Lars Pedersen

Damping added to floors by seated crowds of people

Floor damping is an essential parameter in the evaluation of the dynamic performance of a floor as the amount of floor damping has a significant impact on floor vibration levels. This paper explores the not well understood relationship between floor damping and seated crowds of people. The paper contributes to the understanding by presenting results of controlled experimental investigations that involved crowds of people sitting on a vibrating test floor. In tests, floor damping and floor frequency are identified for various sizes of the crowd. This in itself throws some light on the not well understood relationship, but it is further investigated whether modelling the human crowd as a single-degree-of-freedom spring-mass-damper system attached to the vibrating floor can explain the recorded floor frequency and damping. Thus, a crowd-floor interaction model describes the combined crowd-floor system, and results show that this model is capable of explaining the overall tendency in recorded floor damping and frequency, and the calibration of the interaction model gives some indications of the frequency and damping of the spring- mass-damper system representing the crowd. The paper describes the tests and the methods used to evaluate the appropriateness of modelling a crowd as a spring-massdamper system. Some implications of the observed crowd-floor interaction are discussed in light of the results.

Implications of Interaction Between Humans and Structures

Many civil engineering structures are occupied by humans, and often humans are considered as a static load in calculations. However, active humans on structures can cause structural vibrations. Passive humans might also be present on that structure and they do change the structural system (such as structural damping and therefore also structural vibration levels). The paper addresses this subject and explores implications of having passive humans present on the structure. In experimental tests with a laboratory floor it is examined to which degree the posture of humans passively sitting on the floor influences the damping added to the floor. A numerical case study explores how passive humans may influence vibration levels of a floor.

Sensitivity Study of Stochastic Walking Load Models

On flexible structures such as footbridges and long-span floors, walking loads may generate excessive structural vibrations and serviceability problems. The problem is increasing because of the growing tendency to employ long spans in structural design. In many design codes, the vibration serviceability limit state is assessed using a walking load model in which the walking parameters are modelled deterministically. However, the walking parameters are stochastic (for instance the weight of the pedestrian is not likely to be the same for every footbridge crossing), and a natural way forward is to employ a stochastic load model accounting for mean values and standard deviations for the walking load parameters, and to use this as a basis for estimation of structural response. This, however, requires decisions to be made in terms of statistical distributions and their parameters, and the paper investigates whether statistical distributions of bridge response are sensitive to some of the decisions made by the engineer doing the analyses. For the paper a selected part of potential influences are examined and footbridge responses are extracted using Monte-Carlo simulations and focus is on estimating vertical structural response to single person loading.

Damping Effect of Humans

Passive humans (sitting or standing) might well be present on flooring-systems, footbridges or other structures that carry humans. An active crowd of people might generate structural vibrations, and these might be problematic. The passive crowd of people, however, will interact with the structural system and change its dynamic behaviour and its dynamic characteristics. When predicting structural vibrations it is not common to account for the passive crowd, but the paper will illustrate effects of the presence of a passive crowd on structural behaviour. Numerical and experimental results are presented and discussed.

Human damping and its capacity to control floor vibrations

This paper addresses a damping mechanism not often considered although typically present. The damping mechanism in question is that originating from stationary humans (standing or sitting) on floors. Floors may encounter vertical vibrations due to actions of humans in motion. The vibrations hereby generated can be a problem because stationary humans are excellent vibration sensors and may perceive vibrations as being discomforting. This paper demonstrates that in addition to acting as receivers/perceivers, stationary humans can also add significant damping to the floor which they occupy; and thus assist in reducing the discomforting vibrations. In the analyses the stationary crowd of people are modelled as an auxiliary (spring-mass-damper) system attached to the floor. Experimental results reported in this paper show that this modelling approach is reasonable even though a rigid mass assumption is often used. The latter model does not account for a human damping mechanism. Implications of its presence are evaluated for a set of floors. These evaluations also encompass the scenario that a tuned mass damper (TMD) is fitted to the floor so as to mitigate excessive floor resonant vibrations. The effectiveness of such TMD is shown to reduce substantially during the presence of stationary humans on the floor.

Flooring-Systems and Their Interaction with Usage of the Floor

Some flooring-system designs might be sensitive to their vibrational performance, as there might be the risk that serviceability-limit-state problems may be encountered. For evaluating the vibrational performance of the flooring-system at the design stage, decisions need to be made by the engineer in charge of computations. On a flooring-system often passive humans and/or furniture are present. Often these masses and their way of interacting with the floor mass are ignored in predictions of vibrational behavior of the flooring-system. The paper explores and quantifies how these masses can influence central parameters describing the dynamic behavior of the flooring-system.

Interaction Between Humans and Structures

On structures two types of humans may be present. (1) Active humans and (2) passive humans (sitting or standing on the structure). The active humans can excite the structure and cause structural vibrations. The mass of the passive humans will interact with the structure and basically it changes the structural system (modal characteristics and structural vibration levels). The paper addresses this subject and explores the implications of having passive humans present on the structure.

Sensitivity of Footbridge Response to Load Modeling

The paper considers a stochastic approach to modeling the actions of walking and has focus on the vibration serviceability limit state of footbridges. The use of a stochastic approach is novel, but useful, as it is more advanced than the quite simplistic deterministic load models seen in many design codes. Using a stochastic approach, however, requires a number of decisions to be made (statistical distributions and associated parameters) for walking parameters. These decisions might have an impact on the outcome of serviceability evaluations (bridge acceleration levels), but it is often not a simple matter to foresee their impact. The paper contributes by examining how some of these decisions influence the outcome of serviceability evaluations. The sensitivity study is made focusing on vertical footbridge response to single person loading.

Interaction between Structures and Their Occupants

Structures that carry humans are the subject of the studies of this paper. Active humans may cause structural vibrations, which can be problematic, but passive humans (sitting or standing on the structure) are also potentially present on the structure. In predictions of structural vibration performance, the passive humans are often not modelled, but they will interact with the structure. The paper has focus on the effect that the presence of passive humans has on the structural behaviour and modal characteristics of the structure. Based on findings from measurements, the implications of presence of passive humans are discussed.

Predicting Footbridge Vibrations Using a Probability-Based Approach

Vibrations in footbridges may be problematic as excessive vibrations may occur as a result of actions of pedestrians. Design-stage predictions of levels of footbridge vibration to the action of a pedestrian are useful and have been employed for many years based on a deterministic approach to modeling the action of a pedestrian. The paper employs a probability-based approach to modeling the action of a pedestrian by considering randomness in the behavior of the pedestrian crossing the footbridge. The paper describes the approach and studies implications (sensitivity) of selected decisions made when setting up the probabilistic framework for the predictions of footbridge response.