Investigation on the vehicle-bridge dynamic interaction considering the vertical curvature of bridge and environmental thermal effects.

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Title: Investigation on the vehicle-bridge dynamic interaction considering the vertical curvature of bridge and environmental thermal effects.
Authors: Li, Jiantao1 (AUTHOR), Tan, Jie1 (AUTHOR), Zhu, Xinqun2 (AUTHOR) xinqun.zhu@uts.edu.au, Ruan, Weidong1 (AUTHOR)
Source: Advances in Structural Engineering. Jul2026, Vol. 29 Issue 10, p1918-1935. 18p.
Subjects: Timoshenko beam theory, Temperature effect, Structural dynamics, Dynamic loads, Bridge design & construction, Vibration (Mechanics), Mode shapes
Abstract: River-crossing bridges often utilise curved design to account for the highway profile change, distribute traffic loads and manage water flow. The vehicle-curved bridge interaction (VBI) is complicated, especially combining with environmental thermal effects. These thermo-mechanical interactions differ substantially from those in straight bridges and warrant detailed study. In this study, a curved bridge is modeled as a Timoshenko beam (TB) with pinned supports at both ends. Governing equations are derived using the four-node isoparametric beam element and cubic polynomial shape function. The vehicle is modelled as a half-car model to account for its bouncing and pitching motions. Thermal effects are represented by a linear temperature gradient through the beam depth, which is converted into equivalent thermal loads. An analytical framework that superimposes moving vehicle loads and thermal loads within the coupled motion equations is developed. The dynamic response of the VBI system is analyzed using a zero-order displacement and velocity overshoot (U0-V0) iterative method. The parametric study reveals that: (1) the shear deformation significantly affects high vibration modes; (2) the bridge stiffness increases when the radius of its curvature reduces, which induces the reduction of bridge and vehicle displacement responses; (3) the thermal bending and expansion of the bridge have a large effect on dynamic amplification factor (DAF), while the impact of its curvature on dynamic load coefficient (DLC) becomes dominant for high vehicle speeds. These findings provide valuable insights for the design, analysis, and maintenance of curved bridges operating under combined vehicular and thermal loading conditions. [ABSTRACT FROM AUTHOR]
Copyright of Advances in Structural Engineering is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
  Group: Ti
  Data: Investigation on the vehicle-bridge dynamic interaction considering the vertical curvature of bridge and environmental thermal effects.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Jiantao%22">Li, Jiantao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tan%2C+Jie%22">Tan, Jie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhu%2C+Xinqun%22">Zhu, Xinqun</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> xinqun.zhu@uts.edu.au</i><br /><searchLink fieldCode="AR" term="%22Ruan%2C+Weidong%22">Ruan, Weidong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Advances+in+Structural+Engineering%22">Advances in Structural Engineering</searchLink>. Jul2026, Vol. 29 Issue 10, p1918-1935. 18p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Timoshenko+beam+theory%22">Timoshenko beam theory</searchLink><br /><searchLink fieldCode="DE" term="%22Temperature+effect%22">Temperature effect</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+dynamics%22">Structural dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+loads%22">Dynamic loads</searchLink><br /><searchLink fieldCode="DE" term="%22Bridge+design+%26+construction%22">Bridge design & construction</searchLink><br /><searchLink fieldCode="DE" term="%22Vibration+%28Mechanics%29%22">Vibration (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mode+shapes%22">Mode shapes</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: River-crossing bridges often utilise curved design to account for the highway profile change, distribute traffic loads and manage water flow. The vehicle-curved bridge interaction (VBI) is complicated, especially combining with environmental thermal effects. These thermo-mechanical interactions differ substantially from those in straight bridges and warrant detailed study. In this study, a curved bridge is modeled as a Timoshenko beam (TB) with pinned supports at both ends. Governing equations are derived using the four-node isoparametric beam element and cubic polynomial shape function. The vehicle is modelled as a half-car model to account for its bouncing and pitching motions. Thermal effects are represented by a linear temperature gradient through the beam depth, which is converted into equivalent thermal loads. An analytical framework that superimposes moving vehicle loads and thermal loads within the coupled motion equations is developed. The dynamic response of the VBI system is analyzed using a zero-order displacement and velocity overshoot (U0-V0) iterative method. The parametric study reveals that: (1) the shear deformation significantly affects high vibration modes; (2) the bridge stiffness increases when the radius of its curvature reduces, which induces the reduction of bridge and vehicle displacement responses; (3) the thermal bending and expansion of the bridge have a large effect on dynamic amplification factor (DAF), while the impact of its curvature on dynamic load coefficient (DLC) becomes dominant for high vehicle speeds. These findings provide valuable insights for the design, analysis, and maintenance of curved bridges operating under combined vehicular and thermal loading conditions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Advances in Structural Engineering is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1177/13694332251391484
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: 1918
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      – SubjectFull: Timoshenko beam theory
        Type: general
      – SubjectFull: Temperature effect
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      – SubjectFull: Structural dynamics
        Type: general
      – SubjectFull: Dynamic loads
        Type: general
      – SubjectFull: Bridge design & construction
        Type: general
      – SubjectFull: Vibration (Mechanics)
        Type: general
      – SubjectFull: Mode shapes
        Type: general
    Titles:
      – TitleFull: Investigation on the vehicle-bridge dynamic interaction considering the vertical curvature of bridge and environmental thermal effects.
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            NameFull: Li, Jiantao
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            NameFull: Tan, Jie
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            NameFull: Zhu, Xinqun
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            NameFull: Ruan, Weidong
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            – D: 15
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 10
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