A practical guide to floor vibration serviceability assessment

Welcome to another EngineeringSkills deep dive. In this two-part tutorial series, we’re going to explore floor vibration serviceability. The core questions that we’re going tackle are;

• how do you quantify the likely vibration response of a floor to occupant-induced footfall forces?
• and how do you determine the acceptability of the predicted response?

By the end of this tutorial, you will have a complete framework for simulating occupant-induced vertical floor vibration and a set of limits against which to compare your predictions. In part two of this series, we’ll build up two working examples in Python that demonstrate the complete calculation workflow.

This series is mainly aimed at working engineers who occasionally find themselves needing to perform design-stage assessments of vibration serviceability. The average civil or structural engineer doesn’t generally work with structural dynamics on a daily basis, - so this guide should act as a helpful primer when the need arises.

It will be helpful to have a working knowledge of structural dynamics fundamentals - if you need a refresher, you can take a look at my course, Fundamentals of Engineering Structural Dynamics with Python.

So, with that out of the way, let’s dive in!

1.0 Introduction - the occupant-induced vibration problem

Occupant-induced floor vibration is a serviceability issue, but unlike excessive deflection, it has the potential to be a significant ongoing nuisance to the end user. Thankfully, checking to ensure acceptable vibration performance has become much easier over the last 20 years or so.

As structures have become lighter and, therefore, more susceptible to excitation, the engineering community has responded, dedicating significant research effort to understanding the problem. As a result, numerous design guides have been developed that the working engineer can now turn to.

The guide that we’ll base our discussion on here is, to my mind, probably one of the most straightforward to apply. It’s founded on solid research and a direct application of structural dynamics fundamentals with very limited use of ‘fudge‘ factors to arrive at an outcome.

We’ll be following ‘A Design Guide for Footfall Induced Vibration of Structures’ by Willford and Young and published by the Concrete Centre [1]. Despite the publisher being the Concrete Centre, the guidance is material agnostic.

That said, there is a similar publication aimed at steel structures, ‘Design for Floor Vibrations: A New Approach (P354)‘, published by the Steel Construction Institute (SCI). Both guides follow a broadly similar approach of dividing floors into low and high-frequency structures with low-frequency floors being assessed for resonant response and high-frequency structures being assessed for impulse response.

The SCI guide contains more information on estimating modal properties of steel-specific floorplates. Both are well worth reading, particularly as concise sources of background information on the occupant-induced vibration problem.

Both of the guides cited above are from UK organisations. If you’re in a different part of the world, you’ll likely have local guidance that should be considered. However, the Concrete Centre guidance is so straightforward in its application of fundamental structural dynamics that it should always yield a sensible estimate of response.

It’s worth quickly noting what we’re not covering here; we deal only with vibration in the vertical direction. Lateral or torsional vibrations are far less common in floor structures and, for the most part, are not relevant here.

We’re also not considering the more ’exotic’ case of human-structure interaction, i.e. although the occupants (sources of excitation) may perceive the vibration response, we assume that it has no impact on the dynamic forces they generate.

Human-structure interaction is far more common in the case of lateral vibrations, often seen on footbridge structures. The most notable case of human-structure dynamic interaction was the London Millennium Footbridge. That’s a story for another day…here we’re focusing only on the ‘run of the mill’ nuisance vibration of floors and footbridges.