Kelvin C F Kwok Engineer
Major Works Project Management Office Highways Department The Government of Hong Kong Special
Administrative Region
Chris K P Wong Senior Engineer Major Works Project Management Office Highways Department The Government of Hong Kong Special
Administrative Region
Summary
The performance of stay cables under the rain-wind conditions is a major consideration for Stonecutters Bridge. 1:1 geometric scale sectional model wind tunnel tests were carried out using the same high-density polyethylene pipes as the prototype. Sections of soiled smooth cables of different diameters were initially tested under different wind velocities, azimuth angles and rain intensities for establishing the critical wind speed, azimuth angle and rain intensity that would produce the maximum effects on the cables. Different surface configurations were then applied to the cables and tested again. These included the application of different sizes of helical fillets and dimpled surfaces. Drag coefficient tests were carried out to ensure compliance with the design assumptions and requirements. Damping tests were also carried out for the cables and the results indicated that dampers could be an alternative for the control of rain-wind induced vibrations. Keywords: Stonecutters Bridge; stay cable; rain-wind induced vibration; damping
1. Introduction
It has been reported that stay cables were subject to large vibrations under the combined effects of rain-wind. The exact causes of rain-wind induced vibrations are complicated and there is still no conclusion on the exact mechanism for such vibrations. However, there is a general consensus that the formation of an upper water rivulet on the cable surface is a phenomenon[1][2]. When the cable is sloping in the same direction of the wind with a vertical inclination angle α, an azimuth angle β, when the wind speed is between the range 8~15m/s (Fig. 1) and at medium rain intensity, a water rivulet runs down the cable and there is a coupling between the cable motion and the oscillation of the water rivulet at the circumference of the cable.
U
α β Fig. 1 2. Methodology
2.1 Planning for the test
2.1.1 Sectional models for two representative diameters were selected. The 139mm diameter cable
at an inclination angle 36o represents cables close to the tower while the 169mm diameter cable at an inclination angle 21o represents cables away from the tower. In order to maintain the same Reynolds Number as the prototype, 1:1 scale sectional models were tested[3].
1
2.1.2 To simulate the full scale wind effects, the cables were tested for the following conditions:
(a) (b) (c)
Smooth flow conditions with wind velocities between 5m/s to 20m/s at 2m/s intervals;
Rain intensities between 1mm/hr to 180mm/hr; Azimuth angles from zero to 60o.
2.1.3 Damping tests were also carried out to investigate the effectiveness of using damping devices
for mitigating rain-wind induced vibrations. 2.1.4 Different surface configurations were tested in order to identify the best configuration for
mitigating rain-wind induced vibrations and this included the provision of 2mm helical fillets, 4mm helical fillets, 6mm helical fillets and dimple surfaces. 2.1.5 The Scruton number (Sc) is defined as mζ/(ρD2), where m is mass/length, ζ is damping ratio
relative to critical, ρ is the density of air and D is the cable diameter. The Scruton number of the model was smaller than the prototype and it ensured that any excitation of the prototype would be captured by the model. It also enabled the performance of the cables before and after application of mitigation measures to be compared. A comparison of dynamic parameters of the model and the prototype is shown in Table 1:
Parameter Frequency Damping Sc Mass
Table 1 – Dynamic Parameters[4]
Cable diameter 169mm Cable diameter 139mm
Prototype Model Prototype Model
0.22 to 0.66Hz 0.1% (assumed)
0.63 Hz 0.099%
0.47 to 1.41Hz 0.1% (assumed)
0.91 Hz 0.095%
3.4 0.90 2.1 0.93 118.9 kg/m
31.5 kg/m
51.3 kg/m
23.2 kg/m
2.2 Set up of the testing equipment
2.2.1 An open type wind tunnel was used for the test with the test section situated outside the wind
tunnel. The length of each sectional model was 2.72m. For the 169mm diameter cable, the length of cable subject to wind was 1.4m giving an aspect ratio (length to diameter) of 8.24. The aspect ratio for the 139mm diameter cable was 11.56. The aspect ratios were selected to minimize the end effects and were comparable to other similar tests carried out elsewhere.
A steel frame was set up to hold the cable model at a fixed vertical inclination angle throughout the tests and to rotate horizontally to give the required azimuth angle (Fig. 2). Shower simulating rainfall was sprayed from the top of the wind tunnel. The rain intensity was controllable and was calibrated using a rain gauge. The cables were supported with 2 pairs of linear springs and the springs were selected to enable the cable model to exhibit a frequency as designed for the tests. The displacement of the cable under the combined effects of rain-wind was measured by two transducers installed at the top of the springs.
Fig 2 – Set up of the testing equipment[4]
2
2.2.2 Each model comprised a stainless steel duct wrapped with white HDPE. The helical fillets
were made by fixing 2mm wide PE strips to the model at steps of 0.9m. The dimple surfaces were formed by stamping a regular pattern on the surface of the smooth cable. 2.3 Test Programme
As little was known of the mechanism involved in the rain-wind induced vibrations, a systematic and progressive approach was adopted.
2.3.1 Introductory tests on smooth cable models: For each of the 139mm and 169mm diameter
cable models, with an assumed damping ratio of 0.1% to critical and a pre-set medium rain intensity (80mm/hr), the wind speed and azimuth angle were varied to produce the maximum response thus identifying the critical wind speed and azimuth angle (Table 2).
Table 2 – Test programme of introductory tests on smooth cable models[4] Run No. Cable diameter Surface Angle Rain (mm) configurationIntensity
α β RWT001-0 169 RWT001-1~
9 RWT002-1~
9
smooth 21°
0°
No rain
169 smooth 21°
smooth 36°
80mm/hr25°~ 65°
(at 5° increments)
0°
No rain
RWT002-0 139 139 smooth 85mm/hr36° 25°~ 65°
(at 5° increments)
2.3.2 With the critical wind speed and azimuth angle identified, production tests were carried out
by varying the rain intensity to get the maximum response thus identifying the critical rain intensity (Table 3).
Table 3 - Test programme of production tests on smooth cables[4]
Run No. Cable Diameter (mm)
Surface configuration
Azimuth angle β
Rain intensity 1mm/hr to 180mm/hr (at 10mm/hr increments)
RWT003 169 RWT004 139 introductory tests
smooth Smooth Identified by 2.3.3 With the critical wind speed, azimuth angle and rain intensity identified, production tests were
carried out with enhanced damping levels of 0.3%, 0.6% and 1.0% to study the effectiveness of damping devices (Table 4).
Run No. Table 4 - Test programme of production tests for the enhanced damping levels[4]
Cable Diameter (mm) Surface configuration
cable damping relative to critical
RWT005 169 smooth 0.3%, 0.6%, 1.0% RWT006 139 smooth 2.3.4 With the critical wind speed, azimuth angle and rain intensity identified, production tests were
carried out with inherent damping for different surface configurations (fillets and dimple
surfaces) to find out the effectiveness of each of the different surface configurations (Table 5).
3
Table 5 - Test programme of production tests on helical fillet and cables with dimple surfaces[4]
Run No. RWT007 RWT008 RWT009 RWT010 & 017 RWT011 RWT012 RWT013
Cable Diameter (mm)
169 169 169 169 139 139 139 Surface configuration 2mm helical fillet 4mm helical fillet 6mm helical fillet Dimple surfaces 2mm helical fillet 4mm helical fillet 6mm helical fillet RWT014 139 Dimple surfaces 2.3.5 Because of the small Scruton Number of the cable models, it was expected that the models
might be sensitive to buffeting or vortex-induced vibrations. As such, the introductory tests included the case for “no rain”. The main purpose was to identify the maximum displacement due to buffeting or vortex-induced vibration.(RWT001-0 and RWT002-0). 2.3.6 For a given wind speed or rain intensity, the minimum test duration was fixed to 10 min, in
which the first 8 minutes was to ensure the development of rain/wind induced vibration and the last 2 minutes were used to acquire the vibration time history. The sampling frequency was set at 12.8 Hz for a sampling time of 120 seconds. Two displacement transducers were used to record the displacement time histories and averaged to produce the root-mean-square response (rms) and the maximum amplitude (Amax). 2.4 Test Results
2.4.1 The initial tests for the two cable diameters 139mm and 169mm at azimuth angle 0° and no
rain conditions, yielded maximum amplitudes (Amax) of about 20mm for the range of wind speeds between 5m/s and 12m/s. The results indicated that the effects of possible buffeting or vortex-induced vibration were insignificant. 2.4.2 Maximum rain-wind induced response -
300 500tested point250tested point40020030015010020050100
For 169mm diameter cable, the maximum amplitude was 482.2mm with a r.m.s response of 257.7mm (Fig 3) that happened at an azimuth angle of 30o, wind speed of 12m/s and rain intensity of 75mm/hr. For the 139mm diameter cable, the maximum amplitude was 152.8mm with a r.m.s. response of 101.6mm that happened at an azimuth angle of 35o, wind speed of 10.5m/s and rain intensity of 85mm/hr.
Amax (mm)rms (mm)002040 tesyed point6080100002040 tested point6080100rain intensity (mm/hr)Intensity (mm/hr) Intensity (mm/hr)
rain0 (mm/hr) Fig 3- Rain-wind induced response of 169mm diameter cable at different rain intensities (β=30°, U=12m/s)[4]
4
2.4.3 Effects of damping -
The actual damping provided was 4580determined using the technique of air
40 ζ=0.31%decay traces and calculated based on the 70 ζ=0.67% ζ=0.31%35 ζ=0.91%time history. For the 169mm diameter ζ=0.67%60 ζ=0.91%cable with an enhanced damping level of 300.31% the r.m.s response was 45.8 mm at 5025a wind speed of 12m/s. For higher
4020enhanced damping levels the responses
15were even less (Fig 4). The 139mm 30diameter cable exhibited similar 1020behaviour with enhanced damping levels. 58910111289101112The cables specified in the Stonecutters
U (m/s)U (m/s)Bridge Contract has a required damping of 4% logarithmic decrement (0.64%
Fig 4 –Effects of damping on rain/wind induced response for relative to critical).
169mm diameter cable (β=30°, I=75mm/hr)[4] 5090Amax (mm)rms (mm)2.4.4 Effects of helical fillets -
22201816141210864
10
2468101214468101214204060
2mm 4mm 6mm 2mm 4mm 6mm50
30
Using the assumed inherent damping and critical settings identified, no explicit rain-wind induced vibration phenomenon could be observed from any of the cables with 2mm, 4mm and 6mm fillets (Fig. 5). It was concluded that all the 2mm, 4mm and 6mm helical fillets were effective in reducing rain-wind induced vibrations for the range of wind speeds tested.
Amax (mm)rms (mm)U (m/s)U (m/s)
Fig. 5 - Effects of helical fillets on rain/wind induced response for 169mm diameter cable (β=30°, rain intensity 75mm/hr)[4]
2.4.5 Effects of dimple surfaces -
300 Using the assumed inherent damping and critical settings identified, no explicit rain-wind induced vibration could be observed from the 139mm diameter cable with dimple surfaces. However, medium to strong responses (r.m.s response of 95.6mm and maximum amplitude of 155.9mm) were observed for the 169mm diameter cable at an azimuth angle of 40o and rain intensity of 80mm/hr (Fig. 6). A new dimple (deep oval) pattern was subsequently developed and the
U (m/s)U (m/s)subsequent rain-wind induced response
was found to be small. It was concluded
Fig. 6 – Effects of dimple surfaces on rain/wind induced response from the tests that dimple surfaces were for 169mm diameter cable (S=smooth surface; Da=old dimple - effective in reducing rain-wind induced
shallow oval; Db=new dimple - deep oval)[4] vibrations.
250200S, 30 o S,25o Da,40o Db,25o Db,30o Db,35o Db,40o400300RMS (mm)150Amax ( mm)200 04681012141618100100500246810121416185
2.4.6 Comparison of drag coefficients for different surface configurations -
Drag Coefficients for 169mm diameter cablesBefore choosing a cable configuration which was found to be effective in 1.20disturbing the formation of water rivulets Smooth1.00and hence rain-wind induced vibrations, 2mm fillet0.80drag coefficients of the respective old oval0.60surface configuration should be checked. new oval0.40Drag coefficient tests carried out 4mm filletindicated that only the smooth cable, 0.206mm filletcable with 2mm fillets, old oval and new 0.00oval dimple surfaces complied with the design requirements and exhibited drag
U (m/s)coefficients less than 0.8 for the range of
wind velocity adopted for the design.
Cd202428323640442.5 Discussion and Further Development
The rain-wind vibration tests indicated the possibility of large amplitude vibrations up to 3 times the diameter of the cable. The performance of both aeroelastic and mechanical methods were then investigated. Results indicated that damping devices providing some 0.31% or further enhanced damping to the critical were effective in reducing the rain-wind induced vibrations. Helical fillets and dimple surfaces were effective means for reducing the rain-wind induced vibrations of cables. For cables with 2mm helical fillets and dimple surfaces, they all satisfied the design requirement on drag coefficient and would not impose additional pressure/force onto the bridge structure. The final design of the longest stay cables have external diameters of 187mm with natural frequencies of between 0.22Hz to 0.48Hz. Further tests can be considered at the construction stage to cover the size of 187mm diameter cable. Cables of two different frequencies can be tested for different levels of enhanced damping and possibly with two degrees of freedom for determining the aerodynamic performance of different surface configurations. 2.6 Acknowledgements
The authors wish to express their thanks to Director of Highways, Mr. C. K. Mak, for permission to publish this paper. Any opinions expressed or conclusions reached in the text are entirely those of the authors.
2.7 References
[1] 李文勃, 林志興, 斜拉橋拉索風雨激振机理的實驗研究, 同濟大學土木工程防灾國
家重點實驗室, 上海200092.
[2] MING GU, XIAOQIN DU, “Testing investigation for rain-wind induced
vibration and its control of cables of cable-stayed bridges\".
[3] 何向東, 奚紹中, 抑制斜拉索雨振气動措的風洞試驗研究, 第十屆全國結構風工程
學術會議論文集.
[4] CARDC, Wind Tunnel Investigation on Drag Loading and Rain/Wind
Vibration of Stay Cables of Stonecutters Bridge, 2003.
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