Dynamic Characteristic of the Medium Span Concrete Footbridges

Concrete footbridges, due to their mass, stiffness and damping, are perceived as strucaires more resistant to vibration caused by dynamic action of the users. In order to verify the dynamic behaviour of concrete footbridges, a series of field tests and numerical analyses have been carried out. In the paper, the results of the dynamic field tests of three medium span concrete footbridges with different structural systems （frame, beam and arch footbridges） and their dynamic characteristics （mass, stiffness and damping） are presented. The field tests were carried out for different types of vibration excitation caused by walking, running and jumping persons. Furthermore, the vibrational comfort criteria for footbridges are shortly described and verified for examined structures. The study were supplemented by numerical calculation of natural mode shapes and frequencies of the structures using the 3D FEA （finite element analysis） models with elastic supports elements in order to ensure the compatibility of the calculated and measured mode shapes of the footbridges.

Stability Reliability of the Lateral Vibration of Footbridges Based on the IEVIE-SA Method

Research on the lateral vibrational stability of footbridges has attracted increasing attention in recent years. However, this stability contains a series of complex mechanisms, such as nonlinear vibration, random excitation, andrandom stability. The Lyapunov method is regarded as an effective tool for analyzing random vibrational stability;however, it is a qualitative method and can only provide a binary judgment for stability. This study proposes anew method, IEVIE–SA, which combines the energy method based on the comparison between the input energyand the variation of intrinsic energy (IEVIE) and the stochastic averaging (SA) method. The improved Nakamuramodel was used to describe the lateral nonlinear stochastic vibration of a footbridge, whereby the IEVIE methodwas used to establish the criteria for judging the lateral vibrational stability. Additionally, the SA method was usedto deduce the corresponding backward Kolmogorov equation. Subsequently, the backward Kolmogorov equationwas combined with the stability criterion established by the IEVIE method to analyze the first passage stability. Theproposed method is a semi-analytical, quantitative method that only requires a small calculation. By applying theproposed method to the Millennium Bridge, method effectiveness was verified by comparing it with the MonteCarlo and traditional Lyapunov methods.

Random stability for lateral vibration on footbridge based on IEVIE-PDE method

The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration stability.At present,the Lyapunov method is mainly used to analyze such stability.However,this method is qualitative,and it cannot quantitatively analyze the vibration stability probability.In this study,a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE)is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge.The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge.A combination of the IEVIE method and the probability density evolution(PDE)method is then proposed,in which the IEVIE method is utilized to determine vibration stability.The PDE method is used to obtain the reliability of vibration stability.The proposed method is successfully applied to the Millennium Bridge,and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods.The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.

One-of-a-Kind Footbridge, Lublin, Poland

The paper presents the construction of a steel footbridge in the People’s Park in Lublin.The initiation and development of the architectural design of an interesting and,as it eventually turned out,aesthetically pleasing footbridge is discussed.Two teams of architects and bridge engineers worked in parallel on the design.The design process of the footbridge structure is discussed along with its trial installation and on-site construction.The span of the footbridge is short,but its structure is innovative.For this reason its numerical model was developed used as a basis for an analysis of the dynamic response of the designed structure.The basic element of the acceptance procedure was constituted by a dynamic test load and an analysis of the pedestrian footbridge user comfort.Last but not least,the final section reviews the aesthetic canons of bridges and focuses on the footbridge in question in this context.A statistical measure of the aesthetic impression induced by a visit to the footbridge was applied resulting in a predictable and obvious final aesthetical assessment.

Damage Identification in Footbridges from Natural Frequency Measurements

The present study aims to develop a robust structural damage identification method that can be used for the evaluation of bridge structures. An approach for the structural damage identification based on the measurement of natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. A computational procedure for the direct iteration technique based on the non-linear perturbation theory is proposed to identify structural damage. The presented damage identification technique is applied to the footbridge over the Slunjcica River near Slunj to demonstrate the effectiveness of the proposed approach. Using a limited number of measured natural frequencies, reduction in the stiffness of up to 100% at multiple sites is detected. The results indicate that the proposed approach can be successful in not only predicting the location of damage but also in determining the extent of structural damage.

The Ołowianka Bascule Footbridge in Gdansk-A Bridge That Makes the Difference

In the city of Gdansk in Poland,in the very center of the Baltic capital,on 17th of June 2017,a new draw footbridge was ceremoniously opened to the public.The Olowianka footbridge represents the long-time much needed link between the highly tourist-visited historical old town and Ołowianka Island,where further cultural,tourist and recreation facilities are located.The bridge spans a very busy navigable channel of the Motława River,leading inward towards other city channels,a harbor for many tourist ships and the Gdansk Marina.Being the main navigable entrance to the city center,the Motława is constantly under nautical traffic,so the Ołowianka footbridge operates 24/7,according to a 30-min schedule.The Ołowianka footbridge is an extraordinary acquisition for the city of Gdansk,which immediately became a new landmark and much more in the already very picturesque historic city center.Not just its design,but also its carefully chosen location and its realization at the right moment,has made this bridge indispensable to the inhabitants,visitors and the administration of the city of Gdansk,decisively contributing to further development in the Ołowianka Island area and its surroundings.

Curved footbridges supported by a shell obtained through thrust network analysis

After Maillart's concrete curved arch bridges were built before the Second World War, in the second half of the past century and this century, many curved bridges have been built with both steel and concrete. Conversely, since the construction of Musmeci's shell supported bridge in Potenza, few shell bridges have been constructed. This paper explains how to design a curved footbridge supported by an anticlastic shell by shaping the shell via a thrust network analysis(TNA). By taking advantage of the peculiar properties of anticlastic membranes, the unconventional method of shaping a shell by a TNA is illustrated. The shell top edge that supports the deck has an assigned layout, which is provided by the road curved layout. The form of the bottom edge is obtained by the form-finding procedure as a thrust line, by applying the thrust network analysis(TNA) in a non-standard manner,shaping the shell by applying the boundary conditions and allowing relaxation. The influence of the boundary conditions on the bridge shape obtained as an envelope of thrust lines is investigated. A finite element analysis was performed. The results indicate that the obtained shell form is effective in transferring deck loads to foundations via compressive stresses and taking advantage of concrete mechanical properties.

Vibration control of pedestrian-bridge vertical dynamic coupling interaction based on biodynamic model

The human-induced vertical vibration serviceability of low-frequency and lightweight footbridges is studied based on the moving mass-spring-damper（MMSD） biodynamic model, and the mass damper（TMD） with different optimal model parameters being used to control the vertical vibration.First, the MMSD biodynamic model is employed to simulate the pedestrians, and the time-varying control equations of the vertical dynamic coupling system of the pedestrian-bridgeTMD are established with the consideration of pedestrianbridge dynamic interaction; and the equations are solved by using the Runge-Kutta-Felhberg integral method with variable step size. Secondly, the footbridge dynamic response is calculated under the model of pedestrian-structure dynamic interaction and the model of moving load when the pedestrian pace frequency is consistent with the natural frequency of footbridge. Finally, a comparative study and analysis are made on the control effects of the vertical dynamic coupling system in different optimal models of the TMD. The calculation results show that the pedestrian-bridge dynamic interaction cannot be ignored when the vertical human-induced vibration serviceability of low-frequency and light-weight footbridge is evaluated. The TMD can effectively reduce the vibration under the resonance of pedestrian-bridge, and TMD parameters are recommended for the determination by the Warburton optimization model.

Durability of Stress Ribbon Bridge Checked during Loading Test

Stress ribbon bridges have many advantages and became recently more popular mostly because of their versatile form, slender decks giving a light aesthetic impression and durability assured by post tensioned concrete. The paper presents the first in Poland stress Ribbon Bridge constructed last year. A static and dynamic analyse of the model is presented as well as construction solutions which were used to achieve the highest durability. The bridge was checked during static and dynamic load test. The results of this prove test were compared with results obtained from examination and study of other different bridge structures. It confirmed that the bridge has good dynamic resistance and greater stiffness than assumed in the design.

Bridge Structures with GFRP Composite Deck

In this paper, author’s first part of research of GFRP bridge deck (using ASSET fiber line composite modular system) took part at AGH University of Science and Technology Laboratory of Glass Technology and Amorphous Coatings Department. The analysis consisted spectrometer analysis of chemical constitution of glass fiber, identification of material according to Fourier spectroscopy, electronic scan microscopy (SEM/EDAX) and DTA analysis. The modal FEM analysis of chosen footbridge with light GFRP deck has been presented in the paper.