pith. machine review for the scientific record. sign in

arxiv: 2604.24202 · v2 · submitted 2026-04-27 · 💻 cs.CE

Recognition: unknown

Assessing the dynamic response of long-span bridges under simultaneous wind and traffic loads

Gledson Rodrigo Tondo , Guido Morgenthal
Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:26 UTC · model grok-4.3

classification 💻 cs.CE
keywords long-span bridgeswind-traffic interactiondynamic responsenon-linear interactionsquasi-steady aerodynamicstraffic load synthesisbridge design assessment
0
0 comments X

The pith

Combined wind and traffic loads on long-span bridges produce dynamic responses that differ from linear superposition of separate loads.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a simulation framework that places synthesized traffic and turbulent wind on the same long-span bridge model at the same time. It shows that the resulting structural motions and stresses cannot be recovered by adding the outcomes of wind-only and traffic-only runs. Conventional practice treats the two load sources as independent and combines them linearly, an assumption the simulations contradict. If the finding holds, assessment procedures and serviceability checks for long-span bridges would need to incorporate coupled time-history analyses rather than separate load cases.

Core claim

Modeling concurrent wind and traffic actions on long-span bridges using a quasi-steady aerodynamic formulation together with traffic loads synthesized from vehicle volumes, composition, dynamics, ISO roughness with transverse coherence, and Kármán-spectrum wind turbulence with Davenport coherence produces non-linear interactions that modify the dynamic response. Time-history analyses under these combined actions therefore differ from results obtained by linear superposition of independent load cases, exposing limitations in conventional design assumptions that treat wind and traffic separately.

What carries the argument

Quasi-steady aerodynamic model applied in time-history analysis to traffic loads synthesized from vehicle dynamics and road roughness spectra, run simultaneously with wind turbulence defined by Kármán spectrum and Davenport coherence.

If this is right

  • Non-linear interactions alter the bridge response relative to independent wind-only and traffic-only analyses.
  • Conventional assumptions of linear superposition have limitations for accurate response prediction on long-span bridges.
  • The coupled modeling framework supports more accurate performance assessment under service conditions.
  • Results can be used to refine serviceability criteria and to guide design optimization for long-span bridges.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar coupled analyses could be extended to other load combinations such as wind with temperature or settlement effects.
  • Design guidelines might eventually require coupled simulations for bridges exceeding certain spans or in regions with high concurrent wind and traffic.
  • Validation against full-scale monitoring data from existing long-span bridges would provide a direct test of the predicted non-linear effects.

Load-bearing premise

The quasi-steady aerodynamic model together with traffic loads synthesized from ISO roughness and standard wind spectra is sufficient to represent the real dynamic interactions without large unmodeled nonlinearities or site-specific effects.

What would settle it

Field measurements of acceleration or stress time histories on an instrumented long-span bridge during documented periods of simultaneous wind and traffic, compared against the model's predictions; systematic mismatch in peak values or spectral content would indicate the model misses important interactions.

Figures

Figures reproduced from arXiv: 2604.24202 by Gledson Rodrigo Tondo, Guido Morgenthal.

Figure 1
Figure 1. Figure 1: The Great Belt East Bridge: schematic (top), with the first bending mode (centre, view at source ↗
Figure 2
Figure 2. Figure 2: Cross-section (B, H) and degrees of freedom (h, p, α), mean and turbulent wind components (U, u, w), and aerodynamic forces (D, L, M). The Great Belt Bridge is a suspension bridge with a main span of 1624 m and side spans of 535 m (see view at source ↗
Figure 3
Figure 3. Figure 3: Excerpts of the turbulent wind signal at midspan, in the along-wind direction (top), along-span direction view at source ↗
Figure 4
Figure 4. Figure 4: Examples of 2-axle and 3-axle dynamic vehicle models used in the traffic analysis. view at source ↗
Figure 5
Figure 5. Figure 5: Random road roughness according to ISO 8608, for a road of class B. Transverse profiles are correlated in view at source ↗
Figure 6
Figure 6. Figure 6: Instantaneous configuration of a stochastic traffic simulation in VISSIM, showing different vehicle models view at source ↗
Figure 7
Figure 7. Figure 7: Displacements and rotations (left) of the midspan of the bridge for an individual Case 3, Scenario WT analysis, view at source ↗
Figure 8
Figure 8. Figure 8: Envelopes of displacements and rotations for Scenario W, Scenario T, a linear sum of W and T, and the view at source ↗
Figure 9
Figure 9. Figure 9: Envelope of the three stochastic analyses for Scenario WT, for Case 1 (top), Case 2 (centre) and Case 3 view at source ↗
read the original abstract

Wind-traffic interactions strongly influence the dynamic response of long-span bridges, yet loads are often analysed independently. This work models concurrent wind and traffic and demonstrates that it differs from linear superposition. Traffic is synthesised from volumes, composition, and vehicle dynamics, with vehicles represented as 3D systems. Vehicle-pavement interaction adopts ISO roughness with transverse coherence, and wind turbulence follows the K\'arm\'an spectrum with Davenport coherence. A quasi-steady aerodynamic model supports time-history analysis under combined actions. Results indicate non-linear interactions that change response, revealing limitations of conventional design assumptions. The framework enables accurate performance assessment and informs serviceability criteria and design optimisation for long-span bridges.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a numerical framework for assessing the dynamic response of long-span bridges under simultaneous wind and traffic loads. Traffic is synthesized from volumes, composition, and 3D vehicle dynamics using ISO roughness with transverse coherence; wind uses the Kármán spectrum with Davenport coherence. A quasi-steady aerodynamic model enables time-history analysis of combined actions. The central claim is that the resulting response exhibits non-linear interactions that deviate from linear superposition of separate loads, revealing limitations of conventional independent-load design assumptions.

Significance. If the claimed deviations are shown to arise from physical coupling rather than modeling choices, the work would be significant for bridge engineering by challenging superposition assumptions used in design codes. It could support updated serviceability and optimization criteria for long-span structures. The reliance on standard spectra (Kármán, ISO, Davenport) is a strength for reproducibility, but the absence of quantitative results or validation in the available text limits immediate applicability.

major comments (2)
  1. Abstract: The statement that 'results indicate non-linear interactions that change response' is the load-bearing claim, yet no quantitative metrics (e.g., percentage deviation in mid-span displacement, RMS stress ratios, or spectral differences between combined and superposed cases) are supplied, making it impossible to evaluate the magnitude or statistical robustness of the effect.
  2. Modeling section (quasi-steady aero + load synthesis): The framework applies an independent quasi-steady aerodynamic formulation and open-loop synthesized loads (Kármán wind, ISO traffic) to what appears to be a linear structural model. The paper must demonstrate that any observed deviation from superposition originates from physical mechanisms (motion-induced aeroelastic feedback or vehicle-bridge contact nonlinearities) rather than from the quadratic wind-pressure term, coherence assumptions, or synthesis artifacts; without this, the central claim cannot be substantiated.
minor comments (2)
  1. The abstract and modeling description should specify the bridge type (e.g., suspension vs. cable-stayed) and the details of the structural finite-element or modal model used for time-history integration.
  2. All referenced standards and spectra (ISO roughness, Kármán, Davenport) require explicit citations to the exact documents or papers employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our central claims. We respond to each major comment below and will revise the manuscript to address the points raised.

read point-by-point responses

  1. Referee: Abstract: The statement that 'results indicate non-linear interactions that change response' is the load-bearing claim, yet no quantitative metrics (e.g., percentage deviation in mid-span displacement, RMS stress ratios, or spectral differences between combined and superposed cases) are supplied, making it impossible to evaluate the magnitude or statistical robustness of the effect.

    Authors: We agree that the abstract would be strengthened by including quantitative metrics. In the revised manuscript we will update the abstract to report specific values obtained from the time-history analyses, including the percentage deviation in mid-span displacement, RMS stress ratios, and key spectral differences between the combined-load and linearly superposed cases. These metrics will be drawn directly from the simulation results already presented in the body of the paper. revision: yes

  2. Referee: Modeling section (quasi-steady aero + load synthesis): The framework applies an independent quasi-steady aerodynamic formulation and open-loop synthesized loads (Kármán wind, ISO traffic) to what appears to be a linear structural model. The paper must demonstrate that any observed deviation from superposition originates from physical mechanisms (motion-induced aeroelastic feedback or vehicle-bridge contact nonlinearities) rather than from the quadratic wind-pressure term, coherence assumptions, or synthesis artifacts; without this, the central claim cannot be substantiated.

    Authors: The observed deviations arise from physically grounded nonlinearities in the loading: the quasi-steady aerodynamic model retains the quadratic dependence of wind force on instantaneous velocity (dynamic-pressure term), which is a fundamental physical feature rather than an artifact, and the vehicle-bridge interaction incorporates nonlinear contact forces through the ISO roughness profile with transverse coherence. The structural model is linear, consistent with standard practice for serviceability assessment, but the combined loading is not. In the revised manuscript we will add a new subsection that isolates these effects by comparing the full model against a linearized counterpart (constant mean wind speed for aero forces and linearized contact stiffness). This comparison will quantify the contribution of each physical nonlinearity. We acknowledge that the quasi-steady formulation omits full motion-induced aeroelastic feedback (e.g., flutter derivatives), which we will state explicitly as a modeling limitation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; forward simulation using external standard models.

full rationale

The paper's central demonstration—that concurrent wind+traffic response differs from linear superposition—arises from applying a quasi-steady aerodynamic formulation (with its inherent non-linear terms such as velocity-squared drag) plus synthesized loads from Kármán spectrum, Davenport coherence, and ISO roughness to a structural model. This is a forward time-history simulation whose output difference is a direct consequence of the chosen non-linear load generators, not a fitted parameter or self-referential definition. No equations reduce the claimed non-linear interactions to inputs by construction, and no load-bearing self-citations or uniqueness theorems from the authors are invoked. The framework draws on externally established spectra and models without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain models for wind turbulence and pavement roughness drawn from prior literature, plus the synthesis of concurrent loads; no new entities are introduced and no free parameters are explicitly fitted in the abstract.

axioms (2)
  • domain assumption Quasi-steady aerodynamic model is adequate for time-history analysis of wind loads on the bridge under combined actions.
    Invoked to support the time-history analysis under combined wind and traffic.
  • domain assumption ISO roughness spectrum with transverse coherence and Kármán wind spectrum with Davenport coherence accurately represent real vehicle-pavement and wind turbulence conditions.
    Adopted directly for vehicle-pavement interaction and wind turbulence modeling.

pith-pipeline@v0.9.0 · 5407 in / 1505 out tokens · 105047 ms · 2026-05-07T17:26:38.775173+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

15 extracted references

  1. [1]

    S. R. Chen and J. Wu. Dynamic performance simulation of long-span bridge under combined loads of stochastic traffic and wind.Journal of Bridge Engineering, 15(3):219–230, 2010

    2010

  2. [2]

    Camara, I

    A. Camara, I. Kavrakov, K. Nguyen, and G. Morgenthal. Complete framework of wind-vehicle-bridge interaction with random road surfaces.Journal of Sound and Vibration, 458:197–217, 2019. 8 IABSE SYMPOSIUMCOPENHAGEN2026 - BRIDGING ADVANCED TECHNOLOGIES- STRUCTURAL INNOVATION COPENHAGEN, DK, 2026

    2019

  3. [3]

    T. Wang, W. Han, F. Yang, and W. Kong. Wind-vehicle-bridge coupled vibration analysis.Journal of Traffic and Transportation Engineering, 1(4):293–308, 2014

    2014

  4. [4]

    Y . L. Xu and W. H. Guo. Dynamic analysis of coupled road vehicle and bridge systems.Engineering Structures, 25(4):473–486, 2003

    2003

  5. [5]

    Zhang, C

    J. Zhang, C. Zhu, and C. Ma. Driving safety analysis of wind–vehicle–bridge system considering aerodynamic interference.Journal of Wind Engineering and Industrial Aerodynamics, 245:105649, 2024

    2024

  6. [6]

    G. R. Tondo, I. Kavrakov, and G. Morgenthal. Bayesian non-linear load estimation in long-span bridges via physics- informed gaussian processes. InBridge Maintenance, Safety, Management, Digitalization and Sustainability, pages 3522–3529, 2024

    2024

  7. [7]

    Gledson Rodrigo Tondo, Igor Kavrakov, and Guido Morgenthal. Efficient dynamic modal load reconstruction using physics-informed gaussian processes based on frequency-sparse fourier basis functions.Mechanical Systems and Signal Processing, 225:112295, 2025

    2025

  8. [8]

    Kavrakov, G

    I. Kavrakov, G. Morgenthal, and A. McRobie. Data-driven aeroelastic analyses using enhanced gaussian processes. Journal of Wind Engineering and Industrial Aerodynamics, 253:105848, 2024

    2024

  9. [9]

    G. R. Tondo, I. Kavrakov, and G. Morgenthal. Physics-informed machine learning model for reconstruction of dynamic loads. InIABSE Symposium Istanbul, 2023

    2023

  10. [10]

    Fafard, M

    M. Fafard, M. Bennur, and M. Savard. A general multi-axle vehicle model to study the bridge-vehicle interaction. Engineering Computations, 14(5):491–508, 1997

    1997

  11. [11]

    Control performance of suspension system of cars with pid control based on 3d dynamic model.Journal of mechanical engineering, automation and control systems, 1(1):1–10, 2020

    Mei Tian and Vanliem Nguyen. Control performance of suspension system of cars with pid control based on 3d dynamic model.Journal of mechanical engineering, automation and control systems, 1(1):1–10, 2020

    2020

  12. [12]

    Iso 8608: Mechanical vibration – road surface profiles, 1995

    1995

  13. [13]

    Bogsjö, K

    K. Bogsjö, K. Podgórski, and I. Rychlik. Models for road surface roughness.Vehicle System Dynamics, 50(5):725– 747, 2012

    2012

  14. [14]

    StatBank Denmark

    Road traffic of danish vehicles, 2023. StatBank Denmark

    2023

  15. [15]

    Storebaelt.dk

    Vehicles and vulnerability to wind, 2025. Storebaelt.dk. 9

    2025