Theoretical study on the seismic response of a continuous beam bridge with safe-belt devices

https://doi.org/10.1016/j.soildyn.2021.106948Get rights and content

Highlights

  • (1)

    The simplified model of a continuous beam bridge with safe-belt devices were proposed.

  • (2)

    The theoretical formulas of a continuous bridge with safe-belt devices were derived, such as natural period, beam-end displacement and shear force of fixed pier bottom.

  • (3)

    The effectiveness of these theoretical formulas was verified by comparing the theoretical results with finite element results.

  • (4)

    The influence of the continuous beam bridge's total lateral stiffness and of the safe-belt device's installation position on the aseismic rates was analyzed.

Abstract

To study the seismic responses of a continuous beam bridge with safe-belt devices, theoretical formulas were derived (i.e., natural period, beam-end displacement, shear force at the bottom of the fixed pier). The effectiveness of these formulas was then verified by comparing the theoretical results with finite element results. Finally, the influence of the continuous beam bridge's total lateral stiffness and of the safe-belt device's installation position on the aseismic rates was analyzed. The results showed that the simplified model of a continuous beam bridge with safe-belt devices is effective, and the proposed theoretical formulas can be used for the seismic design of this type of bridges. The total lateral stiffness of continuous beam bridges and the installation position of the safe-belt device have both a great influence on the aseismic rates, which should be optimized to obtain a good aseismic effect. When the stiffness ratio is greater than 7.0 and safe-belt devices are installed on the top of all sliding piers in continuous bridges, safe-belt devices have a good aseismic effect. Furthermore, the natural period of continuous beam bridges with safe-belt devices should not be similar to the characteristic period of the response spectrum after the activation of the safe-belts.

Section snippets

Author statement

Yuqing Tan: Methodology, Validation, Formal analysis, Data Curation, Writing - Original.

Rong Fang: Conceptualization, Methodology, Validation, Writing - Review & Editing, Visualization, Supervision.

Wenxue Zhang:Conceptualization, Writing - Review & Editing, Supervision, Project administration, Funding acquisition.

Hanqing Zhao:Conceptualization, Software, Investigation, Writing - Review & Editing.

Xiuli Du:Writing - Review & Editing, Supervision, Project administration.

Safe-belt device

The safe-belt device contains one belt ①, two locking platens ②, two outer sealing plates ③, two locking shafts ④, one connecting block ⑤, some assembly bolts ⑥, one lower sealing plate ⑦, some fixed bolts ⑧, and two brackets ⑨, (Fig. 1, Fig. 2). Some fixed bolts ⑧ are used to fix the safe-belt device on the top of the sliding pier ⑩. The ends of belt ① are fixed to a girder ⑪ by the two brackets ⑨.

Under normal conditions (no earthquakes), the locking shaft ④ is located at position 1, and there

Natural periods of model 1 and model 2

Model 1 is a continuous beam bridge without safe-belt devices. The interaction between the sliding piers and the girder were neglected, so the simplified model of Model 1 is a single-degree-of-freedom system (Fig. 4a). In Fig. 4a), m is the sum of the girder's mass and 1/3 of the fixed pier's mass; moreover, k and c represent the lateral stiffness and the damping of the fixed pier, respectively. The natural period of Model 1 can be calculated as:T=2πω=2πmk(1-ζ2)where ω is the natural circular

Bridge

A three-span continuous beam bridge was considered in this study to compare the theoretical results with finite element results. In Fig. 5, the span combination was 48 m + 80 m + 48 m, the girder weighed 71630.16 kN, and the distance from the pier's top to the girder's section centroid was 2.56 m. Pier 3 was a fixed pier. Table 1 shows the parameters of the girder and of the piers.

Finite element model

Fig. 6 shows the finite element models of Model 1 and Model 2 in the ANSYS software. In Model 1 and Model 2, the

Influence of the total lateral stiffness and influence of the installation position

The aseismic rate λx of the beam-end displacement in Model 2 can be calculated asλx=1-xx=1-j=1n+1(γjXj1ωdj2Saj)2Sa/ω2

Moreover, the aseismic rate λQ of the shear force at the bottom of the fixed pier in Model 2 can be calculated asλQ=1-QQ=1-j=1n+1(k1(m1mf)+ktotalmfktotalγjXj1Saj)2mSa

Based on the theoretical results of aseismic rate shown in Fig. 22, Fig. 23, Fig. 24, Fig. 25, Fig. 26, Fig. 27, Fig. 28, the influence of the continuous beam bridge's total lateral stiffness and of the

Conclusions

To investigate the seismic responses of a continuous beam bridge equipped with safe-belt devices, a simplified model of Model 2 was proposed and the theoretical formulas of the natural period, of the beam-end displacement, and of the fixed pier bottom's shear force were derived. To verify the effectiveness of the proposed theoretical formulas, a three-span continuous beam bridge was taken as an example, and the theoretical results were compared with finite element results. The influence of the

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant number 51778022).

References (27)

  • F.H. Dezfuli et al.

    Seismic vulnerability assessment of a steel-girder highway bridge equipped with different SMA wire-based smart elastomeric isolators

    Smart Mater Struct

    (2016)
  • S.K. Mishra et al.

    Response of bridges isolated by shape memory-alloy rubber bearing

    J Bridge Eng

    (2016)
  • F.H. Dezfuli et al.

    Smart lead rubber bearings equipped with ferrous shape memory alloy wires for seismically isolating highway bridges

    J Earthq Eng

    (2018)
  • View full text