Heavily skewed bridges can be a real pain to design and build.
Once a bridge’s skew angle creeps over 45°, the challenges of analyzing, designing, detailing, and constructing the bridge increase drastically. However, there are situations where heavily skewed bridges cannot be avoided or the alternatives are no better. In urban environments, this could be due to tight right-of-way constraints, utility conflicts, railroad crossings, or stakeholder impacts. The latter two issues drove the structure layout for a pair of heavily skewed bridges in Milwaukee County, Wisconsin, constructed in 2016 and 2017 as part of the Zoo Interchange megaproject. The bridges were designed by HNTB Corp. as part of the Forward 45 joint venture with CH2M Hill [now Jacobs] and Kapur & Associates.
These two bridges carry I-94 eastbound and westbound over the Hank Aaron State Trail (HAST). The trail, named after the famous baseball player who played for the Milwaukee Braves and Brewers, runs 14 miles from the Waukesha/Milwaukee County line to Lake Michigan and is popular with pedestrians and cyclists. The trail portion running underneath the heavily skewed bridges was part of the Soo Line Railroad before the railroad abandoned it and the state of Wisconsin took over responsibility of the right-of-way to convert it to a trail. Federal law governing the transaction states that the right-of-way is subject to potential reactivation, so the trail alignment could not be substantially altered and minimal rail horizontal and vertical clearances had to be maintained. This, along with I-94 right-of-way constraints, locked the crossing into a skew angle above 60°.
A three-span layout was selected for the bridges after rejecting tunnel and single-span bridge alternatives. A tunnel seemed like a promising option for such a skewed crossing; however, a tunnel would have been about 450 ft long, since the reconstructed I-94 at this crossing provides room for six lanes in each direction plus shoulders. This would have created a cramped and claustrophobic section of an otherwise open and inviting trail. A single-span bridge would have created a similar feel and required a deeper girder section, as well as raising I-94. Another issue with the tunnel alternative was the need to reconstruct I-94 in stages to maintain traffic flow. The tunnel roof would span perpendicular to the trail, so building it in stages along such a heavy skew would be problematic, whereas with a girder structure, the girders span along the roadway alignment, making it much easier to stage construction.
The selected three-span layout provides an approximate 120-ft span over the trail with shorter approach spans. Precast prestressed concrete 54W girders were chosen for the superstructure. The westbound and eastbound bridges have plan skews of 63.2° and 64.7°, respectively. However, due to I-94’s curved alignment, individual girders have varying skews along the bridges which range from about 60° up to 69°. This makes the two bridges among the most skewed in Wisconsin. Each bridge is 95 ft wide and with such high skews, the pier and abutment lengths are more than twice the bridge width. The ratio of span length to bridge width varies from about 1.25 at the main span to 0.85 at the side spans.
Exaggerated bridge thermal movements with the traditional fixed bearing arrangement (top image) and with the mixed bearing arrangement (bottom image). The mixed bearing arrangement allows more uniform movement.
One decision facing bridge designers was what type of bearings and expansion joints to use and where to put them. Typically for a precast prestressed bridge, integral abutments are popular since there is no open joint to collect road salt and debris; however, an integral abutment simply would not work for bridges of this plan size and skew. Bridges expand and contract with temperature changes, concrete shrinks, and prestressed girders shorten over time due to creep so the bridge needs to “breathe.” The bigger the bridge, the more it needs to breathe. An integral abutment with a large skew can no longer flex about its weak axis, making it too restrictive and causing concrete crushing to relieve pent-up stresses.
Decisions about bearings and expansion joints affect the pier design as well. The piers get pulled along as the superstructure breathes by any fixed bearings that lock the pier and superstructure together. The piers also expand and contract due to temperature changes in proportion to their length. This amounts to a lot of strain for the 200-ft-long piers supporting the I-94 over the HAST bridges, especially at the ends of the pier where the movement is the greatest. These temperature strains can create uplift forces in the supporting pile foundations. Whether pile uplift is a problem or not depends on the soil.
The soil conditions at the HAST crossing did not provide much uplift capacity due to a hard gravel layer with potential boulders about 30 ft down, making it impractical to drive piles deep enough into that hard layer to provide sufficient uplift resistance. Additionally, many piles had to be pre-bored to avoid damage to various utilities, including a 96-in.-diam. storm sewer. The pre-boring effectively removes all uplift capacity, so the piers had to be designed for little to no uplift.
It was clear that a 200-ft-long pier would move too much along its length due to internal thermal forces and shrinkage, so each pier cap was designed with an expansion joint near its middle, effectively turning each pier into two piers. This allows each pier section to function independently and drastically reduces the pier movements and forces. However, the bearing types and locations had to be carefully chosen to allow the piers to move independently. Typical modern three-span prestressed precast bridges in Wisconsin have fixed diaphragms at both piers that lock the superstructure to the pier, which would have negated the benefits of the pier cap expansion joint on the HAST bridges.
Using typical fixed diaphragms or bearings at the pier would have caused another problem common to many skewed bridges. The superstructure would tend to rotate in plan view as the bridge expands and contracts. The reason for this rotation is the bridge skew and the fact that the piers are very stiff along their length, but much more flexible in their other direction. A hammerhead pier with a single square or round column does not have this problem, but a 200-ft-long pier with many columns has it in abundance. As the bridge expands or contracts, the piers are so rigid along their length that they restrict any movement in that direction. So instead the movement happens in the direction of least resistance, causing bridge rotation. This wreaks havoc with the expansion joints. One end of the joint would quickly close up, and the concrete traffic barrier plates would be pulled out of alignment and damaged.
The solution to these challenges was a mixed bearing arrangement that used fixed bearings over half of each pier and expansion bearings everywhere else. The sections of fixed bearings, on the right half of the first pier and the left half of the second pier, face each other perpendicularly across the HAST. Each pier cap’s expansion joint sits between the lines of fixed and expansion bearings. A mixed bearing arrangement is sometimes used for steel bridges but rarely for prestressed concrete. This arrangement allows the pier cap expansion joint to function and the bridge to breathe in a uniform way without significant rotation. The piers can breathe along with the superstructure since they are not dragged along in their strong direction. This reduces the pier forces and minimizes pile uplift, allowing for economical piers. The superstructure movement is reduced and controlled to the point that a standard strip seal expansion joint is feasible instead of having to explore more costly joint types.
Maximum bearing displacements (absolute values) under thermal loading from finite element models show significant displacement reductions using the mixed bearing arrangement at higher skews.
LET'S TEST THIS OUT
In May 2018, the Wisconsin Highway Research Program (WHRP) completed a two-year study on the Design and Performance of Highly Skewed Deck Girder Bridges (Project 0092-16-05), with Pinar Okumus from the University of Buffalo as the principal investigator. The main purpose of this research was to recommend design details and practices that might mitigate certain negative effects on deck and bearing elements. The study investigated the typical performance of highly skewed bridges, identified limits for simplified analysis methods, and analyzed different factors which influence the effectiveness of the mixed bearing arrangement.
The bridge was one of two structures instrumented through this study, the other was a steel girder bridge, under short-term live load conditions and long-term (12-month) temperature loading conditions. Strain gauges were cast into the reinforced concrete deck at an acute corner to measure strains from shrinkage and temperature changes. Displacement sensors and strain gauges were placed on prestressed concrete girders to measure shear and flexural strain for a variety of live load configurations. These measurements were also used to validate the researcher’s computer models and evaluate the accuracy of AASHTO LRFD distribution factors with skew correction factors. Displacement sensors were also placed at laminated bearings to measure both the live load displacement and the long-term temperature displacements.
The most relevant field measurements, which show support for the effectiveness of the mixed bearing arrangement, are the transverse bearing movements. The maximum transverse bearing movement at an acute corner (worst case) was limited to 0.28 in. during the observation period. This is less than the computer model, which may indicate some other restraining forces are limiting this movement. With such small transverse bearing movements, the data did not correlate well to the temperature readings. The researcher was not able to perform additional substructure modeling within the confines of this study.
Several key factors that influence the effectiveness of the mixed bearing design were evaluated. These factors include skew angle, pier type, and length-to-width ratio of the deck. These factors were evaluated based on the transverse bearing displacement of theoretical three-span finite-element bridge models. A mixed bearing arrangement was shown to be effective when the skew angle is at least 30°. The rigidity of the pier type plays a significant role in the effectiveness of the mixed bearing arrangement. Concrete encased piles (pier wall) and multi-column piers were shown to benefit more from the mixed bearing arrangement than hammerhead piers, which typically have less torsional stiffness. The span length-to-width ratio was manipulated in two ways: by adjusting the deck width and by adjusting the span length. The base model span lengths were 47 ft, 69.5 ft, and 47 ft. The results showed that using the mixed arrangement reduced transverse bearing displacements for all cases, but suggested a “sweet spot” in the range of 1.5-2.5 for a span length-to-width ratio (using the main span length).
Bearing forces were evaluated based on finite-element models of the HAST bridge. One model used the mixed bearing arrangement and the other used a regular bearing arrangement. Even though the mixed arrangement reduces rotation of the bridge superstructure, the increase in bearing forces in the longitudinal and transverse directions was only 11% and 8%, respectively.
While evaluating bridge end details and the associated effects on transverse deck cracking, the mixed bearing arrangement was included in one model of the instrumented steel girder bridge. Transverse deck cracking was mainly attributed to concrete shrinkage forces and was quantified in finite-element models as plastic tensile strain. Although other bridge end details helped reduce cracking to a greater degree, the mixed bearing arrangement reduced cracking by approximately 11% when compared to a similar model with a regular bearing arrangement. The most significant reduction of transverse cracking due to shrinkage occurred when end diaphragms and bearing lateral restraints were removed from the model.
View of I-94 Eastbound over the Hank Aaron State Trail.
For a variety of bearing fixity arrangements, the mixed bearing arrangement used in the design of the HAST bridge was the most effective in controlling bearing transverse displacements. The mixed bearing arrangement is most effective with high skew angles, rigid pier types, and moderate length-to-width ratios. The mixed bearing arrangement did not cause significant increases in bearing forces relative to forces on a bridge with a regular fixity configuration at the piers. The use of 2-D finite-element models is recommended to accurately predict amplified superstructure transverse movements. The mixed bearing arrangement reduced deck cracking and should be considered as a crack-control method in three-span girder bridges.
Unfortunately, the WHRP study was not able to capture the full effects of pier stiffness and length-to-width deck aspect ratios, which the Wisconsin DOT Bureau of Structures considers significant factors regarding the effectiveness of the mixed bearing arrangement. When investigating the use of mixed bearing design, finite-element modeling is recommended to ensure an effective design. Appropriate use of the mixed bearing arrangement in new bridge design has the potential to reduce pier costs, improve performance, and reduce required maintenance of skewed bridges in Wisconsin.