# Footfall Induced Vibration Analysis

Footfall induced vibration analysis is to evaluate the responses of structures subjected to the actions of human footfalls. The structural responses include nodal accelerations, velocities and response factors etc. The human footfall loads are considered as periodical loads which are represented by a number of harmonic loads according to Fourier series theory. The detailed descriptions of human footfall loads can be found from references 35, 29 and 1 in the Bibliography which are also listed below. Footfall induced vibration analysis utilizes dynamic analysis results (frequencies, mode shapes & modal masses etc) to calculate the structure responses . The outputs of footfall analysis are the maximum responses of the structure for the given ranges of walking frequencies etc. The following three design guides of footfall analysis can be considered:

- Willford, M.R. & Young, P. (2006) A Design Guide for Footfall Induced Vibration of Structures, The Concrete Centre, CCIP-016.
- Smith, A.L., Hicks, S.J., & Devine, P.J. (2009) Design of Floors for Vibration: A New Approach, The Steel Construction Institute, P354.
- AISC Steel Design Guide Series, Floor Vibration Due to Human Activity.

In addition to the three design guides, user defined DLF (Dynamic Load Factor) curve can also be used in footfall analysis if you know the Fourier coefficients of each of the harmonic components of the footfall loads.

As footfall analysis utilizes modal dynamic analysis results, modal dynamic analysis results must be available before doing footfall analysis.

Response factors from footfall analysis are calculated using frequency weighting curves (FWC), i.e. the calculated RMS accelerations times the weighting factors from the chosen frequency weighting curve, then divided by 0.005 m/s2 to get the response factors. Frequency weighting curve can be standard or user defined, there are three standard frequency weighting curves (Wb, Wd and Wg) from BS6841 that can be used directly by footfall analysis. User defined frequency weighting curves can also be used in footfall analysis if it has been defined in Frequency weighting curve table, this makes it possible for GSA footfall analysis to cope with any type of frequency weighting options.

## Modelling Implications

Footfall induced vibration analysis utilizes modal dynamic analysis results and the construction of a GSA model for footfall analysis is the same as that for modal dynamic analysis. See modelling implications of modal dynamic analysis for the requirements of setting up a model for Footfall analysis.

The results of modal dynamic analysis are essential for footfall induced vibration analysis, before doing footfall induced vibration analysis, at least one modal dynamic analysis task with analysis results must exist. As the footfall analysis is only concerned with vertical excitation it may often be appropriate to constrain the modal analysis to exclude horizontal motion by applying additional restraint.

For more details see Analysis Wizard : Footfall Induced Vibration Analysis

## Results

The results of a footfall induced vibration analysis are all nodal results and they include:

**Resonant analysis**

- Maximum acceleration based response factors
- Peak acceleration
- Critical nodes
- Critical walking frequencies

**Transient analysis**

- Maximum velocity based response factors
- Peak velocity
- RMS (Root Mean Square) velocity
- RMQ (Root Mean Quad) velocity
- RMQ Critical nodes
- RMQ Critical walking frequencies

These results can be viewed from contours, diagrams and output tables.

After a footfall induced vibration analysis, chart views that show the plot of response factor versus walking frequency, velocity versus time, etc. are also available for individual response nodes.