Dynamisk personlast og stokastisk lastmodellering til estimering af dynamisk respons

Abstract

This master’s thesis is written by Kristian Johnsen and Alexander Albers in the civil engineering program Structural and Civil Engineering at Aalborg University. The project was written during the period from September 1st, 2023 to June 6th, 2024. The project is titled Dynamic human loading and stochastic modelling of loads for estimating dynamic response, and focuses on stochastic load models for pedestrians crossing footbridges, while addressing the acceleration experienced by these footbridges due to the dynamic loads. The increased demands for material savings and improved properties of building materials mean that structures intended to support people are being constructed lighter and more slender in recent times. However, this leads to a greater risk of undesirably large vibrations due to dynamic loads from pedestrians on structures such as footbridges. These rather large vibrations primarily occur when the lowest eigenfrequecy of the structure is located near the frequency of the dynamic load, which can result in resonance. In existing standards, the pedestrian walking parameters are modelled in a deterministic manner, which means that everyone walks with the same walking frequency and step length while having the same body weight. This does not align with reality, where these parameters vary for each pedestrian. Therefore, it is desired to model the walking parameters stochastically in order to use a more realistic load model. Initially, in order to construct the stochastic model, a review of existing experiments and literature provides an understanding of pedestrian-induced forces. Based on these experiments, a stochastic load model is developed, considering various walking parameters, and modal analysis is employed to determine the dynamic response. The results of these analyses are given as cumulative distribution functions of the maximum accelerations, which gives information about the probability of exceeding a given acceleration. The stochastic model is compared with deterministic methods from existing standards using two different bridge models, one fictitious and one based on a real bridge in Montenegro. The dynamic responses of both bridge models are calculated, and the results using deterministic and stochastic load models are compared. Further, the bridge and stochastic load models are extended by increasing the number of included modal shapes and harmonic load components, leading to more detailed probabilistic estimations of dynamic responses. A multi-harmonic load model is introduced to account for variations in walking parameters during the movement of each individual pedestrian. In reality, these variations occur because pedestrians don’t walk with identical steps. This provides a more accurate reflection of the walking load. All of the aforementioned stochastic load models are investigated within the report, and the results generally show that it highly depends on the specific bridge model, how advanced the load models should be, although rather simple stochastic models appear to be sufficient when working with the bridge models in this project. Finally, the interaction between pedestrians and the structure is explored, analyzing the impact on the dynamic response when considering a coupled system of mass, stiffness and damping. The results indicate that it can be relevant to include human-structure interaction in future research on how structures respond dynamically to pedestrian loads.

A master thesis from Aalborg University

Dynamisk personlast og stokastisk lastmodellering til estimering af dynamisk respons

[Dynamic human loading and stochastic modelling of loads for estimating dynamic response]