26 4A · 2006 7 − 611 −

26 4A·2006 7
Redundancy Evaluation of the Composite Two Steel Plate-Girder Bridges
*·**
Abstract
The composite two plate-girder bridges are generally defined as a non-redundant load path structure because the bridge can
collapse if one of the two girders is seriously damaged by a fatigue crack. In this paper, a numerical study on the evaluation of
the after-fracture redundancy of the composite two-girder bridges was accomplished. The evaluation has been performed on the
simple and three-span continuous bridges with I-section cross beams which serve as transverse bracing, and with or without the
bottom lateral bracing system. The load carrying capacities of the intact and damaged bridges with or without lateral bracing
were evaluated from material and geometric nonlinear analysis, respectively and the redundancy was evaluated for each case. It
was acknowledged from the analytical results that both simple and continuous intact two-girder bridges have sufficient redun-
dancy even without lateral bracing, but it takes an important role to improve the redundancy of damaged bridges.
Keywords : redundancy, composite two-girder bridge, fractured girder, bottom lateral bracing, load carrying capacity
·····························································································································································································································

2-
. 2-
. 3 , I-
.
· .
2- ,
.
·····························································································································································································································
,

.
, AASHTO (2002) (2005)
2-
(non-redundant load
path structure) , 2-
.
,
, , 2 3
.
(redundancy)

(Ghosn ,
1998). ,
. ,
2- (fracture critical
member)
, 2-
.
2-
. , Heins (1980, 1982)

. ASCE-AASHTO
(1985) 2-
, (primary
loads)
. Daniels
(1989) 2-
* (Email : ympk@pusan.ac.kr)
− 612 −
.

.

,

. Tachibana (2000) (2005)
2-
,
,

.
, 2- Frangopol
(1991) 4-
. , Ghosn (1998) 4~10
PSC
,
(load factor
ratio) .
. , 2-
I- (floor beam) 2~3
(stringer)
. , ,
2- ,
I-
.
(Ohtsuka , 1993)

, 2 ,
2-
.
, 2- 1

.
2- ·
. 3
2- ,

· 2-
.
2.1

2 12 m 40 m
40+50+40 m 3 .
(2005)
.
1 6 m
40 cm, 34 cm
.
2-
- (,
2005) SM490
L/15 2.7 m, L/18 2.8 m
. ·
80 cm
.
80%
, 60% 1.0
.
2 .


.
10 m 1.7 m, 5 m

.
26 4A · 2006 7 − 613 −
I- 5m ,
( , 2004)
2/3,
1/3 .
3 .
, X-
, T-200×200×20×20
, 92 .
2.2
2.2.1
4 (S4R)
. 4(a) (b)
.
.


,
15 m(0.375L) .
5(a) (b)
G2 . Daniels
(1989) 2-

. ,
5(c) , ,

.
3.
− 614 −
SM490 , PSC
PC .
(layered shell)
, (, 1999)

0.00625 .
1 .
,
- , 6
tri-linear
0.002 .
2 1.16fck, 0.1fck .
(yield criteria) Von Mises
, Drucker-Prager .
2.2.2
. ,
,
(wd1=50.35 kN/m) . ,

(wd2=18.61 kN/m) .
, DB-24 1 1
, 2 2 ( DB-24-
2Lane) .
1
, ,

(Heins , 1980, 1982;
Daniels , 1989, Ghosn , 1998).
5 G2
DB-24-2Lane
7(a) G2
7(b)
. ,

15/(40+L) ,
0.3
(Daniels , 1989).
2 (
) 5
( ) ,
·
.
, ·
5.
6.
Steel SM490 320 210,000 0.3
Concrete 350 35(3.5) 26,500 0.167
Rebar SD40 400 204,000 -
7.
,
.

ABAQUS Step Model change ,
2 , , (
)
,
. ,
,
.
DB-24-2Lane
Riks method .
3.
3.1

,
· . ·
DB-24-2Lane
.
G2 ( 20 m
) 8
. 8(b)
G2
.

. , 8(a)
·
(G1) G2 2
, 8(b) G2
. G2 G1
. ,

(20 m ) 8(a)
.
,
.
8(a) 8(b)
(0 m ) G1 G2
. ,
. , G1 9(a)
, G2
9(b)
,

. ,


2. Step
Step Model Change
1
2
3) -
4 DB-24-2Lane
)
8. (+DB-24-2Lane
)
− 616 −
15 m )
10 . , 10(b)
G2 ()

. , 10(a) (15m
) G1 1.5 ,
10(b) G2 .
G2
G1
. ,
( 15m )
10(a) .
, 10(b)
G2
. G2
,

.
G1 G2
.
3.1.2
·
3 .
(G2)
, G1
. ,
,
. 11


,
,
.
(G1)
,
.
3.3.3

10. (+DB-24-2Lane
)
3. · (+DB-24-2Lane ) (unit : MPa)

Top Bottom Top Bottom Top Bottom Top
Intact bridge without bracing 0.1 -0.5 -4.0 4.1 -0.3 0.6 -2.9 3.8
Damaged bridge without bracing 79.0 -89.4 -45.8 -17.7 20.8 -21.8 -10.7 -33.6
with bracing 263.5 -255.5 -214.9 185.7 156.4 -159.0 -124.9 98.3
11.
26 4A · 2006 7 − 617 −
12 .

,
45.0 MPa ,
. ,

. ,
0.1fck

.
-( )
13 . 13 D.L. ·
. -
L/100
. L/100 3.3 Ghosn
(1998) 4
(functionality limit state) . 13
·
7.3 cm
47.3 cm(=7.3+
4,000/100) .
4 .
4
DB-24-2Lane 10.9, 14.3
.
. 2
3 ,
DB-24 . ·
95.8 MPa
12. (+DB-24-2Lane )
13. -
− 618 −
, DB-24 31.0 MPa .
, (320-95.8)/
31.0=7.23 DB-24-2Lane ,
,
(
) .
,
DB-24-2Lane 1.0 ,
5.3
.


. 11(b)


.
15 m ) 14 , 3.2.1
5 . 5
·
DB-24-2Lane 9.3 13.5
, .



.
5
DB-24-2Lane 2.7 ,
6.9 .


. ,

.


.
3.3
Daniels (1989) 2-
(
)

. , Ghosn (1998) 6 4
(4~10) (4~12ft)
1
(required load factor ratio)
.
. , LFl

.

14. -
5.

6.

1) Member failure(LFl) 2) Ultimate limit state(LFu) 3) Functionality limit state(LFf) 4) Damaged condition limit state
(LFd)
L/100
26 4A · 2006 7 − 619 −
(2)
ML: DB-24-2-Lane
.
2- (1)
7 . 7 Ru

(≥1.3) .
Rd
(≥0.5) ,
. ,
Rd=0.41 (≥
0.5) ,
.
2-
. ,
DB-24-2Lane
2.7

.


.
DB-24-2Lane
.


5 , 2.5
. ,

.
3.
,
,
.
,

.

.
, (2005) 2 ,
, , 25 2A, pp. 337-
345.
, ,
, 16 1, pp. 1-10.
(2005)
, No. 2003A238.
(1999)
, No. 1999A232.
(2005) .
(2002) Standard Specifications for Highway Bridges.
Frangopol, D. M. and Nakib, R. (1991) Redundancy in highway
bridges, Engineering Journal, AISC, First Quarter, pp. 45-50.
Daniels, J. H., Kim, W., and Wilson, J. L. (1989) Recommended
Guidelines for Redundancy Design and Rating of Two-Girder
Steel Bridges, NCHRP Report 319, TRB.
Ghosn, M. and Moses, F. (1998) Redundnacy in Highway Bridge
Superstructures, NCHRP Report 406, TRB.
Heins, C. P. and Hou, C. K. (1980) Bridge redundancy: effects of
bracing, J. of the Structural Division, Proceedings of ASCE,
Vol. 106, No. ST6, pp. 1364-1367.
Heins, C. P. and Kato, H. (1982) Load redistribution of cracked
girders, Journal of the Structural Division, Proceedings of
ASCE, Vol. 108, No. ST8, pp. 1909-1915.
Idriss, R. L., White, K. R., Woodward, C. B., and Jauregui, D. V.
(1995) After-fracture redundancy of two-girder bridge: testing
I-40 bridges over rio grande, Proceedings of the Fourth Inter-
national Bridge Engineering Conference, pp. 316-326, TRB.
Ohtsuka, M., Takenaka, H, Satoh, T., and Wachi, T. (1993) A prop-
osition for the elimination of the lower lateral bracings of plate-
girder bridges, Bridge and Foundation Engineering(
), Vol. 27, No.11, pp. 33-39. (in Japanese)
Tachibana, Y., Tsujikado, M., Echigo, S., Takahashi, S., and Miki,
C. (2000) A Study of after-fracture redundancy for two-girder
bridges, J. of Construction Management and Engineering,
LF l
M R
M D
LFu LFd LFl Ru ( > 1.3) Rd ( > 0.5)
2- (40 m)
1.41 0.13
9.3 2.7 6.65
1.40 0.41
− 620 −
Task Committee on Redundancy of Flexural Systems of the ASCE-
AASHTO Committee on Flexural Members of the Committee
on Metals of the structural Divisions (1985) State-of-the-art
report on redundant bridge systems, J. of the Structural Engi-
neering, ASCE, Vol. 111, No. 12, pp. 2517-2531.
(: 2005.9.29/: 2005.11.28/: 2005.12.28)