Walking-Induced Vibrations in Buildings: Evaluation and

E R I C E . U N G A R

Walking-Induced Vibrations in Buildings:

Evaluation and Prediction

Acentech, Inc.

Why Consider Walking – Induced Vibrations?

Improved design methods and better materials have led to more flexible floor structures, more easily set into vibration.

People want to live and work without disturbances and annoyances.

Many instruments (e.g., electron microscopes, MRIs) and activities (e.g., micro-surgery) require low vibration environments.

Overview

Vibration Criteria

Human perception and comfort

Sensitive equipment

Prediction

Footfall forces

Floor response analyses

Problems with state of the art

Criteria for Human Perception and Comfort

Human Vibration Response Measured along Body Axes (ISO 2631-2:1969)

Base Response Curve Perception Threshold for Most Sensitive Humans

ISO 2631-2:1989 ANSI S3.29-1983

All axes

Ve

loci

ty (

rms)

m/s

100 μm/s = 4,000 μin/s

One third octave band center frequency, Hz

Limits: Multiples of Base Response Curve (Recommended in Standards)

SPACE USAGE ISO ANSI

Hospitals, ORs, Critical Areas 1 0.7 – 1

Residences - night 1.4 1 – 1.4

Residences - day 2 – 4 1.4 – 4

Offices 4 4

Workshops 8 8

How do Perception Criteria Apply to Walking-Induced Vibrations ?

Perception threshold – and acceptability magnitudes – pertain to steady rms vibrations. Walking-induced vibrations are intermittent; may occur rarely and only for short periods. How can representative values be determined for comparison to rms limits? Averaging over what time interval? .

Criterion re Occasional Disturbances

Vibration Dose Value (VDV)

= Perception-weighted acceleration (m/s2)

T = Total exposure time (sec)

(m/s1.75)

VDV Evaluation

VDV (m/s1.75 )

Occupancy

Adverse Comments

Improbable Possible Probable

Residences – day 16 h 0.2-- 0.4 0.4 – 0.8 0.8 – 1.6

Residences – night 8 h ½ of Residences- day

Office 2 x Residences - day

Workshops 4 x Residences - day

British Standard BS 6472-1:2008 Guide to evaluation of human exposure to vibration in buildings

Criteria for Sensitive Equipment

(BBN - 1953)

Generic Criteria “VC Curves”

100 μm/s = 4,000 μin/s

Base Response Curve

Extensions

(ASHRAE - 1993)

VC-A

VC-B

VC-C

VC-D

VC-E

Vel

oci

ty (

in/s

ec)

Letter designations differ from VC labels

100 μm/s = 4,000 μin/s

More Extensions

(NIST - 2002)

100 μm/s = 4,000 μin/s

Yet More Extensions

(NIST - 2005)

NIST-A

100 μm/s = 4,000 μin/s

Generic Criteria for Some Sensitive Usages

Class μm/s μin/s Usage

VC-A 50 2,000 Micro-surgery, Labs, Microscopes up to 400X

VC-B 25 1,000 Research Optics, Micro-electronics Manufacture

VC-C 12.5 500 Electron Microscopes to 30,000X, MRI Imagers

VC-D 6.25 250 Cell Implant Equipment, Photolithography

VC-E 3.12 125 Unisolated Optical Research Equipment

VC-F 1.46 62.5 Metrology, Standards Research

VC-G 0.76 31.2 Nano-Mechanics Research

Limits for Some Sensitive Instruments

1/3 Octave Band Center Frequency (Hz)

50 μm/s=2000μin/s 100

10

1

Velocity (μm/s)

A

NIST-A

Problems with Equipment Criteria

Commercial equipment •Suppliers tend to be conservative, set criteria for most stringent performance •Performance vs. vibration magnitude? • Acceptability of intermittent disturbances (how often and how long)? •How were vibration limits determined? (on large items) •Generic criteria not relevant

Non-commercial equipment

•Criteria generally unavailable

Prediction of Walking-Induced Floor Vibrations

Design Guides

•“Floor Vibrations due to Human Activity” Steel Design Guide 11 American Institute of Steel Construction (1997) DG-11 •“A Design Guide for Footfall Induced Vibrations of Structures” The Concrete Centre (2006) CCIP-016 •“Design of Floors for Vibration: A New Approach” The Steel Construction Institute (2007) SCI P354 •“Design of floor structures for human induced vibrations” European Commission Joint Research Centre (2009) EUR 24084 EN

Source of Vibration: Footfall Force Pulses

Footfall Force Pulses (Galbraith and Barton 1970)

Subject 1 Oxfords Stockings

Subject 2 Oxfords Stockings

55 steps/min 95 147 203

33 111 155

214

Footfall Pulse Representation (DG-11)

Fm

/W

f0

=1/

t0

Walking Speed (Steps/min)

1/to

Fm/W

Fm/W

1/t0

Force Pulse Representation (EUR 2009)

.

Vibration Response Analysis Tools and Approaches

Modal Analysis

u(x,y,t)

u(x,y,t)=

Modal displacement Mode shape

Mode shapes and natural frequencies found from analysis of free motion

Modal Relations

For point force at

Response to Continuing Footfalls

Force Fourier Series:

Walking (step) frequency

Walking person’s weight

“Dynamic load factor”, from empirical data – depends on step frequency

Modal Steady-State Acceleration Response Component at ω

Subscripts identifying mode are omitted here for clarity.

Damping ratio

Response to Impulse

Subscripts identifying mode are omitted here for clarity.

For short sharp footfall pulse :

Impulse

For any footfall pulse:

Velocity immediately after pulse:

Then motion continues freely

with zero damping

Excitation and Response Approximations

Excitation: Impulse Train

Approximations: •identical pulses repeated at constant interval •no build-up of vibrations from successive pulses

Motion after Single Sharp Impulse

Mode assumed initially at rest; impulse results in v0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Vrms/V0

Natural Frequency/Footfall Frequency

rms Velocity after Impulse / Initial Velocity

0.10%

0.50%

1%

2%

4%

Damping

Steady-State (Fourier Component) Model

Force Fourier Series:

Walking (step) frequency

Walking person’s weight

“Dynamic load factor”, from empirical data – depends on step frequency

Modal Steady-State Acceleration Response Component at ω

Subscripts identifying mode are omitted here for clarity.

Damping ratio

Time (s)

Vel

oci

ty (

mm

/s)

Successive footfall pulses •Not identical •Not uniformly spaced •Not at same location

Excitation is not continuing •Steady-state response is not reached

Shortcomings of Excitation Models

Accounting for not reaching steady state

Acceleration reached at time T after harmonic force application compared to steady-state acceleration:

“Reduction Factor” to multiply steady-state response

Accounting for non-constant location of footfalls: R reduced empirically

T ≈ walking duration, time to traverse floor?

Approaches of Design Guides

Steel Design Guide 11 –Continuing Footfalls

•Focus on fundamental mode, “worst” locations; •Resonance with a footfall harmonic at floor natural frequency

P = Person’s weight = 0.7 kN = 157 lb R = Reduction factor = 0.5 β = Damping ratio = 0.02 to 0.05 for residences and offices

•Relaxed perception criteria are used to account for intermittent excitation.

Steel Design Guide 11 – Footfall Impulse Analysis

•Idealized force pulse shape and empirical parameters functions of walking step frequency •Closed form solution to upper bound velocity at end of pulse. •After pulse: non-decaying vibration at modal natural frequency with upper-bound velocity amplitude

CCIP-016 and SCI P354 -- Footfall Impulse Analysis

•Design Impulse (25% chance of exceedence), empirical Modal velocity at end of pulse

•After pulse: vibration at modal natural frequency with damping- dependent decay, until next footfall pulse. •Time-domain responses of several low modes to single impulse superposed to calculate rms velocity and VDV. • Response to single impulse taken as representative.

(N-s)

CCIP-016 and SCI P354 – Steady-State Analysis

•Calculate (complex) acceleration response of each of lowest 4 structural modes to each of 4 harmonics of a selected step frequency

Dynamic load factors αi given empirically – later slide •Sum the accelerations for each harmonic. •To evaluate perception/comfort, find Response Factor RF = acceleration sum/baseline acceleration at i Calculate total RF for all harmonics •Repeat for other step frequencies.

Concrete Centre CCIP-016 Perception Evaluation

•Plot total RF vs. walking frequency, compare maximum to criteria

Occupancy RF

Critical working areas 1

Residences – day 2 - 4

Residences – night 1 - 4

Offices 4

Workshops 8

Dynamic Load Factors ( CCIP – 016)

European Commission EUR 24084 EN

F(t)/W Measured step forcing from 700 people passages, statistical distribution in 35 classes.

Weight-normalized force pulses due to single step given by 8th order polynomial in time; Coefficients functions of step frequency. Duration of single footfall given by 2nd order polynomial in step frequency.

Statistics of people weights W as published for Europe, in 20 classes.

European Commission EUR 24084 EN

Considers: •Fundamental mode and worst-case forcing location. •Steady-state forcing consists of overlapping force pulses from individual steps, repeated at step frequency.

For many combinations of modal mass, natural frequency, damping:

•Calculates the perception-weighted rms response magnitude for each combination of 20 weight classes and 35 step frequency classes •Applies the joint probability of each set of classes to the rms response magnitudes, determines the cumulative probability distribution of these magnitudes.

European Commission EUR 24084 EN

•Characterizes the modal response in terms of the rms response magnitude with 90 % probability. (OS-RMS90)

•Establishes perception-based usage rating classes corresponding to this metric. •Presents contour plots of OS-RMS90 in the modal mass – natural frequency plane for given damping, including shading for usage rating classes.

European Commission EUR 24084 EN

Contours of OS-RMS90 in Natural-Frequency/Modal-Mass Plane

for β=1%

Contours of OS-RMS90 in Natural-Frequency/Modal-Mass Plane

for β=5%

Contours of OS-RMS90 in Natural-Frequency/Modal-Mass Plane

for β=5%

Note: Damping affects predicted responses

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5

Vrms/V0

Natural Frequency/Footfall Frequency

Ratio of rms Velocity in Footfall Interval to Initial Velocity

Dam

Note: Damping estimates are uncertain (CCIP-016)

Note: Modal properties of floor structures can be

determined precisely, but damping can be estimated only roughly.

Limitations Criteria •Perception criteria provide only rough guidance to acceptability to personnel. •Acceptability criteria for sensitive equipment often incompletely defined or absent. Prediction •Some structural parameters (damping) uncertain •Procedures of guidelines neglect some aspects of the excitations and responses.

The Bottom Line

•Current state of the art does not permit precise prediction of walking-induced vibrations and their effects. •Many satisfactory floor structures have been designed using the available approaches. •There is room for much more work. Significant improvement in the precision of the total prediction process will require addressing many contributing factors.