SAI DESIGNS PA'S FIRST POST-TENSIONED BRIDGE PIER CAP WITH ALGOR FEA

Curved bridge is shown here under construction. Preparations are underway for post-tensioning of the pier cap. The bridge is located near Pittsburgh, Pennsylvania.

The city of Pittsburgh is well known in the bridge building industry. Small wonder with three rivers running through the center of the city. That is why the International Bridge Conference and Exhibition is held in Pittsburgh every year.

This year's conference will include a paper by Ahmad Ahmadi, Ph.D., P.E., Lead Engineer, Research and Development for SAI Consulting Engineers, a leading Pittsburgh-based engineering firm. The subject of Dr. Ahmadi's presentation is his recent design of a curved bridge which utilizes an integral post-tensioned concrete pier cap. This is the first such pier cap design in the Commonwealth of Pennsylvania.

Complex Curved Design

Curved bridges offer some tremendous challenges to engineers. In this case, the inclusion of integral pier caps added to the challenge. It was because of this complexity, and the requirement for a safe design, that Dr. Ahmadi chose to perform finite element analysis using Algor software.

"To have a safe design, forces such as shear, axial, moment and torsion should be computed accurately," says Dr. Ahmadi. "Therefore, the structure should be analyzed in 3-D and influence surfaces prepared for each element of the superstructure and substructure. Later, these surfaces must be loaded with moveable live loads to simulate traffic conditions.

"The design of the bridge was dictated by geometric constraints which needed to be met at the bridge site," he continues. "The bridge roadway had a predefined elevation, the required span lengths of the structure dictated the girder depth and the roadway passing under the structure had a required vertical clearance."

Ahmad Ahmadi, Ph.D. created finite element models to optimize the design of a curved bridge which incorporated a post-tensioned pier cap.

Standard Design Would Not Work

"Standard pier designs place the top of the pier cap below the girder's bottom flanges. This would have placed the underside of the pier arms below the required clearance elevation. The decision to cast the girders into the pier cap averted the unreasonable and expensive alternative of a sharply skewed pier. A sharp pier skew creates a longer pier which adds to the complexity of the superstructure behavior under loadings, especially seismic loads."

Post-Tensioning Necessary

"Since casting the girders into the pier cap resulted in it being segmented from a structural perspective, post-tensioning was necessary. This requirement meant that torsion, moment, shear and axial forces had to be calculated in the pier cap in order to permit a reliable design of the post-tensioning system."

Two Models Created

To perform the analyses, Dr. Ahmadi constructed two Algor FEA models. The first represents the complete structure and utilized 976 beam, 212 truss, 380 brick and 13 boundary elements. The model contains 1463 nodes.

For accurate modeling of the girders, Dr. Ahmadi used separate beam elements for the top flange, web and bottom flange. These elements were centered at different elevations and connected by stiff elements. This permitted determination of the moments at a cross section from the axial forces given in the output. According to Dr. Ahmadi, "This level of analysis produced a more refined design of the girder than acceptable 2-D methods would, thus saving on material costs."

To study the behavior of the pier more closely, Dr. Ahmadi constructed a separate, more detailed model of just the pier. This model contains 514 brick elements, 23 boundary elements and 813 nodes.

A closer view of the curved bridge FEA model.

Analysis Results

"The results of the analyses gave reasonable forces which could be handled by standard materials and averted the problems created by the geometric constraints," says Dr. Ahmadi. "The pier behavior was compared with available full-scale laboratory tests on similar piers and revealed a good correlation."

While specializing in the 3-D analysis and design for bridges, SAI Consulting Engineers, Inc. has handled such diverse assignments as the analysis of nuclear containment systems during decommissioning, thermal analysis of chemical vessels subjected to extreme temperatures and many other analysis projects. SAI is the only consulting engineering firm in Pennsylvania to have developed a 3-D analysis and design package accepted by the Pennsylvania Department of Transportation.

According to Dr. Ahmadi, "Algor software stands out in the numerous user interfaces available for generating and viewing models. To generate influence surfaces for each element of the model, more than 170 load cases were considered. This large amount of data needed to be manipulated for use by our 3-D live load influence surface loader. Algor post processors made it easy to accomplish this task."

Series of photos shows additional details of bridge construction in progress.