31ƒ 3A Á 2011 5œ 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 (E-mail : wschung@khu.ac.kr) w w (E-mail : hinggs@hanmail.net) z Á Á w m œw (E-mail : zoan@khu.ac.kr) z Áw œ w (E-mail : mrhook1@naver.com) 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 2011 5œ 145
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
2. ƒx q t 1. e Case w 4 r Case I (Built-in Edges) s 0.00254qa 4 /D Case II Case III 4 r (Built-in Edges) 0.00008q o a 4 /D 2 vv (Two Opposite Edges Simply Supported) s 0.01289qa 4 /D Kirchhoff e 0.0829qa 2 (O ) 0.0412qa 2 (A ) 0.00515q o a 2 (O ) 0.0115q o a 2 (A ) 0.1235q o a 2 (O ) 0.0102q 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 2011 5œ 147
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
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 18.63 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 2011 5œ 149
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 H1-1 6 7 1.5 3.5 H1-2 7 7 1.5 3.5 H1-3 8 7 1.5 3.5 H1-4 9 7 1.5 3.5 H1-5 10 7 1.5 3.5 H1-6 11 7 1.5 3.5 B1-1 10 6 1.5 3.5 B1-2 10 7 1.5 3.5 B1-3 10 8 1.5 3.5 H2-1 10 7 1.5 3.5 H2-2 10 7 2.0 3.5 H2-3 10 7 2.5 3.5 B2-1 10 7 1.5 3.0 B2-2 10 7 1.5 3.5 B2-3 10 7 7 4.0 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) H1-1 299 367 300 256 655 406 239 H1-2 341 415 314 284 419 384 296 H1-3 371 440 298 304 309 364 353 H1-4 392 460 398 313 344 347 411 H1-5 409 459 394 317 401 357 468 H1-6 419 461 399 327 458 371 525 150
CASE t 4. ú ¼ (B1) y (M y ) (M y ) (M x ) w w» w w» w w s³» B1-1 318 341 303 274 401 317 468 B1-2 409 459 394 317 401 357 468 B1-3 542 570 534 391 401 437 468 ( : 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» H2-1 409 459 394 317 401 357 468 H2-2 449 505 444 345 401 385 468 H2-3 490 550 501 377 401 422 468 CASE ( : kn-m) t 6. ú q ¼ (B2) y (M y ) (M y ) (M x ) w w» w w» w w s³» B2-1 393 451 370 266 316 268 358 B2-2 409 459 394 317 401 357 468 B2-3 423 470 416 363 487 447 586 ( : kn-m) 31ƒ 3A 2011 5œ 151
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. 51-57. wm wz(2008)» w, w», pp. 736-738 w gj pwz(2007) gj p» w, pp. 310-313. 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 6.71. (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. 63-71. Dicleli, M. (2002) Computer-aided limit states analysis of bridge abutments, Electronic Journal of Structural Engineering, Vol. 1, pp. 74-97. 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. 210-212. ( : 2010.5.11/ : 2010.10.12/ : 2011.1.24) 152