ª Œª Œ 26ƒ 1A Á œ pp. 133 ~ 142 ª q { p Coefficients of Moment Equations for Long-Span Soil-Metal Box Structures y*á **Á ***Á **** Choi, Dong Ho

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1 6ƒ 1A Á 006 1œ pp. 1 ~ 14 ª q { p Coefficients of Moment Equations for Long-Span Soil-Metal Box Structures y*á **Á ***Á **** Choi, Dong HoÁLee, Seung JaeÁCho, Yong WooÁPark, Sang-Il Abstract This paper evaluates the moment equations in the 000 Canadian highway bridge code (CHBDC) for soil-metal box structures, which are applicable to the span less than 8 m. Finite element analyses carried out for soil-metal box structures having spans of -1 m using the deep corrugated metal plates under three construction stages; backfill up to the crown, backfill up to the cover depth, and live loading. The coefficients of moment equations are newly proposed based on the results of numerous finite element analyses considering various design variables, such as span length, soil depth, backfill conditions. The validity of the proposed coefficients in the moment equations of the 000 CHBDC is investigated by the comparison with the existing coefficients and numerical results of finite element analyses. The comparisons show that the moments of the 000 CHBDC give good predictions for the span less than 8m, but underestimate for the span greater than 8m, whereas the proposed moments give good estimates of numerical results for the spans of -1 m. In addition, this study suggests the use of high strength steel to satisfy the requirement of design bending strength for the span greater than 8 m. Keywords : soil-metal box structures, moment equations, CHBDC CHBDC(000) 8m¾ ƒ w q { p sƒw. œ ( mvš¾, mvš¾, yw w) š wš x qx q w ~1 m w w q ew ww. { p, mvš, w š w ew m. w, CHBDC(000) { p k» ew w sƒ.» CHBDC(000) w p 8m w ew ew, 8m sƒ., w p ~1 m¾ ew ew. wr, 8m q w { w y w» w š w. w : q, p, CHBDC 1. q.7~7 mm Ì qx q - w l m, k m, q š. w q w w ww - w p w ƒw w w, œ w» gj p w œ» œ ƒ w. w 1997 ü x ¾ q ù, x ex w œ. w q ( w, ) w q e ( w, e ) xw œ y mœ ƒ ƒ w, gj p w z sƒ ƒ ƒw. š x qx q (81 mmü140 mm) w š š, w ƒ š. ü e w ³ ù w w ³ š l w ƒ Duncan et al.(1985) w * z Áw w m œw Áœw ( **w w m œw Áx» ( ***w w m œw ( ****w w m œw Áw œ ( 6ƒ 1A 006 1œ 1

2 1. CHBDC q»w w ew x w x mw.7~7.7 m w w. Duncan et al.(1985) mvšƒ 1.5 m w w { p w x w w { p š w wš, x š CHBDC(000) ³ { p Duncan et al.(1985)» w 8m wwš. q w 1 m ü ƒ œ š ù, w CHBDC(000) w w w ew mw ww w.» CHBDC { p 8m y w, w { p w v w. CHBDC mwš, ü œ - y š w w w, w wwš, w œ š w ew yw { p w.. CHBDC(000) q p CHBDC ³ q w p Duncan et al.(1985) kw, w œ w w x d mw. 1 t 1 CHBDC q w»w w ùküš., (, x e, d ), ( ).7~8.0 m, (R) 0.8~. m, mvš (H) 0.~1.5 m»ww w ƒ ³. Duncan et al.(1985) - y š w w w mw t 1»ww œ ( mvš¾ t 1. CHBDC q»ww w p ( R) 0.8 m. m v ( ).7 m 8.0 m mvš (H) 0. m 1.5 m, mvš¾, yw w) xe p (1) () w. M cf = α D M cd + α L M cl ( 1 + DLA) M hf = α D M hd + α L M hl ( 1 + DLA)», M cf p, M hf xe p w. α D w ƒ (=1.5), α L yw ƒ (=1.75), DLA w mvš (H)ƒ m w M cl, M hl l. w, M cd, M hd xe w p, M cl, M hl xe yw p ƒƒ w, w p ()~ (11) w. M cd = κm D M hd = ( 1 κ)m D M hl = κm L. q œ M hl = ( 1 κ)k R M L», κ p (= ), k R (1) () (4) (5) (6) 14

3 xe p (=0.45H+0.48ß1.0) ƒƒ w. w, M D xe w p w, M L xe y w p w w, (7) (8) w. M = D γd + h M = L k L L k γ( H 0.0)», γ, L L yw j»,, k, k ƒ œ w p w, (9)~ (11) w. (7) w w mvš¾ w w p, w mvš l mvš w w p ƒ ƒ w. w, (8) yw w w p w. ( ) k = D 1 h k = k = H m ( ( )) D 0 h k = H m 8.0m (7) (8) (9) (10) (11-a) (11-b) CHBDC w p x q x q w q p ƒ üswš., x š x qx q wš ù, CHBDC w p w kw., p j» ƒ»,» w p w k x qx q w p w q., CHBDC w p w ƒ.7~8.0 m w., w p w Duncan et al.(1985) ƒ.7~8.0 m w, w w w CHBDC ³ p mw w. w m w, CHBDC ³ wš w p 1 m¾ y w p 10.5 m ( ) ùkü. pƒ ( ) w. ù, p w xw CHBDC ³ w, pƒ ( ) w w w.. ew q q - y w., l q w, x - x (stress-dependent stress-strain relation) œ w ƒ x d w (Duncan, 1979; Duncan Chang, 1970) w v CANDE (1989) w q w. w - w s x š w w w. Choi et al.(004) ew w x - x Duncan. - w w w. - w w w 6ƒ 1A 006 1œ 15

4 Ì (mm) Crown t. x(80ü140 mm) q (mm /mm) (mm /mm) p (mm 4 /mm) (Class A) (Class B) Crown (Class A) (Class B) Crown (Class A) (Class B) t. HS-0 w ƒ w mvš(m) ƒ t (kn/m) HS-0 w Chang(1970) š (hyperbolic model) w. k tx š (confining stress) ƒ f p š. œ 1 e d (layer element) w w w w. w w e w, (CANDE, 1989) w d j e wš, w w w. x(80ü140 mm) qx q w, -» w. x qx q k (E) Ü10 5 MPa, s (ν) 0., 7850 kg/m w. w, xe x ASTM Standard A964/A964M ³ w., 4 w w (s=76 mm), xe Class A (s=114 mm) Class B (154 mm) kw. t ƒƒ ƒ ƒ (Cumulative section) w p ùk ü š w McCavour et al.(1998) x d l y. yw eù p w HS-0 5 w 4 z w Boussinesq k w w w w ƒ w eyw, t mvš ùkü. 4. { qx q š p e. ù, e 6. HS-0 yw w w w j š š, { pƒ w. w, q Ì q, û mvš œ yw w k { pƒ w š. mvš, mvš xe { pƒ w» CHBDC p xe p w w p(total moment) w š., w w w q { mw { p w wš w., q w CHBDC { p k (calculation parameters) mw» w w 5-1 m y w w. 4.1»wx,, xe w w CHBDC { p e š»wx (Rise/Span, R/ ) w w ù - (N f ) š w š ( ) w w. ù œ š»wx R/ (high-rise box) R/ û (low-rise box) ƒ š w p e w»wx 16

5 7. HS-0 yw w w p s w w mw. w ASTM ³ (76 mm ), xe (114 mm 154 mm ) wš. w xe w (A, I) ƒ yw» xe w e, xe xe p w w mw. w e»wx { pƒ 1.7~.7, 1.~1.7 ¾ yw ù, 1.1~1., 0.9~1.1 w w CHBDC p š w k w š q. ASTM ƒ xe w p 5kN w wù 154 mm xe w pƒ p j, 154 mm x w. w, ƒ j p w ƒ CL90, qx q ƒ É 7 mm Ì w.»w x w» œ pƒ j wš, yw w pƒ w, p. w û w pƒ wš, yw w pƒ j w, p w j w., û»wx kw. 4. { p p w œ (yw w), (CL90), q Ì(7 mm), xe (154 mm), û»wx kw CHBDC p mw š w. w, HS- 0 yw w 6 1 w(ll- 1), xe 1 w(ll-), w(ll-), xe w(ll-4) ƒ w { pƒ w w w mw. mvšƒ 0. m 1.5 m w w w 7 w. w ¼ w pƒ ƒw w š, mvš w 1 w(ll-1) { pƒ wš, w ƒ j { p w LL-1 w» w. 5. CHBDC(000) { p 5.1 w p, k w w p. M = D γd + h k γ( H H )D min h (1)», γ,, H mvš, H min mvš 0. m ùkü. (1) w mvš H min ¾ w p, w H min mvš¾ w p w. M D xe p w w p ùküš. (1) (H H min ) w ƒ w M D w, γ w y r š, k γ»»ƒ., 8ƒ ( =.865 m, 5.15 m, m, 7 m, m, 9.1 m, m, 1.15 m) w, H 0. m, 0.9 m, š 1.5 m(, H H min 0m, 0.6m, š 1. m) w p ew mw w ƒ w w r»» w, w w, w 98%. 8 8ƒ w γ y r 6ƒ 1A 006 1œ 17

6 8. p 10. mvš w p w w ùkü š CHBDC w w œ v CANDE-89 mw w FEA Data w w. CHBDC w ƒ w, 10 m w y w w w., ( ) w w w w. = p k (1) w, 9 8ƒ w k γ M D»» w w k ùkü š CHBDC w k k w œ v CANDE-89 mw w FEA Data w w. CHBDC k 0.05 w ù, k ƒ w w yw ùkùš., k, ( ) w w w w. k = (14), k w w mv š w w w p CHBDC p wì 10 w m ¾ v CANDE-89 mw w FEA Data w w ƒ j ƒ» š, p mvšƒ 0. m 10 m zw ( ) p w, w pƒ xe p w» ƒ. w { p 8m w, ew ew w š. 5. yw p k yw w w p (15) w. M = L k L L (15)», L L yw j», ùkü. k CHBDC (11-a), (11-b). k CHBDC H/ 0. š, (16) ƒ w wš w. ad + h b k = ( H ) 0. (16)», a,b w. (16) (15) w L L (H/ ) 0. ù š, 6m» ù w ( ) w (17-a) (17-b) w k = ( H ) m (17-a) 18

7 11. mvš p 1. mvš yw p ( ) 0.00D h k = ( H ) m 1.0m (17-b) 11 ew mw, CHBDC w, ƒ k mvš v CANDE-89 mw w FEA Data w w. CHBDC mvš ew ƒ e w 10% w. 1 yw w p M L mv š 0. m, 0.9 m, 1.5 m w w. CHBDC wš p w p ùkü. 1 w p ew ewš, CHBDC p w p sƒwš, 8 m ƒ ƒ ù w. w p ew 5% wš, yw w w p w ww š q. 5. p κ w q xe w ƒƒ w { p w mwš. ù, p w p xe p w w p, p, κ, w xe p. κ ( ) w CHBDC (18) wš. κ 1. mvš p s M crown = = D M h total (18) 1 ew mw p w ( ) mvš (H) s w. CHBDC w (18) ùküš. 1 mvš ƒw κƒ w w š.» CHBDC 8 m ƒw x w û, w w w w š q., ( ) mvš (H)¾ š w (19) w. κ = ( ) ( H) (19) 5.4 xe p kr (6) CHBDC xe yw p w xe p (k R ) wš. k R ew w yw s š w wš», û mvš 6ƒ 1A 006 1œ 19

8 t 4. CHBDC(000) w CHBDC (000) M D M D = γ + k γ( H 0.0) M D = γ + ( ) k γ( H 0.0) = = k =0.05 = M L p xe p M L =k L L 0.08 k = H m ( ( )) k = H m 8.0m κ= k R =0.45H+0.48ß1.0 M L =k L L k = H m k = H m 1.0m κ=( )( H) xe pƒ sƒ š w» w w. k R mvš w w x w x l (0) (Duncan et al., 1985). 14. Fy=00 MPa xe p w w p, p M cf xe p M hf ƒ ƒ w p,, M Pf w w (1) ³ wš. M cf M Pf, M hf M Pf (1) k R = (0) 5.5 CHBDC(000) q { p w, k, k, κ CHBDC(000) w t 4. wr, yw p xe p, k R x w x l». 6. { m CHBDC(000) (1) () w ƒ ƒ», M Pf = φ h M, φ h = qx q w Fy=00 MPa w ASTM Standard A964/A964M ³ f p w w p ( p ) mvš 0. m, 0.9 m, 1.5 m w ùküš. 14 (a) ASTM (s=76 mm )z p, M cf / M Pf, (b) xe ASTM (s=154 mm )z xe p, M cf /M Pf (c) ASTM x xe y w (s=76 mm)z xe p, M cf /M Pf ùkü 140

9 15. Fy=400 MPa xe p. p 1.0 w ùkü { y w š ƒ 8 m ¾ { w y wš. 15 qx q w ƒ Fy=400 MPa š w 18 w. 15(a) 1 m¾ { w y w š ù 15(b) ASTM xe x { y ƒ. 15(c) x e x w ù küš š 1 m ¾ { y w š. xe x k wù w ƒ š (Fy=400 MPa) qx q y w { p w y w wù š, w mw 1 m¾ ƒ w y w. 7. CHBDC(000) q { p mw. ü œ œ š x q wš 1 m¾ w ew ww. w» w œ š w ww, p e š w e { p š»wx, w w sƒw. w ASTM x xe 114 mm x 154 mm x w sƒw. w e { p»wx w w w š, xe x xe w w p ƒ. w š w ƒ w { p j q Ì 7 mm, CL90, xe 154 mm, û { p j w», k, k, κ w. p w { p 1 m¾ ew w 5% ew. wr, { w y w ASTM wš p w ƒ w. ASTM xe ãš qx q w Fy=400 MPa š w p ƒ g 1 m¾ y w.» CHBDC w w wš 8m w w, p w q { p x qx q w w 1 m¾ w q» w. š x American Association of State Highway and Transfortation Officials (AASHTO) (1996) Standard Specification for Highway Bridges, Washington, D.C. Canadian Standards Association (000) Canadian Highway Bridge Design Code, Ministry of Transportation of Canada, Canada. Choi, D.-H., Kim, G.-N., and Byrne, Peter M. (004) Evaluation of moment equation in the 000 Canadian highway bridge design code for soil metal arch structures, Canadian Journal of Civil Engineering, 1/, pp Duncan, J.M. (1979) BEhavior And Design Of Long-span Metal Culverts, Journal of the Geotechnical Engineering Division, Vol. 105, No., pp Duncan, J.M. and Chang, C.Y. (1970) Nonlinear analysis of stress and strain in soils, ASCE Journal of Geotechnical Division, 95(GM5), pp ƒ 1A 006 1œ 141

10 Duncan, J.M., Seed, R.B., and Drawsky R.H. (1985) Design of corrugated metal box culverts, Transportation Research Record 1008, Transportation Research Board, National Research Council, Washington, DC, pp Katona, M.G., Smith, J.M., Odello, R.S., and Allgoog, J.R.. (1976) CANDE-A Modern approach for structural design and analysis of buried culverts, FHWA-RD McCavour, T.C., Byrne P.M., and Morrison, T.D. (1998) Long-span reinforced steel box culverts, Transportation Research Record 164, Transportation Research Board, National Research Council, Washington, DC, pp Musser, S.C. (1989) CANDE-89-Culvert analysis and design computer program. User manual, FHWA-RD , Federal Highway Administration, Washington, D.C. Standard Specification for Transportation Materials and Methods of Sampling and Testing (ASTM) (1998) American Association of State Highway and Transfortation Officials, Washington, D.C. ( : / : / : ) 14

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