26ƒ 2A Á 2006 3œ pp. 363 ~ 370 ª š w»» d ƒ w ¼ Electromechanical Relation of Conductive Materials with High Electrical Resistance and Its Application to the Estimation of In_situ Stress of Structural Tendons Ÿ Á» Zi, GoangseupÁJun, Kiwoo Abstract It is proposed that the electromechanical relation of the conductive materials with high electrical resistance may be used to estimate the current stress of prestressing tendons. To choose the best conductive material to this end, we studied the electromechanical relations of carbon fibers and metalic heat wires experimentally. The strain of those materials was controlled instead of the stress during the experiment. It is found that the relation of carbon fibers can be modelled by a parabolic(or hyperbolic) function in the early stage of deformation. However because the relation is not consistent when it is unloaded and reload, carbon fibers are not suitable for this purpose. Metallic heat wires show a consistent linear relation during loading and unloading in the elastic deformation and are suitable for this purpose. To estimate the electromechanics relation of metallic wires, we developed a simple formula based on the rigid plasticity. We propose a new kind of prestressing tendons whose stress can be monitored. As a side result of this study, we found that the electromechanical relation of carbon fibers without epoxy matrix becomes almost linear after a certain strain. Keywords : Electromechanical Relation, prestressing tendons, Estimation of In_situ Stress, Metallic heat wires, carbon fibers v p ¼ x wš dw š w»» w w. š w kw» w k p x mw x w. k x» s xk ù w- w»»ƒ w ww y. k w, w w w x ww y.»» dw» w» w w w. w w ¼ d ƒ w ¼ w. we k, p x z ƒ x w x»» w w. w :»», ¼, d,, k 1. œ gj p m k. 1 1 gj p -- ----- w 8 10 ü k w» w» w v p» w. ³ w v p ƒ 1(a) s d j w. v p v p z ƒ,, j v gj p x w. v p k y g t ³» j, w ƒw w k ( 1(b)). v p gj p sƒwš w ƒ w x ¼ d y w. * z Áš w zy lœw (E-mail: g-zi@korea.ac.kr) **š w zy lœw (E-mail: junkiwoo@korea.ac.kr) 26ƒ 2A 2006 3œ 363
1. v p y x ƒ w ¼ d w d w (Saiidi, 1994), q w (Chen, 2001; Chen, 2002; di Scalea, 2003), x w d (Civjan, 1995), ³ w (Azizinamini, 1996). w ³ w w ƒ ë w. ù œ x mw z y ¼ d w» w ƒ w w» w ƒ w, w w w œ w» q š. q w ¼ wš k ƒ w q y dw» w šƒ ƒ v w, e q š w w q v w ƒ (Chen 2002). w, x w v p š gj p w z, d w ¼ d w d w w. ³ w v p t k y w x w» w x w w v w. ƒ ¾ ywš rw d w ( y, 1999). x ƒw» w yƒ»»» w ¼ dw w.,»» w xk ¼ j» w». w»» w ƒ l š. m Ÿ w š k w (Carbon fiber reinforced plastics; w CFRP) š w q w ƒw»», w CFRP w ƒ w š (Abry, 1998; Kupke, 2000; Abry, 2001; Prasse, 2001; Park, 2002; i, 2004). w ƒ. w, s w (Ionic polymer-metal composites, IPMCs) s»» w,», œ w (Nemat-Nasser, 2000; Kim, 2005)ƒ w ù, x w w y š w w w w. ¼ d ƒ w š w k»» x w, š w»» w wš x w. š w ¼ w. 2.»» d w š x ¼ š» w ë»» š w.»» xk x tx. ρ = kε» ρ=δr/r 0 w y, ΔR w y, R 0 x» w, k»», ε x. 3 x ƒ 8 l xk tx w (Sevostianov, 2000). x ù k x w k (1) x w (2) x (deformation history) w. (1) t 1. k x r r r v p k [GPa] s we w (mm/sec) CF_A HTA3K 3,000 235 0.005 CF_B TC35-12K 12,000 240 0.005 CF_C SK f e 3,000 240 0.005 CF_ D HTA3K 3,000 235 3(b) š 364
ρ = f( Δε, ε)»» w» w xk ƒœ ww w dw k dw ( 2). 3.k (Carbon fiber)»» 3.1. x (2) 2. k dw» w x ; (a), (b) d k (Carbon Fiber)»» p q w» w x w x w y d w. Ì 10 mm j q s k, x» j q š jš r p w z wd» (multimeter) w x w d w. x k s ƒ we Toho Tenex HTA3K yg High Gain Industrial imited Tairyfil TC35-12K, š HTA3K s we k SK f e w v v w. 3. k»» ; (a) s we k w ; CF_A, CF_B, (b) s we k w ; CF_C, (c) s we k x w; CF_D 26ƒ 2A 2006 3œ 365
r 4 ƒƒ r k t 1. ¼ 510 mm š 470 mm w w 0.005 mm/sec mw ww. 3.2. x š 3(a) 3(b) x ƒ k. r CF_A CF_B x ƒ ³e xk»» ù kü ù, CF_C s w x (CF_C1, CF_C2, CF_C3)ƒ w š ³ ew. k x 0.01 w» x s xk x» ƒw q w š (Xu, 1996; Cho, 2000; Park, 2001). ρ = n f ( n n f ) +( 1+ 2ν)ε», n k v p, n f q k v p, ν k s. q w, z w w» w(unloading)» w (Xu, 1996; Abry, 1998; Abry, 2001; Prasse, 2001). k»»» p w. s xk ƒw k p x ( 0.01) z w š. 3(a) x. x w w» w 3(b) w kw x w. w w (relaxation) z. 4 w w w x w. w» 2.23 l 26.16¾ s xk ƒw ù, w w k 1.91 0.38 x ƒw w 4. k (CF_B) x»» (3). w w k kƒ w š x ƒw k q w k z» w w k q y w 4 w w ³e. k s p we CFRP w (Xu, 1996) p k w w w kƒ 2.5 j. ù x ƒ v xk ùkù w w ƒ. x w w x 0.01 w w ƒ ƒw.»» w k q w ƒ w q. w wš w w» w w, w, w w y w, x yw w w yƒ w. w 4 k, w(unloading) z, k=1.91~0.83 ƒ w š ƒ w» w k w» z. w, q y j š, w q w y j»ƒ. 4. (Metallic heat wires)»» 4.1. x (Fe) k x x ƒ w p ùkü. š x z w» k»» w p. x f (dislocation) e w q e. š ¼ ¼ ƒ x w q x y w». ¼» w d w ƒw ù,» w 9.68Ü10 8 Ωm d ƒ w x ƒ û. w j (Cr) 22%, (Al) 4%~5%ƒ ƒ 1mm x x 1.85 Ω/m w ƒ. w ƒ œ» l(heater). w k» w 137 Ω/m w w p l w y w dw», DC 10 ma ƒwš, w dw z w dw. w w» w w dw s³e w. 366
5. w- w- w mw x ƒ R = ( ΔV + + ΔV ) I», ΔV +, ΔV ƒƒ w ƒ w, I. x 510 mm x» ew z x» 450 mm w x dw. s w w. s ƒ e z 100 C o 1 w z x ww.»» x w» w ƒ x š w. (a) w- w- w mw x 2%¾ ƒ, (b) w z k ü x. x kƒ x w q w» w š š, x œ q w» w š. 4.2. x š x x 0~0.015 ƒ w x ƒw 5 ùkü. w k 2.02 d š w w k 2.52~2.59 5 w ƒ. (4) 6. k x»» w- w k ew, x m s³ 2.56, t r 0.02 e p š y. k w w kƒ w 91% ù, w 26.7% j. w d 7. w z k ü x 26ƒ 2A 2006 3œ 367
w y l x w. 6 t x ε t, max z w ww k x ε e, max ƒ z š,»» k. k x ε e, max ƒ z z ù x ε t, max -ε e, max x z wš, ƒ 0 ( 6 ). 5 x k x 0.28%~0.32%. 6 l k x w y ρ w x ε w w. ε ρ ρ max = ------------------- + ε k tmax,», ρ max w y, ε t, max =ε e, max x, ε p x. x ε p w d w x ε t, max w z. x k ü x m w w w ƒ y w ( 7). x z k x 0.30%¾ z wwš s 0.20% 5z w w. 7 d ƒ. 5. w k w»» w w» w š w ƒ w (1) w f d w w, (2) xw z k z k kƒ w w, (3) ƒ x y z kƒ w w, (4) x w š w ƒ q š, (5) x k z wš kƒ f w. k x mw r x w ƒ w z. w w d»» ƒ x w, x k w. w x 0~0.015 k z wš kƒ 2.56 f w w š q. x v p ¼ ¼ 0.7% x ƒw. k 4 x q ù w- w w.. 6. ü ¼ d ƒ w v p ¼ 6.1. ¼ w»»» (5) 8. ¼ d ƒ w ¼ 9. ¼ d ƒ w ¼ w d w. š w w d w. ¼ ƒ š w» ¼ w ù s gq ¼ w. š w s w ¼ w w w. 8 ü ¼ d ƒ w ¼ ùkü. x ¼ 9(a) w, x ¼ 9(b) ù x w. ù x ¼ ù x e»ww p š w w. 6.2. d ¼ d ƒ w ¼ d (1) ¼ š w»», (2) š w ¼ w š (3) ¼ w d» w y l w. x w w, w kƒ (5) w x w. ¼ ¼ w z e ew» x ε t,max ùkü e w w d w.» ¼ ü ¼. ü ¼ gj p k kƒ ë w x d 368
x w ù wd mw w y ρ max d w. ρ ε max = ----------- tmax, k i», k i» w. 5 k i 2.02. z x ¼ w d w (5) (6) mw ¼ š w x x w. x ¼, š w» ¼ x ε š w x ε l (5) w x w. ù x ¼ ù x š w w ¼ x ε š w x ε l š ƒ ( ). 8l 2 4νD 2 θ 2 + ε =», D ¼, l ƒƒ ¼ š w ¼, θ ¼ ƒ, ν ¼ s. (7) w ¼ x ¼ w ¼ wš w ¼ d w. 7. ------------------------------ε 4l 2 D 2 θ 2 1 l + 1 1. d ƒ w š w w š k»» x w. k»» ƒ j x w w ƒ j ù d ww. 2. we k p x z»» ƒ s xkƒ x w x, w ƒ ƒ v w. d v w. 3. w w w kƒ w k ü x w ùkþ. w p š w w w y l x w w w. 4.»» w ¼ d ƒ w ¼ d w w. ¼ ¼ y š w, y ƒ ƒ w w x ƒ ƒ. 2005 w w (6) (7) (KRF-2005-003-D00387) m ƒ wš w msƒ k ww 2005 w» 05 w D11. : x ¼ š w w w ¼ š w ¼ w. D D r = --- coste + --- 1 sinte + e 2 3 2 2 dr D D d ---- = --- sinte + --- te 1 cos +----- 2 e 2 2 3 l = θ dr t---- 0 dr t = ---- dr ---- θ dr dr = ---- ---- 0 2 l 2 D = ---θ 2 dr ---- dr (8) (9) (10) (11)» r š w»ww xkw, D ¼, l ƒƒ ¼ š w ¼, θ w ¼ ƒ ( 10). (11) l ¼ x ε š w x ε l tx. l = l( 1 + ε l ) l 2 = ( 1+ 2ε l ) Δ 10. x ¼ w ε = ------ = ------------ = ---- 1 D 2 ( 1 2νε 1 ) ------------------------------ θ 2 4 D 2 ( 1 2νε 1 ) l 2 ( 1+ 2ε l ) ------------------------------θ 2 4 = -------------------------------------------------------------------- 1 = l 2 D2 -----θ 2 4», ', l' x z ¼ š w ¼. (12) 8l 2 2νD 2 θ 2 + ------------------------------ ε 4l 2 D 2 θ 2 + 1 1 l (13) 26ƒ 2A 2006 3œ 369
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