ASG-Bridge-Vibration-Presentation-28-March-2016.pdf

7/26/2019 ASG-Bridge-Vibration-Presentation-28-March-2016.pdf

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Tok o Institute of Technolo Takeuchi Lab

Ben Sitler, PE

Arup Unified Method for Floors, Footbridges, Stairs and Other Structures

Footfall Induced Vibration


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Tok o Institute of Technolo Takeuchi Lab2

Outline

Introduction to Footfall Induced Vibration

Computing the Structural Response

Project Examples

References


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Introduction to Footfall InducedVibration


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When is footfall induced vibration an issue?Introduction to Footfall Induced Vibration

Low Frequency (Resonance) Low Mass (Acc=Force/Mass)

Low Damping

Large Dynamic Loads (Crowds)


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The design problemIntroduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response

Modal (structural) properties:

Loading:

consequences,

acceptability, ?????

Frequency

Modal mass

Mode shape

Damping

Amplitude

Frequency

Duration

Response


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What does a footfall time history look like?Introduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response


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What kinds of excitation frequencies are possible?Introduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response


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So how does this translate into a design load?Introduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response


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What is an appropriate amount of damping?Introduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

AmplificationFactor

(excitation frequency)/(natural frequency)

Steady State Resonant Amplification Factors for SDOF systems

0.02 damping

0.05 damping

0.10 damping

0.20 damping

Damping :: Frequency :: Modal Mass :: Mode Shape

Be suspicious of >2%

Footbridges 0.5~1.5%

Stairs 0.5%

Floors 1~3%


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Modelling AssumptionsIntroduction to Footfall Induced Vibration :: Loading :: Modal Properties :: Response

Damping :: Frequency :: Modal Mass :: Mode Shape

some tips (not exhaustive)Loads Use best estimate, not code values LL: ~0.5kPa typically realistic SDL: upper/lower bound sensitivity study

Model Extent Typically model single floor only Floorplate should capture all modes of interestBoundary Conditions Fixed connections/supports unless true pin Faade vertical fixity may/may not be appropriateMember Modelling Orthotropic slab properties Composite beam (even if nominal studs) Ec,dynamic38GPa Subdivide 6+ elements per span


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What is a good design criteria?Introduction to Footfall Induced Vibration :: Loading :: Modelling :: Response

Situation R RMS Acc @ 5Hz

Low vibration 1 0.005 m/s2

Residential (night) 1.4 0.007 m/s2

Residential (day) 2-4 0.01~0.02 m/s2

Office (high grade) 4 0.02 m/s2

Office (normal) 8 0.04 m/s2

Footbridge (heavy) 24 0.12 m/s2

Footbridge (inside) 32 0.16 m/s2

Footbridge (outside) 64 0.32 m/s2

Stair (high use) 24 0.12 m/s2

Stair (light use) 32 0.16 m/s2

Stair (very light use) 64 0.32 m/s2

0.001

0.01

0.1

1 10 100

Frequency (Hz)

rmsacceleration

(m/s2)

Approximate threshold of humanperception to vertical vibration

T 2t t

RMS RMS

Acc Peak,HarmonicRMS T

R=Acc Acc

AccAcc = =

2


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Computing the Structural Response


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Simplified vs Modal vs Time History MethodsComputing the Structural Response

vs

vs

Modal harmonic

response method

Explicit time history

method


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F

orce

Time

Analytical ModelComputing the Structural Response

P

y

cK

My

Fo

rce

Time


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( ) ( ) ( ) ( ) i t

my t cy t ky t P t P e

Resonant ResponseComputing the Structural Response

Py

cK

M

,F W DLF f harmonic

2 2

2 22

2 22 2 2 2

1 1

1 2

1 2

1 2 1 2

h h

m m

h hh h

m mm m

h h h h

m m m m

dispf f

f f

f ff f

f f f f

f f f f

f f f f

kFRF

k m ic i

i

SDOF Harmonic Steady State Response

excition reponse

acc

FAcc FRF

m

Concrete Centre eq 4.4

h = harmonic forcing freq.

m = modal (structural) freq.


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Transient ResponseComputing the Structural Response

Force

Time

SDOF Impulse RMS Velocity Response

( ) ( ) ( ) ( ) i t

my t cy t ky t P t P e

1.43

1.354 [Ns]weff

n

fI

f

e ff e xc it io n r ep on se

Peak

IVel

m

( ) sintPeakVel t Vel e t

( )RMS mVel RMS Vel t

w = walking forcing freq.

m = modal (structural) freq.Concrete Centre eq 4.10~4.13


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Bobbing Resonant ResponseComputing the Structural Response

12

2 2( )1 s a s s a a adisp

a a a a a

k k m i c c k i cFRFK M iC k i c k m i c

0 0

0 0 0 0

0 0 0 0 0

s s s a p a p s s a p a p s

a a a a a a a a

p p p p p p p p

m y c c c c c y k k k k k y P

m y c c y k k y P

m y c c y k k y

2

2 2

1(1,1) (1, 2) adisp

aa a s a s

a

mDMF FRF FRF

FRF ffk D k D D

f f

2

1 2a aa a

f fD i

f f

2

1 2s ss s

f fD i

f f

2

dispAcc P DMF

( ) ( ) ( ) ( ) i ty t Cy t Ky t P t P e

,aP W GLF harmonic scenario

MDOF Harmonic Response crowd interacting with structure

IStructE Route 2

a = active crowd

p = passive crowd

s = structure


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Programming ImplementationComputing the Structural Response

foreach node

// Get response of governing excitation frequency

RNode = MAX(RNode())

foreach excitation frequency

// Get R Factor

RNode() = AccRMS,Node() / AccRMS,0()

// Get SRSS acceleration

AccRMS,Node()

= (Mode

Harmonic

AccRMS(n,m,h,*h)

2)

foreach mode

// Get modal properties

// modal frequency (), damping () & mass (m)

// displacement at excitation(ne) & response(nr) nodes

// ,

m,m,mm,ne,nr,Wm,m = ...

foreach harmonic

// Get harmonic properties

// dynamic amplification factor(DLF), harmonic freq ()

DLF,h,m,h = ...

// Get RMS acceleration

AccRMS(n,m,h,*h)=RMS(F(m,h,m,mm,ne,nr,DLF,h,Wm,m))

2000 nodes x 20 modes x 4 harmonics x 1.5Hz

frequency range = 2.4E7 calculations

not practical back in 90s, hence the simplified

methods in AISC DG11, AS 5100-2, etc

6000 nodes x 40 modes x 2 harmonics x 6Hz

frequency range (running) = 2.8E8 calculations

Excel VBA is single threaded so no parallel processing

Suggest building with parallel libraries in C#, VB, Python, etc

Footbridge GSA model

Library floor GSA model


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Some Examples


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How can we improve response?Examples

Increase Damping Increase Frequency

Increase Stiffness

Decrease Mass

Increase Mass Isolate


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Further ReadingQuestions?

General Structures (Vertical Resonant or Transient of Pedestrians) Concrete Centre CCIP-016A design guide for Footfall Induced Vibration of Structures

SCI P354 Design of Floors for Vibration

Stadia & Concert Hall (Vertical Resonance of Bobbing Crowd)

IStructE Dynamic Performance Requirements for Permanent Grandstands Subject to

Crowd Action C. Jones, A. Pavic, P. Reynold, R. Harrison Verification of Equivalent Mass-Spring-Damper

Models for Crowd-Structure Vibration Response Prediction

High Use Footbridges (Lateral Synchronous Lock in and Vertical Crowd)

P. Dallard The London Millenium Footbridge

BSI PD 6688-2:2011 Background to National Annex to BS EN 1991-2: Traffic loads on

bridges

Setra Footbridges: Assessment of Vibrational Behaviour of Footbridges under Pedestrian

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contact: [email protected]

ASG-Bridge-Vibration-Presentation-28-March-2016.pdf

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