This article investigates the dynamic and static behaviour of a novel steel hinge connection for the arch of a recently built pedestrian timber bridge. A full-scale model of an arch section was built in laboratory andexperimentally tested at four different stages of construction to properly evaluate the material properties, degree of composite action between the timber members and the stiffness of the connection. The results showed that the composite action was partial with an approximately 70 % reduction of the second moment of area and torsional constant when comparing the numerical and experimental results. The dynamic rotational stiffness of the connection was around 0.9-3.4 MNm/rad (out-of plane bending) and 10.0-27.0 MNm/rad (in-plane bending). The static results indicated that the rotational stiffness was around 2.5-7.5 MNm/rad (out-of plane) and 1.9-9.1 MNm/rad (in-plane). The compressive stiffness could potentially be around 2-8 times larger (4 times on average) than the tensile stiffness of the steel hinge connection.

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.

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. 

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. 

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.

Pedestrian bridges can beneficially be made from timber in order for our society to reach a sustainable future. This positive development is partly made possible due to advances in engineered wood products (e.g. glued laminated timber) and the possibilities for pre-fabrication of structural parts. Timber bridges, especially long and slender, can however be susceptible to uncomfortable vibrations which could be solved by more accurate dynamic analysis in the design phase. Common issues reported by previous research are the difficulties in accurate predictions of the natural frequencies without calibration against experimental results. The purpose with the present research work is therefore to perform dynamic analysis of two pedestrian timber bridges at different construction stages in order to better understand the influence of different structural parts in the numerical models. The results show that the estimated and applied values for the densities of the timber (Norway spruce and Scots pine) are slightly higher than in the norm. Both bridges required calibration of longitudinal stiffness at the supports for the numerical results to agree with the experiments. The railings could be omitted from the numerical models for both bridges, which is in contrast with common engineering practise where they are often considered as an additional mass. The stiffness of the asphalt was required at low temperatures (10 °C and 0 °C). However, the asphalt could be modelled as an additional mass at a high temperature (40 °C) where special care also could be given to the effects of the composite cross-section geometry (timber deck and asphalt). The level of detail for the modelling of the truss joints, the connection truss/crossbeam and the connection deck/crossbeams proved to be an important issue for the Stela bridge. The damping ratios (ζ) increased with an asphalt layer on the bridge and are slightly higher than the values recommended by the norms. This may be relevant to consider in the design phase. However, it may be difficult to derive general conclusions for other pedestrian timber bridges since this thesis only concerns case studies of two bridges. More studies of other types of bridges are therefore necessary in order to confirm or disprove the present results

Gång- och cykelbroar kan med fördel konstrueras med trä för att vårt samhälle ska nå en hållbar framtid. Denna positiva utveckling är delvis möjlig tack vare framsteg inom produktion av träbaserade konstruktionselement (t.ex. limträ) och möjligheter för pre-fabricering av konstruktionsdelar. Träbroar, särskilt långa och slanka, kan dock vara känsliga för obekväma vibrationer vilket kan lösas genom en förbättrad dynamisk bedömning i projekteringsfasen. Vanliga problem som rapporterats i tidigare forskning är svårigheterna med att förutspå egenfrekvenserna utan kalibrering gentemot experimentella resultat. Syftet med det aktuella forskningsarbetet är därför att genomföra dynamisk analys av två gång- och cykelbroar i trä vid olika konstruktionsfaser för att bättre kunna förstå de olika konstruktionselementens inverkan i de numeriska modellerna. Resultaten visar att de uppskattade och tillämpade värdena för träets densitet (gran och tall) är något högre än i normen. Båda broarna krävde kalibrering av longitudinell styvhet vid stöden för att de numeriska resultaten skulle överensstämma med experimenten. Räckena kunde utelämnas från de numeriska modellerna för båda broarna, vilket är i motsats till ingenjörspraxis där de ofta betraktas som en extra massa. Beaktning av asfaltens styvhet krävdes vid låga temperaturer (10 ◦C och 0 ◦C). Asfalten kunde dock modelleras som en extra massa vid hög temperatur (40 ◦C) där särskild hänsyn även kan ges åt effekterna av den sammansatta tvärsnittsgeometrin (trädäck och asfalt). Detaljnivån för modelleringen av fackverkets knutpunkter, kopplingen fackverk/tvärbalk och kopplingen däck/tvärbalkar visade sig vara en viktig faktor för Stela bro. Dämpningen (ζ) ökade med ett asfaltlager på bron vilket indikerar att detta kan vara relevant att ta hänsyn till i projekteringsfasen. Det kan emellertid vara svårt att dra generella slutsatser om andra gång- och cykelbroar i trä eftersom denna avhandling enbart beaktar fallstudier av två broar. Ytterligare studier av andra typer av broar är därmed nödv¨andiga för att bekräfta eller motbevisa de givna resultaten.

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.

The objective of this article is to study the dynamic behaviour of a timber pedestrian bridge by performing in-situ tests 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. The study included numerical calculations with a 2D finite element model. Two modal parameter extraction methods were implemented during the post-processing. The modes of vibration were analysed with the modal assurance criterion (MAC) to ensure their validity. The results show that the presence of the railings during stage 2 increases the resonance frequencies with 0-2 % compared to stage 1, despite an approximately 5 % increase of the total mass of the bridge. The vertical resonance frequencies decreased 12-22 % when the asphalt was installed at stage 3 compared to stage 2, due to an approximately 70 % increase of the total mass and the asphalt’s low stiffness due to a high temperature. The resonance frequencies increased 14-27 % during cold conditions at stage 4 compared to stage 3. This was mainly due to an increased stiffness of the asphalt layer due to a low temperature. Adding railings therefore resulted in a higher overall stiffness of the bridge, whereas asphalt essentially only added mass to the bridge at warm conditions but increased the stiffness at cold compared to warm conditions. The damping ratios increased for each construction stage and were approximately 2-3 % for the finished bridge. The two modal parameter extraction methods produced similar results which ensures that reliable results are obtained. The auto-MAC indicated well-separated modes and the cross-MAC ensured comparison of the same modes. The finite element model showed that some stiffness was lacking for the first bending mode. This stiffness could be due to shear deformation of the plastic pads at the bridge supports.