Keywords

1 Introduction

In recent years, steel-mixed combination structure has been widely adopted in the field of bridges and building structures in China, showing excellent technical and economic benefits.

Researchers like Hu Shaowei [1] discovered through torsion tests on composite girders that the concrete wing plate significantly influences torsional load capacity, with thickness playing a crucial role. They suggested that the maximum torsional load capacity for composite girders occurs at a hoop ratio of 0.54%. Shi Qiyin [2] and colleagues identified the concrete airfoil plate and outer cladding steel as key components in the torsional load capacity of new combined beam structures. They introduced the bending-twisting ratio as a factor affecting member torsional load capacity. Nie [3] and team developed a practical longitudinal shear calculation model for combined beams based on engineering tests. Qiu Wenliang [4] proposed an analytical model for shrinkage creep in steel-concrete composite beams, accounting for concrete slab cracking effects on stiffness and strength. Given the diverse structural forms of steel plate combined girder bridges, understanding the impact of different design parameters on torsional stresses is essential for subsequent construction.

2 Project Overview

This project is based on a 4 × 25 m steel plate combination girder [5]. The superstructure adopts double main girders, 1, 2# middle cross girder and main girder diagonal intersection 15°; 3# middle cross girder and main girder diagonal intersection 10°, two main girder centre spacing is 5.6 m, I-beam girder height is 1.3 m; prefabricated deck slab cantilever flange thickness of 25 cm, the root thickness of 41 cm. Its deck plan is shown in Fig. 1, the fabrication arrangement diagram is shown in Fig. 2. We used ABAQUS [6,7,8] 2020 for modelling and the finite element model is shown in Fig. 3.

Fig. 1.
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Bridge cross-section

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Fig. 2.
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Bearing arrangement plan

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Fig. 3.
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Overall diagram of the baseline model

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3 Torsional Stress Analysis of Design Parameters on the Reference Bridge Example

3.1 Influence Law of Radius of Curvature

Figure 4(a) and Fig. 4(b) depict torsional stress envelope variations in the bridge roof plate and steel main girder at pivot 1 in a small-radius steel plate combination girder under typical working conditions (constant load + out-of-lane offset arrangement). The transverse distribution of torsional stress in the roof plate remains consistent, with numerical differences. A larger roof plate radius results in a more pointed torsional stress envelope curve and uneven stress distribution. Among the outer steel, R100 to R300 exhibit main beam torsional stresses higher than the inner ones by 39.11%, 22.72%, 9.35%, 24.69%, and 11.90%, respectively, with increments less than 0.05 MPa (Fig. 4(a)). In summary, the radius of curvature has a minimal impact on the bridge roof slab's envelope torsional stress.

Fig. 4.
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Torsional stress cloud at center pivot point 1

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In Fig. 4(b), torsional stress distribution along the height of inner and outer steel main girders follows a similar pattern, but with numerical differences. The torsional stress envelope of the outer steel main girder is approximately 1.2 times larger than that of the inner steel main girder. The critical torsional area in the steel main girder occurs around 1/4 of the web height from the bottom plate. For the original bridge with a radius of curvature R = 250 m, the most critical torsional stress value is 71.16 MPa. This value remains consistent at 71.16 MPa for the outer steel girder. With an increase in radius from R100 to R300, the corresponding maximum torsional stress value grows by less than 5.9%, totaling less than 8.7 MPa. Thus, the steel girder's sensitivity to curvature radius is low, but the maximum torsional stress is notably high, reaching 70 MPa, necessitating attention.

3.2 Calculation of the Law of Influence of the Span

Figure 5(a) and Fig. 5(b) show the laws of the torsional stress envelopes of the bridge roof plate and steel main girder at the mid-point 1 of the span of a small-radius steel plate composite girder bridge with the change of the computed span diameter under the typical working condition of (constant load + lane outward deviation arrangement), respectively.

Fig. 5.
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Torsional stress cloud at center pivot 1

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Under typical working conditions, the torsional stress distribution across the bridge's transverse direction in the roof slab remains consistent, with slight numerical differences. The torsional stress envelope value for the outer steel girder is larger than that of the inner girder, indicating the outer girder experiences more unfavorable stress. The change in torsional stress envelope value with increasing computed span diameter does not follow a clear pattern (Fig. 5(a)). For instance, the maximum torsional stress of the steel main girder first increases and then decreases when the span varies from 4 × 20m to 4 × 35m. Similarly, the maximum torsional stress of the concrete slab is less than 0.12MPa in several span configurations, with changes below 0.05MPa. In summary, the influence of calculated span diameter on concrete slab torsional stress is relatively low.

The torsional stress distribution along the height of the steel main girder follows a similar pattern, with only slight numerical differences. The torsional stress envelope value for the outer steel main girder is generally larger than that of the inner girder (Fig. 5(b)). Numerically, the maximum torsional stress of the steel main girder under various computed span diameters is generally above 30 MPa, reaching 93 MPa for the outer steel main girder in the 4 × 35m span. With increasing span diameter, the overall torsional stress of the steel main girder shows an increasing trend; In summary, the calculated span diameter significantly influences steel main girder torsional stress and requires careful consideration.

3.3 Laws Affecting the Number of Steel Beams

Figure 6(a) and Fig. 6(b) show the laws of the torsional stress envelope of the bridge roof plate and steel main girder with the change of the number of steel girders at the midpoint 1 of the span of a small-radius steel plate composite girder bridge under the typical working condition of (constant load + out-of-lane deviation arrangement), respectively.

Fig. 6.
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Torsional stress cloud at center pivot 1

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Under typical working conditions, the torsional stress distribution across the bridge roof plate's transverse direction remains consistent, differing only numerically. The outermost steel main girder experiences a larger torsional stress envelope than the inner and middle girders, making it more unfavorably loaded (Fig. 6(a)). Numerically, the maximum torsional stresses in the roof plate are 3.7% and 43.5% higher in the three-main girder configuration compared to the four-main and two-main girder configurations, respectively. Torsional stresses in the bridge roof slab are below 0.2 MPa for the three types of steel main girders, varying by less than 0.1 MPa. Hence, the bridge roof slab's torsional stress shows low sensitivity to the number of steel main girders.

The torsional stress distribution along the height of the steel main girders follows a similar pattern, with slight numerical differences. The torsional stress envelope of the outer steel main girders is generally larger than that of the inner steel main girders. Numerically, the maximum torsional stresses of the three types of steel girders generally exceed 30 MPa, indicating higher stress levels. With an increase in the number of main girders, the overall trend of the torsional stress envelope of the steel main girders decreases. In summary, the number of steel main girders significantly affects their torsional stress, with double main girders experiencing the most unfavorable conditions.

4 Conclusion

By analysing the effect of each parameter on torsional stresses in small radius combination beams, the following conclusions are drawn:

  1. (1)

    The radius of curvature has a low degree of influence on the torsional stresses in the bridge roof slab, but the maximum torsional stresses in the steel main girders have higher values, especially at larger radii of curvature, which need to be taken into account by the designers. Changes in the radius of curvature will cause non-uniformity in the distribution of torsional stresses in the bridge roof plate and steel main girder, which has a potential impact on the stability of the structure.

  2. (2)

    The torsional stresses of the steel main girders tend to increase with the increase of the calculated span, especially the outer steel main girders are more unfavourably stressed. However, the torsional stress of concrete slab is less affected by the calculated span diameter. It is necessary to choose the calculated span diameter carefully in the design to avoid the structure being affected by excessive torsional stress and to ensure the safety and stability of the bridge.

  3. (3)

    The number of steel girders has a small effect on the torsional stress of the bridge roof slab, but it has a significant effect on the torsional stress of the steel main girder. The torsional stress of the double main girder structure is the most unfavourable, and its torsional stress is at a high stress level, which needs special attention in the design.