Keywords: bridges, grillage method, dynamic load, road roughness, suspension, truck, girder.

The dynamic load on a bridge structure could be a significant component of the imposed loads and it should be assessed accurately in the design and evaluation process. Most of the existing bridges built in the United States are designed according to the Standard American Association of State Highway Transportation Officials (AASHTO) [1] bridge design specification, where the design load was based on the HS20-44 truck model (a 3-axle, 20-ton truck, adopted in 1944). Due to the increase in intensity of heavy truck traffic and to changes in truck configurations since the adoption of the AASHTO model more than 55 years ago, it has become essential to determine the actual dynamic component of the live loads on existing bridges. Moreover, the identification of dynamic load spectra for girder-type bridges is critical for evaluation, rehabilitation and maintenance of under-capacity deficient structures. Field tests and computer simulations are used to determine the dynamic behavior of a bridge under moving vehicles. Advancements in computer technology render computer simulations as a viable, effective and economical method of evaluating bridge-vehicle interactions. However, to ensure their validity, computer simulation models need to be verified before release and implementation with confidence. Thus, comparison of simulation results with experimental data is an accepted means of verification, which is pursued for the proposed model.

In this paper, a three-dimensional (3-D) dynamic model for bridge-road-vehicle interaction system is presented. Slab-on-girder bridges are modeled using a grillage system subjected to multiple moving truckloads. Multi-axle trucks are idealized using a 3-D vehicle model with nonlinear tire-suspension system, having eleven independent degrees of freedom (DOF). Road roughness profiles are generated from random Gaussian Process as well as limited measurements of actual road profiles. Truck wheel loads are applied at any point and then transferred to nodes as equivalent nodal forces. The Newmark- integration method [2] is applied as a numerical algorithm for solving the bridge-road-vehicle interaction equations. A computer program has been developed for this 3-D dynamic model.

The bridge model is based on the grillage method and represents single- as well as multiple continuous span bridges. The grillage model regards the bridge as an assemblage of one-dimensional beams, which are subjected to loads acting in the direction perpendicular to the plane of the assembly. The bridge consists of a set of steel I-girders and a composite reinforced concrete deck slab. Unlike a plane frame, this assemblage of beams incorporates the beam torsional stiffness. For a slab-on- girder bridge, the girders span longitudinally between abutments, with a composite deck spanning transversely across the top of the girders. The longitudinal grillage members are placed coincident with the center lines of bridge girders, while the bridge slab is divided into equivalent transverse beams. The section properties of the longitudinal grillage members are calculated in a manner similar that of composite T-beams.

The vehicle model considered in this study simulates multi-axles trucks, which are assumed to be composed of three components: 1) tire, 2) suspension and 3) truck body. For a 5-axle truck, five rigid masses represent the tractor, semi-trailer, and three tire-axle sets (i.e. front, middle and rear axles). The tractor and semi-trailer are each assigned three DOFs, corresponding to the vertical displacement, pitching rotation about the transverse axis and twisting rotation about the longitudinal axis. The tractor and semi-trailer are interconnected at the pivot point.

Results of the computer-based model analysis, performed on actual slab-on-girder composite bridges with various spans, ranging from 9 to 24 m (30 to 80 ft.), are presented. A parametric study is generated to study the effect of various types of parameters. The major parameters affecting the bridge dynamic response (or the Dynamic Load Factor (DLF)) include road roughness, truck weight, speed and mechanical properties of the tire-suspension system and bridge stiffness and boundary conditions. Results from a 2-D dynamic model are compared with those from the current 3-D model. Results show that the dynamic load factor is highly dependent on road roughness, vehicle suspension, and bridge geometry.

1

AASHTO, "Standard Specifications for Highway Bridges", American Association State Highway and Transportation Officials, Washington, D.C, 1998.

2

Newmark, N.M., "A Method of Computation for Structural Dynamics", American Society of Civil Engineering Journal of Engineering Mechanics, Volume 85, pp. 67-94, 1959.

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