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

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

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

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

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

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):

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

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

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

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

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)

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

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)

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)

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

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)

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

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

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