Analysis of serviceabilty limit state of pedestrian bridges regarding vibrations induced by pedestrians

The advanced engineering technologies and the development of construction materials have brought the new trends in the design and construction of pedestrian bridges. Contemporary footbridges are slender and lightweight long span structures. As a consequence of the small mass and stiffness of the structure, reduction in the fundamental natural frequency of the bridge, results in greater sensitivity to dynamic loadings, especially the human-induced ones. Therefore, a more detailed dynamic analysis becomes necessary in the design of pedestrian bridges. For evaluation of the serviceability limit state of a footbridge, it is necessary that the superstructure response to human-induced vibration is known. As vibration analysis of bridges is very complex, the simplest solutions of vibration problem are the most acceptable to designers. For these reasons, using modal analysis, solutions such as a time depending response of the bridge superstructure were performed in the dissertation. Pedestrian-induced actions are modelled as deterministic forces, defined using the Fourier transform, and their position on the bridge is defined using the Dirac function, Heaviside function and Hermite polynomials. The response function is determined using the author’s algorithms and programs written in Mathematica. The dissertation presents three algorithms, which includes all girder structural systems. For dynamic analysis they are modeled as continuous or discrete oscillatory systems. Moreover, the superstructure of the bridge can be of a constant or a variable mass and flexural stiffness along the span. The response functions for the vertical and horizontal direction of vibration are defined using the same algorithms, with the introduction of the modal characteristics of the structure for the respective direction. The required response can present vertical displacement, horizontal displacement, velocity or acceleration, as well as stress and strain of the observed cross section, since the algorithms include such an option. The possibility option of response presentation trough time histories, significantly simplifies the qualitative and quantitative analysis. This is particularly important for the variation of the parameter, for example, intensity of the constant force, intensity of the amplitude and frequency of the time varying force, speed of the force, damping, and the position of the cross section of interest. The efficiency of the proposed dynamic analysis, carried out according to the above response functions, is shown for three pedestrian bridges of different structural systems and materials applied. The proposed analytical solutions to the vibration problem are easily applicable for various dynamic actions, so that they can represent a great help for designers to estimate the dynamic behavior of pedestrian bridges, which is a prerequisite for a contemporary and acceptable footbridge design principle and, with modern technologies, their quality construction