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A study of the influence of different

types of timber footbridges on the

natural frequency of vibration

Vanessa Bao, J.Carlos Santos, Julio Vivas,Soledad Rodrguez, Abel Vega and Keith Crews

Vanessa [email protected]


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cetemas

In recent yearsin Spaindemand for timber footbridges has increased considerably

Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews


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demand for timber footbridges has increased considerably

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In recent yearsin Spain


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In recent yearsin Spain

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Normative SERVICIABILITY LIMIT STATE OF VIBRATION IN FOOTBRIDGES

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VIBRATIONS Frequencies of risk of resonance (Hz)

Vertical and longitudinal 1.25 - 4.60

IAP-11.Regulation relating to loads in the design and planning of road bridges, 2011

Frequency (Hz) 0-1 1-1.7 1.7-2.1 2.1-2.6 2.6-5 >5

Range 1

Range 2

Range 3

Range 4

STRA, 2006.Service dtudes techniques des routes et autoroutes

Classification of pedestrian comfort and risk or resonance cuased by pedestrian traffic:

Range 1. maximum risk of resonance

Range 2. medium risk of resonance

Range 3. low risk of resonanceRange 4. negligible risk of resonance

Verification by appropriate dynamic studies of the vibrational response when the

bridge is of a new structural type or uses new materials (different to steel or concrete)

Vertical natural frequency range classification



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Objectives

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To evaluate the numerical and experimental frequencies of vibration ofseveral timber footbridges

To analyse the lower experimental frequencies of vibration in order to

classify the footbridges by risk of resonance and comfort criteria

To study the influence of span in natural frequency for first modal shape inbending


To analyse the design of simple supported timber footbridges in relation to

serviceability limit state of vibration


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Timber footbridges. design

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Main girders

Diagonals

Secondary beams

Joists

Deck

Design of simple supported timber footbridges studied



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L (m)

Timber footbridges. dimensions

cetemasEurocode 5 (UNE EN 1995-1-1:2006)

IAP-11

ROBOT Software

L w wg hg m

[m] [m] [mm] [mm] [kg]

1 15.6 1.5 185 858 4725

2 10.6 2 185 561 2442

3 18.6 2 185 924 6336

4 9.1 2 185 462 2107

5 14.6 2 185 726 4191

6 7.6 1.5 185 462 1601

7 5.8 1.5 185 330 974

8 21.6 1.5 190 952 6886

L=span of the bridge (m)

w=width of the bridge (m)

wg=width of main girder (mm)

hg=height of main girder (mm)m=mass of bridge (kg)

Dimensions, cross section of main girders and mass


w (m)

Wg

hg

Determination of mass of bridges: volume (m3) * Density (Kg/m3),

considering a general density of 550 Kg/m3 (Pinus sylvestris)


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

1 15.6 1.5 185 858 4725


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

2 10.6 1.5 185 561 2442


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

3 18.6 2 185 924 6336


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

4 9.1 2 185 462 2107

l li i l d d d b l d i h


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

5 14.6 2 185 726 4191

V B J C l S J li Vi S l d d R d Ab l V d K i h C


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L w wg hg m

[m] [m] [mm] [mm] [kg]

6 7.6 1.5 185 462 1601

V B J C l S t J li Vi S l d d R d Ab l V d K ith C


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L w wg h

g m

[m] [m] [mm] [mm] [kg]

7 5.8 1.5 185 330 974

Vanessa Bao J Carlos Santos Julio Vivas Soledad Rodrguez Abel Vega and Keith Crews


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cetemas


L w wg h

g m

[m] [m] [mm] [mm] [kg]

8 21.6 1.5 190 952 6886



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Numerical calculationsExperimental tests Theoretical calculations

Equation derived from closed-form

solutions for pinned-pinned single

span beams

f1bf1a f1c

Using structural analysis software

ROBOT

Dynamic tests

Experimental natural frequency of

first bending mode (Hz)Theoretical natural frequency of

first bending mode (Hz)

Numerical natural frequency of first

bending mode (Hz)

Methodology



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Dynamic tests

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Vanessa Bao J Carlos Santos Julio Vivas Soledad Rodrguez Abel Vega and Keith CrewsVanessa Bao J Carlos Santos Julio Vivas Soledad Rodrguez Abel Vega and Keith Crews


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Dynamic tests

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CONFIGURATION


accelerometers

impact hammer

Data logging

Cronos IMC Equipment

IMC Devices software

PCB 3711B112G accelerometers:

-sensibility: 1000 mV/g

-measurement range: 2g

PCB 086D20 impulse force test hammer



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Dynamic tests

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CONFIGURATION


accelerometers

impact hammer

Data logging





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Dynamic tests

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CONFIGURATION


accelerometers

impact hammer

Data logging



Data processing

IMC Famos

LMS Test Lab

Analisys of FRF: selection of

modal shape and natural

frequency

FFT (Fast Fourier

Transformation)

Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith CrewsVanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews


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Dynamic tests

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FRFMODAL SHAPES



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Dynamic tests

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CONFIGURATION




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Dynamic tests

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, , , g , g



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Results

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, , , g , g

Evaluation of the numerical and experimental vibrational frequenciesEXP. THEOR. NUM.

N. of

Bridge

Hg f1a f1b f1c

[%] [Hz] [Hz] [Hz]

1 14.50 7.01 5.50 5.58

2 16.60 8.37 7.21 7.06

3 14.40 4.88 4.08 4.11

4 28.90 9.58 7.29 7.45

5 15.90 5.59 5.02 5.11

6 15.30 13.67 10.94 11.2

7 13.70 15.88 12.73 13.9

8 15.10 4.54 3.32 3.33

r=0.995 r=0.994

Hg = humidity of beamsf1a = experimental natural frequency of first bending mode

f1b = theoretical natural frequency of first bending mode calculated by Equation (1)

f1c = numerical natural frequency of first bending mode calculated by ROBOT

r= correlation coefficient

High correlation coefficient between:

experimental and theoretical results (0.995)

experimental and numerical results (0.994)



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Results

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g g

Evaluation of the numerical and experimental frequencies of vibrationEXP. THEOR. NUM. EXP.-THEOR. EXP.-NUM. THEOR.-NUM.

f1a f1b f1c Relative Error Relative Error Relative Error

[Hz] [Hz] [Hz] % % %

1 7.01 5.50 5.58 0.21 0.20 0.01

2 8.37 7.21 7.06 0.14 0.16 0.02

3 4.88 4.08 4.11 0.16 0.16 0.01

4 9.58 7.29 7.45 0.24 0.22 0.02

5 5.59 5.02 5.11 0.10 0.08 0.02

6 13.67 10.94 11.2 0.20 0.18 0.02

7 15.88 12.73 13.9 0.20 0.12 0.09

8 4.54 3.32 3.33 0.27 0.26 0.00

r=0.995 r=0.994 19.1% 17.5% 2.0%

The relative error between

theroretical and numerical

results was of 2.0%


experimental and theroretical

results was of 19.1%


experimental and numerical

results was of 17.5%

There has not been a good estimation of the mass of footbridges in order to predict the theoretical

and numerical natural frequencies.



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Results

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Classification of the footbridges by comfort criteria and risk of resonance

span EXP. Resonance Risk

N. of

Bridge[m] f

1a[Hz] IAP-11 SETRA

1 15.6 7.01 (>4.6 Hz) No risk (>5 Hz) Range 4


3 18.6 4.88 (>4.6 Hz) No risk (2.6-5 Hz) Range 3


5 14.6 5.59 (>4.6 Hz) No risk (2.6-5 Hz) Range 3



8 21.6 4.54 (


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Results

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Influence of span in natural frequency for first modal shape in bending

The simple supported and straight timber footbridges with a span longer than 20 m and a width

between 1.5 and 2 m presented first frequencies of vibration lower than 5 Hz.

There was a decreasing relationship between the natural frequency of the first bending mode and

the span for the experimental results of these 8 timber footbridges.

A span between 20 and 25 m could be the limit of manufactured timber footbridges with this designaccording to serviceability limit state of vibration (comfortability).


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Thank you foryour attention

Vanessa Bao

[email protected]

J.Carlos Santos

[email protected]

Julio Vivas

[email protected]

Soledad Rodrguez

[email protected]

Abel Vega

[email protected]

Keith Crews

[email protected]

www.mediamadera.comwww.cetemas.es
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