Footfall analysis – Background

Introduction

Footfall analysis is a method used to assess vibrations of structures caused by human walking or other activities. Modern lightweight and flexible structures, such as long-span floors, bridges, or stairs, are more sensitive to these vibrations than in the past. The aim of the analysis is to verify that the vibration levels remain within acceptable limits for user comfort and do not interfere with sensitive equipment.

This analysis is performed during the design stage, employing validated numerical models to predict the dynamic response of the structure under pedestrian loads. The methodologies implemented SCIA Engineer are based on established design guidelines, including:

• SCI P354 [1]

• CCIP-016 [2]

• AISC DG11[3]

Footfall induced vibration

Transient vs Steady-State dynamic response

As an introduction to the dynamic behaviour of structures under pedestrian loads, it is important to understand the two fundamental types of vibration response: transient and steady-state. This foundation will help us later analyse different structures based on their stiffness and determine which type of response typically dominates in each case.

When a pedestrian steps onto a floor or bridge, the structure experiences vibrations that evolve over time. These vibrations can be described by two main types of dynamic response:

• The transient response refers to the initial, time-dependent reaction of the structure immediately after the pedestrian load is applied. It captures the short-term vibrations that occur as the structure adjusts to the sudden excitation. This response usually diminishes quickly as energy dissipates through damping.

• The steady-state response describes the ongoing, sustained vibrations once the transient effects have settled. It represents the regular, repeating vibration pattern caused by continuous pedestrian movement, which may resonate with the structure’s natural frequencies and cause amplified vibration levels.

Classification of Structures

The type of vibration response a structure exhibits under footfall excitation depends primarily on its stiffness and the corresponding vertical natural frequencies. Based on these characteristics, structures are commonly classified into two categories:

• High-frequency structures, which are stiff and mainly exhibit transient impulsive vibrations, and

• Low-frequency structures, which are flexible and prone to resonant vibrations.

This basic classification guides the selection of appropriate analytical methods and modelling approaches for footfall vibration assessment.

High-frequency structures

High-frequency structures typically have fundamental vertical natural frequencies above approximately 10.5 Hz. Examples include stiff and rigid constructions such as heavily reinforced concrete slabs or short-span steel floors. The dynamic behavior of these structures under footfall excitation is characterized by the following key aspects:

• Dominant transient vibrations: The response is mainly caused by impulsive forces generated by individual footfalls.

• Rapid decay of vibrations: Due to the structure’s high stiffness and damping, vibrations quickly diminish before the next step occurs.

• Negligible steady-state resonance: Sustained resonant vibrations are generally not significant in these structures.

• Modelling approach: Footfall excitation can be effectively modelled as a series of independent impulsive loads.

From a design and analysis perspective, the primary focus is on evaluating the peak transient response rather than on steady-state vibration levels. Because transient vibrations do not accumulate significantly, discomfort caused by resonance is unlikely. Consequently, simplified analytical methods that consider impulsive loading are often sufficient for assessing footfall-induced vibrations in high-frequency structures.

Low-frequency Structures

Low-frequency structures typically have a fundamental vertical natural frequency below approximately 10 Hz. These structures are generally more flexible and include examples such as long-span floors, footbridges, or lightweight composite slabs. Their dynamic response to footfall excitation exhibits distinct characteristics compared to high-frequency structures:

• Dominant steady-state (resonant) vibrations: Because the natural frequency of the structure can coincide with the frequency of walking or its harmonics, resonance can occur and amplify the vibrations over time.

• Gradual build-up of vibration: The energy input from each footstep accumulates, leading to sustained or increasing vibration levels as the pedestrian continues walking.

• Significant interaction with pedestrian frequency: Resonance is more likely if the structural mode shape aligns with the excitation direction and frequency.

• Modelling approach: The response must account for both transient and steady-state components, with emphasis on the steady-state resonance.

From a design and analysis perspective, it is crucial to evaluate whether resonant vibrations exceed acceptable comfort criteria, as they tend to persist and can lead to discomfort for occupants or interfere with sensitive equipment. More detailed analytical methods are required for low-frequency structures, including modal analysis and consideration of harmonic components of the walking load.

Periodic Loading and Resonance

In the case of low-frequency (flexible) structures, the walking load is not treated as a series of isolated impulses but rather as a periodic, harmonic force. This reflects the fact that human walking generates repeated, rhythmic forces at frequencies corresponding to the walking step frequency (fundamental frequency, typically around 1-2 Hz) and its higher harmonics. These periodic forces can coincide with the natural frequencies of the structure, leading to resonance and significantly amplified vibration levels.

To capture this behaviour, design guidelines use the following approach:

• The dynamic pedestrian load is decomposed into a Fourier series, which represents it as a sum of sinusoidal components, where the fundamental frequency corresponds to the basic walking pace and the higher harmonics represent additional periodic components of the load.

• For each harmonic, the guidelines specify a coefficient (representing its relative amplitude) and a phase angle (defining its timing) to fully describe the harmonic content of the walking force.

• A frequency range is defined for the fundamental frequency, specifying lower and upper frequency limits. The frequency ranges of the higher harmonics are simply multiples of the fundamental range.

• The response of the structure is calculated for each harmonic within its frequency range and then combined to obtain the total expected vibration level.

In SCIA Engineer, this methodology is implemented as follows:

• The frequency range for the fundamental frequency is defined in the Footfall load case, using the parameters:

  • Walking frequency – min

  • Walking frequency – max

• This frequency range is divided into discrete frequencies according to the user-defined (see Footfall load case):

  • Walking frequency – step

• This produces a set of fundamental frequencies, and for each of these, the corresponding higher harmonic components are automatically generated as multiples of the fundamental.

• The coefficients and phase angles for each harmonic are predefined by the selected design guideline or can be specified by the user. These values can be found in:

  • the Footfall analysis coefficients.

• The structural response to all harmonic components is then combined into the overall result based on the chosen Combination method in the Footfall load case.

Model adjustment according to design codes

Correct structural modelling is essential to obtain reliable results in footfall analysis. Each design code defines specific procedures for how structures should be represented in the calculation. Therefore, it is necessary to follow the recommendations given in the respective design methods.

In general:

• the SCI P354 approach focuses mainly on steel floor systems,

• the CCIP-016 reflects the specific behaviour of concrete and composite elements,

• the AISC DG11 recommendations provide detailed procedures for steel-framed systems.

While these approaches differ in detail, they share the common goal of ensuring a conservative and practically applicable design.

For further information, see [1–3].

References

[1] Smith, A.L., Hicks, S.J. and Devine, P.J. (2009), Design of Floors for Vibration: A New Approach (Revised Edition, February 2009), The Steel Construction Institute, Silwood Park, Ascot, Berkshire, England.

[2] Willford, M. and Young, P. (2006), A Design Guide for Footfall Induced Vibration of Structures: A Tool for Designers to Engineer the Footfall Vibration Characteristics of Buildings or Bridges, CCIP-016, Concrete Centre, Camberley, UK

[3] Murray, T.M., Allen, D.E., Ungar, E.E. and Davis, D.B. (2016), Design Guide 11: Vibrations of Steel-Framed Structural Systems Due to Human Activity (Second Edition), American Institute of Steel Construction.