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Dynamic analysis of a pedestrian timber cable-stayed bridge
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.ORCID iD: 0009-0002-1067-9697
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.ORCID iD: 0000-0003-2104-382X
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Building Materials.ORCID iD: 0000-0002-5347-4467
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The dynamic behaviour of a pedestrian timber cable-stayed bridge is analysed by in situ testing and numerical modelling in this article. Two in situ dynamic tests were performed at warm conditions: (1) on the finished bridge and (2) on the stay cables of the finished bridge. The main interests of this study are: a) investigation of the reduced axial stiffness of the stays, b) application of the connection stiffnesses between the timber members and c) evaluation of different modelling alternatives for the deck. The equivalent E-moduli of the stay cables were estimated by calculating the stay cable forces from the experimental resonance frequencies. Applying the reduced values on the E-moduli of the stays provided more accurate numerical results for the first bending mode. The connection stiffnesses between the timber members were shown to mainly affect the lateral modes. The asphalt layer was shown to add some stiffness to the bridge deck even at high temperatures. Modelling the CLT and asphalt layer with a composite layup gave sufficiently accurate results compared to a more detailed modelling alternative for the bridge deck. The experimental damping ratios of the bridge were considerably lower than the values in technical guidelines except for the first lateral mode. 

Keywords [en]
Pedestrian timber cable-stayed bridge; Equivalent E-modulus; Slip modulus; Finite element analysis; Dynamic analysis
National Category
Civil Engineering Infrastructure Engineering Structural Engineering
Research subject
Civil and Architectural Engineering, Structural Engineering and Bridges; Civil and Architectural Engineering
Identifiers
URN: urn:nbn:se:kth:diva-372993OAI: oai:DiVA.org:kth-372993DiVA, id: diva2:2014174
Funder
Swedish Transport Administration, BBT 2022-021J. Gust. Richert stiftelse, 2020-00611
Note

QC 20251127

Available from: 2025-11-17 Created: 2025-11-17 Last updated: 2025-11-27Bibliographically approved
In thesis
1. Dynamics of pedestrian timber bridges: Experimental and numerical analyses at various stages of construction
Open this publication in new window or tab >>Dynamics of pedestrian timber bridges: Experimental and numerical analyses at various stages of construction
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Construction of pedestrian timber bridges is an important step towards creating a more sustainable future. However, bridges with resonance frequencies close to the pedestrian pacing frequencies can be susceptible to uncomfortable vibrations. Previous research work has shown that numerical models often require specific adjustments to agree with experimental results. The purpose of the present research project has therefore been to perform experimental and numerical dynamic analyses of five pedestrian timber bridges at different construction stages to increase the general knowledge regarding the implementation of more accurate finite element models.

The results showed that calibration of the longitudinal stiffness at the supports were required for the girder and truss bridges in Papers I-II. The connection stiffnesses between the timber members were required to calibrate the truss and arch bridges in Papers III-IV. The stiffness of the pile foundations was implemented in Paper III to calibrate the first bending mode. A simplified model of the pile foundations by modelling the soil with springs provided adequate results compared to a detailed model with solid elements. The partial composite action of the mechanically connected arch segments and vertical web members was quantified from laboratory experiments and was subsequently implemented in the numerical model of the finished arch bridge in Paper IV, which reduced the stiffness of the first lateral and torsional modes. The reduced axial stiffness of the stays due to their deformed catenary shape was implemented to fine-tune the first bending mode for the cable-stayed bridge in Paper V. The asphalt could generally be modelled as a mass at warm temperatures, but consideration of the asphalt stiffness was required at cold temperatures. Certain structural aspects such as the asphalt continuity at bridge ends and continuity between individual cross-laminated timber elements were also introduced. Railings with in-plane stiffness affected the mass and stiffness of the bridges equally much. The damping ratios typically increased with an asphalt layer on the bridge, especially for modes of vibration with large deformation of the asphalt. These damping ratios were in many cases considerably higher than the values from technical guidelines.

Several model uncertainties were identified and discussed such as the variability in material properties and stiffness definitions as well as climate variations between the construction stages. However, the aforementioned main factors that affected the dynamic properties of each bridge were established. The main conclusion is that most bridges required detailed consideration of certain structural aspects to achieve calibrated results. 

Abstract [sv]

Konstruktion av gång- och cykelbroar i trä är ett viktigt steg mot att skapa en mer hållbar framtid. Broar med resonansfrekvenser i närheten av gångfrekvenserna för gångtrafikanter kan emellertid vara känsliga för obekväma vibrationer. Tidigare forskning har visat att numeriska modeller ofta kräver specifika justeringar för att överrensstämma med de experimentella resultaten. Syftet med det aktuella forskningsprojektet har därför varit att genomföra experimentella och numeriska dynamiska analyser av fem gång- och cykelbroar i trä vid olika konstruktionsskeden för att förbättra den generella kunskapen kring implementering av mer exakta finita element modeller.

Resultaten visade att kalibrering av longitudinell styvhet vid brostöden behövdes för balk- och fackverksbroarna i Artiklarna I-II. Styvheter vid anslutningarna mellan de olika träelementen behövdes för att kalibrera fackverks- och bågbroarna i Artiklarna III-IV. Styvheten för pålfundamenten implementerades i Artikel III för att kalibrera den första böjningsmoden. En förenklad modell för pålfundamenten där jorden modellerades med fjädrar gav adekvata resultat jämfört med en detaljerad modell med solida element. Den partiella samverkan för de mekaniskt sammansatta bågsegmenten och vertikala stagen kvantifierades från experiment i laboratorie och implementerades följdaktligen i den numeriska modellen av den färdiga bågbron i Artikel IV, vilket reducerade styvheten för den första laterala moden och den första vridmoden. Den reducerade axiella styvheten för snedstagen till följd av deras deformerade kedjeform implementerades för att finjustera den första böjmoden för snedkabelbron i Artikel V. Asfalten kunde generellt bli modellerad som en massa vid varma temperaturer, medan beaktande av asfaltens styvhet krävdes vid kalla temperaturer. Särskilda strukturella aspekter såsom asfaltens kontinuitet över broändarna samt kontinuitet mellan individuella korslimmade träelement blev också presenterat. Räcken med styvhet i planet påverkade massan och styvheten av broarna lika mycket. Dämpningsfaktorerna ökade generellt sett med ett asfaltslager på bron, i synnerhet för vibrationsmoder med stor deformation av asfalten. Dessa dämpningsfaktorer var i många fall betydligt högre än värdena från tekniska normer.

Åtskilliga osäkerheter identifierades och diskuterades såsom variabiliteten i materialegenskaperna och formuleringen av styvheterna samt variationer i klimatet mellan konstruktionsstegen. De ovannämnda viktigaste faktorerna som påverkade de dynamiska egenskaperna för varje bro blev emellertid fastställda. Den främsta slutsatsen är att de flesta broarna behövde detaljerat beaktande av vissa strukturella aspekter för att uppnå kalibrerade resultat. 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2025. p. 90
Series
TRITA-ABE-DLT ; 2545
Keywords
Pedestrian timber bridge, Experimental modal damping ratio, Dynamic finite element analysis, Slip modulus, Axial withdrawal stiffness, Partial composite action, Soil-structure interaction, Asphalt layer, Gång- och cykelbro i trä, Experimentell modal dämpning, Dynamisk finita element analys, Förskjutningsmodul, Axiell utdragsstyvhet, Partiell samverkan, Jord-bro interaktion, Asfaltlager
National Category
Structural Engineering
Research subject
Civil and Architectural Engineering, Structural Engineering and Bridges
Identifiers
urn:nbn:se:kth:diva-373014 (URN)978-91-8106-488-9 (ISBN)
Public defence
2025-12-15, Kollegiesalen, Brinellvägen 8, KTH Campus, public video conference link https://kth-se.zoom.us/j/64248423433, Stockholm, 12:30 (English)
Opponent
Supervisors
Funder
Swedish Transport Administration, 2022-021J. Gust. Richert stiftelse, 2020-00611
Note

QC 20251121

Available from: 2025-11-21 Created: 2025-11-18 Last updated: 2025-12-08Bibliographically approved

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Battini, Jean-MarcCrocetti, Roberto

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