Dynamic Response and Design of Steel Structures Subjected to Pedestrian-Induced Loads

Abstract

The present thesis investigates the dynamic performance of steel members under the effect of pedestrian induced dynamic forces. Towards this objective, the study adopts two main methodologies: (a) controlling the member natural frequencies to mitigate possible resonance phenomena under human-induced dynamic forces and (b) controlling acceleration levels induced in members to ensure they fall below acceptable perception levels. While present design Canadian and American structural steel design provisions do not offer explicit natural frequency requirements, they limit member slenderness to 200 for compression members and 300 for tension members. These limits partly control the natural frequency but omit the influence of axial load level, and neither fully capture the effect to cross-sectional asymmetry, as may be the case in angle members, nor fully account for member end-connection details. Within this context, the present research presents four contributions towards advancing the state of the art related to the analysis and design of steel members under human activities. The first contribution examines the natural vibration response of axially loaded members with wide-flange sections. A parametric study is conducted using closed-form analytical solutions and shell finite element modelling. The study characterizes the effect of axial loads on the member natural frequencies and proposes slenderness limit thresholds based on target natural frequencies that capture the axial load level. In this respect, this part of the study develops an improved serviceability criterion than simply satisfying member slenderness requirements in the present standards.

The second contribution extends the investigation to members with angle cross-sections, which are prone to torsional–flexural coupling owing to cross-sectional asymmetry, an aspect not addressed in the first contribution. A closed-form solution is developed to determine the torsional flexural natural frequency of pin-ended members with equal leg angles. The analytical model is complemented with shell finite element modelling to tackle more general cases involving unequal leg angles and members with gusset plate end connections. A subsequent parametric investigates the effect of axial force, cross-sectional geometry, member span, and boundary conditions on the natural frequency of angle members. The findings show that satisfying present slenderness criteria does not guarantee consistent natural frequencies across members with angle cross-sections and flags the need to develop more elaborate criteria to control excessive vibrations. The third contribution formulates a general thin-walled beam finite element formulation for the natural vibration analysis of steel members. The solution captures torsional-flexural coupling induced by cross-sectional asymmetry, and the effects of axial loading, warping, and rotary inertia. The formulation is equipped with a feature that enables the seamless modelling of the boundary conditions of gusset-plate ended connections, in which the member is considered fixed about the axis normal to the gusset but nearly pinned about the gusset axis, both axes being non-principal. The findings reveal that gusset plate end connections significantly elevate the natural frequency of the member, when compared to pinned-ended members. A simplified energy-based solution is also developed to estimate the natural frequency of members with gusset-end connections, and a dimensionless design chart is provided to streamline the calculation procedure in a design environment. While the previous three contributions centre around quantifying the natural frequency of steel members, the final contribution transitions to the full transient response evaluation under the time- dependent loading is induced by human walking. Towards this objective, a general purpose thin-walled beam finite element formulation is developed for the fully dynamic analysis of thin-walled beams. In addition to capturing the effects of coupling induced by cross-sectional asymmetry, axial loading, warping, and rotary inertia, the formulation incorporates the effect of damping and develops the energy equivalent force vector that characterizes the temporal and spatial distributions of forces induced by human walking. The discretized equations of motion are then solved using the Newmark time integration scheme, and the predictions of the model are validated against benchmark solutions. A parametric study explores the effects of axial force magnitude, damping model, damping ratio, boundary conditions, and characteristics of the walking function on the member acceleration response. The results are benchmarked against established human comfort thresholds. The model thus provides a basis to assess the dynamic performance of steel members against established acceleration thresholds. In summary, the present thesis advances methods of dynamic analysis of steel members. By integrating analytical solutions, energy-based approximate methods, and finite element modelling techniques, the study offers a possible framework for the analysis and design of steel members under the effect of dynamic loads induced by pedestrian-induced loads.