5.2.1 Reviews of steel bridge modeling
Steel through-truss bridges are conventionally idealized as statically determinate structures, and the truss connections of such bridges are commonly idealized as pin-ended. However, these bridges are instead highly indeterminate, and their gusset plates, rivets, fasteners, and bolts allow the moments to transfer through the rigid joints (Liu et al. 2013). Many researchers have stated that the correlations between experimental responses and the responses of nonlinear finite element models that use beam elements have confirmed that the rigid frame behavior of steel trusses governs their inelastic behavior (Frangopol and Nakib 1989; Lee et al. 1991; Nagavi and Aktan 2003).
Nagavi and Aktan (2003) conducted a sensitivity study to establish the most critical parameters that govern the nonlinear behavior of a Pratt truss bridge (located in Franklin County, Ohio) and to simulate the most accurate nonlinear bridge models. The authors noticed that the trusses of such bridge deformed in a way similar to a frame with rigid joints and it could be considered a Vierendeel truss with diagonals. This category of trusses is usually considered to exhibit highly indeterminate structural behavior. In addition, they made comparisons between the structural behavior of three-dimensional (3D) models constructed using different combinations of finite elements, and destructive field test results for a through-truss bridge with riveted gusset plates. Models constructed using only truss elements representing all of the structural elements of the bridge produced a structural behavior that differed considerably from the field test results. On the contrary, the behavior of the 3D model constructed with beam elements and rigid joints was closer to the observed experimental responses. Therefore, they concluded that when constructing more accurate finite element steel bridge models, truss members should be modeled rigidly connected to the truss joints.
5.2.2 Finite element modeling
A finite element model of the Guo-Fang Bridge was developed to study the bridge’s behavior under substained loading. Figure 5.4 shows a typical 3D model created using Abaqus software (version 6.14), which considered material and geometric nonlinearities in the analysis. The geometry and material properties for 3D bridge models were chosen using engineering design and construction drawings and included two main trusses, upper and lower lateral bracings, floor beams, and stringers.
The bridge model comprised of 7,791 nodes. The total number of degrees of freedom amounted to 34,961, and the meshes of the floor system (i.e., longitudinal stringers and lateral floor beams), diagonal webs, and verticals were modeled using the three-node Timoshenko open-section beam elements (B32OS), with two Gauss points per element representing the open section characteristics. The top and bottom chords and the end posts were modeled using 3D linear three-node beam elements (B32). In addition, the upper floor beams close to both ends were modeled with B32 elements, while the remaining upper floor beams were modeled with B32OS elements. Both the B32OS and B32 3D elements used integration at 13 Gauss points, where five were equally separated in each flange and three were symmetrically arranged along the height of the web. According to previous studies, it should also be noted that the joints connecting the upper and lower floor systems and the two main truss members were modeled with rigid constraints, accounting for the section overlapping of the beam elements.
The weight of the concrete deck was considered, but any composite action between the concrete slab and the steel superstructure was neglected, and the equivalent weight of the concrete slab was equally distributed on the longitudinal stringers across the floor beams.
5.2.2.1 Boundary conditions
It is common to make the simple assumption that the supports have fixed, pinned (hinge), or roller boundary conditions without accounting for the soil or foundation stiffness. These issues will be addressed in the last chapter of this thesis. The boundary conditions of the Guo-Fang Bridge finite element model follow AASHTO specifications (AASHTO 2012). The hinge boundary is assumed at one end (i.e., restrained in three translational directions) while the roller boundary is modeled for the other end of the bridge (i.e., the vertical and lateral movements are constrained and only the longitudinal motion is allowed).
5.2.2.2 Load types
As for the case of the pedestrian bridge, two load types were considered: (1) the dead load, and (2) the live (e.g. traffic) load. These were then implemented on the bridge model with the same procedure followed for the pedestrian bridge.
Dead load
The through-truss bridge total dead load (DL) consisted of the self-weight of the steel structure and concrete slab and the superimposed dead load (SDL) representing non-structural dead loads that remain permanently on the structure. The total DL after original construction was estimated accounting for (1) the self-weight of the steel structure (7,938 kN) and the weight of the concrete slab (8,540 kN), (2) the weight of asphalt concrete (AC), ground rail, and add-ons (3676 kN), and (3) an additional estimated overall SDL, consisted of the parapets and sidewalks (636 kN) corresponding to a uniform pressure load of 490 N/m2.
Live load: HS 20-44 truck
According to AASHTO LRFD Bridge Design Specifications (AASHTO 2007), a notional live load is described and used in this study. Based on the specification, a notional live load is defined as follows: “a group of vehicles routinely permitted on highways of various states.” It does not intend to represent any specific truck or illegal overloads, nor does it represent a specific short duration or special load. It allows for the combination of lane loads and design truck loads for variation of combinations. Consideration under nominal load factor is selected for the notional live load depending upon the
target limit state or load combinations. In lieu of these individual load cases, the notional load is scaled by load factors to represent a variety of cases in the LRFD bridge specification.
The standard HS 20-44 truck load was selected as live load (AASHTO 2007) for evaluating the load-carrying capacity of the bridge after damage or failure of its members. As shown in Figure 5.5, the HS 20-44 truck comprises of three axles: one 35 kN (8 kip) front axle, one 145 kN (32 kip) middle axle, and one 145 kN (32 kip) rear axle. The distance between the front and middle axles is fixed at 4.27 m (14 ft.), and the distance between the middle and rear axles varies between 4.27 m and 9.14 m (14 ft. and 30 ft.). For this study, the distance between the middle and rear axles is kept constant at 4.27 m (14 ft.).
Figure 5.5: Configuration of HS 20-44 truck (AASHTO 2007) 145 kN(32 kip) 9.14 m
4.27 m
The uniform load may be continuous or discontinuous as necessary to produce the maximum force effect (AASHTO 2014). The configuration of dead load and live load is shown in Figure 5.6.
Figure 5.6: Configuration of DL (upper) and live load (lower)