Why is footfall important?
Vibration can affect the use of a building, with serious consequences.
If you have ever experienced a “lively” floor, you will understand why footfall vibration can be a problem. A floor designed solely for strength can have a distinctly perceptible, even disturbing dynamic response to walking. Often, the vibration is tolerated. However, when the vibration disrupts the use of the building, the economic consequences can be considerable.
Another class of footfall vibrations are those which cannot be felt by people, but can affect sensitive equipment like MRIs or microscopes. These low level disturbances can be even more challenging to deal with than perceptible vibration, since they are more difficult to predict and the equipment’s sensitivity is not always well defined.
The Standard of Care for footfall vibration design.
In some cases a dynamic analysis of the structure is warranted. This requires a finite element model, which is commonplace in most other fields of engineering design and analysis.
The standard of care for structural engineers and architects is often defined in terms of what other professionals engaged in the same field are doing. However, when it comes to footfall vibration, the standard of care is not always clear. For critical buildings, or those with unusual framing, a genuine dynamic analysis of the structure may be warranted, while simpler buildings may rely upon techniques that are based on structural dynamics principles, but are very much simplified. This is a call made by the design professional on every project, but it is not always easy to make.
AISC Design Guide 11 (DG11) has gained recognition as the reference document for footfall vibration. Hence, it might be assumed that the use of DG11 is necessary and sufficient for meeting the standard of care. However, as Willford, Field, and Young pointed out, in an ASCE publication (Ref. 1).
"In view of the importance of achieving an acceptable vibration environment in modern facilities it is perhaps surprising that the design methods employed by most structural and vibration engineers comprise very simple and semi-empirical hand calculations based on research available in the 1970’s."
So what is the Standard of Care? Can it be argued that the use of DG11 is sufficient in all cases? While the simplified approach of DG11 may be adequate for some buildings, there is a chance it will not capture some of the structural behavior that should be considered in the design.
How is floor vibration handled in building projects?
U.S. practitioners have a limited "toolbox" in dealing with floor vibration. A specialty vibration consultant can bring additional tools to the project.
When floor vibration is mentioned in project specifications, it seems that DG11 is universally cited, even when steel is not the primary material of construction. Unfortunately, there is no equivalent document published by the American Concrete Institute (ACI) covering footfall vibration. Nor is footfall mentioned in ASCE 7 (Minimum Design Loads for Buildings and Other Structures).
Concrete floors are not immune to footfall vibration. It is well known that post-tensioned slab floors can be lively, but even the deeper pan-and-joist systems should be analyzed for vibration for sensitive occupancies such as laboratories. The underpinnings of DG11, if well understood, can just as well be applied to concrete structures. However, extra care must be taken with concrete. For example, calculation of the effective moment of inertia of concrete members in the possible presence of cracking requires special consideration.
Given this situation, it is wise to consult a specialty consulting firm for both steel and concrete buildings. In addition to advanced analysis tools, this firm should be able to bring test and measurement expertise to the table. Experience in this area demonstrates that a consultant is familiar with the “real world” when it comes to footfall vibration.
Software is available to assist the engineer.
Footfall analysis with non-FEA or FEA-based software.
Basically, the software is of two types, the first being a software-assisted non-FEA implementation of DG11. FloorVibe is the best known software of this type. The other class of software is FEA-based. The footfall analysis in the GSA suite of OASYS(TM) software is based upon a finite element model of the structure, and employs a methodology that originated in the United Kingdom. ESI Engineering has also developed an FEA-based methodology which is based on DG11 but uses the real modal masses instead of the fictitious “panel” weight from DG11. FEA allows the real modes and frequencies to be analyzed, with actual walker and receiver locations considered. Even for FEA-based implementations there are differences between the UK approach and DG11. Eventually, these difference need to be resolved by consensus among the experts in the field.
The figure below shows predicted footfall vibration for a very long walking path in a laboratory building. This data was generated from a SAP2000 FEA by ESI’s software and is overlaid on the floor plan to show the complex pattern resulting from the walking path. This approach clearly communicates results and allows the architect and engineer to assess suitability for sensitive occupancies.
What part of DG11 is applicable to my design?
DG11 can be confusing in this respect.
There is an important distinction between floors that are susceptible to a buildup to resonance and those that are not. Chapters 4 and 5 of DG11 apply resonance for walking and rhythmic activity, respectively, while Chapter 6 applies to situations where buildup to resonance is not possible. The methodologies presented for these two situations are drastically different.
How are we to determine which one is appropriate? Since Chapter 6 is entitled “Design for Sensitive Equipment”, it may be tempting to assume that buildup to resonance does not need to be considered on floors with sensitive equipment. However, this might be an unconservative assumption. It is assumed that these floors are designed with natural frequencies high enough to prevent a buildup to resonance. This frequency is taken to be 8.8 Hz in DG11, which corresponds to four times (the fourth harmonic) the maximum walking speed of 2.2 Hz. What if you have sensitive equipment on a floor with a natural frequency of, say 8 Hz? The prudent approach is to compute vibration using both Chapter 4 and Chapter 6.
What vibration criterion should be applied for any particular situation?
Careful judgement is required to avoid an over-conservative design, or worse.
Either acceleration or velocity forms the basis for most vibration criteria. A simple acceleration limit of 0.5% g, where g is the acceleration of gravity, is used in DG11, Chapter 4. The premise is that this limit should eliminate most problems relating to human comfort. It was calibrated for use with the DG11 calculation methodology for application to an office environment. More sensitive occupancies such as residential day, residential night (sleep), and surgical operating rooms are covered in ANSI S2.71-1983. The working group ANSI S12 WG44 on healthcare facilities has also published its own set of recommendations. This includes a level for "patient rooms and other patient areas" equal to the ANSI level for residential night. This may be conservative for a patient area not used for sleep.
The so-called VC (vibration criteria) curves are an extension of the general ANSI criteria curves to lower levels of vibration. The VC curves have been extended down to extremely low amplitudes to apply to ultra-sensitive operations such as micro-electronics production. For these low amplitude criteria, the measurement technique becomes critical, and prediction of such low levels is difficult.
The manufacturers of MRIs have done a reasonable job in publishing vibration criteria that make sense. The same cannot be said for some other equipment manufacturers. Fortunately, the VC curves have provided a useful set of generic criteria. In specifying a particular VC curve as part of the project requirements, you should be aware that meeting the lower VC curves can have a significant impact on cost.
How do field measurements compare to predictions?
Real buildings are complex systems, so do not expect an exact agreement between measurements and predictions.
Buildings are complex systems of structural and non-structural elements and the forces due to footfall are unpredictable. No honest practitioner would claim that his or her predictions agree with measurements all of the time. Under controlled conditions, predictions are normally validated to within reason. FEA-based predictions of floor frequency are commonly within ten percent of the measured frequency. Predictions of the amplitudes of peaks in a spectrum generated by footfall are generally less accurate, since these depend on the specific characteristics of the walker.
Field measurements of acceleration over some chosen duration of time are typically made with sensitive accelerometers. When a Fourier Transform (FT) is applied to the time signal, the result is in the frequency domain, which is where things get mathematically complex. The frequency domain result, or spectrum, depends upon the band of frequency used to compute the FT, so careful judgment (or specific guidance) is required.
The Bottom Line.
Footfall analysis should be an integral part of the design process.
For buildings where low vibration is critical, simply running a piece of software to check your design for a “typical” bay may not be adequate. Unless you are confident in your understanding of the complexities of footfall, you should probably turn to an expert who has worked in this area for many years. The consultants at ESI Engineering are prepared to help with all of your questions on footfall vibration.
- Willford, M., Field, C. and Young, P., “Improved Methodologies for the Prediction of Footfall-Induced Vibration,” Building Integration Solutions, Proceedings Architectural Engineering Conference, Omaha, NE, ed by M. Ettouney, ASCE (2006).