ª Œª Œ 26ƒ 1A Á 2006 1œ pp. 75 ~ 89 ª» w LCC Lifetime Reliability Based Life-Cycle Cost-Effective Optimum Design of Steel Bridges Ÿ Á zûá Á½ x Lee, Kwang-MinÁCho, Hyo-NamÁCha, Cheol-JunÁKim, Seong-Hun Abstract This paper presents a practical and realistic Life-Cycle Cost (LCC) optimum design methodology of steel bridges considering time effect of bridge reliability under environmental stressors such as corrosion and heavy truck traffics. The LCC functions considered in the LCC optimization consist of initial cost, expected life-cycle maintenance cost and expected life-cycle rehabilitation costs including repair/replacement costs, loss of contents or fatality and injury losses, road user costs, and indirect socio-economic losses. For the assessment of the life-cycle rehabilitation costs, the annual probability of failure which depends upon the prior and updated load and resistance histories should be accounted for. For the purpose, Nowak live load model and a modified corrosion propagation model considering corrosion initiation, corrosion rate, and repainting effect are adopted in this study. The proposed methodology is applied to the LCC optimum design problem of an actual steel box girder bridge with 3 continuous spans (40 m+50 m+40 m=130 m), and various sensitivity analyses of types of steel, local corrosion environments, average daily traffic volume, and discount rates are performed to investigate the effects of various design parameters and conditions on the LCC-effectiveness. From the numerical investigation, it has been observed that local corrosion environments and the number of truck traffics significantly influence the LCC-effective optimum design of steel bridges, and thus realized that these conditions should be considered as crucial parameters for the optimum LCC-effective design. Keywords : Life-Cycle Cost, Indirect Cost Model, Steel Bridge, Optimization, Time-variant Reliability, Corrosion Model» w ù s³ m mw y w» w» (Life-Cycle Cost: w LCC) w. w LCC»,»»,»» y,, š z- sww x ƒe w yw. w LCC w» w w w w y l q y š w. w Nowak yw (1993),, š w š w w. LCC 3 (40 m+50 m+40 m=130 m) š,, y, m w LCC z w Áš w. mw y, s ³ m, š mw, w LCC w w e, w y LCC w š w q. w :»,,, y,, 1. ü œ»,, v w ù œ» wš ƒ. š w w,» w, *w w w (E-mail: kmlee1973@hanmail.net) ** z Áw w œw w Áœw (E-mail: ryfid@hanyang.ac.kr) *** z Áw» œ (Email: cjcha@kistec.or.kr) ****( ) gf lp (E-mail: manccong@envc.co.kr) 26ƒ 1A 2006 1œ 75 z»» w š w. w wz (1997) w gj p w û š š. x (Two Main Girder Steel Bridges)ù qx qx (Corrugated Steel Plate Girder Bridge) x ƒ y š ƒ w»
» (Life-Cycle Cost: w LCC) d» x w w š. ƒ z y w» w œ» w,» z» z LCC š w ƒ w. w, ¾ ³ w» yw» w eù e (Al-Shaleh, 1994; Farkas, 1996; zû., 1998). ¾ w LCC w Ÿ w ƒ», LCC z š w ù. y w w LCC w» w» w (time-variant degrading resistance) w w z (stochastic extreme load effects) y w, v,,, w w k w y v w. w w y y w w Á ƒ w v ù y w w. w LCC w w ƒ w š.» w ù mw y w» w LCC w. w LCC»,»»,»» y,, š z- sww x ƒe w yw. w LCC w» w w w w y l q y š w. w Nowak yw (1993),, š» z š w. LCC 3 (40m+50m+40m=130m) š,, y, m w LCC z w Áš w. 2. LCC y w LCCƒ š y w w w. w» T life» LCC yw. [ (, )] = C 1 E C T X T life T life + t = 1 J [ (, )] + E[ C Fk ( X, t) ] E C Mj X t j = 1 k = 1 ---------------------------------------------------------------------------------- K ( 1 + r) t» EC [ T ( XT, life )] = l X» T life w» LCC; C I =» ; EC [ Mi ( Xt, )] = j w t» ; EC [ Fk ( Xt, )] = w k k w t» ; r=w (1) ùkù,» LCC»»», v,,, w w k» sw w. wr (1) wš š» w»ƒ ƒ w x ƒey w» w w (discount rate) r š w w. w» LCC ƒ w LCC ƒ ƒ w, y w (2). Minimize Subjec to EC [ T ( XT, life )] G j 0 j = 1, 2,, J p Fk p Fkallow k = 1, 2,, k X L X X U (2-a) (2-b (2-c) (2-d)», X = w Ì, ¼ l; G j =x, w, ; P Fkallow =, v,,, w x q y ; X U, X L = œw l w 2.1» (Initial Cost)» z,»,, w, y œ, œz œ» ¾ w ƒ n w» w. w» LCC w w w š q. w» y. C I = C ID + C IC + C IT», C ID = zá ; C IC = œ y ; C IT = (3) œ œ sw,,, œ x t s ww w. œ w zá œ ³ ü ƒ» ( w», http://www.cmcost.com, 2001) w w w. 2.2» (Expected Maintenance Cost)» LCC w Wen (3) 76 ª Œª Œ
Kang(1997) w» LCC w j, w w» LCC š w w. w» LCC w j» y w š ƒ v w. w ù s Á y» l w w š w. LCC z w ƒ š LCC e w» w (4)» T life y š w y w. EC [ MJ ( Xt, )] = C Mj f Mj () t», C Mj = j w ; f Mj (t)= j w t y 2.3» (Expected Rehabilitation Cost)»» ú w w k w q y l w. w q y y w,» š w x d š v ƒ (Melchers, 1987). w» š w k k w q y Á w w. EC [ Fk ( Xt, )] = C Fk PXt T (, )», k=w k w ; C Fk =w k k w ; PXt T (, ) =w w w q y l q y wr (5) C Fk w. (4) (5) C FSk C DRk = C DRk + C IRk +[ C H r rk + C U ( t rk ) + C E ( t rk )]», C DR = ; C IR = ; C H = y ; C U = ; C E = z- ; r rk = œ» š ; t rk = œ» (6) C DR (http: // www.csr.co.kr) ƒ y w ù š w š x( p, 2002;» œ, 2000 ) w w. š y C H œ m š w (Human Capital Approach) w m (, 1997) s œ» š l m w w (http://traffic.metro.seoul.kr). = 2.4 z- (Road User Cost and Socio-economic Losses) (6) œ» {w w z- swwš. w m w ¾ š w ƒeƒ. w ù z- öe w. ù, l,, w v œ w w œœ n» w» w w z- w j. 1 w (Vehicle Operating Cost), (Time Delay Cost), š (Accident Costs), rw (Comfort and Convenience Costs), y w (Environmental Costs) 5 w (Berthelot et al., (6) 1. w (Berthelot et al., 1996) 26ƒ 1A 2006 1œ 77
1996). w w w š (De Brito and Branco, 1995; zû, 2004). w š w yw. C U = C TDC + C VOC C = TDC C = TDC J j = 1 n p0j T 0j u 10j I 1 r i i = 1 Δt d0 + I I r n i T P 0j 0j u + 10j n Pij T ij u 1ij i = 1 j = 1 J j = 1 T 0j I u 2J 1 r i i = 1 I J r i T 0j u + 2j i = 1 j = 1 Δt d0 + ( ) T ij u 2i I J r i T 0j u 3ij l di u 4ij l d0 + i = 1 j = 1 L di l di l 0 l 0 Δt = -------- --------- di, Δt = ------- ------- υ dwi υ d0 d υ 0w υ 0n Δt di Δt + di (7-a) (7-b) (7-c) (7-d)», C TDC = ; C VOC = w ; i= m p j w ; j= w ( y ƒ, k,,, xp, x p ); n Pij = ; T ij = s³ m (Average Daily Traffic, ADT); u 1j = s³ ƒe; u 2j =ƒ s³ ; u 3j =ƒ z ¼ s³ ; u 4j = w ¼ s³ ; r i = w i z z ; Δt d0 = w ƒ ; l 0, l d = w ¼ z ¼ ; υ on, υ 0w, u0w= k œ k w m ; υ d,υ = dwi k œ k z m (7) w» w œ w m z, z v w. w w l m p j m, z, ƒ z (y m ) ¼ w w mw ww. mw v EMME/2 v5.1(inro Consultants Inc., Montreal, Canada) w. EMME/2 v5.1 w mw ww» w m p j m w O-D(Origin-Destination) m z e, v [ ( ) T ij u 2j ] Δt + di w. w w w p ww m mw p w (volume delay function) w z w w. w» (1999) ü p mw. wr z All-or-Nothing, (iterative assignment), w (incremental assignment), (multi pass assignment), y mw (probability assign- ment) w, œm p mw m» ƒwš (, 2000). w wš, m mw k w mƒ ƒ w All-or-Nothing w. z- œ w» w w q z. (1996) w w w z- q z w» w z w» w n - (Input-Output: w I-O) (Kuribayashi and Tazaki, 1983) w y w. (1996) y œ w q z 1 (First Round Losses) 1 q z š w 2 (Second Round Losses) w w., z- w œ w» { w w e w œ m p j w e. LCC w w z- n y w zû (2004) y w w. w zû (2004) z- sƒ w p w mw t(y n - l ), s w p v w» w w w w š w. p ü w t» ùw w. z- w» w Seskin (1990) ƒ. Seskin(1990) w z-,, ƒƒ 150%~50% ƒ š. 3. w š 3.1 w 3.1.1» w kw y (5)» w» w š q w k w w v w.» w q w k w y 78 ª Œª Œ
w k ƒ q w k w y w. gj p q œe { { w w k ƒƒ gj p q v ww k. w x w w k y. x { : ( ) = Z G F y γ mfg M GDl λ GDl g L l = 1 M GL DF I beam», Z G = x w { ; F y = x w ; γ mfg = x { w y ; M GDl = qp, x, q w w x w { p; M GL =yw w x w { p; λ GDl = w l w y ; DF=yw w y ; I beam = w y x : ( ) = S G F y γ msg S GDL λ GDL g L l = 1 S GL DF I beam», S G = x w ; γ msg = x w y ; S GDl = qp, x, q w w x w ; S GL =yw w x w ˆ (8) (9) ƒ ¹ ¼ v r z, {l ˆ z, ƒ r z l. l ¹ ¼ AASHTO(1996) AISC(1994) m ˆ. wr x l w k w w y w. ( ) = δ all δ L DF I beam g (8) (9) (10)», δ all = w x ; δ L =yw w wr, v w k w k wù. w v w k w yw w w Zhao Haldar(1994)ƒ w v w q f» w. w Zhao Haldar(1994)ƒ w v ³ w yw v w w, yw w ww» w z. w Pedro Albrecht (Albrecht, 1983) z. 3.1.2» wyw w» ù m w y ƒ š y w w û ƒw y ƒ š. w yw z w» w Nowak(1993) yw w. Nowak(1993) yw û m w w { ƒ z w. Nowak m w ƒ ƒw yw s w m w y ƒ w Type-I em š. w Nowak w w» w w Type-I e s s³ μ Mn t r σ Mn v w. (12) w w (Ang and Tang, 1984). μ Mn = σ u n + μ+( γ σ a n ) σ Mn = ( π 6) ( σ a n ) ln[ ln( n) ] + ln4 π = ln( ) u n (12-a) (12-b)» ; a n 2 n ; = ---------------------------------------- + a 2 a n n n= m z ; μ, σ= m w w» s( ³ s) s³ t r ; γ=0.577216( ) 3.1.3 w û w. w v Ì w. 2 w e š. ùk ù w xk w v 1/4 x w. wr w v w. w d w.» ww ew x w j e q w.,,, k y (Albrecht, 1984). w dw» w w (Albrecht and Naeemi, 1984; Ellingwood, 1999). w w β logn logn d = -------------------------------------- ( S R ) 2 m( S Q ) 2 + (11)», β= ; N, N d =ƒƒ ƒ w j w j ; S R, S Q = w w j t r ; m=s-n 2. x e 26ƒ 1A 2006 1œ 79
d» w w w w dw w š w. (13) Ellingwood (1999) w» z w d w. () i T REP + T CI t< i+ 1 p i t (13-a) (13-b)», p i (t)=i» t w ¾ ( :μm); C= ; m= ; T CI, T REP =» (13) w w { w w z w w. w (13) C, m, T CI, T REP y w t w w y ƒ. w w s³ t r w» w 50,000z ww ƒ l w ww. 3.1.4 q y w (5),» w» w š w k k w q y v. ƒ ù T w kw, T z t q y w (Stewart, 2001). ( ) T REP () = C ( t i T REP T CI ) m () = p i 1 ( ) p i t i T REP v w (11) Pedro Albrecht. w ww w w w k w w ww LCC y š pƒ w. l w w q y w» w { p - l (Parallel-Series System). w w» w» w q y l ƒ w k w w š w w» l w w w q y w ww w. 3.2 š 3 LCC w p Fk ( X, t T) (, ) p f ( X, T) p f X T+ t = ---------------------------------------------- 1 p f X T (, ) (14)», P f ( X, T+ t), P f ( X, T) =» T+t T q y (14),» q y wyw, w w k š w w. q y w» w» 1 ƒ w k w w w w 1-2 p(advanced First-Order Second- Moment, AFOSM). wr 3. LCC š x (m) 40 m+50 m+40 m=130 s(m) 12.145 m (Skew) 90 o ( ) 4(3) Box 2 w DB/DL-24 (HS-20/0.75) t 1. l 3 gj p SM490 (f y =3,200 kgf/cm 2, f a =1,900 kgf/cm 2 ) : f ck =270 kgf/cm 2 : 8 : SD40(f y =4,000 kgf/cm 2 ) 80 ª Œª Œ
š. ùkù LCC š w (Structural Analysis), w (Reliability Analysis), (Optimization), š LCC (LCC Evaluation). ù ƒ š w š, LCC y š w z z.,» (variable linking method),» (constraint deletion method), w» (structural reanalysis technique) w y» approximation technique)» (multi-level optimization method) z j» w. w ƒƒ» w w ù š x( Ÿ, 2000). 4. e š 4.1 ƒ w w LCC w z š w» w, 3 ¼ 130 m(=40 m +50m+40m) x ew w. w t 1 ùkü, 4 s e ùkü. û e š w s ³ m w s³ m ƒ š ƒ w. 5 6 ƒƒ EMME/2 w mw ww» w 5. š m p j 6. š m p j t 2. 20» s³ m ( ) Year 2007 2011 2015 2019 2023 2027 I 15,419 18,487 21,276 23,850 25,936 26,758 II 15,606 19,047 21,914 24,562 26,711 27,557 III 14,424 17,596 20,262 22,716 24,703 25,486 I 1,793 2,076 2,290 2,456 2,554 2,575 II 1,847 2,139 2,358 2,529 2,630 2,653 III 1,707 1,977 2,180 2,339 2,433 2,452 p I 10,057 11,984 13,531 14,882 15,883 16,238 II 10,360 12,347 13,937 15,325 16,358 16,723 III 9,576 11,406 12,886 14,174 15,129 15,467 I: V~ ; II: ~J ; III: J ~ IV 4. š. w t 2 3 œ z 20 w ƒ s³ m ù küš. 7 LCC ùküš. ùkù x 4(b) Áw v Ì(tfu, t fl), q Ì(tw) e (hw) w. wr LCC ww x w w š w š,» ( m, 2000) w w x, w w, v, š œw š w. 26ƒ 1A 2006 1œ 81
p t 3. 20» s³ m ( ) Year 2007 2011 2015 2019 2023 2027 I 29,450 42,486 55,760 69,408 81,320 86,162 II 29,762 43,774 57,432 71,480 83,750 88,734 III 27,508 40,430 53,103 66,108 77,455 82,065 I 3,419 4,771 6,002 7,147 8,008 8,292 II 3,522 4,916 6,180 7,360 8,246 8,543 III 3,225 4,543 5,713 6,807 7,628 7,895 I 19,179 27,541 35,462 43,310 49,800 52,286 II 19,757 28,376 36,525 44,599 51,289 53,848 III 18,262 26,213 33,772 41,249 47,436 49,804 I: V~ ; II: ~J ; III: J ~ IV 7. LCC t» w y w w ALM(Augmented Lagrange Multiplier) BFGS(Broy don-fletcher-goldforb- Shanno) w. w w wk y w (Golden Section Method) w. š y» v x w š ADS(Automated Design Synthesis; Vanderplaats, t 4. œ w (Ü10,000 ) (1/ton) 133,09 133,09 (1/ton) 41.99 51.918 (1/m 2 ) 23.60-1986) w ww. ü (Ü10,000 ) 4.2» w l ü š Áš w w ƒwš. š wù ü w LCC d z mw» w œ t t (, 2004) ƒ w ƒ œ w š t 4 ùkü. wr» w x œ 7% 3% ƒ w (De Brito and Branco, 1995). w. LCC š w kƒ w, y,, y,, z-.» v w q y w» w (8), (9) (11) x v w k š w. t 5 6 LCC w š w k w Á w l( Á, Á, œ», ) w. t 5. l w k v (Ü10,000 ) Retrofit ü Bolting repair 175/ton 3.12/ton (s» ) 185/ton 3.12/ton (s» ) 450/ e»» 4 3 m m (2 ) m m t 6. l w š w 4.00 % m (2003) m š 1.2 œ m š w m 220 / km (http://traffic.metro.seoul.kr) s m š 190 / km 35 (1997) 2,100 s³ 21,517 / w m 82 ª Œª Œ
t 7.»e w Retrofit Bolting repair m m m m ( Ü10,000 ) 38,196 (3%) 38,196 (1%) 450 (100 %) 450 (100%) ( Ü10,000 ) 1,425,450 (97%) 7,127,250 (99%) - - ( Ü10,000 ) 1,463,646 (100%) 7,165,446 (100%) 450 (100%) 450 (100%) t 8. m y l e y sxk s³ š x x w (kgf/cm 2 ) F y ³ s 3552.0 0.12 Nowak (1993) x { w y γ mfg ³ s 1.11 0.11 Nowak (1993) x w y γ msg ³ s 1.14 0.12 Nowak (1993) qp w y λ alphalt ³ s 1.00 0.25 Nowak (1993) gj p w y λ conc ³ s 1.05 0.10 Nowak (1993) w y λ steel ³ s 1.03 0.078 Nowak (1993) yw w y DF ³ s 0.926 0.124 Zokaie (1991) w y ( 1, 3) I beam ³ s 1.045 0.10 Nowak (1994) w y ( 2) I beam ³ s 1.027 0.10 Nowak (1994) w w w y ( 11) Sτ ³ s - 0.1718** Albrecht (1983) T 15 0.3 Nowak (1999) Maunsell Ltd (1999) CI» T REP ³ s ³ s 20 0.25 / ( y ) C, M ³ s 34/0.65 0.09/0.10 / ( w y ) C, M ³ s 80/0.593 0.42/0.40 Albracht Naeemi(1984) ** C w t r e (», 2000) l (http://www.csr.co.kr) ƒ, w w ƒ w, š x( p, 2002;» œ, 2000) w k w. t 7» Á w š. s³ m w w z- ƒƒ 150% 50% w. t 7 97-99%» mm ƒ w œ LCC w š w q. LCC w» w v w w ƒ y y p e sxk, s³ t 8 w. t 8 l w x(nowak, 1993, 1994, Zokaie et al., 1991; Albrecht, 1983; Albracht and Naeemi, 1984; Maunsell Ltd, 1999)» wš. 4.3. q y w y m z LCC, y m q y e z š w» w» e w t 9 6ƒ Case š w q y w. 8 2» y w { s³ t r ùkü. ùk t 9. q y š w Case Case ID s³ m y Case 1 s³ m ƒw y Case 2 y Case 3 s³ m ƒw y Case 4 y Case 5 ü s³ m - Case 6 s³ m - 8. 2» w { ù y (Case 2, 4) w { ƒ ƒw y (Case 1, 3) w 26ƒ 1A 2006 1œ 83
9. 2» { p 10. 2» q y ùkùš, w» z w wš» e š. wr ƒw y s³ w { w t r ƒ j ƒw y w, (13) t 8» w { w ƒw y y y w w j». 9 s³ m w yw» 2 p e w ùk üš. yw w s³ t r w» w, m» DB-18 w w HS-20 p w Nowak v(nowak, 1993) w., HS-20 p w yw p s³ m (y mw ) w Case 1, 2 1.0~1.55 š, s³ m (y mw ) w Case 3, 4( m ADTVƒ ) 1.0~1.53 ùkû. m» j w mw y w. 10 2 { w» q y w, y, š m w ùküš.,, Case 1, 3 ƒw y û q y ƒ, p Case 1 m š ƒw y x w ùký. ü w Case 5 6 m q y š. 4.4. š 4.4.1. s³ m w w š LCC, y w w. t t 10. LCC š y w Case A3 ƒw y Case B3» ƒw y Case C3 ƒw y 3 % Case D3 LCC y Case E3 ü - Case A4 ƒw y Case B4» ƒw y Case C4 ƒw y Case D4 LCC y Case E4 ü - Case I Case II ENV-U y Case III ƒ LCC ü - Case IV ENV-U Case V y Case VI ü - 4 % 3% 4% 84 ª Œª Œ
w (t 10 ). 11 x Case I~IV»» LCC š. ùkù 3% w (Case I, II, III) ù y x 80%» ƒ LCC ƒ, 4% w (Case IV, V, VI) x 85%» ƒ LCC ƒ ùkû. w w 3% w Case A3-E3 x 80%ƒ CaseI-III w t 11 w š, w w w w 4% w Case A4-E4 x 85%ƒ Case IV-VI w t 12 w 11. m w x y» LCC 3 w t 2 m ƒ w, w y y t 10 10ƒ Case (Case A3~E3, Case A4~E4) š w LCC ww. w ƒ LCC (equivalent LCC optimum design)» w w x ƒ ( zû, 1998), ƒ» LCC Á w» w x 60%~100% w 5%» ww. ƒ x» w 6ƒ Case(Case I~IV) w LCC ƒ ww LCC. ƒƒ t mw,» Case B3, B4 2.09 m š, LCC Case C3~E3 C4~E4 2.50 m. LCC ƒ» 19.6% j. p ( 4) w v Ì Case B3, B4 14, 13, 10 mm š, Case C3~E3 21, 18, 11 mm, C4~E4 19, 18, 11 mm. LCC ƒ w v Ì» ƒ w ƒƒ 50~35%, 38%, 10% Ë. w, w j» ƒ j LCCd z š q w. wr t y Case C3~E3 w ùkû, Case C4~E4 w w ùküš. w 8 ùkù l w ù q.»» w w e m y g LCC ww š, w. w 3% w Case(case C3~E3) 4% w Case(Case C4~E4) w 11 t 11 12 ƒ. l m w y w LCC e w j.»,»,» (» retrofit,» v )» LCC 12 ùkü. Case B3 B4» 6.87 Case C3~D3 Case C4~D4 LCC 7.29~7.31 7.16~7.18 ùkû.» LCC w 6.4~4.2%. w 12 ùkù» Case B3 B4» 26ƒ 1A 2006 1œ 85
t 11. ew (3% w ) (Case A3)» (Case B3) LCC ƒ LCC ƒw y y Case C3 Case I Case D3 Case II Case E3 Case III (m) 2.00 2.09 2.50 2.50 2.50 2.50 2.50 2.50 1 10/12/12 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 v Ì 2 12/12/14 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 / Ì/ 3 16/12/16 10/10/10 13/10/10 14/10/10 13/10/10 14/10/10 13/10/10 14/10/10 w v Ì 4 26/12/24 14/10/13 21/11/18 21/12/18 21/11/18 21/12/18 21/11/18 21/12/18 (mm) 5 16/12/16 10/10/10 13/10/10 13/10/10 13/10/10 13/10/10 13/10/10 13/10/10 6 12/12/14 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 ( )» 0.81755 0.68687 0.73128 0.73714 0.72954 0.73714 0.75934 0.76014» 0.12552 0.12886 0.14386 0.14401 0.14385 0.14401 0.00000 0.00000» retrofit cost 0.01905 0.15373 0.00979 0.00899 0.00584 0.00501 0.00271 0.00260» v 0.06838 0.14208 0.03218 0.02603 0.03326 0.02691 0.03260 0.02650» LCC 1.03050 1.11153 0.91711 0.91617 0.91250 0.90856 0.79465 0.79824 t 12. ew (4% w ) (Case A4)» (Case B4) LCC ƒ LCC ƒw y y Case C4 Case IV Case D4 Case V Case E4 Case VI (m) 2.00 2.09 2.50 2.50 2.50 2.50 2.50 2.50 1 10/12/12 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 v 2 12/12/14 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 Ì/ Ì/ 3 16/12/16 10/10/10 11/10/10 12/10/10 11/10/10 12/10/10 11/10/10 12/10/10 w v Ì 4 26/12/24 14/10/13 19/11/18 20/11/18 19/11/18 20/11/18 19/11/18 20/11/18 (mm) 5 16/12/16 10/10/10 11/10/10 12/10/10 11/10/10 12/10/10 11/10/10 12/10/10 6 12/12/14 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 10/10/10 ( )» 0.81755 0.68687 0.71826 0.71994 0.71595 0.71994 0.74335 0.74934» 0.09259 0.09505 0.10611 0.11245 0.10611 0.11245 0.00000 0.00000» retrofit cost 0.01541 0.12052 0.00863 0.00801 0.00319 0.00299 0.00308 0.00210» v 0.04950 0.10911 0.03233 0.02603 0.03446 0.02011 0.03565 0.02999» LCC 0.97505 1.01155 0.86533 0.86643 0.85971 0.85549 0.78209 0.78143 LCC ƒƒ 11.12, 10.12 š, LCC Case C3~D3 Case C4~D4 ƒƒ 9.17~9.13, 8.55~8.66» ƒ 21.8~17.6%. w» y w» LCC š w k w q y, w» ƒw» q. wr 12 ü, ü w Case E3 E4» d Case C3~D3 C4~D4 w 4.1%~3.8% LCC d 15.4~10.6%. w» w w» y ü w j» q. 12 l x 85% w» LCC» LCC w ƒw y y w ƒƒ 0.127% 0.493% š.» ww LCC d w t w x w LCC w LCC š w ww w. 4.4.1. s³ m w w š 3% w w LCC Cases C3~E3 4% w w LCC Cases C4~E4 w ùkû. ù y p w w w ƒ, w w w» w t 13 6ƒ w m w ƒ LCC ww š, 86 ª Œª Œ
12. m w w ƒ Casequf t 13. ƒ LCC š m y w Case VII Case VIII ƒw y y 3% Case IX ü - m Case X ƒw y Case XI y 4% Case XII ü - 13. m w x y» LCC w w. 13 m Case VII-XII x ƒ LCC w»» LCC ùkü. 3% w Case VII, VIII, IX w LCC x 65%, 70%, 75%ƒ š, 4% w Case X, XI, XII w LCC x 70%, 70%, 75%. m ( 11) w y, m w» LCC» w f y w e w. 14 ƒ Case LCC»» LCC š. 14 ùkù 14. m w w ƒ Case ü LCC» d w. 11 13 ùkù 26ƒ 1A 2006 1œ 87
m w ü w LCC x y LCC ƒ w». 5.» w ù mw y w» w» (Life-Cycle Cost: w LCC) w, w, w w LCC z w Áš w. LCC l. 1. LCC w» ù» y ƒ. x j» ƒ j LCC z d. 2. LCC w»»»» LCCd LCC w» LCCƒ» w» LCC.» y wš» w k w y LCC y j. 3.» x w LCC w. w LCC ww y ƒ w q. 4. l y, m mw, w LCC w w e w š w w q. 5. š w» d LCC d ƒ v š,» q y w, m w x LCC ƒ»» d y w q. š x (2004) œ t t. m (2003) w LCC» l. 1 š. m /» œ (2000) œ.» œ š, BR-2000- R1-37. w» (2001) ƒ».» (1999)». š. mxz(2000)». p (2002) œ e. Ÿ (2000) q Life-Cycle Cost. w. w w., (1997) m š. m š, 97-09. zû(1998) x v (CAOD-sb).», 1 š. w wz(1997) š y y w. š. Albrecht, P. (1983) S-N Fatigue Reliability Analysis of Highway Bridges. Probabilistic Fracture Mechanics and Fatigue Methods: Application for Structural Design and Maintenance, ASTM STP 798. Albrecht, P. and Naeemi, A.H. (1984) Performance of Weathering Steel in Bridges. National Cooperative Highway Research, Report 272. Al-Shaleh, K.S. (1994) Optimum design of straight steel box girder bridges. Ph.D. Dissertation, Georgia. Ang, A. H-S. and Tang, W.H. (1984) Probability Concepts in Engineering Planning and Design, Vol I and II, John Wiley, 1984. Berthelot, C.F., Sparks, G..A., Blomme, T., Kajner, L., and Nickeson, M. (1996) Mechanistic-probabilistic vehicle operating cost model. Journal of Transportation Engineering, ASCE, 1996 122(5): 337-341. Cho, H.N., Lee, K.M., and Choi, Y.M. (2004) Life-Cycle Cost Effective Optimum Design of Steel Bridges. Journal of constructional Steel Research, Vol. 60, No. 11, 1585-1613. De Brito, J. and Branco, F.A. (1995) Road bridges functional failure costs and benefits. Canadian Journal of Civil Engineering, 25, 261-270. Ellingwood, E.R., Naus, D.j. (1999) Condition Assessment and Maintenance of Aging Structure in Critical Facilities A probabilistic Approach. Case Study in Optimal Design and Maintenance Planning of Civil Infrastructure Systems, ASCE, pp 45-5 Farkas, J. (1996) Optimum design of welding bridges. Welding in the World, 38, 295-306. Inro (1999) EMME/2 User's Manual, Software Release 9.0. Kuribayashi, E. and T. Tazaki. (1983) Outline of the earthquake disaster. pp. 67-90 in : Report on the Disaster Caused by the Miyagi-ken-oki Earthquake of 1978, Report No. 159, Public Work Research Institute, Ministry of Construction, Japan. Lee, J.C. (1996) Reliability-based cost effective aseismic design of reinforced concrete frame-wall building. Ph.D dissertation, University of California Irvine. Maunsell LTD. and Transport Research Laboratory (2000) Optimum Maintenance Strategies for different Bridge Type: Bridge Data. Final Report, The Highways Agency, London. Melchers, R.E. (1987) Structural Reliability, Analysis and Prediction. Ellis Horwood Ltd., West Sussex, England. Nowak, A.S. (1993) Calibration of LRFD Bridge Design Code. National Cooperative Highway Research: Final Report Nowak, A.S., Yamai, A.S., and Tabsh, S.W. (1994) Probabilistic Model for Resistance of Concrete Bridge Girder. ACI Structure Journal, Vol. 91, No. 3, pp. 269-276. Seskin, S.N. (1990) Comprehensive framework for highway economic impact assessment methods and result. Transportation Research Record 1274, Transporationa Research Board, Washington, D.C., 24-34. Stewart M.G. and Hossain, M.B. (2001) Time-dependant Deflection, Serviceability Reliability and Expected Cost for RC beams. Structural Safety and Reliability, Corotis et. al. (eds). Vanderplaats, Garret N. (1986) ADS: A FORTRAN Program for Automated Design Synthesis. Engineering Design Optimization, INc, Santa Barbara, California. 88 ª Œª Œ
Wen, Y.K. and Kang, Y.K. (1997) Optimal seismic design based on life-cycle cost. Proc. of the International Workshop on Optimal Performance of Civil Infrastructure Systems, ASCE, Portland, Oregon, 194-210. Zhao, Z. Haldar, A., and Breen Jr, F.L (1994) Fatigue-reliability evaluation of steel bridges. Journal of Structural Engrg., ASCE, 120(5), 1608-1623. ( :2005.4.19/ :2005.10.31/ :2005.10.31) 26ƒ 1A 2006 1œ 89