1. Footfall Analysis (Footfall induced vibration analysis)
20/04/2017
Footfall Analysis (Footfall induced vibration analysis)

2. Footfall analysis 1. Introduction 2. Basic theory
3. How to evaluation footfall responses
4. How to create GSA model for footfall analysis
5. Running footfall analysis
6. Results of footfall analysis

3. Footfall analysis 1. Introduction Why do footfall analysis
The uses of high strength materials make structure lighter and prone to vibration
High requirements from clients about the dynamic behaviour of the buildings (more quiet buildings)
Footfall analysis is to calculate the vertical responses (response factor, acceleration & velocity etc) of buildings and bridges subjected to the dynamic loads from human footfalls
It is a serviceability limit state analysis to determine the disturbance level of structure vibration on human or to precision equipments in the building

4. Footfall analysis
2. Basic theory – resonant responses (in control for low frequency structures, e.g. f < 15 Hz)
Interpretation of footfall loads (key to footfall analysis)
It is considered as periodical loads
The periodical footfall loads are decomposed into a number of harmonic components (e.g. 4 harmonic components for Arup method)
Footfall analysis (the basic analysis is harmonic analysis)
Harmonic analysis is carried out for each of the harmonic components of the footfall loads
Responses for each harmonic components of footfall loads can be known
Total responses
The total responses are calculated using the responses from each of the harmonic components using SRSS (Square Root of the Sum of the Squares) method

5. Footfall analysis 2. Basic theory – resonant responses
An example of footfall loads from SCI 354 (f = 1.8 Hz & W = 700 N)

6. Footfall analysis
Basic theory – transient responses (in control for high frequency structures, e.g. f > 15 Hz)
Resonance will not occur since structure natural frequencies are many times higher than footfall frequency
Impulse response analysis is carried out assuming each footfall is an impulse load
Interpretation of footfall loads
Each footfall is considered as an impulse load to the floor, from experiments and statistics, the impulse of footfall loads for mode ‘m’ is (statistical & not theoretical results):

7. Footfall analysis
Basic theory – transient responses (in control for high frequency structures)
Footfall analysis
The peak velocity response at response node ‘r’ for mode ‘m’ due to the impulse at excitation node ‘e’ is
The variation of the velocity at response node ‘r’ for mode ‘m’ along with time is

8. Footfall analysis
Basic theory – transient responses (in control for high frequency structures)
Footfall analysis
The total velocity responses are the sum of the responses from each of the modes considered
The RMS velocity is

9. Footfall analysis 3. How to evaluate footfall responses
Human perception to vibrations
Basic threshold of human perception to vibrations
Response factors

10. Footfall analysis 3. How to evaluate footfall responses
Human perception to vibrations
It is not the same for the same acceleration level if the frequency of the vibration is different.
The most sensitive frequencies to human is from 4 to 8 Hz (maybe human body’s natural frequencies are between 4 – 8 Hz)
It is more logical to use response factor rather than the absolute acceleration to determine the disturbance level of floor vibration to humans

11. Footfall analysis 3. How to evaluate footfall responses
Figure on the right shows the basic threshold of human perception to vibration (BS4672), response factor = 1.0
It is used to calculate the response factor (used as denominator in response factor calculations)

12. Acceptance levels of response factors (BS6472)
Footfall analysis
3. How to evaluate footfall responses
Response factor
It is the ratio of Root-Mean-Square acceleration/velocity over basic threshold of acceleration/velocity
Acceptance levels of response factors (BS6472)
Place
Time
Exposure to continuous vibration
Hospital operating theatres & precision laboratories
Day
Night 1
Residential
2 to 4
1.4
Office 4
Workshops 8

13. Footfall analysis 4. How to create GSA model for footfall analysis
The similarities to modal analysis model
Footfall analysis uses modal analysis results (frequencies and mode shapes). The construction of GSA model for footfall analysis is more or less the same as for constructing a model for modal analysis
The differences from modal analysis model
Footfall analysis is for serviceability limit state checks and the magnitudes of the vibration are very small, so the stiffness used in modal analysis for footfall analysis may be slightly higher than for other analysis (e.g. seismic response analysis)

14. Footfall analysis 4. How to create GSA model for footfall analysis
Stiffness consideration of the structure model for footfall analysis
Inclusion of columns in floor modeling
Include columns for more accuracy if possible
Ignore columns for simplicity when floor connections to columns are pin or column stiffness are relatively small (e.g. large span floor)
Beam-column connections
Considered as fixed for most of the connections that are not truly pins
Considered as pin for those connections that are truly pins
Concrete Young’s modulus – higher than that for static analysis
Normal weight – 38 GPa (Es/Ec ratio = 5.39)
Light weight – 22 GPa (Es/Ec ratio = 9.32)

15. Footfall analysis Running footfall analysis
Modal analysis needs to be run and the requirements are
All modes with frequencies up to 15Hz should be included (resonant response requirement)
The highest frequency is at least twice of the lowest frequency (transient response requirement)
Excitation method
Self excitation – fast, but not very accurate, especially for low response areas
Full excitation – slow, but accurate
Response and excitation nodes
They can be defined by node lists to include those nodes that are interested and exclude those nodes not interested

16. Footfall analysis Running footfall analysis Damping
Constant
From modal analysis
Use damping-frequency relationship table
Number of footfalls
It equals the ratio of the longest floor length over the length of foot steps
Walker’s body weight (typically 70 – 76 kg)

17. Footfall analysis Running footfall analysis Excitation forces
Floor (Arup or SCI method)
Stair (Arup or SCI method)
AISC SDGS 11
User defined (can be used to simulate group people dancing etc)
Minimum & maximum walking frequencies
The range of walking frequencies to be considered
There is a limit for highest and lowest frequencies that can be considered due to the applicability of the formulae and the method

18. Footfall analysis 6. Results of footfall analysis
Results of footfall analysis – output table or contour on graphic
Resonant analysis
Maximum response factors
Peak acceleration
Critical nodes and critical walking frequencies
Transient analysis
Maximum response factor
Peak velocity
RMS velocity
RMQ velocity

19. Footfall analysis 6. Results of footfall analysis
Results of footfall analysis – chart view
Resonant analysis (for the chosen node)
Response factor versus walking frequency
Acceleration versus harmonic forcing frequency
Dynamic load factor versus forcing frequency
Participation factor versus modes
Transient analysis (for the chosen node)
Velocity versus walking frequency
Velocity versus time