡ݅. ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥᯕᬊ⦽ɚ⦽vࠥ
⠪aŝᱶᮥᗭ}⦹ʑ᭥⦹ᩍᦿᱩᨱᕽᗭ}⦽⨹ℕ2B4-52ෝ
┾⦹ᩡᮝ໑, ᯕ ⨹ℕෝ ᭥⦽ ᇡᱶᱶ ᜅ✙ౠ-┡ᯕ ༉ߙᮡ Fig.
8(a)᪡z݅. ᱶᱶᜅ✙ౠ-┡ᯕ༉ߙ᮹Ğᬑ᪡ษ₍aḡಽ, ℁ɝ
┡ᯕT3 ၰT4۵⮉℁ɝ᮹ࠥᝍᨱ᭥⊹⎑ᮝ໑, ॒a᮲ಆት᮹
ʫᯕ(=ƑƄƗîÞ×íÕÒƄƁƉƀß,ƀ=102mm)᮹݉໕⡎ᮥw۵⎹Ⓧญ✙
ᜅ✙ౠ S2۵ ᯕ ᜅ✙ౠ᮹ ݉໕ ᔢ݉Ğĥᖁᯕ ⨹ℕ᮹ ᔢ݉ŝ
ᯝ⊹⦹ࠥಾ᭥⊹⎑݅. ᔢᇡ᮹⎹Ⓧญ✙ᜅ✙ౠS1ᮡᜅ✙ౠS2᪡
࠺ᯝ⦽ ᙹ⠪ᖁᔢᨱ ᭥⊹⎑݅.
ᜅ✙ౠŝ ┡ᯕ᮹ ݉໕ಆᮡ Eq. (3)᮹ ⦹ᵲᇥ႑ᮉ ၰ ✙్ᜅ
Ǎ᳑᮹ᱩᱱ⧕ᕾჶᮥᱢᬊ⦹ᩍǍ⦹ᩡ݅. ᯲ᷪᬊ⦹ᵲᨱݡ⦽ᙹḢ
┡ᯕ᮹݉໕ಆእಽᱶ᮹⦽݅ᮭ᮹⦹ᵲᇥ႑ᮉķ(%)ಽᇡ░┡ᯕ
T1᮹݉໕ಆᮥǍ⦽⬥, ᜅ✙ౠ-┡ᯕ༉ߙbᱩᱱᨱᕽ᮹⠪⩶᳑Õ
ᮥ ᱢᬊ⍽ ༉ु ᜅ✙ౠŝ ┡ᯕ᮹ ݉໕ಆᮥ đᱶ⦹ᩡ݅.
ķÞÜß á ÞſîƂà ÎíÒß âĸ á ÕÓíÑÞÎíÏÎ à ÎíÒß âÓÓíÓ á ÑÎíÒ
ᩍʑᕽ, á ÔÕ à ×íÎƄƁƉâÞÎÕ à ×íÑƄƁƉßŇîŇƀá ÕÓíÑ ĸ á ÐÓíÒ â×í×ÒƄƁƉâÐÏŇîŇƀá ÓÓíÓ
ᜅ✙ౠ᮹ᮁ⬉vࠥ۵ᯕםྙ3ᰆ᮹ₙŁྙ⨭᮹ႊჶᮝಽǍ⦹
ᩡᮝ໑, ┡ᯕ᮹ ᮁ⬉vࠥ۵ ℁ɝ᮹ ⧎ᅖvࠥಽ ≉⦹ᩡ݅. ੱ⦽
ᱩᱱᩢᩎ᮹ᮁ⬉vࠥ۵Eq. (12)ಽᇡ░Ǎ⦹ᩡ݅. ᯕםྙ᮹3ᰆ᮹
ႊჶᮝಽǍ⦽bᜅ✙ౠ᮹ᮁ⬉vࠥĥᙹŃƑ(=ƄƁƑîƄƁƉ)۵Table 6ŝz݅. ᜅ✙ౠS2۵Ɂᩕᯕၽᔾ⦹ḡᦫ۵Ŕᨱ᭥⊹⦹အಽ
ᱡᯱ᮹ႊჶᨱ᮹⦽ᯕᜅ✙ౠ᮹᮲ಆᔢ┽ၰ℁ɝᨱ᮹⦽Ǎᗮ⬉ŝ
ෝŁಅ⦹۵ᮁ⬉vࠥĥᙹŃÎᮥ≉⦹ᩡᮝ໑, ӹນḡᜅ✙ౠ᮹ᮁ⬉
vࠥĥᙹŃÎᮡ ⨹ℕ 2B4-52᮹ ⮉℁ɝእƉƄ(=1.0), ᱥ݉℁ɝ
እƉƔ(=0.452), əญŁᱥ݉ĞeእſîƂ(=1.21)ᮥᯕᬊ⦹ᩍEq. (9) ಽᇡ░đᱶ⦹ᩡ݅. ⨹ℕ2B4-52᮹⎹Ⓧญ✙ᦶ⇶vࠥa28MPa ᅕ᯲݅ᮝအಽ⎹Ⓧญ✙vࠥ᮹ᩢ⨆ᮥŁಅ⦹۵ᜅ✙ౠ᮹ᮁ⬉vࠥ
(a) Indeterminate Strut-Tie Model of Combined Load Transfer Mechanism
(b) Procedure for Determining Provided Width of a Nodal Zone Boundary
(c) Provided Withds (Areas) of Struts and Ties (d) Provided and Required Widths of Nodal Zone Boundaries
Fig. 8. Provided Cross-sectional Widths (Areas) of Struts, Ties, and Nodal Zone Boundaries in Statically Indeterminate Strut-Tie Model of Beam 2B4-52
Table 6. Effective Strengths of Concrete Struts in Statically Indeterminate Strut-Tie Model of Beam 2B4-52
ŃƑ(=ƄƁƑîƄƁƉ) Effective Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO
(2010) ACI 318 (2011) Present Study Strut Number
S1 0.80 0.82 0.85 0.85 0.85 0.92
S2 0.80 0.82 0.85 0.85 0.85 1.00
S4 0.80 0.65 0.47 0.43 0.64 0.59
S5 0.48 0.65 0.47 0.44 0.64 0.83
S6 0.80 0.65 0.47 0.43 0.64 0.74
ƄƁƑ: effective strength of concrete strut; Refer to Fig. 8(a) for strut number.
Table 7. Strength Evaluation of Beam 2B4-52 by Statically Indeterminate Strut-Tie Model of Combined Load Transfer Mechanism (a) Strength Verification of Struts and Ties at the First Failure State
S1 0.92 21.8 20.1 48.8 23.9 30.1 1.263
S2 1.00 21.8 21.8 233.2 104.9 136.8 1.305
S4 0.59 21.8 12.8 79.6 60.7 48.6 0.800 ×
S5 0.83 21.8 18.1 161.1 87.4 98.3 1.125
S6 0.74 21.8 16.2 79.6 48.1 49.1 1.022
T1 1.00 437.0 437.0 62.8 143.7 154.9 1.078
T3 1.00 431.0 431.0 184.3 427.7 600.0 1.403
T4 1.00 431.0 431.0 233.2 541.0 600.0 1.109
(b) Strength Verification of Struts and Ties at the Second Failure State
S2 1.00 21.8 21.8 233.2 104.9 53.0 0.505 ×
S5 0.83 21.8 18.1 277.2 150.3 27.2 0.181 ×
T3 1.00 431.0 431.0 233.2 541.0 258.0 0.477 ×
T4 1.00 431.0 431.0 233.2 541.0 167.4 0.309 ×
failure
(c) Strength Verification of Nodal Zones Node
No.
Node Type Ńƃ
,ƀ (mm2) Ńƌ
ƄƁƉ (MPa)
ƄƁƌ (MPa)
Ɠ (kN)
(mm)
Safety
1 CCT 0.80 306×102,
102×102 1.39 21.8 30.2
R 147.0 47.7 102.0 2.138 O
S4 63.6
77.2 144.2 1.868 O
S5 178.9
T3 189.5 61.5 102.0 1.658 O
2 CCT 0.80 - 0.80 21.8 17.4
S1 39.1 22.0 136.8 6.232 O
S4 63.6 35.8 229.3 6.413 O
T1 50.2 28.2 184.0 6.518 O
3 CTT 0.80 - 0.80 21.8 17.4
S6 63.6 35.3 210.4 5.954 O
T1 50.2 28.2 184.0 6.518 O
T4 39.1 22.0 102.0 4.646 O
4 CCC 0.80 376×102,
102×102 1.54 21.8 33.5
V 147.0 43.0 102.0 2.369 O
S1 39.1
79.4 170.7 2.149 O
S5 178.9
S6 63.6
S2 228.6 67.0 136.8 2.043 O
Ɠ: cross-sectional force at nodal zone boundary at the 98.1%(=80.0+18.1) of experimental failure load; V: applied load (= 98.1%% of experimental
Table 8. Ultimate Strengths of Deep Beams Evaluated by Statically Indeterminate Strut-Tie Models
©ƒƃƑƒî©ƁſƊ (a) Total Results
Eff. Strut Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO (2010)
ACI 318 (2011)
Present Study Inv estigators
Smith and Vantsiotis(1982) 1.42 1.27 1.76 1.83 1.33 1.12
Tan et al.(1995) 1.68 1.52 1.97 1.30 1.41 1.30
Teng et al.(1996) 1.22 1.22 1.52 1.66 1.17 0.93
Tan et al.(1997a) 1.37 1.19 1.67 1.26 1.09 1.03
Tan et al.(1997b) 1.62 1.35 1.92 1.42 1.26 1.27
Tan and Lu(1999) 1.60 1.34 1.72 1.32 1.46 1.07
Shin et al.(1999) 1.20 1.29 1.77 1.62 1.12 1.03
Oh and Shin(2001) 1.42 1.29 1.50 1.30 1.28 1.25
Kim and Park(2005) 1.46 1.29 1.68 1.63 1.24 1.08
Total Mean 1.42 1.28 1.70 1.52 1.26 1.13
STDEV 0.29 0.24 0.34 0.38 0.22 0.22
The indeterminate strut-tie model of Fig. 1(c) and Chae(2012)’s load distribution ratio were used.
(b) Results Classified by Shear Span-to-Effective Depth Ratio Eff. Strut Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO (2010)
ACI 318 (2011)
Present Study Rat io of ſîƂ
ſîƂ ïÎí×
(68)*
Mean 1.62 1.38 1.79 1.20 1.32 1.18
STDEV 0.35 0.27 0.42 0.28 0.22 0.17
Îí× = ſîƂ ïÏí×
(138)*
Mean 1.36 1.23 1.64 1.61 1.24 1.10
STDEV 0.25 0.23 0.32 0.31 0.24 0.22
Ïí× = ſîƂ = Ðí×
(35)*
Mean 1.18 1.17 1.59 1.64 1.15 1.07
STDEV 0.24 0.29 0.46 0.54 0.27 0.27
*: no. of beams
(c) Results Classified by Compressive Strength of Concrete Eff. Strut Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO (2010)
ACI 318 (2011)
Present Study Stren gth of Concr ete
ƄƁƉ= Ð×MPa (63)*
Mean 1.45 1.29 1.74 1.80 1.34 1.11
STDEV 0.21 0.16 0.20 0.37 0.17 0.14
Ð× ïƄƁƉ= Ó×
(120)*
Mean 1.45 1.31 1.70 1.44 1.27 1.13
STDEV 0.34 0.27 0.40 0.34 0.23 0.22
ƄƁƉðÓ×
(58)*
Mean 1.28 1.16 1.56 1.32 1.11 1.11
STDEV 0.33 0.31 0.44 0.34 0.29 0.28
(d) Results Classified by Flexural Reinforcement Ratio Eff. Strut Strength Bergmeister et al.
(1993)
MacGregor (1997)
FIB (2010)
AASHTO (2010)
ACI 318 (2011)
Present Study Flexu ral Rebar Rat io
Ň = ×íÒŇƀ (66)*
Mean 1.43 1.33 1.56 1.27 1.29 1.25
STDEV 0.29 0.24 0.35 0.27 0.22 0.21
×íÒŇƀïŇ = Ňƀ (143)*
Mean 1.39 1.23 1.70 1.54 1.20 1.07
STDEV 0.34 0.27 0.40 0.34 0.26 0.26
Ň ðŇƀ (32)*
Mean 1.44 1.30 1.82 1.83 1.36 1.07
STDEV 0.26 0.23 0.24 0.52 0.21 0.16
Fig. 9. Ultimate Strengths of Deep Beams Evaluated by using Statically Indeterminate Strut-Tie Model ĥᙹŃÏ۵Eq. (11)ᨱᕽᱶ᮹⦽ၵ᪡zᯕ1.0ᯕࡹ໑, ᕽbᜅ✙ౠ
᮹↽᳦ᱢᯙᮁ⬉vࠥĥᙹŃƑ۵bᜅ✙ౠ᮹ŃÎsŝz݅. b ႊჶᨱ
᮹⦽ᜅ✙ౠS1 ၰS2᮹ᮁ⬉vࠥđᱶŝᱶᨱݡ⦽ᖅᮡᔾఖ⦽݅.
⨹ℕ2B4-52᮹ɚ⦽vࠥ۵ᜅ✙ౠ, ┡ᯕ, əญŁᱩᱱᩢᩎ
Ğĥ໕॒᮹↽ݡ݉໕ᱢŝ⦥݉໕ᱢ᮹ⓍʑෝእƱ⦹ᩍbᗭ ᮹ vࠥෝ á☁⦹۵ ⩥⧪ ᵝ ᜅ✙ౠ-┡ᯕ ༉ߙ ᖅĥʑᵡᕽ᮹
ႊჶᮝಽǍ⦹ᩡ݅. ᜅ✙ౠၰᱩᱱᩢᩎĞĥ໕᮹↽ݡ݉໕ᱢᮡ
ḡᦶ❱᮹Ⓧʑၰᜅ✙ౠŝ┡ᯕ᮹᭥⊹॒ᮥŁಅ⦹۵ACI 445 (2002)᮹ႊჶᮝಽǍ⦹ᩡᮝ໑, ┡ᯕ᮹↽ݡ݉໕ᱢᮡ┡ᯕ᮹᭥⊹
ᨱ႑⊹ࡽ℁ɝ᮹݉໕ᱢᮝಽ≉⦹ᩡ݅. Fig. 8(b)۵4ჩᱩᱱᩢᩎ ᮹Ğĥ໕ŝอӹ۵ᜅ✙ౠ᮹↽ݡ݉໕⡎đᱶŝᱶᮥ, Fig. 8(c)۵
ᜅ✙ౠ᮹↽ݡ݉໕⡎ၰ┡ᯕ᮹↽ݡ݉໕ᱢᮥ, əญŁFig. 8(d)۵
1ჩၰ4ჩᱩᱱᩢᩎĞĥ໕᮹↽ݡ݉໕⡎ᮥᅕᯙäᯕ݅. ᜅ✙ౠŝ
┡ᯕ᮹⦥݉໕ᱢᮡᯕ⨹ℕ᮹ᝅ⨹❭ƕ⦹ᵲ149.9kNᯕ᯲ᬊ
⧁ভ᮹ᜅ✙ౠŝ┡ᯕ᮹݉໕ಆᮥᯕॅᗭ᮹ᮁ⬉vࠥಽӹ٥ᨕ
Ǎ⦹ᩡᮝ໑, ᱩᱱᩢᩎĞĥ໕᮹⦥݉໕ᱢᮡFig. 8(d)᪡zᯕ
ᱩᱱᩢᩎᨱᩑđࡽᜅ✙ౠ(ੱ۵┡ᯕ)᮹݉໕ಆᮥᱩᱱᩢᩎĞĥ໕
ᙹḢႊ⨆᮹݉໕ಆᮝಽ⊹⪹⦽⬥ə݉໕ಆᮥᱩᱱᩢᩎ᮹ᮁ⬉v
ࠥಽ ӹ٥ᨕ Ǎ⦹ᩡ݅.
⎹Ⓧญ✙ᜅ✙ౠ᮹ᩍ్ᮁ⬉vࠥsᵲ⩥ᩑǍ᮹ᜅ✙ౠᮁ⬉v
ࠥsᮥᯕᬊ⦹ᩍ⨹ℕ2B4-52᮹ɚ⦽vࠥ⠪aŝᱶᮡTable 7ᨱᔢᖙ⯩ᗭ}⦹ᩡ݅. ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮥᯕᬊ⦽ɚ⦽v
ࠥ⠪a℁ɝ⎹Ⓧญ✙ʫᮡᅕ᮹⦹ᵲᱥݍີ⍅ܩ᷹ᮥǍᖒ⦹۵
⦹ӹ᮹ᗭaᯝ₉ᱢᮝಽ❭ƕࡹᨕࠥ݅ෙᗭॅಽǍᖒࡽ݅ෙ
⦹ᵲᱥݍີ⍅ܩ᷹ᨱ᮹⧕⇵aᱢᯙ⦹ᵲᯕᱥݍࡹ۵äᮝಽᅕᦹ
݅. Table 7(a)ᨱӹ┡ӽäŝzᯕ, ⨹ℕ2B4-52 ᇡᱶᱶᜅ✙ౠ-
┡ᯕ༉ߙ᮹1₉❭ƕ۵ᙹḢ✙్ᜅີ⍅ܩ᷹ᮥǍᖒ⦹۵Ğᔍ
ᜅ✙ౠS4a↽ݡಽၼᮥᙹᯩ۵⦹ᵲ, ᷪᝅ⨹❭ƕ⦹ᵲ᮹80%ᯙ
119.9kNᨱᕽၽᔾ⦹ᩡ݅. 1₉❭ƕ⬥ᇡᱶᱶᜅ✙ౠ-┡ᯕ༉ߙᮡ
ᩍᇥ᮹ ݉໕ᱢᮥ aḡŁ ᯩ۵ ⦹ᇡ ᙹ⠪ ┡ᯕ ၰ Ğᔍ ᜅ✙ౠ
