AERODYNAMIC RESPONSE OF LONG SPAN CABLE STAYED CONCRETE BRIDGE

Transcription

1 AERODYNAMIC RESPONSE OF LONG SPAN CABLE STAYED CONCRETE BRIDGE FX. Supartono *) ABSTRACT This paper presents the result of aerodynamic study and wind tunnel test carried out on Melak Bridge. Being located in East Kalimantan island of Indonesia, the bridge is designed as a long span cable stayed concrete bridge with 340 meters of mid span, meters wide for 2 lanes of traffic, and total length of 680 meters. Due to narrow width of the bridge, its aerodynamic behavior under wind loads was carefully studied, including a wind tunnel testing. For this purpose, a rigid section model was made and mounted elastically on a dynamic test frames simulating the dynamic characteristics of the bridge. Then the model was tested and studied in both turbulent and smooth flow conditions representing of those at the bridge site, in order to be able to determine the aerodynamic response characteristics and any tendency to flutter and vortex shedding instability. KEYWORDS Wind tunnel, aerodynamic study, cable stayed bridge, long span concrete bridge, flutter stability, vortex shedding. 1 INTRODUCTION Melak Bridge is located in Kutai Barat, East Kalimantan, Indonesia, which is a double-pylon cable stayed bridge with three spans of 170m 340m 170m (see Figure 1.1 & 1.2). The bridge deck represents an open cross section with twin side girders of prestressed concrete with 14.20m wide and 2.40m high (see Figure 1.3). The pylons have a slightly curved A-shape with about 108m high (see Figure 1.4). Figure 1.1 Melak Bridge (Artist Impression) *) Vice President of HAKI, Vice President of Asian Concrete Federation (ACF), Associate Professor of UI Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 1

2 K4 P1 P2 K5 Figure 1.2 General configuration of the bridge Figure 1.3 Cross section of the deck In accordance with requirement of the Indonesian Concrete Bridge Code SNI T for special bridge category (e.g. cable stayed bridge, suspension bridge, etc), the service life time of this bridge was determined to be 100 years [1]. To ensure the safety of the bridge under wind loads during construction stage and service stage, an aerodynamic study as part of the design process was carried out by PT. Partono Fondas Engineering Consultant [2] in cooperation with the State Key Laboratory for Disaster Reduction in Civil Engineering (SLDRCE) of Tongji University (Shanghai, PR China), and particularly to undertake the wind tunnel test and study on the wind-resistant performance of this bridge [3]. Thus, objectives of this study are: To proof that the aerodynamic stability of the bridge under wind loading is satisfactory, by doing a section model of the bridge deck that is mounted elastically on a dynamic test frame, simulating the characteristics of the completed bridge and/or during construction stage. Should the stability and/or response characteristics prove not to be satisfactory, modifications to the aerodynamic cross section could be made for further testing. Determination of the response under design wind speeds and permits the assessment of aerodynamic loads. Analytical techniques would be used Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 2

3 incorporating the results of the section model tests with dynamic analyses of the prototype to define the wind loading of the structure. Assess the Aerodynamic Derivatives, i.e. the so-called Flutter Coefficients. Due to limited number of pages in this paper, discussion will be limited around the flutter stability problem. Figure 1.4 General configuration of the pylon 2 WIND SPEEDS AT THE BRIDGE SITE 2.1 BASIC WIND SPEED According to the meteorological data obtained from the BMG, it is known that the bridge site is surrounded by a plain terrain with boundary hedges, occasional small farm structure, houses and trees. Thus, the terrain category of the bridge site can be classified into Type II, the exponent (α) of power law of the mean wind profile is 0.16, and the basic wind speed (means the yearly-maximum mean wind speed at the Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 3

4 elevation of 10 meter for a return period of 100 years) over the terrain at the bridge site is 30.0m/s (U10=30.0m/s). 2.2 DESIGN WIND SPEED As the design level of the bridge deck surface at its mid-span is 31.5m from the MWL (Mean Water Level = 0.00), thus the design wind speed at bridge deck level for the service state (Ud) can be determined as follow: U d = U 10 ( ) 0.16 = = 36.1m s (2.1) For construction period, the design wind speed at bridge deck level (U d) can be taken as 0.84 times of that for the service state, which is equivalent to consider the return period of 10 years. U d s = 0.84U d = = 30.2 m s (2.2) 2.3 SITE FLUTTER CHECKING WIND SPEED Based on the fact that the main span length of Melak Bridge is 340m and the terrain around the bridge site is of Type II, according to the Wind Resistant Design Guideline for Highway Bridges [4], considering the influence of turbulence on wind speed and the incomplete correlation of winds along the bridge span, the coefficient µf can be set to 1.295; while for the comprehensive safety factor K, considering the uncertainties in the wind tunnel test, design and construction of bridge, it can be set to 1.2. Thus, the flutter checking wind speed for the service state of Melak Bridge with a return period of 100 years can be determined as follow: [U cr ] = Kµ f U d = =56m/s (2.3) For construction state, the return period is considered as 10 years, and then the flutter checking wind speed is determined as follow: [U s cr ] = Kµ f U s d = =47m/s (2.4) 3 DYNAMIC ANALYSIS OF BRIDGE STRUCTURE Based on the material criteria defined on the design of Melak Bridge (designed by PT. Partono Fondas), the modal analyses were carried out for the service state and the longest single-cantilever state of the bridge structure, by using the finite element software ANSYS. In the finite element (FE) model of the bridge, the bridge pylon and deck were modeled with 3D beam elements; the cables were modeled with 3D truss elements, on which the equivalent module of elasticity was used to considering effect of the initial tension and weight on the stiffness. According to the Reference [5], and considering the effect of vibration of whole bridge structure and the spatial behavior of vibration, the equivalent mass and mass moment of inertia of the bridge deck should be employed in simulating the mass system of the section model. The equivalent mass and mass moment of inertia of deck of the prototype bridge can be determined as follow: d ~ 2 m eq = M Lg ϕ d (x)dx (3.1) Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 4

5 J x meq ~ = M ϕ 2 θx (x)dx (3.2) L g ~ where M is the generalized mass of the corresponding mode; d = x, y, z; ϕ x (x), ϕ y (x), ϕ z (x) and ϕ θx (x) are the mode function values of deck longitudinal, vertical and lateral displacement and torsional angle at the coordinate of x respectively; L g is the total length of the bridge deck. The first 10 modes and their natural frequencies of service state as well as the corresponding major mode features are shown in the Table 3.1. The corresponding mode shapes are given in the Figures 3.1.a to 3.1.j. Table 3.1 Dynamic characteristics of the bridge in service state Mode Frequency [Hz] Period [Sec] Major Features of Mode Longitudinal drift First order symmetric lateral First order anti-symmetric lateral First order symmetric vertical First order anti-symmetric vertical Second order symmetric lateral Second order symmetric vertical Second order anti-symmetric vertical Third order symmetric vertical First order symmetric torsion of the girder Fig 3.1.a 1 st Mode Shape, f = 0.107Hz Fig 3.1.b 2 nd Mode Shape, f = 0.139Hz Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 5

6 Fig 3.1.c 3rd Mode Shape, f = 0.227Hz Fig 3.1.d 4th Mode Shape, f = 0.227Hz Fig 3.1.e 5th Mode Shape, f = 0.335Hz Fig 3.1.f 6th Mode Shape, f = 0.460Hz Fig 3.1.g 7th Mode Shape, f = 0.571Hz Fig 3.1.h 8th Mode Shape, f = 0.650Hz Fig 3.1.i 9th Mode Shape, f = 0.758Hz Fig 3.1.j 10th Mode Shape, f = 0.792Hz Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 6

7 4 WIND TUNNEL TEST OF SECTION MODEL 4.1 EQUIPMENT AND INSTRUMENTATION The section model wind tunnel tests for wind-induced vibration were carried out in the TJ-1 Boundary Layer Wind Tunnel of the State Key Laboratory for Disaster Reduction in Civil Engineering of Tongji University, Shanghai, PR China. TJ-1 Boundary Layer Wind Tunnel is an open-circuit low-speed tunnel with a test-section of being 1.8 meter wide, 1.8 meter high and 14 meter long. The fan power is 90kW, and the wind speed ranges from 0.5 to 30m/s for unoccupied case. The non-uniformity index of smooth flow (δu/u) within the cross section, excluding the boundary areas, is less than 1.0%; and the corresponding turbulence intensity (Iu) within the same area is less than 1.0%. The signals of wind-induced vibration were acquired and processed with a system composed of three piezoelectric accelerometers, a multi channel charge amplifier (TS5865), a data acquisition A/D board (NI, PCI-6052E), a PC and corresponding computer programs for data acquisition and processing. Figure 4.1 Wind Tunnel Test in Tongji University 4.2 BASIC SIMILARITY REQUIREMENTS AND MODEL PARAMETERS The 2D spring-suspended rigid section model was employed in the tests. The section models were suspended with 8 springs from two testing frames installed outside the wind tunnel. The geometric length scale (λl) was determined to be 1/40 according to the dimensions of the prototype bridge deck cross-section as well as the testing Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 7

8 section of the wind tunnel and the required direct testing approach for wind-induced vibration. To diminish the influence of the 3D flow around the two ends of the section model on the test results, the length of the section model was designed to be 1.74 meter so that the ratio of length over width of the section model was about 4.9 and the gaps between the model ends and the side walls of wind tunnel were about 30mm. The rigid section model frame was made of steel, while the deck slab was made of wood in order to ensure the similarity of the deck shape. Besides the geometric similarity, the following three groups of dimensionless parameters should be kept in consistence between the model and the prototype in the wind tunnel test of rigid spring-suspended section model: U U f t Elastic parameters:, or (frequency ratio) f v B f t B f v Inertia parameters: meq J meq r, or e ρb 2 ρb 4 b (ratio of gyration radius) Damping parameters: ξv, ξt (damping ratio) where U represents wind speed; fv and ft are the natural frequencies of vertical and torsional vibrations, respectively; B is the deck width, b is half width of deck; meq and Jmeq are equivalent mass and mass moment of inertia of the bridge deck per unit length; ρ is air density; re is equivalent gyration radius of the bridge deck; ξv and ξt are damping ratios of vertical and torsional vibrations, respectively. According to the suggestions about the damping ratio presented in Wind Resistant Design Guideline for Highway Bridges [4], the model damping ratios of Melak Cable Stayed Bridge are set to be 1.0% and 2.0% because of the adoption of prestressed concrete structure in the bridge. As a result, the designed and measured parameters of section model and the corresponding parameters of prototype, obtained in the light of the similarity requirements mentioned above, are presented in the Table 4.1 for the service state and the longest single-cantilever state, on which the fundamental natural frequencies of vertical and torsional vibrations of the both structural states were selected for the simulation of elastic parameters [3]. The mass and mass moment of inertia of the section model were designed according to the equivalent mass and mass moment of inertia of the prototype bridge deck to consider the spatial behavior of the vibration of the prototype bridge and the effects of the vibrations of pylons and cables [6]. The measured damping ratios of vertical and torsional vibrations undulated a little bit for the various attitudes of the section model with different attack angle of wind. Two cases of structural damping ratio were investigated in the flutter and vortex-excited resonance tests of the service state and the longest single-cantilever state. However, due to the influence of the installed devices for additional damping, the measured natural frequencies of the section model were a little bit different in the two cases of structural damping. Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 8

9 Table 4.1 Design parameters of the section model Scale Ratio Model Parameter Sym Unit Prototype Flutter Vortex Flutter Vortex Deck length L m /40 1/ Deck width B m /40 1/ Deck height H m 2.4 1/40 1/ S E R V I C E S T A T E C O N S T R U C T I O N Equivalent Mass Equivalent Mass Moment of Inertia Equivalent Gyration Radius Basic Vertical Frequency Basic Torsional Frequency Frequency Ratio Equivalent Mass Equivalent Mass Moment of Inertia Gyration Radius Vertical Frequency Torsional Frequency Frequency Ratio M eq kg/m /40 2 1/ J meq kg m 2 /m /40 4 1/ r m /40 1/ f b Hz f t Hz ~ ~ ε M eq kg/m / J meq kg m 2 /m / r m / f b Hz f t Hz ε CHECKING OF FLUTTER STABILITY The test for checking the flutter stability was carried out for the service state and the longest cantilever construction state in the smooth flow with wind attack angles of -3, 0 and 3. The conventional direct test approach and the 2DOF-coupled vertical and torsional vibration approach were adopted in the test. Flutter was observed under the Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 9

10 wind attack angles of -3, 0 and 3. The critical point is determined when the aerodynamic negative damping exceeds the structural positive damping and this is often regarded as the criteria for the determination of the flutter critical wind speed of a bridge. For the service state, in order to meet the requirements of damping simulation of the flutter model system, attached damping devices are used and at last the vertical and torsional damping ratio is about 2.1% and 1.9%, respectively. The variation curves of ξ vs U m and f vs U m of the section model system were measured under 2DOF-coupled vibration state vertical bending and torsion, where ξ and f are the total damping ratio and frequency of the vertical or torsional vibration of section model system in smooth flow. The testing cases and results are shown in Table 4.2. When the torsional damping ratio is about 1.0%, the flutter critical wind speeds of the section model in the service state are 19m/s, 21m/s and larger than 26m/s, which is equal to 106m/s, 117m/s and larger than 145m/s in actual bridge for the -3o, 0o and +3o wind attack angles, respectively, by the criteria of when aerodynamic negative damping exceeds the structural positive damping to determine the flutter critical wind speed of the bridge [3]. Table 4.2 Critical flutter wind speed in the section model test Flutter wind speed [m/s] Service state Longest single-cantilever state Attack angle ξt=1% ξt=2% ξt=1% ξt=2% +3 >145 >186 >111 > >172 >111 > >111 Site flutter checking wind speed [56m/s] [47m/s] The Figure 4.2 shows the instability feature on the bridge deck vibration amplitudes when the wind speed achieves the value of flutter critical wind speed on the -3o wind attack angle, which represents wind speed of 106m/s in actual bridge service state. Figure 4.2 Instability feature on the bridge deck vibration amplitudes Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 10

11 When the torsional damping ratio is about 2.0%, the flutter critical wind speeds of the section model of the service state are 22m/s, larger than 24m/s and larger than 26m/s, which is equal to 157m/s, larger than 172m/s and larger than 186m/s in actual bridge for the -3o, 0o and +3o wind attack angles, respectively, by the same criteria as above mentioned [3]. Thus, the service state of Melak Cable Stayed Bridge possesses enough flutter stability. Figure 4.3 shows the relationship of Aerodynamic Damping Ratio vs Wind Speed in Wind Tunnel for the Service State; Figure 4.4 shows the relationship of Frequency vs Wind Speed in Wind Tunnel for the Service State [3]. Figure 4.3 Relationship of Aerodynamic Damping Ratio vs Wind Speed in wind tunnel for the service state Figure 4.4 Relationship of Frequency vs Wind Speed in wind tunnel for the service state 5 DISPLACEMENTS DUE TO WIND LOADS The displacements of main sections of bridge deck and pylon due to the static wind loads (induced by the design wind speed) are listed in the Table 5.1, calculated by using the software AutoFBA developed by SLDRCE for the flutter and buffeting problems of the bridges. It has been noted that the vertical and lateral displacements of deck at the middle of main span due to the static wind loads are 0.01m and 0.007m at the service state, and 0.004m and 0.023m at the longest single-cantilever state, respectively [3]. Table 5.1 Displacements of main sections due to static wind Bridge state Section location Long. disp. [m] Vert. disp. [m] Lat. disp. [m] Mid-main span of Service state deck 4E Pylon top E Longest single-cantilever state End of single-cantilever 4E Pylon top E Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 11

12 However, attention should be drawn on the total wind-induced responses for the design of bridge structures which are consisting of the unfavorable combinations of static wind and buffeting responses. It is calculated by using the software AutoFBA that the maximum of total displacements of bridge deck at the middle of main span due to the wind loads are 0.22m~0.248m (vertical) and 0.091m~0.118m (lateral) at the service state. The maximum of total displacements of bridge deck are 0.231m~0.264m (vertical) and 0.059m~0.069m (lateral) at the longest single-cantilever state (at the end of cantilever) [3]. The lower and upper limits of the displacements are corresponding to the damping ratios 2% and 1%, respectively (see Table 5.2). Bridge state Service state Table 5.2 Maximum of the total displacements of main sections Damping ratio Long. disp. [m] Vert. disp. [m] Lat. disp. [m] 1% 2% 1% 2% 1% 2% Mid-main span of deck Pylon top E-04 5E End of Longest single-cantilever single-cantilever state Pylon top E-04 3E CONCLUSION Based on the dynamic analyses and the section model test on the wind-resistant performance of Melak Cable Stayed Bridge and its performance under wind loading, we may draw the following major conclusions: (1) Design wind speed at the bridge deck level of Melak Bridge is 36m/s and 30.2m/s respectively for the service and construction states, while the corresponding site flutter checking wind speed can be determined to be 56m/s and 47m/s respectively. (2) The results of dynamic analyses show that the natural frequencies of the fundamental vertical bending and torsional modes of the service state are 0.227Hz and 0.792Hz respectively, that means the ratio of torsional frequency to vertical bending frequency is (3) The results of flutter test demonstrate that critical flutter induced wind speed is 106m/s with the structural damping ratio of 1% in service state and 123m/s in the longest cantilever state with wind attack angles of -3. If the structural damping ratio is set to above 1%, the corresponding flutter wind speed can still be increased. Therefore, the Melak Cable Stayed Bridge is proven to be stable enough against flutter for the service state as well as the construction states under the winds with the attack angles between -3 and 3. (4) It is noted that the maximum displacements of bridge deck at the middle of main span due to the static wind loads induced by the design wind speed are 0.22m~0.248m (vertical) and 0.091m~0.118m (lateral) at the service state. The maximum of total displacements of bridge deck at the end of cantilever are Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 12

13 0.231m~0.264m (vertical) and 0.059m~0.069m (lateral) at the longest single-cantilever state. The lower and upper limits of the displacements are corresponding to the damping ratios 2% and 1%, respectively. REFERENCES [1] Indonesian Ministry of Public Works (2004), Indonesian concrete bridge design code (SNI T ), Indonesian Standard Bureau. [2] PT. Partono Fondas Engineering Consultant (2007), Design report of Melak cable stayed bridge. [3] State Key Laboratory for Disaster Reduction in Civil Engineering (2008), Wind tunnel study on wind-resistant performance of Melak Cable Stayed Bridge, Tongji University, Shanghai, PR China. [4] Xiang, H.F., et al. (2004), Wind resistant design guideline for highway bridges (JTG/T D ), People s Communication Publishing House, PR China. [5] Zhu L.D., Xiang H.F. (1995), Mass-system simulation of section model for bridge flutter, Structural Engineers No. 4, [6] China Communications Highway Planning, Design and Research Institute (2004), Code for Design of Highway Bridges (JTG D ), People s Communication Publishing House, PR China. [7] Zhu Le-Dong (2003), Design of section model mass system and response conversion for vortex-excited vibration test, Proc. of the 11 th National Academic Conference on Structural Wind Engineering, Sanya, Hainan, PR China, [8] Ding Quan-Shun (2001), Refinement of coupled flutter and buffeting analysis for long-span bridges, Doctoral Dissertation of Tongji University, Shanghai, PR China. ACKNOWLEDGEMENTS Sincere thanks should go to the State Key Laboratory for Disaster Reduction in Civil Engineering (SLDRCE) and Prof. Song Jinzhong of Tongji University, Shanghai, PR China, for the great support and collaboration on this project. Seminar dan Pameran HAKI Aerodynamic Response of Long Span Cable Stayed Concrete Bridge 13