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  1. ๊ธฐ๋Œ€ํ•™๊ต ๊ฑด์ถ•๊ณตํ•™๊ณผ ๊ต์ˆ˜ (Professor, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)
  2. ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ๊ฑด์ถ•๊ณตํ•™๊ณผ ์กฐ๊ต์ˆ˜ (Assistant Professor, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)
  3. ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ์ผ๋ฐ˜๋Œ€ํ•™์› ๊ฑด์ถ•๊ณตํ•™๊ณผ ์„์‚ฌ๊ณผ์ • (Graduate Student, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)



๋ณด, ๊ณก๋ฅ  ์—ฐ์„ฑ๋น„, ๋ณ€์œ„ ์—ฐ์„ฑ๋น„, ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ
beams, curvature ductility ratio, displacement ductility ratio, lightweight aggregate concrete

1. ์„œ ๋ก 

์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ(reinforced concrete, RC) ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์€ ์ผ๋ฐ˜์ ์œผ๋กœ ์ฃผ์ฒ ๊ทผ์˜ ํ•ญ๋ณต์‹œ์ ๋ถ€ํ„ฐ ์ตœ๋Œ€๋‚ด๋ ฅ๊นŒ์ง€์˜ ๋ณ€ํ˜• ์ •๋„๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š” ๊ณก๋ฅ  ์—ฐ์„ฑ๋น„ ๋˜๋Š” ๋ณ€์œ„ ์—ฐ์„ฑ๋น„๋กœ ํ‰๊ฐ€๋œ๋‹ค(Lee 2013)(8). ์—ฌ๋Ÿฌ ์—ฐ๊ตฌ์ž(Ahmad and Barker 1991; Han et al. 2001)(1,5)๋Š” ๋‹ค์–‘ํ•œ ๋ณ€์ˆ˜๋ฒ”์œ„์—์„œ RC ๋ณด์˜ ์—ฐ์„ฑ์„ ์‹คํ—˜์ ์œผ๋กœ ํ‰๊ฐ€ํ•˜๊ณ  ์žˆ์ง€๋งŒ, ๊ณก๋ฅ  ๋˜๋Š” ๋ณ€์œ„ ์—ฐ์„ฑ๋น„๋ฅผ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋Š” ์„ค๊ณ„๋ชจ๋ธ์— ๊ด€ํ•œ ์—ฐ๊ตฌ๋Š” ์—ฌ์ „ํžˆ ๋ฏธ๋ฏธํ•˜๋‹ค. ํŠนํžˆ ๋ช‡๋ช‡ ์—ฐ๊ตฌ์ž(Pam et al. 2001a, 2001b; Arslan and Cihanli 2010)(2,10,11)๋Š” ๊ณก๋ฅ  ์—ฐ์„ฑ๋น„์˜ ๋ชจ๋ธ์„ ์ œ์•ˆํ•˜๊ณ  ์žˆ๋Š”๋ฐ, ๋Œ€๋ถ€๋ถ„ ๋ณดํ†ต ์ฝ˜ํฌ๋ฆฌํŠธ(normal-weight concrete, NWC) ๋ณด์˜ ์‹คํ—˜๊ฒฐ๊ณผ์— ๊ธฐ๋ฐ˜ํ•˜๊ณ  ์žˆ์–ด ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ(lightweight aggregate concrete, LWAC) ๋ณด์˜ ์—ฐ์„ฑ์„ ์˜ˆ์ธกํ•˜๋Š” ๋ฐ ๋‹ค์†Œ ํ•œ๊ณ„๊ฐ€ ์žˆ๋‹ค(Yang et al. 2020b)(19).

๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ(LWAC)๋Š” ๊ณจ์žฌ ์ž์ฒด์˜ ๋‚ฎ์€ ๊ฐ•๋„๋กœ ์ธํ•ด ๊ด€ํ†ตํŒŒ๊ดด ๋˜๊ธฐ ๋•Œ๋ฌธ์— ์ตœ๋Œ€ ๋‚ด๋ ฅ ์ดํ›„ ๋ถ€์žฌ์˜ ๋‚ด๋ ฅ์ €ํ•˜๋Š” NWC๋ณด๋‹ค LWAC์—์„œ ๋” ๊ธ‰๊ฒฉํ•˜๋‹ค(Yang and Mun 2009)(17). ๋”ฐ๋ผ์„œ ๋™์ผํ•œ ์ฃผ์ฒ ๊ทผ ๋น„์—์„œ LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์€ ์ผ๋ฐ˜์ ์œผ๋กœ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๋‹ค(Bernardo et al. 2016)(3). Yang et al.(2020a)(20)์€ LWAC ๋ณด์˜ ์—ฐ์„ฑ์€ NWC ๋ณด๋ณด๋‹ค ํ‰๊ท  7.6 % ๋‚ฎ์œผ๋ฉฐ, ๊ทธ ๋‚ฎ์Œ์˜ ์ •๋„๊ฐ€ ์ฃผ์ฒ ๊ทผ ์ง€์ˆ˜๊ฐ€ ๋‚ฎ์„์ˆ˜๋ก ์ฆ๊ฐ€ํ•จ์„ ๋ณด๊ณ ํ•˜์˜€๋‹ค. Sin et al.(2011)(16)์€ LWAC ๋ณด์˜ ์—ฐ์„ฑ์€ ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰์ด 19 % ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ์•ฝ 9 % ๊ฐ์†Œํ•จ์„ ๋ณด์˜€๋‹ค. ์ด์™€ ๊ฐ™์ด LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์€ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ์„ ๊ฐ€๋Šฅ์„ฑ์ด ๋†’์œผ๋ฏ€๋กœ RC ๋ณด์˜ ๊ณก๋ฅ  ๋˜๋Š” ๋ณ€์œ„ ์—ฐ์„ฑ๋น„์˜ ๋ชจ๋ธ์—์„œ ์ด์— ๋Œ€ํ•œ ๊ณ ๋ ค๊ฐ€ ํ•„์š”ํ•˜๋‹ค.

์ด ์—ฐ๊ตฌ์˜ ๋ชฉ์ ์€ LWAC ๋ณด์—์„œ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์— ๋Œ€ํ•œ ํ•ฉ๋ฆฌ์ ์ธ ๋ชจ๋ธ์„ ์ œ์‹œํ•˜๋Š” ๊ฒƒ์ด๋‹ค. ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ ๋ชจ๋ธ์€ ๊ณก๋ฅ ($\mu_{\phi}$) ๋ฐ ๋ณ€์œ„($\mu_{\Delta}$) ์—ฐ์„ฑ๋น„์˜ ๊ฐœ๋…์œผ๋กœ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. $\mu_{\phi}$ ๋ฐ $\mu_{\Delta}$์— ๋Œ€ํ•œ ๊ธฐ๋ณธ ๋ฐฉ์ •์‹์€ ์œ„ํ—˜๋‹จ๋ฉด์—์„œ ๋ณ€ํ˜•๋ฅ  ์ ํ•ฉ์กฐ๊ฑด ๋ฐ ํž˜์˜ ํ‰ํ˜•์กฐ๊ฑด๊ณผ ๋ณด ๊ธธ์ด์— ๋”ฐ๋ผ ์ด์ƒํ™”๋œ ๊ณก๋ฅ  ๋ถ„ํฌ(Park and Paulay 1975)(12)๋กœ๋ถ€ํ„ฐ ์œ ๋„๋˜์—ˆ๋‹ค. ์œ ๋„๋œ $\mu_{\phi}$ ๋ฐ $\mu_{\Delta}$์˜ ๋ชจ๋ธ์€ RC ๋ณด์˜ ์—ฐ์„ฑ์— ์ค‘์š”ํ•œ ํ•จ์ˆ˜๋“ค์˜ ๋ณ€์ˆ˜์—ฐ๊ตฌ๋ฅผ ํ†ตํ•˜์—ฌ ๋‹จ์ˆœํ™”ํ•˜์˜€๋‹ค. ์ตœ์ข…์ ์œผ๋กœ ์ œ์‹œ๋œ ๋‹จ์ˆœ๋ชจ๋ธ์€ ๊ธฐ์กด ์—ฐ๊ตฌ์ž๋“ค์˜ 120๊ฐœ์˜ ์‹คํ—˜๊ฒฐ๊ณผ(Shin 1988; Ahmad and Barker 1991; Park and Kim 1999; Han et al. 2001; Maghsoudi and Bengar 2006; Jung et al. 2007; Sin et al. 2011; Carmo et al. 2013; Bernardo et al. 2016; Im et al. 2020; Yang et al. 2020b)(1,3-7,9,13,15,16,19)์™€์˜ ๋น„๊ต๋ฅผ ํ†ตํ•˜์—ฌ ๊ทธ ์ •ํ™•๋„๋ฅผ ํ‰๊ฐ€ํ•˜์˜€๋‹ค.

2. ๊ธฐ์กด ๋ชจ๋ธ์˜ ๋ถ„์„

์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ(RC) ๋ณด ๋‹จ๋ฉด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์€ ์ผ๋ฐ˜์ ์œผ๋กœ ๊ณก๋ฅ  ์—ฐ์„ฑ๋น„($\mu_{\phi}$) ๋˜๋Š” ๋ณ€์œ„ ์—ฐ์„ฑ๋น„($\mu_{\Delta}$)๋กœ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ํ‰๊ฐ€๋  ์ˆ˜ ์žˆ๋‹ค(Park and Paulay 1975)(12).

(1)
$\mu_{\phi}=\dfrac{\phi_{n}}{\phi_{y}}$

(2)
$\mu_{\Delta}=\dfrac{\Delta_{n}}{\Delta_{y}}$

์—ฌ๊ธฐ์„œ, $\phi_{n}$์™€ $\phi_{y}$๋Š” ๊ฐ๊ฐ ์ตœ๋Œ€๋‚ด๋ ฅ ๋ฐ ํ•ญ๋ณต์‹œ์ ์˜ ๊ณก๋ฅ ์„, $\Delta_{n}$์™€ $\Delta_{y}$๋Š” ์ตœ๋Œ€๋‚ด๋ ฅ ๋ฐ ํ•ญ๋ณต์‹œ์ ์˜ ๋ณ€์œ„๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ์ด์žฅ์—์„œ๋Š” ์‹(1) ๋ฐ (2)์— ๋Œ€ํ•œ ๊ธฐ์กด ์ œ์•ˆ๋ชจ๋ธ(Pam et al. 2001a, 2001b; Arslan and Cihanli 2010; Yang et al. 2020a)(2,10,11,20)๋“ค์ด LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์„ ์˜ˆ์ธกํ•˜๋Š”๋ฐ ์„ค๊ณ„์‹์œผ๋กœ์„œ์˜ ํ•œ๊ณ„๋ฅผ ์ค‘์ ์ ์œผ๋กœ ๋ถ„์„ํ•˜์˜€๋‹ค.

2.1 ๊ณก๋ฅ  ์—ฐ์„ฑ๋น„

Pam et al.(2001a, 2001b)(10,11)์€ ๋น„์„ ํ˜• ํ•ด์„์„ ์ด์šฉํ•˜์—ฌ NWC ๋ณด์—์„œ ์ฝ˜ํฌ๋ฆฌํŠธ ์••์ถ•๊ฐ•๋„($f_{ck}$)์™€ ์ฃผ์ฒ ๊ทผ๋น„($\rho_{s}$)์— ๋”ฐ๋ฅธ ๊ท ํ˜•์ฒ ๊ทผ๋น„($\rho_{b}$)๋ฅผ ์‚ฐ์ •ํ•˜์˜€์œผ๋ฉฐ, ์ด๋กœ๋ถ€ํ„ฐ RC ๋ณด์˜ $\mu_{\phi}$๋ฅผ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์•ˆํ•˜์˜€๋‹ค.

(3a)
$\mu_{\phi}=9.5\left(f_{ck}\right)^{-0.3}\left(\dfrac{\rho_{s}}{\rho_{b}}\right)^{-0.75}$ for $\rho_{s}^{'}=0$

(3b)
\begin{align*} \mu_{\phi}=10.7\left(f_{ck}\right)^{-0.45}\left(\dfrac{\rho_{s}-\rho_{s}^{'}}{\rho_{b}}\right)^{-1.25}\\ \left(1+95.2(f_{ck})^{-1.1}\left(\dfrac{\rho_{s}^{'}}{\rho_{s}}\right)^{3}\right) \end{align*} for $\rho_{s}^{'}>0$

์—ฌ๊ธฐ์„œ, $\rho_{s}^{'}$๋Š” ์••์ถ•์ฒ ๊ทผ๋น„๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ์‹(3)์—์„œ ๋‚˜ํƒ€๋‚ธ ๋ฐ”์™€ ๊ฐ™์ด Pam et al.(2001a, 2001b)(10,11)์˜ ๋ชจ๋ธ์€ $f_{ck}$์™€ $\rho_{s}/\rho_{b}$๋กœ RC ๋ณด์˜ ์—ฐ์„ฑ์„ ํ‰๊ฐ€ํ•˜๊ณ  ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ ์ด ๋ชจ๋ธ์€ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜๋Š” LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์„ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋Š” ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ์ง€ ์•Š๋‹ค.

Arslan and Cihanli(2010)(2)์€ 50 MPa ์ด์ƒ์˜ $f_{ck}$๋ฅผ ๊ฐ–๋Š” NWC ๋ณด์—์„œ์˜ $\mu_{\phi}$๋ฅผ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์•ˆํ•˜์˜€๋‹ค.

(4)
$\mu_{\phi}=40\left(\dfrac{\rho_{s}}{\rho_{b}}\right)^{-1.18}\left(f_{ck}\right)^{-0.17}\left(f_{y}\right)^{-0.42}$

์—ฌ๊ธฐ์„œ, $f_{y}$๋Š” ์ฃผ์ฒ ๊ทผ์˜ ํ•ญ๋ณต๊ฐ•๋„๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ์‹(4)์— ๋‚˜ํƒ€๋‚ธ ๋ฐ”์™€ ๊ฐ™์ด Arslan and Cihanli(2010)(2)์˜ ๋ชจ๋ธ์€ $f_{ck}$, $\rho_{s}/\rho_{b}$ ๋ฐ $f_{y}$์˜ ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ๋Š”๋ฐ, Pam et al.(2001a, 2001b)(10,11)์— ์˜ํ•ด ์ œ์‹œ๋œ ์‹(3)๊ณผ ๋น„์Šทํ•œ ํ˜•ํƒœ๋ฅผ ๊ฐ€์ง€๊ณ  ์žˆ๋‹ค. Arslan and Cihanli(2010)(2)์˜ ๋ชจ๋ธ๋„ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜๋Š” LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์„ ๋ฐ˜์˜ํ•  ์ˆ˜ ์žˆ๋Š” ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ์ง€ ์•Š๋‹ค. ์ด์™€ ๊ฐ™์ด Pam et al.(2001a, 2001b)(10,11) ๋ฐ Arslan and Cihanli (2010)(2)์˜ ๋ชจ๋ธ๋“ค์€ NWC ๋ณด์˜ ์‹คํ—˜๊ฒฐ๊ณผ์— ๊ธฐ๋ฐ˜ํ•˜์—ฌ ์ œ์‹œํ•˜๊ณ  ์žˆ์–ด LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์„ ๊ณผ๋Œ€ํ‰๊ฐ€ํ•  ๊ฐ€๋Šฅ์„ฑ์ด ๋†’๋‹ค.

2.2 ๋ณ€์œ„ ์—ฐ์„ฑ๋น„

Yang et al.(2020a)(20)์€ ๊ตฌ์ถ•๋œ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค์˜ ๋ถ„์„์„ ํ†ตํ•˜์—ฌ LWAC ๋ณด์˜ $\mu_{\Delta}$๊ฐ€ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๊ฒŒ ์žˆ์Œ์„ ๊ฐ•์กฐํ•˜์˜€๋‹ค. ๋˜ํ•œ 2๊ฒฝ๊ฐ„ LWAC ๋ณด์˜ $\mu_{\Delta}$๋Š” ์‹คํ—˜๊ฒฐ๊ณผ์˜ ํšŒ๊ท€๋ถ„์„์œผ๋กœ๋ถ€ํ„ฐ ์ฃผ์ฒ ๊ทผ ์ง€์ˆ˜($\omega_{s}=\rho_{s}f_{y}/f_{ck}$)์˜ ํ•จ์ˆ˜๋กœ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ํ‰๊ฐ€๋  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์˜€๋‹ค.

(5)
$\mu_{\Delta}=6.09\operatorname Exp\left[-9.963\omega_{s}\right]$

์‹(5)์—์„œ ๋‚˜ํƒ€๋‚ธ ๋ฐ”์™€ ๊ฐ™์ด Yang et al.(2020a)(20)์˜ ๋ชจ๋ธ๋„ $\omega_{s}$์˜ ํ•จ์ˆ˜๋กœ ์ œ์‹œ๋˜๊ณ  ์žˆ๊ธฐ ๋•Œ๋ฌธ์— Pam et al.(2001a, 2001b)(10,11) ๋ฐ Arslan and Cihanli(2010)(2)์˜ ๋ชจ๋ธ์—์„œ ์ ์šฉ๋œ ๋™์ผํ•œ ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ๋‹ค. ํ•˜์ง€๋งŒ, Yang et al.(2020a)(20)์˜ ๋ชจ๋ธ์€ ์ œํ•œ์ ์ธ ๋ณ€์ˆ˜๋ฒ”์œ„๋ฅผ ๊ฐ–๋Š” 12๊ฐœ์˜ 2๊ฒฝ๊ฐ„ LWAC ๋ณด ์‹คํ—˜๊ฒฐ๊ณผ์— ๊ธฐ๋ฐ˜ํ•˜์—ฌ ์ œ์‹œ๋˜์—ˆ๋‹ค. ํŠนํžˆ, ์ด ๋ชจ๋ธ๋„ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜๋Š” LWAC ๋ณด์˜ ์†Œ์„ฑํšŒ์ „๋Šฅ๋ ฅ์„ ๋ฐ˜์˜ํ•  ์ˆ˜ ์žˆ๋Š” ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ์ง€ ์•Š๋‹ค.

3. ๊ณก๋ฅ  ๋ฐ ๋ณ€์œ„ ์—ฐ์„ฑ๋น„ ๋ชจ๋ธ

3.1 ๊ธฐ๋ณธ ๋ฐฉ์ •์‹

Tํ˜• ๋‹จ์ˆœ๋ณด์˜ ํ•ญ๋ณต์ƒํƒœ์™€ ์ตœ๋‚ด๋‚ด๋ ฅ ์‹œ์ ์—์„œ ์ค‘๋ฆฝ์ถ• ๊นŠ์ด๋Š” ๋Œ€๋ถ€๋ถ„ ํ”Œ๋žœ์ง€ ๋‚ด(Yang et al. 2020b)(19)์— ์žˆ๋‹ค. ๋˜ํ•œ ์—ฐ์†๋ณด์˜ ๊ฒฝ์šฐ ์†Œ์„ฑํžŒ์ง€๋Š” ํ”Œ๋žœ์ง€์˜ ์ธ์žฅ์ €ํ•ญ์ด ๋ฌด์‹œ๋˜๋Š” ์žฅ๋ฐฉํ˜• ๋‹จ๋ฉด์˜ ๋ถ€๋ชจ๋ฉ˜ํŠธ ์˜์—ญ์—์„œ ์šฐ์„  ํ˜•์„ฑ๋œ๋‹ค. ๋”ฐ๋ผ์„œ ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ํ”Œ๋žœ์ง€๋ฅผ ๋ฌด์‹œํ•œ ์žฅ๋ฐฉํ˜• ๋ณด์˜ ๋‹จ๋ฉด์—์„œ $\mu_{\phi}$์™€ $\mu_{\Delta}$์˜ ๊ธฐ๋ณธ ๋ฐฉ์ •์‹์„ ์œ ๋„ํ•˜์˜€๋‹ค. ์‹(1)์˜ $\phi_{n}$์™€ $\phi_{y}$๋Š” ์œ„ํ—˜๋‹จ๋ฉด์—์„œ ๊ตฌ์„ฑ ์žฌ๋ฃŒ๋“ค์˜ ๋ณ€ํ˜•๋ฅ  ๋ฐ ์ค‘๋ฆฝ์ถ• ๊นŠ์ด๋กœ๋ถ€ํ„ฐ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ •๋ฆฌํ•  ์ˆ˜ ์žˆ๋‹ค(Park and Paulay 1975)(12).

(6)
$\mu_{\phi}=\dfrac{\epsilon_{cu}/c_{n}}{\epsilon_{sy}/(d_{s}-c_{y})}$

์—ฌ๊ธฐ์„œ, $c_{y}$์™€ $c_{n}$์€ ๊ฐ๊ฐ ํ•ญ๋ณต์ƒํƒœ ๋ฐ ์ตœ๋Œ€๋‚ด๋ ฅ์ƒํƒœ์—์„œ์˜ ์ค‘๋ฆฝ์ถ• ๊นŠ์ด๋ฅผ, $\epsilon_{sy}$์™€ $\epsilon_{cu}$๋Š” ๊ฐ๊ฐ ํ•ญ๋ณต์ƒํƒœ์—์„œ ์ฃผ์ฒ ๊ทผ์˜ ํ•ญ๋ณต๋ณ€ํ˜•๋ฅ ๊ณผ ์ตœ๋Œ€๋‚ด๋ ฅ์ƒํƒœ์—์„œ์˜ ์ฝ˜ํฌ๋ฆฌํŠธ ์••์ถ•์—ฐ๋‹จ ๊ทนํ•œ๋ณ€ํ˜•๋ฅ ์„, $d_{s}$๋Š” ์ฃผ์ฒ ๊ทผ์˜ ๊นŠ์ด๋ฅผ ์˜๋ฏธํ•œ๋‹ค. Fig. 1์—๋Š” ํ•ญ๋ณต ๋ฐ ์ตœ๋Œ€๋‚ด๋ ฅ ์‹œ์ ์—์„œ ์žฅ๋ฐฉํ˜• ๋ณด๋‹จ๋ฉด์˜ ๊ฐ ๊ตฌ์„ฑ ์žฌ๋ฃŒ๋“ค์˜ ๋ณ€ํ˜•๋ฅ ๊ณผ ์‘๋ ฅ๋ถ„ํฌ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ํ•ญ๋ณต์ƒํƒœ์—์„œ๋Š” ์ฃผ์ฒ ๊ทผ์˜ ๋ณ€ํ˜•๋ฅ ์ด ํ•ญ๋ณต์— ๋„๋‹ฌํ•˜๊ธฐ ์ง์ „์˜ ์ƒํƒœ์ด๋ฏ€๋กœ ์••์ถ•์กด์˜ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ์ด ํƒ„์„ฑ์ƒํƒœ์— ์žˆ์„ ๊ฐ€๋Šฅ์„ฑ์ด ๋†’๋‹ค(Yang et al. 2014)(18). ๋”ฐ๋ผ์„œ ์••์ถ•์กด์˜ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ์„ ๋‹จ๋ฉด ๊นŠ์ด์— ๋”ฐ๋ผ ์„ ํ˜• ๋ถ„ํฌํ•œ๋‹ค๋Š” ๊ฐ€์ •๊ณผ ํ•จ๊ป˜ ํž˜์˜ ํ‰ํ˜•์กฐ๊ฑด์œผ๋กœ๋ถ€ํ„ฐ $c_{y}$๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ •๋ฆฌํ•  ์ˆ˜ ์žˆ๋‹ค.

Fig. 1. Distribution of stresses and strains at different states

../../Resources/kci/JKCI.2021.33.1.031/fig1.png

(7a)
$c_{y}=\left[\dfrac{-B_{1}\pm \sqrt{B_{1}^{2}-4A_{1}C_{1}}}{2A_{1}}\right]$

(7b)
$A_{1}=0.5E_{c}\epsilon_{sy}b_{w}$

(7c)
$B_{1}=A_{s}^{'}E_{s}\epsilon_{sy}+A_{s}f_{y}$

(7d)
$C_{1}=-A_{s}^{'}E_{s}\epsilon_{sy}d^{'}-A_{s}f_{y}d_{s}$

์—ฌ๊ธฐ์„œ, $b_{w}$๋Š” ๋ณด์˜ ํญ์„, $E_{c}$์™€ $E_{s}$๋Š” ๊ฐ๊ฐ ์ฝ˜ํฌ๋ฆฌํŠธ์™€ ์ฒ ๊ทผ์˜ ํƒ„์„ฑ๊ณ„์ˆ˜๋ฅผ, $A_{s}^{'}$์™€ $d^{'}$๋Š” ๊ฐ๊ฐ ์••์ถ•์ฒ ๊ทผ์˜ ๋‹จ๋ฉด์  ๋ฐ ๊นŠ์ด๋ฅผ, $A_{s}$๋Š” ์ฃผ์ฒ ๊ทผ์˜ ๋‹จ๋ฉด์ ์„ ์˜๋ฏธํ•œ๋‹ค. ์‹(6)์—์„œ $c_{n}$์€ ์ตœ๋Œ€๋‚ด๋ ฅ ์ƒํƒœ์—์„œ ๊ฐ ๊ตฌ์„ฑ ์žฌ๋ฃŒ๋“ค์˜ ๋ณ€ํ˜•๋ฅ  ๋ถ„ํฌ ๋ฐ ํž˜์˜ ํ‰ํ˜•์กฐ๊ฑด์œผ๋กœ๋ถ€ํ„ฐ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ •๋ฆฌํ•  ์ˆ˜ ์žˆ๋‹ค.

(8a)
$c_{n}=\left[\dfrac{-B_{2}\pm \sqrt{B_{2}^{2}-4A_{2}C_{2}}}{2A_{2}}\right]$

(8b)
$A_{2}=0.85f_{ck}\beta_{1}b_{w}$

(8c)
$B_{2}=A_{s}^{'}E_{s}\epsilon_{cu}-A_{s}f_{y}$

(8d)
$C_{2}=-A_{s}^{'}E_{s}\epsilon_{cu}d^{'}$

์—ฌ๊ธฐ์„œ, $\beta_{1}$๋Š” ๋“ฑ๊ฐ€์‘๋ ฅ๋ธ”๋ก์˜ ๊นŠ์ด๊ณ„์ˆ˜๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ์ด์— ๋”ฐ๋ผ ์‹(6)~(8)๋กœ๋ถ€ํ„ฐ RC ๋ณด์˜ $\mu_{\phi}$๋ฅผ ๊ณ„์‚ฐํ•  ์ˆ˜ ์žˆ๋‹ค. ํ•œํŽธ, ์‹(2)์—์„œ $\Delta_{y}$์™€ $\Delta_{n}$์€ ๋ณด ๊ธธ์ด์— ๋”ฐ๋ผ ์ด์ƒํ™”๋œ ๊ณก๋ฅ ๋ถ„ํฌ(Fig. 2)์™€ ๋“ฑ๊ฐ€์†Œ์„ฑํžŒ์ง€๊ธธ์ด($L_{p}$)๋ฅผ ๋ชจ๋ฉ˜ํŠธ ๋ฉด์ ๋ฒ•์„ ์ด์šฉํ•˜์—ฌ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์‚ฐ์ •ํ•  ์ˆ˜ ์žˆ๋‹ค.

(9a)
$\Delta_{y}=\dfrac{1}{2}\phi_{y}\left(\dfrac{a^{2}}{3}+A_{3}a_{s}+A_{3}^{2}\right)$

(9b)
$\Delta_{n}=\phi_{y}\left(\dfrac{L^{2}}{24}-\dfrac{1}{2}B_{3}\right)+\phi_{n}\dfrac{1}{2}B_{3}$

(9c)
$A_{3}=0.5L-a_{s}$

(9d)
$B_{3}=L_{p}^{2}+0.5L_{P}A+A^{2}$

์‹(9)์—์„œ $L_{p}$๋Š” ๋‹ค์Œ์˜ ์‹์—์„œ ์ œ์‹œํ•˜๊ณ  ์žˆ๋Š” Priestley and Park(1987)(14)์˜ ๋ชจ๋ธ์„ ์ด์šฉํ•˜์˜€๋‹ค.

(10)
$L_{p}=0.08a_{s}+0.022d_{b}f_{y}$

์—ฌ๊ธฐ์„œ, $a_{s}$๋Š” ์ „๋‹จ๊ฒฝ๊ฐ„์„, $d_{b}$๋Š” ์ฃผ์ฒ ๊ทผ์˜ ์ง๊ฒฝ์„ ์˜๋ฏธํ•œ๋‹ค. ์ด์— ๋”ฐ๋ผ ์‹(2), (9) ๋ฐ (10)์œผ๋กœ๋ถ€ํ„ฐ RC ๋ณด์˜ $\mu_{\Delta}$๋ฅผ ๊ณ„์‚ฐํ•  ์ˆ˜ ์žˆ๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” $c_{y}$์™€ $c_{n}$์— ์ง์ ‘์ ์œผ๋กœ ๊ฒฐ์ •๋˜๊ธฐ ๋•Œ๋ฌธ์— ์ฝ˜ํฌ๋ฆฌํŠธ์™€ ์ฒ ๊ทผ์˜ ์—ญํ•™์  ํŠน์„ฑ์— ํ˜„์ €ํ•œ ์˜ํ–ฅ์„ ๋ฐ›์Œ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค(Lee 2013; Yang et al. 2014)(8,18). ๋”ฐ๋ผ์„œ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์—์„œ NWC๋ณด๋‹ค ์ตœ๋Œ€์‘๋ ฅ ์ดํ›„ ์ทจ์„ฑ์ ์ธ ๊ฒฝํ–ฅ์„ $\beta_{1}$(Yang et al. 2013)(21)์— ๋ฐ˜์˜ํ•œ๋‹ค๋ฉด, LWAC ๋ณด์˜ ์—ฐ์„ฑ์€ NWC ๋ณด๋ณด๋‹ค ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋  ๊ฐ€๋Šฅ์„ฑ์ด ๋†’๋‹ค(Yang et al. 2020a)(20).

Fig. 2. Distribution of curvature along beam length

../../Resources/kci/JKCI.2021.33.1.031/fig2.png

3.2 ์ฃผ์š” ๋ณ€์ˆ˜์˜ํ–ฅ ํ‰๊ฐ€

Fig. 3์—๋Š” RC ๋ณด์˜ ๋™์ผํ•œ ๋‹จ๋ฉด์ƒ์„ธ์—์„œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰($\rho_{c}$)์— ๋”ฐ๋ฅธ $\mu_{\phi}$ ๋ฐ $\mu_{\Delta}$๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ์ ์šฉ๋œ ๋ณ€์ˆ˜๋ฒ”์œ„๋Š” $\omega_{s}$๊ฐ€ 0.125~0.25, $\rho_{c}$๊ฐ€ 1,400~2,300 kg/m3์ด์—ˆ์œผ๋ฉฐ, $f_{ck}$์™€ $f_{y}$๋Š” 24 MPa์™€ 400 MPa๋กœ, ์••์ถ•์ฒ ๊ทผ ์ง€์ˆ˜($\omega_{s}^{'}$)์™€ $a_{s}/d_{s}$๋Š” ๊ฐ๊ฐ 0 ๋ฐ 4๋กœ ๊ณ ์ •ํ•˜์˜€๋‹ค. ์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ(RC) ๋ณด์˜ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” $\rho_{c}$๊ฐ€ 39 % ๊ฐ์†Œํ•  ๋•Œ ๊ฐ๊ฐ 47 % ๋ฐ 28 % ๊ฐ์†Œํ•˜์˜€๋‹ค. ๋˜ํ•œ, ๊ทธ ๊ฐ์†Œ ๊ธฐ์šธ๊ธฐ๋Š” $\omega_{s}$๊ฐ€ ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ๋” ํ˜„์ €ํ•˜์˜€๋‹ค. ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰($\rho_{c}$)์ด 1,400 kg/m3์ธ RC ๋ณด์˜ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” $\omega_{s}$๊ฐ€ 0.125์ผ ๋•Œ 0.25๋กœ ์ฆ๊ฐ€ํ•  ๋•Œ ๊ฐ๊ฐ 47 % ๋ฐ 76 % ๊ฐ์†Œํ•˜์˜€๋‹ค. ์ด๋Š” $\omega_{s}$์˜ ๊ฐ์†Œ๊ฐ€ ์••์ถ•์กด์„ ํ‚ค์›Œ RC ๋ณด์˜ ์—ฐ์„ฑ์— ๋ฏธ์น˜๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์—ญํ•™์  ํŠน์„ฑ์˜ ์˜ํ–ฅ์ด ๋”์šฑ ์ปค์กŒ๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ๋”ฐ๋ผ์„œ LWAC ๋ณด์˜ $\mu_{\phi}$์™€ $\mu_{\Delta}$์˜ ๋ชจ๋ธ์€ NWC๋ณด๋‹ค ๋‚ฎ์€ ์—ญํ•™์  ํŠน์„ฑ์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๋Š” $\rho_{c}$์˜ ํ•จ์ˆ˜๋ฅผ ๋ฐ˜๋“œ์‹œ ๊ณ ๋ คํ•˜์—ฌ์•ผ ํ•œ๋‹ค.

3.3 ๋ชจ๋ธ์˜ ๋‹จ์ˆœํ™”

3.1์ ˆ์—์„œ ์ œ์‹œ๋œ ๋ฐ”์™€ ๊ฐ™์ด $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” ์‹(6)~(10)๋กœ๋ถ€ํ„ฐ ์‚ฐ์ •ํ•˜์—ฌ์•ผ ํ•˜๋ฏ€๋กœ ๊ทธ ๊ณ„์‚ฐ๊ณผ์ •์ด ๋งค์šฐ ๋ณต์žกํ•˜๋‹ค. ๋”ฐ๋ผ์„œ ์ด ๋ชจ๋ธ๋“ค์€ ๋‹จ์ˆœ์‹์œผ๋กœ ์ผ๋ฐ˜ํ™”๋˜์—ˆ๋Š”๋ฐ, ๋ณ€์ˆ˜์—ฐ๊ตฌ์—์„œ ์–ป์–ด์ง„ ๊ฒฐ๊ณผ์ธ $\omega_{s}$๊ฐ€ ์ฆ๊ฐ€ํ•˜๊ฑฐ๋‚˜ $\rho_{c}$๊ฐ€ ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ๊ฐ์†Œํ•˜๋Š” ์—ฐ์„ฑ์˜ ์˜ํ–ฅ์„ ๋ฐ˜์˜ํ•˜์˜€๋‹ค. ์ ์šฉ๋œ ๋ณ€์ˆ˜๋ฒ”์œ„๋Š” $\omega_{s}$๊ฐ€ 0.03~0.5, $\omega_{s}^{'}$๊ฐ€ 0~0.005, $\rho_{c}$๊ฐ€ 1,400~2,300 kg/m3์ด๋‹ค. $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” ์ฃผ์š” ์˜ํ–ฅ ๋ณ€์ˆ˜์ธ $\omega_{s}$์™€ $\rho_{c}$๋ฅผ ํ•จ์ˆ˜๋กœ ์„ ์ •ํ•˜์˜€์œผ๋ฉฐ, ๊ฐ๊ฐ ๋ฐ˜๋น„๋ก€์™€ ๋น„๋ก€ ๊ด€๊ณ„๋กœ ์กฐํ•ฉํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ ๋‹จ์ˆœ์‹์€ ์ด๋“ค์˜ ์ฃผ์š”์˜ํ–ฅ ๋ณ€์ˆ˜๋“ค์„ ๋ฐ˜๋ณต์ ์œผ๋กœ ์กฐํ•ฉํ•˜๋ฉด์„œ ์ƒ๊ด€๊ณ„์ˆ˜๊ฐ€ ๊ฐ€์žฅ ๋†’์€ ๋•Œ๋กœ ์‚ฐ์ •ํ•˜์˜€์œผ๋ฉฐ, ๊ทธ ์‹์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค(Fig. 4).

Fig. 3. Effect of different parameters on plastic rotation capacity

../../Resources/kci/JKCI.2021.33.1.031/fig3.png

(11)
$\mu_{\phi}=0.43\left[\dfrac{\omega_{s}^{0.7}}{(1+\omega_{s}^{'})^{7}}\left(\dfrac{\rho_{o}}{\rho_{c}}\right)^{0.6}\right]^{-1.5}$

(12)
$\mu_{\Delta}=0.62\left[\dfrac{\omega_{s}^{0.7}}{(1+\omega_{s}^{'})^{3}}\left(\dfrac{\rho_{o}}{\rho_{c}}\right)^{0.5}\left(\dfrac{a_{s}}{d_{s}}\right)^{0.1}\right]^{-1.3}$

์—ฌ๊ธฐ์„œ, $\rho_{o}$๋Š” ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰์˜ ์ฐธ๊ณ ๊ฐ’(2,300 kg/m3)์„ ์˜๋ฏธํ•œ๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ LWAC ๋ณด์˜ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” ์‹ (11)๊ณผ (12)์— ์ œ์‹œ๋œ ๋ฐ”์™€ ๊ฐ™์ด $\rho_{c}$์˜ ํ•จ์ˆ˜๋ฅผ ํฌํ•จํ•จ์œผ๋กœ์„œ NWC ๋ณด์™€ LWAC์˜ ๋ณด์˜ ์—ฐ์„ฑ์„ ํ•ฉ๋ฆฌ์ ์œผ๋กœ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋‹ค.

4. ์ œ์‹œ๋œ ๋ชจ๋ธ๊ณผ ์‹คํ—˜๊ฒฐ๊ณผ์™€์˜ ๋น„๊ต

4.1 ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค ๊ตฌ์ถ•

์ œ์‹œ๋œ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” ์„ค๊ณ„์‹์œผ๋กœ์˜ ์‹ ๋ขฐ์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•ด์„œ ํœจ์œผ๋กœ ์ง€๋ฐฐ๋œ RC ๋ณด์˜ ์‹คํ—˜๊ฒฐ๊ณผ๋“ค(Shin 1988; Ahmad and Barker 1991; Park and Kim 1999; Han et al. 2001; Maghsoudi and Bengar 2006; Jung et al. 2007; Sin et al. 2011; Carmo et al. 2013; Bernardo et al. 2016; Im et al., 2020; Yang et al. 2020b)(1,3-7,9,13,15,16,19)์„ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šคํ™” ํ•˜์˜€๋Š”๋ฐ, $\mu_{\phi}$์— ๋Œ€ํ•œ ์‹คํ—˜๊ฒฐ๊ณผ๊ฐ€ ๋งค์šฐ ๋ฏธ๋ฏธํ•˜์˜€๋‹ค. ๋”ฐ๋ผ์„œ ์ด์žฅ์—์„œ ์ œ์‹œ๋œ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค๋Š” $\mu_{\Delta}$์— ๋Œ€ํ•œ ์‹คํ—˜๊ฒฐ๊ณผ๋งŒ์„ ๊ฐ€์ง€๊ณ  ์ œ์•ˆ๋ชจ๋ธ์˜ ์‹ ๋ขฐ์„ฑ์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šคํ™”๋œ ์‹คํ—˜๊ฒฐ๊ณผ๋“ค์€ $\rho_{s}$๊ฐ€ 0.002~0.077, $\rho_{s}'$๊ฐ€ 0~0.017, $\rho_{c}$๊ฐ€ 1,578 kg/m3~2,400 kg/m3, ์ „๋‹จ๊ฒฝ๊ฐ„-๊นŠ์ด๋น„($a_{s}/d_{s}$)๊ฐ€ 2.9~6.7 ๋ฐ $f_{ck}$๊ฐ€ 20~115 MPa์˜ ๋ฒ”์œ„์— ์žˆ์—ˆ๋‹ค. Fig. 5์— ๋‚˜ํƒ€๋‚ธ ๋ฐ”์™€ ๊ฐ™์ด LWAC ๋ณด์—์„œ๋Š” $\rho_{s}$๊ฐ€ 0.01~0.02, $f_{ck}$๋Š” 40~60 MPa, $a_{s}/d_{s}$๊ฐ€ 2.5~4์˜ ๋ฒ”์œ„๊ฐ€ ๋Œ€๋ถ€๋ถ„์ด์—ˆ๋‹ค. ๋˜ํ•œ, NWC์—์„œ๋Š” $\rho_{s}$๊ฐ€ 0.003~0.02, $f_{ck}$๋Š” 20~40 MPa, $a_{s}/d_{s}$๊ฐ€ 4~5.5์˜ ๋ฒ”์œ„๊ฐ€ ๋Œ€๋ถ€๋ถ„์ด์—ˆ๋‹ค.

Fig. 4. Generalization of ductility ratio

../../Resources/kci/JKCI.2021.33.1.031/fig4.png

Fig. 5. Frequency of flexure-governed beams

../../Resources/kci/JKCI.2021.33.1.031/fig5.png

4.2 ์‹คํ—˜๊ฒฐ๊ณผ์™€์˜ ๋น„๊ต

์ด์ „์˜ ์ ˆ์—์„œ ๊ตฌ์ถ•๋œ ์‹คํ—˜๊ฒฐ๊ณผ์™€ ์ œ์‹œ๋œ ๋ชจ๋ธ๋“ค๊ณผ์˜ ๋น„๊ต๋ฅผ ์œ„ํ•ด์„œ Pam et al.(2001a, 2001b)(10,11)๊ณผ Arslan and Cihanli(2010)(2)์˜ ๋ชจ๋ธ๋“ค์€ ์‹(10)์— ์‹(9)๋ฅผ ๋Œ€์ž…ํ•œ ํ›„ ์‹(2)๋ฅผ ์ด์šฉํ•˜์—ฌ $\mu_{\Delta}$๋กœ ํ™˜์‚ฐํ•˜์˜€๋‹ค. Fig. 6์—๋Š” ๊ธฐ์กด ๋ชจ๋ธ ๋ฐ ์ด ์—ฐ๊ตฌ์—์„œ ์ œ์‹œ๋œ ๋ชจ๋ธ์— ์˜ํ•œ ์˜ˆ์ธก๊ฐ’๊ณผ ์‹คํ—˜๊ฐ’์˜ ๋น„๋“ค์˜ ํ‰๊ท ($\gamma_{m}$) ๋ฐ ํ‘œ์ค€ํŽธ์ฐจ($\gamma_{s}$)๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. Pam et al.(2001a, 2001b)(10,11)์˜ ๋ชจ๋ธ์€ $\mu_{\Delta}$๋ฅผ ๋ถˆ์•ˆ์ „์ธก์œผ๋กœ ์˜ˆ์ธกํ•˜์˜€๋Š”๋ฐ, ๊ทธ ๋ถˆ์•ˆ์ „์ธก์˜ ์ •๋„๋Š” $\rho_{c}$๊ฐ€ ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ ์‹คํ—˜๊ฒฐ๊ณผ์™€์˜ ๋น„๊ต์—์„œ Pam et al.(2001a, 2001b)(10,11)์˜ ๋ชจ๋ธ์˜ $\gamma_{m}$๋Š” LWAC ๋ณด์—์„œ 0.42๋กœ์„œ NWC ๋ณด๋ณด๋‹ค ์•ฝ 27 % ๋‚ฎ์•˜๋‹ค. Arslan and Cihanli (2010)(2)์˜ ๋ชจ๋ธ๋„ Pam et al.(2001a, 2001b)(10,11)์˜ ๋ชจ๋ธ๊ณผ ๋น„์Šทํ•œ ๊ฒฝํ–ฅ์„ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ์‹คํ—˜๊ฒฐ๊ณผ์™€์˜ ๋น„๊ต์—์„œ Arslan and Cihanli (2010)(2)์˜ ๋ชจ๋ธ์˜ $\gamma_{m}$๋Š” LWAC ๋ณด์™€ NWC ๋ณด์—์„œ ๊ฐ๊ฐ 0.77 ๋ฐ 0.79์ด์—ˆ๋‹ค. ๋ฐ˜๋ฉด, Yang et al.(2020a)(20)์˜ ๋ชจ๋ธ์€ ๋Œ€๋ถ€๋ถ„์˜ ์‹คํ—˜๊ฒฐ๊ณผ๋ฅผ ์•ˆ์ „์ธก์œผ๋กœ ์˜ˆ์ธกํ•˜์˜€๋Š”๋ฐ, ๊ทธ ์•ˆ์ „์ธก์˜ ์ •๋„๊ฐ€ NWC ๋ณด์—์„œ ํ˜„์ €ํ•˜๊ฒŒ ๋†’์•˜๋‹ค. ์‹คํ—˜๊ฒฐ๊ณผ์™€์˜ ๋น„๊ต์—์„œ Yang et al.(2020a)(20)์˜ ๋ชจ๋ธ์˜ $\gamma_{m}$์€ LWAC ๋ณด์™€ NWC ๋ณด์—์„œ ๊ฐ๊ฐ 2.14 ๋ฐ 2.16์ด์—ˆ๋‹ค. ์ด์™€ ๊ฐ™์ด ๊ธฐ์กด ์ œ์•ˆ๋ชจ๋ธ๋“ค์€ $f_{ck}$์™€ ์ฒ ๊ทผ๋น„์— ๊ด€๋ จ๋œ ํ•จ์ˆ˜($\rho_{s}$, $\rho_{b}$ ๋ฐ $\rho_{s}^{'}$)๋งŒ์„ ํฌํ•จํ•˜๊ณ  ์žˆ์–ด ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ข…๋ฅ˜์— ๋”ฐ๋ผ ๋ณ€ํ™”๋˜๋Š” RC ๋ณด์˜ ์—ฐ์„ฑ์„ ๊ณ ๋ คํ•˜์ง€ ๋ชปํ•˜๊ณ  ์žˆ๋‹ค. ์ด์— ๋ฐ˜ํ•ด, ์ œ์•ˆ๋ชจ๋ธ์€ $\rho_{c}$์™€ ์ฒ ๊ทผ๋น„์— ๊ด€๋ จ๋œ ํ•จ์ˆ˜์— ๊ด€๊ณ„์—†์ด $\gamma_{m}$ ๋ฐ $\gamma_{s}$๊ฐ€ ๊ฐ๊ฐ 0.98 ๋ฐ 0.20์œผ๋กœ์„œ RC ๋ณด์˜ $\mu_{\Delta}$๋ฅผ ๋Œ€์ฒด๋กœ ์ž˜ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ์ด๋•Œ LWAC ๋ณด์—์„œ $\gamma_{m}$์™€ $\gamma_{s}$๋Š” ๊ฐ๊ฐ 0.94 ๋ฐ 0.20์ด์—ˆ์œผ๋ฉฐ, NWC ๋ณด์—์„œ๋Š” ๊ฐ๊ฐ 1.02 ๋ฐ 0.20์ด์—ˆ๋‹ค. ๋”ฐ๋ผ์„œ RC ๋ณด์˜ $\mu_{\Delta}$๋Š” $\rho_{c}$์˜ ํ•จ์ˆ˜์˜ ๋ฐ˜์˜์œผ๋กœ LWAC ๋ณด์—์„œ ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜๋Š” ์—ฐ์„ฑ์„ ์ž˜ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋‹ค.

Fig. 6. Comparison of test results for $\mu_{\Delta}$ with predicted values

../../Resources/kci/JKCI.2021.33.1.031/fig6_1.png

../../Resources/kci/JKCI.2021.33.1.031/fig6_2.png

5. ๊ฒฐ ๋ก 

์ด ์—ฐ๊ตฌ์—์„œ๋Š” ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ(LWAC) ๋ณด์˜ ๊ณก๋ฅ ($\mu_{\phi}$) ๋ฐ ๋ณ€์œ„ ์—ฐ์„ฑ๋น„($\mu_{\Delta}$)๋ฅผ ํ•ฉ๋ฆฌ์ ์œผ๋กœ ํ‰๊ฐ€ํ•˜๊ธฐ ์œ„ํ•œ ๋ชจ๋ธ์„ ์ œ์‹œํ•˜์˜€๋‹ค. ์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ(RC) ๋ณด์˜ $\mu_{\phi}$์— ๋Œ€ํ•œ ์‹คํ—˜ ๋ฐ์ดํ„ฐ๋Š” ๋งค์šฐ ๋ถ€์กฑํ•˜๋ฏ€๋กœ ์ œ์•ˆ ๋ชจ๋ธ์˜ ๊ฒ€์ฆ์€ $\mu_{\Delta}$์— ํ•œ์ •ํ•˜์˜€๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰์„ ๊ณ ๋ คํ•œ $\mu_{\phi}$ ๋ฐ $\mu_{\Delta}$์˜ ๋ชจ๋ธ์ œ์‹œ๋กœ๋ถ€ํ„ฐ ๋‹ค์Œ๊ณผ ๊ฐ™์€ ๊ฒฐ๋ก ์„ ์–ป์—ˆ๋‹ค.

1) ์œ„ํ—˜๋‹จ๋ฉด์˜ ๋ณ€ํ˜•๋ฅ  ์ ํ•ฉ์กฐ๊ฑด ๋ฐ ํž˜์˜ ํ‰ํ˜•์กฐ๊ฑด๊ณผ ๋ณด์˜ ๊ธธ์ด์— ๋”ฐ๋ผ ์ด์ƒํ™”๋œ ๊ณก๋ฅ ๋ถ„ํฌ๋กœ๋ถ€ํ„ฐ ์œ ๋„๋œ $\mu_{\phi}$์™€ $\mu_{\Delta}$๋Š” ๋‹จ์œ„์šฉ์ ์ค‘๋Ÿ‰($\rho_{c}$)์ด 39 % ๊ฐ์†Œํ•  ๋•Œ ๊ฐ๊ฐ ํ‰๊ท  47 % ๋ฐ 28 % ๊ฐ์†Œํ•˜์˜€๋Š”๋ฐ, ๊ทธ ๊ฐ์†Œ ๊ธฐ์šธ๊ธฐ๋Š” ์ฃผ์ฒ ๊ทผ ์ง€์ˆ˜($\omega_{s}$)๊ฐ€ ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ๋”์šฑ ํ˜„์ €ํ•˜์˜€๋‹ค.

2) ์œ ๋„๋œ $\mu_{\Delta}$๋Š” ๋ณ€์ˆ˜์—ฐ๊ตฌ๋ฅผ ๊ธฐ๋ฐ˜์œผ๋กœ $\omega_{s}$, ์••์ถ•์ฒ ๊ทผ ์ง€์ˆ˜($\omega_{s}^{'}$), $\rho_{c}$ ๋ฐ ์ „๋‹จ๊ฒฝ๊ฐ„-๊นŠ์ด ๋น„($a/d_{s}$)์˜ ํ•จ์ˆ˜๋ฅผ ๊ฐ–๋Š” ๋‹จ์ˆœ๋ชจ๋ธ๋กœ ์ผ๋ฐ˜ํ™”ํ•˜์˜€๋‹ค.

3) Pam et al.๊ณผ Arslan and Cihanli์˜ ๋ชจ๋ธ์€ $\mu_{\Delta}$๋ฅผ ๋ถˆ์•ˆ์ „์ธก์œผ๋กœ ์˜ˆ์ธกํ•˜์˜€๋Š”๋ฐ, ๊ทธ ๋ถˆ์•ˆ์ „์ธก์˜ ์ •๋„๋Š” $\rho_{c}$๊ฐ€ ๊ฐ์†Œํ•จ์— ๋”ฐ๋ผ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ๋ฐ˜๋ฉด Yang et al.์˜ ๋ชจ๋ธ์€ $\mu_{\Delta}$๋ฅผ ์•ˆ์ „์ธก์œผ๋กœ ์˜ˆ์ธกํ•˜์˜€์ง€๋งŒ, ๊ทธ ์•ˆ์ „์ธก์˜ ์ •๋„๊ฐ€ ๋ณดํ†ต ์ฝ˜ํฌ๋ฆฌํŠธ ๋ณด์—์„œ 2.14์ด์—ˆ๋‹ค.

4) ์ œ์‹œ๋œ $\mu_{\Delta}$์˜ ๋ชจ๋ธ์€ $\rho_{c}$์™€ ์ฒ ๊ทผ๋น„์— ๊ด€๋ จ๋œ ํ•จ์ˆ˜์— ๊ด€๊ณ„์—†์ด ์‹คํ—˜๊ฒฐ๊ณผ๋ฅผ ์ž˜ ์˜ˆ์ธกํ•˜์˜€๋Š”๋ฐ, ์‹คํ—˜๊ฒฐ๊ณผ ๋Œ€๋น„ ์˜ˆ์ธก๊ฐ’์˜ ๋น„์˜ ํ‰๊ท ๊ณผ ํ‘œ์ค€ํŽธ์ฐจ๊ฐ€ ๊ฐ๊ฐ 0.98 ๋ฐ 0.20์ด์—ˆ๋‹ค.

5) ์ œ์‹œ๋œ $\mu_{\Delta}$์˜ ๋ชจ๋ธ์€ $\rho_{c}$์˜ ํ•จ์ˆ˜๋ฅผ ๋ฐ˜์˜ํ•จ์œผ๋กœ์จ LWAC ๋ณด์—์„œ ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜๋Š” ์†Œ์„ฑํšŒ์ „ ๋Šฅ๋ ฅ์„ ํ•ฉ๋ฆฌ์ ์œผ๋กœ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋‹ค.

๊ฐ์‚ฌ์˜ ๊ธ€

์ด ์—ฐ๊ตฌ๋Š” 2017๋…„๋„ ์ •๋ถ€(๋ฏธ๋ž˜์ฐฝ์กฐ๊ณผํ•™๋ถ€)์˜ ์žฌ์›์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ(๊ณผ์ œ๋ฒˆํ˜ธ: No. 2017R1A2B3008463) ์ง€์›์— ์˜ํ•˜์—ฌ ์ˆ˜ํ–‰๋œ ์ค‘๊ฒฌ์—ฐ๊ตฌ์‚ฌ์—…๊ณผ 2018๋…„๋„ ์ •๋ถ€(๊ต์œก๋ถ€)์˜ ์žฌ์›์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ์˜ ๊ธฐ๋ณธ์—ฐ๊ตฌ์ง€์›์‚ฌ์—…(๊ณผ์ œ๋ฒˆํ˜ธ: No. 2018R1D1A1B07050275)์˜ ์—ฐ๊ตฌ๋น„ ์ง€์›์œผ๋กœ ์ˆ˜ํ–‰๋˜์—ˆ์œผ๋ฉฐ, ์ด์— ๊ฐ์‚ฌ๋“œ๋ฆฝ๋‹ˆ๋‹ค.

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