Dr. Willard H. (Bill) Wattenburg

February 28, 1995
W. H. Wattenburg, D. B. McCallen, R. C. Murray

Abstract: A new modular multi-lane steel freeway bridge is constructed from surplus railroad flatcar decks. It can be erected on site in a few days' time. It has been built and static load tested for emergency freeway bridge repair. This inexpensive modular bridge may also have broad application around the world for low-cost bridges in areas where funds are limited. We have performed an extensive computer dynamic analysis which indicates that this simple modular design is as strong and dynamically stable as many contemporary freeway bridges, and, when used for emergency repairs, it can withstand severe aftershocks expected immediately after a major earthquake.

A new modular steel, multi-lane freeway bridge was constructed and evaluted in March 1994 by the California Department of Transportation (Caltrans) as a temporary bridge for emergency freeway repair. To our knowledge, this is the first multi-lane modular bridge design of this size that can be erected on-site within a few days' time without extensive site preparation or ground disturbance to restore traffic over damaged freeway sections such as those that collapsed in the 1994 Northridge earthquake and the recent earthquake in Japan. Because of its potential importance for emergency response and other infrastructure uses described herein, we independently performed a computer dynamic analysis of a model of the bridge at the Lawrence Livermore National Laboratory to determine its earthquake response characteristics.

The modular bridge design first proposed by Wattenburg and constructed by Caltrans is shown in the photo of Figure 1. The as-built modular bridge uses only one standard structural module, inexpensive surplus railroad flatcar decks. However, structurally equivalent modules can be constructed from ordinary steel I-beams. This design is unique because it has its own base support for the column structures (bents) and it requires only simple steel fasteners. This modular bridge is relatively low cost compared to standard steel truss and prestressed concrete freeway bridges of equal strength which cost three to five times as much and require months to construct.

The Modular Bridge Design: The modular bridge constructed by Caltrans is shown in Fig 2. The individual 10 ft. wide by 53 ft. long flatcar modules (Fig. 2a) are massive steel frame structures which are designed to carry loads of up to 50 tons. The flatcar modules are coupled together in interlocked fashion such that the module connections emulate pinned joints (Fig. 2b). The 50 ft. wide roadway deck of the assembled bridge consists of four flatcars side by side which span 53 ft. between two vertical piers (Fig. 2c). The piers are constructed with a single flatcar in the horizontal direction (on top) supported by two half-flatcar vertical columns. The pier structure provides its own foundation with a horizontally placed flatcar on the ground at the foot of each pier. In the transverse direction, two diagonal steel braces are added to provide stability and stiffness to the assembled pier structure. Strong surplus boxcar center beams are used for the diagonal braces. In the longitudinal direction, the underside of the bridge is left open without obstruction to allow for passage of traffic from cross streets or railroads spanned by the bridge.

Vertical steel cables are used to constrain the top and bottom horizontal modules of the piers so that the vertical columns between them cannot come out of their joint sockets in the horizontal modules. The four adjoining flatcars on the top which form the bridge roadway are coupled together side by side by inserting simple U-bolt brackets into matching stake slots on the sides of each flatcar deck (Fig. 2).

Ten surplus railroad flatcars were required for the bridge shown in Fig 4. The Caltrans prototype was erected in ten days by a construction crew of four, utilizing one 50,000 lb. capacity crane. As suggested by Abolhassan Asteneh-Asl, Professor of Civil Engineering at the University of California at Berkeley, the interconnection of the flatcars was accomplished in "Lego-block" fashion to minimize the need for special brackets and to reduce assembly time. The ends of the vertical column flatcar modules are cut in a configuration such that their beam ends project into and around the support beams of the horizontal modules above and below.

Caltrans tested the as-built modular bridge with a static load of 110 tons at center span. The observed vertical deflection of the bridge deck was only 1/8 inch under this heavy loading. We decided to analyze the stand-alone, 53 ft. long bridge section shown in figure 2 for its ability to withstand significant seismic ground motion, in particular, earthquake aftershocks. Reasenberg and Jones (3,4,5) have studied the aftershock sequences from a number of California earthquakes and the hazard associated with earthquake aftershocks. In the first week after the main event there is a 58% chance of a large aftershock and a 10% chance of an even larger event. If a temporary bridge is immediately erected to replace a damaged bridge, say on the first day or two following an earthquake, it is quite likely that it will be subjected to a significant aftershock within the first week.

The Computer Model: We constructed a finite element model of this modular bridge as shown in Fig. 4. The finite element model discretizes the structure into a number of small, or "finite", elements and the stiffness behavior of each element is mathematically defined. By appropriate summation of the elements to form the overall structure, a system of coupled simultaneous equations are formed which, when solved, provide a time history of the displacements, velocities and accelerations of the structure. Forces and stresses in the individual structural elements are then obtained from the displacements. For the finite element model shown in Fig. 4, the system of equations defining the dynamic motion of the structure contained 7080 equations.

To ensure that the ground motion used in the seismic analysis of the modular bridge was representative of a severe aftershock, we applied the measured ground motion from the April 1992 Petrolia-Cape Mendocino earthquake. The records were obtained from the California Division of Mines and Geology strong motion instrumentation array at the Painter Street Overcrossing site in Rio Dell, California (6). The north-south component of motion at this site was quite strong with maximum accelerations equal of 0.55 times the acceleration of gravity. It was felt these records would be representative of a ground motion from a strong aftershock at close proximity to an earthquake epicenter. We applied simultaneous three component motion to the bridge model where both horizontal components of motion are defined by the north-south component of the Petrolia earthquake record.

In typical bridge structures, the bridge deck is supported by the abutments when the bridge deck starts to rock back and forth during seismic shaking. However, this bridge used as a temporary freeway bridge typically will not have strong abutment support during the time that it is being erected, and it will likely be loosely coupled to existing freeway structures for some time after erection. Thus, this temporary bridge must be self-sufficient in its ability to withstand the forces generated by earthquake ground motion. To reflect this in the computer simulation, the bridge model in Fig. 4 was assumed to stand alone and the base of the pier columns were assumed to behave as pin connections.

In our model, the bridge behaves as a truss structure in the lateral direction because of the diagonal braces in each bent (column structure) as shown in Fig. 4. Because traffic must flow under the bridge, diagonal bracing is not employed in the longitudinal direction between the bents. Thus, the structure acts as a frame in the longitudinal direction with stiffness provided by bending of the bent columns. In addition to the weight of the structure, a weight of 35 tons was added to the deck to account for the potential weight of vehicles and decking material. To reflect the as-built condition of the Caltrans bridge, the connections of all structural members were assumed to be pin connections. For analysis purposes, the damping of the structure was assumed to be 5% critical damping in the first few modes of vibration.

The computer simulation of the seismic response of the bridge structure consisted of a direct integration time history solution in which the response of the structure was calculated every 0.02 seconds of the twenty-second earthquake record for a total of 1000 time steps. The actual computation was performed with the NIKE3D (7) finite element program on a CRAY YMP computer.

Dynamic Analysis Results. The seismic response of the bridge section at a selected instant of time is shown in Fig. 4 (displacements amplified by 100) along with the acceleration time history at the top of the structure. With the diagonal bracing, the structure is quite stiff in the transverse direction and there is little amplification of the ground motion at the deck level. In the longitudinal direction the accelerations at the top of the structure are over 1g. Thus significant amplification of the ground motion occurred. However, a check of member stresses from the seismic analysis indicated that the stress levels in the massive steel members were well below allowable yield stresses (i.e. the stress level at which permanent deformation of the material commences), and the stresses were also below allowable values given in standard design guides. While this analysis did not address the integrity of the structural joints, the computer simulation does indicate that the main structural members have adequate strength to ensure the structure will not fail under significant earthquake ground motion. Caltrans has determined that the module joints formed by interlaced beams (Fig. 2) as used in their modular bridge will support the development of the full strength of the structural modules.

Previous computer simulation work with existing short-span overcrossings (8) allowed a comparision of the dynamic characteristics of this modular bridge with an actual short-span bridge. Figure 6 shows the computed natural modeshapes of a typical permanent bridge, the Painter Street Overcrossing in Rio Dell, California, and the transverse and longitudinal modes of the modular bridge structure. The frequencies of the modular bridge are in the same frequency range as the frequencies of the simple overcrossing. Thus the fundamental dynamic characteristics of the stand-alone modular bridge section are not unlike the dynamic characteristics of typical permanent bridge structures.

Both the measured and computed transverse deck accelerations for the Painter Street Overcrossing in the 1992 Petrolia-Cape Mendocino earthquake were on the order of 1g. This is close to the computed accelerations for the modular bridge (see Fig. 4). The primary difference between the dynamic responses is that the stand-alone modular bridge, not attached to embankments, tends to vibrate longer because it has less inherent damping than the Painter Street bridge. The typical permanent bridge benefits from high damping as a result of energy dissipation in the approach embankment soils to which it is attached.

The designer of this modular bridge was inspired by the realization that surplus flatcars are an abundant source of strong steel modules with structural features that allow easy connection of these modules to make a modular bridge. The computer model we have analyzed herein uses simplified structural modules that represent only the main beams and cross supports found in the typical flatcar design. Secondary structural components that add even more strength to the flatcar were omitted in our model. The simple modules in our model can easily be built out of standard I-beam material (e.g. surplus steel I-beams) should an agency want to build this bridge without use of flatcars.

Summary: Our dynamic analysis indicates that a stand-alone section of this modular bridge can withstand strong ground motion expected after a major earthquake. This modular design provides a relatively safe temporary freeway bridge which can be erected quickly after an earthquake. This could substantially enhance the post-earthquake response of transportation agencies. The static and dynamic test results indicate that this inexpensive modular bridge could also be used for permanent bridges in many areas where funds are not available for bridges of current design. Modular steel bridge structures in general could capitalize on the economies of design and construction available from mass production of bridge components. The concept of prefabrication has become ingrained in the process of building construction in the United States and extension to the bridge community seems inevitable. Professor Astaneh-Asi of U. C. Berkeley has recently proposed a modular steel permanent bridge concept (9) which would employ interconnection of modular steel bridge segments for essentially the entire bridge.

Many underdeveloped countries lack critical transportation facilities. There is a large amount of surplus steel I-beam material in the world that they could use to build this modular bridge if surplus flatcars are not available. Surplus steel beams are usually as structurally strong as new material. Building steel modules adequate for this bridge design requires little skill other than cutting and welding the steel beams together. Underdeveloped countries could build versions of this modular bridge to provide vital transportation for their people long before they can afford the elegantly designed prestressed concrete or steel truss bridges to which we are accustomed in developed nations. Furthermore, this modular bridge can be erected and/or relocated relatively easily by communities that do not have extensive bridge design and construction capability.