Structural Design of Yeonwha Suspension Footbridge

Transcription

1 Structural Design of Yeonwha Suspension Footbridge Jinwoo Jeong 1*, Jajung Koo 2, Inbeom Kim 3 and Sheungwhan Ahn 4 1* Senior Engineer, Structural Design Team, COSPi Co., Ltd., Korea (jwjeong@cospi.co.kr) 2 Director, COSPi Co., Ltd., Korea (koojj@cospi.co.kr) 3 Executive Director, COSPi Co., Ltd., Korea (beomi@cospi.co.kr) 4 Representative Director, COSPi Co., Ltd., Korea (ahn@cospi.co.kr) Abstract - The paper introduces the design process and characteristics of Yeonwha suspension footbridge with convex stabilising cables, and a 230m span, located in the southern coast island of Korea. Long span suspension footbridges always have with low stiffness, low mass, low damping, and low natural frequency. Consequently, they can suffer severe serviceability problems and be destroyed by aeroelastic instability. In design stage, it is important to estimate the stiffness, serviceability, and aeroelastic instability. Through the wind tunnel tests, those are verified. 1. INTRODUCTION Yeonhwa suspension footbridge presented in this paper as shown in Fig. 1 is located in the southern coast island of Korea, and the bridge connecting Yeonwha Island and Banha Island is positioned as one of the most important bridges to improve the convenience of local residents and promote the general development in the area. Modern footbridges have been a growing trend towards the construction of slender, light-weight, and aesthetic structure [1-3]. At the present moment, suspension or cable stayed bridge types are the most suitable types for a long span footbridges. Long span suspension footbridges are always with low stiffness, low mass, low damping and low natural frequency. Consequently, they can suffer severe serviceability problems and be destroyed by aeroelastic instability. In the design stage, it is important to estimate the stiffness, serviceability, and aeroelastic stability. Methods to increase stiffness of suspension footbridge are generally known as follow [4]; a) to increase of girder stiffness, b) to reduce the cable sag, c) to add mass, d) to pre-stress convex stabilising cables under the deck, e) to apply diagonal hanger cables, f) to apply stress ribbons, etc. But one of the most efficient and convenient method for application for footbridge is to apply the pre-stressed convex stabilising cable. Overall footbridge stiffness will be ensured by pre-stressing of the stabilization cable. Furthermore, the lateral and upward displacement for wind loads is significantly decreased. For pre-tensioned suspension footbridges, the vibration properties can be tuned by introducing different pre-tensions into the convex stabilising cables. This feature is useful when improving the structural behavior of such kind of cable structures and minimize excessive lateral vibration [5]. As the span increases, wind actions become more critical in bridge design, and for the longest suspension bridges, extensive wind studies, such as wind-tunnel tests are normally undertaken. Fig. 1: Perspective view of Yeonwha suspension footbridg

2 2. DESCRIPTION OF THE FOOTBRIDGE A general view of the bridge is shown in Fig. 2. the main feature of the bridge is the pre-tensioned by means of lateral parabolic cables added on both sides of the footbridge. These parabolic cables are connected to the deck by means of transverse tie cables and anchored on the block. The footbridge has a total length of 230.0m. There are two side spans 37.5m, 22.5m long, plus the central span between the steel pylons on the concrete pier, which is 170.0m long. The deck is a steel box girder with 0.7m of height, 4.0m of width, and 3.0m in the effective width. The tower P1 and P2 are 28.0m high. The cable s sag to span ratio is 1/10, and the spacing of the two main twin cables is 3.0m. 3. DESIGN CONDITIONS 3.1 Design Loads It has been considered of dead and live loads as shown in Table 1. The wind loads are obtained from the wind tunnel test, and are considered as the START OF BRIDGE STA END OF BRIDGE STA WN2 반하도 39.7 BH WN1 연화도 BH BH-01AN AN2 AN3 AN4 WN4 WN3 PLAN START OF BRIDGE STA END OF BRIDGE STA EL EL EL BH-01 E L.(+) BANHA ISLAND YEO NHWA ISLAND EL EL S=-4.263% S=+4.263% AN2,4 AN1, A2 A SPACE FOR VESSEL PASSING (107mX25m) 1 50/9 50/ EL /14 50/10 50/ EL EL EL EL WN3 EL EL BH-02 E L.(+) A.H.H.W.L (EL.1.700) WP1 P2 P1 EL EL BH-03 E L.(+) ELEVATION Fig. 2: Plan and elevation of the footbridge Table 1: Dead & Live loads Dead load Steel box girder (included longitudinal and horizontal stiffeners, diaphragms) kn/m Deck surfacing (wood) Railing (one side) kn/m2 kn/m Water pipe kn/m kn/m kn/m2 Live load Crowd (L>130m, Korean Highway Bridge Design Code, 2015) (for just design of deck plate) Table 2: Mechanical Properties of a SC strand Standard outer diameter (7-wire strand 15.2mm) 19.6 mm Cross sectional area mm2 Modulus of elasticity Nominal mass GPa g/m MPa Tensile strength

3 equivalent static buffeting load. And also, temperature, settlement, manufacturing and install tolerances are considered. 3.2 Materials The steel box girder and pylons used SM400 and SM490 respectively. All cables used the SC strand (epoxy resin coated PC strand) where each of the wires is coated in thin film. As a result, the fretting of wires can be prevented by coating the thin film epoxy resin respectively, and the fatigue strength of 4,000,000 times or more is possessed in stress range 245N/mm 2. They also have an excellent rust prevention performance [6]. 4. FE ANALYSIS AND RESULTS 4.1 Analysis Model and Method The footbridge has been modeled with beam and cable element which is elastic catenary element, in the program Midas Civil as shown in Fig. 3. Initial shape of the cable is one of the important parameters in the modeling of suspension bridges. The shapefinding analysis determines the coordinates of the main and stabilising cables and initial tension of cables, which satisfies the design parameters at the initial equilibrium state under full dead loads. additional loads (Vehicle, wind load, etc.) This is due to the fact that sufficient tension forces are induced into the main cables and hangers under the initial equilibrium state loading. It is thus possible to perform a linearized analysis for the additional static loads at the completed state by converting the tension forces in the main cables and hangers resulting from the initial equilibrium state loading into increased geometric stiffness of those components. This linearized analytical procedure to convert section forces to geometric stiffness is referred to as the linearized finite displacement method. This procedure is adopted because a solution can be found with relative ease within acceptable error limits in the completed state analysis. In case of suspension footbridges, it cannot be assumed that the footbridge behaves linearly for additional loads because the additional loads are greater than dead loads. Thus, it must consider the geometry nonlinear after shape-finding analysis. 4.2 Analysis results Fig. 4 shows the displacement of the deck under the action of live, wind, temperature, and settlement. The deflection for the live load is 255.4mm, (L/665) which is satisfied the deflection limit L/350. [7] Fig. 3: Analysis model updated the coordinates and initial pretensions In case of highway suspension bridges, it can be assumed that the bridge behaves linearly for Live Load Wind (vertical dir.) Temperature Settlement Wind (horizontal dir.) Fig. 4: Vertical and horizontal displacement of design loads Table 3: Cable forces Name Construction of cable D+P (kn) Max. (kn) Fu (kn) S.F. Ratio Remarks Suspension cable CSM619 Twin Pu Hanger cable CSM601 Mono Pu Stabilising cable CSM619 Mono Pu Tie cable CSM601 Mono or Twin Pu Table 4: Natural frequencies of the footbridge Character of eigen-mode Natural frequencies f i (Hz) Mode no. Drag Mode 1 st symmetric st anti-symmetric Vertical Mode 1 st symmetric st anti-symmetric nd symmetric nd anti-symmetric Torsional Mode 1 st symmetric

4 In addition, vertical and horizontal displacements for wind load are 723.4mm and 477.5mm respectively, which is considered equivalent static load from the wind tunnel test. Table 3 shows d+p, maximum forces of the suspension, hanger, stabilising, and tie cables. Free vibration analysis is an important part towards understanding the dynamic characteristics of a structure. Natural frequencies and vibration mode shapes are the basic vibration properties for structures, and they influence the response under the dynamic load. The results are contained in Table WIND RESISTANCE DESIGN Design basic wind speed V 10 for this footbridge was determined to be 40.0m/s (10-min mean with 100-year return period) based on Korean highway bridge design code, [7] and surface roughness category is defined as I (coastal areas). Construction basic wind speed V c is defined as 23.68m/s (10-min mean with 5-year return period and 80% nonexceedance probability). The design wind speeds under design and construction conditions are 54.9m/s, 32.6m/s at height 30.0m respectively. The critical flutter velocity V cr is 66.0m/s (1.2V d ) in wind angle ±2.5 and 19.8m/s (0.3V cr ) in wind angle ±5.0 as shown in Fig. 6. In order to evaluate the aerodynamic stability, wind tunnel tests with 1:15 scaled sectional models and a 1:50 scaled aeroelastic model of the completed footbridge were carried out in TE Solution in Korea. 5.1 Deck section model test The primary section consists of steel deck with cross beam evenly spaced at 2.5m as shown in Fig. 5. As a results, vortex induced vibrations are not occurred in vertical and torsional direction at low wind speed, but the torsional flutter is occurred in wind speed 59.4m/s when α=-2.5. To improve the aerodynamic behavior, 2 nd to 6 th sections are proposed; 40 fairing, 0.4m length horizontal extension, installation deflector under the section, installation the inner plate, and closing the section with finishing material respectively. The results are shown in Fig. 6. The 6 th section indicated no vortexinduced vibration and flutter on ±5 angle of attack. But the finish materials can be damaged and destroyed and not make sure the stability. Thus, the final section was discussed to use steel box section and shown to have a good wind resistant performance from the additional test. The most important test for the deck, as well as for the other components, is the definition of the static aerodynamic coefficient as a function of the angle of attack. This test is made in wind tunnel tests Fig. 5: Primary section model for test Flutter velocity, Vcr (m/s) Wind angle, degree Fig. 6: Flutter velocity Primary section 2nd Section 3rd section 4th section 5th section 6th section Drag coefficient Lift coefficient Moment coefficient Wind angle, degree (a) completed stage Drag coefficient Lift coefficient Moment coefficient Wind angle, degree (b) under-construction stage Fig. 6: Aerodynamic coefficient for completed and construction stages on the sectional models of the deck. As shown in

5 Figure 6, the aerodynamic coefficients of the final section indicated drag (C D ), lift (C L ), and moment (C M ) coefficient 0.39, -0.57, and in zero-angle of attack respectively. The drag coefficient is very low, when compared to other existing bridge decks. 5.2 Aeroelastic model test The full bridge model aerodynamic test to check the serviceability and safety of the footbridge is performed about completed bridge and construction stage configurations as shown in Fig. 7. All tests conducted in this project for the (a) completed stage (b) under-construction stage Fig. 7: Areoelastic model for completed and under-construction stages completed bridge configuration passed the target wind speed with no flutter instability and no vertexinduced vibrations observed. Buffeting responses as shown in Table 5 in this model are entirely higher than the section model test due to turbulence intensity. The equivalent buffeting load from this response is calculated and used to check structural safety of this footbridge. This footbridge is planned to erect the shallow box girder following the program of pylons to mid-span. According to the erection plan, the test is conducted for 1 st stage and last stage among the erection sequence. All tests conducted with the underconstruction stages also passed the target wind speed with no occurrence of flutter instability. 6. VIBRATION SERVICEABILITY The footbridge design guideline in Korea recommends avoiding the natural frequency of 1.5Hz to 2.3Hz. The vertical 1 st and 2 nd frequencies are Hz and 0.658Hz, respectively which are lower than 1.5Hz and the dynamic response to the pedestrians does not need to be checked. Table 6 compares the serviceability criteria in terms of acceleration set forth in the four standards. In this study, serviceability of wind induced vibration through the wind tunnel test is estimated with Eurocode. The test have shown that vertical acceleration 0.7m/s 2 can be occurred in wind speed 18m/s (3-second gust wind speed) which is Beaufort wind scale 8 (17.2m/s~20.7m/s; generally impeded progress ). Thus, this footbridge will be closed to all pedestrians and traffics in over 18m/s wind. 7. CONCLUSION Introducing pre-tensioned side cables in inclined plane can significantly improve the lateral stiffness, Table 5: Buffeting response for completed bridge (V d =54.9m/s, turbulent boundary layer) Class Horizontal Vertical Torsional 1/2 span 1/4 span 1/2 span 1/4 span 1/2 span 1/4 span Mean (mm) Peak (mm) Max. (mm) Table 6: Acceleration Criteria Standard Vertical Acceleration(m/s 2 ) Horizontal Acceleration(m/s 2 ) BS 5400 a max 0.5 f No requirements Eurocode a max 0.7 a max 0.2 (for walking individual) a max 0.4 (for walking group) ISO times base curve (ISO2631-1) 60 times base curve (ISO2631-2) Bro 2004 a RMS 0.5 No requirements

6 and greatly suppress the lateral deflection induced by lateral applied loads, as well as vertical loads. Through the wind tunnel tests, the final section has been shown to have a good aerodynamic stability, and the flutter critical wind speed is up to 70m/s. Of course, there is no vortex shedding vibration observed in the section model testing. Full bridge model aerodynamic test for the completed bridge and construction stage configurations indicate no vortex-induced vibrations and flutter instability. REFERENCES [1] Guidelines for the design of footbridges, Fib bulletin 32, [2] Andreas Keil, Pedestrian Bridges, DETAIL Practice, [3] Design of Lightweight Footbridges for Human Induced Vibrations, JRC Scientific and Technical Reports, [4] Vadims Goremikins, Karlis Rocens, Dmitrijs, Raimonds Ozolis, Behavior of Cable Truss Web Elements of Prestressed Suspension Bridge, 4 th International Conference CIVIL ENGINEERING, [5] Ming-Hui Huang, Dynamic Characteristics of Slender Suspension Footbridges, PhD Thesis, Queensland University of Technology, [6] Kei Hirai, Tukasa Kashiwazaki, Naoyasu Hirayama, Takatugu Fujikawa, Keizou Tanabe, Introduction of high performance cable system composed of epoxy resin coated PC strand, [7] KRTA, Korean Highway Bridge Design Code,, 2015.