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Dynamics of pedestrian timber bridges: Experimental and numerical analyses at various stages of construction
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.ORCID iD: 0009-0002-1067-9697
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 [en]
Pedestrian timber bridge, Experimental modal damping ratio, Dynamic finite element analysis, Slip modulus, Axial withdrawal stiffness, Partial composite action, Soil-structure interaction, Asphalt layer
Keywords [sv]
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: urn:nbn:se:kth:diva-373014ISBN: 978-91-8106-488-9 (print)OAI: oai:DiVA.org:kth-373014DiVA, id: diva2:2014482
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
List of papers
1. Dynamic testing and numerical modelling of a pedestrian timber bridge at different construction stages
Open this publication in new window or tab >>Dynamic testing and numerical modelling of a pedestrian timber bridge at different construction stages
2023 (English)In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 279, article id 115429Article in journal (Refereed) Published
Abstract [en]

This article studies the dynamic properties of a single span pedestrian timber bridge by in-situ testing and numerical modelling. The in-situ dynamic tests are performed at four different construction stages: (1) on only the timber structure, (2) on the timber structure with the railings, (3) on the timber structure with railings and an asphalt layer during warm conditions and (4) same as stage 3 but during cold conditions. Finite element models for the four construction stages are thereafter implemented and calibrated against the experimental results. The purpose of the study is to better understand how the different parts of the bridge contribute to the overall dynamic properties. The finite element analysis at stage 1 shows that longitudinal springs must be introduced at the supports of the bridge to get accurate results. The experimental results at stage 2 show that the railings contributes to 10% of both the stiffness and mass of the bridge. A shell model of the railings is implemented and calibrated in order to fit with the experimental results. The resonance frequencies decrease with 10–20% at stage 3 compared to stage 2. At stage 3 it is sufficient to introduce the asphalt as an additional mass in the finite element model. For that, a shell layer with surface elements is the best approach. The resonance frequencies increase with 15–30% between warm (stage 3) and cold conditions (stage 4). The stiffness of the asphalt therefore needs to be considered at stage 4. The continuity of the asphalt layer could also increase the overall stiffness of the bridge. The damping ratios increase at all construction stages. They are around 2% at warm conditions and around 2.5% at cold conditions for the finished bridge.

Place, publisher, year, edition, pages
Elsevier BV, 2023
Keywords
Pedestrian bridge, Timber, Railings, Asphalt, Dynamic analysis, Finite element modelling
National Category
Civil Engineering
Research subject
Civil and Architectural Engineering, Structural Engineering and Bridges
Identifiers
urn:nbn:se:kth:diva-324493 (URN)10.1016/j.engstruct.2022.115429 (DOI)000954303900001 ()2-s2.0-85145980986 (Scopus ID)
Funder
Swedish Transport Administration, BBT 2019- 028J. Gust. Richert stiftelse, 2020-00611
Note

QC 20230426

Available from: 2023-03-02 Created: 2023-03-02 Last updated: 2025-11-18Bibliographically approved
2. Dynamic analysis of a pedestrian timber truss bridge at three construction stages
Open this publication in new window or tab >>Dynamic analysis of a pedestrian timber truss bridge at three construction stages
2024 (English)In: Structures, E-ISSN 2352-0124, Vol. 59, article id 105763Article in journal (Refereed) Published
Abstract [en]

This article investigates the dynamic behaviour of a single span pedestrian timber truss bridge by in situ testing and numerical modelling. The in situ dynamic tests were performed at three different construction stages: (1) on only the truss structure, (2) on the finished bridge without the asphalt layer and (3) on the finished bridge with the asphalt layer. The objective is to better understand how the different parts of the bridge contribute to the overall dynamic properties. The experimental results show that the damping ratios increased significantly for the first lateral mode (from 1.0 to 3.8%) and the first torsional mode (from 1.2 to 3.5%) between stage 2 and stage 3 due to the asphalt layer. The damping ratio is around 1.6% for the first bending mode for the finished bridge. The experimental and numerical results indicate that the stiffness of the asphalt layer is important to consider at stage 3 (10 degrees C) for the first lateral and torsional mode, but not for the first bending mode. Finally, it was concluded that longitudinal springs must be applied at the pot bearings in order to get agreement with the experimental results at all the three stages.

Place, publisher, year, edition, pages
Elsevier BV, 2024
Keywords
Pedestrian bridge, Timber, Railings, Asphalt, Dynamic analysis, Finite element modelling
National Category
Infrastructure Engineering
Identifiers
urn:nbn:se:kth:diva-343061 (URN)10.1016/j.istruc.2023.105763 (DOI)001141906800001 ()2-s2.0-85185840720 (Scopus ID)
Note

Not duplicate with DiVA 1741105

QC 20240206

Available from: 2024-02-06 Created: 2024-02-06 Last updated: 2025-11-18Bibliographically approved
3. Dynamic analysis of a pedestrian timber bridge considering the connections and pile foundations
Open this publication in new window or tab >>Dynamic analysis of a pedestrian timber bridge considering the connections and pile foundations
2025 (English)In: Structures, E-ISSN 2352-0124, Vol. 74, article id 108550Article in journal (Refereed) Published
Abstract [en]

This article investigates the dynamic behaviour of a pedestrian timber truss bridge by in situ testing and numerical modelling. The in situ dynamic tests were performed at three different construction stages: (1) on the finished bridge without the asphalt layer, (2) on the finished bridge with the asphalt layer at warm conditions and (3) same as stage 2 but at cold conditions. The interest of this study is that some modelling details that are usually not considered in the numerical modelling of pedestrian timber bridges are important for this bridge. The stiffness at the connections must be considered in order to obtain accurate numerical results for both lateral and bending modes. The stiffness of the pile foundations has an influence on the first bending mode. In addition, the experimental damping ratio for the first lateral mode is much higher than the values recommended in the design codes.

Place, publisher, year, edition, pages
Elsevier BV, 2025
Keywords
Asphalt, Axial withdrawal stiffness, Dynamic analysis, Finite element modelling, Pedestrian bridge, Slip modulus, Soil–structure interaction, Timber
National Category
Infrastructure Engineering Construction Management
Identifiers
urn:nbn:se:kth:diva-361799 (URN)10.1016/j.istruc.2025.108550 (DOI)001446247300001 ()2-s2.0-86000611787 (Scopus ID)
Note

QC 20250401

Available from: 2025-03-27 Created: 2025-03-27 Last updated: 2025-11-18Bibliographically approved
4. Dynamic and stability analyses of a pedestrian hybrid steel-timber arch bridge with composite timber arches
Open this publication in new window or tab >>Dynamic and stability analyses of a pedestrian hybrid steel-timber arch bridge with composite timber arches
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The dynamic and static behaviour of a pedestrian hybrid steel-timber arch bridge is investigated in this article. The main interest of this study is the modular design of the timber arches consisting of mechanically connected glulam beams. The individual arch segments are interconnected with a novel steel hinge connection. Dynamic and static tests were performed on a full-scale model of an arch segment (3.95 m long) in a laboratory. In situ dynamic tests were performed on the finished bridge. The results showed that the partial composite action of the arches affected the out-of-plane modes of vibration and critical buckling load of the bridge substantially. The stiffness of the steel hinge connections in the arches reduced the critical buckling load of the bridge slightly. The analysis also showed that the slip modulus between the structural elements affected both the dynamic and buckling behaviours. Finally, the experimental damping ratios were around 1-1.5 % for the bridge which is similar to the recommended values in the technical guidelines. 

Keywords
Pedestrian arch bridge; Mechanically connected timber beam; Finite element analysis; Partial composite action; Slip modulus
National Category
Infrastructure Engineering Civil Engineering Structural Engineering
Research subject
Civil and Architectural Engineering; Civil and Architectural Engineering, Structural Engineering and Bridges
Identifiers
urn:nbn:se:kth:diva-372989 (URN)
Funder
Swedish Transport Administration, BBT 2022-021J. Gust. Richert stiftelse, 2020-00611
Note

QC 20251128

Available from: 2025-11-17 Created: 2025-11-17 Last updated: 2025-11-28Bibliographically approved
5. Dynamic analysis of a pedestrian timber cable-stayed bridge
Open this publication in new window or tab >>Dynamic analysis of a pedestrian timber cable-stayed bridge
(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
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:nbn:se:kth:diva-372993 (URN)
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

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