INNOVATIVE METHODS OF CONCRETE BRIDGE DESIGN
Design engineers use finite element analysis to optimize the benefits of concrete materials on large bridge projects.

by: Greg Shafer, P.E., Senior Bridge Engineer
Jerry Pfuntner, P.E., Bridge Engineer

Operated by the Expressway and Rapid Transit Authority of Thailand, the Bang Na-Bang Pli-Bang Pakong Expressway in Bangkok is an elevated roadway built in the median of an existing highway. Currently, 12 kilometers of the 54 kilometer-long bridge are operational with completion expected early in the year 2000.

December 30, 1998, Pittsburgh, Pennsylvania - Civil engineers and bridge developers worldwide must design bridges and elevated roadways to conform to both natural and urban landscapes while ensuring sound construction, durability and aesthetic value at the lowest cost. The combined cost of the design, materials, construction and maintenance is an important factor in many design decisions made by today's engineers.

Engineers at J. Muller International (JMI) Bridge Engineering Consultants, based in San Diego, CA, meet these challenges with innovative designs often using a precast segmental concrete construction for bridges and viaducts throughout the United States, Europe and Asia. When designing bridges of 3,000 meters or more, special care must be taken to minimize the quantity of materials used and to accurately determine maximum loads and post-tensioning requirements. Therefore, the engineers use computer-aided drawing and finite element analysis (FEA) tools from Pittsburgh-based ALGOR, Inc. to ensure their designs are refined before construction begins.

The following discussion chronicles two ways in which engineers from JMI use ALGOR's design and analysis tools to produce concrete bridge and viaduct designs. The first instance combines the traditional civil engineering practice of strut-and-tie analysis with FEA to study the local effects of external post-tensioning in segmental concrete box girders.

The second instance uses FEA to study the load effects of trucks on the box girder superstructure of the Bang Na-Bang Pli-Bang Pakong Expressway in Bangkok, Thailand. The engineers used FEA to more accurately predict structural behavior, reducing the structure cost while maintaining the required strength and serviceability.

The firm also has applied similar analysis techniques to various other bridge designs, including the Northumberland Strait Crossing on Prince Edward Island, Canada and the H-3 Windward Viaduct in Hawaii.

Working with Concrete

Engineers at JMI have found that prestressed concrete structures exhibit excellent durability with virtually no cracking and minimal maintenance requirements. Box girder bridges are aesthetically pleasing in high profile and urban environments, and they add to rather than detract from the landscape. They have significant fatigue resistance and overstrength capacity. These aspects combine to produce a bridge that is both durable and adds significant value to a community.

The use of prestressing allows precast segmental bridges to be designed so that concrete stresses are maintained well below the tensile cracking stress of concrete. This provides the durability found in concrete segmental bridges because cracking in the deck slab is virtually eliminated. This is a significant advantage over reinforced concrete bridge decks, which must crack in order for the embedded reinforcement to resist the loads caused by vehicles. Cracking causes water and road salts to permeate the bridge deck, which can result in further cracking, increase maintenance costs and jeopardize the integrity of the bridge.

These post-tensioning tendons induce compression along a box girder span. The tendons are threaded through deviation saddles located in the void of the box girder segment, which transfer large forces created by the deviation to the surrounding areas.

There are many complex design aspects in precast segmental bridge design; most of them relate to the application of post-tensioning. JMI engineers use transverse post-tensioning to pre-compress the top slab against the local forces induced from vehicular traffic. Determining the longitudinal post-tensioning specifications requires significant effort. The tendon configuration, sizes and stressing forces are computed using a time-dependent analysis. Special segments are required to anchor and route the tendons through the span. A concrete diaphragm at the end of each span is designed and detailed to resist the anchorage forces from the longitudinal post-tensioning tendons. Segmental bridges with external tendons also require "deviation saddles," which act as harping points for the longitudinal tendons. These complex segments also require a special analysis.

In addition to these detailed design aspects, one of the greatest challenges of precast segmental bridge design is determining the most cost-effective erection scheme, box girder proportions and post-tensioning configuration. Bridge design experience and superior analysis tools and methods can significantly reduce bridge construction costs.

This diagram shows the placement of post-tensioning tendons within the void of a box girder segment. Post-tensioning tendons are placed transversely across each individual box girder segment and longitudinally along the entire box girder cross section.

Combining Strut-and-Tie Analysis with FEA

As with any structural analysis, the area of interest must be divided into discontinuous and beam-type regions. For combined strut-and-tie and finite element models, the beam-type regions exist where plane sections may be assumed to remain planar and are modeled with plate/shell finite elements. A strut-and-tie model is made of truss elements and assembled directly onto the finite element plate/shell model. This allows modeling of a complete load path of the discontinuous forces that spread into the surrounding sections. The combined model can show the internal forces of both the strut-and-tie model and the surrounding plate/shell elements of the finite element model.

A combined strut-and-tie model and finite element model was used in the analysis of a trapezoidal, precast segmental box girder section, containing a deviation saddle. Large forces generated by the deviation of the tendons were transferred through the deviation saddle to the surrounding thin webs and bottom slab. The forces in these elements had to be determined for the design.

The engineers developed the strut-and-tie model by determining the load path of the discontinuous forces through the deviation rib. First, the compressive forces were outlined and tensile zones identified. A reinforcement pattern that provides tension ties through the corresponding tensile zones was chosen. Compressive struts and tension ties were then determined so that a complete load path was formed.

The development of the strut-and-tie model can take several iterations to produce a model that closely follows the load path through the discontinuous region. In the accompanying model, the finite elements, which are continuous through the discontinuity region, represent the bending stiffness of the deviation saddle. This particular truss model was constructed to ensure that the strut-and-tie model did not contribute to the bending stiffness by acting compositely with shell elements.

x = Fixed Edge c = Symmetrical Edge Engineers at J. Muller International Bridge Engineering Consultants, based in San Diego, CA, combined traditional strut-and-tie analysis with FEA software, such as that from ALGOR, Inc., Pittsburgh, PA, in the analysis of this trapezoidal, precast segmental box girder deviation segment. This technique enabled them to analyze both the discontinuous and beam-type regions of the structure using a truss and plate/shell model.

A half-segment model was used because the segments and loads were symmetrical. The edges at the centerline of the segment were fixed in rotation about the longitudinal axis and transverse displacement. All other edges were fully fixed. The strut-and-tie model nodes were released in the vertical and transverse directions and fixed against the longitudinal translation.

The required time for the analysis was reduced because a single model was used to determine the effects of both the discontinuous and beam-type regions. Analyzing the two regions together also gave a better sense of the overall behavior in the element. The engineers received force output for effects in the slabs and webs. For example, the tensile force behind a post-tensioning anchorage block and the bending effects it causes in the web could now be determined. This analysis method enhances strut-and-tie model technology so that JMI engineers are not limited by their analysis capabilities as new designs are developed.

JMI engineers use ALGOR's Superdraw III design program to create many components of their designs because of the ease in which different finite elements can be combined into one model. Engineers created a combined beam and plate/shell element model to study the box girder of the Bang Na-Bang Pli-Bang Pakong Expressway in Bangkok.

Designing the High Road

The expressway presented JMI engineers with several challenging design considerations and limitations:

• The engineers needed an exceptionally wide box girder to support 6 lanes (27 meters) of traffic. Several box girder designs had to be considered to compare overall use of materials, load-bearing capabilities, which include significant live loading effects from traffic, and method of assembly.
• The expressway has 36 elevated ramps, including 10 ramps that lead into major interchanges, and two elevated toll plazas, one at each end. The 80-meter wide toll plazas support up to 12 tollbooths plus toll surveillance buildings. This extreme increase in width at the toll plazas, as well as the increased width at the ramps, required the engineers to use a support system different from the one chosen for the lane traffic.
• Because of the location of the expressway in the median of an existing highway, the engineers were severely limited in the positioning of the main support columns. The columns could only be placed in a narrow 5-meter strip in the center and side medians of the project. Furthermore, storm water runoff from the existing highway is channeled into the medians and could not be blocked by the columns.
• The long length of the structure and visibility from the highway below meant creating a dramatic, aesthetically pleasing column that minimizes the quantity of materials used. Each column supports a 27-meter wide box girder with an average span of 42 meters of roadway between each column.
• Because of the congested existing roadway and limited construction space, JMI engineers needed to create a design that reduced the amount of work required on-site.

JMI engineers specifically designed box girders, columns and portal frames to meet all of the design considerations. ALGOR's Superdraw III and linear static stress analysis software was important to the optimization of the box girder design.

Box Girders
Beginning work on the project in September 1995, the engineers chose a single-cell box girder 27 meters wide with slender flanges for the main portion of the project. Typically, spans of this width would be supported by multiple box girders; however, the engineers determined that twice the number of precast segments would be needed as well as a special column cap to transfer the vertical loads to the columns using a multiple box girder design.

A multi-cell box girder also was considered. This design was simpler, the post-tensioning more easily arranged and the casting of concrete was more easily performed. However, expensive temporary measures would be needed to mitigate stresses and deformations in the cross-section during the span-by-span assembly. Eventually, the engineers determined that the single-cell box girder was the most economically feasible.

Each precast segmental box girder is comprised of 16 to 18 individual box girder segments, weighing 85 tons each. Each 2.55 meter-long segment has two inclined struts that support the center of the roadway and is transversely post-tensioned with strand tendons anchored at the edges of the slabs. The segments are post-tensioned together to form a span using tendons anchored in the end diaphragms and deviated at discrete points within the span.

A typical box girder segment of the Bang Na-Bang Pli-Bang Pakong Expressway is lifted into place by a swivel crane attached to a large erection girder.

Once the type of box girder was determined, JMI engineers created a finite element model of the box girder cross section. The purpose of the model was to optimize the design and reduce the quantity of materials used and to ensure the cross section could withstand the loading effects of heavy truck traffic on the deck of the viaduct.

In other cases, JMI engineers have used plate influence surfaces, which are published in standard textbooks, to determine the effects of live loading on bridge decks. By creating a finite element model, the engineers created a surface of influence specifically for the bridge deck of concern. This eliminated conservative assumptions imposed by using textbook values, which are more generalized, and enabled the engineers to further optimize the design.

JMI engineers used plate/shell elements to represent the top and bottom slabs of the box girder. Beam elements represented the struts of the box girder segments while boundary elements represented the column supports for the box girders. Boundary elements were used instead of nodal boundary conditions because the supports were not oriented along the global axes. Furthermore, the columns were not modeled because they were not of concern in this analysis. Additional boundary conditions were added to fully constrain the box girder cross section.

The engineers then evaluated the truck loading on the bridge deck. They used three types of loading: the HS25-44 standard set by the AASHTO code, alternating military loading and an overload vehicle specified by the owner. The second standard is in place to ensure the expressway could withstand loading from military use.

To determine the critical placement of the loads for acquiring maximum stresses on the deck, the engineers began by placing the loads in two areas of concern: in areas directly above a strut support and in areas between two struts. Influence surfaces for the plate/shell elements were developed by placing unit loads on the bridge deck at many different locations in separate load cases. The effects of the unit loads on a particular section were combined to evaluate the effect of a truck at the critical loading location. The most significant local effect was the slab stresses perpendicular to the line of traffic. The effects of global bending of the box girder were considered in a separate analysis, which included the longitudinal post-tensioning and time-dependent effects.

The engineers also were concerned about the local deflection of the bridge deck. The AASHTO requirements limit local deflections of a cantilever slab to the slab length divided by a factor of 300. This limits the dynamic effects on the deck under live loading. The engineers consider the dynamic effects of vibration from the trucks using an amplification factor of 30 percent according to the standard specifications.

Once the model was drawn and boundary conditions and loading applied, the engineers ran the model through ALGOR's linear static stress processor to determine the maximum stresses and deflections across the bridge deck. While both the stresses and deflection were within the allowable limits, the areas between two struts furthest from the supports exhibited the highest stress. Higher levels of local deflection were noted at the edges of the bridge deck.

Several iterations of this process were required to optimize the final design for both the amount of materials needed and the loading effects. Nonetheless, using this process, the engineers were able to verify the design quickly and use approximately 10% less material compared to traditional design methods. Based on the large scale of the structure and the $1 billion net value of the project, the gains from the analysis of the finite element model were significant.

JMI engineers used ALGOR's linear static stress analysis software to determine areas of maximum stress and local deflection resulting from the movement of large trucks across the expressway bridge deck. The model at top shows the stresses resulting when a load is placed near the center of the bridge deck. The model at bottom shows the deflection resulting from loading at one edge of the deck.

Columns
Because the expressway is extremely long and has foundations that are limited in width, the engineers designed the lower portion of the column with two slender "legs" spaced as far apart as possible to resist the transverse bending moment and to allow the flow of storm water. These legs are joined by a beam at the mid-height of the column with the "arms" of the column extending upward at a 35-degree angle. This open y-shape provides a wider base for stability of the box girder on its bearings and provides an open area for the support of the erection girder, used to assemble the precast segmental box girder sections. It also gives the impression that the girder box is virtually floating for aesthetic appeal.

JMI engineers explored the possibility of using the slender, inclined arms for the upper portion of the column without a tie across the top of the column; however, they determined that the gravity loads on the arms far exceeded the capacity of the section. Therefore, inclined elastomeric bearings are positioned on the top of the column normal to the axis of the arm so vertical concentric loads are resisted by axial forces along the column arms without bending.

Non-concentric vertical loads are broken down into a concentric load and transverse moment. The transverse moment is resisted by equal and opposite axial forces in the arms plus a lateral shear force, which causes shear distortion of the elastomeric bearings. The shear distortion is a critical design parameter and was limited to ensure sufficient fatigue resistance.

Buffer blocks between the box girder and column arms restrain lateral movement. The buffer blocks engage after the structure has moved laterally by 25 mm. The distribution of loads to the column arms is different before and after the buffer blocks engage; thus engineers conducted a detailed analysis to capture the true effects of this system under concentric loading and transverse moments.

Segmental Portal Frames
In locations where the expressway width is increased to accommodate ramps and toll plazas, a single column in the center of the roadway is no longer sufficient to support the superstructure. In these areas, multiple box girders are supported on portal frames. These frames span the highway below and are typically comprised of two bays. Because over 100 of these portal frames will be used in the project, the precast segmental method was chosen to speed construction and limit the amount of work that would be performed over the existing roadway below.

These large portal frames are designed to support multiple box girders at locations where the expressway width is increased to accommodate 36 elevated ramps and two elevated toll plazas.

Before the first span was assembled, a full-scale load test was performed on a box girder in the casting yard. The theoretical maximum ultimate load was placed on the girder. The span exhibited behavior that was consistent with the designers' expectations. Work began on the construction of the expressway in March 1996. The Expressway and Rapid Transit Authority is opening the expressway in stages as it is completed. Currently, 12 kilometers of the 54 kilometer-long bridge are operational with completion expected early in the year 2000.

Benefiting from FEA Software

With FEA, engineers can model the behavior of complex segments and geometry to determine if the overall design is a practical solution for the project at hand. In addition, faster computing times and improved computer hardware enable engineers to model more complicated designs with challenging design parameters. This means civil engineers and bridge designers are not limited to existing designs.