ª Œª Œ 31ƒ 3A Á œ pp. 145 ~ 152 ª ú w Rational Sectional Force and Design Improvement of Abutment Wing-Wall Á½ yá Á x Chung, WonseokÁKim, MinhoÁ

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1 31ƒ 3A Á œ pp. 145 ~ 152 ª ú w Rational Sectional Force and Design Improvement of Abutment Wing-Wall Á½ yá Á x Chung, WonseokÁKim, MinhoÁAn, Zu-ogÁChoi, Hyukjin Abstract Current Bridge Specification for Highway Bridges adopts a simplified method to determine sectional forces of abutment wing by dividing its area into four sections. This simplified method was developed in Japan when numerical analysis was not mature and computer resources were expensive. This simplified method has been with us without modification. This study evaluates the problem of current design practice to improve the design guideline for abutment wing. In this study, a finite element model of abutment wing based on shell elements was developed to obtain accurate sectional force. In addition, foreign design specifications regarding abutment wing were thoroughly examined. It has been observed that sectional forces obtained from the simplified method produce inaccurate results under various geometric shapes. Thus, it is recommended that two dimensional plate analyses should be adopted for future design of abutment wing wall. Keywords : Abutment, wing wall, sectional force, FE analysis, plate analysis, representative section ú w w ú 4 ù š 1 ep yw w š. w r w ³ ü» k š. w w ú w» w ú ep w ƒ¾ 2 š q w w x» w. w w ú w ü ³ w. w ú ƒ ü w w w, x» r w ú x d d ùküš w w. w :, ú,, w w, qw, t 1. m w w. ú (Wing Wall) yw w ww d w m ww m d l w w w. ú j d x swx ù x e e, m, k yw. d x ú ú ƒ ù w w xk x ƒ š xk, swx ú ú ¼ ƒ 5 m wù m y w z Á w m œw ( w w ( z Á Á w m œw ( z Áw œ w ( w œ š. ú { ƒ ƒ ƒ¾ ƒ š w ew.» w (2008) 5 ú y» š 2 š q w w š ³ wš. w w r ú ¼ ƒ 8 m w ú 4 ù š ep rw w r wš. w» r w w» (½ š, 2005) w 14%, 41% w w š š. w ù ƒ¾ v š. 31ƒ 3A œ 145

2 r w w» w w š w w ƒ. ew v ry š w w v w 3 w ü w w w w. w w q w w w ú wš, w z w ú w ƒ ƒ w». p ü IT» y» wš w IT» w w mw w š z ú. p,» w tƒ ƒ ƒ œw» w š w v w š w. ú w x» š w w r sƒwš w. w ú ep w ƒ¾ 2 š w w w ú x w wš w w. ú w wš k w e w. x ú s³ t wš x š w w ú ww. 2. ü ú ü» (2008) ú yw w ww m q w w. q š ep q y» š 2 š q w. š wš. ù 2 š q w w ú ¼ ƒ 8 m 1 ú ww w wš. ü» w š ú w. 1 A D a-b e-f fp w» A D w m w g w š a-b e-f s g w wš. B C b-c c-d ep w. b-c b-b' b'-c c-d c- c' c'-d ww ƒ ƒ w e w w wš. 1 b- b' b ¼ p w w š, b'-c M b, c-c' M c, c'-d M d w w wš.» w (2002) ú w ³ ü» w ú w w r j ù ƒ ùküš. ü» ú m m š w w š wš ù» m (Active Earth Pressure) w e ³ wš., 3ƒ w ww m w š ³ wš. ƒ e, ú ƒ ƒ 90, ú x d k. AASHTO Standard Specification(2002) AASHTO LRFD Bridge Design Specification(2007) ú w ü w š ú ¼ ú w e wš. w f Bridge Manual(2009) ú l y ep w w š ³ wš m m w «wš. w ú ¼ w w wš ú ƒ, s, ƒ,» ú ó ¾ ƒ w. p Bridge Design Manual(2004) ú ¼ w w wš. ü» w ú s ep» 1. r w ú (» w 2008) 146

3 2. ƒx q t 1. e Case w 4 r Case I (Built-in Edges) s qa 4 /D Case II Case III 4 r (Built-in Edges) q o a 4 /D 2 vv (Two Opposite Edges Simply Supported) s qa 4 /D Kirchhoff e qa 2 (O ) qa 2 (A ) q o a 2 (O ) q o a 2 (A ) q o a 2 (O ) q o a 2 (A ) ep wš. ú ¼ w g» j ƒ ù ú ƒ sww ú ¼ w 1ft(30.48cm) ¼ y w ³ wš. EURO CODE(2002), w w w w š ³ w œ x w ú wwš ù ú ¼ w w ³ wš. ü» wš w w» w š y. ü m» m m y kw wš, ü» m w» d ³ wš. ú w ³ p w š. ƒ ep w 1 r w š kw w wš š q. 3. ú w» w xw» w» (Decleli, 2002) ƒ w. ú»ww w q 2., ú w w w m q (Timoshenko and Woinowsky-Krieger, 1970) w t ƒ ƒ w w. w 4 š q 2 q w w w e q w e w w y w. w w v w w w swwš ABAQUS(2007). w w 2 3ƒ š w. Case I 4 š (Built-in Edges) ƒx q sw k š, Case II 4 š ƒx q k, Case III 2 (Two Opposite Edges Simply Supported) ƒx q sw k. t 1 š w Kirchhoff q e ùkü. ƒƒ w w w(out-of-plane) w jš ¼ Ì(L/t) 10, 20, 50, 100, 1000 y j w w w. ABAQUS œw general-purpose finitestrain element S4 (w ü 4 ƒ š ) kw. S4 ƒ Ì y z w x š w ew w (Chung and Sotelino 2006)». 3 Ì y w. L/tƒ 10 ( ̃ É ) w w ƒ 14% j ù q ̃, L/tƒ f w w e ƒ 2% ü ewƒš y w. š ƒ z w x(transverse Shear Deformation) š w w, k w e z w x š w Kirchhoff q w w». ̃ É q z w š w w ³yw Mindlin q w w, L/t 100 { w w Kirchhoff q w w 31ƒ 3A œ 147

4 3. 4. (Case I) 5. (Case II). š q L/t 10 14%ƒ z w x w q w. 4 Case I w w mw w e w. 2(a) A w w ƒ e w 2% ùkü š ù, O Ì y ƒ ew. 5 Case II w e w, 2(b) O x p Ì ƒ w e 0.5% ü ew A y p 2% ùküš. 6 Case III O w e w 6. (Case III) q ̃ w e ewƒš. q Ì w ùküš y wš. w w» w s ü w Ì w mw w w w z w x j w». 4. ú t w w w w Kirchhoff q w w e w w mw ew e y w k w k w. w ú y w w w w wš e w» w. w š ú ü w e x l ƒ š t (Representative Section) w. t» ú, s w y j wš w ww. w ƒƒ» w w x ü» ú y k w. ú x ƒ j w. w x Tx œ 95% w sww 6 m 12 m. w Tx ƒ, Tx ƒ û š ù œ 5%. š ú w Tx d x ú w. d x ú 7(a) ùkù ú (H1), ú ¼ (B1), ú q¼ (B2), ú (H2) w ú 1:1 š w. ƒ ƒ ú 148

5 7. ú t (H1) 6~11 m, ú ¼ (B1) 6~7 m, ú q¼ (B2) 3~4 m, ú (H2) 1.5~2.5 m. t 7(b) ú (H1) 10 m, ú ¼ (B1) 7 m, ú q¼ (B2) 3.5 m, ú (H2) 1.5 m w. 5. ú t w w w kn/m xk m 3 š w, ƒ w 9.8 kn/m ƒ w w 2 š w w ƒ š w. w w w (Mesh) xkƒ ƒx w ƒ¾ x ƒ 2:1 w. w w S4 w ú w w ww. w ú d ƒ w ú q» q š ƒ w. y ú wù l w 3 w,» w š ƒ w ú w ww. 8 t s ùkü. M y d š d e ùküš, Mx w š wš y w. 8 0 ƒà ù x w ùe ƒ q. w 4 w w. š wù ƒ w y jš, ù 3 t š g w w mw., ú (H1) w B1, B2, H2 t š jš H1 6~11 m¾ y j w. B1, H2, B2 w 8. t s w ww w e t 2.» ú (A, B, C, D) ù wš. ù D A š š w y w.,» D ùe d w w w w w. A, B, C w w w.», A w w ( M y ) s³e wš, B ( M y ) C ( M x ) w w e ùkü. 31ƒ 3A œ 149

6 9 t 3 H1 y w» ùkü. H1 6 m 11 m¾ yw» A w w 24%¾, B w w 61%¾ j.,» A B w w d d. w ( )» ƒ M y t 2. ( : m) CASE H1 B1 H2 B2 H H H H H H B B B H H H B B B w»».» B C 1 c» 45 o ù ³ wš., 13(c) B2ƒ h' j (α <45 o ) D m ƒ B š w w.» ep w w A D p w H1 ƒw wì ƒw ƒ ú»ww x w ³ew ƒw. w p w ¼ p y w» w ƒ x ú (A ) ù t 3 A» ³ew w. C 9 H1 ƒw» 69% d 30% d y. ú»ww x xk m w w»., 13(b) B2 h' (α=45 o )» ú ƒ j ( 13(a)) m j» w w M y ƒ, ú ƒ û ( 13(c)) D w m w ƒwš w w M x ƒ». M x 13(b) B2ƒ h' ƒ e ùkü. 10 t 4 ú ¼ (B1) y w» w. A» w 1~5% d B1 y CASE 9. H1 y 10. B1 y t 3. ú (H1) y (M y ) (M y ) (M x ) w w» w w» w w s³» ( : kn-m) H H H H H H

7 CASE t 4. ú ¼ (B1) y (M y ) (M y ) (M x ) w w» w w» w w s³» B B B ( : kn-m) 11. H2 y 12. B2 y w ùkû. B C w B1 ƒw d ƒw. B C» t 4 B1 y w. B1 ƒw D B C sw m j» w». B1 8 m w w w e 3% ü ù kü. x» wš ú ¼ ƒ 8 m 2 š qw w w ³ k w q. 11 t 5 ú (H2) y» w w, A CASE ± 4% ü ùkü. B C H2ƒ ƒw w» w ƒš. 12 t 6 ú q ¼ (B2) y. A» w w 2~6%,» d ùküš w. B C» w w 15% j ùkü ùe d. r xw» w w w ú x d ùe d ùküš w t 5. ú (H2) y (M y ) (M y ) (M x ) w w» w w» w w s³» H H H CASE ( : kn-m) t 6. ú q ¼ (B2) y (M y ) (M y ) (M x ) w w» w w» w w s³» B B B ( : kn-m) 31ƒ 3A œ 151

8 13. ú»ww wš., x ü» w š w 2 q 1 ùe w w yw wš. 6. ú» w wš r w» w ú ep w ƒ¾ 2 š q w w w ú x w wš, x» w. w x ú s³ t wš x š w w ú ww. l. 1. w ü w w w, xw» w w ú x d d ùküš w wš. 2. ú ú y w.» M y w w 24% d 61% d.» M x w w 69% d 30% d ùkü. 3. x ü» wš w 2 q 1 w w yw wš. w w y w q w w yw w ù, ƒ mw ú»ww swwš y ƒ w r v w. 4. ú w ù w x w jš Ì y ww. š x ½ š,, ³(2005) ú e r w w, gj pwz, w gj pwz, 17 «5y, pp wm wz(2008)» w, w», pp w gj pwz(2007) gj p» w, pp AASHTO LRFD Bridge Specifications (2007) 4 th Edition, American Association of State Highway and Transportation officials, Washington D.C. AASHTO Standard Specifications for Highway Bridges (2002) 17 th Edition, American Association of State Highway and Transportation officials, Washington D.C. ABAQUS/Standard User s Manual - Version (2007) ABAQUS, Inc., Pawtucket, R.I. Chung, W. and Sotelino, E.D. (2006) Three-dimensional finite element modeling of composite girder bridges. Engineering Structures, Vol. 28, No. 1, pp Dicleli, M. (2002) Computer-aided limit states analysis of bridge abutments, Electronic Journal of Structural Engineering, Vol. 1, pp Euro Code 1 (2002), Section 4, Actions on Structures, European Committee Standardisation. Timoshenko and Woinowsky-Krieger (1970) Theory of Plates and Shells, 2nd Edition. McGraw Hill. WisDOT Bridge Design. (2009) Wisconsin Department of Transportation. WVDOH Bridge Design Manual (2004) West Virginia Department of Transportation. Žž ž «(2002) Á «, pp ( : / : / : ) 152

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