Bridge analysis, design + assessment

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Case Study

West 7th Street Bridge

  • Design and analysis of what is believed to be the world's first precast network arch bridge

  • Analysis of numerous post-tensioning layouts and a variety of construction stages

  • Eigen buckling and nonlinear analysis studies carried out to evaluate crown deflections

West 7th Street Bridge

The Texas Department of Transportation (commonly known as TxDOT) was retained by Fort Worth city authorities to advise on suitability of upgrading and strengthening the existing West 7th Street Bridge to allow for wider pedestrian footways and potential future light rail traffic. When this was proved to be not the best course of action a decision was made to replace the structure with a new precast network arch replacement. TxDOT chose to use LUSAS Bridge analysis software to assist with its design of the new bridge and investigate and optimise the post-tensioning required.


The original West 7th Street Bridge structure was built in 1913, had been extended in 1953 and was nearing the end of its service life. Investigations by TxDOT into the suitability of upgrading and strengthening the bridge to allow for wider pedestrian footways and potential future light rail traffic, as requested by Fort Worth city authorities, showed that extensive replacement and rehabilitation would have been required, and this ultimately resulted in a decision being made to replace the structure.

The new bridge is constructed from precast arches, pre-tensioned floor beams and precast, stay-in-place deck panels and is believed to be the world's first precast network arch bridge. It comprises six 163'-6" (50m) long spans, 88'-0" (27m) wide, that carries four lanes of traffic (two in each direction) along with two pedestrian sidewalks over the Trinity River, a park and a city street. Two planes of tightly-spaced hangers at 58" (1.47m) spacing pass cleanly through 5" (125mm) by 4" (100mm) stainless steel tubes cast into the tie at a 55 degree angle, and allow for each of the 102 floor beams to be supported by four hangers, eliminating the need for longitudinal stringers. 1.75" (45mm) diameter post-tensioning rods connect the floor beams to the arch. A standard 8.5" (216mm) deck spans the 9'-6" (2.9m) distance between beams. Roadway vertical curve geometry is accommodated by adjustable floor beam pedestals. The substructure consists of 6'-6" (2m) diameter mono-shafts supporting 7'-3" x 5'-0" (2.2m by 1.55m) oval cross-section columns.

West 7th Street Bridge

Challenges faced

In designing the 23'-6" (7.2m) high concrete arches one challenge was to determine how they could be economically precast and transported. The solution was to make the arch elements as slender as possible to minimise weight and use a span-to-rise ratio of only 0.13 to keep the centre of gravity very low. In addition, arches were cast horizontally, before raising into a vertical position using a specially-designed lifting tower and transporting to site. TxDOT bridge designers were aware that cracking in the arch was a real possibility during handling and if it occurred, it would lower the rib buckling limit. As a result, post-tensioning was specified for the rib as well as the tie. 

West 7th Street Bridge - casting of arches

West 7th Street Bridge

Night-time casting of arch Detail of knuckle showing ducts and cooling tubes

Cooling tubes were used in the knuckle regions and casting was carried out during the night to avoid excessive heat differential. The low-shrinkage, low-heat, low-permeability, high-slump, and high-strength requirement for the concrete used resulted in one of the most sophisticated mixes ever produced for a TxDOT project. 

In position, the arches are set end-to-end with only a 100mm gap, leaving no opportunity for field post-tensioning. As a result, 100% of the longitudinal tie post-tensioning had to be installed while the arches were in the casting yard. Since the arch self weight generated less than 25% of the axial service tension in the tie, the slender element experienced tremendously high compression forces prior to placing floor beams and other subsequent gravity loads. To reduce the unbraced length and prevent any lateral movement of the 2'-0" x 4'-6" (610mm x 1.4m) tie during stressing, a series of small curves was added to the ducts causing regular contact with the four 19-strand tendons. For speed, cost, and appearance, no rib cross-bracing was used. 

West 7th Street Bridge - raising of completed arch
Raising of completed arch

Modelling with LUSAS

TxDOT used LUSAS Bridge analysis software to assist with its detailed design of the arches. 3D thick beam elements modelled the arch rib and tie and 3D bars represented the hangers. To model the knuckle joints thick shell elements were used - with this modelling methodology being verified using a 3D solid model of the knuckle joint. The main aim of the analysis was to keep the arch concrete free of tension for durability, aesthetics and to maintain consistency in the analytical assumption of uncracked sections. Due to the connection details and slenderness of the hangers, any LUSAS model that produced compression in the hangers was deemed unsuitable and a modified configuration was evaluated. Dean Van Landuyt, Principal Engineer, Texas DOT explains the process involved: "Once initial section sizing calculations had been performed, we then used LUSAS to analyse numerous post-tensioning layouts for a variety of construction stages. This involved first stage post-tensioning, raising of arches, second stage post-tensioning, floor beam installation, deck casting, and wind and live loading. Then, once a tendon layout that satisfied all stress limits had been found, strength checks were made and the tendon profiles approved."

West 7th Street Bridge arch model

Arch modelling methodology showing the use of thick beam elements (magenta) for the arch rib and tie, and shell elements (green) for the knuckle region. Tendon layout and the use of ' outrigger' beams, used to connect the bar elements that model the hangers to the elements in the arch rib and tie, are also shown.

West 7th Street Bridge construction sequence model

Construction sequence modelling for a single span.

Eigen buckling studies were undertaken for initial stability analysis of the completed structure. The lowest Eigen buckling value of 13.3 was found to occur for the Service I load combination comprising six lanes of traffic and wind load. The resulting arch buckling mode showed a maximum deformation at the arch crowns in the direction of the wind loading. A more rigorous nonlinear buckling analysis was also performed and, for this, seven different factored loadings from AASHTO LRFD Bridge Design Specification Load Combinations I, III and V were examined. The LUSAS model revealed that, even for the most severe condition, Strength III (transverse wind), the crown deflection at a load factor of two was only 2 (50mm) and the load-displacement curve was nearly linear.

First three eigenmodes obtained from a three lane loading assessment

A further LUSAS study was undertaken to investigate the negative consequences of initial out-of-straightness of the arch in the lateral direction that might arise from improper casting, improper storage, variation in modulus of elasticity due to bleed water migration during the horizontal casting, or some other unknown cause. To generate the most severe initial out-of-straightness arch profile, an Eigen analysis was carried out using the load factors for the Strength V load combination with six lanes loaded.  The displaced profile was then used in a nonlinear analysis with the same loading applied and with the initial out-of-straightness profile scaled so that the crown lateral displacement was 6 (150mm). Even with this drastic initial out-of-straightness of the arch in the lateral direction, the additional crown deflection was only 2 (108mm) at a load factor of two, and the load-displacement curve still had not levelled out.

Load / Displacement graph for a node at the crown of the arch

Casting of the arches started in July 2012 and was completed in February 2013. Arch erection began in May 2013 and was completed in 5 weeks. Floor beam installation began in July 2013. The bridge was completed ahead of schedule and officially opened on 15th November 2013.

West 7th Street Bridge - floor beam setting

Floor beam setting

West 7th Street Bridge -  precast deck panel installation

Precast deck panel installation

West 7th Street Bridge - nearing completion

Bridge tour during the 2013 PCI Annual Convention and Bridge Conference

West 7th Street Bridge - open to traffic. Photo:Russell Springfield

As completed. The bridge features recessed in-arch lighting units.

"Once initial section sizing calculations had been performed, we then used LUSAS to analyse numerous post-tensioning layouts for a variety of construction stages... then, once a tendon layout that satisfied all stress limits had been found, strength checks were made and the tendon profile approved."

Dean Van Landuyt, Principal Engineer, Texas Department of Transportation

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