Stana Živanović

Benchmark Footbridge for Vibration Serviceability Assessment under the Vertical Component of Pedestrian Load

Vibration serviceability criteria are governing the design and determining the cost of modern, slender footbridges. Efficient and reliable evaluation of dynamic performance of these structures usually requires a detailed insight into the structural behavior under human-induced dynamic loading. Design procedures are becoming ever more sophisticated and versatile, and for their successful use, a thorough verification on a range of structures is required. The verification is currently hampered by a lack of experimental data that are presented in the form directly usable in the verification process. This study presents a comprehensive experimental data set acquired on a box-girder footbridge that is lively in the vertical direction. The data are acquired under normal operating conditions and are presented using a range of descriptors suitable for easy extraction of desired information. This will allow researchers and designers to use this bridge as a benchmark structure for vibration serviceability checks under the vertical component of the pedestrian loading. In addition, capabilities of a sophisticated force model (developed for walking over rigid surfaces) to predict vibrations on this lively bridge are investigated. It was found that there are discrepancies between computed and measured responses. These differences most likely are a consequence of the pedestrian-structure interaction on this lively bridge. The interaction was then quantified in the form of pedestrian contribution to the overall damping of the human-structure system.

Probabilistic Modeling of Walking Excitation for Building Floors

Slender floor structures are becoming increasingly prone to excessive vibration due to human-induced walking excitation. To prevent discomfort of floor occupants and/or malfunctioning of sensitive equipment, it is necessary to have a reliable means of estimating floor vibration in the design phase. For accurate estimation of the floor vibration, both reliable excitation and structural models are required. This paper concentrates on the former by evaluating the performance of the existing force models and suggesting their improvement. For this a force model adopted in the United Kingdom by the Concrete Society was applied to four nominally identical floors using their experimentally identified modal properties. After comparison with experimental data the drawbacks of the force model were identified after which an improved model of the walking-induced dynamic force, based on the combination of two existing methodologies used separately for low- and high-frequency floors, is proposed. The improved model accounts for the intersubject variability in the walking force with respect to the pacing frequency, step length, and forcing magnitude. Moreover, it includes all relevant frequency components of the walking force into analysis, removing the need for classification of floors as low or high frequency. The proposed approach should help designers and building owners to make more informed decisions when evaluating vibration serviceability of floor structures.

Identification and Modelling of Vertical Human-Structure Interaction

Slender footbridges are often highly susceptible to human-induced vibrations, due to their low stiffness, damping and modal mass. Predicting the dynamic response of these civil engineering structures under crowd-induced loading has therefore become an important aspect of the structural design. The excitation of groups of pedestrians and crowds is generally modelled using moving loads but also the changes in dynamic characteristics due to human-structure interaction are found to significantly affect the footbridge response. The present contribution investigates the influence of the presence of the pedestrians onto the dynamic characteristics of the occupied structure by means of an extensive experimental study on a footbridge in laboratory conditions. The analysis shows that the natural frequencies slightly reduce due to the additional mass but more significant is the observed increase in structural damping. Similar observations are made on a in situ footbridge. This interaction is simulated using a coupled human-structure model in which the human occupants are represented by simple biomechanical models.

Design and Construction of a Very Lively Bridge

In recent years, an increasing number of light structures has been reported to exhibit substantial vertical vibrations when exposed to pedestrian-induced dynamic loading. It is believed that pedestrians interact with lively structures by altering their walking style and changing the dynamic properties of the vibrating system. As the existing vibration serviceability guidelines do not address these pedestrian-structure interaction effects, they cannot predict the structural dynamic response accurately. Fundamental understanding of the pedestrian-structure interaction is currently limited since most reported observations are of qualitative nature. To improve understanding and develop models of human interaction with lively structures, a purpose-built experimental facility that can be excited by human walking is required.

Modal properties of beam-and-block pre-cast floors

This article describes a combined experimental and analytical approach to investigating modal properties of beam and block (B&B) building floors. A rarely performed dynamic testing of a representative sample of four nominally identical B&B open plan suspended ground floors in a real-life building has been carried out using state-of-the-art modal testing featuring a pair of simultaneously operating electrodynamic shakers and multi-channel data acquisition. The testing demonstrated that the floors have considerable transverse stiffness able to engage sizeable parts of the floor area in a manner similar to orthotropic plates. Although nominally identical, the four floors have somewhat different modal properties. In general, although open plan, the B&B floors tested developed considerable levels of non-proportional damping. This is possibly a consequence of friction between non-monolithic floor elements (in the beam-to-block and/or block-to-block contacts). By back analysis, using experimentally measured static stiffness and modal properties, a simple mathematical model of a rectangular simply supported orthotropic plate was verified as an applicable method for the calculation of modal properties of B&B floors tested. However, somewhat surprisingly, for this method to work, it was necessary to assume approximately 2.5 times higher bending stiffness than that of just the beams in the B&B floors, which are the only structural elements in this type of construction. Transverse stiffness was estimated to be 8% of this enhanced main stiffness. This is probably due to composite action of the in situ cast non-structural sand and cement screed and/or engaged friction stiffness between non-monolithically connected beams and blocks.

VSATs software for assessing and visualising floor vibration serviceability based on first principles

Vibration serviceability of building floors is becoming a governing design criterion for many open plan building floors. To make correct decisions about floor vibration performance, calculating only the highest vibration response of the floor is not sufficient anymore. Because of the considerable complexity of the problem and shortcomings of practically all codified procedures for checking floor vibration serviceability, it is prudent to use not one but several assessment strategies while making sure that application of the first principles in structural dynamics is preserved. Also, rather than focusing on a single highest response value, calculating distribution of the highest responses at each floor point is the way forward to obtain a more informed vibration serviceability check. Finally, easy link to commercial structural analysis packages and dynamic testing results, comprehensive but quick dynamic response calculation and effective visualisation of the measured and calculated vibration responses are of paramount importance in modern floor vibration serviceability design (for new structures) and assessment (for existing structures). To address all these issues, this paper presents Vibration Serviceability Assessment Tools (VSATs), a MATLAB‐based software package, developed to aid not only assessment of vibration serviceability of floors, but also development of new floor designs and research into their vibration behaviour. Its operation and application of a number of procedures useful for vibration serviceability assessment together with pertinent visualisation tools is presented to increase awareness of various state‐of‐the‐art procedures available nowadays.

Influence of Low-Frequency Vertical Vibration on Walking Locomotion

Walking locomotion has been a subject of studies in diverse research fields, such as computer, medical, and sport sciences, biomechanics, and robotics, resulting in improved understanding of underlying body motion and gait efficiency and pathology (when present). Only recently, a detailed understanding of kinematics and kinetics of the walking locomotion has become an important requirement in structural engineering applications due to an increasing sensitivity of modern, lightweight, low-frequency, and lightly damped footbridges to pedestrian-induced dynamic excitation. To facilitate development, calibration and verification of pedestrian models requires experimental characterization of walking gait parameters and understanding whether and how these parameters are influenced by the structural vibration. This study investigates whether low-frequency vibrations in the vertical direction affect seven walking locomotion parameters: pacing frequency, step length, step width, angle of attack, end-of-step angle, trunk angle, and amplitude of the first forcing harmonic. Three participants took part in a testing program consisting of walking on a treadmill placed on both stationary and vibrating supporting surfaces. The collected data suggest that an increasing level of vibration results in an increase in step-by-step variability for the majority of parameters. Furthermore, the existence of the self-excited force, previously observed only in numerical simulations of walking on pre-excited bridge decks, was confirmed. In addition, the deck vibration tended to have a beneficial effect of reducing the net force induced into the structure when walking at a pacing rate close to the vibration frequency. Finally, it was found that the vibration level perceptible by a pedestrian is one to two orders of magnitude larger than that typical of a standing person, and that the sensitivity to vibration decreases as the speed of walking increases.

Vibration Performance of Bridges Made of Fibre Reinforced Polymer

Due to favourable mechanical and physical properties, and the potential to provide a resilient and low-carbon infrastructure, fibre-reinforced polymer (FRP) material has increasingly been used for construction of highway and pedestrian bridges. Relative low mass, low damping and low stiffness make these bridges sensitive to dynamic excitation, which may lead to discomfort of human occupants and larger dynamic amplification of stress and deformation than is encountered in structures made of traditional structural materials. Consequently, design might be governed by a vibration serviceability state. Lack of data on vibration performance of FRP structures and non-existence of a state-of-the-art vibration serviceability design guideline means that current practice is conservative, often meaning only short-span FRP bridge solutions are executed. To fully exploit the benefits of using FRP material and to extend its use beyond current practice requires a better understanding of dynamic behaviour.

Experimental Investigation of Reykjavik City Footbridge

This study describes experimental investigation of a 160 m long footbridge in Reykjavik. The bridge is a continuous post tensioned concrete beam spanning eight spans, the longest being 27.1 m. In plan, the structure has eye-catching spiral shape. Modal testing of the structure was conducted to identify its dynamic properties. As many as seven modes of vibration were identified in the low-frequency region up to 5 Hz. After this a series of controlled tests involving up to 38 test subjects were performed. These were designed to test vibration performance of the footbridge under various loading scenarios such as: single person either walking or jumping, group of people walking, jogging or jumping and stream of pedestrians. The severity of vibration responses of the bridge for different scenarios was then evaluated against vibration serviceability criteria defined in a guideline. It was found that the vibration performance of the bridge is quite satisfactory for wide range of loading conditions.

ERRORS IN NUMERICAL SOLUTION OF EQUATION OF MOTION OF LIGHTLY DAMPED SDOF SYSTEM NEAR RESONANCE

This study investigates the error which occurs when numerically integrating the equation of motion of a single degree of freedom system excited by a harmonic force near resonance. The Constant Average Acceleration method was considered in particular as it features in many finite element software packages. It was found that a considerable error in the calculated responses occurs in systems with low damping due to the well known phenomenon of period elongation. However, the error is reduced for systems with higher damping and/or when smaller time step is used. With regard to this, recommendations are given as to the time steps required to obtain solutions with a pre-defined level of accuracy.