Comfort evaluation of a double-sided catwalk due to wind-induced vibration

Transcription

1 Comfort evaluation of a double-sided catwalk due to wind-induced vibration *Siyuan Lin ) and Haili Liao ) ), ) Research Center for Wind Engineering, SWJTU, Chengdu 60-03, China, linsiyuan0@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 63-(997) 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.. 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 ) Graduate Student ) Professor

2 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. 007). The mechanism of unique coupling between vertical and lateral vibrations of catwalk was discussed in the buffeting analysis(li, Wang et al. 04). The influence of cross bridge interval was evaluated only for catwalk s buffeting response (Kwon, Lee et al. 0). 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 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.. Wind Tunnel test The analyzed catwalk is designed for Dongting Lake highway suspension bridge of which the main span length is 480m and sag ratio is /0. The span configuration is 460m (south span) +480m (mid span) +49m (north span) for the main cable. The catwalk rope is parallel to the main cable with a separation distance of.5m. There are cross bridges are distributed every 85m along the span, with in each side span and 7 in mid span. Gantries are distributed every 4.5m 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.m 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..

3 (a) Elevation view (b) Lateral view Fig. Detailed design of the catwalk section To investigate the aerodynamic performance of catwalk at large angle of attack, as Fig. shows, a :5 scale model is tested in the XNJD- wind tunnel under smooth flow to get the tri-component static aerodynamic coefficients, with the angle of attack varying from -0 to 0 every degree each. The section model of catwalk is.m long, 0.84m wide and 0.9m 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. FD ( ) FL ( ) M z ( ) CD ( ) CL( ) CM ( ) () V HL V BL V B L where C D (α), C L (α), C M (α) are the drag force, lift force and pitching moment force coefficients respectively, F D, F L, M z 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. 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.link0 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

4 static aerodynamic coefficients 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 009),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 C D C L C M angle of attack(deg) Fig.. 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 0 modes are listed in Table. And the first lateral bending, vertical bending and torsion modal shape are shown in Fig.5~Fig.7.

5 Table Natural modal frequencies and shapes Mode number Characteristics of modal shapes Modal frequency(hz) st symmetric lateral bending st anti-symmetric lateral bending st anti-symmetric lateral bending+ st anti-symmetric vertical bending+ st anti-symmetric torsion 4 st anti-symmetric lateral bending+ st anti-symmetric vertical bending+ st anti-symmetric torsion 5 st symmetric vertical bending st symmetric torsion st lateral bending of right side span st symmetric lateral bending+ st symmetric torsion 9 st lateral bending of left side span st anti-symmetric longitudinal floating D Longitudinal Vertica Latera Fig.5 First lateral bending modal shape

6 3D Longitudinal Vertica Latera Fig.6 First vertical bending modal shape 3D Longitudinal Vertica Latera Fig.7 First torsion modal shape 3. 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

7 velcity (m/s) one-dimensional wind velocity fields. The FFT (Fast Fourier Transform) technique (Deodatis 996)was adopted to further improve the computational efficiency. Then random field in terms of lateral and vertical components was generated at 4 locations along the span of the catwalk with a separation of around 8 meters. The other details for simulating the wind field are listed in Table. 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 Parameters for simulating the wind field Number of simulated nodes 4 V 0 5m/s Separation of frequency 04 Upper limit of frequency Hz Lower limit of frequency 0.Hz Longitudinal wind spectra Simiu Spectra Vertical wind spectra Lumley-Panofsky spectra Ground roughness length z m Decaying factor C z 0 Decaying factor C y 6 Decaying factor C w 8 Time interval 0.5s Note: V 0 =5m/s is considered as the maximum wind speed for construction according to engineering practice. 6 4 velcity time (s) (a) Part of the vertical wind velocity series

8 PSD(m /s) velcity (m/s) 5 velcity time (s) (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. 000 Simulation spectrum Target spectrum E Frequency(Hz) (a) Longitudinal wind velocity PSD

9 PSD(m /s) 000 Simulation spectrum Target spectrum E Frequency(Hz) (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. u( t) ' w( t) Lb ( t) U B( CLLu ( CL CD) Lw ) U U u( t) ' w( t) Db ( t) U B( CDDu ( CD CL) Dw ) U U u( t) ' w( t) Mb( t) U B( CM Mu CM Mw ) 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. The buffeting analysis was conducted at 0 attack angle, the related aerodynamic static coefficients and derivatives are C L =0.00, C D =0.4709, C M =-0.087, C D =0, C L =0.3783, C M = Self-excited force in FE analysis Based on Scanlan s flutter theory(scanlan 978), the self-excited force can be expressed using 8 flutter derivatives as follows. * h * B * * h * p * p Lse U ( B)( KH KH K H3 K H4 KH5 K H6 ) U U B U B

10 * p * B * * p * h * h Dse U ( B)( KP KP K P3 K P4 KP5 K P6 ) U U B U B * h * B * * h * p * p M se U ( B )( KA KA K A3 K A4 KA5 K A6 ) 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, H, P, A (i=, 6) are the flutter derivatives. * * * i i i L se, D se and M se stand for the self-excited lift, drag and pitching moment, their direction and relation with B and is shown in Fig. 0. Lse M se a attack angle Dse wind Fig. 0 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. [ F i ] [ C i ]{ X} [ K i ]{ X} se se se i i Where [ C ],[ K ] are the aerodynamic damping and stiffness matrix respectively. In that se se case, self-exited force realized using the Matrix 7 element in ANSYS, which has 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. C C C H H n H K K K ' ' ' * L * L * L, x, 3 C C C H A A A K K K ' ' ' * * M * M * M 4 0,,, n 3 A A * A n K n K P C D K * * * 3 4 0, x( ), * ( ) * H H3 K * * H5 C L 5 A C M K P P H A P C D K * ' * * * * P C D K P C D K * ' * ' 3 5

11 ay_psd (m /s 3 ) az_psd (m /s 3 ) ay (m/s ) az (m/s ) Where C, C are the derivatives of lift coefficients and pitching moment coefficients ' L ' M considering attack angle;k is the reduced frequency; nx, 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.0. Their power spectra density is shown in Fig.. From Fig xx, the response frequency is close to the st lateral and vertical bending modal frequency, thus indicating the accuracy of the time domain buffeting analysis ay 0.4 az time (s) time (s) (a) Vertical acceleration time history (b) lateral acceleration time history Fig.0 Time history of acceleration response of the middle node in the mid span 0. ay_psd 0. az_psd E-3 E-3 E-4 E-4 E-5 E frequency (Hz) frequency (Hz) (a) Vertical acceleration PSD (b) lateral acceleration PSD Fig. PSD of acceleration response of the middle node in the mid span 4. Comfort Evaluation of Catwalk under Construction

12 Frequency weighting factor 4.Comfort Evaluation Based On ISO 63 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 for evaluating the incidence of motion of sickness(apply to motion frequencies below 0.5Hz)(Standardization 997). 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, T Arms [ a ( t) dt] T 0 w Where a w is the frequency weighted acceleration, T is the lasting time of vibration. This standard recommends a single frequency weighting W f 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. W f Frequency(Hz) Fig. Frequency weighting curves for principal weighting Table3 Reactions to various of magnitudes of overall vibration Frequency weighted RMS acceleration Subjective Response a w (m s - ) a w <0.35 Not uncomfortable 0.35 a w <0.63 A little uncomfortable

13 0.5<a w < 0.8<a w <.6.5<a w <.5 a w > Fairly uncomfortable Uncomfortable Very uncomfortable Extremely uncomfortable 4. Comfort Evaluation Based on Annoyance Rate Model Compared to ISO , 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. 04) 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: W fj,4 f f,0 f 4 8 f,8 f 80 The vibration intensity aw is given by, a W a w fj rms where a rms 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

14 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, m vn j ij m j ( wi ) j (, ) m v p i j j nij j A a Where A(a wi ) is the annoyance rate of the i th vibration intensity a wi ; n ij is the number of subjective response of the j th type of the i th vibration intensity; v j is the membership value of the j th type of unacceptable range, and v j =(j-)/(m-);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 nij p( i, j) m n Considering the continuous distribution, calculation formula of annoyance rate is represented as (ln( u/ aw) 0.5 ln ) A( awi) exp( ) v( u) du, u umin ln j ij ln Where a w is the frequency weighted vibration intensity; ln ln( ), is the vibration coefficients, and change from 0. to 0.5, based on trial research; vu ( ) is the fuzzy membership function of vibration intensity, is shown as follows: v( u) 0, u umin v( u) a ln( u) b, umin u u v( u), u umax Where u min is the top limit of no feeling to vibration of the occupant; u max is the bottom limit of Extremely uncomfortable to vibration of human being. The coefficients of a,b can be obtained from the following equation: aln( umin ) b 0, aln( umax ) b. max

15 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: ) The comfort evaluation method based on ISO 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. ) The method based on ISO 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 mm in diameter decreases the annoyance rate by around 4%, while narrowing the cross bridge interval decreases the annoyance rate by.4% 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 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

16 increase the comfort level of the catwalk during wind-induced vibration, while the latter one has minor effect. Cas e No. Cross bridg e interv al(m) Table 4 Calculation cases and results Gantry rope diameter (mm) Frequency weighted RMS acceleration a w (m/s ) Correspondin g subjective response Annoyance rate y z y z y z %.87 % % 9.66% uncomfortabl % 7.7% e % 7.70% % 7.3% % 5.58% REFERENCES Deodatis, G. (996), "Simulation of Ergodic Multivariate Stochastic Processes", Journal of Engineering Mechanics. (8), Kwon, S.-D., Lee, H., Lee, S. and Kim, J. (0), "Mitigating the Effects of Wind on Suspension Bridge Catwalks", Journal of Bridge Engineering. Li, S. and Ou, J. (009), "Analysis of Dynamic Behavior of Catwalks of Long-span Suspension Bridge without Wind-resistant Cable", Journal of Highway & Transportation Research & Development. 6(4), Li, Y., Wang, D., Wu, C. and Chen, X. (04), "Aerostatic and buffeting response characteristics of catwalk in a long-span suspension bridge", Wind and Structures, an International Journal. 9(6), Journal of Sound & Vibration. 60(), Standardization, I.O.f. (997), ISO 63- Mechanical vibration and shock-evaluation of human exposure to whole body vibration-part : general requirements, Tang, C., Zhang, Y., Zhao, G. and Yan, M.A. (04), "Annoyance Rate Evaluation Method on Ride Comfort of Vehicle Suspension System", Chinese Journal of Mechanical Engineering. 7(), Zheng, S., Liao, H. and Li, Y. (007), "Stability of suspension bridge catwalks under a wind load", Wind and Structures. 0(4),