comfort evaluation of a double-sided catwalk due to wind-induced vibration · 2016-08-23 ·...
TRANSCRIPT
Comfort evaluation of a double-sided catwalk due to wind-induced vibration
*Siyuan Lin1) and Haili Liao2)
1), 2) Research Center for Wind Engineering, SWJTU, Chengdu 610-031, China,
ABSTRACT
Buffeting response of a double-sided catwalk designed for Dongting Lake
suspension bridge under construction was investigated with considering wind load
nonlinearity, geometric nonlinearity and self-excited forces. The buffeting analysis was
conducted in time domain using an APDL-developed program in the finite element
software ANSYS. The wind velocity series was simulated using the spectra
representation method. Static aerodynamic coefficients are derived from section model
wind tunnel test. The effects of cross bridge interval and the gantry rope diameter on
buffeting response were discussed in detail. Referring to the ISO 2631-1(1997) standard
and the annoyance rate model, comfort of the catwalk due to wind-induced vibration
was evaluated. The results show locations near the bridge tower have a lower level of
comfort than the other parts of the catwalk. Enlarging the gantry rope size, as well as
decreasing the cross bridge interval would increase the comfort level. Moreover, the
effect of gantry rope diameter was obvious than that of cross bridge interval. Annoyance
rate model can evaluate the comfort level quantitatively compared to the ISO standard.
1. Introduction
Catwalk structures are temporary walkways used in the erection of main cables in
suspension bridges, consisting of a few ropes, steel cross beams, wooden steps, and
porous wire meshes at the bottom and both sides. When the catwalk is not fixed on the
main cables, the catwalk system is more vulnerable to the wind-induced vibration. Due
to turbulent component in the natural wind, the catwalk will vibrate randomly. When the
wind speed exceeds a certain value, the vibration causes adverse effects for those who
work on the site. The construction personnel will produce the EMG changes, organ
1)
Graduate Student 2)
Professor
function and phenomenon of subjective perception of decline. Meanwhile, their irritability,
error rate would increase, resulting in fatigue easily, thereby reducing the efficiency of
construction and affecting the quality of main cable erection. Therefore, it is necessary
to evaluate the comfort level of catwalk due to wind induced vibration.
In terms of catwalk, researchers put their focus on the aerostatic stability and buffeting
response. The influence of yaw angle and turbulent wind were considered to analyze
the stability of catwalk by using the nonlinear finite element method(Zheng, Liao et al.
2007). The mechanism of unique coupling between vertical and lateral vibrations of
catwalk was discussed in the buffeting analysis(Li, Wang et al. 2014). The influence of
cross bridge interval was evaluated only for catwalk’s buffeting response (Kwon, Lee et
al. 2012).
In terms of comfort evaluation, a lot of researches have been done based on the
vibration of vehicles, high-rise buildings, offshore platforms etc. The evaluation of
comfort for those structures was always focused on the level of human subjective
feelings to the vibration based on traditional methods. However, the level of subjective
feelings is influenced by many factors, including the psychological and physiological
ones. So the traditional methods can hardly evaluate the comfort level quantitatively.
Taking the double-sided catwalk of Dongting Lake highway suspension bridge under
construction as an example, this study evaluates its comfort due to wind-induced
vibration referring to the ISO 2631-1-1997 standard and annoyance rate model. Section
model wind tunnel test was conducted to get static aerodynamic coefficients of the
catwalk section. The fluctuating wind field was simulated using the spectral
representation method. With these parameters, nonlinearity of wind load was
considered in buffeting response analysis, as well as geometric nonlinearity of catwalk.
The results show locations near the bridge tower have a lower level of comfort than the
other parts of the catwalk. Both enlarging the gantry rope size and decreasing the cross
bridge interval would increase the comfort level, but the cross bridge interval has a
minor effect. Annoyance rate model can evaluate the comfort level quantitatively
comparing to the ISO standard.
2. Wind Tunnel test
The analyzed catwalk is designed for Dongting Lake highway suspension bridge of which the main span length is 1480m and sag ratio is 1/10. The span configuration is 460m (south span) +1480m (mid span) +491m (north span) for the main cable. The catwalk rope is parallel to the main cable with a separation distance of 1.5m. There are 11 cross bridges are distributed every 185m along the span, with 2 in each side span and 7 in mid span. Gantries are distributed every 42.5m or 50m along the span. The left side and right side of the catwalk has a distance of 35.4m. Each side of the catwalk is 4.2m in width. The catwalk rope is size of φ54 type and gantry rope is the size of φ60.Detailed design of the catwalk section is shown in Fig.1.
(a) Elevation view (b) Lateral view
Fig.1 Detailed design of the catwalk section
To investigate the aerodynamic performance of catwalk at large angle of attack, as
Fig. 2 shows, a 1:5 scale model is tested in the XNJD-1 wind tunnel under smooth flow
to get the tri-component static aerodynamic coefficients, with the angle of attack varying
from -20°to 20°every degree each. The section model of catwalk is 2.1m long, 0.84m
wide and 0.29m high, of which is made up of steel, meshwork and wood. Drag force, lift
force and pitching moment force coefficients are derived from the following formula and
shown in Fig. 3. The testing results from different wind speeds are identical thus
indicating the influence of Reynolds number can be neglected.
2
( )( )
1
2
DD
FC
V HL
2
( )( )
1
2
LL
FC
V BL
2 2
( )( )
1
2
zM
MC
V B L
(1)
where CD(α), CL(α), CM(α) are the drag force, lift force and pitching moment force
coefficients respectively, FD, FL, Mz are the measured drag force, lift force and pitching
moment respectively, α is the angle of attack, ρ is the air density, V is the wind velocity,
H, B, L are the height, width and length of the catwalk model respectively.
3. Buffeting analysis of catwalk in time domain
3.1 Finite Element Model
Catwalk is the typical cable-truss structure, which is stabilized by the initial tension
in the ropes. With the loads acting on the catwalk, the deformation including the rigid
body displacement and strain develops, thus changing the structure stiffness. So the
influence of large deformation and prestress should be considered in the finite element
model.Link10 element is used to model the catwalk rope and gantry rope, which cannot
hold compression.Beam44 element, is adopted to model the steel beams, gantries and
cross bridges. Cross bridges are modeled by an equivalent beam with the same mass
and stiffness properties. Handrail column, hand rope and meshwork network have less
contribution to the whole stiffness of the catwalk, so they are represented by some
equally-distributed mass on the finite element model. Bridge tower has little influence on
the dynamic properties of the catwalk(Li and Ou 2009),so the bridge tower is neglected
in the finite element model. Nodes on the tower top and ends of the catwalk are
constrained all degrees of freedom. The three dimensional finite element model is
shown in Fig.4.
-20 -15 -10 -5 0 5 10 15 20
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
stat
ic a
ero
dy
nam
ic c
oef
fici
ents
angle of attack(deg)
CD
CL
CM
Fig.2. Catwalk section model of
Dongting Lake suspension bridge
tested in wind tunnel
Fig. 3. Static aerodynamic coefficients of
catwalk for Dongting Lake suspension bridge
Fig. 4. Full finite element model of catwalk for Dongting Lake suspension bridge
With the finite element above, its modal analysis was conducted and the first 10
modes are listed in Table 1. And the first lateral bending, vertical bending and torsion
modal shape are shown in Fig.5~Fig.7.
Table 1 Natural modal frequencies and shapes
Mode
number
Characteristics of modal shapes Modal
frequency(Hz)
1 1st symmetric lateral bending 0.04802
2 1st anti-symmetric lateral bending 0.09281
3 1st anti-symmetric lateral bending+1st
anti-symmetric vertical bending+1st
anti-symmetric torsion
0.09528
4 1st anti-symmetric lateral bending+1st
anti-symmetric vertical bending+1st
anti-symmetric torsion
0.09682
5 1st symmetric vertical bending 0.13332
6 1st symmetric torsion 0.13783
7 1st lateral bending of right side span 0.13932
8 1st symmetric lateral bending+1st
symmetric torsion
0.14342
9 1st lateral bending of left side span 0.14967
10 1st anti-symmetric longitudinal floating 0.18947
Fig.5 First lateral bending modal shape
3D Longitudinal
Vertica
l
Latera
l
Fig.6 First vertical bending modal shape
Fig.7 First torsion modal shape
3.2 Simulation of Wind Field
The fluctuating wind velocity field was simulated by the spectral representation
method with the Cholesky explicit decomposition of cross-spectral density matrix. It is
assumed that fluctuating wind field characteristics changes along the direction of span
but also change along the direction of height. It is usually assumed that the wind
fluctuations in three orthogonal directions are mutually uncorrelated. The overall 3-D (i.e.
three components of natural wind) wind velocity field can be simplified into many
3D Longitudinal
Vertica
l
Latera
l
3D Longitudinal
Vertica
l
Latera
l
one-dimensional wind velocity fields. The FFT (Fast Fourier Transform) technique
(Deodatis 1996)was adopted to further improve the computational efficiency. Then
random field in terms of lateral and vertical components was generated at 142 locations
along the span of the catwalk with a separation of around 18 meters. The other details
for simulating the wind field are listed in Table 2. The wind velocity of the middle node in
the mid span is chosen to verify the simulated time series. The velocity pieces are
shown in Fig. 8.
Table 2 Parameters for simulating the wind field
Number of simulated nodes 142
V10 15m/s
Separation of frequency 1024
Upper limit of frequency 2Hz
Lower limit of frequency 0.1Hz
Longitudinal wind spectra Simiu Spectra
Vertical wind spectra Lumley-Panofsky spectra
Ground roughness length z0 0.03m
Decaying factor Cz 10
Decaying factor Cy 16
Decaying factor Cw 8
Time interval 0.25s
Note: V10=15m/s is considered as the maximum wind speed for construction
according to engineering practice.
0 200 400 600 800 1000
-8
-6
-4
-2
0
2
4
6
ve
lcity (
m/s
)
time (s)
velcity
(a) Part of the vertical wind velocity series
0 200 400 600 800 1000
-10
-5
0
5
10
15
ve
lcity (
m/s
)
time (s)
velcity
(b) Part of the longitudinal wind velocity series
Fig.8 Simulated wind velocity of the middle node in the mid span
When the time series of wind velocity is simulated, the power spectra density can be
calculated using the FFT. As Fig.9 shows, the simulation spectrum fits the target
spectrum well, indicating the correctness of the simulation.
1E-3 0.01 0.1 1
0.01
0.1
1
10
100
1000
PS
D(m
2/s
)
Frequency(Hz)
Simulation spectrum
Target spectrum
(a) Longitudinal wind velocity PSD
1E-3 0.01 0.1 1
0.01
0.1
1
10
100
1000
PS
D(m
2/s
)
Frequency(Hz)
Simulation spectrum
Target spectrum
(b) Vertical wind velocity PSD
Fig.9 Comparison of simulation PSD and target PSD
3.3 Buffeting force model
The buffeting force caused by fluctuating wind is usually expressed in the
quasi-steady form. Aerodynamic admittance is introduced to correct the quasi-steady
formulae. So the buffeting forces acting on the catwalk are given as follows.
2 '1 ( ) ( )( ) (2 ( ) )
2b L Lu L D Lw
u t w tL t U B C C C
U U
2 '1 ( ) ( )( ) (2 ( ) )
2b D Du D L Dw
u t w tD t U B C C C
U U
2 2 '1 ( ) ( )( ) ( 2 )
2b M M u M M w
u t w tM t U B C C
U U
where Lu , Lw , Du , Dw , Mu , Mw where are aerodynamic admittance function,
reflecting the connection between fluctuating wind and buffeting force. For simplicity,
aerodynamic admittance function is set as constant 1. The buffeting analysis was
conducted at 0 attack angle, the related aerodynamic static coefficients and derivatives
are CL=0.0101, CD=0.4709, CM=-0.0187, CD’=0, CL’=0.3783, CM’=-0.02.
3.4 Self-excited force in FE analysis
Based on Scanlan’s flutter theory(Scanlan 1978), the self-excited force can be
expressed using 18 flutter derivatives as follows.
2 * * 2 * 2 * * 2 *
1 2 3 4 5 6
1(2 )( )
2se
h B h p pL U B KH KH K H K H KH K H
U U B U B
2 * * 2 * 2 * * 2 *
1 2 3 4 5 6
1(2 )( )
2se
p B p h hD U B KP KP K P K P KP K P
U U B U B
2 2 * * 2 * 2 * * 2 *
1 2 3 4 5 6
1(2 )( )
2se
h B h p pM U B KA KA K A K A KA K A
U U B U B
Where is the air density, U is mean wind velocity, B is the width of the catwalk,
/K B U is reduced frequency, * * *, ,i i iH P A (i=1, 2…6) are the flutter derivatives.
Lse, Dse and Mse stand for the self-excited lift, drag and pitching moment, their direction
and relation with B and is shown in Fig. 10.
a
wind
Dse
Lse
M se
attack angle
Fig. 10 Self-excited forces on catwalk section
To facilitate the calculation in the finite element software ANSYS, the self-excited force
can be rewrote in the following matrix form.
[ ] [ ]{ } [ ]{ }i i i
se se seF C X K X
Where [ ],[ ]i i
se seC K are the aerodynamic damping and stiffness matrix respectively. In that
case, self-exited force realized using the Matrix 27 element in ANSYS, which has 12
degrees of freedom, to represent the aerodynamic damping and stiffness.
To facilitate the calculation, flutter derivatives are derived from the closed form
suggested by Simiu and Scanlan.
' ' '* * *
1 2 3 2, ,
2 2 2
L L Lx
C C CH H n H
K K K
' ' '* * * *
4 1 2 3 20, , ,
2 2 2
M M M
n
C C CH A A A
K K K
*** 314 * *
1 3
0, ( ) , ( )x
AAA n K n K
H H *
1
1DP C
K * '
2
1
2DP C
K
* '
3 2
1
2DP C
K * '
5
1
2DP C
K
*
5
1LH C
K *
5
1MA C
K
* * * *
4 6 6 6 0P P H A
Where ' ',L MC C are the derivatives of lift coefficients and pitching moment coefficients
considering attack angle;K is the reduced frequency; ,xn n are transforming factors for
vertical motion and torsional motion respectively.
3.5 Buffeting Response of Catwalk
By conducting the time domain analysis, we can get the buffeting responses of the
catwalk. The lateral and vertical acceleration response of the middle node in the mid
span is shown in Fig.10. Their power spectra density is shown in Fig.11.
From Fig xx, the response frequency is close to the 1st lateral and vertical bending
modal frequency, thus indicating the accuracy of the time domain buffeting analysis.
0 50 100 150 200
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
ay (
m/s
2)
time (s)
ay
0 50 100 150 200
-0.4
-0.2
0.0
0.2
0.4
az (
m/s
2)
time (s)
az
(a) Vertical acceleration time history (b) lateral acceleration time history
Fig.10 Time history of acceleration response of the middle node in the mid span
0.01 0.1 1
1E-5
1E-4
1E-3
0.01
0.1
ay_
PS
D (
m2/s
3)
frequency (Hz)
ay_PSD
0.01 0.1 1
1E-5
1E-4
1E-3
0.01
0.1
az_
PS
D (
m2/s
3)
frequency (Hz)
az_PSD
(a) Vertical acceleration PSD (b) lateral acceleration PSD
Fig.11 PSD of acceleration response of the middle node in the mid span
4. Comfort Evaluation of Catwalk under Construction
4.1Comfort Evaluation Based On ISO 2631 standard
According to the buffeting analysis results in the previous section, the catwalk vibrates
in a frequency range less than 0.5 Hz. So vibration of the catwalk is evaluated based on
the part of ISO 2631-1-1997 for evaluating the incidence of motion of sickness(apply to
motion frequencies below 0.5Hz)(Standardization 1997). Referring to the standard, the
weighted root mean square (RMS) of the acceleration shall be determined first.
Although the vibration shall be assessed only with respect to the overall weighted
acceleration in the z-axis, using this method to evaluate the vibration of the catwalk in
the y-axis can also indicate the comfort level qualitatively to some extent. The weighted
RMS acceleration value is given by,
1
2 2
0
1[ ( ) ]
T
rms wA a t dtT
Where wa is the frequency weighted acceleration, T is the lasting time of vibration.
This standard recommends a single frequency weighting Wf for the evaluation of the
effects of vibration on the incidence of motion sickness. In this study, it is assumed the
time fluctuating wind acting on the catwalk is the same, so the vibration time is
neglected in the evaluation. When the weighted RMS acceleration is calculated, the
comfort level can be determined referring to Table 3.
0.01 0.1 1 10
0.01
0.1
1
Fre
qu
en
cy w
eig
htin
g fa
cto
r
Frequency(Hz)
Wf
Fig.12 Frequency weighting curves for principal weighting
Table3 Reactions to various of magnitudes of overall vibration
Frequency weighted
RMS acceleration
aw(m·s-2)
Subjective Response
aw <0.315 Not uncomfortable
0.315≤aw<0.63 A little uncomfortable
0.5<aw<1 Fairly uncomfortable
0.8<aw<1.6 Uncomfortable
1.25<aw<2.5 Very uncomfortable
aw >2 Extremely
uncomfortable
4.2 Comfort Evaluation Based on Annoyance Rate Model
Compared to ISO 2631-1-1997, this method based on annoyance rate model can
further estimate quantitatively the number of constructors on site who feel discomfort
due to vibration. A fuzzily random evaluation model on the basis of annoyance rate for
human body’s subjective response to vibration, with relevant fuzzy membership function
and probability distribution given is presented. When assessing the vibration comfort,
many different psychological, psychophysical and physical factors, such as individual
susceptibility, body characteristics and posture together with the frequency, direction,
magnitude and duration of vibration are relevant in development of unwanted
effects.(Tang, Zhang et al. 2014) The annoyance threshold acceleration determined by
the two valued logic method cannot describe the ambiguity and randomness existing in
human response to vibration environments, which results in many uncertainties in the
vibration comfort based reliability analysis. All these uncertainties were analyzed from a
view point of psychophysics. The membership function and corresponding conditional
probability distribution were determined based on the format of field survey table and
laboratory findings.
A fuzzy stochastic model for human response to vibrations was presented. SONG, et al,
combined the fuzzy logic method, the probability theory and the experimental statistics,
to advance a new evaluation index, i.e., annoyance rate method.
Annoyance rate is the rate of unacceptable response under certain vibration intensity.
The vibration sensitivity is different according to different range of frequency. The root
mean square (vibration intensity) of weighted frequency is adopted internationally as the
foundation for evaluating the vibration comfort. The vertical general frequency weighted
function can be expressed as follows:
.5
1
0.5 ,0 4
1,4 8
8 ,8 80
fj
f f
W f
f f
The vibration intensity wa is given by,
w fj rmsa W a
where arms is the RMS acceleration value. Annoyance rate indicates the ratio of people
who cannot accept the external stimulus to the total statistical people. It can be used to
determine the annoyance threshold for vibration comfort. Annoyance threshold means
the limit of acceleration on the premise of ensuring acceptable comfort. Under discrete
distribution, the annoyance rate can be expressed as,
1
1
1
( ) ( , )
m
j ij mj
wi jmj
ij
j
v n
A a v p i j
n
Where A(awi) is the annoyance rate of the ith vibration intensity awi; nij is the number of
subjective response of the jth type of the ith vibration intensity; vj is the membership value
of the jth type of unacceptable range, and vj=(j-1)/(m-1);m is the class number of the
subjective response, if the class of “no vibration feeling”, “a little vibration feeling”,
“medium vibration feeling”, “strong vibration feeling”, “Extremely uncomfortable” are
adopted to describe the subjective response of occupant ,
then m=5; p(i, j) represents the difference of the subjective feeling degree of the
occupant, and
1
( , )ij
m
ij
j
np i j
n
Considering the continuous distribution, calculation formula of annoyance rate is
represented as
min
2 2
ln
2
lnln
(ln( / ) 0.5 )1( ) exp( ) ( ) ,
22
wwi
u
u aA a v u du
u
Where aw is the frequency weighted vibration intensity; 2
ln ln(1 ) , is the
vibration coefficients, and change from 0.1 to 0.5, based on trial research; ( )v u is the
fuzzy membership function of vibration intensity, is shown as follows:
min
min max
max
( ) 0,
( ) ln( ) ,
( ) 1,
v u u u
v u a u b u u u
v u u u
Where umin is the top limit of “no feeling” to vibration of the occupant; umax is the bottom
limit of “Extremely uncomfortable” to vibration of human being.
The coefficients of a,b can be obtained from the following equation:
min
max
ln( ) 0,
ln( ) 1.
a u b
a u b
4.3 Parameter Study
As a temporary structure, old materials such as the gantry ropes from finished
projects may be used to assemble the catwalk for the sake of economy. So there are
many options for the catwalk rope sizes. However, the change in rope size will result the
change of dynamic properties for catwalk, thus affecting the comfort level during
construction. Cross bridge, which links two sides of the catwalk and increases the
torsional stiffness of catwalk, is also an important part in the catwalk structure. The
interval of cross bridges along the span (i.e. the number of the cross bridges) depends
on the demand of engineering practice. A narrow cross bridge interval would waste
materials and increasing the construction cost, even though the safety of the catwalk is
ensured adequately. However, wider cross bridge interval may cause smaller stiffness,
affecting structural safety and decreasing comfort level due to vibration.
In that case, a set of rope size and cross bridge intervals listed in Table 4 are chosen to
find out their influence on the vibration comfort. With each parameter changes, buffeting
analysis and comfort evaluation using two methods would be repeated. According to
engineering practice, old materials are seldom used on the catwalk rope. The influence
of catwalk rope size is neglected.
As previous stated, different cases were calculated and comfort level is listed in Table 4.
From Table.4, we can find that these two methods of evaluating comfort yield consistent
results. By comparing the results, the following conclusions can be summarized:
1) The comfort evaluation method based on ISO 2631-1-1997 reaches the consistent
results with the annoyance rate method. The wind-induced vibration of the catwalk
would cause the constructors feel uncomfortable, while the least annoyance rate of 5.58%
in the z-axis.
2) The method based on ISO 2631-1-1997 can only evaluate the vibration comfort
qualitatively, while the annoyance rate method can give a quantitative result.
3) Enlarging the gantry rope size and narrowing the cross bridge interval would
decrease the frequency weighted RMS acceleration and annoyance rate in both y and
z-axis.
4) Enlarging the gantry rope size 12mm in diameter decreases the annoyance rate by
around 4%, while narrowing the cross bridge interval decreases the annoyance rate by
2.14% at most. So enlarging the gantry rope size is more efficient than decreasing the
cross bridge interval.
5. Concluding Remarks
Both the method based on ISO 2631-1-1997 and annoyance rate can evaluate the
vibration comfort of the catwalk and reach a consistent result. However the latter one
can give a quantitative result compared to the qualitative result given by the former one.
Both enlarging the gantry rope diameter and reducing the cross bridge interval can
increase the comfort level of the catwalk during wind-induced vibration, while the latter
one has minor effect.
Table 4 Calculation cases and results
Cas
e
No.
Cross
bridg
e
interv
al(m)
Gantry
rope
diameter
(mm)
Frequency
weighted RMS
acceleration
aw
(m/s2)
Correspondin
g subjective
response
Annoyance rate
y z y z y z
1 185 48 1.02 1.05
uncomfortabl
e
9.80% 11.87
%
2 185 54 0.99 1.02 7.40% 9.66%
3 185 60 0.92 0.97 7.28% 7.72%
4 164 60 0.88 0.95 7.24% 7.70%
5 148 60 0.88 0.94 6.10% 7.13%
6 93 60 0.87 0.92 5.63% 5.58%
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