MS12.5 - Human-Induced Vibrations in Floors, Staircases and Stadia

Vibration serviceability of floors due to walking loads has become an important design criterion as a result of advancements in construction technology that lead to more slender and lightweight building floors. Current design guidelines require the assessment of the vibration performance of floors based on a single walking pedestrian, modelled as a fixed load, expressed as the summation of deterministic harmonic components. However, the effect of the walking path on the dynamic response of floors has not received any attention in the guidelines that generally consider the walking force as a stationary load applied to the antinodes of the floor mode shapes. Furthermore, due to the stochastic nature of the pedestrian walking force, the deterministic approaches adopted by the current guidelines can give unreliable vibration response estimation. The present paper aims to investigate the dynamic response of simply supported rectangular floors under a single walking pedestrian. At first, a deterministic loading model is assumed; then a probabilistic approach is adopted taking into account the stochastic nature of pedestrian walking force. From the deterministic standpoint, the present study reports an exact closed-form solution to calculate the dynamic response of floors subjected to a pedestrian walking load modelled as a summation of harmonic loads moving along a generic walking path. The critical walking paths which can provide the maximum dynamic response are derived and expressed analytically as a function of floor dimension and mode shape. Then, an approximated closed-form solution is proposed to calculate the vibration response of floors due to a moving resonant harmonic load along the critical walking paths. Results showed that considering the worst-case loading scenario as a design criterion could be conservative due to the fact that there is a low probability that pedestrians walk along the critical walking paths at the perfect resonant condition. Thus, it is essential to consider a probability-based vibration analysis to assess the vibration serviceability of floors. The probabilistic approach takes into account the randomness of several parameters such as step frequency, pedestrian velocity, dynamic force amplitude, pedestrian weight, and walking path. Monte Carlo simulations are carried out for floors with different geometric and dynamic characteristics to provide simplified procedures which allow the probabilistic prediction of the vibration response of floors. According to the numerical results, the present study introduces cumulative probability functions that allow estimating the probability that the maximum acceleration is higher than a certain percentage of the peak acceleration corresponding to the worst-case loading scenario, obtained through the approximated closed-form solution.

This paper presents a mathematical model of synchronisation of multiple people during cyclic daily activities such as walking, running, jumping and bouncing. Providing that quality models of individual loading for these activities do exist, the sync model is the key component towards an urgently needed yet reliable model of artificial dynamic loading due to multiple active occupants. A model proposed here describes the effect of external and internal factors on the crowd dynamics. The former includes periodic external stimuli on the body motion of individuals, such as perceptible vibration of the ground and music beats. The later addresses the mutual interaction between individuals, such as possibility to see, hear or touch each other. Modelling approach is inspired by the existing models of coupled pendulums while the governing equations feature Mathieu-type behaviour. For the sake of simplicity and efficiency, the model is kept linear and deterministic. All modelling parameters have a physical interpretation and their values can be calibrated to match experimental measurements.

Cross-laminated timber (CLT) is a wood-based multilayer composite made of several thin layers glued together in a crosswise manner. Modern manufacturing techniques resulted in CLT panels with remarkable stiffness properties and unique aesthetic appeal. CLT panels are commonly produced in a rectangular shape, while CLT floors are typically an assembly of prefabricated panels connected together on the site. Floors are usually simply supported on two opposite edges (SFSF) or all four edges (SSSS). Still, architectural design often requires non-conventional, complex-shaped floors with openings and boundary conditions that differ from those mentioned above. High stiffness-to-mass ratio of the CLT panels enabled structural engineers to design long-span CLT floors. However, they are prone to vibrations induced by active people; thus, vibration serviceability assessment often governs their design. There are different design guidelines for the design of CLT floors. Proposed design methods range from traditional, formulated to limit the fundamental frequency and/or static deflection, to modern performance-based assessment approaches. All these guidelines are limited to SFSF and SSSS rectangular floors. Furthermore, neither of them takes into account the inter-panel connections in vibration serviceability assessment. Bearing all this in mind, available CLT design guidelines do not apply to non-conventional CLT floors. On the other hand, Arup's design guideline for footfall-induced vibrations offers a universal assessment framework that applies to any floor structure regardless of its geometry, material, and boundary conditions. It has gained a good reputation globally for being robust and reliable in designing concrete and composite floors. This paper presents a numerical vibration analysis of a complex-shaped CLT floor with openings that can be used as a standard floor structure of residential-commercial buildings. Based on its size and shape, the floor is assembled using five CLT panels. It was found that the panel orientation, inter-panel connections, and their position in the floor outline significantly affect the floor modal properties. Numerical simulations of vibration response induced by single pedestrian walking showed that some floor configurations are better than others from the vibration serviceability assessment point of view.

The construction industry contributes a significant percentage of CO2 emission globally. Therefore, using renewable structural materials is beneficial from a sustainability perspective. Building with timber has gained an unstoppable rise in popularity. After decades of dominance of concrete and steel civil engineering structures, the revival of timber structures started with low-rise residential buildings due to the limited size and mechanical properties of the raw timber material. However, the emergence of cross-laminated timber (CLT) in the 1990s made timber structures competitive against reinforced concrete and steel structures for multi-storey buildings as well. CLT is a prefabricated engineering wood product, usually composed of an odd number of crosswise glued layers. Besides being eco-friendly, CLT is characterised by outstanding strength, stiffness, fire resistance, esthetics, and speeds up construction. However, due to the high stiffness-to-weight ratio, lightweight long-span CLT floor systems are susceptible to vibration induced by human cyclic activities, such as walking, running and jumping. Excessive vibration can lead to occupants' discomfort or malfunction of vibration-sensitive equipment, such as lasers and microscopes. CLT floors are more complex when compared to monolith reinforced concrete floors. Connections between adjoining CLT panels, orthotropic properties of timber and crosswise layer arrangement can significantly affect modal properties of the assembled floor. Consequently, there is no simple analytical expression that can be used to determine structural modal parameters, such as modal mass, stiffness and damping, needed for vibration serviceability analysis of CLT floors. In this paper, an experimental modal analysis was carried out to identify modal properties of several CLT floors with different boundary conditions, the number of panels in a floor assembly and the inter-panel connections. Influence of the latter on the floor modal properties is particularly studied and discussed.