A Study on Application of Mixed Girder in Steel Box Girder Bridge
A Study on Application of Mixed Girder in Steel Box Girder Bridge
A Study on Application of Mixed Girder in Steel Box Girder Bridge
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A <str<strong>on</strong>g>Study</str<strong>on</strong>g> <strong>on</strong> Applicati<strong>on</strong> <strong>of</strong> <strong>Mixed</strong> <strong>Girder</strong> <strong>in</strong> <strong>Steel</strong> <strong>Box</strong><br />
<strong>Girder</strong> <strong>Bridge</strong><br />
Hyosang HWANG 1 Kabsoo KYUNG 2 and Hyungi MOON 3<br />
1 Dept. <strong>of</strong> Civil Eng., Korea Maritime University<br />
(D<strong>on</strong>gsam 2d<strong>on</strong>g, Busan City, Korea)<br />
E-mail:hhs0259@naver.com<br />
2 Pr<strong>of</strong>essor, Inst., Structual machanics, Korea Maritime University University<br />
(D<strong>on</strong>gsam 2d<strong>on</strong>g, Busan City, Korea)<br />
E-mail:kyungks@hhu.ac.kr<br />
By the completi<strong>on</strong> <strong>of</strong> the Che<strong>on</strong>gpung <strong>Bridge</strong>, <strong>in</strong> December 2010, hav<strong>in</strong>g a ma<strong>in</strong> span length <strong>of</strong> 372m,<br />
Korea has become the third country hav<strong>in</strong>g a hybrid, cable-stayed bridge with ma<strong>in</strong> span length <strong>of</strong> l<strong>on</strong>ger<br />
than 300m, follow<strong>in</strong>g France and Japan. Start<strong>in</strong>g with Che<strong>on</strong>gpung <strong>Bridge</strong>, hybrid cable-stayed bridge,<br />
extradosed bridge, and mixed girder bridges which are under c<strong>on</strong>structi<strong>on</strong> or <strong>in</strong> design phase.<br />
In civil projects, steel and c<strong>on</strong>crete are the most comm<strong>on</strong> materials used to c<strong>on</strong>struct hybrid structures. The<br />
ma<strong>in</strong> purpose <strong>of</strong> hybrid structures is to create superior structural characteristics, which cannot be achieved<br />
<strong>in</strong> the structures comprised <strong>of</strong> a s<strong>in</strong>gle material or type <strong>of</strong> member, by comb<strong>in</strong><strong>in</strong>g dissimilar materials or<br />
members. Hybrid structures can be coarsely classified <strong>in</strong>to composite structure and mixed structure.<br />
The core technology <strong>of</strong> the steel-c<strong>on</strong>crete mixed girder structure is the design <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> between<br />
the steel girder <strong>of</strong> the ma<strong>in</strong> span and the c<strong>on</strong>crete girder <strong>of</strong> the side span. S<strong>in</strong>ce the detailed design standard,<br />
related studies, and reference data for the design <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong>s are not sufficiently available yet, the<br />
applicati<strong>on</strong> and spread <strong>of</strong> mixed girder structure are fac<strong>in</strong>g difficulties.<br />
To this end, the authors have c<strong>on</strong>ducted structural analysis with the model <strong>of</strong> a real bridge to acquire<br />
technical data and evaluate feasibility, <strong>in</strong> additi<strong>on</strong> to structural, behavioral characteristics. The focus was to<br />
<strong>in</strong>vestigate the stress transfer mechanism <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong>s <strong>of</strong> mixed girders.<br />
Key Words : steel-c<strong>on</strong>crete mixed girder, C<strong>on</strong>necti<strong>on</strong>, shear c<strong>on</strong>nector<br />
1. INTRODUCTION<br />
By the completi<strong>on</strong> <strong>of</strong> the Che<strong>on</strong>gpung <strong>Bridge</strong>, <strong>in</strong> December 2010, hav<strong>in</strong>g a ma<strong>in</strong> span length <strong>of</strong> 372m, Korea<br />
has become the third country hav<strong>in</strong>g a hybrid, cable-stayed bridge with ma<strong>in</strong> span length <strong>of</strong> l<strong>on</strong>ger than 300m,<br />
follow<strong>in</strong>g France and Japan. The Che<strong>on</strong>gpung <strong>Bridge</strong> is the first hybrid cable-stayed bridge <strong>in</strong> Korea.Start<strong>in</strong>g<br />
with Che<strong>on</strong>gpung <strong>Bridge</strong>, hybrid cable-stayed bridge, extradosed bridge, and mixed girder bridges which are<br />
under c<strong>on</strong>structi<strong>on</strong> or <strong>in</strong> design phase.<br />
A hybrid structure implements its functi<strong>on</strong>ality by be<strong>in</strong>g comb<strong>in</strong>ed with different types <strong>of</strong> materials <strong>in</strong> the<br />
member level or structural system level. In civil projects, steel and c<strong>on</strong>crete are the most comm<strong>on</strong> materials<br />
used to c<strong>on</strong>struct hybrid structures. The ma<strong>in</strong> purpose <strong>of</strong> hybrid structures is to create superior structural<br />
characteristics, which cannot be achieved <strong>in</strong> the structures comprised <strong>of</strong> a s<strong>in</strong>gle material or type <strong>of</strong> member,<br />
by comb<strong>in</strong><strong>in</strong>g dissimilar materials or members. Hybrid structures can be coarsely classified <strong>in</strong>to composite<br />
structure and mixed structure.<br />
The core technology <strong>of</strong> the steel-c<strong>on</strong>crete mixed girder structure is the design <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> between the<br />
steel girder <strong>of</strong> the ma<strong>in</strong> span and the c<strong>on</strong>crete girder <strong>of</strong> the side span. S<strong>in</strong>ce the detailed design standard, related<br />
studies, and reference data for the design <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong>s are not sufficiently available yet, the applicati<strong>on</strong><br />
and spread <strong>of</strong> mixed girder structure are fac<strong>in</strong>g difficulties. To this end, the authors have c<strong>on</strong>ducted structural<br />
analysis with the model <strong>of</strong> a real bridge to acquire technical data and evaluate feasibility, <strong>in</strong> additi<strong>on</strong> to<br />
structural, behavioral characteristics. The focus was to <strong>in</strong>vestigate the stress transfer mechanism <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong>s<br />
<strong>of</strong> mixed girders.<br />
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2. MIXED GIRDER<br />
(1) Characteristics <strong>of</strong> mixed girder<br />
A mixed structure refers to the structural system c<strong>on</strong>sists <strong>of</strong> dissimilar materials <strong>in</strong> comb<strong>in</strong>ati<strong>on</strong>. Similarly, a<br />
mixed girder c<strong>on</strong>sists <strong>of</strong> steel girders and c<strong>on</strong>cretes girder mixed <strong>in</strong> the l<strong>on</strong>gitud<strong>in</strong>al directi<strong>on</strong>. Generally, a<br />
mixed girder system provides significant advantages by us<strong>in</strong>g light-weight steel girders <strong>in</strong> the ma<strong>in</strong> spans and<br />
c<strong>on</strong>crete or PDC girders <strong>in</strong> the side spans. In this structure, the bend<strong>in</strong>g moment <strong>in</strong> the ma<strong>in</strong> span is reduced by<br />
the difference <strong>in</strong> the weights <strong>of</strong> the steel girder and c<strong>on</strong>crete girder, and the problem <strong>of</strong> the upward reacti<strong>on</strong><br />
force at end bear<strong>in</strong>g po<strong>in</strong>ts which can occur when the side span is shorter than the ma<strong>in</strong> span can be resolved. In<br />
additi<strong>on</strong>, the travel performance <strong>of</strong> vehicles is improved, result<strong>in</strong>g <strong>in</strong> reduced ma<strong>in</strong>tenance cost. <strong>Mixed</strong> girders<br />
are ma<strong>in</strong>ly applied to hybrid cable-stayed bridges, extradosed bridges, and girder bridges.<br />
(2) Classificati<strong>on</strong> by c<strong>on</strong>necti<strong>on</strong><br />
The c<strong>on</strong>necti<strong>on</strong>s between the steel girders and c<strong>on</strong>crete girders <strong>of</strong> mixed girder structures can be classified <strong>in</strong>to the<br />
three types <strong>of</strong>: bear<strong>in</strong>g plate type; fill<strong>in</strong>g c<strong>on</strong>crete type; and shear c<strong>on</strong>nector type. Fig. 1 is the schematic view <strong>of</strong> the<br />
three type <strong>of</strong> c<strong>on</strong>necti<strong>on</strong>s.<br />
(a) Bear<strong>in</strong>g plate (b) Fill<strong>in</strong>g c<strong>on</strong>cerete (c) Shear c<strong>on</strong>nector<br />
Fig.1 Schematic diagram <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong>.<br />
3. STRUCTURAL ANALYSIS<br />
(1) <strong>Bridge</strong> <strong>of</strong> the present <str<strong>on</strong>g>Study</str<strong>on</strong>g><br />
The Shiotsubo <strong>Bridge</strong> is a mixed girder type, two c<strong>on</strong>t<strong>in</strong>uous span bridge at Takasatomura, Yama-gung,<br />
Fukushima-ken, Japan. Due to the restricti<strong>on</strong> <strong>of</strong> the topology, the bridge has approximately 2:1 <strong>of</strong> unbalanced<br />
span lengths. About 70% <strong>of</strong> the l<strong>on</strong>ger span is built with steel girder. Fig. 2 and Fig. 3 show the plan view and<br />
the cross-secti<strong>on</strong>al view <strong>of</strong> the bridge, respectively.<br />
Fig.2 Plan view <strong>of</strong> the bridge.<br />
2<br />
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(a) <strong>Steel</strong> <strong>Girder</strong><br />
Fig.3 Cross-secti<strong>on</strong>al view <strong>of</strong> the <strong>Bridge</strong>.<br />
(b) Pc <strong>Girder</strong><br />
The c<strong>on</strong>necti<strong>on</strong> <strong>of</strong> the bridge is a fill<strong>in</strong>g-c<strong>on</strong>crete, rear-side bear<strong>in</strong>g plate type. With the bear<strong>in</strong>g plate positi<strong>on</strong>ed<br />
at the rear, the fill<strong>in</strong>g c<strong>on</strong>crete and PSC comp<strong>on</strong>ent form a c<strong>on</strong>t<strong>in</strong>uous structure to transfer force by the<br />
rear plate and the shear c<strong>on</strong>nector <strong>of</strong> composite shape flange, and prestress is applied by PS steel member. Fig.<br />
4 shows the structural detail <strong>of</strong> c<strong>on</strong>necti<strong>on</strong> part <strong>in</strong> the Shiotsubo <strong>Bridge</strong>.<br />
Fig.4 Strucrural detail <strong>of</strong> c<strong>on</strong>necti<strong>on</strong> part <strong>in</strong> Shiotsubo bridge.<br />
The steel shell which comprises the c<strong>on</strong>necti<strong>on</strong> part c<strong>on</strong>sists <strong>of</strong> 15 cells. The steel shell is provided with<br />
perforated steel sheet shear c<strong>on</strong>nector (perfob<strong>on</strong>d rib) and filled up with high-flow<strong>in</strong>g c<strong>on</strong>crete. The<br />
pre-stress<strong>in</strong>g method is c<strong>on</strong>ducted by extend<strong>in</strong>g the steel wire from the PC girder to the rear plate.<br />
(2) Analysis model<br />
With the design draw<strong>in</strong>gs and structural calculati<strong>on</strong> sheet <strong>of</strong> the Shiotsubo <strong>Bridge</strong>, 3D grid analysis was<br />
c<strong>on</strong>ducted by l<strong>in</strong>ear analysis to analyze the complicated behavior <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong>.<br />
a) Model A(Frame analysis model)<br />
To verify the model by comparis<strong>on</strong> with the structural calculati<strong>on</strong> <strong>of</strong> the Shiotsubo <strong>Bridge</strong>, a frame model<br />
was c<strong>on</strong>structed hav<strong>in</strong>g the same nodes and cross-secti<strong>on</strong> as those <strong>of</strong> exist<strong>in</strong>g structural model, as shown <strong>in</strong> Fig.<br />
5.<br />
Fig.5 Frame analysis model <strong>of</strong> the bridge.<br />
b) Detailed analysis model <strong>of</strong> c<strong>on</strong>necti<strong>on</strong> part<br />
Detailed analysis model <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> part was modelled to analyze the local behavior <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong><br />
part. Fig. 6 and Fig. 7 show the detailed analysis model .<br />
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Fig.6 Detailed structual analysis model.<br />
Fig.7 PC Wire modelled with rod elements.<br />
The detailed analysis model represented 3.75m <strong>of</strong> the PC girder and steel girder <strong>in</strong>clud<strong>in</strong>g the c<strong>on</strong>necti<strong>on</strong> part<br />
<strong>of</strong> the bridge. The steel members, c<strong>on</strong>crete members and the PC steel members were modelled by 4-node shell<br />
elements, 8-node solid elements, and beam elements, respectively.<br />
c) Model B(frame model + detailed analysis model <strong>of</strong> c<strong>on</strong>necti<strong>on</strong> part)<br />
For effective load transfer <strong>in</strong> the model, the beam elements <strong>of</strong> the frame model and the elements <strong>of</strong> the detailed<br />
analysis model were comb<strong>in</strong>ed us<strong>in</strong>g the rigid l<strong>in</strong>k. Fig. 8 shows the frame + detailed analysis model.<br />
Fig.8 Model B comb<strong>in</strong>ed frame model and detail model.<br />
(2) Model validai<strong>on</strong><br />
a) Model A<br />
In the validati<strong>on</strong> process, <strong>on</strong>ly dead loads were applied and the live loads (w<strong>in</strong>d load, snow load, temperature<br />
load, creep and shr<strong>in</strong>kage) were not taken <strong>in</strong>to c<strong>on</strong>siderati<strong>on</strong>. Table 1 presents the load cases applied <strong>in</strong> the<br />
structural analysis. In the validati<strong>on</strong> process, <strong>on</strong>ly dead loads were applied and the live loads (w<strong>in</strong>d load, snow<br />
load, temperature load, creep and shr<strong>in</strong>kage) were not taken <strong>in</strong>to c<strong>on</strong>siderati<strong>on</strong>. Table 1 presents the load cases<br />
applied <strong>in</strong> the structural analysis.<br />
Table 1 Load Case.<br />
NO.<br />
Load Case<br />
Self-weight <strong>of</strong> ma<strong>in</strong> girder<br />
<br />
Self-weight <strong>of</strong> slab<br />
Upper deck and other self-weights<br />
C<strong>on</strong>structi<strong>on</strong> Step 1<br />
C<strong>on</strong>structi<strong>on</strong> Step 8<br />
Surface load (pavement, curbs)<br />
Surface load (guide rail, median strip)<br />
In the first stage validati<strong>on</strong> <strong>of</strong> the present structural analysis model, the self-weight <strong>of</strong> the ma<strong>in</strong> girder classified<br />
as deal load <strong>in</strong> the structural calculati<strong>on</strong> sheet was compared with the reacti<strong>on</strong> force obta<strong>in</strong>ed by structural<br />
analysis. Here, the self-weight <strong>of</strong> the ma<strong>in</strong> girder comprised <strong>of</strong> the load cases <strong>of</strong> ~ <strong>in</strong> Table1. Table 2<br />
presents the reacti<strong>on</strong> forces at A1, P1, and A2 po<strong>in</strong>ts obta<strong>in</strong>ed from the structural calculati<strong>on</strong> sheet and the<br />
structural analysis.<br />
In Table 2, while the errors at the A1 and A2 po<strong>in</strong>ts are relatively large by 4.7% and 3.1%, respectively, that<br />
at the P1 was very accurate by 0.01%. S<strong>in</strong>ce the total error is accurate by 0.3%, it could be judged that the<br />
structure model and the applied loads are appropriate.<br />
4<br />
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Table 2 Comparis<strong>on</strong> <strong>of</strong> the reacti<strong>on</strong> forces at bear<strong>in</strong>g po<strong>in</strong>ts.<br />
Classificati<strong>on</strong> A1 Po<strong>in</strong>t P1 Po<strong>in</strong>t A2 Po<strong>in</strong>t Total ( )<br />
Reacti<strong>on</strong> forces<br />
by ma<strong>in</strong> girder<br />
weight<br />
Sheet 3173.49 22817.64 1550.06 27541.19<br />
Analysis 3032.29 22820.15 1597.75 27450.19<br />
Error rate 4.70 % 0.01 % 3.1 % 0.3 %<br />
In the sec<strong>on</strong>d stage model validati<strong>on</strong>, the secti<strong>on</strong> forces <strong>of</strong> the structural calculati<strong>on</strong> sheet and structural<br />
analysis were compared. Load case <strong>of</strong> before compositi<strong>on</strong> and after compositi<strong>on</strong> are summarized as follows,<br />
locati<strong>on</strong> <strong>of</strong> elements is shown Fig. 9. The secti<strong>on</strong> forces <strong>of</strong> the structural calculati<strong>on</strong> and sum <strong>of</strong> secti<strong>on</strong> forces<br />
<strong>of</strong> before and after compositi<strong>on</strong> obtraned from structural analysis were compared <strong>in</strong> Table 3.<br />
Fig.9 Locati<strong>on</strong> <strong>of</strong> elements.<br />
- Before compositi<strong>on</strong>: self-weigh <strong>of</strong> the ma<strong>in</strong> girder (the load case; ++++ <strong>of</strong> Table1) before the<br />
compositi<strong>on</strong> was taken <strong>in</strong>to c<strong>on</strong>siderati<strong>on</strong><br />
- After compositi<strong>on</strong>: <strong>on</strong>ly the dead loads (the load case; + <strong>of</strong> Table 1) applied to the ma<strong>in</strong> girder after the<br />
compositi<strong>on</strong> were taken <strong>in</strong>to c<strong>on</strong>siderati<strong>on</strong><br />
Table 3 Comparis<strong>on</strong> <strong>of</strong> the bend<strong>in</strong>g moments at the bear<strong>in</strong>g po<strong>in</strong>ts.<br />
Classificati<strong>on</strong><br />
Dead load <strong>in</strong> the structural<br />
calculati<strong>on</strong> sheet<br />
Sum <strong>of</strong> the bend<strong>in</strong>g moments<br />
before and after compositi<strong>on</strong><br />
Moment-y (kNm)<br />
El. No.[6] El. No.[ [13] El. No.[I[23] El. No.[I[33]<br />
67485 11636 -221077 657<br />
52541 1952 -229886 965<br />
(a) Bend<strong>in</strong>g moment diagram <strong>of</strong> structural calculati<strong>on</strong>.<br />
5<br />
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(b) Bend<strong>in</strong>g moment diagram <strong>of</strong> structural analysis.<br />
Fig.10 Comparis<strong>on</strong> <strong>of</strong> the bend<strong>in</strong>g moments <strong>of</strong> structural calculati<strong>on</strong> and analysis.<br />
The results <strong>of</strong> the structural analysis were somewhat different from those <strong>of</strong> the structural calculati<strong>on</strong> sheet,<br />
which was though to be caused by the auxiliary loads <strong>of</strong> the steel girder which were omitted <strong>in</strong> the calculati<strong>on</strong><br />
and/or difference <strong>in</strong> positi<strong>on</strong>s which were not presented <strong>in</strong> the draw<strong>in</strong>gs <strong>of</strong> the Shiotsubo <strong>Bridge</strong>. However, as<br />
shown <strong>in</strong> Fig. 10, the bend<strong>in</strong>g moments obta<strong>in</strong>ed by the structural calculati<strong>on</strong> and the structural analysis show<br />
the diagrams <strong>of</strong> similar pr<strong>of</strong>ile, and the focus <strong>of</strong> the present study is <strong>on</strong> the behavioral characteristics <strong>of</strong> the<br />
c<strong>on</strong>necti<strong>on</strong> caused by the changes <strong>of</strong> the structural detail, it was judged that the structural analysis model <strong>of</strong> the<br />
bridge was appropriate.<br />
b) Model B<br />
For the applied loads, <strong>on</strong>ly the fixed loads were applied exclud<strong>in</strong>g live loads. Fig. 11 shows the maximum<br />
deflecti<strong>on</strong> <strong>of</strong> the two models.<br />
(a) Model A.<br />
(b) Model B.<br />
Fig.11 Comparis<strong>on</strong> <strong>of</strong> the model A and model B.<br />
The deflecti<strong>on</strong>s at the Element 6 which were the largest showed about 3% <strong>of</strong> difference by were 209.5mm and<br />
202.4mm, respectively, which was thought to be caused by the error <strong>in</strong> the weight calculati<strong>on</strong> <strong>of</strong> the detailed<br />
model <strong>of</strong> the comb<strong>in</strong>ed c<strong>on</strong>necti<strong>on</strong>.<br />
The stress calculated us<strong>in</strong>g the secti<strong>on</strong> force <strong>of</strong> the Element 13 <strong>of</strong> the fram analysis model, which is equivalent<br />
to the detailed model secti<strong>on</strong> <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> part, and the stress obta<strong>in</strong>ed by the structural analysis <strong>of</strong> the<br />
detailed model <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> were 3.2 MPa and 4.1 MPa, respectively. While the difference is about 28%,<br />
it is not significant s<strong>in</strong>ce the stress level is very low.<br />
Summariz<strong>in</strong>g the above discussi<strong>on</strong>, s<strong>in</strong>ce the deflecti<strong>on</strong>s and stresses show <strong>in</strong>significant difference, it could<br />
be judged that the behavioral characteristics <strong>of</strong> the two models are the same, and thus, the model B is effective.<br />
6<br />
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(4) Detailed structural analysis <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> part<br />
a) Implementati<strong>on</strong> <strong>of</strong> the perforb<strong>on</strong>d rib effect <strong>of</strong> the stuctural analysis model<br />
In this study, c<strong>on</strong>crete and perforb<strong>on</strong>d rib were presumed to be partially comb<strong>in</strong>e, and the effect <strong>of</strong> perforb<strong>on</strong>d<br />
rib was implemented, applied to the c<strong>on</strong>necti<strong>on</strong> part, through detailed analysis.<br />
The analysis model was model B, and the load c<strong>on</strong>diti<strong>on</strong> applied to the detailed analysis model was the live<br />
load <strong>of</strong> DB-24 <strong>of</strong> Korean design load. The live load <strong>of</strong> DB-24 was applied by simultaneous load<strong>in</strong>g <strong>on</strong> all <strong>of</strong> the<br />
three car lanes and as c<strong>on</strong>centrated loads at the po<strong>in</strong>ts where the bend<strong>in</strong>g moment was greatest. As shown <strong>in</strong><br />
Fig. 12, the dead loads applied as l<strong>in</strong>e loads and c<strong>on</strong>centrated loads <strong>in</strong> the fram analysis were transformed <strong>in</strong>to<br />
distributed loads and applied <strong>in</strong> the detailed structural model. The prestress<strong>in</strong>g applied at the c<strong>on</strong>necti<strong>on</strong> part<br />
was substituted by temperature load by referr<strong>in</strong>g to the actual structural calculati<strong>on</strong> sheet.<br />
(a) Transformed <strong>in</strong>to and applied as uniform load.<br />
(b) Prestress<strong>in</strong>g substituted by temperature load.<br />
Fig.12 Load<strong>in</strong>g c<strong>on</strong>diti<strong>on</strong>s <strong>of</strong> detailed structural analysis.<br />
Table 4 Positi<strong>on</strong>s <strong>of</strong> the representative elements <strong>of</strong> the structure model.<br />
<br />
<br />
Left bottom <strong>of</strong> the steel pier shell rear plate<br />
was def<strong>in</strong>ed to be the orig<strong>in</strong> po<strong>in</strong>t, and the<br />
elements were expressed with (x, y, z) coord<strong>in</strong>ates<br />
system<br />
<br />
Element No.: 24603 (solid)<br />
Coord<strong>in</strong>ates: (20, 2421, 2560)<br />
Between the anchored bear<strong>in</strong>g plates <strong>of</strong> the<br />
PC steel wire close to rear plate and subject<br />
to c<strong>on</strong>centrated stress<br />
<br />
Element No.: 3966 (plate)<br />
Coord<strong>in</strong>ates: (0, 2421, 2560)<br />
Between the anchors <strong>of</strong> the PC steel wire<br />
subject to c<strong>on</strong>centrated stress<br />
Element No.: 19407 (plate)<br />
Coord<strong>in</strong>ates: (1514, 2361, 290)<br />
Between the elastic l<strong>in</strong>ks where stress flows<br />
smoothly and not c<strong>on</strong>centrated<br />
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Comb<strong>in</strong>ati<strong>on</strong> method<br />
Table 5 Stress <strong>in</strong>side the steel pier shell.<br />
C<strong>on</strong>crete <strong>in</strong> the steel pier<br />
shell<br />
Rear plate<br />
PBL <strong>in</strong> the steel pier shell<br />
Fully synthesized model -0.698 MPa 4.577 Mpa 16.823 Mpa<br />
Partially synthesized<br />
-0.630 MPa 3.966 MPa 14.676 MPa<br />
model<br />
Difference Approx. 10.7% Approx. 3.5% Approx. 8.9%<br />
The po<strong>in</strong>ts where local stress c<strong>on</strong>centrati<strong>on</strong> may occur due to the geometrical shape or characteristics <strong>of</strong> the<br />
structural analysis were excluded, and the representative elements <strong>of</strong> the rear plates, fill<strong>in</strong>g c<strong>on</strong>crete part,<br />
perforb<strong>on</strong>d rib parts were presented <strong>in</strong> Table 4. Table 5 presents the results <strong>of</strong> the structural analysis compar<strong>in</strong>g<br />
the average stresses <strong>of</strong> the parts.<br />
The result <strong>of</strong> the structural analysis showed that the stress <strong>of</strong> the fully composite model was somewhat greater<br />
than that <strong>of</strong> the partially composite model. The stress reduc<strong>in</strong>g ratios <strong>of</strong> the latter compare with the former were<br />
10.7%, 3.5%, and 8.9% at the c<strong>on</strong>crete part, rear plate, and perforb<strong>on</strong>d rib part, respectively. The reas<strong>on</strong> <strong>of</strong><br />
which was thoght to be the f<strong>in</strong>ite stiffness <strong>of</strong> the partially composite model compared to the fully composite<br />
model hav<strong>in</strong>g <strong>in</strong>f<strong>in</strong>ite stiffness, and the effect <strong>of</strong> perforb<strong>on</strong>d rib was implemented through the structural<br />
analysis <strong>of</strong> the present study. When the effect <strong>of</strong> perforb<strong>on</strong>d rib was applied, the change <strong>of</strong> the stress <strong>in</strong> the<br />
fill<strong>in</strong>g c<strong>on</strong>crete <strong>in</strong> the steel shell was the greatest, while that <strong>in</strong> the rear plate was the smallest. This was thought<br />
to be because <strong>of</strong> the <strong>in</strong>direct effect through the c<strong>on</strong>crete part, different from the c<strong>on</strong>crete part and the perforb<strong>on</strong>d<br />
rib part applied to elastic l<strong>in</strong>k directly.<br />
b) Load transfer <strong>in</strong> the c<strong>on</strong>nector element<br />
The c<strong>on</strong>necti<strong>on</strong> part should be designed with a structure that can transfer stress smoothly for the secti<strong>on</strong><br />
forces applied <strong>on</strong> the c<strong>on</strong>necti<strong>on</strong> faces <strong>of</strong> the steel girder and PC girder which have different stiffness. In this<br />
study, the fill<strong>in</strong>g c<strong>on</strong>crete rear bear<strong>in</strong>g pate was adopted due to wide applicati<strong>on</strong> and provides smooth stress<br />
transfer s<strong>in</strong>ce fill<strong>in</strong>g c<strong>on</strong>crete and PC girder are c<strong>on</strong>nected. The dom<strong>in</strong>ant secti<strong>on</strong> forces <strong>of</strong> the Shiotsubo<br />
<strong>Bridge</strong> are bend<strong>in</strong>g moment and shear force, due to the c<strong>on</strong>t<strong>in</strong>uous girder structure <strong>of</strong> the bridge. In this secti<strong>on</strong>,<br />
the structural analysis was c<strong>on</strong>ducted us<strong>in</strong>g the c<strong>on</strong>diti<strong>on</strong>s (analysis model, applied loads) <strong>of</strong> secti<strong>on</strong> a) to<br />
analyse behavioral characteristics through the distributi<strong>on</strong> <strong>of</strong> the shear force and axial force <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong><br />
elements <strong>in</strong> the steel shell.<br />
At the c<strong>on</strong>necti<strong>on</strong> part, load is transferred to c<strong>on</strong>crete through the bear<strong>in</strong>g plate and shear c<strong>on</strong>nector. Fig. 12<br />
shows the l<strong>on</strong>gitud<strong>in</strong>al distributi<strong>on</strong> <strong>of</strong> the shear force applied to perforb<strong>on</strong>d rib.<br />
(a) PBL <strong>in</strong> the steel pier shell.<br />
(b) Shear force distributi<strong>on</strong> <strong>of</strong> the upper PBL <strong>of</strong> upper flange.<br />
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(c) Shear force distributi<strong>on</strong> <strong>in</strong> the PBL <strong>of</strong> upper/lower flanges. (d) Shear force distributi<strong>on</strong> <strong>in</strong> the PBL web.<br />
Fig.13 Shear force distributi<strong>on</strong> <strong>in</strong> l<strong>on</strong>gitud<strong>in</strong>al directi<strong>on</strong> <strong>in</strong> perforb<strong>on</strong>d rib.<br />
Fig. 13(a) shows the positi<strong>on</strong> <strong>of</strong> the perforb<strong>on</strong>d rib <strong>in</strong> the steel shell, which were numbered from to . The<br />
perforb<strong>on</strong>d ribs <strong>in</strong> Fig. 13(b) ( ~ ) were located <strong>on</strong> top <strong>of</strong> the steel shell, symmetrical to the center l<strong>in</strong>e <strong>of</strong><br />
the cross-secti<strong>on</strong>. As shown <strong>in</strong> the graph, the perforb<strong>on</strong>d ribs located almost symmetrically show similar distributi<strong>on</strong><br />
<strong>of</strong> shear forces. The greatest shear force was approximately 19 kN at the beg<strong>in</strong>n<strong>in</strong>g po<strong>in</strong>t <strong>of</strong> the and<br />
<strong>of</strong> perforb<strong>on</strong>d ribs, which was thought to be the result <strong>of</strong> the shear delay effect by the steel webs <strong>on</strong> both<br />
sides.<br />
The graphs <strong>in</strong> Fig. 13(c) compare the distributi<strong>on</strong> <strong>of</strong> the shear forces <strong>in</strong> the perforb<strong>on</strong>d ribs <strong>of</strong> the upper and<br />
lower flanges, where, ~ were <strong>on</strong> the upper flange and ~ were <strong>on</strong> the lower flange. The distributi<strong>on</strong>s <strong>of</strong><br />
the perforb<strong>on</strong>d ribs <strong>on</strong> the l<strong>in</strong>es vertical to the l<strong>on</strong>gitud<strong>in</strong>al axis show similar trends but <strong>in</strong> the opposite directi<strong>on</strong>s.<br />
The forces <strong>of</strong> the perforb<strong>on</strong>d rib <strong>on</strong> the upper flange showed positive (+) directi<strong>on</strong>, which agrees with the<br />
behavior <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> located <strong>in</strong> the negative moment secti<strong>on</strong>.<br />
The graph <strong>of</strong> Fig. 13(d) shows the stress distributi<strong>on</strong> <strong>of</strong> the perforb<strong>on</strong>d rib <strong>of</strong> web. While <strong>of</strong> perforb<strong>on</strong>d rib<br />
was <strong>in</strong> positive (+) directi<strong>on</strong> with a magnitude <strong>of</strong> almost zero, and the shear forces <strong>of</strong> the and <strong>of</strong> perforb<strong>on</strong>d<br />
rib were the greatest by -50.9 kN. Therefore, it was judged that the shear force <strong>of</strong> the perforb<strong>on</strong>d rib <strong>of</strong><br />
web is <strong>in</strong> the negative (-) directi<strong>on</strong>.<br />
Fig.14 Def<strong>in</strong>iti<strong>on</strong> <strong>of</strong> the cross-secti<strong>on</strong>s <strong>of</strong> steel pier shell.<br />
Three cross-secti<strong>on</strong>s were def<strong>in</strong>es as shown <strong>in</strong> Fig. 14, to <strong>in</strong>vestigate the distributi<strong>on</strong> <strong>of</strong> the axial forces <strong>in</strong> the<br />
upper/lower flanges and webs <strong>of</strong> the steel shell. No. 1 and No. 3 <strong>of</strong> cross-secti<strong>on</strong>s were at the ends <strong>of</strong> the steel<br />
shell and No. 2 was located at the center <strong>of</strong> the steel shell.<br />
Fig. 15 shows the distributi<strong>on</strong> <strong>of</strong> the axial forces <strong>of</strong> the cross-secti<strong>on</strong>s at various positi<strong>on</strong>s <strong>of</strong> the flange. The<br />
axial forces were based <strong>on</strong> the c<strong>on</strong>cept <strong>of</strong> representative forces which were the products <strong>of</strong> the average<br />
cross-secti<strong>on</strong> (3198 ) and average stress.<br />
The axial forces <strong>of</strong> the upper flange <strong>in</strong> the No. 1, No. 2, and No. 3 <strong>of</strong> cross-secti<strong>on</strong>s were 64.4 kN. 10.6 kN,<br />
and 5.8 kN, respectively. In the similar manner, those <strong>in</strong> the lower flange were (-)77.9 kN, (-)66.6 kN, and<br />
(-)37.4 kN, respectively. The distributi<strong>on</strong> shows the trend <strong>of</strong> decrease from No. 1 to No. 3<strong>of</strong> cross-secti<strong>on</strong>s. It<br />
was judged that, regard<strong>in</strong>g the force <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong>, the load transferred from the steel girder to the flange is<br />
transferred to the perforb<strong>on</strong>d rib and to c<strong>on</strong>crete.<br />
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Fig.15 Axial force distributi<strong>on</strong> <strong>of</strong> the<br />
cross-secti<strong>on</strong>s <strong>of</strong> the flange.<br />
Fig.16 Axial force distributi<strong>on</strong> <strong>of</strong> the<br />
cross-secti<strong>on</strong>s <strong>of</strong> the c<strong>on</strong>crete.<br />
Fig. 16 show the distributi<strong>on</strong> <strong>of</strong> the secti<strong>on</strong> force <strong>of</strong> the c<strong>on</strong>crete <strong>on</strong> the checked cross-secti<strong>on</strong>. The axial<br />
forces <strong>on</strong> the No. 1 close to the steel girder was 8.9 kN, No. 2 at the center <strong>of</strong> the steel shell was 9.36 kN, and<br />
the No. 3 close to the PSC girder was 9.56 kN, show<strong>in</strong>g a trend <strong>of</strong> <strong>in</strong>crease from No. 1 to No. 3 cross-secti<strong>on</strong>,<br />
opposite from the trend <strong>in</strong> the flange. It was judged that the load born by the c<strong>on</strong>crete part <strong>in</strong>creased as the axial<br />
force <strong>in</strong> the flange decreased.<br />
4. CONCLUSION<br />
The behavioral characteristics <strong>of</strong> the Shiotsubo <strong>Bridge</strong>, Japan, was analyzed by full-system analysis and<br />
detailed structural analysis to <strong>in</strong>vestigate the applicability <strong>of</strong> mixed girders <strong>in</strong> steel box girder bridges. For the<br />
optimal design <strong>of</strong> the c<strong>on</strong>necti<strong>on</strong>s part which are the most important parts <strong>of</strong> mixed girder bridges, the behaviors<br />
<strong>of</strong> the c<strong>on</strong>necti<strong>on</strong> elements were analyzed from the changes <strong>of</strong> the elements. The transiti<strong>on</strong> <strong>of</strong> the axial<br />
forces and shear forces <strong>in</strong> steel pier shell were analyzed to <strong>in</strong>vestigate the load transfer mechanism.<br />
The c<strong>on</strong>clusi<strong>on</strong> obta<strong>in</strong>ed from the study is summarized as follows;<br />
(1) The results <strong>of</strong> the structural analyses <strong>of</strong> the rigid model shar<strong>in</strong>g nodes and the model us<strong>in</strong>g l<strong>in</strong>ear elastic<br />
l<strong>in</strong>ks were compared to implement the effect <strong>of</strong> partial synthesis. The result <strong>of</strong> the structural analysis showed<br />
that the fully synthesized model provides somewhat higher stress than that <strong>of</strong> partially synthesized model,<br />
which was thought to be caused by the stiffness value <strong>of</strong> the partially synthesized model compared with that <strong>of</strong><br />
the fully synthesized model which had <strong>in</strong>f<strong>in</strong>ite stiffness. It could be judged that PBL effect was implemented<br />
by the structural analysis program <strong>of</strong> the present study.<br />
(2) The behavioral characteristics <strong>of</strong> the steel pier shell were analyzed by def<strong>in</strong><strong>in</strong>g the target PBL po<strong>in</strong>ts and<br />
the cross-secti<strong>on</strong> <strong>in</strong> the c<strong>on</strong>necti<strong>on</strong> elements <strong>of</strong> the steel pier shell and compar<strong>in</strong>g the distributi<strong>on</strong>s <strong>of</strong> shear<br />
forces and axial forces. It could be judged that the load transmitted from the steel girder to the flange was<br />
transferred to the PBL and then to the c<strong>on</strong>crete <strong>in</strong> the steel pier shell.<br />
REFERENCES<br />
1) G.H.Kang, : Experimental study <strong>on</strong> behavior <strong>of</strong> perfob<strong>on</strong>d rib shear c<strong>on</strong>nectors : Y<strong>on</strong>sei University(2006).<br />
2) C<strong>on</strong>structi<strong>on</strong> Eng<strong>in</strong>eer<strong>in</strong>g Institute. : Report <strong>on</strong> the c<strong>on</strong>necti<strong>on</strong> behavior analysis and safety analysis <strong>of</strong> hybrid bridges : Y<strong>on</strong>sei<br />
University (2004).<br />
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