Upload
everaldo-pletz
View
234
Download
0
Embed Size (px)
Citation preview
7/27/2019 frequencias naturais
1/29
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]
7/27/2019 frequencias naturais
2/29
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
7/27/2019 frequencias naturais
3/29
demand for timber footbridges has increased considerably
cetemas
In recent yearsin Spain
7/27/2019 frequencias naturais
4/29
In recent yearsin Spain
cetemas
7/27/2019 frequencias naturais
5/29
Normative SERVICIABILITY LIMIT STATE OF VIBRATION IN FOOTBRIDGES
cetemas
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
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
6/29
Objectives
cetemas
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
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
To analyse the design of simple supported timber footbridges in relation to
serviceability limit state of vibration
7/27/2019 frequencias naturais
7/29
Timber footbridges. design
cetemas
Main girders
Diagonals
Secondary beams
Joists
Deck
Design of simple supported timber footbridges studied
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
8/29
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
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
w (m)
Wg
hg
Determination of mass of bridges: volume (m3) * Density (Kg/m3),
considering a general density of 550 Kg/m3 (Pinus sylvestris)
7/27/2019 frequencias naturais
9/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
L w wg h
g m
[m] [m] [mm] [mm] [kg]
1 15.6 1.5 185 858 4725
7/27/2019 frequencias naturais
10/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
L w wg h
g m
[m] [m] [mm] [mm] [kg]
2 10.6 1.5 185 561 2442
7/27/2019 frequencias naturais
11/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
L w wg h
g m
[m] [m] [mm] [mm] [kg]
3 18.6 2 185 924 6336
7/27/2019 frequencias naturais
12/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
7/27/2019 frequencias naturais
13/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
7/27/2019 frequencias naturais
14/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
7/27/2019 frequencias naturais
15/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
7/27/2019 frequencias naturais
16/29
Timber footbridges. dimensions
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
L w wg h
g m
[m] [m] [mm] [mm] [kg]
8 21.6 1.5 190 952 6886
Vanessa Bao J Carlos Santos Julio Vivas Soledad Rodrguez Abel Vega and Keith Crews
7/27/2019 frequencias naturais
17/29
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
Vanessa Bao J Carlos Santos Julio Vivas Soledad Rodrguez Abel Vega and Keith Crews
7/27/2019 frequencias naturais
18/29
Dynamic tests
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
7/27/2019 frequencias naturais
19/29
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
Dynamic tests
cetemas
CONFIGURATION
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
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
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
7/27/2019 frequencias naturais
20/29
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
Dynamic tests
cetemas
CONFIGURATION
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
accelerometers
impact hammer
Data logging
Cronos IMC Equipment
IMC Devices software
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
7/27/2019 frequencias naturais
21/29
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
Dynamic tests
cetemas
CONFIGURATION
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
accelerometers
impact hammer
Data logging
Cronos IMC Equipment
IMC Devices software
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
7/27/2019 frequencias naturais
22/29
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
Dynamic tests
cetemas
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
FRFMODAL SHAPES
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
23/29
Dynamic tests
cetemas
CONFIGURATION
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
24/29
Dynamic tests
cetemas
, , , g , g
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
25/29
Results
cetemas
, , , 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)
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
26/29
Results
cetemas
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%
The relative error between
experimental and theroretical
results was of 19.1%
The relative error between
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.
Vanessa Bao, J.Carlos Santos, Julio Vivas, Soledad Rodrguez, Abel Vega and Keith Crews
7/27/2019 frequencias naturais
27/29
Results
cetemas
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
2 10.6 8.37 (>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
4 9.1 9.58 (>4.6 Hz) No risk (>5 Hz) Range 4
5 14.6 5.59 (>4.6 Hz) No risk (2.6-5 Hz) Range 3
6 7.6 13.67 (>4.6 Hz) No risk (>5 Hz) Range 4
7 5.8 15.88 (>4.6 Hz) No risk (>5 Hz) Range 4
8 21.6 4.54 (
7/27/2019 frequencias naturais
28/29
Results
cetemas
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).
7/27/2019 frequencias naturais
29/29
Thank you foryour attention
Vanessa Bao
J.Carlos Santos
Julio Vivas
Soledad Rodrguez
Abel Vega
Keith Crews
www.mediamadera.comwww.cetemas.es
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]