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1、Finite Elements in Analysis and Design 42 (2006) 950–959www.elsevier.com/locate/finelReviewFinite element analysis of vehicle–bridge interactionLeslaw Kwasniewskia,?, Hongyi Lib, Jerry Wekezerb, Jerzy MalachowskicaWarsaw
2、 University of Technology, Al. Armii Ludowej 16, 00-637 Warszawa, Poland bFlorida A received in revised form 21 January 2006; accepted 21 January 2006 Available online 13 March 2006AbstractThis paper presents results of
3、the finite element (FE) analysis of dynamic interaction between a heavy truck and a selected highway bridge on US 90 in Florida. FE analysis of vehicle–bridge interaction was conducted using commercial program LS-DYNA an
4、d the super computer at the Florida State University. Development and implementation of a detailed FE truck model with 3D suspension systems, pneumatic and rotating wheels, appropriate contact algorithms, allowed for rea
5、listic representation of the actual vehicle dynamic loading. Several static and dynamic field tests were performed on the same bridge. The experimental data was used for validation of the FE models of the bridge and the
6、truck. Numerical results were found to match well with the experimental data. Results presented in the paper demonstrate a significant potential of using computational mechanics and LS-DYNA code for thorough investigatio
7、n of the vehicle–bridge interaction, dynamic impact factors, and the ultimate loading of bridges. ? 2006 Elsevier B.V. All rights reserved.Keywords: Vehicle–bridge interaction; Impact factor; Bridge dynamics; Finite elem
8、ent analysis; Computer simulation; LS-DYNAContents1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950 2. Description of the modeled bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 951 3. Field test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952 4. Development of FE bridge model . . . . . . . . . . . . . . . . . . . .
12、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9524.1. FE model of the truck . . . . . . . . . . . . . . .
13、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9535. Validation of FE models . . . . .
14、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954 6. Numeri
15、cal and experimental analysis of vehicle–bridge interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954 7. Summary an
16、d conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17、. . . . 957 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18、 . . . . . . . . . . . . . . . . . . . . 958 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9581. IntroductionNonlinear finite element (FE) methods are nowadays commonly used to solve engineering problems. One such? Corresponding
20、author. Tel.: +48 227519552; fax: +48 228256532. E-mail addresses: l.kwasniewski@il.pw.edu.pl (L. Kwasniewski),lihongy@eng.fsu.edu (H. Li), wekezer@eng.fsu.edu (J. Wekezer),malachowski@wme.wat.edu.pl (J. Malachowski).016
21、8-874X/$ - see front matter ? 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.finel.2006.01.014engineering area is the efficient management of highway fa- cilities, especially bridges, where the knowledge of actual
22、 dy- namic load effects, load carrying capacity, and current condi- tion is critical in making management decisions and in estab- lishing permissible weight limits. Significant dynamic effects can be triggered by increas
23、ingly heavier vehicles, which are now used on our highways [1,2].Additional dynamic effects are accounted for by dynamic impact factors introduced in bridge design codes. The impact factor IM [13], also referred to as952
24、 L. Kwasniewski et al. / Finite Elements in Analysis and Design 42 (2006) 950–959Truckon east boundSouth North1.075 m1 2 3 45 x 2.400 m =12.000 m5 61.075 m0.62 m 0.62 m 0.62 m 0.62 m 0.7 m 0.7 m2.500 m 2.500 mTruckon wes
25、t boundFig. 2. Bridge cross section and truck positions during field experiments.3. Field testStatic and dynamic tests were conducted on the bridge. Two trucks loaded with 12 concrete blocks each (Fig. 5) were used for l
26、oading. The front, drive, and rear axle loads were 50 kN (11.24 kip), 100 kN (22.48 kip) and 169 kN (38.0 kip), respec- tively. The total weight was approximately 319 kN (71.7 kip), which is close to the 325 kN (73.1 kip
27、) as specified byAASHTO standard specifications for the HS 20–44 truck [13]. The static test results were used to determine the wheel load distribution factors for girders and as reference data for calcu- lation of impac
28、t factors. The longitudinal truck position was determined to yield the maximum stresses at the middle sec- tion of the first span. The dynamic tests included passes of one and two trucks side-by-side, with and without a
29、piece of wood positioned across the deck. A wooden plank, 40 mm (1.57 in) thick and 400 mm (15.7 in) wide was placed across the middle section of the east span to simulate major deterioration of the deck surface. Moreove
30、r, it was expected that the plank would help excite dominant flexural modes corresponding to low fre- quencies [16]. Two truck speeds were used: medium—48 km/h (30 mph) and high-speed—80 km/h (50 mph). The east span and
31、the middle span were instrumented for all tests (Fig. 1). Displacement, strain, and acceleration data were collected at the selected points where the bridge response was expected to be well represented. Additionally, fou
32、r accelerom- eters were placed on one of the vehicles to provide data for validation of the truck model. More details of the test data and experimental results are presented in [17].4. Development of FE bridge modelThe F
33、E model of one span includes all five structural com- ponents: the slab, six beams, bridge barriers, diaphragms, and neoprene pads. Fig. 3 shows a cut-away segment of the FE model for one span. Concrete parts of the brid
34、ge are built of fully integrated solid elements with eight or six nodes. All re-Fig. 3. A cut-away section of the FE bridge model.bars and strands are modeled using 1D bar elements with nodes coinciding with correspondin
35、g nodes of the solid elements. The locations of some rebars in the FE model were slightly re- aligned whenever necessary to fit into geometric FE mesh of the bridge. Neoprene pads are represented by 3D solid elements wit
36、h viscoelastic material properties [18]. Dimensions of ele- ments in the bridge model were optimized considering the lo- cation of the reinforcement, requirements for tire-deck contact algorithm, integration time step [1
37、8] and total number of FE elements. Each girder has 24 No.13 1860 MPa low-relaxation straight strands at the bottom flange. The mesh size requirement makes it unable to model individually all 24 strands; therefore sev- e
38、ral strands were lumped together to represent the correct stiff- ness of the girder cross section. A special LS-DYNA material model called “cable” [18] was applied to introduce prestressing forces in the rod elements. Th
39、is material model allowed for in- troduction of initial tensile force by defining appropriate initial elongation. The prestress model appears to be critical when the bridge girders are loaded up to failure. Over 204,000
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