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,

linsiyuan01@gmail.com

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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