Keywords

1 Introduction

Prestressed concrete, due to its excellent structural performance and economic benefits, has been widely applied in fields such as bridges and high-speed railways. Precast U-beams, as a new type of prestressed concrete structural element, are increasingly used in modern rail transit systems due to their convenience in construction, environmental friendliness, and superior structural performance. Urban rail transit elevated bridges widely employ precast U-shaped beams because their track slabs (slab tracks) are located at the bottom of the two webs, serving as a supporting structure. This arrangement's notable advantage is its low construction height. Compared to traditional upper-bearing beams such as box beams and I-beams, it offers benefits like lower construction height, high-quality factory prefabrication, and savings on building materials [1, 2]. With the rapid development of urban rail transit in China, many cities extensively use precast U-shaped beams of prestressed concrete in elevated rail transit bridges [3]. Particularly, the post-tensioning method in the field of precast U-beams has developed a comprehensive design and construction system, with numerous corresponding scientific research achievements [4,5,6]. In recent years, the use and research of pre-tensioned precast U-beams have gradually increased [7, 8]. The adoption of a mixed tensioning method for precast U-shaped beams in Qingdao Metro Line 8 further promotes the widespread application of prestressed concrete precast U-beams in elevated rail transit bridges [9]. U-shaped beams, as a type of open thin-walled structure, exhibit significant spatial characteristics in their stress properties: longitudinal bending stresses are borne jointly by the side webs and bottom slab, designed according to full prestressed concrete structure standards; the slab track directly bears the train load and transfers it to the webs, showing transverse bending characteristics, designed according to reinforced concrete structure standards [10, 11]. However, a critical gap in existing research is the comprehensive understanding of the stress characteristics of the slab track, particularly in its connection to the webs. This gap is crucial as the connection area between the slab track and the webs is often prone to longitudinal cracking, a problem whose causes have not been sufficiently explored. Addressing this knowledge gap is essential for advancing the design and durability of prestressed concrete structures in urban rail transit systems.

Therefore, this study aims to thoroughly investigate the stress characteristics of prestressed concrete precast U-shaped beam slab tracks, with a specific focus on the transverse bending, shear lag effects, and the stress characteristics at the critical connection between the slab track and the webs. This study is based on the Qingdao Metro research project “Study on the Comprehensive Mechanical Properties of Precast U-Beams with Prestressed Concrete Using the Pre-Tensioning Method”. It selects cast-in-place precast U-beams for the investigation of the slab track's transverse bending, shear lag effects, and the stress characteristics at the connection between the slab track and the webs (neck skew). Additionally, it incorporates finite element analysis to study the stress performance of the slab track.

2 Introduction to Slab Track Test and Finite Element Analysis

2.1 Testing Program

The selected U-shaped standard span is 30 m, with the overall appearance of the beam in a “U” shape and the webs designed in an arc shape, resulting in a calculated span of 28.7 m. The slab track is thickened to 0.4 m at the beam ends over a length of 1.2 m. At the mid-span section, the slab track is 4.08 m wide and 0.26 m thick; at the end sections, it is 4.68 m wide and 0.4 m thick; an increase in thickness is applied at the connection between the web and the slab track for the neck skew. The thickened sections at the ends are reinforced with tension steel bars at both the upper and lower edges, whereas the non-thickened sections are only reinforced at the lower edge, with the upper edge having structural reinforcement. The experiments on the U-beam slab track include static load tests for bending performance, shear lag effect tests, and stress state measurements at the neck skew.

The static load test for the slab track bending performance is a supplementary part of the main beam load test. The loading method utilizes a steel structure portal reaction frame in combination with a synchronized jack system for loading. The transverse loading points simulate train wheel pairs, with a spacing of 1.4 m between loading points, as shown in Fig. 1. In Fig. 2, the loading force P1 on the bottom slab simulates the wheel-rail load, with the maximum loading value being 1.2 times the train axle load. The loading force P2 on the web is the loading value after exceeding 1.2 times the designed load.

The experiment employs three testing methods: affixing strain gauges to the concrete surface, welding rebar meters to the reinforcement, and embedding strain gauges within the concrete. Strain gauges are placed on three test sections of the half-span U-beam: the mid-span section, the 1/4 span section, and the section 0.5 m from the support, as illustrated in Fig. 3. Rebar meters and concrete strain gauges are placed on three test sections on the right half-span: the mid-span section, the center loading face, and the side loading face, as depicted in Fig. 4.

Fig. 1.
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Lateral Layout of Loading Points on the Reaction Frame

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Fig. 2.
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Cross-Section for Testing Lateral Strain Gauges in Concrete (unit: cm)

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Fig. 3.
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Test Section for Rebar Meter and Concrete Strain Gauge (unit: cm)

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2.2 Finite Element Model of Slab Track

The finite element analysis employed both linear and nonlinear analyses to meticulously simulate the structural behavior of precast U-shaped beams under various load conditions. A spatial solid finite element model was constructed using ANSYS. In the model, Solid45 elements were used for concrete due to their ability to accurately simulate three-dimensional stress states in solid structures, which is essential for understanding the stress distribution within the beams. Additionally, Link8 elements were utilized for both prestressed strands and ordinary reinforcement bars because of their proficiency in modeling the behavior of slender structural members under tension, which is crucial for simulating the prestress applied to the beams. The ANSYS finite element models are shown in Figs. 4 and 5.

Fig. 4.
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ANSYS Solid Model

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Fig. 5.
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Diagram of Element Division

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3 Shear Lag Effect of Slab Track

Based on the ANSYS finite element analysis results, the distribution curves of the normal stress in the concrete of the slab track at the mid-span and the 1/4 span sections are drawn, as shown in Fig. 6.

Fig. 6.
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Curve of longitudinal stress distribution in slab track concrete after prestress release

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During the load test study, when the loading level K = 1.0, the strain increments measured by the embedded steel strand strain gauges in the slab track at the mid-span and the 1/4 span sections are converted into concrete stress. The distribution curves of the longitudinal normal stress in the concrete of the slab track are drawn, as illustrated in Fig. 7.

Based on the finite element analysis and experimental test results, the following conclusions can be drawn: As shown in Fig. 7, the finite element analysis of the longitudinal normal stress on the bottom plate closely matches the actual measurements at the mid-span, with differences observed at the quarter span section due to its location in the experimental loading area. According to the finite element analysis, taking into account the shear lag effect, it can be determined that the shear lag coefficient at the mid-span section is 1.09, and at the 1/4 span section, it is 1.08. Analysis of the experimental results shows that the distribution of longitudinal normal stress in the slab track does not vary significantly, suggesting that the impact of the shear lag effect can essentially be disregarded.

Fig. 7.
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Curve of longitudinal stress distribution in slab track concrete at load level K = 1.0

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4 Analysis of Transverse Bending Mechanical Properties

The transverse bending normal stresses at the mid-span section and the center loading section (where stress concentration occurs) under load level K = 1.0 are extracted from the finite element model, as shown in Figs. 8 and 9.

Fig. 8.
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Stress contour map of transverse stress at Mid-span section

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Fig. 9.
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Stress contour map of transverse stress at 1/4 Section

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From the linear elastic finite element analysis results shown in Figs. 8 and 9, it can be observed that even in sections with stress concentration, the maximum compressive stress in the upper concrete of the slab track is 4.0 MPa, which is significantly lower than the concrete's design compressive strength [12]. For non-loading sections, such as the mid-span and 1/4 sections, the maximum tensile stress in the lower concrete of the slab track is 1.88 MPa, not exceeding the limit tensile strength.

5 Conclusions

For the commonly used single-track 30 m standard span precast U-beams in rail transit, under the influence of live loads, the shear lag effect should be considered. The shear lag coefficient at the mid-span section is 1.09, and at the quarter-span section, the shear lag coefficient is 1.08.

Despite stress concentration in certain sections, the maximum compressive stress in the slab track's upper concrete remains well below the design strength, and the maximum tensile stress in non-loading sections does not exceed the concrete's tensile strength limit.

The precast U-shaped beam slabs of prestressed concrete exhibit distinct stress characteristics under various conditions, including transverse bending, shear lag effects, and stress concentrations at the web-to-bottom slab junctions. These findings are instrumental in understanding the structural behavior of railway bridge components under load.

Furthermore, the implications of our findings for the design, construction, and maintenance of railway bridges are significant. By integrating the shear lag effect and stress characteristics into design practices, engineers can enhance the durability and reliability of railway bridge components, potentially leading to more efficient material use and longer service lives.